NBS MONOGRAPH 1

Energy Dissipation by Fast Electrons

Addendum for

NBS Monograph No. 1

Energy Dissipation by Fast Electrons

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USCOMM-NBS-DC

UNITED STATES DEPARTMENT OF COMMERCE • Frederick H. Mueller, Secretary NATIONAL BUREAU OF STANDARDS . A. V. Astin, Director

Energy Dissipation by Fast Electrons

L. V. Spencer

National Bureau of Standards Monograph 1

Issued September 10, 1959

For sale by the Superintendent of Documents, U.S. Government Printing 0£5ce Washington 25, D.C. - Price 45 cenw
Contents

Page

1. Introduction 1

2. Methods and input information « 2

2.1. Calculation of moments 2

2.2. Calculation of the energy dissipation distribution from its moments 5

2.3. Choice and preparation of input data 8

3. Tabulations and their description 10

3.1. Description of the tables 10

3.2. Interpolation 12

3.3. Comparisons with experimental data 13

4. References 70

II
Energy Dissipation by Fast Electrons

L. V. Spencer

Tabulations are given of the energy dissipated by fast electrons at dififerent distances from monoenergetic electron sources, for plane perpendicular and point isotropic sources. A summary of the theoretical methods and data utilized, and a table of spatial moments

are also included.

1. Introduction

This Monograph belongs to a series of reports on radiation physics data being prepared with the support of the Office of Naval Research and the Atomic Energy Commission.

Earlier reports of this series were designed in part to present input data necessary for the preparation of this report, which gives results of extensive calculations of electron penetration taking into

account both nuclear elastic scattering and electron slowing down. The tabulations given here are designed to answer the following type of problem : If electrons of kinetic energy Eq are produced at a

point or on a plane in a material with atomic number Z, the electrons wUl travel away from their point

of origin, dissipating energy to the material as they go. Eventually each electron will have completely

given up its initial energy. What will be the spatial distribution of the energy transferred to the sur- rounding material?

Two types of electron sources are considered, namely point isotropic sources emitting electrons of

energy Eo equally in all directions, and plane sources emitting electrons of energy Eo only in a single

direction which is perpendicular to the source plane. Superposition of the point source data for different

Eo will give data for more complete source spectra, such as the beta-ray spectra from a radioactive

isotope or from mixed fission products. Superposition of the point sources at different spatial locations

will give results descriptive of surface and volume beta-ray source geometries. Similarly, the data for

the plane perpendicular source may be applied to the case of a beam of electrons injected into a material,

since the integral of the energy deposition on any plane perpendicular to the beam is independent of

the beam width and can therefore be calculated as though the beam were infinitely wide, thus constituting a plane perpendicular source. The calculations presented here were programed for the IBM 704 digital computer at NBS. The

methods which were used were essentially those outlined in [1].^ Results are given for Eq varying in approximately logarithmic intervals from 0.025 to 10 Mev, for the following materials: C, Al, Cu, Sn,

Pb, air, and polystyrene. In the case of Sn and Pb, some of the lower and some of the higher values

of Eo have been omitted, the lower values because the range and cross-section data are unreliable near

the atomic binding energies, the higher values because radiation straggling, which has not been taken

into account, tends to dominate at high energies.

The medium is assumed to be homogeneous, extending in all directions around the source a distance

greater than the electron range. The electrons are assumed to slow down continuously until their initial kinetic energy has been completely exhausted. The neglect of range straggling due to large singleenergy losses occurring in both radiative and inelastic collisions makes the data somewhat inaccurate;

but the errors are probably important only for very large distances from the source, where only a minor

fraction of the energy is dissipated. Since a major effort is required to improve the results further,

and since experimental studies show generally good agreement where comparisons have been made,

it is felt that the data are of sufficient accuracy and usefulness to justify their publication.

' Figures in brackets indicate the literature references at the end of this Monograph.

1
The remainder of this Monograph is divided into two parts, the first outHning the methods and data

which were used to make the calculations and the second presenting and describing the tabular data.

Section 3 describing the tabular data, has been made almost completely self-contained so that persons

who need data but do not wish to follow the derivations may turn immediately to this latter section and

find all the information they require.

Since the basic theoretical methods used to calculate electron energy dissipation distributions have

already been given in considerable detail in [1]. We only sketch the arguments and procedures here.

The assumption that electrons lose their energy continuously established a relation between the

residual range r of the electrons, measured along their path, and the average rate of energy loss, i.e., the stopping power {dEjdr):

where 0<^E'CEo is the kinetic energy of an electron which has slowed down but not lost its energy

completely. This equation is the basis for the tabulations of electron ranges [2]. It is convenient to measure both distances and residual ranges in units of ro=r{Eo) . For an electron source located on the plane 2=0 which emits electrons of kinetic energy Eq in the direction perpendicular

to this plane and towards increasing z, the distance of a point from the source plane will be conveniently

identified by a dimensionless parameter x=z/ro- Similarly, we replace the residual range r by a dimensionless ratio t=rjro. We define the flux of electrons, I(t,d,x)2ir d{cos d)dt, as the number of electrons

per second that cross a small spherical probe of unit cross sectional area at a distance x from the source, having residual ranges between t and t-\-dt and obliquities between 6 and 6-\-dd relative to the direction

from the source to the probe.

The electron flux must satisfy a transport equation, which has the following form in steady state conditions for the plane perpendicular source:

where 6 is the angle between the electron directions {6' ,4>') and {6,<t>) before or after a collision. This is basically a continuity equation. The terms on the left describe a rate of change in Iit,9,x) due to slowing

down (first term) and due to spatial displacement (second term). The terms on the right describe a

rate of change in the flux due to elastic collisions (first term) and due to generation of electrons by the

source. The last term, describing a unit-electron source current, is the product of three Dirac delta

functions which guarantee that the electrons are generated only at a;=0, t= 1 , and cos 6=1. If the source

is constant with time, I(t,d,x) must also be constant with time, and therefore the rates of change in this quantity must balance one another.

The function S{t,Q) which appears in the first term on the right of (2) requires a precise definition:

The quantity 2TS(t,Q)d{cosQ)dt is the probability that an electron having kinetic energy corresponding

to t will undergo, while slowing down from t-\-dt to t, an elastic collision which results in a deflection

through an angle between 9 and Q-\-dQ. S{t,Q) is equal to rJSI<j{E,Q), where A^^ is the number of atoms

per gram of material, E is the kinetic energy corresponding to t, a is the elastic scattering cross section

in a centimeters squared per steradian, per atom, and is measured in grams per square centimeter.

The procedure for solving (2) utilizes an expansion in spatial moments and spherical harmonics.

2. Methods and Input Information

2.1. Calculation of Moments

(1)

0 J -1

Thus, if

(3) and

(4)

2
an interlinked system of equations for the Iniit) can be derived from (2):

Further analysis is dependent upon the fact that the scattering coefficients Si{t) can be obtained accurately from the suitable formula

s,(«= re)

where di and a are constants. This analytic form, which is accurate over a very ^vide range of t, Z,

and £"0 values, is made plausible by a derivation due to C. Blanchard which is given in appendix A

of [1]. Expression (6) makes it possible to obtain from (5) a set of recursion relations linking "residual

range moments" iT; defined bv

Derivation of the recursion relations satisfied by the Ini will not be given, but it is essentially that

outlined in [1, Appendix C] with m=p+n + )i, and (1 — a)"?-^;. They are

lA-a H [d^ +y2 +m+i] (1 + ay'

The system of eq (8) has a complicated appearance, but it contains one fundamental simplifying

feature, namely that aU the terms appearing in each equation have superscripts m' > m. This means

that a knowledge of the I^l for m'^-m makes possible a solution for m and then chainwise for lower

values of m. The procedure for solving eq (8) is based on this feature, together with the fact that all the sums converge essentially like a geometric series. By starting the solution at sufficiently large

wimitiai=-W") it becomes unimportant whether or not terms m' >M are accurately represented, since

they contribute a neghgible amount to the low values of rn which are of primary interest.

The first step in the machine programing consists of a numerical determination of the /^^ through

solution of (8). For this purpose it is convenient to restate (8) in a simpler form. We make the

following definitions

\\Jra) [d^ +y2 +m]'

01:1=^: (Ar)' T'ltr. (9) i=o Vl+a/

In terms of these quantities, and by means of the summation device [1, eq 27], we can rewrite (8) in the

form of coupled equations to be evaluated successively ia the order stated below:

i';:,=c^i+j^i^i-\ (10)

Equations (9) and (10) exhibit more clearly the progression of the solution from large to small

values of m. It is clear that given initial values T^, C^i, and these same quantities maybe deter3
mined in turn for M—1, M—2, etc., down to m= 0. To complete the analysis, therefore, it is necessary

to give some device for estimating the initial values. Two choices have been used: In some cases, particularly for large a, the /J^ and C^, were set equal to zero. More frequently, a crude estimate of

these quantities was used, which was based on approximate evaluation of the sums in (8) for large M,

namely

r«. (u)

The expressions (11) break the M linkages and permit calculation of approximate values for and

C^i with as many n, I combinations as desired.

The foregoing equations are now almost ideally suited for machine computation. Because of

the rapidity of the computer operations, there is hardly any limitation to the values of M which are

practical. After some preliminary exploration, M was made sufficiently large that any further increase

would not change the results for small m significantly in the eighth place. For most of the calculations

M=50 proved sufficient for this, but for energies Eo> 2 Mev, M=150 was used. As a final check,

comparisons were made with values of Iqq obtained from (7), with /oo(0 = l,

=l+2:^/|^{^-^tan-^VhFT}' a<-l. (12)

Calculation of numerical values for represents a major objective of the machine program, since

these numbers describe the total flux of electrons integrated over all directions. The procedure just

described for obtaining them has proved very rapid and satisfactory.

Once the I^o have been obtained, we are in a position to calculate the energy dissip .tion distribution liz), which is the end product of our investigation. If I{z)dz is the energy dissipated per square

centimeter in the plane layer between z and z-\-dz, then I{z) is an integral over /o(f, x), namely

For our purposes it is advantageous to rewrite (13) in scaled form in terms of a de-dimensionalized function J{x) =I{z)/{dE/dr)E^ : Jix)=£dte(t)Io(t,x), (13')

where eit)={dE/dr)/(dE/dr)B^. Note that €{t) = l at t=l. Equations (13) and (13') express the as- sumption that each electron contributing to the flux Io{t,x) at x dissipates energy at the average rate dE/dr per unit pathlength traveled.

Our procedure is to calculate first the spatial moments of J(x), and from these obtain the function itself. To obtain the J„ we use an approximate analytical representation for e{t), namely

.(o»|:..[%tf]'"^.

Inserting this expression into (13'), and then calculating spatial moments of both sides, we obtain an

expression for «/„ in terms of the /"o

Jn=i:A,C-l (15)

4
The representation (14) contains four constants At, which require four conditions for their determination. Since e(0 is a ratio of stopping powers, it can be evaluated numerically for different tj values.

We may then require our representation to equal e{tj) at t=tj. Each value of j then corresponds to one

condition to be fulfilled by our representation. By a suitable choice of tj values, the representation can

be made to resemble closely the actual function e{t). For this purpose, the values ti=l, ^2^0. 5, and

<3«0.1 were selected. Instead of selecting a fourth condition similar to these three, however, the condition was chosen that the total energy dissipated must always equal the initial kinetic energy- £"0 of

the electrons. This is expressed by the integral

Jo=J' dxj^ dte(t)Io{t,x), (16)

which takes the form

4 Jo-±Aj'--^-j^l^. (17)

This condition insures that the stopping power is correctly expressed "on the average"; and it partially

compensates for inaccuracies in (14) which arise from the difficulty of representing {dE/dr) simultaneously at low and high energies. When combined with the other three expressions obtained from (4) by setting t=tj, we have a set of simultaneous linear equations whose solution yields the Af. A short

machine program was included to accomplish this and then, with the results, to evaluate the sums (15).

In summary, the machine program for calculating moments J„ of the energy dissipation distribution ^(a;) consists of a section which solves the moment eqs (8) by means of the recursion eq (9) to (11), a section to determine the Ai, and a final section to perform the sums (15). As input data, values of

the constants di, a, and M are required for the first section, and Eo, /"o, idE/dr)B^, ti, U, and the values

{dEldt)i~Q_f, and (dE/dt) t^o.i for the second section.

The preceding discussion outlines the calculation of moments J„ for the plane perpendicular source. Also of interest are the moments for the plane isotopic source from which one can obtain the moments

of the point isotropic sources (see eq 28). Note that in the case of the plane isotropic source, each

element of area on the source plane emits electrons equally in aU directions. Only minor modifications

are needed in the equations already given to obtain equations from which a calculation of plane isotropic source moments can be made. In particular, the factor 5(cos0 — 1) must be replaced by ^ in the last term of (2), a factor dio must be included in the last term of (5) and (8), and in (9) the expression for

To; must also include a factor 5,o. Otherwise all equations are identically the same for both source

types.

2.2. Calculation of the Energy Dissipation from its Moments

The method which was used to calculate the energy dissipation distributions was the "function

fitting" method outlined in [1], in which several terms are added together to represent the distribution,

all terms having the same functional form but differing in the value of a scale parameter. The repre- sentation is expected to be accurate if its moments agree with the known moments of the distribution,

if the functional form has been well chosen, if it is smooth, nonoscillatory, positive, single-peaked, and

if it is correct at x=0.

The chief advantage and also the chief difficulty with this method for calculating a fimction from

its moments arise from its all-or-nothing character. To obtain values for all the scale parameters and

"strength" parameters in the representation, it is necessary to solve simultaneously a set of nonlinear

equations. The solution of these equations may be acceptable on the basis of the above-mentioned

criteria. In this case the representation is expected to be very accurate. On the other hand, solution

of the equations may lead to coefficients which are complex, too large, or too small, and which give a representation which is uneven or oscillatory in nature and not representative of the desired distribution

at all. Because the solution of the equations may "fail" in this way, perhaps more often than it may

succeed, the function-fitting method is not well suited to digital computer operations. Nevertheless,

because only this method had proved successful in hand computations, it was necessary to attempt its use in systematic machine computations.

5
The expectations tliat frequent failures would be encountered with any function-fitting machine

program led us to take three precautions. (1) The functional form selected contained a number of

parameters which could be given values arbitrarily. This was to make possible a wide variety of modifications in this function without having to write new codes. It turned out that many of these arbitrary

parameters were unnecessary. (2) In each machine calculation, at least five different attempts were made to calculate the distribution, each attempt corresponding to a different value of one of the arbitrary parameters. Thus, several tabulations of the distribution were usually obtained in the same

machine run. (3) Where several comparable tabulations occurred, the^^e were graphed and compared

both visually and in regard to their analytic form. A choice was made of the distribution best satis- fying the criteria. It almost always turned out that if two or more such approximate distributions

agreed about equally well with the basic criteria, they agreed with each other to within 1 or 2 percent,

except for very small J{x).

Calculation of the spatial distributions proceeded as in [1]. Even and odd moment sets were considered as descriptive of even and odd functions J^^^{x) and J°^^{x), which yield J{x) through the combinations

J{-x)^y2[J''"^{x)-J^^{x)]. (18)

The functions t7*^*°(x) and J°^^{x) were calculated from the following analytic expressions:

(l-aox^) J--(x) =i aSi {a,-a, e-^'^^-'\ (19)

(1-aoX^) J'^'*(x) =|: a, (a,-a, |) (^l-^J,-^/ (20)

where the constants were usually assigned the values ao=l, ai = l, and a2=0. The constant A, which

controls the asymptotic trend of all the terms, was determined by iteration from the expression

In {Jn-2IJn) _ /2j\

2{VA^+^ + (-4/12)-ViV-7/4+(A/12)}'^~'^'"'""'°"^-

The precise value of A is not critical except for large |a;|, where J{x) is very small; and (21) gives a fairly

reasonable value for this constant since it corresponds to a simple but realistic approximate form

[1, Section 7 and Appendix E],

J{x)'^{\-x)-^'h-^''^'~'K (22)

The constant y was assigned integral or half-integral values, usually not greater than 1 nor less than —2. The constant /3o was given the value unity, and the constant /3i was given five different values in succession, namely VO.9, VO.6, VO-4, VO I, and V0.04, each yielding a separate representation of J{x),

The other six constants in each of the expressions (19) and (20), namely z = l to 4, and z =3,4. were determined so that five moment equations obtained from (19) and five from (20) were satisfied,

and so that two other features of J{x) were given correctly,

jo<i<i(o) = l, (23)

and

(24)

Equation (23) , together with the moment equations derived from (20) give the following system of simultaneous equations:

J„-aoJn+2 ^ ^^^n^,^

3^ 5_ 7^ 9^

l=Z;ao (25)

i=0
where w„ indicates a number discussed below. Similarly, (24) together with the moment equations

derived from (19) give the system

^^L^^^=±a,^^\ n=0, 2, 4, 6, 8,

a

* -±7I2ii-y2)A^=[a,+a^(y+A)]^a,. (-Jti) «+i ! = 1 1 =0 Note that the at and for J®"*", obtained by solution of (25), are quite different from the corresponding

values for J°^^, obtained from solution of (26)

.

The number w„ appearing in both (25) and (26) is defined by the expression ,

(/x x"(l— x)^e-'*^/"-^'. (27)

Machine calculation of these numbers presented an interesting problem, since quite a few are needed,

and they must be determined with great accuracy. For this purpose, recursion relations similar to those

of [1, Appendix E] were derived. It was found that by estimating co„ for a very large n, say n=50,

and then by working back to small values of n using the recursion relations, very precise values could

be obtained. Actually, there was more to the problem than this, since accurate absolute values were

desired, whereas the method just sketched gives only accurate relative values. In any case, a simple

and rapid machine program was devised for this purpose.

Solutions of (25) and (26) were programed for the computer, and the resulting parameters were

then used in an additional routine which tabulated and J°^^ from (19) and (20). Finally, these

tabulations were combined as in (18) to obtain J{x). In the solution of (25) and (26), if ^2 and ^3 turned

out to be complex, the remainder of the calculation was omitted and another calculation was attempted

with a new value of /Sj. Solutions involving complex /3, were not acceptable because of being inherently

oscillatory. Of the many calculations, perhaps half were not completed because of this type of failure. The preceding discussion is largely descriptive also of the calculations of J(x) for a point isotropic source; but there were a number of differences worth noting. Point isotropic source moments could

be easily obtained from plane isotropic source moments, which were actually computed directly, by

use of the prescription

Point l80troplo_ Plane Isotropic (28)

From these moments A was then determined, using (21). The representation of J(x) for the point

isotropic source differed somewhat from (19) because of the added condition that J{0) = 1. This was

ensured by addition of an extra term:

(l-aox')Jix) = il+a,x)(l-xye-^^'^'-^^+a,p^a,^,(j^(^l-j^^ (29)

Moments of (29) have the form

Jn-aoJn+2- (a,„+aia>„+i) ^.^ ^^^^„+,^ ^^^^ 2, 4, 6, 8, (30)

ttlWn+l »=0

where the a)„ are as defined by (27). To complete the set of equations, one more was added to express

the condition that

1=0 dt^ ^

The parameters A, y, /3o, and /3, were specified as already indicated, and a^, di were set equal to unity.

It happened repeatedly that none of the solutions obtained from the prearranged set of values

of fii were acceptable. When this occurred, the parameter next to be given new values was 7. On

occasion it proved necessary to use several different values for 7 before obtaining an acceptable result

but in no case was it necessary to modify the other parameters.

508105 0 - 59 -2
2.3. Choice and Preparation of Input Data

Three types of input data are required for the calculations outlined in the preceding section, namely

electron stopping powers, electron ranges, and elastic scattering cross sections; but none of this information enters directly into the equations which are solved. Instead, a set of derived parameters is used

which includes a, the rf,, and the At. Thus, after obtaining the basic physical data, a very substantial

effort is required to determine the numerical values of the actual equation parameters. In this subsection the physical data is first discussed and then the preparation of the equation parameters is outlined.

Extensive tabulations of range and stopping-power data have been prepared by Nelms [2,3]. We

used the data of [2], corrected for density effect according to Sternheimer [4]. This data is based on

values for the mean excitation potential obtained by Mather and Segre [5]. The nuclear elastic scattering cross section which was used was essentially the Mott cross section

(a) modified to take into account screening by the atomic electrons. Values for the ratio a/o-R of the

Mott cross section to the Rutherford cross section were taken from the tabulations of Doggett and

Spencer [6]. Also used were unpublished values determined by Doggett and Spencer for several additional atomic numbers Zj. The screening modification was accomplished through use of Moliere's

expression for the screening parameter ri [7]. To take into account deflections due to collisions with

atomic electrons, the nuclear elastic scattering cross section was modified by a factor [(Z^+Z)/Z^](l + e), in accordance with a correction due to Fano [8] to the usual prescription which replaces the factor Z^

in the cross section by Z(Z-f- 1). Due to the remarkable scaling of electron penetration phenomena with the range Vq (see, e.g., [1], slowing-down and scattering properties of the medium all find expression through the single function

Sit, 0). For reasons of computational convenience, we represented this function in the form

S{t,e) = (3/4)A^^ (ZM)0o(Z+ 1 ) (1 +€) (^+ mc'nmc'y[E(E+ 2mc')]-'ro[l +2,,- cos 6]-'{ X 1 + 7r(Z/137)

cosx/V2) [1+27? -cos Qy'^-\-[{a/aR)-l-Tr(Z/lS7)0 cosx sin^e][l 4-2»?-cos e]2[l-cD3 9]-^}, (31)

where the quantity in curly brackets can be recognized as cr/V^ to within a minor modification, and

Ai^^=Avogadro's number,

6.65205X10 cm^ is the Thompson cross section,

0=[E{E-\-2inc^)]i/ (E+mc^) is the electron velocity divided by c,

mc^ is the rest energy of the electron,

<r is the Mott scattering cross section,

e=(Z+l)-i (in4„)-' ^u,,-\n [o.ieZ'^^^ (l+3.33 y^)]}'

''^4 Lo.885(137)J E{E+2mc') [1-13+3.76 [j^^J J,

cosx=Re-^ —y —) ^ y, and

['G+'il5)K'-'il?J

<rR=\NJ^{Z|A)<i>^Z{E+mcy{mcy[E{E+2mc^)]-\l-cosQ)-\

In (31), note that (3/4)A^x(ZM)<^o= 0.300 cmVg, a tabulation of cos x has been given in [6], and the constant —M,n is a number in the neighborhood of 5. Everything in (31) is known except the value of

8
—u^, which affects only a correction to a correction. To be systematic in "guessing" the value of —Wto* the few values in [8] were plotted against log Z and interpolations were made from a rough curve drawn through the points.

To discuss the further processing of the data, it is convenient to give the different terms in (31)

shorter names. In particular, we define G, C(G), D{Q), and F{Q) as follows:

G{E) = i3/mA{Z/A)MZ+l){l + e){E-hmer{mcy[E/iE+2mc')]-'r(E),

(7(0) = [l +277-cose]-^

z>(e)=[l+27?-cose]-3/^

ir(e)= { (o-/<r„)-l-7r(Z/137^)cosx sin|e } (1 -cosG)-^ (32)

Using these definitions, S{t, Q) can be written

iSit, e) = G'{(7(e)+V|7r(Z/3/137) cosx D{e)-\-F{e)}. (33)

The expansion in Legendre coefficients of C(6) and D{Q) is a simple matter and has been given

in [1]. On the other hand, F{Q) is only known numerically, and its harmonic expansion is therefore not

so easy to obtain. Our procedure consisted of approximating F(Q) by a four term polynomial in

(1 —cosG) over each of the angular ranges 45° to 90°, 90° to 135°, and 135° to 180°,

TO)=i:/*(l-cose)^-', (34)

i=0

and by a three-term polynomial of the same type over the range 0° to 45°. Note that in each 45°

range the /< in (34) assume different values. These coefficients were determined so that (34) agreed

with the tabulated values of F{Q) at 15° intervals. With the analytic approximations (34), it is possible to accomplish the integrations (4) to obtain coefficients Fi. The procedure actually followed was

that of determining a 12X12 matrix which, multiplied by the twelve tabulated values i^(15°), F{30°),

etc., would yield in turn the first twelve harmonic coefficients Fi, F2, . . . F12. The matrix multiplications were then performed by machine.

Having determined all the Ci, Di, and Fi, the coefficients Si(t) were then calculated from the

expression

tSl(t)=G(E)'^C,+^f^^^{Z0/l37) cos xl>j+i^j j- (35)

for all the energies and elements listed in tables 1 and 2, plus one lower energy, namely 0.01 Mev.

In the last stage of the preparation of the data, ratios Si{t)/Si{t) were determined from (35). The

representation (6) requires these ratios to be independent of t. Actually, they are weakly energy dependent, and to this extent (6) is in error. To minimize the effect of this error, the ratios di/di were

set equal to (S;(l)/5'i(l), so that the mo§t penetrating part of the range of the electrons is traveled before

the approximation (6) incurs appreciable error:

l=iiFinally, to obtain a and di we notice from (35) that tSiit) depends only on E, not on Eq. Therefore,

according to (6), the quantity

^=tSAt), (37)

also depends only on E, and not on Eq. This makes it very easy to calculate a and di from the tabular

values of (35). One evaluates (37) for two values of t, namely <=1 and t=ti, corresponding to Eq and

9
the next lower energy recorded. Simultaneous solution of these two equations yields a and d^:

" US,{t{)-S,{l)

'

a

(38)

Combination of c?i with the ratios dijdi then give all the c?,'s. This completes the preparation of the data, except for compounds and mixtures, in which case it is necessary to determine the Si from an average over Si values for the constituent elements, in proportion to their fraction of the mixture by weight.

3. Tabulations and Their Description

3.1. Description of the Tables

The following quantities appear in table 1

Z, the atomic number; results are given for Z=6 (carbon), 13 (aluminum), 29 (copper), 50 (tin),

and 82 (lead), and in addition for air and polystyrene. Air is assumed to be 0.755 nitrogen, 0.232

oxygen and 0.013 argon by weight, and polystyrene is taken to be CgHg.

Eq, the initial source energy of the electrons; results are given for £"0=0.025, 0.05, 0.1, 0.2, 0.4, 0.7,

1, 2, 4, and 10 Mev, except that some of the highest and lowest values have been omitted in the case

of tin and lead.^ {dE/dr)EQ, the stopping power of electrons at the initial (source) energy.

rQ=r{Eo), the residual range of electrons at energy Eq.

X, the distance from the source in units of Vq. This quantity refers to z/vq for plane perpendicular

sources and to p/ro for point isotropic sources, where z is measured along a perpendicular to the source plane and p is measured radially out from the source point.

J{x), the de-dimensionalized energy dissipation distribution, for plane perpendicular and point

isotropic sources, see eqs (13) and (13')- For plane perpendicular sources, {dE/dr)EQJ{x) = I(z), where

I{z)dz is the energy dissipated per cm^ in the plane layer between z and z-\-dz by electrons initially

given kinetic energy Eq assuming 1 electron/cm^ to be generated at the source plane.^ For point iso- tropic sources, {dE/dr)EQJ{x) = I{p), where I{p)dp is the average energy per electron dissipated in the

spherical shell between p and p-\-dp. In the case of the plane perpendicular sources, J{x) has been

given for positions on both sides of the source plane. Occasional negative values of J{ —x) represent

spurious effects due to imperfections in the representation. They have been included because they

give some guidance regarding the expected accuracy for a;=|— a;|. One does not expect the value

J{x) to be more accurate than plus or minus the corresponding value at —x, where that value is negative.

Note that the discontinuity at the source plane is unity, and that in the case of both point isotropic

and plane perpendicular sources the integral over x gives (Eo/ro) / {dE/dr) e^. Along with the tabulated energy dissipation distributions and the associated range and stopping

power values at the source energy, we have included many other pieces of data in table 1 in order to give a fairly complete record of the computations. These are:

(o')/o'k(^), the ratio of the Mott to the Rutherford nuclear elastic scattering cross sections which was used as input data [6]

SiH), given by (35) for t=r{E)lr{Eo) = l, i.e., for E=Eo;

di, a, quantities characterizing the representation (6) of the scattering coefficients St{t) ; Ai, A2, A3, Ai, the coefficients At in the analytic approximate representation (14) of the stopping

power e= (dE/dr)/ {dE/dr)

Ef^, ^PTi^ ^PLP^ ^j^g values of the constant A in eq (19) to (22) for the point isotropic and plane

perpendicular source geometries, respectively. Theoretically the same, these values differ because

2 A calculation for 0.1 Mev source energy in Pb has been included to facilitate calculat)ons for energies below 0.7 Mev. Since the binding energy of the

if electrons in Pb is ~0.07 Mev, the numbers in this table are not to be taken seriously.

' For a beam source, H.z)dz represents the average eneigy per electron dissipated in the plane layer between z and z+dz. 10
they were obtained from (21) using different moment sets. The extent of the difference, as it affects the distribution in the manner indicated in (22), serves to indicate a region of large x in which the data

are unreUable. There is no simple way to identify this region explicitly, since the representations (19, are more accurate than the expression (22) from which the constants A were determined. But when

the difference in A values leads to widely different values for (18), one doesn't expect the tabulated

values of J{x) to be accurate. Note that the assumption of continuous energy loss makes J{x) inaccurate in the same region anyway.

In table 2 the moments /^o""^ ^ have been recorded which were used to obtain the energy dissipation distributions. According to (7) these represent averages of the residual range function over the n'ih. spatial moment /„o(0 of the flux distribution. In other words,

where Ioit,x)dt is the flux of electrons having residual ranges between t and t-\-dt crossing a small spherical

probe of unit cross sectional area at a distance x from the source. The different columns in table 2 correspond to fixed values of p. Enough p values have been included to make possible calculations of

electron spectra by reconstruction from these "residual range moments". Similarly, the 7^0 can be

combined with new representations of the stopping power of the type given by (14) to yield improved

calculations of energy dissipation distributions, or perhaps calculations, using the stopping power of

air, which give results corresponding to measurements of air ionization in a cavity chamber. Note

that each number in table 2 ends in a symbol £"-71 which stands for XIO'"; thus 0.1000000-01, is to be

interpreted as 0.1X10"S or 0.01. Two sets of curves are given to illustrate data in table 1. In figure 1 curves are drawn of the

energy dissipation distributions for plane perpendicular sources in copper. Each curve corresponds to

11
Figure 2. Energy dissipation distribution for point

isotropic sources of initial energy Eo=0.7 Mev in

different materials.

0 0.1 02 OJ 0.4 0.5 0.6 a7 0.8 09

a different source energy. The curves show marked sunilarity for nonrelativistic source energies,

which illustrates the scaling with range. They also show the tendency at relativistic energies for elec- trons to dissipate their energy farther out from the source, more in the manner of protons and a particles.

Figure 2 gives distributions J(x) for point isotropic sources corresponding to different Z values, for an

initial energ}' £"0=0.7 Mev. These curves show clearly the trend towards greater energy dissipation near the source for larger Z values.

3.2. Interpolation

Three types of interpolation are of interest, nameh' interpolation in x, interpolation in £"0, and

interpolation in Z. The fairly fine mesh in x, namely Ax= 0.025, should make possible an interpolation everywhere of

precision comparable with the number of digits tabulated, although a quadratic, rather than imear,

interpolation formula may be required.

Interpolation in source energy £0 is a fairly simple matter over most of the {Eo,x) region covered

by the tabulations. This is because the curves have a strong tendency to preserve their shape through

source energy changes. Because logarithmically spaced soiu"ce energies have been used, interpolation

should be based on the variable log £0 rather than £0. For energies between 4 Mev and 10 Mev, and

for large x values, there occur substantial shape changes which require a more sophisticated interpolation

procedure which takes into account the analytic form of the approximating functions. Thus, for example, it should be substantially more accurate to interpolate the function { IfA In J(x)-\-x/(l—x) }, if a power series representation is used for the interpolation, even though the value of «7(x) must then be

obtained from a diflFerence between terms which aflfect the value of J{x) exponentially.

Interpolation in Z is more difficult because of progressive shape changes with Z which result in great changes from one curve to the next. Accurate interpolation will therefore often require that the

anah'tic form (22) be taken into account. This can be done in the manner already mentioned, by

interpolating a well-chosen function of J{x), such as {llA\uJ{x)-'rx/{l—x)}, rather than J{x) itself. The value of J(x) can be obtained from this function utilizing a value for the constant A which is also interpolated from the A^^ or A^ values of table 1.

12
Of special interest are interpolations for compounds and mixtures. Here it should be noted that the

single, most important, determining piece of input data is the Si{l), which is nearly proportional to Z+1. One can therefore average Z over the constituent elements in the compound and use this value

in an interpolation of the type discussed in the preceding paragraph.

Interpolation can be used to modify the results presented here to correspond to more accurate range

and stopping power data; but changes of this type will almost certainly be small because they affect the calculations chiefly through the factor ro in the Si values. A 3-percent change in Tq would have about

the same effect on the calculations as a 3-percent change in the atomic number. A similar change in the stopping power at all electron energies would have no effect because of the scaling which is utililzed in de-dimensionalizing J(x). Thus, new range and stopping power values can replace those presented

in table 1 for most purpos.es, without further modifications in the results. It should be mentioned that in a number of cases solutions were accepted for which one of the

j(3i exceeded unity by a small amount, say 2 percent. Because of this, the extreme asymptotic values of

J{x), i.e., for x» 1, do not always follow closely the trend of (22). This is noticeable mostly for the low

Z elements. Interpolation will be less accurate when this occurs, but the values of J{x) involved are small enough and inaccurate enough for other reasons that this should not matter.

3.3. Comparisons With Experimental Data

A number of experiments are available for comparison with the data presented here, and fortunately

they are of high quality. By and large, the values in table 1 agree with the results recorded in [1], which

in turn compared well with experiments due to Frantz using monoenergetic electrons incident perpendicularly on beryllium, aluminum, and gold [9]. Other results of [1] proved to be in good agreement with

experiments using P^^ beta ray sources in air (Clark, Brar, and Marinelli, point isotropic source geometry)

[10], and in polystyrene (Loevinger, [11] plane isotropic source geometry).

Since the publication of [1], further experiments and calculations have been made by Huffman [12]. Huffman's results pertain to a monoenergetic electron beam incident perpendicularly on aluminum,

with measurement of the energy dissipated in plane layers of air. His source energies are all in the

proximity of 0.1 Mev. Huffman performed calculations, using the simplified method given in [1] which

assumes a to be infinite. His theoretical values were in fair agreement with his experiments.

A fine summary of aU this work is given in the Encyclopedia of Physics, vol. 34, in a review article by Birkhoff [13].

13
3

J(x)

-0.4 0

2

t -

Figure 4. Comparison of ex- perimental results of Griin

[14] with theoretical data

interpolated from table 1.

Although the data presented in this Monograph relate to energy dissipated in the material, rather than

in an air probe, it is instructive to compare some of these new tabular data with Huffman's experimental

results for 0.1 Mev electrons. Such a comparison is given in figure 3. The experimental results have

been scaled to compare with J{a) by use of range and stopping power values from [1]. Agreement is seen to be very good, actually a little better than in the case of Huffman's calculations. Perhaps the use of a finite a, which permits a slightly better representation of the energy dependence of S(t,Q) even

at low energies, causes the difference between the two calculations.

The most complete experiment of this type is that of A. E. Griin, who made extremely detailed

and consistent measurements of the energy dissipation distribution of rather low energy electrons

(0.005 to 0.054 Mev) in air [14]. Griin determined the energy dissipation in plane layers of air perpendicular to a beam source, and his values include positions behind the source plane. In fact, Griin's

experiments exhibit with remarkable clarity the discontinuity at the source plane, and he uses this feature

as an experimental determination of the stopping power of electrons at these (low) source energies.

Results from table 1 have been interpolated to obtain a comparison with Griin's curve for 0.032

Mev, and this is shown in figure 4. Both curves are absolute, having been normalized to unit electron source strength, so that the discontinuity measures the stopping power in Mev-cmVg- Substantial

disagreement occurs only in two areas. One is at large penetrations, where the experimental curve

is high due to the straggling in range which has been omitted from the calculations. The other is for penetrations behind the source, where the theoretical representation breaks down due to the calculation

of small differences between even and odd component distributions.

Comparisons at higher energies (~2 Mev) in aluminum have been made with earlier work by

Trump, Wright, and Clark [15] and indicate fairly good agreement. In high-Z materials, at both

high and low energies, where one expects the schematization to break down, there do not appear to be experimental results at present.

Construction of the computer programs and applications of the computer were accomplished in collaboration with Mrs. Sally Peavy of the NBS Computer Laboratory. Calculation of input data was accomplished with the aid of R. Bach and Joel Rogers. Graphing of the computer output for the

purpose of selection of suitable results was accomplished with the help of Mrs. Ann Nelms. Many

people aided this project in other ways.

14
Table 1. Energy Dissipation Function, J(x), and Input Data

CARBON

Z = 6, Eq = 0.025 Mev

STOPPING POWER

(dE/dr)T^ = 9.97 Mev(cm2/g)

RESIDUAL RANGE

= O.OOUl g/cm^

OTHER PARAMETERS

h

= 1.080 h = 0.8079 a = -107.8 = 0.2708

0.7751 h

= 0.0380

aPI'P= 0.9124 = -0.1167

SCATTERING COEFFICIENTS

e I H

15° 1.004 1 1.090

30 1.003 2 2.770

45 0.998 3 4.867

60 0.990 4 7.272

75 0.979 5 9.977

90 0.966 6 12.87

105 0.953 7 15.90

120 0.940 8 19.04

135 0.928 9 22.68

150 0.920 10 26.43

165 0.9U 11 30.26

180 0.912 12 34.16

X

0.000

0.025

0.050

0.075

0.200

0.225

0.250

0.275

0.300

0.325

0.350

0.375

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

J(x)

1.000

1.016

1.041

1.072

0.100 1.111

0.125 1.158

0.150 1.211

0.175 1.272

1.340

1.415

1.497

1.586

1.682

1.785

1.893

2.008

0.400 2.127

0.425 2.251

0.450 2.379

0.475 2.508

POINT ISOTROPIC SOURCEPLANE PERPENDICULAR

SOURCE

J(x) J(-x) X

J(x) J(x) J(-x)

1.422

1.519

1.615

1.713

0.422

0.341

0.266

0.200

0.500

0.525

0.550

0.575

2.636

2.763

2.883

2.994

2'. 671 2^580

2J+72

2.350

-0.009

-0.012

-0.013

-0.008

1.812

1.9U

2.022

2.133

0.144

0.103

0.081

0.077

0.600

0.625

0.650

0.675

3.088

3.161

3.203

3.203

2.216

2.070

1.910

1.735

-0.003

0.002

0.006

0.008

2.242

2.346

2.444

2.534

0.078

0.079

0.079

0.078

0.700

0.725

0.750

0.775

3.149

3.025

2.813

2.496

1.543

1.334

1.090

0.872

0.008

0.008

0.007

0.004

2.615

2.685

2.742

2.783

0.076

0.072

0.066

0.058

0.800

0.825

0.850

0.875

2. 064

1.523

0.925

0.397

0.634

0.409

0.219

0.085

0.001

-0.002

-0.004

-0.003

2.806

2.808

2.787

2.7a

0.048

0.036

0.022

0.007

0.900

0.925

0.950

0.975

0.091

0.007

0.000

0.000

0.019

0.001

0.000

0.000

-0.001

-0.000

-0.000

-0.000

Z = 6, E_ = 0.05 Mev

STOPPING POWER

(dE/dr) = 5.95 Mev(cm2/g)

RESIDUAL RANGE

= 0.00479 g/cm^

OTHER PARAMETERS

Ai =

A2 =

di = 1.115 a = 12.76

A^I= 0.7913 A3 =

A^^^= 0.9343 A^ =

0.7176

1.438

-2.387

1.231

SCATTERING COEFFICIENTS

e I H

15° 1.004 1 1.034

30 1.001 2 2.687

45 0.990 3 4.800

60 0.974 4 7.274

75 0.953 5 10.04

90 0.930 6 13.04

105 0.905 7 16.23

120 0.882 8 19.58

135 0.862 9 23.06

150 0.846 10 26.64

165 0.836 11 30.29

180 0.833 12 34.00

508105 0-59-3

X

0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

0.200

0.225

0.250

0.275

0.300

0.325

0.350

0.375

0.400

0.425

0.450

0.475

POINT

ISOTROPIC

SOURCE

J(x)

1.000

1.008

1.024

1.049

1.082

1.123

1.172

1.230

1.296

1.369

1.451

1.540

1.637

1.742

1.854

1.973

2.099

2.231

2.368

2.510

PLANE PERPENDICULAR

SOURCE

J(x) J(-x) X

1.363

1.443

1.526

1.615

0.363

0.290

0.224

0.167

0.500

0.525

0.550

0.575

1.713

1.825

1.950

2.075

0.123

0.096

0.086

0.081

0.600

0.625

0.650

0.675

2.195

2.310

2.418

2.518

0.076

0.071

0.066

0.061

0.700

0.725

0.750

0.775

2.609

2.688

2.754

2.805

0.056

0.050

0.044

0.038

0.800

0.825

0.850

0.875

2.837

2.847

2.834

2.793

0.032

0.026

0.019

0.012

0.900

0.925

0.950

0.975

POINT ISOTROPIC

SOURCE

J(x)

2.654

2.798

2.939

3.072

3.189

3.279

3.325

3.303

3.185

2.948

2.600

2.174

1.715

1.255

0.819

0.446

0.178

0.039

0.003

0.000

PLANE

PERPENDICULAR

SOURCE

J(x) J(-x)

2.725 0.005

2.630 -0.001

2.513 -0.005

2.378 -0.008

2.229 -0.007

2.066 -0.007

1.888 0.000

1.696 0.004

1.490 0.007

1.270 0.008

1.039 0.007

0.803 0.004

0.571 0.001

0.358 -0.002

0.184 -0.003

0.068 -0.003

0.014 -0.001

0.001 -0.000

0.000 -0.000

0.000 -0.000

15
Table 1. Energy Dissipation Function, J(x), Jind Input Data - Continued

1

STOPPING POWER

(dE/dr)„ = 3.71 Mev(cm2/g)

RESIDUAL RANGE

= 0.0159 g/cm^

OTHER PARAMETERS

= 1.0^2 A^ = 0.7075

a = 39.12 A = 0.8655

2 A^^= 0.77U A3 = -1.031

aP^P= 0.9168 A, = 0.4576

SCATTERING COEFFICIENTS

e I H

15° 1.004 1 1.016

30 0.996 2 2.702

U5 0.976 3 4.908

60 0.946 4 7.542

75 0.909 5 10.54

90 0.868 6 13.84

105 0.826 7 17.42

120 0.786 8 21.23

135 0.751 9 25.24

150 0.725 10 29.43

165 0.708 11 33.78

180 0.702 12 38.26

STOPPING PO'aTER (dE/dr)^^ = 2.52 Kev(cmVg)

RESIDUAL RANGE

= 0.0498 g/cm^

OTHER PARAMETERS

= 1.033 A;i^ = 0.6437 a = 18.89 A2 = 0.8923

A^"^^ 0.7726 A3 =-0.9961

A^^^= 0.9216 A, = 0,4600

SCATTERING COEFFICIENTS

e I H

15" 1.003 1 0.9815

30 0.987 2 2.666

45 0.954 3 4.912

60 0.906 4 7.634

75 0.846 5 10.77

90 0.781 6 U.28

105 0.7U 7 18.11

120 0.651 8 22.24

135 0.596 9 26.64

150 0.554 10 31.28

165 0.527 11 36.14

180 0.518 12 41.19

CARBON

Z = 6, Eq = 0.1 Mev

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

J. J(x) J(x) J(-x)

0.000 1.000 1.341 0.341

0.025 1.011 1.424 0.270

0.050 1.029 1.508 0.204

0.075 1.054 1.595 0.145

0.100 1.086 1.687 0.097

0.125 1.124 1.786 O.O62

0.150 1.169 1.895 0.045

0.175 1.221 2.013 0.045

0.200 1.279 2.130 0.050

0.225 1.344 2.241 0.053

0.250 l.a5 2.345 O.056

0.275 1.493 2.442 O.O58

0.300 1.578 2.528 0.058

0.325 1.669 2.603 0.056

0.350 1.767 2.664 0.052

0.375 1.871 2.708 0.046

0.400 1.981 2.734 0.038

0.425 2.097 2.737 0.027

0.450 2.218 2.716 O.OI4

0.475 2.344 2.669 0.001

Z = 6, Eq = 0.2 Mev

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) J(x) J(-x)

0.000 1.000 1.294 0.294

0.025 1.008 1.368 0.228

0.050 1.022 1.444 0.168

0.075 1.042 1.522 0.115

0.100 1.068 1.606 0.071

0.125 1.100 1.698 o.oa

0.150 1.138 1.800 0.027

0.175 1.181 1.911 0.029

0.200 1.231 2.022 0.035

0.225 1.286 2.126 0.040

0.250 1.347 2.224 0.044

0.275 1.4U 2.3U 0.047

0.300 1.488 2.395 0.048

0.325 1.567 2.463 0.048

0.350 1.653 2.518 0.045

0.375 1.745 2.557 0.040

0.400 1.843 2.577 0.032

0.425 1.948 2.576 0.021

0.450 2.059 2.551 0.009

0.475 2.176 2.503 -0.003

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x) J(x) J(-x)

0.500

0.525

0.550

0.575

2.474

2.605

2.736

2.864

2.599

2.507

2.399

2.278

-0.009

-0.005

-0.014

-0.009

0.600

0.625

0.650

0.675

2.983

3.084

3.154

3.174

2.U5

2.001

1.844

1.671

-0.004

0.001

0.005

0.007

0.700

0.725

0.750

0.775

3.116

2.952

2.667

2.266

1.481

1.275

1.054

0.824

0.008

0.008

0.006

0.003

0.800

0.825

0.850

0.875

1.782

1.276

0.822

0.465

0.593

0.377

0.197

0.074

0.000

-0.002

-0.003

-0.003

0.900

0.925

0.950

0.975

0.218

0.076

0.016

0.001

0.015

0.001

0.000

0.000

-0.001

-0.000

0.000

0.000

X

POINT- ISOTROPIC

SOURCE

J(x)

PLANE PERPENDICULAR

SOURCE

J(x) J(-x)

0.500

0.525

0.550

0.575

2.298

2.425

2.552

2.676

2.433

2.344

2.242

2.128

-0.012

-0.016

-0.013

-0.008

0.600

0.625

0.650

0.675

2.789

2.878

2.929

2.928

2.004

1.869

1.721

1.558

-0.003

O.OCl

0.0C4

0.006

0.700

0.750

0.775

2.861

2.472

2.132

1.380

1.186

0.978

0.762

0.007

0.007

0.005

0.003

0.800

0.825

0.850

0.875

1.702

1.220

0.753

0.387

0.545

0.344

0.178

0.066

0.000

-0.002

-0.003

-0.002

0.900

0.925

©.950

0.975

0.171

0.071

0.027

0.009

0.013

0.001

0.000

0.000

-0.001

-0.000

-0.000

-0.000

16
Table 1. Energy Dissipation Function, J(x), and Input Data - Continued

STOPPING POWER

(dE/dr) = 1.92 Mev(cm2/g)

RESIDUAL RANGE

= 0.U3 g/cm^

OTHER PARAMETERS

di = 1.016 h

= 0.5A17 a = 9.779 = 0.94.22 D.7603 =-0.8166

0.9091 h

= 0.3327

SCATTERING COEFFICIENTS

e a/tr

' R

I H

15° 1.002 1 0.9221

30 0.977 2 2.555

U5 0.929 3 4.766

60 0.860 A 7.481

75 0.776 5 10.64

90 0.683 6 14.22

105 0.590 7 18.16

120 0.501 8 22.44

135 0.425 9 27.04

150 0.366 10 31.94

165 0.328 11 37.10

180 0.316 12 42.51

CARBON

Z = 6, Eq = 0.4 Mev

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE X

J(x) J(x) J(-x)

0.000 1.000

1.007 1.296 0.176

0.050 1.018 1.362 0.125

0.075 1 035

0.100 1.056

0.125 1.081 1.584 0.017

0.150 1.112 1.674 0.006

0.175 1.147 1 TIL 0 on

0.200 1.187 0.018

0.225 1.231 1.967 0.026

0.250 1.281 2.055 0.031

0.275 1.335 2.134 0.036

0.300 1.394 2.205 0.038

0.325 1.458 2.264 0.038

0.350 1.527 2.310 0.037

0.375 1.602 2.340 0.032

0.400 1.681 2.352 0.025

0.425 1.766 2.344 0.016

0.450 1.855 2.3U 0.004

0.475 1.949 2.262 -0.006

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE X

J(x) J(x) J(-x)

0.500 2.048

0 '5?') 2.107 -0.015

0 '550 2 254 2.012 -0.012

2-358 -1-

.

0.600 2.U51 1X.7Q? / 7^ -0 . 003

0.625 2 543 1.670 0.001

0.650 2.601 1.536 0.004

0.675 2.611 1 3Q0 0.005

0.700 2.544 1 231 0.006

0.725 2.380 1.058 0.006

0.750 2.126 0.873 0.005

0.775 1.813 0.681 0.002

0.800 1.466 0.488 0.000

0.825 1.098 0.307 -0.002

0.850 0.731 0.160 -0.003

0.875 0.401 0".060 -0.002

0.900 0.157 0.012 -0.001

0.925 0.031 0.001 -0.000

0.950 0.001 0.000 -0.000

0.975 0.000 0.000 -0.000

STOPPING POV/ER (dE/dr)^^ = 1.71 Mev(cm^/g)

RESIDUAL RANGE = 0.311 g/cm^

OTHER PARAf^ETERS - 1.004 A^ = 0.4643 a = 5.157 Ag = 0.9U2

A^'^^= 0.7383 A3 = -0.5978

A^^= 0.8842 A. = 0.2193

SCATTERING COEFFICIENTS

e I s^ 15" 1.001 1 0.8413

30 0.970 2 2.362

U5 0.911 3 4.444

60 0.828 4 7.022

75 0.728 5 10.05

90 0.617 6 13.50

105 0.505 7 17.31

120 0.400 8 21.50

135 0.308 9 26.01

150 0.238 10 30.84

165 0.194 11 35.97

180 0.179 12 41.39

Z = 6, Eq = 0.7 Mev

POINT PLANE

fSOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) J(x) J(-x)

0.000 1.000 1.176 0.176

0.025 1.004 1.227 0.131

0.050 1.013 1.279 0.089

0.075 1.025 1.334 0.052

0.100 1.040 1.394 0.022

0.125 1.060 1.462 0.022

0.150 1.083 1.539 -0.006

0.175 1.110 1.625 -0.001

0.200 1.140 1.712 0.007

0.225 1.174 1.795 O.OU

0.250 1.213 1.872 0.020

0.275 1.255 1.942 0.025

0.300 1.301 2.004 0.029

0.325 1.351 2.056 0.030

0.350 1.405 2.097 0.030

0.375 1.463 2.123 0.027

0.400 1.525 2.134 0.021

0.425 1.591 2.126 0.013

0.450 1.661 2.098 0.003

0.475 1.735 2.050 -0.007

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE X

J(x) J(x) J(-x)

0.500 1.813 1.985 -0.013

0.525 1.894 1.907 -0.014

0.550 1.977 1.819 -0.011

0.575 2.060 1.724 -0.007

0.600 2.1a 1.623 -0.003

0.625 2.213 1.513 0.000

0.650 2.268 1.394 0.003

0.675 2.288 1.265 0.005

0.700 2.253 1.123 0.005

0.725 2.137 0.970 0.005

0.750 1.929 0.805 0.004

0.775 1.642 0.632 0.002

0.800 1.306 0.458 0.000

0.825 0.963 0.293 -0.002

0.850 0.644 0.155 -0.003

0.875 0.372 0.059 -0.002

0.900 0.168 0.012 -0.001

0.925 0.049 0.001 -0.000

0.950 0.006 0.000 -0.000

0.975 0.000 0.000 -0.000

17
Table 1. Energy Dissipation Function, J(x) , and Input Data - Continued

CARBON

Z = 6, E = 1.00 Mev

STOPPING POWER

(dE/dr)g =1.64 Mev(cniVg)

RESIDUAL RANGE = 0.4.91 g/cm^

OTHER PARAMETERS

= 0.9994 A^ = 0.4211 a = 3.373 A2 = 0.8811

A^-^= 0.7135 A = -0.4549

PT P

^ A = 0.8553 A^ = 0.1527

SCATTERING COEFFICIENTS

e aft^R

15° 1.000 1 30 0.967 2 2.171

45 0.903 3 4.104

60 0.814 4 6.510

75 0.705 5 9.348

90 0.586 6 12.59

105 0.466 7 16.20

120 0.352 8 20.16

135 0.254 9 24.45

150 0.179 10 29.06

165 0.131 11 33.96

180 0.115 12 39.15

X

0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

0.200

0.225

0.250

0.275

0.300

0.325

0.350

0.375

0.400

0.425

0.450

0.475

POINT

ISOTROPIC SOURCE

J(x)

1.000

1.003

1.009

1.018

1.030

1.045

1.064

1.085

1.110

1.138

1.169

1.203

1.241

1.282

1.327

1.376

1.428

1.484

1.545

1.609

PLANE PERPENDICULAR

SOURCE

POINT PLANE

ISOTROPIC PERPENDICULAR

SOUFCE SOURCE

J(x)

1.140

1.180

1.223

1.268

1.319

1.376

1.443

1.520

1.598

1.672

1.742

1.806

1.864

1.913

1.952

1.979

1.992

1.988

1.966

1.924

J(-x)

0.140

0.103

0.069

0.039

0.014

-0.003

-0.010

-0.006

0.002

0.008

0.014

0.019

0.023

0.025

0.025

0.023

0.019

0.012

0.004

0.005

X

0.500

0.525

0.550

0.575

0.600

0.625

0.650

0.675

0.700

0.725

0.750

0.775

0.800

0.825

0.850

0.875

0.900

0.925

0.950

0.975

J(x)

1.677

1.747

1.819

1.888

1.949

1.997

2.027

2.032

2.001

1.927

1.797

1.603

1.339

1.014

0.655

0.324

0.097

0.010

0.000

0.000

J(x)

1.866

1.795

1.7U

1.626

1.532

1.431

1.322

1.203

1.073

0.931

0.778

0.617

0.452

0.295

0.160

0.063

0.014

0.001

0.000

0.000

J(-x)

-0.011

-0.013

-0.011

-0.007

-0.003

-0.000

0.002

0.004

0.005

0.005

0.004

0.002

0.000

-0.001

-0.002

-0.002

-0.001

-0.000

-0.000

-0.000

STOPPING POWER

(ciE/dr)p =1.62 Mev(cmVg)

RESIDUAL RANGE = 1.11 g/cm^

OTHER PARAI'iETERS = 1.021 Ai = 0.3432 a = 1.365 A2 = 0.9489

A^'^^= 0.6539 A_ = -0.4613

PLP ^

A = 0.7815 A. = 0.1692

SCATTERING COEFFICIENTS

0 I H

15° 1.000 1 0.5895

30 0.963 2 1.681

45 0.894 3 3.200

60 0.797 4 5.107

75 0.680 5 7.373

90 0.551 6 9.976

105 0.421 7 12.90

120 0.298 8 16.12

135 0.192 9 19.63

150 0.111 10 23.42

165 0.059 11 27.48

180 0.042 12 31.79

18

Z = 6, E = 2.00 Mev

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) J(x) J(-x)

0.000 1.000 1.064 0.064

0.025 1.001 1.088 0.042

0.050 1.005 1.114 0.021

0.075 1.011 1.144 0.005

0.100 1.020 1.180 -0.006

0.125 1.030 1.225 -0.009

0.150 1.041 1.278 -0.003

0.175 1.052 1.332 0.003

0.200 1.065 1.385 0.008

0.225 1.079 1.438 0.012

0.250 1.095 1.491 0.014

0.275 I.IU 1.542 0.015

0.300 1.134 1.592 0.013

0.325 1.157 1.639 0.010

0.350 1.183 1.681 0.007

0.375 1.213 1.715 0.004

0.400 1.247 1.741 0.002

0.425 1.285 1.755 -0.000

0.450 1.328 1.756 -0.002

0.475 1.377 1.741 -0.003

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x) J(x) J(-x)

0.500 1.431 1.709 -0.003

0.525 1.490 1.659 -0.003

0.550 1.553 1.593 -0.002

0.575 1.616 1.515 -0.001

0.600 1.675 1.431 -0.001

0.625 1.722 1.341 0.000

0.650 1.749 1.2U 0.001

O.f.75 1.751 1.140 0.001

0.700 1.722 1.026 0.002

0.725 1.656 0.901 0.002

0.750 1.547 0.766 0.001

0.775 1.389 0.621 0.001

0.800 1.181 0.469 0.000

0.825 0.928 0.318 -0.000

0.850 0.647 0.182 -0.001

0.875 0.371 0.078 -0.001

0.900 0.151 0.019 -0.000

0.925 0.031 0.002 -0.000

0.950 0.001 0.000 -0.000

0.975 0.000 0.000 -0.000
Table 1, Energy Dissipation Function, J(x), and Input Data - Continued

CARBON

Z = 6, 4.00 Mev

STOPPING POWER

(dE/dr)^ =1.67 Mev(cm2/g)

RESIDUAL RANGE

r„ = 2.32 g/cm^

OTHER PARAJIETERS = l.OAl a = 0.6220

A^^^= 0.5522

A^^^= 0.6549

^1 = \

=

A =

A =

0.29^8

0.9285

-0.3785

0.1522

SCATTERING COEFFICIENTS

e 0/0^ I H

15° 0.999 1 0.3992

30 0.962 2 1.U5

A5 0.890 3 2.193

60 0.790 4 3.517

75 0.669 5 5.101

90 0.537 6 6.929

105 0.403 7 8.992

120 0.277 8 11.28

135 0.168 9 13.78

150 0.084 10 16.49

165 0.031 11 19.41

180 0.013 12 22.52

X

0,000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

0.200

0.225

0.250

0.275

0.300

0.325

0.350

0.375

0.400

0.425

0.450

0.475

POINT ISOTROPIC

SOURCE

J(x)

1.000

0. 999

1.000

1. C03

1.006

1.011

1.017

i.025

1.033

1.042

1.051

1.060

1.069

1.078

1.090

1.103

1.120

1.142

1.168

1.201

PLANE PERPENDICULAR

SOURCE

POINT PLANE ISOTROPIC PERPENDICULAR

SOURCE SOURCE

J(x)

1.031

1.038

1.047

1.060

1.075

1.094

1.117

1.145

1.178

1.217

1.261

1.309

1.357

1.400

1.439

1.473

1.501

1.523

1.538

1.545

J(-x)

0.031

0.024

0.018

0.012

0.t)08 0.C03

0.000

-0.002

-0.004

-0.004

-0.003

-0.002

-0.000

0.001

0.002

0.003

0.004

0.004

0.004

0.004

X

0.500

Q.525

0.550

0.575

0.600

0.625

0.65C

0.675

0.700

0.725

0.750

0.775

0.800

0.825

0.850

0.875

0.900

0.925

0.950

0.975

J(x)

1.239

1.281

1.324

1.367

1.410

1.449

1.482

1.506

1.514

1.501

1.457

1.372

1.232

1.028

0.760

0.456

0.184

0.033

0.001

0.000

J(x)

1.543" 1.531

1.509

1.474

'1.426

1.365

1.289

1.2C0

1.097

0.981

0.853

0.714

0.564

0.411

0.263

0.136

0.048

0.008

0.000

0.000

J(-x)

0,003

0.002

0,000

-0.001

-0,003

-0,004

-0.CC5

-O.-OO3

-0.001

0.001

0.003

0,003

0,003

0.001

-0.000

-0,002

-0.002

-0.001

-0.000

-0.000

Z = 6, Eg = 10.00 Mev

STOPPING POWER

(dE/dr)p = 1.75 Mev(cmVg)

RESIDUAL RANGE = 5,83 g/cra2 OTHER PARAMETERS

dj^ = 1.071 a = 0.2370

A^^= 0,4129

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

h

=

A2 =

A3 =

A^^^= 0.4788 A, =

4

0,25U

1.005

-0.5297

0.2734

SCATTERING COEFFICIENTS

e

I H

15" 0.999 1 0,2051

30 0.961 2 0.5920

45 0.888 3 l.UO

60 0.788 4 1,838

75 0.666 5 2,679

90 0.532 6 3.655

105 0.397 7 4.762

120 0.269 8 5.995

135 0.159 9 7.351

150 0.074 10 8.827

165 0.021 11 10.42

180 0.002 12 12.12

0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

0.200

0.225

0.250

0.275

0.300

0.325

0.350

0.375

0.400

0.425

0.450

0.4'i'5

J(x)

1.000

0.999

0.999

1.000

1.002

1.004

1.007

1.009

1.011

1.013

1.015

1.017

1.019

1.022

1.025

1.029

1.034

1.040

1.048

1.057

J(x)

1.007

1.007

1.009

1.013

1.019

1.027

1.037

1.049

1.064

1.079

1.095

1.108

1.120

1.134

1.150

1.169

1.190

1.214

1.240

1.267

J(-x)

0.007

0.007

0.005

0.005

0.004

0.003

0.003

0.002

0.001

-0.000

-0.001

-0.001

-0.001

-0.001

0.000

0.000

0.000

0.000

0.000

0.000

0.500

0.525

0.550

0.575

0.600

0.625

0.650

0.675

0.700

0.725

0.750

0.775

0.800

0.825

0.850

0.875

0.900

0.925

0.950

0.975

POINT

ISOTROPIC SOURCE

J(x)

1.070

1.087

1.109

1.137

1.169

1.204

1.239

1.273

1.303

l'.326 1.336

1.324

1.279

1.184

1.018

0.767

0.444

0.143

0.010

0.000

PLANE PERPENDICULAR

SOURCE

J(x)

1.296

1.325

1.352

1.373

1.384

1.378

1.349

1.297

1.232

1.157

1.071

0.969

0.847

0.698

0.521

0.324

0.U3

0.033

0.000

0.000

J(-x)

0.000

0.000

0.001

0.001

0.000

0.000

o-.ooo 0.000

0.000

0.000

0.000

0.000

0.000

0.000

0,000

0,000

0.000

0.000

0.000

0.000

19
Table 1. Energy Dissipation Function, J(x) , and Input Data - Continued

STOPPING POl-ffiR (dE/dr)^^ = 8.50 MevCcmVg)

RESIDUAL RAi:OE r = 0.00167 p/cm^

o OTHER PARAITTERS

ALUMINW!

Z = 13, Eq = 0.025 Mev

POniT PLAUE

ISOTROPIC PERPEKDICDLAR

SOURCE SOURCE

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

= 2.0^9 a = -17.87

aP'^T= 1.500

A^^-'^= 1.729

^1

=

^2 = 0.75U

0.4987

A^ = -0.3392

A, = 0.0861

4 SCATTERING COEFFICIENTS

X 0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

J(x) J(x)

1.000 2.009

1.026 2.22A

1.080 2.419

1.161 2.593

1.265 2.743

1.391 2.870

1.531 2.973

1.679 3.054

J(-x)

1.009

0.809

0.640

0.506

0.410

0.350

0.316

0.292

X 0.500

0.525

0.550

0.575

0.600

0.625

0.650

0.675

J(x)

3.456

3.420

3.324

3.165

2.943

2.663

2.339

1.983

J(x)

1.939

1.743

1.545

1.347

1.151

0.959

0.774

0.601

J(-x)

0.007

0.008

0.008

0.008

0.007

0.006

0.005

0.003

9 I h 0.200 1.832 3.111 0.268 0.700 1.612 0.443 0.002

15° 1.010 1 2.170 0.225 1.990 3.U5 0-241 0.725 1.241 0.305 0.000

30 1.015 2 5.399 0.250 2.154 3.153 0.750 0.887 0.193 -0.000

45 1.016 3 9.302 0.275 2.325 3.135 0.183 0.775 0.573 0.108 -0.001

60 1.010 4 13.65

75 1.001 5 18.29 0.300 2.499 3.090 0.153 0.800 0.320 0.051 -0.001

90 0.988 6 23.10 0.325 2.674 3.018 0.122 0.825 0.143 0.019 -0.000

105 0.973 7 28.00 0.350 2.844 2.920 0.092 0.850 0.046 0.005 -0.000

120 0.959 8 32.94 0.375 3.006 2.797 0.064 0.875 0.008 0.001 -0.000

135 0.946 9 38.92

150 0.936 10 44.97 0.400 3.153 2.653 0.041 0.900 0.001 0.000 -0.000

165 0.930 11 51.07 0.425 3.280 2.492 0.024 0.925 0.000 0.000 -0.000

180 0.928 12 57.20 0.4f0 3.378 2.316 0.013 0.950 0.000 0.000 -0.000

0.475 3.440 2.131 0.008 0.975 0.000 0.000 -0.000

Z = 13, E^ = 0.05 Mev

STOPPING P'^WEF (dE./dr/Ty = ?.14 Kev(cmVg)

RESIDUAL RAJT,E r = 0.00561 g/cm^

OTHER PARAl^ERS

di = 2.190 a = 33.52

A^^= 0.1582 PLP

A = 1.829

A. =

a; =

0.6818

1.500

-2.445

1.260

SCATTERING COEFFICIENTS

X 0.000

0.025

0.050

0.075

0.100

0.T25

0.150

0.175

POINT

ISOTP'^PIC SOURCE

J(x)

1.000

1.017

1. '61 1.131

] .224 1.338

1.470

1.620

PLANE PERPENDICULAR

SOURCE

J(x)

1.972

2.180

2. 2 2.546

2.703

2.842

2.960

3.055

J(-x)

0.972

C.773

0.607

0.478

0.385

0.328

0.295

0.270

O.pOO

0.525

0.550

0.575

0.600

0.625

0.650

0.675

POINT

ISOTROPIC SOURCE

J(*)

3.506

3.456

3.340

3.153

2.896

2.580

2.221

1.839

PES'" q:dtcular

SOURCE

J(*) J(-x)

] .918 1.710

1 .1 1. J3

1.089

0.692

0.706

0.534

0.003

0.005

0.006

0.007

0.006

0.006

0.004

0.003

e a/a' R

i Si 0.200 1.783 3.124 0.245 0.700 1.453 0.382 0.001

15° 1.013 1 2.126 0.225 1.958 3.167 0.218 0.725 1.080 0.254 0.000

30 1.017 2 5.440 0.250 2.U1 3.181 0.191 0.750 0.742 0.153 -0.001

45 1.013 3 9.587 0.275 2.330 3.168 0.163 0.775 0.456 0.081 -0.001

60 0.999 4 U.36

75 0.979 5 19.59 0.300 2.520 3.125 0.134 0.800 0.241 0.035 -0.001

90 0.955 6 25.18 0.325 2.708 3.053 0.106 0.825 0.102 0.012 -0.000

105 0.928 7 31.04 0.350 2.890 2.952 0.079 0.850 0.030 0.003 -0.000

120 0.902 8 37.10 0.375 3.060 2.826 0.055 0.875 0.005 0.000 -0.000

135 0,879 9 43.29

150 0.861 10 49.56 0.400 3.213 2.675 0.034 0.900 0.000 0.000 -0.000

165 0.850 11 55.89 0.425 3.342 2.505 0.018 0.925 0.000 O.'OOC -0.000

180 0.846 12 62.24 0.450 3.440 2.319 0.008 0.950 0.000 0.000 -0.000

0.475 3.497 2.122 0.004 0.975 0.000 0.000 -0.000

20
Table 1. Energy Dissipation Function, J(x), and Input Data - Continued

STCPPIKG POWER

(dE/dr)_ =3.24 Mev(cmVg)

RESIDUAL RMGE

=a0183 g/cm2

OTHER PARAMETERS

d-^ = 2.145 Ai = 0.6884 a = 35.45 Ag = 0.9293

A^l= 1.580 A^ = -1.089

^ A^LP= 1.833 A, = 0.4714

SCATTERING COEFFICIENTS

e

a/aR

I SI

15° 1.015 1 2.086

30 1.017 2 5.478

45 1.004 3 9.840

60 0.997 4 14.97

75 0.941 5 20.74

90 0.898 6 27.02

105 0.852 7 33.73

120 0.808 8 40.80

135 0.769 9 48.18

150 0.738 10 55.79

165 0.719 11 63.62

180 0.712 12 71.62

STOPPING POWER

(dE/dr)^ = 2.22 Mev(cmVg)

RESIDUAL RANGE

Tq = 0.0570 g/cm^

OTHER PARAMETERS

d-,^ = 2.118 k-j^ = 0.6285 a = 20.70 A2 = 0.9389

A^l= 1.575 A3 = -1.056

aP^P= 1.832 A. = 0.4883

SCATTERING COEFFICIENTS

e a/a^ I h

15° 1.018 1 2.021

30 1.013 2 5.437

45 0.988 3 9.929

60 0.943 4 15.31

75 0.883 5 21.46

90 0.815 6 28.26

105 0.743 7 35.64

120 0.674 8 43.52

135 0.613 9 51.85

150 0.566 10 60.57

165 0.536 11 69.64

180 0.526 12 79.00

ALUMINUM

z = 13, E^ = 0.10 Mev

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE

X J(x) J (. -X^ 0.000 1.000 1.916 0.916

0.025 l!021 U • /Xo

0.050 1,066 2.324 0.555

0.075 2.501 0.429

0.100 1.221 2.659 0.342

0.125 1.327

0.150 1.451 2.913 0.267

0.175 3.004 0.248

0.200 1 7'?9 J. . ' ^7 3.068 0.228

0.225 1.900 3.105 0.204

0.250 2.069 3.112 0.179

0.275 2 2Z.3 3.091 0.151

0.300 3.040 0.122

0.325 2.594 2.961 0.093

0.350 2.764 2.856 0.066

0.375 2.924 2.726 0.042

0.400 3.068 2.577 0.02-4 0.425 3.192 2.412 0.012

0.450 3.287 2.235 0.006

0.475 3.346 2.049 0.004

Z = 13, E^ = 0.20 Mev

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x) J(x) J(-x)

0.000

0.025

0.050

0.075

1.000

1.016

1.053

1.110

1.822

2.022

2.205

2.372

0.822

0.636

0.482

0.365

0.100

0.125

0.150

0.175

1,185

1.276

1.383

1.503

2.521

2.653

2.763

2.850

0.287

0.245

0.226

0.213

0.200

0.225

0.250

0.275

1.635

1.778

1.928

2.085

2.910

2.943

2.948

2.924

0.198

0.178

0.156

0.131

0.300

0.325

0.350

0.375

2.245

2.405

2.563

2.714

2.872

2.793

2.690

2.566

0.104

0.077

0.052

0.031

0.400

0.425

0.450

0.475

2.853

2.973

3.068

3.128

2.425

2.270

2.104

1.930

0.015

0.006

0.003

0.002

POINT PLANE ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x) J(x) J(-x)

0.500

0.525

0.550

0.575

3.361

3.321

3.220

3.052

1.857

1.660

1.462

1.263

0.004

0.006

0.006

0.006

0.600

0.650

0.675

2.819

0 coo 2.5-^9 2.194

1.831

1.067

0.0/1

0.696

0.528

0.006

A AAC 0.003

0.002

0.700

0.725

0.750

0.775

1.456

1.090

0.750

0.462

0.379

0.252

0.152

0.081

0.001

-0.000

-0.001

-0.001

0.800

0.825

0.850

0.875

0.243

0.102

0.030

0.005

0.035

0.012

0.003

0.000

-0.001

-0.000

-0.000

-0.000

0.900

0.9«i5 0.950

0.975

0.000

A AAA u . uuu 0.000

0.000

0.000

0.000

0.000

0.000

-0.000

-0.000

-0.000

-0.000

POINT ISOTROPIC

SOURCE

PLANE PERPENDICULAR

SOURCE

X

J(x) J(x) J(-x)

0.500

0.525

0.550

0.575

3.U3

3.106

3.010

2.853

1.750

1.566

1.380

1.194

0.003

0.004

0.005

0.005

0.600

0.625

0.650

0.675

2.640

2.376

2.072

1.737

1.009

0.829

0.658

0.499

0.005

0.004

0.003

0.002

0.700

0.725

0.750

0.775

1.386

1.038

0.714

0.438

0.358

0.238

0.U3

0.075

0.001

-0.000

-0.000

-0.000

0.800

0.825

0.850

0.875

0.228

0.094

0.027

0.004

0.033

0.011

0.002

0.000

-0.001

-0.000

-0.000

-0.000

0.900

0.925

0.950

0.975

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

-0.000

-0.000

-0.000

-0.000

21
. Energy Dissipation Function, J(x),and Input Data - Continued

ALUMINUM

STOPPING POWER

(clE/dr)_ = 1.72 Mev(cinVg)

Eo RESIDUAL RANGE

Tq = 0.162 g/cm2

OTHER PARA>WERS

= 2.094

a = 9.679

A^'^^= 1.547

aP^= 1-.805

A-L = 0.5291

A2 = 0.9542

A3 = -0.8196

A^ = 0.3363

SCATTERING COEFFICIENTS

e 0/0^ I 15° 1.019 1 30 1.008 2 45 0.968 3 60 0.903 4

75 0.818 5 90 0.722 6 105 0.621 7 120 0.525 8 135 0.441 9 150 0.376 10

165 0.334 11 180 0.320 12

1.898

5.218

9.666

15.08

21.33

28.34

36.03

44.34

53.21

62.60

72.45

82.73

Z = 13, Eq = 0.40 Mev

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

POINT ISOTROPIC

SOURCE

PLANE PERPENDICULAR

SOURCE X

j(x) J(x) J(-x) X

J(x) J(x) J(-x)

0.000

0.025

0.050

0.075

1.000

1.031

1.043

1.089

1.680

1.859

2.025

2.177

0.680

0.376

0.274

0.500

0.525

0.550

0.575

2.788

2.752

2.665

2.527

1.585

1.419

1.251

1.083

0.002

0.003

0.004

0.004

0.100

0.125

0.150

0.175

1.150

1.224

1.312

1.410

2.315

2.438

2.542

2.624

0.208

VJ . J. ' u 0.167

0.163

0.600

0.650

0.675

2.342

2.116

1.853

1.561

0.917

0.755

0.600

0.456

0.004

0.003

0.002

0.001

0.200

0.225

0.250

0.275

1.9.9

1.636

1.761

1.891

2.679

2.708

2.710

2.684

0.155

U .14<i 0.125

0.104

0.700

0.725

0.750

0.775

1.252

0.942

0.652

0.401

0.328

0.219

0.133

0.070

0.001

-0.000

-0.000

-0.001

0.300

0.325

0.350

0.375

2.025

2.160

2.293

2.422

2.631

2.553

2.453

2.334

0.081

0.057

0.035

0.018

0.800

0.825

0.850

0.875

0.210

0.086

0.025

0.004

0.031

0.010

0.002

0.000

-0.000

-0.000

-0.000

-0.000

0.400

0.425

0.450

0.475

2.540

2.644

2.725

2.776

2.202

2.058

1.906

1.748

0.006

0.001

-0.001

0.000

0.900

0.925

0.950

0.975

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

-0.000

-0.000

-0.000

-0.000

Z = 13, E^ = 0.70 Mev

STOPPING POWER

(dE/dr)^^ =1.55 Mev(om2/g)

RESIDUAL RANGE

= 0.349 g/cm^

OTHER PARAMETERS

d-^ = 2.084 a =4.755

aPTI= 1..497 A^^^= 1.747 A,

= 0.452 = 0.9030 = -0.5669 = 0.2118

SCATTERING COEFFICIENTS

e I

15° 1.019 1 30 1.003 2 45 0.954 3 60 0.874 4

75 0.773 5 90 0.658 6 105 0.538 7 120 0.424 8 135 0.324 9 150 0.247 10

165 0.198 11 180 0.181 12

22

1.722

4.801

8.979

14.11

20.10

26.87

34.35

42.49

51.24

60.57

70.43

80.79

X

0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

0.200

0.225

0.250

0.275

0.300

0.325

0.350

0.375

0.400

0.425

0.450

0.475

POINT

30TR0PIC

SOURCE

J(x)

1.000

1.009

1.031

1.066

1.113

1.170

1.238

1.3U

1.400

1.492

1.591

1.696

1.804

1.9U

2.024

2.131

2.232

2.321

2.394

2.U1

PLANE PERPENDICULAR

SOURCE

POINT ISOTROPIC SOURCE

PLANE

PERPENDICULAR

SOURCE

J(x) J(-x) X J(x) J(x) J(-x)

1.535

1.686

1.828

1.961

0.535

0.394

0.278

0.193

0.500

0.525

0.550

0.575

2.456

2.431

2.361

2.247

1.459

1.310

1.160

1.008

0.000

0.002

0.002

0.003

2.085

2.199

2.299

2.378

0.139

0.115

0.113

0.115

0.600

0.625

0.650

0.675

2.093

1.906

1.678

1.426

0.858

0.711

0.569

0.437

0.003

0.003

0.002

0.001

2.434

2.465

2.471

2.450

0.113

0.107

0.095

0.080

0.700

0.725

0.750

0.775

1.155

0.880

0.618

0.387

0.317

0.214

0.132

0.071

0.001

-0.000

-0.000

-0.001

2.404

2.334

2.243

2.136

0.062

0.042

0.024

0.010

0.800

0.825

0.850

0.875

0.207

0.088

0.026

0.004

0.032

0.011

0.002

0.000

-0.000

-0.000

-0.000

-0.000

2.015

1.885

1.748

1.605

0.001

-0.003

-0.003

-0.002

0.900

0.925

0.950

0.975

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

-0.000

-0.000

-0.000

-0.000
Table 1. Energy Diasipation Function, J(x) , and Input Data - Continued

STOPPING POWER

(dE/dr)g^ = 1.51 MevCcmVg)

RESIDUAL RANGE

^0 - 0.545 g/ca^

OTHER PARAMETERS

dl = 2.093 = 0.4150 a = 2.965 = 0.8046

aPti, 1.U7 h

= -0.2985

aPLP, 1.690 = 0.0790

SCATTERING COEFFICIENTS

e I St

15« 1.020 1 1.565

30 1.001 2 4.395

45 0.947 3 8.262

60 0.861 4 13.04

75 0.752 5 18.64

90 0.628 6 25.01

105 0.499 7 32.07

120 0.377 8 39.78

135 0.270 9 48.11

150 0.187 10 57.02

165 0.134 11 66.47

180 0.116 12 76.U

STOPPING POWER

(dE/dr)Eg =1.51 Mev(cm2/g)

RESIDUAL RANGE

= 1.21 g/cm^

OTHER PARAMETERS

dl = 2.112 Ai = 0.3274

a = 1.288 Ag = 0.9604

a"^ 1.294 Aj = -0.4639

A^= 1.513 A, = 0.1761

SCATTERING COEFFICIENTS

e i H

15« 1.020 1 1.189

30 0.999 2 3.373

45 0.939 3 6.392

60 0.846 4 10.16

75 0.727 5 14.62

90 0.594 6 19.71

105 0.455 7 25 .a

120 0.323 8 31.69

135 0.207 9 38.50

150 0.118 10 45.83

165 0.061 11 53.65

180 0.042 12 61.95

t0810» 0 -49 •«

ALUMINUM

Z = 13, Eo = 1«00 Mev

POINT

ISOTROPIC SOURCE

PLANE PERPENDICULAR

SCCRCE X J(x) J(x) J(-x)

0.000

0.025

0.050

0.075

1.000

1.007

1.024

1.052

1.436

1.688

1.807

0.436

0.216

0.143

0.100

0.125

0.150

0.175

1.090

1.136

1.191

1.254

1.921

2.128

2.210

0.097

0.079

0.084

0.200

0.225

0.250

0.275

1.324

1,401

1.483

1.570

2.269

2.306

2.318

2.305

0.086

0.083

0.076

0.065

0.300

0.325

0.350

0.375

1.662

1.756

1.850

1.944

2.268

2.208

2.127

2.029

0.050

0.034

0.019

0.006

0.400

0.425

0.4?0

0.475

2.034

2.115

2.184

2.232

1.918

1.797

1.670

1.538

-0.002

-0.005

-0.005

-0.003

Z ? 13, Eo = 2.00 Mev

POINT

ISOTROPIC SOURCE

PLANE

1 PERPENDICULAR

SOURCE X J(x) J(x) J(-x)

0,000

0.025

0.050

0.075

1.000

1.002

1.012

1.027

1.252

1.333

1.415

1.500

0.252

0.177

0.114

0.065

0.100

0.125

0.150

0.175

1.049

1.076

1.109

1.U8

1.589

1.683

1.778

1.865

0.034

0.021

0.022

0.030

0.200

0.225

0.250

0.275

1.192

1.241

1.294

1.353

1.938

1.993

2.030

2.048

0.036

0.040

0.040

0.038

0.300

0.325

0.350

0.375

1.416

1.482

1.552

1.624

2.045

2.021

1.976

1.911

0.033

0.026

0.017

0.007

0.400

0.425

0.450

0.475

1.698

1.770

1.837

1.895

1.828

1.731

1.623

1.508

-0.001

-0.006

-0.008

-0,007

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE X

J(x) J(x) J(-x)

0.500 2.253 1.402 -0.001

0.525 2.238 1 .e04 u . UUl

0.550 2.184 1.124 0.002

0.575 2.088 0.982 0.002

0.600 1.956 0.841 0.003

0.625 1.789 nu nno . uu« 0.650 1.589 0.567 0.002

0.675 1.362 0.439 0.001

0.700 1.116 0.323 0.001

0.725 0.861 0.221 0.000

0.750 0.614 0.138 -0.000

0.775 0.393 0.076 -0.001

0.800 0.216 0.035 -0.000

0.825 0.094 0.012 -0.000

0.850 0.029 0.003 -0.000

0.875 0.005 0.000 -0.000

0.900 0.000 0.000 -0.000

0.925 0.000 0.000 -0.000

0.950 0.000 0.000 -0.000

0.975 0.000 0.000 -0.000

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE X J(x) J(x) J(-x)

0.500 1.936 1.388 -0.005

0.525 1.953 1.265 -0.002

0.550 1.936 1.139 0.000

0.575 1.882 1.010 0.001

0.600 1.788 0.879 0.002

0.625 1.659 0.748 0.003

0.650 1.499 0.619 0.002

0.675 1.313 0.493 0.002

0.700 1.105 0.375 0.001

0.725 0.883- 0.267 0.000

0.750 0.658 0.175 -0.000

0.775 0.446 0.102 -0.001

0.800 0.263 0.050 -0.001

0.825 0.127 0.019 -0.000

0.850 0.045 0.005 -0.000

0.875 0.009 0.001 -0.000

0.900 0.001 0.000 -0.000

0.925 0.000 0.000 -0.000

0.950 0.000 0.000 -0.000

0.975 0.000 0.000 -0.000

23
Table 1. Energy Dissipation Function, J(x), and Input Data - Continued

ALUMINUM

Z = 13, E = 4.. 00 Mov

STOPPING POWER

(dE/dr)„ =1.56 Mev(cmVg)

^o

RESIDUAL RANGE

r =2.51 g/cm^

POINT PLANE ISOTROPIC PERPENDICULAR

SOURCE SOURCE

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

OTHER PARAMETERS

= 2.176

a = 0.5808

aPTI= 1.065

A^ = 0.2857

Ag = 0.92U

A^ =-0.3746

A^^^= 1.2U A^ = 0.1645

SCATTERING COEFFICIENTS

e at

R

i

15° 1.020 1 0.7995

30 0.998 2 2.284

45 0.936 3 4.355

60 0.840 4 6.961

75 0.718 5 10.07

90 0.580 6 13.64

105 0.438 7 17.66

120 0.302 8 22.11

135 0.183 9 26.96

150 0.091 10 32.21

165 0.033 11 37.84

180 0.013 12 43.84

STOPPING POWER

(dE/dr),^ = 1.66 Mev(cm2/g)

RESIDUAL RANGE

=6.22 g/cm^

OTHER PARAMETERS

dj^ = 2.288

aPTI= 0.7789 A3 =

A^^^= 0.9059 A^ =

SCATTERING COEFFICIENTS

0.2366

1.032

-0.614A

0.3458

e ^^R i H

15° 1.020 1 0.4078

30 0.997 2 1.173

45 0.935 3 2.251

60 0.838 4 3.619

75 0.714 5 5.261

90 0.575 6 7.164

105 0.431 7 9.317

120 0.294 8 11.71

135 0.174 9 U.34

150 0.081 10 17.20

165 0.023 11 20.27

180 0.002 12 23.57

24

X

J(x) J(x) J(-x) X J(x) J(x) J(-x)

0.000

0.025

0.050

0.075

1.000

1.000

1.004

1.010

1.107

1.119

1.140

0.075

0.107

0.098

0.088

0.077

0.500

0.525

0.550

0.575

1.631

1.666

1.686

1.687

1.4^7

1.366

1.257

1.151

0.007

0.003

0.000

-0.002

0.100

0.125

0.150

0.175

1.020

1.033

1.049

1.069

1.228

1.303

1.400

1.507

0.064

0.049

0.032

0.015

0.600

0.625

0.650

0.675

1.664

1.613

1.529

1.409

1.037

0.917

0.790

0.659

-0.003

-0.004

-0.004

-0.003

0.200

0.225

0.250

0.275

1.091

1.118

1.148

1.181

I.6O4

1.686

1.752

1.800

0.000

-0.010

-0.017

-0.020

0.700

0.725

0.750

0.775

1.251

1.059

0.839

0.607

0.526

0.397

0.277

0.174

-0.002

-0.001

0.001

0.001

0.300

0.350

0.375

1.219

-1 . 262

l!308

1.359

1.829

1.837

1.825

1.793

-0.018

-0.012

-0.004. 0.005

0.800

0.850

0.875

0.386

0 203

0.080

0.020

0.093

0.040

0.013

0.002

0.001

0.001

0.000

0.000

0.400

0.425

0.450

0.475

1.414

1.472

1.530

1.584

1.74A

1.683

1.612

1.533

0.013

0.016

0.015

0.011

0.900

0.925

0.950

0.975

0.002

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

z = 13, E^ = 10.00 Mev

POINT PLANE POINT PLANE ISOTROPIC PERPENDICULAR

SOURCE SOURCE

J(x) J(x)

0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

0.200

0.225

0.250

0.275

0.300

0.325

0.350

0.375

0.400

0.425

0.450

0.475

1.000

0.999

1.001

1.003

1.008

l.OU

1.021

1.028

1.037

1.044

1.051

1.057

1.062

1.071

1.083

1.099

1.122

1.153

1.191

1.238

1.023

1.027

1.034

1.044

1.061

1.085

1.120

1.164

1.211

1.256

1.300

1.342

1.382

i.as

1.451

1.480

1.503

1.519

1.528

1.528

J(-x)

0.023

0.020

0.016

0.013

0.010

0.008

0.006

0.004

0.003

0.002

0.002

0.001

0.000

-0.000

-0.001

-0.001

-0.002

-0.002

-0.002

-0.001

0.500

0.525

0.550

0.575

0.600

0.625

0.650

0.675

0.700

0.725

0.750

0.775

0.800

0.825

0.850

0.875

0.900

0.925

0.950

0.975

ISOTROPIC

SOURCE

J(x)

1.290

1.3a

1.390

1.432

1.465

1.485

1.486

1.462

1.408

1.316

1.181

0.999

0.778

0.533

0.298

0.119

0.027

0.002

0.000

0.000

PERPENDICULAR

SOURCE

J(x) J(-x)

1.517 -0.001

1.492 0.000

1.453 0.001

1.397 0.002

1.324 0.003

1.232 0.003

1.122 0.003

0.999 0.001

0.865 -0.001

0.724 -0.003

0.580 -0.003

0.437 -0.002

0.300 -0.001

0.179 0.001

0.086 0.001

0.028 0.001

0.005 0.000

0.000 0.000

0.000 0.000

0.000 0.000
Table 1. Energy Dissipation Function, J(x) , and Input Data - Continued

COPPER

STOPPING POWER

(dE/dr)„ =6.91 MevCcmVg)

RESIDUAL RANGE

=0.00210 g/cm2

OTHER PARAMETERS = 3.826 A^ = 0.64-65 a = -4.7A5 A^ = 0.8729

A^^ 3.023 A^ = -0.94.36 A^^^= 3.431 A, = 0.j!aA2

SCATTERING COEFFICIENTS

e

' R ^

15° 1.013 1 4.847

30 1.035 2 11.32

45 1.055 3 18.48

60 1.066 4 25.84

75 1.070 5 33.12

90 1.066 6 40.U

105 1.059 7 46.80

120 1.050 8 53.03

135 1.041 9 59.51

150 1.034 10 65.07

165 1.030 11 71.36

180 1.028 12 76.81

Z = 29, Eq = 0.025 Mev

rUirJi PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x) J(x) J(-x)

0.000 1.000

0.025 1.069 3.430 1.792

0.050 1.250 3.678 1.504

0.075 1.519 x.<i?4

0.100 1.849 3.94ii 1,U4<

0.125 2.211 3.951 0.869

0.150 2.575 3.883 0.730

0.175 2.916 3. '49 n Aon

0.200 3.218 a cAA n con 0.225 o / cn 0.250 3.697 3.124 0.375

0.275 3.823 2.882 0.304

0.300 3.997 2.631 0.238

0.325 4.060 2.374 0.179

0.350 4.056 2.114 0.129

0.375 3.979 1.856 0.088

0.400 3.828 1.605 0.057

0.425 3.603 1.365 0.036

0.450 3.313 1.139 0.022

0.475 2.968 0.930 0.015

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) J(x)

0.500 2.585 0. '41 u .Uil

0.525 2.183 0.575 0.009

0.550 1.782 0.432 0.007

0.575 1.402 0.313 0.006

0.600 1.058 0.217 0.004

0.625 0.760 0.142 0.002

0.650 0.514 0.087 0.001

0.675 0.323 0.049 0.000

0.700 0.184 0.025 -0.000

0.725 0.093 0.011 -0.000

0.750 0.040 0.004 -0.000

0.775 0.014 0.001 -0.000

0.800 0.003 0.000 -0.000

0.825 0.001 0.000 -0.000

0.850 0.000 0.000 -0.000

0.875 0.000 0.000 -0.000

0.900 0.000 0.000 -0.000

0.925 0.000 0.000 -0.000

0.950 0.000 0.000 -0.000

0.975 0.000 0.000 -0.000

STOPPING POWER

(dE/dr)EQ = -^-^^ Mev(cmVg)

RESIDUAL RANGE = 0.00689 g/cm^

OTHER PARA11ETERS \

= 4.779 Al = 0.5326

a = -22.11 ^2 = 1.589

aPti= 3.628 A3 = -1.011

APr'P= 4.130 \

= -0.1106

SCATTERING COEFFICIENTS

0 0/0^ I s^

15° 1.026 1 5.006

30 1.054 2 12.32

45 1.072 3 21.37

60 1.076 4 31.28

75 1.067 5 41.80

90 1.047 6 52.64

105 1.022 7 63.61

120 0.995 8 74.57

135 0.970 9 85.41

150 0.950 10 96.03

165 0.937 11 106.4

180 0,932 12 116.5

1 = 29, E^ := 0.05 Mev

POINT

ISOTROPIC

SOURCE

PLANE PERPENDICULAR

SOURCE

X

J(x) J(x) J(-x)

0.000

0.025

0.050

0.075

1.000

1.108

1.344

1.676

3.230

3.657

3.971

4.171

2.230

1.815

1.469

1.190

0.100

0.125

0.150

0.175

2.067

2.483

2.895

3.278

4.262

4.249

4.144

3.972

0.974

0.811

0.688

0.590

0.200

0.225

0.250

0.275

3.617

3.901

4.123

4.271

3.743

3.476

3.183

2.875

0.502

0.415

0.329

0.249

0.300

0.325

0.350

0.375

4.335

4.310

4.192

3.986

2.560

2,247

1.943

1.653

0.180

0.124

0.081

0.052

0.400

0.425

0.450

0.475

3.700

3.346

2.946

2.518

1.381

1.131

0.905

0.705

0.033

0.022

0.015

0.011

POINT PLANE ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x) J(x) J(-x)

0.500 2.085 0.534 0.009

0.525 1.668 0.391 0.007

0.550 1.283 0.274 0.005

0.575 0.944 0.184 0.003

0.600 0.658 0.116 0.001

0.625 0.430 0.069 0.000

0.650 0.259 0.037 -0.000

0.675 0.141 0.018 -0.000

0.700 0.067 0.008 -0.000

0.725 0.027 0.003 -0.000

0.750 0.009 0.001 -0.000

0.775 0.002 0.000 -0.000

0.800 0.000 0.000 -0.000

0.825 0.000 0.000 -0.000

0.850 0.000 0.000 -0.000

0.875 0.000 0.000 -0.000

0.900 0.000 0.000 -0.000

0.925 0.000 0.000 -0.000

0.950 0.000 0.000 -0.000

0.975 0.000 0.000 -0.000

25
1

Table 1, Energy Diifipation Function, J(x), and Input Data - Continued

COPPER

STOPPING POWER

(dE/dr)E = 2.72 MevCeoVg)

0 RESIDUAL RANGE

To = 0.0221 g/ov?

OTHER PARAMETERS

dj^ = 4.971 Ai = 0.6U6

a = -45.31 Ag = 1.054

A^'^^s 3.808 Aj = -1.240

aPLP= 4.342 A/ = 0.5a2

SCATTERING COEFFICIENTS

e i

15" 1.038 1 5.083

30 1.070 2 13.01

45 1.082 3 22.86

60 1.073 4 34.12

75 1.045 5 46.

U

90 1.003 6 59.56

105 0.952 7 73.27

120 0.900 8 87.40

135 0.852 9 101.8

150 0.813 10 116.4

165 0.789 11 131.1

180 0.780 12 145.. 8

Z = 29, Eg = 0.10 Mev

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) U \ Ay J( -x)

?< . ?n<cxx 0.025 1.079 3.596 1.812

0.050 1.279 3.870 1.479

0.075 1.572 1 91 n

n 1 nn u . xuu X • 7<cO 1 1 m

0.125 2.310 4.071 0.834

0.150 2.700 3.963 0.706

0.175 3.074 1 705

u .cUU "X tine 0.225 3.712

0.250 3.952 3.056 0.323

0.275 4.123 2.771 0.245

0.300 4.214 2.480 0.178

0.325 4.218 2.189 0.124

0.350 4.132 1.903 0.083

0.375 3.957 1.627 0.053

0.400 3.698 1.366 0.034

0.425 3.368 1.122 0.021

0.450 2.983 0.899 0.013

0.475 2.561 0.701 0.010

POINT PLANE

ISOTROPIC PERPENDICULAR SOURCE SOURCE

X

J(x) J(-x)

ft 'jftn 9 1 9A 0.529 0.007

0.525 1.700 0.385 0.005

0.550 1.302 0.268 0.004

0.575 0.950 0.177 0.002

U.DUU U.054 0.110 0.001

0.625 0.420 0.064 0.000

0.650 0.247 C.034 -0.000

0.675 0.130 0.016 -0.000

U» f uu U.UDU 0.006 -0.000

0.725 0.023 0.002 -0.000

0.750 0.007 0.001 -0.000

0.775 0.002 0.000 -0.000

0.800 0,000 0.000 -0.000

0.825 0.000 0.000 -0.000

0.850 0.000 O.OCO -0.000

0.875 0.000 0.000 -0.000

0.900 0.000 0.006 -0.000

0.925 0.000 0.000 -0.000

0.950 0.000 0.000 -0.000

0.975 0.000 0.000 -0.000

Z = 29, E = 0.20 Mev

STOPPING POWER

(dE/dr)g =1.89 Mev(omVg)

RESIDUAL RANGE

= 0,0678 g/cm^

OTHER PARAMETERS = 5.125 a = 39.73

A^^s 3.901

A^^= 4.452

Ao

= 0.6033

= 1.008 = -1.143 = 0.5313

SCATTERING COEFFICIENTS

0 POINT ISOTROPIC

SOURCE

PLANE PERPENDICULAR

SOURCE

X

0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

J(x) J(x) J(-x)

1.000

1.070

1.253

1.520

1.845

2.201

2.564

2.913

3.081

3.470

3.737

3.886

3.928

3.880

3.760

3.591

2.081

1.674

1.345

1.090

0.898

0.755

0.643

0.547

0.500

0.525

0.550

0.575

0.600

0.625

0.650

0.675

POINT PLANE ISOTROPIC PERPENDICULAR

SOUHCE SOURCE

J(x) J(x) J(-x)

1.974

1.571

1.196

0.865

0.589

0.372

0.215

0.111

0.485

0.351

0.243

0.159

0.098

0.055

0.028

0.013

0.006

0.005

0.004

0.002

0.001

0.000

-0.000

-0.000

e a/a

' R

i H

0.200 3.234 3.384 0.456 0.700 0.050 0.005 -0.000

0.225 3.513 3.150 0.371 0.725 0.018 0.002 -0.000

15« 1.050 1 4.999 0.250 3.737 2.895 0.291 0.750 0.005 0.000 -0.000

30 1.082 2 13.19 0.275 3.895 2.624 0.219 0.775 0.001 0.000 -0.000

45 1.085 3 23.66

60 1.057 4 35.94 0.300 3.977 2.3a 0.158 0.800 0.000 0.000 -0.000

75 1.004 5 49.69 0.325 3.976 2.063 0.107 0.825 0.000 0.000 -0.000

90 0.931 6 64.66 0.350 3.889 1.787 0.069 0.850 0.000 0.000 -0.000

105 0.848 7 80.66 0.375 3.718 1.521 0.041 0.875 0.000 0.000 -0.000

120 0.763 8 97.52

135 0.687 9 115.08 0.400 3.469 1.271 0.024 0.900 0.000 0.000 -0.000

150 0.626 10 133.24 0.425 3.153 1.040 0.014 0.925 0.000 0.000 -0.000

165 0.587 11 151.89 0.450 2.785 0.830 0.010 0.950 0.000 0.000 -0.000

180

26

0.573 12 170.98 0.475 2.385 0.645 0.007 0.975 0.000 0.000 -0.000
Table 1. Energy

STOPPING POWER

(dE/dr)2Q = l'^'^ Mev(cnVg)

RESiroAL RANCffi Tq = 0.191 g/cm^

OTHER PARAMETERS

di = 5.159 Ai = 0.5130 a = 11.06 Aj = 1.003

a'^^s 3.857 A3 = -0.8755

A^= 4.406 A^ = 0.3598

SCATTERING COEFFICIENTS

e i H

1.059 1 4.732

30 1.089 2 12.80

U5 1.080 3 23.38

60 1.032 4 36.03

75 0.952 5 50.45

90 0.847 6 66.42

105 0.729 7 83.74

120 0.611 8 102.3

135 0.505 9 121.9

150 0.420 10 U2.4

165 0.366 11 163.8

180 0.348 12 185.9

STOPPING POWER

(dE/dr)^ =1.33 Mev(cinVg) RSSIDDAL RANGE = 0.409 g/cm'

OTHER PARAMETERS

dl = 5.172 Al = 0.4427 a s 5.029 A2 = 0.9364

3.717 h = -0.6005

aPI-p^ 4.249 A4 = 0.2214

SCATTERING COEFFICIENTS

e a/a i S^

15" 1.064 1 4.3U

30 1.091 2 11.86

45 1.074 3 21.91

60 1.013 4 34.08

75 0.9U 5 48.11

90 0.788 6 63.81

105 0.648 7 81.02

120 0.508 8 99.59

135 0.382 9 119.4

150 0.282 10 U0.4

165 0.218 11 162.4

180 0.196 12. 185.4

isaipation Function, J(x),and Input

COPPER

Z = 29, Eg = 0.40 Mev

POINT PLANE

ISOTROPIC PERPENDICULiUl

SOURCE SOURCE X

J(x) J(-x)

0.000

0.025

0.050

0.075

1.000

1.059

1.214

1.442

2.806

3.161

3.416

3.571

1.806

1.441

1.148

0.9a

0.100

0.125

0.150

0.175

1.721

2.027

2.341

2.644

3.633

3.608

3.507

3.345

0.753

0.631

0.539

0.459

0.200

0.225

0.250

0.275

2.924

3.168

3.364

3.502

3.138

2.902

2.652

2.396

0.382

0.304

0.232

0.171

0.300

0.325

0.350

0.375

3.573

3.570

3.492

3.339

2.U0

1.886

1.638

1.400

0.121

0.083

0.055

0.035

0.400

0.425

0.450

0.475

3.117

2.837

2.511

2.156

1.173

0.962

0.769

0.597

0.021

0.013

0.008

0.005

Z = 29, Eg = 0.70 Mev

POINT PLANE

ISOTROPIC PEaiPEKDICULAR

SOURCE SOURCE

X

0.000

0.025

0.050

0.075

J(x)

1.000

1.045

1.166

1.348

J(x)

2.523

2.846

3.086

3.242

J(-x)

1.523

1.194

0.932

0.735

0.100

0.125

0.150

0.175

1.574

1.829

2.094

2.356

3.315

3.310

3.232

3.092

0.595

0.500

0.431

0.372

0.200

0.225

0.250

0.275

2.599

2.810

2.980

3.100

2.906

2.690

2.462

2.231

0.310

0.246

0.185

0.135

0.300

0.325

0.350

0.375

3.165

3.170

3.1U

2.995

1.999

1.769

1.5U

1.326

0.094

0.064

0.041

0.025

0.400

0.425

0.450

0.475

2.817

2.585

2.309

2.002

1.118

0.9E3

0.7U

0.583

0.015

0.009

0.006

0.004

Data - Continued

POINT ISOTROPIC

SOURCE

PLAf!E PERPENDICULAR

SOURCE

X

J(x) J(x) J(-x)

0.500

0.525

0.550

0.575

1.789

1.430

1.093

0.794

0.449

0.324

0.224

0.147

0.004

0.003

0.002

0,002

0.600

0.625

0.650

0.675

0.542

0.344- 0.199

0.102

0.090

0.051

0,027

0,012

0,001

0,000

-0,000

-0,000

0.700

0.725

0.750

0.775

0.046

0.017

0.005

0.001

0.005

0 on? 0.000

0.000

-0,000

-0 000

-0.000

-0.000

0.800

0.825

0.850

0.875

0.000

0.000

0.000

0.000

0.000

0.000

0,000

0,000

-0.000

-0.000

-0.000

-0.000

0.900

0.925

0.000

0,000

8:888

0,000

0,000

0.000

0.000

-0.000

-0.000

-0.000

-0.000

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE X

J(x) J(x) J(-x)

0.500 1.679 0.442 0.003

0.525 1.356 0.323 0.002

0.550 1.048 0.226 0.002

0.575 0.771 0.150 0.001

0.600 0.534 0.094 0.001

0.625 0.345 0.054 0.000

0,650 0.204 0.029 -0.000

0,675 0.108 0.013 -0.000

0,700 0.050 0.005 -0.000

0,725 0.020 0.002 -0.000

0.750 0.006 0.000 -0.000

0,775 0.001 0.000 -0.000

0.800 0.000 0.000 -0.000

0.825 0.000 0.000 -0.000

0.850 0.000 0.000 -0.000

0.875 0.000 0.000 -0.000

0.900 0.000 0,000 -0.000

0.925 0.000 0.000 -0.000

0,950 0.000 0.000 -0.000

0,975 0.000 0.000 -0.000

27
Table 1. Energy Dissipation Function, J(x), and Input Data - Continued

COPPER

Z = 29, = 1.00 Mev

STOPPING POWER

(dE/dr)^, = 1.29 Mev(craVg)

o RESIDUAL RANGE

= 0.639 g/cm^

OTHER PARAlffiTERS d^ = 5.207 A^ = 0.4033

a = 3.091 A^ = 0.8887

aPTI= 3.576

.PLP

A^ = -0.4454

= 4.087 A^ = 0.1534

SCATTERING COEFFICIENTS

e o/a

' R

I

15° 1.066 1 3.934

30 1.092 2 10.91

45 1.072 3 20.26

60 1.004 4 31.68

75 0.896 5 44.92

90 0.761 6 59.83

105 0.610 7 76.25

120 0.460 8 94.07

135 0.325 9 113.2

150 0.218 10 133.5

165 0.150 11 155.0

180 0.126 12 177.5

0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

0.200

0.225

0.250

0.275

0.300

0.325

0.350

0.375

0.400

0.425

0.450

0.475

POINT

ISOTROPIC

SOURCE

PLANE PERPENDICULAR

SOURCE

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

J(x) J(x) J(-x) X J(x) J(x) J(-x)

1.000

1.036

1.134

1.284

2.320

2.617

2.845

3.003

1.320

1.021

0.783

0.607

0.500

0.525

0.550

0.575

1.638

1.339

1.050

0.784

0.456

0.337

0.239

0.162

0.003

0.002

0.002

0.001

1.473

1.688

1.917

2.146

3.089

3.104

3.051

2.936

0.486

0.409

0.356

0.313

0.600

0.625

0.650

0.675

0.552

0.363

0.219

0.119

0.103

0.061

0.033

0.016

0.001

0.000

-0.000

-0.000

2.363

2.556

2.716

2.834

2.772

2.576

2.366

2.152

0.264

0.209

0.156

0.112

0.700

0.725

0.750

0.775

0.056

0.022

0.007

0.002

0.006

0.002

0.001

0.000

-0.000

-0.000

-0.000

-0.000

2.904

2.922

2.884

2.792

1.937

1.723

1.512

1.307

0.077

0.051

0.032

0.019

0.800

0.825

0.850

0.875

C.OOO 0.000

0.000

0.000

0.000

0.000

0.000

0.000

-0.000

-0.000

-0.000

-0.000-

2.644

2.446

2.206

1.932

1.109

0.923

0.750

0.594

0.011

0.006

0.004

0.003

0.900

0.925

0.950

0.975

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

-0.000

-0.000

-0.000

-0.000

29, = 2.00 Mev

STOPPING PO'.ffiR (dE/dr)„ = 1.30 Mev (om2/g)

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

POINT PLANE ISOTROPIC PERPENDICULAR

SOURCE SOURCE

RESIDUAL RANGE

r„ = 1.42 g/cm2

OTHER PARAMETERS

^1 = 5.304 0.3259

a = 1.297 ^2 = 0.9372

A^I= 3.153 S

= -0.4319

/LP^

3.602 \

= 0.1688

SCATTERING COEFFICIENTS

e a/a I Si

15* 1.0^8 1 2.995

30 1.093 2 8.401

45 1.068 3 15.76

60 0.993 4 24.84

75 0.876 5 35.49

90 0.729 6 47.59

105 0.566 7 61.05

120 0.405 8 75.77

135 0.259 9 91.69

150 0.U5 10 108.7

165 0.071 11 126.9

180 0.046 12 146.0

28

X

0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

0.200

0.225

0.250

0.275

0.300

0.325

0.350

0.375

0.400

0.425

0.450

0.475

J(x)

1.000

1.019

1.075

1.163

1.279

i.a6

1.569

1.731

1.894

2.051

2.195

2.317

2.411

2.469

2.486

2.457

2.382

2.259

2.093

1.890

J(x)

1.904

2.153

2.357

2.512

2.618

2.674

2.681

2.639

2.550

2.423

2.268

2.098

1.919

1.746

1.551

1.365

1.184

1.008

0.843

0.688

J(-x)

0.904

0.659

0.471

0.345

0.273

0.240

0.222

0.205

0.179

0.144

0.104

0.069

0.043

0.024

0.013

0.007

0.003

0.003

0.003

0.003

X

0.500

0.525

0.550

0.575

0.600

0.625

0.650

0.67:

0.700

0.725

0.750

0.775

0.800

0.825

0.850

0.875

0.900

0.925

0.950

0.975

J(x)

1.658

1.408

1.151

0.900

0.668

0.465

0.300

0.175

0.091

0.040

0.015

0.004

0.001

0.000

0.000

0.000

0.000

0.000

0.000

0.000

J(x)

0.547

0.421

0.312

0.221

0.148

0.093

0.054

0.028

0.012

0.005

0.001

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

J(-x)

0.003

0.002

0.002

0.001

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000
Table 1. Energy Dissipation Fimction, J{x), and Input Data - Continued

STOPPING POVffiR (dE/dr)^ = 1.36 Mev(cm2/g)

RESIDUAL RATJGE r = 2.92 g/cm^ OTHER PARAMETERS

d-,^ = 5.567 A;l =

a = 0.564.5 A^ =

A^'^^= 2.596

aPLPz^ 2.965 A, =

0.2836

0.8990

-0.3550

0.1724.

SCATTERING COEFFICIENTS

e I

15° 1.068 1 2.008

30 1.093 2 5.680

U5 1.066 3 10.74

60 0.988 4 17.04

75 0.868 5 24.50

90 0.716 6 33.03

105 0.549 7 42.59

120 0.383 8 53.12

135 0.234 9 64.58

150 0.116 10 76.93

165 0.040 11 90.13

180 o.ou 12 104.2

COPPER

Z = 29, Eo = 4.00 Kev

POINT PLANE ISOTROPIC PERPENDICULAR

SOURCE SOURCE X

0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

0.200

0.225

0.250

0.275

0.300

0.325

0.350

0.375

0.400

0.425

0.450

0.475

J(x)

1.000

1.007

1.032

1.074

1.130

1.201

1.284

1.378

1.481

1.590

1.704

1.815

1.920

2.011

2.081

2.124

2.133

2.106

2.039

1.933

J(x)

1.407

1.546

1.732

1.947

2.151

2.296

2.357

2.358

2.321

2.258

2.173

2.072

1.958

1.831

1.693

1.546

1.393

1.236

1.077

0.919

J(-x)

0.407

0.313

0.259

0.233

0.215

0.181

0.129

0.0S3

0.056

0.041

0.033

0.026

0,021

0.016

0.012

0.009

0.006

0.004

C.002

0.001

X

0.500

0.525

0.550

0.575

0.600

0.625

0.650

0.675

0.700

0.725

0.750

0.775

0.800

0.825

0.850

0.875

0.900

0.925

0.950

0.975

POINT ISOTROPIC SOURCE

J(x)

1.787

1.607

1.399

1.172

0.938

0.711

0.505

0.330

0.195

0.102

0.045

0.016

0.004

0.001

0.000

0.000

0.000

0.000

0.000

0.000

PLANE PERPENDICULAR

SOURCE

J(x)

0.767

0.623

0.489

0.370

0.268

0.183

0.117

0.069

0.036

0.017

0.006

0.002

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

J(-x)

0.001

0.000

-0.000

-0.000

-0.000

-0.000

-0.000

0.000

0.000

0.000

0.000

O.OOC

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

Z = 29, Eq = 10.00 Mev

STOPPING POWER

(dE/dr)g = 1.45 Mev(cm2/g)

RESIDUAL RANGE

= 7.17 g/cm^ OTHER PARAMETERS

d, = 6.060

POINT PLANE ISOTROPIC PERPENDICULAR

SOURCE SOURCE

POINT PLANE ISOTROPIC PERPENDICULAR

SOURCE SOURCE

a = 0.2020 A^ = A^^= 2.348 A3 =

A^^^= 2.043 ^4 =

0.2252

1.082

-0.7722

0.4649

SCATTERING COEFFICIENTS

e °\ -t H

15" 1.069 1 1.018

30 1.094 2 2.903

45 1.066 3 5.530

60 0.987 4 8.839

75 0.865 5 12.79

90 0.712 6 17.35

105 0.543 7 22.48

120 0.375 8 28.18

135 0.224 9 34.42

150 0.105 10 a.18

165 0.029 11 48.45

180 0.003 12 56.21

X

0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

0.200

0.225

0.250

0.275

0.300

0.325

0.350

0.375

0.400

0.425

0.450

0.475

J(x)

1.000

1.000

1.006

1.017

1.033

1.055

1.082

1.115

1.153

1.197

1.247

1.302

1.362

1.426

1.494

1.563

1.631

1.694

1.746

1.781

J(x)

1.160

1.209

1.267

1.336

1.420

1.519

1.625

1.723

1.803

1.864

1.903

1.920

1.9U

1.884

1.832

1.761

1.673

1.574

1.464

1.346

J(-x)

0.160

0.113

0.074

0.043

0.024

0.017

0.016

0.019

0.020

0.020

0.019

0.016

0.012

0.007

0.003

-0.001

-0.002

-0.002

-0.002

-0.001

X

0.500

0.525

0.550

0.575

0.600

0.625

0.650

0.675

0.700

0.725

0.750

0.775

0.800

0.825

0.850

0.875

0.900

0.925

0.950

0.975

J(x) J(x)

1.792

1.771

1.712

1.612

1.468

1.284

1.068

0.835

0.606

0.401

0.238

0.123

0.053

0.017

0.003

0.000

0.000

0.000

0.000

0.000

1.219

1.086

0.947

0.805

0.663

0.525

0.395

0.280

0.182

0.107

0.055

0.024

0.008

0.002

0.000

0.000

0.000

O.COO

0.000

0.000

J(-x)

0.000

0.001

0.001

0.001

0.001

0.001

0.000

0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

29
Table 1. Energy Dissipation Function, J(x), and Input Data - Continued

STOPPING POWER

(dE/dr)-, =3.55 Mev(cm2/K)

0 RESIDUAL RANGE = 0.008^0 p/cra^

OTHER PARAMETERS = 6.467 A^ = 0.5778

a = -6.385 A^ = 1.618

A^'^'^ 5.218 Aj = -2.491

A^^P= 5.913 A, = 1.295

SCATTERING COEFFICIENTS

6 cr /a

' R

I Si

15« 1.018 1 7.668

30 1.060 2 17.62

45 1.120 3 28.50

60 1.173 4 39.62

75 1.207 5 50.62

90 1.225 6 61.24

105 1.230 7 71.34

120 1.229 8 80.84

135 1.229 9 89.70

150 1.221 10 97.90

165 1.219 11 105.4

180 1.219 12 112.3

TIN

Z = 50, Eg = 0.05 Mev

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x) J(x) J(-x)

0.000 1.000 3.995 2.995

0.025 1.167 4.491 2.424

0.050 1.572 4.702 2.003

0.075 2.096 UJOU 1.686

0.100 2.661 4.571 1.427

0.125 3.221 4.354 1.197

0.150 3.744 4.080 0.988

0.175 4.195 3.763 0.800

0.200 4.547 3.415 0.634

0.225 4.779 3.049 0.490

0.250 4.879 d,,bi / 0.309

0.275 4.842 2.310 0.270

0,300 4.00 1.957 0.191

0.325 4.389 1.625 0.132

0.350 4.004 1.321 0.088

0.375 3.545 1.050 0.058

0.400 3.041 0.813 0.037

0.425 2.522 0.611 0.023

0.450 2.017 0.U5 0.014

0.475 1.550 0.312 0.009

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) J(-x)

0.500 1.140 n 9nQ nU,UU9 nn? 0.525 0.798 0,134

n nno U .UUj

0,081 0.001

0.046 0.000

0.600 0.189 0.024 0.000

0.625 0.099 0.011 -0.000

n ny7 0.005 -0.000

0 67'? n ni Q 0,002 -0.000

0.700 0.007 0,001 -0,000

0.725 0.002 0.000 -0,000

\J • f ?u u .uuu 0.000 -0,000

n nnn 0.000 -0.000

0.800 0,000 0.000 -0.000

0.825 0.000 0.000 -0,000

0.850 0.000 0.000 -0,000

0.875 0.000 0.000 -0,000

0.900 0.000 0.000 -0,000

0.925 0.000 0.000 -0.000

0.950 0.000 0,000 -0.000

0.975 0.000 0,000 -0.000

STOPPING POm

(dE/dr)^ = 2,29 Mev(cin2/g)

RESIDUAL RAIIGE = 0.0265 g/cm^

OTHER PARAMETERS

^1 = 7.442 ^1 = 0.6132 a = -10,76 ^2 = 1.161

aPti= 6.029 ^3 = -1.549

aPlp^ 6.865 h

= 0.7748

SCATTERING COEFFICIENTS

e a /a

' R

I H

15* 1,115 1 8,205

30 1.223 2 20,01

45 1.284 3 33.87

60 1.277 4 49.01

75 1.197 5 64.94

90 1.055 6 81.33

105 0,869 7 97.89

120 0.664 8 1U.4

135 0,467 9 130.8

150 0.305 10 146.9

165 0.198 11 162.6

180 0.161 12 177.8

Z = 50, Eq = 0.10 Mev

POINT PLANE ISOTROPIC PERPENDICULAR

SOURCE SOURCE X J(x) J(x) J(-x)

0.000 1.000 4,087 3.087

0.025 1.173 4.593 2.539

0.050 1.603 4.879 2.075

0.075 2.180 4.895 1.711

0.100 2.815 4.691 1.430

0.125 3.436 4.379 1.194

0.150 3.992 4.035 0.981

0.175 4,446 3.672 0.786

0.200 4.771 3.295 0.612

0.225 4.951 2,908 0.462

0.250 4.980 2,520 0.337

0.275 4.861 2.U0 0.236

0.300 4.607 1,779 0.161

0.325 4.239 1.U4 0,106

0.350 3.782 1.144 1,069

0,375 3.269 0.882 0,045

0.400 2,730 0.660 0,029

0.425 2,196 0.479 0,018

0.450 1.696 0.334 0.011

0.475 1.251 0.224 0.006

POINT PLANE ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) J(x) J(-x)

0.500 0,877 0.143 0.003

0.525 0.579 0.086 0.001

0.550 0.357 0.049 0.000

0.575 0,203 0.025 0.000

0.600 0,105 0.012 -0.000

0.625 0,049 0.005 -0.000

0.650 0,019 0.002 -0.000

0.675 0,007 0.001 -0.000

0.700 0.002 0.000 -0.000

0.725 0,000 0.000 -0.000

0.750 0,000 0.000 -0.000

0.775 0.000 0.000 -0.000

0.800 0,000 0.000 -0.000

0.825 0.000 0.000 -0.000

0.850 0.000 0.000 -0.000

0.875 0.000 0.000 -0.000

0.900 0.000 0.000 -0.000

0.925 0.000 0.000 -0.000

0,950 0.000 0.000 -0.000

0,975 0.000 0.000 -0.000

30
Table 1. Energy Disfipation Function, J(x), and Input Data - Continued

TIN

Z = 50, Eg = 0.20 Mev

STOPPING POWER

(dE/dr)^ =1.60 Mev(cmVg)

RESIDUAL RANGE

r = 0.0805 g/om^

0 OTHER PARAMETERS

dl = 8.129 A^ = 0.5730

a = -35.95 Ag = 1.083

aPti= 6.512 A^ = -1.237

A^= 7.438 A = 0.5813

SCATTERING COEFFICIENTS

e oh^R

I

15» 1.072 1 8.362

30 1.161 2 21.30

45 1.232 3 37.15

60 1.262 4 55.19

75 1.246 5 74.88

90 1.188 6 95.87

105 1.101 7 117.8

120 0.999 8 140.5

135 0.899 9 163.8

150 0.815 10 187.4

165 0.760 11 211.2

180 0.741 12 235.3

STOPPING POWER

(dE/dr)^ =1.27 Mev(cin2/g)

RESIDUAL RANGE

r- = 0.225 g/om

OTHER PARAKETERS

= 8.547 a = 16.16

aPTI= 6.636

A^P= 7.582

Al =

A2 =

^3 =

A, =

0.4939

1.031

-0.8945

0.3696

SCATTERING COEFFICIENTS

e ^ h

15' 1.096 1 8.049

30 1.197 2 21.18

45 1.264 3 37.77

60 1.276 4 57.15

75 1.227 5 78.83

90 1.126 6 102.5

105 0.988 7 127.8

120 0.832 8 154.5

135 0.682 9 182.4

150 0.557 10 211.4

165 0.475 11 2a.

2

180 0.446 12 271.9

POINT

ISOTROPIC SOURCE

PLANE PERPENDICULAR

SOURCfi

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) X J(x) J(x) J(-x)

0.000

0.025

0.050

0.075

1.000

1.180

1.617

2.192

4.076

4.637

4.791

4.704

3.076

2.401

1.948

1.616

0.500

0.525

0.500

0.575

0.694

o.ui

0.261

0.U2

O.lOfi 0.061

0.033

0.016

0.001

0.001

0.001

0.000

0.100

0.125

0.150

0.175

2.812

3.408

3.932

4.351

4.491

4.204

3.869

3.499

1.342

1.101

0.888

0.702

0.600

0.625

0.650

0.675

0.070

0.030

0.011

0.004

0.007

0.003

0.001

0.000

0.000

0.000

0.000

0.000

0.200

0.225

0.250

0.275

4.641

4.786

4.780

4.628

3.111

2.715

2.326

1.952

0.542

0.409

0.299

0.211

0.700

0.725

0.750

0.775

0.001

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.300

0.325

0.350

0.375

4.343

3.949

3.474

2.952

1.602

1.287

1.002

0.759

o.iu

0.094

0.058

0.034

0.800

0.825

0.850

0.875

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.400

0.425

0.450

0.475

2.417

1.900

1.430

1.024

0.557

0.394

0.267

0.173

0.019

0.010

0.005

0.002

0.900

0.925

0.950

0.975

0.000

0.000

©.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

Z = 50, Eo = 0.40 Mev

POINT

ISOTROPIC

SOURCE

PLANE PERPENDICULAR

SOURCE

POINT ISOTROPIC

SOURCE

POINT PERPENDICULAR

SOURCE

X

J(x) J(x) J(-x) X

J(x) J(x) J(-x)

0.000

0 02"; 0.050

0.075

1.000

1.156

1.543

2.058

3.724

4.264

4.447

4.395

2.724

2.104

1.693

1.402

0.500

0.525

0.550

0.575

0.596

0.374

0.218

0.117

0.091

0.052

0.027

0.013

0.001

0.001

0.000

0.000

0.100

0.150

0.175

2.620

3.633

4.000

4.200

3.920

3.590

3.228

1.168

0.961

0.773

0.604

0.600

0.625

0.650

0.675

0.056

0.024

0.009

0,003

0.006

0.002

0.001

0.000

-0.000

-0.000

-0.000

-0.000

0.200

0.225

0.250

0.275

4.2a

4.347

4.318

4.162

2.852

2.745

2.108

1.760

0.459

0.337

0.240

0.164

0.700

0.725

0.750

0.775

0.001

0.000

0.000

0.000

0.000

0.000

0.000

0.000

-0.000

-0.000

-0.000

-0.000

0.300

0.325

0.350

0.375

3.893

3.530

3.098

2.625

1.439

1.150

0.896

0.678'

0.109

0.070

0.044

0.027

0.800

0.825

0.850

0.875

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

-0.000

-0.000

-0.000

-0.000

0.400

0.425

0.450

0.475

2.141

1.675

1.252

0.889

0.496

0.349

0.235

0.151

0.016

0.009

0.005

0.003

0.900

0.925

0.950

0.975

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

-0.000

-0.000

-0.000

-0.000

508105 0-59-5 31
Table 1. Energy Dissipation Function, J(x), and Input Data - Continued

STOPPING PO'.JER (dE/dr)E = 1-16 Mev(cmVg)

RESIDUAL RANGE

= 0.475 g/cra^

OTHER PARAMETERS

^1 = 8.797 h

=

a = 5.083 ^2 = 0.9362

6.U8 = -0.5806

7.361 = 0.2150

SCATTERING COEFFICIENTS

e a/a

R

i

15° 1.109 1 7.351

30 1.216 2 19.72

A5 1.279 3 35.67

60 1.277 54.59

75 1.208 5 76.09

90 1.078 6 99.84

105 0.907 7 125.6

120 0.718 8 153.1

135 0.535 9 182.3

150 0.385 10 212.8

165 0.285 11 2U.7

180 0.251 12 277.6

TIN

Z = 50, Eq = 0.70 Mev

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x)

0.000 1.000 3.353 2.353

0.025 1.126 3.851 1.788

r\ AC r\ 0 .050 T / / / 1.4a4 i .410 0.075 1 .872 4.015 1.150

0.100 2.344 3.853 0.954

0.125 2.806 3.608 0.786

0.150 3.214 3.314 U.DJD

0.175 3.538 2.991 0.500

0.200 3.757 2.652 0.382

0.225 3.861 2.311 0.281

0.250 3.848 1.976 0.199

3. '24 1.658 0.135

U. JUL)

n cr\r\ 3.500 1.363 0.088

0.325 3.193 1.095 0.055

0.350 2.823 0.858 0.033

0.375 2.413 0.654 0.019

0.400 1.988 0.483 0.012

0.425 1.573 0.34^ 0.007

0.450 1.189 0.235 0.004

0.475 0.855 0.153 0.003

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

J(x) j(,x; J(, -x; 0.500 0.580 0.094 0.002

0.525 0.370 0.054 0.001

0.550 0.218 —U .UUU 0.575 0.118 0.014 -0.000

0.600 0.058 0.006 -0.000

0.625 0.025 0.002 -0.000

0.650 0.009 U.UUX —U.UUU

0.675 0.003 0.000 -0.000

0.700 0.001 0.000 -0.000

0.725 0.000 0.000 -0.000

0.750 0.000 0.000 -0.000

0.775 0.000 0.000 -0.000

0.800 0,000 0.000 -0.000

0.825 0.000 0.000 -0.000

0.850 0.000 0.000 -0.000

0.875 0.000 Q.OOO -0.000

0.900 0.000 0.000 -0.000

0.925 0.000 0.000 -0.000

0.950 0.000 0.000 -0.000

0.975 0.000 0.000 -0.000

STOPPING POWER

(dE/dr)_ =1.13 Mev(cmVg)

RESIDUAL RANGE = 0.738 p/cm^

OTHER PARAMETERS

^1 = 8.972 A^ = 0.3919

a 2.920 A2 = 0.8830

6.193 A3 = -0.4221 aPLP= 7.056 A^ = 0.U72

SCATTERING COEFFICIENTS

e I

Si

15° 1.115 1 6.684

30 1.223 2 18.11

45 1.284 3 32.99'

60 1.277 4 50.82

75 1.197 5 71.22

90 1.055 6 93.94

105 0.869 7 118.7

120 0.664 8 145.4

135 0.467 9 173.9

150 0.305 10 203.9

165 0.198 11 235.3

180 0.161 12 268.1

32

z = 50, E^ =: 1.00 Mev POINT PLANE

ISOTROPIC PERPEJIDICULAR SOURCE SOURCE

X J(x) J(x) J(-x)

0.000 1.000 3.031 2.031

0.025 1.103 3.418 1.619

0.050 1.367 3.673 1.273

0.075 1.729 3.765 1.003

0.100 2.135 3.689 0.806

0.125 2.539 3.479 0.661

0.150 2.905 3.186 0.540

0.175 3.204 2.863 0.427

0.200 3.417 2.538 0.325

0.225 3.531 2.221 0.239

0.250 3.543 1.916 0.169

0.275 3.454 1.625 0.116

0.300 3.273 1.353 0.076

0.325 3.013 1.102 0.048

0.350 2.691 0.875 0.029

0.375 2.326 0.675 0.018

0.400 1.942 0.504 0.010

0.425 1.558 0.362 0.006

0.450 1.197 0.250 0.004

0.475 0.876 0.165 0.002

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) J(x) J(-x)

0.500 0.606 0.103 0.001

0.525 0.394 0.060 0.000

0.550 0.238 0.033 0.000

0.575 0.132 0.016 -0.000

0.600 0.066 0.007 -0.000

0.625 0.029 0.003 -0.000

0.650 0.011 0.001 -0.000

0.675 0.004 0.000 -0.000

0.700 0.001 0.000 -0.000

0.725 0.000 0.000 -0.000

0.750 0.000 0.000 -0.000

0.775 0.000 0.000 -0.000

0.800 0.000 0.000 -0.000

0.825 0.000 0.000 -0.000

0.850 0.000 0.000 -0.000

0.875 0.000 0.000 -0.000

0.900 0.000 0.000 -0.000

0.925 0.000 0.000 -0.000

0.950 0.000 0.000 -0.000

0.975 0.000 0.000 -0.000
Table 1. Energy Dissipation Function, J(x),and Input Data - Continued

(dE/dr)^ = 1.16 t/ev(cmVg)

STOPPING POWER

RESIDUAL RAI:GE = 1.61 g/cm^

OTHER PARAI^ETERS

d-L = 9.229 =

a = 1.201 A^ = A^^= 5.3U A^ = A^= 6.068 A, =

TIN

Z = 50, Eq = 2.00 Mev

POINT PLANE ISOTROPIC PERPQIDICULAR

SOURCE SOURCE

POINT PLANE ISOTROPIC PERPENDICULAR

SOURCE SOURCE

0.3167

0.9157

-0.3981

0.1658

SCATTERING CCEFEICIENTS

0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

J(x)

1.000

1.055

1.209

1.^36

1.706

1.993

2.271

2.522

J(x)

2. A93

2.815

3.0^5

3.170

3. m

3.098

2.933

2.716

J(-x)

1.A93

1.155

0.876

0.661

0.510

0.U12

0.3^8

0.295

X

0.500

0.525

0.550

0.575

0.600

0.625

0.650

0.675

J(x)

0.775

0.5^0

0.352

0.212

0.117

0.058

C.025

0.0C9

J(x)

0.160

0.100

0.059

0.032

0.016

0.007

0.003

0.001

J(-x)

0.002

0.001

0.000

-0.000

-0.000

-0.000

-0.000

-0.000

e i

0.200 2.726 2.470 0.242 0.700 0.003 0.000 -0.000

0.225 2.872 2.211 0.186 0.725 0.001 0.000 -0.000

15° 1.121 1 5.036 0.250 2.950 1.948 0.132 0.750 0.000 0.000 -0.000

30 1.231 2 13. 8A 0.275 2.95^ 1.690 0.087 0.775 0.000 0.000 -0.000

A5 1.290 3 25.52

60 1.275 4. 39.72 0.300 2.884 1.4^2 0.052 0.800 0.000 0.000 -0.000

75 i.m 5 56.19 0.325 2.7-i3 1.209 0.029 0.825 0.000 0.000 -0.000

90 1.028 6 7^.73 0.350 2.539 0.99^ 0.015 0.850 0.000 0.000 -0.000

105 0.825 7 95.21 0.375 2.282 0.798 0.008 0.875 0.000 0.000 -0.000

120 0.602 8 117.5

135 0.390 9 lil.U O.AOO 1.988 0.624. 0.005 0.900 0.000 0.000 -0.000

150 0.2U 10 167.0 0.4.25 1.673 0.A72 0.004. 0.925 0.000 0.000 -0.000

165 0.098 11 19A.0 0.^50 1.355 0.345 0.004 0.950 0.000 0.000 -0.000

180 0.058 12 222.4. 0.^75 1.050 0.24.1 0.003 0.975 0.000 0.000 -0.000

50, E-, = 4.. 00 Mev

STOPPING PC'^

(dE/dr)g =1.23 Mev(cm2/g)

o RESIDUAL RANGE

2 Pq = 3.29 g/cm

OTHER PARAMETEHS

POINT PLAirE ISOTROPIC PKRPEJIDICULAR- SOURCE SOURCE

POINT PLANE

ISOTROPIC PERPEiroiCULAR

SOURCE SOURCE

d]^ = 9.905 a = 0.5076

A^'^^= 4.281

A^P= 4.558

^2 =

0.2757

0.8755 = -0.353^

A^ = 0.2022

SCATTERING COEFFICIENTS

9 i

15° 1.123 1 3.335

30 1.23U 2 9.263

U5 1.292 3 17. 2i

60 1.274 U 27.06

75 1.179 5 38.57

90 1.017 6 51.65

105 0.807 7 66.22

120 0.578 8 82.20

135 0.359 9 99.51

150 0.178 10 118.1

165 0.059 11 137.9

180 0.018 12 158.9

0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

0.200

0.225

0.250

0.275

0.300

0.325

0.350

0.375

0.4.00 0.^25

0.U50

O.A75

J(x)

1.000

1.02^

1.096

1.207

1.3^9

1.513

1.690

1.871

2.046

2.20-i 2.336

2.430

2.-478 2.472

2.411

2.293

2.124

1.911

1.665

1.400

J(x)

1.895

2.037

2.221

2.4.24

2.613

2.7U

2.776

2.697

2.537

2.334

2.108

1.878

1.653

1.436

1.231

1.038

0.861

0.699

0.553

0.424

J(-x)

0.895

0.761

0.606

0.443

0.294

0.185

0.136

0.137

0.149

0.139

0.111

0.079

0.051

0.029

0.013

0.002

-0.002

-0.004

-0.003

-0.002

0.500

0.525

0.550

0.575

0.600

0.625

0.650

0.675

0.700

0.725

0.750

0.775

0.800

0.825

0.850

0.875

0.900

0.925

0.950

0.975

J(x) J(x)

1.130

0.871

0.635

0.434

0.013

0.004

0.001

0.000

0.000

-O.COC -0.000

-0.000

-0.000

-0.000

-0.000

-0.000

0.313

0.221

0.148

0.093

0.275 0.054

0.158 0.0^9

0.081 0.014

0.036 0.006

0.002

0.001

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

J(-x)

-0.002

-0.001

-0.000

-0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

O.OOC 0.000

0.000

0.000

33
Table 1. Energy Diaaipation Function, J(x), and Input Data - Continued

TIN

STOPPING ?o\m.

(dE/drjj, =1.33 Mev(cmVg)

RESIDUAL RANGE

= 7.95 g/om^

Z = 50, = 10.00 Mev

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

OTHER PARAMETERS

= 11.50 A^ =

a = 0.1689 A„ =

.PTI 2 = 2.801 ^3 =

A^^^= 3.166 A =

4 SCATTERING COEFFICIENTS

0.1902

1.295

-1.267

0.7827

X

0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

J(x)

1.000

1.004

1.020

1.049

1.091

1.146

1.215

1.294

J(x)

1.436

1.545

1.668

1.794

1.902

1.973

2.011

2.036

J(-x)

0.436

0.328

0.209

0.097

0.013

-0.022

-0.012

0.008

0.500

0.525

0.550

0.575

0.600

0.625

0.650

0.675

J(x)

1.712

1.541

1.335

1.105

0.864

0.632

0.424

0.258

J(x)

0.759

0.608

0.472

0.354

0.254

0.173

0.110

0.065

J(-x)

-0.007

-0.006

-0.004

-0.002

-0.001

-0.000

0.000

0.000

I 0.200 1.382 2.053 0.026 0.700 0.139 0.034 0.000

9 h 0.225 1.476 2.060 0.040 0.725 0.065 0.015 0.000

15" 1.124 1 1.662 0.250 1.574 2.050 0.050 0.750 0.026 0.006 0.000

30 1.235 2 4.616 0.275 1.671 2.018 0.055 0.775 0.008 0.001 0.000

45 1.292 3 8.592

60 1.274 4 13.48 0.300 1.764 1.962 0.053 0.800 0.002 -0.000 0.000

75 1.177 5 19.22 0.325 1.848 1.876 0.045 0.825 0.000 -0.000 0.000

90 1.013 6 25.74 0.350 1.917 1.760 0.032 0.850 0.000 -0.000 0.000

105 0.801 7 33.00 0.375 1.966 1.618 0.017 0.875 0.000 -0.000 0.000

120 0.569 8 40.96

135 0.348 9 49.59 0.400 1.988 1.454 0.004 0.900 0.000 -0.000 0.000

150 0.165 10 58.85 0.425 1.978 1.278 -0.005 0.925 0.000 -0.000 0.000

165 0.045 11 68.72 0.450 1.930 1.098 -0.009 0.950 0.000 -0.000 0.000

180 0.003 12 79.18 0.475 1.842 0.923 -0.009 0.975 0.000 -0.000 0.000

34
Table 1. Energy Dissipation Function, J(x), and Input Data - Continued

LEAD

Z = 82, Eq =0.10 Mev

STOPPING PO'VER POINT PLANE POINT PLANE

(riE/dr)^ =1.97 Vlmv(cm^/e) ISOTROPIC PERPENDICULAR ISOTROPIC PERPENDICULAR

SOURCE SOURCE SOURCE SOURCE

RESIDUAL RANGE

J(x) Jvx;_ J\-x) J(x) JW JQ-x). 0.0313 sr/cm^ X X =

0.000 1.000 5.264 4.264 0.500 0.163 0.018 0.001 OTHER PARAMETERS 0.025 1.470 5.834 3.439 0.525 0.081 0.008 0.000

di = 10.90 A = 0.5U2 0.050 2.374 5.822 2.816 0.550 0.037 0.003 0.000

a = -5.084 A2 = 1.1310 0.075 3.384 5.490 2.304 0.575 0.015 0.001 -0.000

aPti, 9.759 A3 = -1.552 0.100 4.348 5.000 1.858 0.600 0.005 0.000 -0.000

_4PLP_ 11.18 A^

= 0.6977 0.125 5.149 4.430 1.466 0.625 0.002 0.000 -0.000

0.150 5.708 3.838 1.126 0.650 0.000 0.000 -0.000

SCATTERING COEFFICIENTS 0.175 5.986 3.249 0.841 0.675 0.000 0.000 -0.000

9 i

Si 0.200 5.980 2.688 0.608 0.700 0.000 0.000 -0.000

15" 1.074 1 13.56 0.225 5.713 2.168 0.427 0.725 0.000 0.000 -0.000

30 1.230 2 29.52 0.250 5.232 1.704 0.289 0.750 0.000 0.000 -0.000

45 1.479 3 46.58 0.275 4.597 1.301 0.189 0.775 0.000 0.000 -0.000

60 1.728 4 64.12

75 1.896 5 81.67 0.300 3.874 0.963 0.119 0.800 0.000 0.000 -0.000

90 1.936 6 98.84 0.325 3.128 0.689 0.072 0.825 0.000 0.000 -0.000

105 1.842 7 115.4 0.350 2.415 0.475 0.042 0.850 0.000 0.000 -0.000

120 1.640 8 131.1 0.375 1.778 0.314 0.023 0.875 0.000 0.000 -0.000

135 1.385 9 145.8

150 1.U3 10 .159.6 0.400^ 1.244 0.198 0.012 0.900 0.000 0.000 -0.000

165 0.969 11 172.4 0.425 0.824 0.119 0.006 0.925 0.000 0.000 -0.000

180 0.908 12 184.7 0.450 0.514 0.068 0.003 0.950

t).975

0.000 0.000 -0.000

0.475 0.300 0.036 0.001 -0.001 0.000 -0.000

Z = 82, Eq = 0.70 Mev

STOPPING POWER

(dE/dr)_, = 1.02 Mev(craVg)

RESIDUAL RANGE = 0.544 g/cm^

OTHER PARAMETERS

A-^ = 15.90

a = 6.172

^1 =

A2 = A^^ 12.80 A

J =

A^^^= U.82 A, =

4

0.4133

0.9603

-0.5993

0.2256

SCATTERING COEFFICIENTS

9 i

15° 1.098 1 13.68

30 1.290 2 34.41

45 1.564 3 59.30

60 1.819 4 87.92

75 1.971 5 119.8

90 1.966 6 154.5

105 1.801 7 191.6

120 1.510 8 230.8

135 1.159 9 271.9

150 0.830 10 3U.5

165 0.595 11 358.5

180 0.511 12 403.5

POINT

ISOTROPIC SOURCE

PLANE PERPENDICULAR

SOURCE

POINT ISOTROPIC SOURCE

PLANE PERPENDICULAR

SOURCE X J(x) J(x) J(-x) X J(x) J(x) J(-x)

0.000

0.025

0.050

0.075

1.000

1.393

2.236

3.176

4.576

5.105

5.068

4.708

3.576

2.789

2.194

1.722

0.500

0.525

0.550

0.575

0.042

0.017

0.006

0.002

0.004

0.001

0.000

0.000

0.000

-0.000

-C.OOO

-0.000

0.100

0.125

0.150

0.175

4.005

4.615

4.956

5.023

4.187

3.603

3.016

2.462

1.336

1.015

0.749

0.533

0.600

0.625

0.650

0.675

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

-0.000

-C.OOO

-0.000

-0.000

0.200

0.225

0.250

0.275

4.836

4.438

3.887

3.246

1.958

1.515

1.136

0.823

0.3.65 0. 239

1. U9

0.089

0.700

0.725

0.750

0.775

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

-0.000

-0,000

-C.OOO -0.000

0.300

0.325

0.350

0.375

2.579

1.946

1.389

0.934

0.573

0.3S1

o.2^a

0.144

0.050

0.027

0.014

0.007

0.800

0.825

0.850

0.875

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

-0.000

-C.OOO

-0.000

-0.000

0.400

0.425

0.450

0.475

0.588

0.345

C.187

0.093

0.081

0.043

0.021

0.009

0.003

0.002

0.001

0.000

0.900

0.925

0.950

0.975

0.000

-0.000

-0.000

-0.000

0.000

0.000

0.000

0.000

-0.000

-0.000

-0.000

-0.000

35
Table 1. Energy Dissipation Function, J{x), and Input Data - Continued

LEAD

Z = 82, Eq = 1.00 Mev

STOPPING POi/TER (dE/dr)g^ = 1.01 Hev(cm2/g)

RESIDUAL RANGE

d^ = 16.75

OTHER PARA1''ETERS h

=

a = 2.890 A2 =

aPTI= 12. 3^ A3 = aPLP= U.23

SCATTERING COEFFICIENTS

0.3810

0.9006

-0./M2

0.1625

e i H

15° 1.108 1 12.U

30 1.315 2 31.72

45 1.599 3 55.21

60 1.857 u 82.51

76 2.000 5 113.2

90 1.975 6 U7.0

105 1.777 7 183.4

120 1.4U 8 222.2

135 1.05c 9 263.2

150 0.683 10 306.1

165 0.422 11 350.7

180 0.328 12 396.9

POINT

ISOTROPIC SOURCE

PLANE

PERPENDICTTLAR SOURCE X

J(x) J(x) J(-x) X

0.000

0.025

0.050

0.075

1.000

1.329

2.053

2.880

4.208

4.730

4.736

4.438

3.208

2.469

1.927

1.509

0.500

0.525

0.550

0.575

0.100

0.125

0.150

0.175

3.629

4.195

4.530

4.621

3.978

3.451

2.913

2.398

1.172

0.893

0.662

0.474

0.600

0.625

0.650

0.675

0.200

0.225

0.250

0.275

4.484

4.153

3.675

3.107

1.924

1.503

1.140

0.835

0.325

0.213

0.133

0.079

0.700

0.725

0.750

0.775

0.300

0.325

0.350

0.375

2.504

1.918

1.392

0.953

0.589

0.398

0.256

0.156

0.044

0.024

0.013

0.006

0.800

0.825

0.850

0.875

0.400

0.425

0.450

0.475

0.611

0.365

0.209

0.102

0.089

0.048

0.024

0.011

0.003

0.002

0.001

0.000

0.900

0.925

0.950

0.975

POINT ISOTROPIC

SOURCE

J(x)

0.047

0.019

0.007

0.002

PLAICE PERPa:DICULAR

SOURCE

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

-0.000

-0.000

-0.000

J(x)

0.004

0.002

0.001

0.000

0.001 0.000

0.000 0.000

O.OOC C.OOC

0.000 0.000

C.OOO

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

J( -X)

0.000

-0.000

-0.000

-0.000

-0.000

-C.OOO

-0.000

-0.000

-0.000

-0.000

-C.OOO -0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

-0.000

STOPPING TO'IER (dE/dr)E =1.04 V\»v(cm^/g)

o RESIDUAL RANGE

= 1.82 g/cm2

OTHER PARAMETERS

dl = 17.46 h

= 0.3433 a = 1.144 h = 0.4377

aPti= 10.26 h

= 0.6620

aPlp= 11.72 h

= -0.4430

SCATTERING COEFFICIENTS

e 0/0^ i s^

15° 1.120 1 9.317

30 1.334 2 24.27

45 1.638 3 42.94

60 1.897 4 65.09

75 2.029 5 90.42

90 1.979 6 118.7

105 1.745 7 149.6

120 1.366 8 183.1

135 0.924 9 218.8

150 0.513 10 256.7

165 0.222 11 296.5

180 0.119 12 338.1

36

z = 82, Eo = 2.00 Mev

POINT ISOTROPIC

SOURCE

PLANE PERPENDICULAR

SOURCE

X J(x) J(x) J(-x:) 0.000

0.025

0.050

0.075

1.000

1.199

1.663

2.232

3.412

3.971

4.070

3.902

2.412

1.745

1.352

1.090

0.100

0.125

0.150

0.175

2.792

3.265

3.603

3.780

3.596

3.224

2.817

2.403

0.875

0.682

0.511

0.369

0.200

0.225

0.250

0.275

3.792

3.647

3.368

2.987

2.000

1.623

1.283

0.985

0.255

0.169

0.107

0.066

0.300

0.325

0.350

0.375

2.540

2.067

1.606

1.185

0.733

0.527

0.363

0.240

0.039

0.023

0.013

0.007

0.400

0.425

0.450

0.475

0.827

0.543

0.333

0.188

0.150

0.088

0.048

0.025

0.004

0.002

0.001

0.000

POINT PLANE

ISOTROPIC PEPJENDICULAR

SOURCE SOURCE

X

J(x) J(x) J(-x)

0.500 0.097 0.011 0.000

0.525 0.045 0.005 -0.000

0.550 0.019 0.002 -0.000

0.575 0.007 O.OCl -0.000

0.600 0.002 0.000 -0.000

0.625 0.001 o.(5oo -0.000

0.650 0.000 0.000 -0.000

0.675 0.000 0.000 -0.000

0.700 0.000 0.000 -0.000

0.725 0.000 0.000 -0.000

0.750 0.000 0.000 -0.000

0.775 0.000 0.000 -0.000

0.800 0.000 0.000 -0.000

0.825 0.000 0.000 -0.000

0.850 0.000 0.000 -0.000

0.875 0.000 0.000 -0.000

0.900 0.000 0.000 -0.000

0.925 0.000 0.000 -o.obo

0.950 0.000 0.000 -0.000

0.975 0.000 0.000 -0.000
Table 1. Energy Dissipation Function, J(x)5 and Input Data - Continued

STOPPING POWER

(dE/dr) =9.65 Mev(cm2/g)

o RESIDUAL RANGE

= 0.00U6 g/cm^

OTHER PARAJ'ETERS

d]_ = 1.286 = orZAO

a =-65.85 A2 = 1.16^

aP'^^= 0.9233 = -1.801 ,

A^^^^= 1.080 A^ = 0.9126

SCATTERING COEFFICIENTS I H

1 1.306

2 3.299

3 5. '766 8.575

5 11.63

6 U.87

n 18.23

8 21.67

9 25.17

10 28.70

11 32.22

12 35.72

AIR

E = 0.025 Mev

POINT PLANE ISOTROPIC PERPENDICUIJIR SOURCE SOURCE

X J(x) J(x) JC -X)

0.000 1.000 1 . 53c 0. 538

i . U±l 1.651 0.434

0.050 1 .034 1.763 0.339

u.u 0 i .UoV l.E7b 0.257

0.100 1.115 1.990 0.191

r\ IOC 1 .1 /<d 2.107 0.145

i . 'ij ' 2.227 0.122

0.175 1.3i' 2.348 O.llo

0.200 1.405 2.463 0.114

1 • jU/d 2 . 5dc 0.111

1 • oUV 2.662 0.106

i • I <A- 2.74A 0.101

0.300 1.846 2.811 0.094

0.325 1.976 2.862 0.085

0.350 2.111 2.893 0.075

0.375 2.251 2.904 0.062

0.4.00 2.394 2.890 0.048

0.425 2.537 2.850 0.033

0.450 2.679 2.784 0.017

0.475 2.815 2.691 0.004

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE X J(x) J 1.x; J(, -xj

0.500 2.-943 2 -. ? /?+ n nnA — U . UUD 0.525 3.056 2.438 -0.010

n ceo 0. 550 2.288 -0.008

C. 5 '5 3 .21c 2.126 -0.003

0.600 3.252 1.956 0.001

0.625 3 •24-3 1.776 0.005

0 . 650 1.588 0.007

v ,0 /z> _> • uou U . \JVJO

0.700 2.867 1 .lo3 U.UUO

U . /^d? 2. 5V' u.y/i A AAA U.UUo

V, lj\J 2.<;4o 0.758 0.004

0.552 0.001

0.800 1.356 0.364 -0.001

0.825 0.679 0.206 -0.002

0.850 0.461 0.093 -0.003

0.875 0.170 0.028 -0.002

0.900 0.033 0.004 -0.001

0.925 0.002 0.000 0.000

0.950 0.000 0.000 0.000

0.975 0.000 0.000 0.000

STOPPING PO'.ffiR (dE/dr) E = 5.77 MevCcm^/g) RESIDUAL RAIIGE = 0.00496 g/cm^ OTHER PARAf-'ETERS

d-^ = 1.329 A-^ = 0.7547

a = 16.71 A2 = 0.8725

aP'^^= 0,9498 A^ = -1.192

^PLP^ 1.114 A^ = 0.5644^ SCATTERING COEFFICIENTS

I

1 1.254

2 3.249

3 5.791

4 8.757

5 12.06

6 15.64

7 19.43

8 23.40

9 .27 . 51 10 31.72

11 36.02

12 40.38

E =0.05 Mev

o POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) J(x) J(-x)

0.000 1.000 1.497 0.497

0.025 1.013 1.609 0.396

0.050 1.036 1.721 0,305

0.075 1.070 1.834 0.227

0.100 1.114 1.950 0,165

0.125 1.168 2.070 0.123

0.150 1.231 2.194 0.105

0.175 1.303 2.320 0.100

0.200 1.385 2.433 0.099

0.225 1.475 2.547 0.097

0.250 1.574 2.644^ 0.094

0.275 1.681 2.728 0.089

0.300 1.795 2.796 0.084

0.325 1.917 2.847 0.076

0.350 2.045 2.878 0.066

0.375 2.178 2.887' 0.054

0.400 2.316 2.872 0.040

0.425 2.457 2.831 0.026

0.450 2.600 2.763 0.011

0.475 2.741 2.671 -0.001

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) J(x) J(-x)

0.500 2.878 2.557 -0.009

0.525 3.007 2.424 -0.010

0.550 3.122 2.278 -0.007

0.575 3.217 2.121 -0.002

0.600 3.279 1.953 0.002

0.625 3.295 1.774 0.005

0.650 3.248 1.584 0.007

0.675 3.117 1.384 0.008

0.700 2.884 1.174 0.007

0.725 2.558 0.958 0.006

0.750 2.139 0.741 0.003

0.775 1.691 0.533 0.001

0.800 1.245 0.345 -0.001

0.825 0.833 0.192 -0.002

0.850 0.483 0.083 -0.002

0.875 0.223 0.024 -0.001

0.800 0.070 0.003 -0.000

0.925 0.011 0.000 -0.000

0.950 0.000 0.000 -0.000

0.975 0.000 0.000 -0.000

37
Table 1. Energy Dissipation Function, J(x), and Input Data - Continued

STOPPING POWER

(clE/dr)p =3.60 Mev(om2/g)

RESIDUAL RANGE

= 0.0164 g/cm^

OTHER PARa>;ETERS

i-^ = 1.2670 A^ = 0.6992 a = 29.16 A2 = 0.9039

A^^= 0.9328 A3 = -1.048

aP^^= 1.101 A^ = 0.4452

SCATTERING COEFFICIENTS

I

1 1.225

2 3.247

3 5.882

4 9.019

5 12.58

6 16.49

7 20.70

8 25.18

9 29.89

10 34.79

11 39.87

12 45.08

E = 0.10 Mev

0

rUIIi r PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x) J(x) J(-x)

0.000 1.000 1.453 0.453

0.025 1.013 1.562 0.356

0.050 1.036 1.672 0.268

0.075 1.06S 1.782 0.194

U . LUU 1 .lUK 1.896 0.135

0.125 1.158 2.014 0.096

0.150 1.216 2.137 0.079

0.175 1.282 2.262 0.079

i. j5d 2.380 0.082

0.225 1.439 2.487 0.083

0.250 1.529 2.583 0.083

0.275 1.626 2.664 0.080

0.300 1.731 2.730 0.C76

0.325 1.843 2.779 0.069

0.350 1.961 2.807 0.060

0.375 2.084 2.812 0.048

0.400 2.213 2.793 0.035

0.425 2.345 2.748 0.020

0.450 2.480 2.678 0.005

0.475 2.616 2.585 -0.006

ruxru PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x) J(x) J(-x)

0. 500 2.749 2.472 -0.011

0.525 2.876 2.344 -0.011

0.550 2.993 2.205 -0.007

0.575 3.090 2-055 -0.002

ri Ann 1.895 0.002

0.625 3.181 1.725 0.005

0.650 3.138 1.543 0.006

0.675 3.008 1.351 0.007

U. I\)\J 1.149 0.006

0.725 2.466 0.940 0.005

0.750 2.098 0.730 0.003

0.775 1.695 0.527 O.OCl

0.800 1.275 0.343 -0.001

0.825 0.863 0.191 -0.002

0.850 0.496 0.083 -0.002

0.875 0.218 0.024 -0.001

0.900 0.060 0.003 -0.000

0.925 0.006 0.000 -0.000

0.950 0.000 0.000 -0.000

0.975 0.000 0.000 -0.000

STOPPING POV/ER

(dE/clr)5; =2.45 MevCcmVg)

RESIDUAL RANGE

r = 0.0513 g/cm^

0 OTHER PARAMETERS

d;i^ = 1.246 k-^ = 0.6401 a = 18.84 A2 = 0.9019

0.928 A3 = -1.004

aP^P= 0.1100 A^ = 0.4624

SCATTERING COEFFICIE^ITS i h

1 1.183

2 3.206

3 5.894

4 9.143

5 12.88

6 17.04

7 21.59

8 26.48

9 31.67

10 37.14

11 42.90

12 48.89

38

E =0.20 Mev

0

POINT PLANE

ISOTROPIC PERPENDICUI.AR SOURCE SOURCE

X

J(x) J(x) J(-x)

0.000 1.000 1.395 0.395

0.025 1.009 1.493 0.306

0.050 1.027 1.592 0.225

0.075 1.052 1.693 0.156

0.100 1.085 1.797 0.103

0.125 1.126 1.906 0.069

0.150 1.174 2.022 0.056

0.175 1.230 2.140 0.058

0.200 1.293 2.251 0.063

0.225 1.363 2.352 0.067

0.250 1.440 2.442 0.068

0.275 1.525 2.518 0.068

0.300 1.616 2.579 0.065

0.325 1.714 2.623 0.060

0.350 1.818 2.647 0.051

0.375 1.929 2.649 0.040

0.400 2.045 2.628 0.028

0.425 2.167 2.583 0.014

0.450 2.292 2.514 0.000

0.475 2.421 2.425 -0.009

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x) J(x) J(-x)

0.500 2.551 2.319 -0.013

0.525 2.677 2.200 -0.011

0.550 2.794 2.071 -0.007

0.575 2.892 1.932 -0.002

0.600 2.959 1.783 0.001

0.625 2.975 1.624 0.004

0.650 2.921 1.454 0.006

C.675 2.786 1.273 0.006

0.700 2.578 1.083 0.006

0.725 2.311 0.886 0.004

0.750 1.992 0.688 0.003

0.775 1.626 0.496 0.001

0.800 1.228 0.322 -0.001

0.825 0.827 0.179 -0.002

0.850 0.466 0.078 -0.002

0.875 0.195 0.022 -0.001

0.900 0.048 0.003 -0.000

0.925 0.004 0.000 -0.000

0.950 0.000 0.000 -0.000

0.975 0.000 0.000 -0.000
Table 1. Energy Dissipation Function, J(x), and Input Data - Continued

STOPPING PC'/ffiR (dE/dr),^ = 1.89 y8v(cm2/g) RESIDUAL RiVNGE ro = O.H'!' g/cm2 OTHER PARAMETERS

di = 1.227 Al = 0.5361 a = 9.408 0.9248

0.9134 h

= -0.7547

1.084 0.2938

SCATTERING COEFFICIENTS

I H 1 1.109

2 3.067

3 5.712

4 8.952

5 12.72

6 16.97

7 21.65

8 26.73

9 32.17

10 37.96

11 44.06

12 50.46

AIR

E =0.40 Mev

0

POINT PLANE

ISOTROPIC FERPENDICUI.AR SOURCE SOURCE

X

J(x) J(x) J(-x)

0.000 1.000 1.314 0.314

0.025 l.OOS 1.400 n.237

0.050 1.022 1.486 C.l6g

0.075 1.043 0,109

0.100 1.070 1.666 C.064

0.125 1.102 1.763 0.035

0.150 l.Ul 1.867 0,027

0.175 1.186 1 97A 0 03'?

0.200 1.237 2.074 0.041

0.225 1.293 2.165 0.047

0.250 1.355 2.245 0.051

0.275 1.423 2.311 0.053

0.300 1.497 2.364 0.052

0.325 1.576 2.399 0.048

0.350 1.660 2.415 0.041

0.375 1.749 2.411 0.032

0.400 1.843 2.385 0.020

0.425 1.942 2.336 0.007

0.450 2.0U 2.266 -0.005

0.475 2.149 2.179 -0.012

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) J(x) J(-x)

0.500 2.255 2.079 -0.013

0.525 2.358 1.969 -0,010

0.550 2.455 1.850 -C,006

0.575 0.537 1.724 -0.002

0.600 2.592 1.591 0.001

0.625 2.606 1.448 0.003

0.650 2.560 1.297 0.005

0.675 2.443 1.136 0,005

0.700 2.262 0.967 0.005

0.725 2.030 0.792 0.004

0.750 1.752 0.616 0.002

0.775 1.434 0.445 0.000

0.800 1.088 0.290 -0,001

0.825 0.737 0,161 -0,002

0.850 0.418 C.070 -0,002

0.875 0.177 0.020 -0,001

0.900 0.044 0.003 -0.000

0.925 0.004 0.000 -0.000

0.950 O.OCO 0.000 0.000

0.975 0.000 0.000 C.OOO

E = 0.70 Mev

0

STOPPING POWER

(dE/dr)£ = 1.70 Mev(cm2/g)

RESIDUAL RANGE = 0.317 g/cm^ OTHER PARAMETERS = 1.215 o = 4.830

A^^= 0.9157

A^^^= 1.090

^2 =

0.4343

0.9874

A3 = -0.7402

A4 = 0.3184

SCATTERING COEFFICIENTS

i

1

2

34

56

7

8910

1112

1.007

2.822

5.302

8.368

11.96

16.04

20.57

25.51

30.84

36.52

42.59

48.96

X 0.000

0.025

0.050

0.075

0.100

0.125

0.150

O.l'^S

0.200

0.225

0.250

0.275

0.300

0.325

0.350

0.375

0.400

0.425

0.450

0.475

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

J(x)

POINT ISOTROPIC SOURCEPLANE PERPENDICULAR

SOURCE

1.000

1.004

1.013

1.028

1.049

1.075

LIO*^

1.143

1.185

1.231

1.283

1.339

1.400

1.466

1.535

1.609

1.686

1.766

1.84?

1.931

J(x) J(-x) X J(x) J(x) J(-x)

1.271

1.347

1.423

1.501

0.271

0.200

0.136

0.083

0.500

0.525

0.550

0.575

2.013

2.092

2.164

2.224

1.827

1.722

1.612

1.496

-0.012

-0.009

-0.005

-0.002

1.581

1.667

1.758

1.851

0.042

0.018

0.012

0.020

0.600

0.625

0.650

0.675

2.262

2.267

2.224

2.118

1.374

1.246

i.'ilo 0.968

0.001

0.003

0.004

0.004

1.937

2.014

2.080

2.134

0.030

0.038

0.043

0.046

0.700

0.725

0.750

0.775

1.948

1.729

1.477

1.198

0.819

0.667

0.516

0.370

0.004

0.003

0.002

0.000

2.172

2.195

2.198

2.182

0.046

0.042

0.036

0.026

0.800

0.825

0.850

0.875

0.902

0.609

0.346

0.148

0.239

0.132

0.056

0.016

-0.001

-0.002

-0.002

-0.001

2.145

2.088

2.013

1.925

0.014

0.002

-0.008

-0.013

0.900

0.925

0.950

0.975

0.038

0.003

0.000

0.000

0.002

0.000

0.000

0.000

-0.000

-0.000

-0.000

-0.000

39
Table 1. Energy Dissipation Function, J(x), and Input Data - Continued

STOPPING POWER

(dE/dr)p =1.65 Kev(cin2/g)

RESIDUAL RANGE

= 0.^97 g/cm^

OTHER PARAJ'ETERS

d-|_ = 1.223 A-L = 0.3807 a = 2.968 Ag = 1.205

AP'ri=. 0.8594. A3 = -1.095

aP^-P= 0.1022 = 0.509ii SCATTERING COEFFICIENTS

i Si

1 0.9151

2 2.582

3 7.721

5 11.08

6 U.90

7 19.15

8 23.82

9 28.87

10 34.29

11 40.05

12 46.

u

AIR

E = 1.00

0 Mev

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) Tfx') J( -x)

0.000 1.000 1.186 0.186

0.025 1.001 1.239 0.135

0.050 1.007 1.294 0.090

0.075 1.017 1.352 0.050

0.100 1.032 1.416 0.020

0.125 1.051 1.487 0.002

0.150 1.073 1.567 -0.003

0.175 1.100 1.654 -0.003

0.200 1.132 1.737 0.011

0.225 1.167 1.814 0.018

0.250 1.206 1.882 0.024

0.275 1.250 1.942 0.028

0.300 1.298 1.990 0.030

0.325 1.349 2.025 0.030

0.350 1.405 2.046 0.028

0.375 1.465 2.049 0.023

0.400 1.529 2.035 0.016

0.425 1.597 2.000 0.007

0.450 1.669 1.946 -0.003

0.475 1.743 1.875 -0.010

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

J(x) J{ -X)

0.500 1.820 1.789 -0.013

0.525 1.897 1.693 -0.012

n c CO 0.550 1.590 -0.008

0.5o li.'oi 1 1.482 -0.004

0.600 2.086 1.367 -0.001

0.625 2.105 1.247 0.002

0.650 2.076 1.119 0.004

0.0/5 n r\OC. i.yoD 0.984 0.005

0.700 1.837 0.842 0.005

0.725 1.648 0.695 0.004

U. /^U 0.546 0.002

0.400 0.001

U. oUU 0.265 -0.001

0.825 0.628 0.151 -0.002

0.850 0.370 0.068 -0.002

0.875 0.166 0.020 -0.001

0.900 0.045 0.003 -0.000

0.925 0.004 0.000 0.000

0.950 0.000 0.000 0.000

0.975 0.000 0.000 0.000

E =2.00 Mev

0 STOPPING PO'^R POINT PLANE POINT PLANE

(dE/dr)„ = 1.68 MevfcmVe) ISOTROPIC PERPENDICULAR ISOTROPIC PERPENDICULAR

^0 SOURCE SOURCE SOURCE SOURCE

RESIDUAL RANGE J(x) J(x) J(-x) J(x) J(x) = 1.10 g/cra X X

J(-x)

0.000 1.000 1.096 0.096 0.500 1.495 1.673 -0.004

OTKER PARAJ'IETERS 0.025 0.993 1.115 0.070 0.525 1.568 1.610 -0.009

di = 1.251 k-^ = 0.2699 0.050 0,989 1.138 0.046 0.550 1.645 1.531 -0.010

a = 1.230 A2 = 1.856

0.075 0.988 1.165 0.025 0.575 1.724 1.440 -0.009

A^'''^= 0.7775 A3

aP^-'P= 0.9236 A^

= -2.638 0.100 0.990 1.198 0.008 0.600 1.797 1.340 -0.005 = 1.512

0.125 0.995 1.240 -0.003 0.625 1.851 1.233 -0.001

0.150 1.003 1.294 -0.007 0.650 1.863 1.118 0.002

SCATTERING COEFFICIENTS 0.175 1.014 1.358 -0.005 0.675 1.811 0.995 0.004

I h 0.200 1.028 1.423 -0.001 0.700 1.691 0.865 0.005

1 0.6902 0.225 1.045 1.485 0.003 0.725 1.525 0.726 0.005

2 1.966 0.250 1.066 1.543 0.007 0.750 1.331 0.582 0.003

3 3.738 0.275 1.089 1.597 0.009 0.775 1.113 0.437 0.002

4 5.955

5 8.592 0.300 1.116 1.645 0.012 0.800 0.875 0.298 -0.000

6 11.62 0.325 1.447 1.687 0.013 0.825 0.627 0.176 -0.002

7 15.01 0.350 1.182 1.721 0.014 0.850 0.387 0.083 -0.002

8 18.75 0.375 1.221 1.746 0.013 0.875 0.186 0.027 -0.001

9 22.83

10 27.22 0.400 1.264 1.760 0.012 0.900 0.057 0.004 -0.000

11 31.23 0.425 1.313 1.762 0.009 0.925 0.006 0.000 -0.000

12 36.91 0.450 1.368 1.749 0.005 0.950 0.000 0.000 -0.000

0.475 1.428 1.720 0.001 0.975 0.000 0.000 0.000

40
Table 1. Energy Dissipation Fiinction, J(x), and Input Data - Continued

STOPPING POWER

(dE/dr)r. = 1.78 }\ev(cm^/g) RESIDUAL RANGE

= 2.26 g/cni2 OTHER parai:eters

d-i^ = 1.326 A^^ = 0.262A ^ a = 0.5283 A2 = 1.034-

A^'''^= 0.6663 A3 = -0.6649

aP^P= 0.7867 A^ = 0.3688

scattering coefficients

I S„

1 0.4384

2 1.3U

3 2.513

A 4.028

5 5.837

6 7.924

7 10.28

8 12.89

9 15.74

10 18.83

11 22.14

12 25.68

stopping pootr

(clE/dr)p =1.97 Mev(cm2/g)

o residual range

Tq = 5.44 g/cm^

other parameters

^1 = 1.682 ^1 = 0.1200 a = 0.1557 ^2 = 1.942

aPti= 0.5002 h

= -2.596

aPlp= 0.5760 h

= 1.534

SCATTERING COEFFICIENTS

i H 1 0.2266

2 0.6534

3 1.257

4 2.026

5 2.951

6 4.024

7 5.240

8 6.5^4

9 8.082

10 9.700

11 11.45

12 13.32

AIR

E = 4.00 Mev

0 POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X j(x) J(x) J(-x)

0.000 1.000 1.038 0.038

0.025 0.998 1.046 0.028

0.050 0.997 1.056 0.019

0.075 0.998 1.069 0.011

0.100 1.000 1.087 0.004

0.125 1.004 1.110 -0.000

0.150 1.009 1.142 -0.003

0.175 1.016 1.184 -0.003

0.200 1.024 1.230 -0.002

0.225 1.033 1.274 -0.000

0.250 1.044 1.317 0.001

0.275 1.057 1.359 0.002

0.300 1.071 1.398 0.003

0.325 1.087 1.435 0.003

0.350 1.105 1.468 0.004

0.375 1.125 1.497 0.004

0.400 1.147 1.520 0.004

0.425 1.171 1.537 0.004

0.450 1.197 1.544 0.003

0.475 1.226 1.541 0.002

E = 10.00 Mev

o

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x) J(x) J(-x)

0.000 1.000 1.010 0.010

0.025 0.997 1.008 0.009

0.050 0,995 1.009 0.008

0.075 0.994 1.011 0.008

0.100 0.993 1.014 0.007

0.125 0.992 1.019 0.006

0.150 0.993 1.027 0.006

0.175 0.993 1.036 0.005

0.200 0.994 1.047 0.004

0.225 0.996 1.060 0.003

0.250 0.999 1.075 0.003

0.275 1.001 1.092 0.002

0.300 1.005 1.111 0.001

0.325 1.008 1.132 -0.000

0.350 1.012 1.155 -0.001

0.375 1.016 1.18X -0.002

0.400 1.020 1.207 -0.003

0.425 1.026 1.234 -0.004

0.450 1.033 1.260 -0.005

0.475 1.041 1.284 -0.006

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x) J(x) J(-x)

0.500

0.525

0.550

0.575

1.257

1.291

1.328

1.367

1.526

1.496

1.450

i;388

0.001

-0.001

-0.003

-0.004

0.600

0.625

0.650

0.675

1.40s

1.447

1.479

1.496

1.312

1.224

1.129

1.027

-0.004

-0.003

-0.001

0.001

0.700

0.725

0.750

0.775

1.486

1.438

1.343

1.191

0.916

0.797

0.669

0.543

0.002

0.002

0.002

0.002

0.800

0.825

0.850

0.875

0.978

0.716

0.437

0.198

0.395

0.261

0.143

0.057

0.001

-0.000

-0.001

-0.001

0.900

0.925

0.950

0.975

0.055

0.008

0.003

0.005

0.013

0.001

0.000

0.000

-0.000

-0.000

-0.000

-0.000

POINT ISOTROPIC SOURCEPLANE

PERPE^;DICULAR

SOURCE

X

J(x) J(x) J(-x)

0.500

0.525

0.550

0.575

1.051

1.063

1.079

1.099

1.303

1.3U

1.314

1.301

-0.007

-0.007

-0.007

-0.004

0.600

0.625

0.650

0.675

1 .123 l!l54

1.193

1.238

1.279

1.252

1.220

1.179

0.001

0.007

0.012

0.015

0.700

0.725

0.750

0.775

1.285

1.322

1.330

1.290

1.127

1.059

0.968

0.849

0.016

0.014

0.007

-0.004

0.800

0.825

0.850

0.875

1.184

0.996

0.728

0.420

0.695

0.511

0.315

0.142

-0.018

-0.028

-0.023

-0.000

0.900

0.925

0.950

0.975

0.162

0.031 - 0.001 - 0.000 -

0.029

-0.009

-0.004

-0.000

0.020

-0.017

0.005

0.000

41
Table 1. Energy Dlitlpatlon Function, J(x) , and Input Data - Continued

STOPPING PCl^

(d'E/dr)^ = 11.2 Mev(cmVg)

^0 RESIDUAL RANGE

r = 0.00125 K/cm^

0 OTHER PARAMETERS

dl = 0.9338 h

= 0.7245 a = -63.71 ^^2 = h

=

1.169

0.6711 -1.781

aPlp, 0.7937 0.8868

SCATTERING C0EFV"ICIENTS I

1 0.9i87

2 1.467

3 4.251

4 6.360

5 8.733

6 11.28

7 13.94

8 16.71

9 19.91

10 23.19

11 26.55

12 29.98

STOPPING POWER

(dE/dr)j; =6.64 Mev(omVg)

RESIDI'AL RANGE

Tq = 0.00428 g/cm^

OTHER PARAMETERS

= 0.9697 A^ = 0.7637 a = 13.56 Ag = 0.9428

aP'''I= 0.6898 A3 = -1.383

A^^^= 0.8173 A^ = 0.6763

SCATTERING COEI'FICIENTS i

1 0.9031

2 2.349

3 4.202

4 6.375

5 8.807

6 11.45

7 14.27

8 17.23

9 20.31

10 23.48

11 26.72

12 30.02

POLYSTYRENE

E = 0.025 Mev

POINT

ISOTRCPIC SOURCE

PLANE PERPENDICULAR

SOURCE

X J(x) J(x) J(-x)

0,000

0.025

0.050

0.075

1.000

1.010

1.027

1.052

1.342

1.414

1.488

1.565

0.342

0.278

0.218

0.163

0.100

0.125

0.150

0.175

1.084

1.123

1.169

1.221

1.647

1.735

1.833

1.942

0.116

0.079

0.058

0.053

0.200

0.225

0.250

0.275

1.280

1.346

1.419

1.499

2.055

2.164

Z.270

2.370

0.055

0.057

0.058

0.059

0.300

0.325

0.350

0.375

1.585

1.679

1.779

1.886

2.465

2.553

2.631

2.698

0.058

0.057

0.055

0.051

0.400

0.425

0.450

0.475

1.999

2.118

2.242

2.370

2.750

2.786

2.800

2.791

0.04:

0.037

0.028

0.016

E =0.05 Mev

0

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) J(x) J(-x)

0.000 1.000 1.300 0.300

0.025 1.010 1.369 0.240

0.050 1.026 1.440 0.186

0.075 1.049 1.516 0.137

0.100 1.079 1.599 0.097

0.125 1.114 1.693 0.070

0.150 1.156 1.801 0.059

0.175 1.205 1.916 0.057

0.200 1.259 2.029 0.056

0.225 1.321 2.139 0.054

0.250 1.389 2.245 0.052

0.275 1.464 2.346 0.050

0.300 1.545 2.U2 0.048

0.325 1.634 2.530 0.045

0.350 1.729 2.609 0.042

0.375 1.832 2.677 0.038

0.400 1.941 2.732 0.033

0.425 2.058 2.770 0.027

0.450 2,181 2.788 0.021

0.475 2.311 2.784 0.013

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x) J<x) J(-x)

0.500

0.525

0.550

0.575

2.500

2.631

2.761

2.884

2.754

2.690

2.601

2.491

0.003

-0.008

-0.016

-0.016

0.600

0.625

0.650

0.675

2.998

3.095

3.168

3.206

2.367

2.231

2.082

1.919

-0.011

-0.004

0.002

0.006

0.700

0.725

0.750

0.775

3.196

3.123

2.967

2.710

1.739

1.540

1.321

1.083

0.009

0.010

0.010

0.007

0.800

0.825

0.850

u . P / 5

2.338

1.850

1.274

0.831

0.576

0.341

0.154

0.003

-0.001

-0.004

-0.005

0.900

0.925

0.950

0.975

0.243

0.034

0.000

0.000

0.042

0.004

0.000

0.000

-0.003

-0.001

-0.000

0.000

POINT ISOTROPIC SOURCEPLANE PERPENDICULAR

SOUHCE

X J<x) J(x) J(-x)

0.500

0.525

0.550

0.575

2.U8

2.587

2.729

2.867

2.754

2.697

2.614

2.510

0.005

-0.003

-0.009

-0.011

0.600

0.625

0.650

0.675

2.996

3.107

3.191

3.237

2.390

2.254

2.105

1.939

-0.009

-0.004

0.001

0.005

0.700

0.725

0.750

0.775

3.231

3.156

2.993

2.724

1.754

1.549

1.323

1.078

0.007

0.008

0.008

0.006

0.800

0.825

0.850

0.875

2.334

1.826

1.238

0.657

0.819

0.560

0.325

0.142

0.003

-0.001

-0.003

-0.004

0.900

0.925

0.950

0.975

0.221

0.028

0.000

0.000

0.037

0.003

0.000

0.000

-0.002

-0.000

0.000

0.000

42
Table 1. Energy Dlfslpatlon Function, J(x), and Input Data > Continued

STOPPING POWER

(dE/dr)p s -i.13 Mev(cm2/g)

RESIDUAL RANGE

Tq = C.0U2 g/em^

OTHER PARA^T^ERS

dj_ = 0.9090 h

= 0.7102 a = 45.20 h

= 0.8488

aP^^= 0.6738 h

= -0.9880

aP^P= 0.8051 h

= 0.4290

SCATTERING COEFFICIENTS

I H

1 0.8894

2 2.367

3 4.303

4 6.618

5 9.254

6 12.17

7 15.32

8 18.68

9 22.23

10 25.93

11 29.78

12 33.75

POLYSTYRENE

E = 0.10 Mev

0

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x) JV *^ 0.000 1.000 1.252 0.252

0.025 1.011

0.050 1.028 1.391 0.146

0.075 1.052 1.469 0.105

0.100 1.082 1.561 0.078

0.125 1.119 1 668

0.150 1.161 1.778 0.064

0.175 1.206 1.£'86 0.059

0.200 1.252 1.991 0.055

0.225 1.302 2.093 0.051

0.250 1.358 2.192 0.046

0.275 1.419 2.287 0.042

0.300 1.487 2.376 0.038

0.325 1.562 2.457 0.034

0.350 1.644 2.531 0.029

0.375 1.734 2.593 0.025

0.400 1.832 2.643 0.021

0.425 1.938 2.676 0.017

0.450 2.054 2.690 0.013

0.475 2.178 2.682 0.009

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) J(-x)

0.500 2.310 2.649 0.005

0.525 2.448

0.550 2.590 2.509 -0.001

0.575 2.733 2.410 -0.003

0.600 2.871 2.299 -0.004

0.625 2.996 -0—w . OOA wW*f 0.650 3.095 2.036 -0.003

0.675 3.151 1.880 -0.001

0.700 3.146 1.705 0.002

0.725 3.057 1.509 0.005

0.750 2.868 1.293 0.006

0.775 2.577 1.057 0.006

0.800 2.203 0.809 0.004

0.825 1.762 0.559 0.000

0.850 1.269 0.329 -0.002

0.875 0.762 0.147 -0.004

0.900 0.325 0.040 -0.002

0.925 0.066 0.004 -0.000

0.950 0.002 0.000 -0.000

0.975 0.000 0.000 -0.000

STOPPING POWER

(dE/dr)2^ = 2.79 Mev(oin2/g) RESIDUAL RANGE = 0.0448 p/cm^

OTHER PARAMEH'ERS \

= 0.9034 Ai = 0.6469 a = 20.18 A2 = 0.8812

0.6770 A3 = -0.9830

aPlp= 0.8119 \

= 0.4548 SCATTERING COEFFICIENTS i

1 0.8607

2 2.340

3 4.314

4 6.709

5 9.472

6 12.56

7 15.94

8 19.59

9 23.47

10 27.57

11 31.87

12 36.35

E =0.20 Mev

0

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(it) J(x) J(-x)

0.000 1.000 1.237 0.237

0.025 1.008 1.297 0.185

0.050 1.020 1.359 0.137

0.075 1.038 1.424 0.093

0.100 1.060 1.494 0.056

0.125 1.087 1.573 0.029

0.150 1.118 1.663 0.015

0.175 1.155 1.766 0.015

0.200 1.197 1.872 0.021

0.225 1.244 1.974 0.026

0.250 1.296 2.073 0.031

0.275 1.354 2.166 0.035

0.300 1.417 2.254 0.038

0.325 1.486 2.333 0.039

0.350 1.561 2.403 0.038

0.375 1.642 2.461 0.036

0.400 1.729 2.504 0.032

0.425 1.824 2.531 0.025

0.450 1.^25 2.537 0.016

0.475 2.034 2.520 0.004

POINT PLANE

ISOTROPIC PERPENDICULAR

soracE SOURCE

X

J(x) J(x) J<-x)

0.500 2.150 2.480 -0.007

0.525 2.272 2.418 -0.015

0.550 2.399 2.338 -0.017

0.575 2.525 2.244 -0.013

0.600 2.645 2.138 -0.008

0.625 2.750 2.022 -0.002

0.650 2.834 1.892 0.002

0.675 2.885 1.748 0.005

0.700 2.891 1.586 0.007

0.725 2.836 1.404 0.008

0.750 2.704 1.201 0.007

0.775 2.476 0.979 0.005

0.800 2.137 0.744 0.002

0.825 1.688 0.509 -0.001

0.850 1.159 0.294 -G.OO4

0.875 0.625 0.127 -0.004

0.900 0.216 0.032 -0.002

0.925 0.029 0.003 -0.000

0.950 0.000 0.000 -0.000

0.975 0.000 0.000 -0.000

43
Table 1. Energy Dissipation Function, J(x) , and Input Data - Continued

STCPPIMC POV/ER (dE/dr)EQ = 2.13 Hev(cmVg)

RESIDUAL RANGE = 0.129 g/cm^

OTHER PARA^^ETERS

d-^ = 0.8909 = 0.5^U

a = 9.898 A2 = 0.92A2

aP'^^= 0.6689 Aj = -0.7832

aPlp= 0.8040 a^ = 0.3U5

SCATTERING COEFFICIENTS

I H

1 0.8092

2 2.243

3 4.. 188

/V 6.576

5 9.361

/0 12.51

7 15.98

8 19.76

9 23.82

10 28.

U

11 32.70

12 37.49

STOPPING PO'//ER (dE/dr)„ =1.89 Mev(cm /g)

RESIDUAL RANGE

To = 0.281 g/cm^

OTHER PARAMETERS

d-L = 0.8808 A^ = 0.^652

a = 5.200 A2 = 0.9275 aPTI= 0.6502 A^ = -0.6353

A^^P= 0.7821 A^ = 0.2A26

SCATTERING COEFFICIEJITS I

1 0.7387

2 2.075

3 3.906 ^ 6.174

5 8.8a

6 11.87

7 15.24

8 18.93

9 22.91

10 27.17

11 31.70

12 36.48

POLYSTYRENE

E = 0.40 Mev

o

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x)

0.000 1.000 1.186 0.186

0.025 1.006 1.237 0.142

0.050 1.017 1.290 0.100

0.075 1.031 1.346 0.063

0.100 1.049 1.407 0.032

0.125 1.070 1.476 0.010

0.150 1.096 1.555 0.001

0.175 1.125 1.646 0.001

0.200 1.159 1.740 0.008

0.225 1.197 1.831 0.015

0.250 1.238 1.918 0.020

0.275 1.285 2.000 0.025

0.300 1.335 2.076 0.029

0.325 1.390 2.145 0.031

0.350 1.451 2.204 0.032

0.375 1.516 2.252 0.030

0.400 1.586 2.286 0.026

0.425 1.662 2.303 0.020

0.450 1.744 2.300 0.011

0.475 1.832 2.277 0.000

E = 0.70

0 Mev

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) J(x) J(-x)

0.000 1.000 1.140 0.140

0.025 1.004 1.180 0.104

0.050 1.012 1.221 0.071

0.075 1.023 1.266 0.042

0.100 1.038 1.315 0.017

0.125 1.055 1.371 -0.001

0.150 1.075 1.438 -0.010

0.175 1.098 1.515 -0.007

0.200 1.123 1.596 -0.000

0.225 1.151 1.675 0.006

0.250 1.181 1.750 0.012

0.275 1.213 1.822 0.017

0.300 1.249 1.888 0.021

0.325 1.287 1.948 0.024

0.350 1.330 2.000 0.025

0.375 l-.37g 2.042 0.024

0.400 1.431 2.071 0.022

0.425 1.489 2.086 0.016

0.450 1.554 2.083 0.009

0.475 1.626 2.061 0.000

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x) J(-x)

0.500 1.926 2.232 -0.010

0.525 2.026 2.168 -0.016

0.550 2.129 2.090 -0.016

0.575 2.232 2.002 -0.012

0.600 2.330 1.904 -0.006

0.625 2.416 1.798 -0.002

0.650 2.484 1.681 0.002

0.675 2.524 1.551 0.005

0.700 2.526 1.405 0.006

0.725 2.476 1.243 0.007

0.750 2.361 1.063 0.006

0.775 2.163 0.867 0.004

0.800 1.871 0.659 0.002

0.825 1.482 0.450 -0.001

0.850 1.021 0.260 -0.003

0.875 0.555 0.112 -0.003

0.900 0.193 0.029 -0.002

0.925 0.026 0.002 -0.000

0.950 0.000 0.000 -0.000

0.975 0.000 0.000 -0.000

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE X

J(x) J(x) J(-x)

0.500 1.705 2.019 -0.009

0.525 1.792 1.960 -0.014

0.550 1.884 1.889 -0.015

0.575 1.980 1.808 -0.011

0.600 2.074 1.719 -0.006

0.625 2.157 1.624 -0.002

0.650 2.217 1.519 0.001

0.675 2.245 1.402 0.004

0.700 2.232 1.273 0.005

0.725 2.150 1.129 0.006

0.750 2.050 0.970 0.006

0.775 1.864 0.795 0.004

0.800 1.608 0.609 0.002

0.825 1.287 0.420 -0.001

0.850 0.921 0.246 -0.003

0.875 0.550 0.109 -o.db3

0.900 0.240 0.029 -0.002

0.925 0.057 0.002 -0.000

0.950 0.003 0.000 -0.000

0.975 0.000 0.000 -0.000

44
Table 1, Energy Dissipation Function, J(x), and Input Data - Continued

STOPPING POlffiR (dE/dr)„ = 1.82 Mev(cm2/g)

RESIDUAL RANGE

= 0.U3 g/omOTHER PARAMETERS

= 0.8767 A^ = 0.4222 a = 3.391 A2 = 0.884.7 A^^= 0.6288 A^ = -0.4664

A^^^= 0.7565 A, = 0.1595

SCATTERING COEFFICIENTS

I H

1 0.6770

2 1.908

3 3.608

4 5.726

5 8.224

6 11.08

7 14.26

8 17.75

9 21.54

10 25.60

11 29.93

12 34.51

POLYSTYRENE

E = 1.00

0 Mev

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

J(x) •J \ ILJ 0.000 1.000 1.110 0.110

0.025 1.003 1.142 0.081

0.050 1.008 1.176 0.054

0.075 1.016 1.212 0.030

0.100 1.026 1.253 0.010

0.125 1.039 1.300 -0.005

0.150 1.054 1.357 -0.012

0.175 1.072 1.424 -0.010

0.200 1.093 1.496 -0.003

0.225 1.117 1.566 0.003

0.250 1.143 1.634 O.OOP

0.275 1.172 1.698 0.013

0.300 1.204 1.758 0.017

0.325 1.239 1.812 0.020

0.350 1.278 1.860 0.021

0.375 1.319 1.899 0.021

0.400 1.364 1.928 0.020

0.425 1.412 1.943 0.016

0.450 1.463 1.943 0.009

0.475 1.517 1.925 0.001

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) ij V Ay

0.500 1.575 —U.UU/

0.525 1.636 1.836 -0.013

0.550 1.70C 1.770 -0.014

0.575 1.766 1 .o9d r\ r\'\ 1 —U.Uli

0.600 1.834 1.D14 —U.UU/

0.625 1.900 1.526 -0.003

0.650 1.962 1.430 0.001

0.675 2.013 1.324 U.UUJ

0.700 2.042 1.206 0.0C5

0.725 2.032 1.0/4 U.UUD

0.750 1.963 0.928 0.005

0.775 1.818 0.767 0.004

0.800 1.582 0.594 C.002

0.825 1.253 0.416 -0.001

0.850 0.854 0.249 -0.003

0.875 0.450 0.113 -0.003

0.900 0.150 0.031 -0.002

0.925 0.023 0.003 -0.000

0.950 0.006 0.000 -0.000

0.975 0,010 0.000 -0.000

STOPPING POUER

(dE/dr)g = 1.79 Mev(cmVg)

o RESIDUAL RAJIGE r =1.00 g/cm^

o

^ OTHER PARAMETERS

= 0.8960 A^ = 0.3442

a = 1.370 A^ = 0.9492

A^'^-^= 0.5780 = -0.4675

A^^^= 0.6926 A^ = 0.1740

SCATTERING COEFFICIENTS

I H

1 0.5179

2 1.477

3 2.814

4 4.492

5 6.486

6 8.779

7 11.35

8 U.19

9 17.29

10 20.63

11 24.20

12 28.00

E = 2.00

0 Mev

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) J(x)

0.000 1.000 1.058 0.058

0.025 1.000 1.074 0.043

0.050 1.002 1.092 0.02^

0.075 1.006 1.112 0.015

0.100 1.011 1.136 0.004

0.125 1.018 1.165 -0.005

0.150 1.027 1.203 -0.009

0.175 1.038 1.251 -0.009

0.200 1.050 1.305 -0.005

0.225 1.064 1.378 -0.002

0.250 1.080 1.410 0.001

0.275 1.098 1.461 0.003

0.300 1.118 1.510 0.006

0.325 1.140 1.556 0.008

0.350 1.164 1.599 0.009

0.375 1.191 1.637 0.010

0.400 1.220 1.669 0.010

0.425 1.251 1.693 0.010

0.450 1.285 1.708 0.008

0.475 1.322 1.710 0.005

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X

J(x) J(-x)

0.500 1.361 1.698 0.001

0.525 1.403 1.669 -0.004

0.550 1.448 1.623 -0.008

0.575 1.495 1.562 -0.010

0.600 1.544 1.490 -0.008

0.625 1.594 1.412 -0.005

0.650 1.644 1.326 -0.002

0.675 1.688 1.233 0.001

0.700 1.720 1.131 0.003

0.725 1.725 1.017 0.004

0.750 1.687 0.889 0.005

0.775 1.589 0.748 0.004

0.800 1.415 0.593 0.002

0.825 1.157 0.430 0.000

0.850 0.823 0.269 -0.002

0.875 0.461 0.131 -0.003

0.900 0.167 0.040 -0.002

0.925 0.026 0.004 -0.000

0.950 0.001 0.000 -0.000

0.975 0.001 0.000 -0.000

45
Table 1. Energy Dissipation Fiinction, J(x), and Input Data - Continued

STOPPING POi^

(dE/dr)TM =1.84 Mev(cmVg)

RESIDUAL RANGE

= 2.10 g/om^

OTHER PARAMETERS' = 0.9138 A^ = 0.2982

a = 0.6231 A^ = 0.9289

A^'^^= 0.4952 A =-0.3859

PT P A = 0.5886 A^ = 0.1588

SCATTERING COEFFICIENTS I S^

1 0.3508

2 1.006

3 1.927

4 3.092

5 4.394

6 6.093

7 7.909

8 9.922

9 12.13

10 14.51

11 17.08

12 19.82

POLYSTYRENE

E =4.00 Mev

0 POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x)

0.000 1.000 1.025 0.025

0.025 0.999 1.030 0.019

0.050 0.999 1.036 0.014

0.075 1.000 1.045 0.009

0.100 1.002 1.056 0.005

0.125 1.006 1.070 0.001

0.150 1.010 1.090 -0.002

0.175 1.015 1.117 -0.002

0.200 1.021 1.150 -0.002

0.225 1.028 1.183 -0.001

0.250 1.036 1.217 -0.000

0.275 1.046 1.251 0.000

0.300 1.057 1.285 0.001

0.325 1.069 1.320 0.001

0.350 1.082 1.353 0.002

0.375 1.097 1.386 0.002

0.400 1.114 1.418 0.002

0.425 1.132 1.447 0.003

0.450 1.152 1.472 0.003

0.475 1.173 1.493 0.002

POINT PLANE

ISOTROPIC PERPENDICULAR

SOURCE SOURCE

X J(x) «V —

/

0.500 1.197 1.508 0.002

0 526 1 223 1.514 0.001

0.550 1.250 1.509 0.000

1.280 1.490 -0.001

0.600 1.312 1.454 -0.002

0 62'5 1 '3Z.6 1.401 -0.003

0.650 1 "381 1.331 -0.003

0 676 1 /.T8 1.250 -0.002

0.700 1.453 1.160 -0.000

0 73*5 J. .<(,0<f 1.060 0.001

0 7*50 X . ^wX 0.949 0.002

0 77'? 1X .£fO A87r 0.824 0.002

0.800 i.ao 0.684 0.002

0.825 1.230 0.528 0.001

0.850 0.933 0.363 -0.000

0.875 0.560 0.203 -0.001

0.900 0.224 0.077 -0.001

0.925 0.044 0.013 -0.000

0.950 0.002 0.000 0.000

0.975 0.000 0.000 0.000

E = 10.00 Mev

0 STOPPING POV/ER (dE/dr)E =1.94 Mev

RESIDUAL RANGE

= 5.26 g/cm^

OTHER PARAMETERS

= 0.9486 Aj_ =

a = 0.2341 Ag =

0.3688 A^ =

0.4265 A, =

aPti=

aPI'P=

0.2476

1.040

-0.6041

0.3168

SCATTERING COEFFICIENTS

X 0.000

0-.025 0.050

0.075

0.100

0.125

0.150

0.175

POINT

SOTROPIC SOURCE

1.000

0.999

0.999

0.999

1.000

1.001

1.003

1.006

I 0.200 1.008

1 0.1799 0.225 1.011

2 0.5194 0.250 1.012

3 1.001 0.275 1.013

4 1.614

5 2.352 0.300 1.015

6 3.209 0.325 1.017

7 4.182 0.350 1.019

8 5.265 0.375 1.021

9 6.457

10 7.754 0.400 1.024

11 9.153 0.425 1.028

12 10.65 0.450 1.033

0.475 1.040

PLANE PERPENDICULAR

SOURCE

POINT ISOTROPIC SOURCE

J(x) J(x) J(-x) J<x)

1.008

1.009

1.011

1.013

0.008

0.007

0.006

0.005

0.500

0.525

0.550

0.575

iiot?

1.078

1.100

1.017

1.022

1.028

1.035

0.004

0.003

0.002

0.001

0.600

0.625

0.650

0.675

1.128

1.159

1.192

1.225

1.044

1.054

1.065

1.078

-0.000

-0.001

-0.002

-0.002

0.700

0.725

0.750

0.775

1.257

1.285

1.305

1.310

1.092

1.108

1.125

1.143

-0.001

-0.001

-0.001

-0.001

0.800

0.825

0.850

0.875

1.289

1.22S

1.102

0.889

1.162

1.182

1.202

1.224

-0.000

0.000

0.000

0.001

0.900

0.925

0.950

0.975

0.577

0.229

0.024

0.000

PLANE PERPENDICULAR

SOURCE

J(x)

1.245

1.266

1.287

1.305

1.319

1.328

1.328

1.316

1.286

1.233

1.152

1.042

0.910

0.761

0.596

0.413

0.227

0.074

0.006

0.000

J(-x)

0.001

0.001

0.001

0.001

0.001

0.001

0.001

.0.000

-0.001 -0.002

-0.003 -0.002

0.000

0.002

0.003

0.002

-0.001 -0.002

-0.000

0.000

46
Table 2. Spatial Moments, Plane Isotropic Source

n p=-l/2 ^ /n y2 5/2 7//> '/2 »/2 '/2

025 23

0 0«200623E 01 0>&63423E 00 0>398403E-00 0.284237E-00 0.220907E -00 0.180648E-00 0.152797E'-00

2 0.207134E-00 0.353090E -01 0.128270E-01 0.613529E-02 0<341688E -0 2 0.209981E-•02 0.138322E -02

4 0.554574E-01 0.665209E'-02 0.179023E -02 0.659319E-03 0.291312E -0 3 0.145455E-•03 0.793759E -04

6 0.203295E-01 0tl90310E'-02 0.410774E -03 0.124023E-03 0.457380E -04 0.193494E-04 0.906069E -05

8 —03 n.l 7'^l "^CiF •03 0.316172E-04 —04 0.369538E-•05 n«l*i1cazi.flF'-0 5

1

0

V t CO ^ 1 J ±L, "03 —04 0.980682E-05 —0 5 0.893686E-06 -06

12 •03 n . 1 7 An ? ft F — 04 0.349565E-05 —Q 6 0.255850E-•06 n^A/iARQI U*0HO07X^F'"07

ME V = 0« 07 Z- 0 •

0 0 0.195082E 01 0(676671E 00 0»ifl2986E -00 0.297812E-00 0.233046E'-00 0.191482E-00 0.162529E'-00

2 0t200989E-00 0.364758E'-01 0.137752E'-01 0.676858E-02 0.384528E -02 0.239959E-02 0.160O09E--02

4 0.536731E-01 0.690895E'-02 0.195421E -02 0.7474O0E-03 0.340233E -03 0.174055E-•03 0.969176E'-04

6 0tl959«lE-01 0.i97824E'-02 0.452009E'-03 0.142820E-03 0.546787E -04 0.238712E-04 0.il4826E^-04

8 0.706352E'"03 0.367520E-04 A«l 71HAAF

Int 0.465632E-05 n . 1 o77nAF. 10 U • 'U # / *fr / t 0.290559E'-03 —04 0. 114620E-04 n - 3'5Sfl71 Fi \J » D 3J O 1 IC 0.114313E-•05 n./i.QCR7nF.~06

12 0tl3210'tE'-03 -04 0.409748E-05 -0 5 0.330825E-06 lA.'so'aF. u • i l*f J V jJ

c

-06

0*10 Z = •

0 0 0<19e330E 01 0.670026E 00 0.404333E'-00 0.289734E-•00 Ot226809E -00 0.185014E-•00 0.156713E^-00

2 0.208707E-00 0.362987E-01 0.133567E'-01 0.644678E-02 0.361474E'-0 2 0.223311E-02 0.147723E^-02

4 0>&65488E-01 0.692826E'-02 0.189422E'-02 0.706300E-03 0.315200E'-03 0.158682E-03 0.871933E--04

6 0.20S796E-01 0tl99788E'-02 0.438975E'-03 0. 134514E-03 0.502319E -04 0.214793E-04 0.101517E--04

g 0.717894E'-03 0.132406E'-03 0.345695E-04 —04 0.415208E-05 n.l 77AA2F'-05

1 n 1 u 0.296977E'-03 0.472980E' 0.107789E-04 —0 5 05 n.U • '37A^RnF. J f 07 O U L -06 0.135706E-03 0.190424E'—04 0.385476E-•05 —0 6 0 • 29 1667E-06 n«Qfil77flF' V m 7 Q X 1 IOC -0 7 MEV3 0 • 20 Z = 6«

0 0 0el96614E 01 0.673518E 00 0.408867E'-00 0.293959E-00 0«229569E'-00 0.188389E-00 0.159745E'-00

2 9t208310E-0O 0,368629E-01 0.137127E'-01 0.666916E-•02 0«376064E'-02 0.233345E-02 0. 154901E--02

4 0.56664&E-01 0.707560E-02 0.196121E'-02 0.739035E-•03 0.332597E'-03 0.168598E-03 0.931771E^-04

6 0.209639E-01 0.204653E--02 0.456729E'-03 0.141740E-•03 0.534919E^-04 0.230790E-04 0.109920E'-04

3 0» 9147^1E~02 0.736484E-03 0.138155E-03 0.365888E-•04 -04 n.Z..A.OA7 7F —'05 -05

10 0 « ^^4^9 11E"'02 0.304840E-03 0.494290E'-04 0. 114406E-•04 -0 5 U • i 1 1 4L~"0 5 0 • 414468E*-06

12 0*232330£~02 0.139289E--03 0.199145E'-04 0.409837E-05 0»105592E'-0 5 '06 Otl08611E^-06

HE V = 0 • 40 Z

= 6>

0 0 0«19369&E 01 0.679556E 00 0.416776E'-00 0.301370E-00 0.236247E'-00 00 0.165115E^-00

2 0.207728E-00 0,378685E-01 0. 143514E'-01 0.707140E-•02 0.402638E^-02 0.251725E-02 0.168114E^-02

4 0.570670E-01 0.736060E--02 0.208820E'-02 0.801071E-03 0.365690E^-03 0.187550E-03 0.104667£^-03

6 0.212698E-01 0»214846E-02 0.492294E'-03 0.156075E-03 0.599568E'-04 0.262600E-04 0.126697E'-04

6 0.933468E-02 0.778572E-03 0.150292E'-03 0.407707E-•04 0 • 135722E'-04 0.520584E-05 0.221945E--05

10 0«4551i4E-02 0.324045E-03 0.541621E'-04 0.128676E-04 0t376705E^-0 5 0.129462E-05 0«495360E^-06 12 0»239109E-02 0.148731E-03 0.219492E'-04 0.464441E-05 0.1 22645E'-05 0.378596E-06 0, 131545E--06

0, 70 Z = 6 •

0 0 0.16S794E 01 0<689981E 00 0.43064eE -00 0.314500E-•00 0.248124E'-00 0.205044E- 00 0.174782E--00

2 0.205297E-00 0,394641E -01 0.154562E -01 0.779301E-02 0.451406E--0 2 0.286008E-02 0.193067E--02 4 0ib7ia54E-01 0.781980E -02 0.231200E -02 0.915316E-03 0.428453E^-0 3 0.224297E-03 0.127342E--03

6 0»21&602E-01 0>231680E -02 0.556385E -03 0.183165E-03 0.725907E'-04 0.326416E-04 0.161086E--04

3 0.849804E -03 0.172641E -03 0.488608E-04 0.168616E-04 0.667180E- 05 n-7077RRF--0 5 10 0«469773E'"02 0.357313E -03 0t630519E -04 Ot 156866E-04 0.460490E'-05 0.170122E- 05 n*A71S1flF--06 12 0*248636E-02 0tl65449E -03 0.258421E -04 0.574361E-05 0.156373E-05 0.50e058E- 06 V u J, O £. -0 6 MEVa 1< 00 Z= 6»

0 0 0tl63977E 01 0.700595E 00 0.445051E -00 0.328306E-00 0.260727E-00 0.216466E- 00 0tl85162E--00

2 0«202286E-00 0.410641E'-01 0«166306E -01 0,85a396E-02 0.506017E-02 0.325033E- 02 0.221848E--02 4 0.570851E-01 0.829187E'-02 0.255706E -02 0.104529E-02 0.501924E-03 0.268309E- 03 Oil55022E--03

6 0«21769eE-01 0.249421E'-02 0.628434E'-03 0.214957E-03 0.879253£^-04 0.406066E- 04 0.205042E--04

3 0.926540E'-03 0. 198337E -03 0.586055E-04 0«209760E-04 0.856511E- 05 "05

1 n 0«393849E'-03 0.734754E -04 0.191584E-04 0.611089E-05 0.224176E- 05 0«913156E--06 0.184127E'-03 0»304a57E -04 C.712373E-05 0.205235E-05 0.684509E-06 0 • 2 549 IBE"-06

MEV« 2* 00 Z =

0 0 0«16&^56£ 01 0.736579E 00 0.496049E -00 0.378611E-00 0.307593E-00 0.259600E- 00 -00

2 0. ia9832E-00 04464625E'-01 0.210603E -01 0.117631E-01 0.735947E-02 0.495445E- 02 0.351326E--02 4 0.553143E-01 0.990914E'-02 0.352464E'-02 0.160502E-02 0.839901E-03 0.481925E- 03 0.295569E--03

6 0«217104E-01 0i311271E'-02 0.923544E'-03 0.359467E-03 0.163541E--03 0.826386E- 04 0.450919E--04

a 0»99682^E-02 0. 119e48E-02 0.306839E'-03 0.104899E-03 0.424534E--04 0.192703E-04 0.952003E--05 10 0.505878E-02 0.525255E'-03 0.1ie637E'-03 0.362749E-04 0.132632E--04 0.548194E- 05 0.24ai85E--05 12 0.27&556E-02 0.252211E-03 0.510573E'-04 0.141477E-04 0.472665E--05 0.179683E- 05 0.75222aE--06

47
Toble 2. Spotial Moments, Plane Isotropic Source — Continued

n p=-l/2 1/2

7Vz V2 3/2

MEV = 00 Z =

0 O.lSlTCtE 01 0i78330OE 00 0« 567490E 00 0« 452743E -00 0»379255E -00 0> 327453E -00

2 OtlTSitOlE-OO -01 0 • 284224E -01 0. 1752iyE -01 0.118231E -01 0. 845708E -02

4 0.536'»25E-01 0.125918E -01 0 • 534768E -02 0. 278311E -02 0. 162094E -02 0. 101666E -02

6 0.220'.20t-01 0.'t22722E -02 0 153779E -02 0. 70207i£ -03 0.364277E -03 0. 205ei9E -03

8 0. 105517t-01 0.172299E -02 0 • 552072E -03 0. 22b029E -03 0. 106431E -03 0. 550514E -04

10 0» i562't3c-02 0»793759E -03 228121E —03 0 • 849866E -04 A 1 1 t f\ i. C —04 0 « 176029E — 04

12 0« 313770E-02 0»39e'*76£ -03 0. 1040b3E —03 0. 356 32 1 £ -04 A 1 A O A 1 /. C 0 • 14 jU^4t —0 4 0 • 638771E — 05

MEV = 10< 00 1

= 6 •

0 0.131270E 01 0«830168E 00 0 • 680953E 00 0« 579212E 00 0«508263£ 00 0 • 454913E -00

2 0. 1559'.3E-00 0.682'.16£ -01 0, 431202E -01 0. 305003E -01 0.229145E -01 0. 179008E -01 0.512't65E-01 0.17a329E -01 0« 967636E -02 0. 605345E -02 0.409141E -02 0. 290878E -02

6 0.226702E-01 Oa6671'teE -02 0« 322119E -02 0. 183102E -02 0.113e48£ -02 0. 750981E -03

a 0.116375E-01 0.2993'.0E -02 0» 131213E -02 0. 688322E -03 0.398903E -03 0. 246943E -03

10 n £ /. D c r _A T -02 0« 6061 1 ^ £ —03 296468E -03 9^ 5 738E — Qij 12 -03 0* -03 0 4 140390E-03 -04 0 • "T W 4 7 V Ofc>

mev= 0* 025 Z«13 •

00 0* ^Qfl 1 1 P ^ 7 U 1 wX C -00 0 • 276646E-00 U*^XH107C —00 174667E — yy

2 O.lSlO't'.E-OO 0.26969SE -01 0* 100702E -01 0. 490342E -02 0.276502E -02 Oa 171482E -02

* 0.301676E-01 0>390208E -02 0 • 110239E -02 0. 420086E-03 0. 190391E -03 0. 969603E -04

6 0.856798E-02 0»87£361E -03 0 • 201491E -03 0. 635733E-04 0«242509E -04 0. 105396E -04

8 0.296188E-02 0.252766E -03 o» 489806E -04 0. 132303E-04 0»43&98e£ -05 Oa 166067E -05

1

0

U403HU2 it -Oi, 0* 143590E -04 339694E-05 A_OQAo"7*^C U*77UO (!Jt -06 0 -06

1

2

y • !>U3^0*^t v3 -04 0. 4ai525E -05 n*• 1C1455E-05 -06 0 • 808429E -07

MEV = 0> 05 Z = 13 •

0

n 1AQAC'7C Al UftlvoUsfc 01 0.670578E 00 0 • 405047E-00 0 • 290399E-00 0.226403E -00 0 • 185544E -00

2 0.1'.i»237E-00 0.2756275 -01

A* 107315E-01 0. 537920E-02 0.309902E -02 0. 195399E-02

<» 0.262923E-01 0.395'.26E -02 0 • 117931E-02 0. 46e200E-03 0.219179E -03 0. 114599E -03

6 0.788767E-02 0>878980E -03 0 • 214536E-03 0. 711238E -04 0.282572E -04 0. 127076E -04

8 0.267656E-02 0.2'»9209E-03 0 • 516923E-04 0. 147654E-04 0.511241E-05 0. 202318E -05

10 0« 103406E~02 0.829032E -04 0* 149865E -04 0 • 376e06£-05 0.115824E -05 0 • 409936E -06

12 0«'»38749E~03 0.309'.03E -04 0 • 496351E-05 0* 111598E -05 0.30a789E-06 Oa 989538E -07

MEV = 10 1

= 13 •

0 0«198161E 01 0.670368E 00 0« 404776E-00 0« 290147E-00 04226177E -00 0> 185342E-00

2 0 • 146022E~00 0.278011E -01 0* 107991E -01 0 • 540427E--02 0.310972E -02 0 • 195892E -02 0.288370E-01 0.'t01017E-02 0* 119195E-02 0. 472056E-03 0.220571E -0 3 0< 115158E-03

6 0.8072'tOE-02 0.89'»2'»6E-03 0« 217362E-03 0. 718395E-04 0.284736E-04 0« 127806E-04

8 0.27'»59'.E-02 0.253993E-03 0* &24374E-04 0. 149249E-04 0.515314E -05 0. 203466E -05

10 0.106227E-02 0.645683E -04 0* 152067E-04 0. 3e0881£-05 0.116707E-05 0. 411990E-06

12 0.'f509SilE-03 0.315657E-0it 0* 503610E-05 0. 112746E-05 0.310888E-06 0. 993416E-07

11^2

Oi288689E-00

0.630584E-02

0.672671E-03 0.123733E-03 0.305046E-04

0.907878E-05

0>308e58E-05

0.412875E-00

0.143801E-01

0.214480E-02 0.517044E-03

0.160386E-03 0.583467E-04

0.237363E-04

0il47<>48E-00 0.113752E-02

0.537560E-04

0.504572E-05 0.701182E-06

0.126677E-06

0.276991E-07

0.157189E-00

0.131334E-02 0.649416E-04

0.626382E-05

0.884914E-06 0.161399E-06

0.354584E-07

Otl57008E-00

0.131568E-02 0.651802E-04 0.528995E-05

0>888262£-06 0.161857E-06

0.355116E-07

MEV= 0.20

0 0.196899E 01 0.672936E 00 0. 408108E -00 0.293251E-00 0.228954E -00 0. 187822E- 00 0.159235E -00

2 0.146858E-00 0.282834E -01 0. 110631E -01 0.556312E-02 0.321259E -02 0. 202934E- 02 0.136601E -02

4 0.292205E-01 0.411316E -02 0. 123302E -02 0.491523E- 03 0.230870t -03 0. 121054E- 03 0.687649E -04

6 0.821866E-02 0.921919E -03 0. 226242E -03 0.753583E- 04 0.300634E -04 0. 135694E- 04 0.671034E -05

8 0.280425E-02 0.262719E -03 0. 54e013E -04 0.157344E- 04 0.547370E -05 0. 217552E- 05 0.955305E -06

10 0.108691E-02 0.876569E -04 0. 159367E -04 0.402910E-05 0.124493E -0 5 0. 442765E- 06 0.175H5E -06

12 0.461912E-03 0.327586E -04 0. S28603E -05 0. 119540E- 05 0.332619E -06 0. 107159E- 06 0.385920E -07

MEV = 0.40 Z = 13.

0 0.193635E 01 0.679681E 00 0. 416941E -00 0.301525E-00 0.236386E -00 0. 194477E- 00 0.165228E -00

2 0.147251E-00 0.293022E -01 0. 116914E -01 0.596068E-02 0.347761E -02 0. 221430E- 02 0.150005E -02 4 0.297308E-01 0.433772E -02 0. 133306E -02 0.541517E-03 0.258190E -03 0. 137048E- 03 0.786518E -04

6 0.845498E-02 0.96499bE -03 0. 248660E -03 0.847212E-04 0.344369E -04 0. 157911E- 04 0.791580E -05

8 0.291013E-02 0.283540E -03 0. 609966E -04 0.179663E- 04 0.638735E -0 5 0. 258676E- 05 0.U5471E -05

10 0.113599E-02 0.953750E -04 0. 179177E -04 0.465794E-05 0.147446E -0 5 0. 535669E- 06 0.215901E -06

12 0.485642E-03 0.35tt826E -04 0. 599229E -05 0.139605E- 05 0.398775E -06 0. 131513E- 06 0.483693E -07

MEV = 0.70 l- 13.

0 0.187981E 01 0.691746E 00 0. 433023E -00 0.316764E- 00 0.250183E -00 0. 206905E- 00 0.176469E -00

2 0. 146628E-00 0.309853E -01 0. 128202E -01 0.670338E- 02 0.398536E -0 2 0. 257520E- 02 0.176531E -02

<> 0.302548E-01 0.471874E -02 0. 151811E -02 0.638412E- 03 0.312868E -03 0. 169848E- 03 0.993286E -04

6 0.875637E-02 0.109522E -02 0. 291370E -03 0.103493E- 03 0.435351E -04 0. 205489E-04 0.105598E -04

8 0.305865E-02 0.320925E -03 0. 731157E -04 0.225748E- 04 0.835180E -0 5 0. 350039E- 05 0.161012E -05

10 0.120931E-02 0.109582E -03 0. 218859E -04 0.599017E- 05 0.198224E -0 5 0. 7486a5E- 06 0.312329E -06

12 0.522856E-03 0.417679E -04 0. 743783E -05 0.183096E- 05 0.548839E -06 0. 188911E- 06 0.721932E -07

48
Table 2. Spatial Moments, Plane Isotropic Source — Continued

n 1/2 3/2 5/2 9/2 11/2

MEV = 1 • 00 Z = 13 •

= 0 0 0.182231E 01 0.704d39E 00 0.333553E-00 0.265546E-00 0.220853E-0O 0.189164E-00

2

n ^ 5 7 a '^ne •J • J« 1 -01 A»1»A1 1 1 1F~A7 A- 7AQn7AF—A7

4 0.305702E-01 0.512369E -02 0.173089E-02 0.755215E-03 0.361105E-03 0.211923E-03 0.126461E-03

6 -02 U.^o9383t— U4 U. 142249t U4

8 0.318603E-02 0«3623S2E -03 0.377958E-04 0.285036E-04 0.110013E-04 0.478198E-05 0.227082E-05

10 0.127528E-02 0.123&98E -03 0.267912E-04 0.774726E-05 0.268762E-05 0.105787E-05 0.457731E-06

12 0.557496E-03 0«483042E -04 0.925672E-05 0.241700E-05 0.762668E-06 0.274703E-06 0.109331E-06

MEV = 2 .00 2 = 13

0 0 0.167676E 01 0.739576E 00 0.500452E 00 0.383056E-00 0.311804E-00 0.263525E-00 0.228488E-00

z -01 n»i.S07')l7F«-fl7 h 0.317096E-01 0.645579E'-02 0.248215E-02 0.119390E-02 0.651216E-03 0.386159E-03 0.243305E-03

6 0.163376E'-02 AU«30Diy7t~U*t - CiL&l OOFkAZi U.^2Uwl9t U4

a 0.363200E-02 0.514562E'-03 0.146902E-03 0.544688E-04 0.235091E-04 0.112521E-04 0.581382E-05

10 0.i51186E-02 0il869S6E'-03 0.475634E-04 0.159122E-04 0.625337E-05 0.274463E-05 0.130794E-05

12 0.6a4319E-03 0.753012E'-04 0.173055E-04 0.528451E-05 0.190997E-05 0.775567E-06 0.343609E-06

MEV = 4aOO Z'13

0 0 0.150159E 01 0.787877E 00 0.574821E 00 0.460590E-00 0.387016E-00 0.334933E-00 0«29S827E-00

2 Oi464647E-01 A - fiAQ7<t7P*A7 U* out) / W£ U*OlA4Z7t U2 0.331942E-01 O.B82940E-02 0.403105E-02 0.220652E-02 0«133540E-02 0.863653E-03 0«386106£-03

6 O.H0345E-01 0.243461E'-02 A Q 7 7 ^ O Q c n a 0. 4764 8 7 E—03 0 • 933312E'**04

8 0t435153E-02 0.£i37b63E--03 0.297896E-03 0. 131682E-03 0.658744E-04 0*358163E-04 0.207039E-04

10 0.191754E-02 0.326544E-03 0. 105281E-03 0.427361E-04 Otl98007E-04 0»100343E-04 0*54332l£-05

12 0.914927E-03 0.140016E--03 0.413833E-04 0. 155664E-04 0#673228£-05 0.320202E-05 0«16342&E-05

MEV=10..00 2

== 13

0 0 0.129644E 01 0.656174E 00 0.691847E 00 0.591925E 00 0«&2168eE 00 0*468 &47E-00 0«424465E-00

2 0. 130406E-00 0.615027E-01 0.403513E—01 0 a 1 ^A7? 1 F—0

1

W • A 4** t & * b V A

<f 0.358792E-01 0.139454E-01 0.803401E-02 0.524067E-02 0.365803E-02 0.26A966E-02 0.201231E-02

0.134213E-01 0.452050E-02 0.235675E-02 U • 7 lO JO^C U J A.^A&I U*4^9Hvc.~U3 10P_A^

8 0.589135E-02 0.176588E-02 0.846984E-03 0.474291E-03 0.289414E-03 0.186988E-03 0.125M4E-03

10 0.2a6321E-02 0.776773E-03 0.346458E-03 0.182493E-03 0.105479E-03 0.64S669E-04 0«4l7M9E-04

12 0.149531E-02 0.371636E-03 0.155339E-03 0.774461E-04 0.426287E-04 0r25073SE-04 0*154«4«E-04 MEV 0<i025 2"29.

0 0 0«21«9^7E 01 0>63^19E 00 0.360036E-00 0.249416E-00 0.190304E-00 0.153676E-00 0«128804E-00

2 0.996314E-01 0«16940aE-01 0.618359E-02

h 0.131741E-01 0.165209E-02 0.459264E-03 0.173260E-03 0.779974E-04 0.395361E-04 0.2184**E-04

6 0>261674E-02 0.262912E-03 0.594974E-04 0» 185793E-04 0.702894E-05 0.303451E-05 0» 144491E-05

e 0.6»7843E-03 0.554368E-04 0.1062 3E-04 0.283690E-03 0.927317E-06 0*349098E-06 0.146167E-06

10 0.193843E-03 0.1411 ;9E-04 0.234' 76E-05 0.549354E-06 0.158273E-06 0.528662E-07 0.197616E-07

12 0«M1671E-04 0.412 18E-05 0.60 ;781E-06 0.126494E-06 0.326097E-07 0.979522E-08 0.330834E-08

MEV- 0> 05 Z"29<

0 0 0t203129E 01 0.-S0473E 00 0.392086E-00 0.278414E-00 0.216735E-00 0.176055E-00 0.14S688E-00

2 0*846634E-01 0.168327E-01 0.678815E-02 0.900419E—03

't 0.101974E-01 'i.l53258E-02 0.48423eE-03 0.201378E-03 0.979357E-04 0.528703E-04 0.307e86E-04

0.iad200E-02 ;j.226240E-C> 0.593475E-04 O.4O73OOE—05

8 0»427152E-03 0.442080E--04 0.995816E-05 0.3''4015E-05 0.11125,0E-05 0.4614e2E-06 0.2102S5E-06

10 0.115815E-03 0.104336E-04 0.206502E-03 0.558605E-06 0.182480E-06 0.680232E-07 0.2801S5E-07

12 0«353668E-04 0.282725E-05 0.499959E-06 Ool21603E-06 0.35922''E-07 0.121723E-07 0«45783SE-08

MEV-- 0« 10 z« 29i»

0 0 0»201498E 01 0.663686E 00 0.396179E-00 0.282183E-00 0.219080E-00 0.179024E-00 0.1S1343E-00

2 0.822757E-01 0.167139E-01 0.68ia46E'

<> 0,969035E-O2 0,149053E-02 0.47870-' "js 0.201583E-03 C.990235E-04 0.539022E-04 0*3160''7£-04 0.172055E-02 0.215478E-03 0.5758971. -04 0*911 ~j^9E~04

8 0.38798eE-03 0.412166E-04 0.9475a4E-05 0.294210E-05 0.109216E-05 0.458704E-06 0.2-X2eiE-06

10 0.102871E-03 0.952165E-05 0.192605E-05 0.530688E-06 0.176141E-06 0.665847E-07 0.i77662E-07

12 0.307274E-04 0.252569E-05 0.4fe6992E-06 0.113361E-06 0.340708E-07 0.117231E-07 0.447056E-08

MEV. Oi 20 z- 29.t

0 0 0.198355E 01 0.669973E 00 0.404267E-00 0.289673E-00 0.225754E-00 0.184965E-00 0.156&69E-00

2 0.806730E-01 0.169690E-01 0.706935E-02 0.372680E-02 0.223266E-02 0.145239E-02 0.100146E-02

4 0.94362eE-02 0.150941E-02 0.497904E-03 0.213928E-03 0.106773E-03 0.588807E-04 0.349066E-04

6 0.166107E-02 0.216913E-03 0.597770E-04 0.218430E-04 0.940569E-05 0.452821E-05 0.236705E-05

8 0,370971E-03 0.4116a6E-04 0.978755E-05 0.312321E-05 0.118643E-05 0.508271E-06 0.238194E-06

10 0.973453E-04 0.942574E-05 0.197610E-05 0.561018E-06 0.191054E-06 0.738611E-07 0.314179E-07

12 0<287&34E-04 0.247603E-05 0.465168E-06 0.119145E-06 0.368228E-07 0.129868E-07 0.506299E-08

49
Toble 2. Spotiol Moments, Plone Isotropic Source — Continued

n p=-l/2 1/2 Vz V2 9/2 / ^

MEV- 0*40 Z- 29 •

0 0 0.19'»377E Oi 0.&78134E 00 00 0.299613E- 00 0.234665E-00 0. 192933E- 00 0«163836£- 00

2 0,807058E-01 0.176946E- 01 0.755310E- 02 0.404847E- 02 0.245524E-02 0.161240E- 02 0.112025E- 02 0.160539E- 02 03 0.240007E-03 n . A A ? 11 1 F — V » OO £. ^ 3 xC 04 0.409435E- 04

6 0.170655E-02 0.23398'tE- 03 0.667792E- 04 0.250794E- 04 O.UO^S'fE-O'f 0.541726E- 05 0.287752E-05

6

n . "sn tt.iA. 1 A c — n 'A W • JO t u J 0,ttB60bZ- 0^ 0*11 DA&kF- 04 0.364917E- 05 06 0.297816E- 06

10 0.101558E-03 0.103596E- Oh 0.226239E- 05 0.664481E-06 0.232963E-06 0.923745E- 07 0.401822E- 07

12 OtSOlbSSE-O** 0.273872E- 05 0.537052E- 06 0.142652E-06 0.455052E-07 0.165039E- 07 0.659689E- 08

MEV = 0. 70 2 = 29 •

0 0 0.188348E 01 0.69051'.E 00 0.431365E- 00 0.3151.82E-00 0.248745E-00 0.205605E- 00 0.175290E- 00

2 0.813055E-01 0.189550E- 01 0.838471E- 02 0.460502E- 02 0.284356E-02 0.ie9376E- 02 0.133065E- 02 0f996169E'"02 0.1786it3E- 02 0.635590E- 03 0.288856E-03 Oil50668E-03 0«861210E- 04 0.526060E- 04

6 0.181938E-02 0.268300E- 03 0.806377E- 04 0.315300E- 04 0. 143479E-04 0.723496E- 05 0.393471E- 05

6 0a'tl88'»'tE-03 0.527576E- Oh 0.137934E- 04 0.475303E- 05 0.192562E-05 0.871723E- 06 0.428619E'-06

10 0.112761E-03 0.12<t397E- Oh 0.288673E- 05 0.891563E-06 0.326288E-06 0.134307E- 06 0.603825E- 07

12 0.3<»0616E-0'> 0.335052E- 05 0.700382E- 06 0. 196351E-06 0.656365E-07 0.248086E- 07 0.102887E-07

M£V = 1.00 Z<>29«

0 0 0.182812E 01 0.703219E 00 0.448657E-00 0.331791E-00 0.263926E-00 0.219377E-00 0.ie7816E -00

2 0.817533E-01 0.202903E-01 0.930545E--02 0.523912E-02 0.329553E-02 0.2226eOE-02 0.158312E -02

it 0.103283E-01 0.198668E-02 0.739939E-03 0.347898E-03 0.186389E-03 0.108897E--03 0.677511E -04

6 0.193513E-02 0.307521E-03 0.974657E--04 0.397076E-04 0.186852E-04 0.969129E--05 0.539951E -05

0 0.455'tl3E-03 0.t20579E-Oh 0.171958E-04 0.620847E--05 0.261580E-05 0.122455E--05 0.619968E -06 10 0,125019E-03 0.149609E-04 0.369509E-05 0.120140E-05 0.459370E-06 0.195437E-06 0.913410E -07 12 0 • 38't329E-04 0.«10960E-05 0.917469E-06 0.271824E-06 0.953161E-07 0.375769E-07 0.161811E -07

MEV = 2. 00 z- 29 •

0 0 0.167823E 01 0.739201E 00 0.499899E-00 0.382497E-00 0.31i274E-00 0.263030E-00 0.22802aE-00

2 0.835772E-01 0.246550E- 01 0.124760E-01 0.751944E-02 0.497948E-02 0.350465E-02 0.2S7621E-02

0»115887E-01 0.270781E-02 0.114223E-02 0.589076E-03 0.339622E-03 0.210789E-03 0.138021E-03

6 0.234902E-02 0.<t60^26E-03 0.168465E-03 0.767389E-04 0.395653E-04 0.221668E-04 0.132000E--04

Q 0«592132E~03 0.100587E-03 0.326786E-04 0. 133999E-04 0.627919E'~05 0.322103E-05 0.176665E--05 10 0.172851E-03 0.260051£-0't 0.762307E-05 0.285131E-05 0.122828E-05 0.582725E-06 0.297051E--06 12 0.561913E-04 0.760516E-05 0.203558E-05 0.701440E-06 0.280184E-06 0.123884E-06 0.591026E--07

MEV = ht 00 z» 29 •

0 0 0,149518E 01 0.789798E 00 0.577916E 00 0.463916E-00 0.390316E-00 0.338120E-00 0.298875E--00

2 0.862193E-01 0.322005E-01 0.185875E-01 0.122910E-01 0.874185E-02 0.651889E- 02 0.502901E--02 0.416983E-02 0.207707E-02 0.121260E-02 0.520865E-03 0.366259E--03

6 0.309853E-02 0.812827E-03 0.360649E-03 0. 190685E-03 0.111142E-03 0.691255E-04 0.450861E--04

Q 0.86299'tE-03 0.199720E-03 0.803840E-04 0.390628E-04 0.122406E-04 0.748151E-05

10 0.275566E-03 0.572869E-04 0.211766E-04 0.955434E-05 0.482620E-05 0.263112E-05 0.151769E--05 12 0.972393E-04 0.183979E-0'> 0.630392E-05 0.266063E-05 0.126489E-05 0.651950E-06 0.3S6802E--06

MEV=10« 00 z« 29 •

0 0 0»12a370E 01 0.860967E 00 0.700630E 00 0.602247E 00 0.532648E 00 0.479729E- 00 0.437653E--00 2 0.92096<tE-01 0.'t7405'fE-01 0.326040E-01 0.244578E-01 0.192215E-01 0.155727E- 01 0.128968E- 01 0.180872E-01 0.799009E-02 0.495631E-02 0.341245E-02 0.18e029E-02 0.146109E- 02

6 0.'»96602E-02 0.195283E- 02 0.1H742E-02 0.719047E-03 0.493373E-03 0.353227E- 03 0.260868E- 03

8 0.163932E-02 0.5853tlE- 03 0.312812E-03 0.190020E- 03 0.846082E- 04 0.59ei61E- 04

10 0.610969E-03 0.200692E- 03 0.100997E- 03 0.583044E-04 0.363136E-04 0.237926E- 04 0.16ie02E- 04

12 0.2'f«663E-03 0.7Se668E- 04 0.361751E-04 0.199466E-04 0.119233E-04 0.752331E- 05 0.493993E- 05 MEV = 0. 05 Z = 50.

0 0 0.211954E 01 0.6<>3694E 00 0.371104E-00 0.259326E-00 0.198934E-00 0.161231E-00 0>135490E-00

2 0.657000E-01 0.123535E-01 0.484113E-02 0.245494E-02 0.143179e-02 0.913340E- 03 0.620441E- 03 0.610643E-02 0.870923E-03 0.267379E-03 0.109232E-03 0.281186E- 04 0.162837E- 04

6 0.882671E-03 0,1027'»2E-a'3 0.261691E-04 0.901196E- 05 0.370317E-05 0.171620E- 05 0.869128E- 06

6 Ot 165809E-03 0. 164108E-0it C.358895E-05 0.107203E- 05 0.157859E- 06 0.711381E-07

10 0.372759E-04 0.322182E-05 0.619234E-06 0.163696E-06 0.524763E-07 0.192548E- 07 0.782418E- 08

12 0.957510E-05 0.736<>62E-06 0.1265a4E-06 0.300484E-07 0.869734E-08 0.289509E- 08 0.107201E-08

MEV = 0. 10 Z»50 •

0 0 0.206696E 01 0.653575E 00 0.383376E-00 0.270443E-00 0.208691E-00 0.169821E- 00 0.143126E- 00

2 0.58860'tE-Ol 0.11789'»E- 01 0.480885E- 02 0.250900E- 02 0.149522E-02 0.970175E- 03 0.668235E-03

if 0.5035'»eE-02 0.772687E- 03 0.249928E- 03 0.106290E-03 0.527669E-04 0.290244E- 04 0.171916E- 04

6 0.671967E-03 0.846850E- 04 0.229124E- 04 0.828367E- 05 0.354430E-05 0.169993E- 05 0.886783E- 06

8 0.116840E-03 0.125775E- 04 0.293975E- 05 0.927912E- 06 0.349903E-06 0.149137E- 06 0.696441E- 07

10 0.2<t3686E-0'. 0.229e82E- 05 0.474477E- 06 0.133241E-06 0.450062E-07 0.172898E- 07 0.731798E- 08

12 0t581877E-05 0.'.d9851E- 06 0.907249E- 07 0.229879E-07 0.704258E-08 0.246560E- 08 0.955220E- 09

50
Table 2. Spatial Moments, Plane Isotropic Source — Continued

D=-|/9 / t 3/? /

1

5/9 / ^ / ^ 9/2 11/2

MEV = 0<i2C Z =^50 •

c 0.20ia97E SI 0.feo2398E 00 0.395172E -00 0.281254E-00 0.218255E -00 0.178291E -00 0.150687E--00

2 CSalifSTE-Ol Oa 116695E -01 0»492287E'-02 0»262969E—02 0«159510E -02 0»104945E -02 Oi /3101 ft "03

1* 0.i.52350E-02 0t739115E -03 0.249685E -03 0. 109743E-03 0.559286E -04 0.314334E -04 0>189588E'-04

6 0.579002E-03 0.7tj0S83E -04 0.222154E -04 0«835840E-05 0t369575E -0 5 0«182244E -05 0 • 973638E'-06

C a 96bl67E-0^ Ctlll701E -04 0.275912E -05 0i911258E-06 0«357022E -06 0.157267E -06 0.755853E'-07

10 0» 193'»92E-0't 0. 19o575E-05 0.430482E'-06 0.127045E-06 0.447867E -07 C.178604E -07 0>7ei358£'-08

12 0«i>43693E-03 0.403319E -06 0.795103E -07 0.212496E-07 0.681999E -08 0.248799E -08 0<100003E'-08

MEV = 0. 40 Z =^50 •

0 0.19606e£ 01 0.674639E 00 0.410328E -00 0.295324E-00 0.230813E -00 Oil89483E -00 O1I6O73OE'-00

2 — 01 "02 u* 1 ly su ic —02 U«ii7 1 lot — 02 -03 0»43S57iE-02 0.769632E -03 0.272686E'-03 0.124176E-03 0.650711E -04 0.374099E -04 0.229944E'-04 G«ol2866E ~04 —0 5 U* ^^JU04L — 05 U* 122191t'-05

S C. 92'h9't3E-0it 0.115844E -04 0.303927E'-05 Ot 105390E-05 0t430089E -06 0. 196178E -06 0.971900E'-07

10 C.18363eE-0<f 0.202650E -05 0.473365E -06 0.147373E-06 Of 543780E -07 0.225629E -07 0.102221E'-07

12 C.i,17223£-05 C.412643E -06 0.870680E'-07 C,246440E-C7 0.831279E -0 8 0.316839E -08 0<132422E'-08

MEV = 0. 70 Z

= 50 •

0 0al88633E 01 0>6902e6£ 00 0.431057E.-00 0.314890E-O0 0.248479E'-00 0>203364E -00 0.175072E'-00 0.598760E'-02 "ft 0 — n 5 "02 C.450't72E-02 0.864804E'-03 0.324840E'-03 0.154425E-03 0>836886E'-04 0.494447E -04 0.310913E--04

6 0 • 58744'f £—03 0 • :'4i435t -04 0.302626E'-04 U« 123i94L—04 -0 5 0« 314519E -05 0 • 1 77 533t'"05

6 0.992870C-04 0.137491E'-04 0.388414E'-05 0. 142900E-05 0.612625E -06 0t291443E -06 0.149758E'-06 iO 0.200526E-04 0.245479E'-05 0t620705E'-06 0.206232E-06 0«80ifl79E'-07 0.350049E'-07 0.165421E--07

12 C.462383E-05 C.508623E'-06 0.116672E-06 0.354156E-07 0.126889E'-07 0.509944E'-08 0.223419E--08

MEV= 1. 00 Z = 50 •

0 0.182016E 01 0t703028E 00 0.451152E'-00 0.334208E-00 0.266149E'-00 0.221403E'-00 0«lS9666E-00

2 0»536072£~01 -01 0.676105E-02 ft . 0 64QR7F'—02 -02 0il272*4E-"02

<» Oa469954E-02 0.979837E'-03 0.388001E-03 0. 191744E-03 0.107121E'-03 Oi648768E'-04 0.416502E-04

C«631781E-03 0« 110616E'-03 0.377907E.-04 0« 163844E—04 0«812906E'-05 0 • 441436E'-05 0.256094E-05

8 0.109639E-03 0.16&3e2E'-04 0t5O3272E'-05 0.195318E-05 0.375396E'-06 0«432564E'-06 0.229737E-06

10 0a226675E-04 C.305452E'-05 0.830089E-06 0.292508E-06 0«119888E'-06 0.544909E -07 0.267503E-07

12 0.533797E-05 C.&4S013E'-06 0.160413E-06 0.518768E-07 0.196272E'-07 0.827416E'-08 0.37827'iF--na

MEV = 2« 00 2 = 50 •

0 0.166229E 01 0.743289E CO 0.505939E 00 0.388619E-00 0. 31709 0£'-00 0.268463E'-00 0.233085E-00

2 0.177901E'-01 0.941511E-02 U • 3o / £3 J t~U2 0.399784E-02 U • ZoIt^IL'-02 0.215871E--02

<t 0.554613E-02 0.142079E--02 0.639671E-03 0«347359£-03 0.209028E'-03 0.134t566E'-03 0.909600E-04

6 U • 0£0£ r O c U

J

0.180549E'-03 0.715387E-<)4 0»347490E~04 0.189103E-04 U » 1 1 1 UOUC'-04 0>6<85eeE--05

8 0.157029E-03 0.301202E-04 0.107200E-04 0.473557E-05 0i236377E'-05 0.128091E'-05 0t737*15E-06

10 0.352365E-04 0<604830£'-05 0.196107E--05 0.797090E-06 0.368629E'-06 0.1B6067E'-06 0>100210E-06

12 0.894329E-03 0.139298E-05 0.415794E-06 0.156869E-06 0.677315E'-07 0«320631E'-07 0.142548E-07

M£V = 4« 00 Z« 50 •

0 0.147129E 01 0.797057E 00 0.589712E 00 0.476666E-00 0.403018E'-00 0.350432E-00 0>310682E-00

2 0 • 6043 SbE—0

1

Ot244225£'-01 0.147884E--01 0.7%1759E'-02 0<56&533E'-02 0.446090E-02

4 0.704963E-02 0.239096E'-02 0il27496E-02 Ot784646E-03 0.521921E-03 0.365321E-03 0t265324E--03 0.121655E-02 0.360559E--03 0.173800E-03 0»980988E—04 0.603830E-04 0.393625E-04 0i267563£-04

6 0.263396E-03 0.698191E-04 0.308944E-04 0.161936E-04 0.932378E--05 0.571517E-05 0.366782E-05

10 0.663068E-04 0.160149E-04 0.657447E-05 0.322799E-05 0»175164E-05 0.101643E-05 0<619664E-06

12 OtlB8108E-0'f 0.416192E-05 0.159766E-05 0i739569E-06 0.380376E-06 0.210013E-06 0.122194E-06

MEV=10« 00 Z«50 •

0 0.12S340E 01 0i872687E 00 0i722447E 00 0.628176E 00 0«560420E 00 0.508263E 00 0<466373E-00

2 0.691817E-01 0t3b958fiE--01 0.281765E-01 0»219391E-01 0.177696E-01 0.147676E-01 0>125030E--01 4 0.106504E-01 0i529093E-02 0.352000E-02 0.255667E-02 0»194688E-02 0.152929E-02 0.12288eE--02 6 0.234724E-02 0.105830E-02 0.659050E-03 0»452881E-03 0.328258E-03 0.246446E-03 0.189831E--03

8 0.633232E-03 0.263255E-03 0.154970E-03 0. 101557E-03 0.705565E-04 0.509503E-04 0t3784«7E--04 10 0.195631E-03 0.758088E-04 0.424,738E-04 0«2&6945E-04 0.178652E-04 0.124654E-04 0.a96770E-05

12 0.669040F-04 0.243809E--04 0.130781E-04 0«792272E-05 0.513129E-05 0.347468E-05 0.243123E--05 KEV = 0. 10 Z = 82

0 0<21339eE 01 0.637042E 00 0.362973E-00 0.252034E-00 0.192578E--00 0.15W63E-00 0.130559E-•00

2 C.414345E-01 0f762347E--02 Ct310S13E-02 0.160132E-02 0.948747E-03 0.614243E-03 0i423010£-•03 0.24847e£-02 0.361457E--03 C.113903E-03 0.478044E-04 0.235856E--04 0.129462E-04 0.767128E-05

6 0.240327E-03 C.288851E--04 0.762417E-05 0.271958E-05 0.115560E--05 0.552679E--06 0<288240E-06

a C.311030E-04 0.321144E-05 0.733694E-06 0.228559E-06 0.855548E-07 0.363336E'-07 0.169484E-07

10 C.493435E-03 C.448808E--06 0.907413E-07 0.251646E-07 0.843635E-08 0.322722t-08 0.136331E-•08 12 C.912627E-05 0.744238E--07 0.135318E-07 C.338876E-06 0.103045E--08 0.359067E-09 0.138741E-•09

51
Table 2. Spatial Moments, Plane Isotropic Source — Continued

n 1/? It 3/? 5/? /

1

9/9 11/9

MEV = Oa 20 2 = 82

0 0«208503E 01 0.65014 IE 00 Ot379085E -00 0t266540E -00 0»205256E -00 0. 166792E -00 0> 140429E -00

2 043579<flE-01 0.73193'.E -02 0.305595E -02 0. 163054E -02 0.991963E -03 0.655821E -03 0.459453E -03

h 0.192109E-02 0.306302E -03 0. 102961E -03 0.453997E -04 0.233028E -04 0. 132160E -04 0.805073E -05

6 Ot 166777E-03 0.221426E -04 0.629961E -05 0.238635E -05 0> 106586E -0 5 0.531799E -06 0«2B7680£ -06

6 0.19<»256E-0'» 0.222825E -05 0.553039E -06 C.lb4513£ -06 C.732142E -07 0.327026E -07 0.159456E -07

10 Q.278030E-05 0«282167E -06 0.623668E -07 0. 186514E -07 0 •667502E -08 0 • 2 70442E -08 0» 120227E -08

12 0><t6'>950E~06 0»42't621E -07 0>34a229E -08 0.230386E -08 0«752316E -09 Ot279325£ -09 0 • 1 14254E -09 M£V = Ot 40 2 = 82

0 0 0.200135E 01 0.666398E 00 0«399654E -00 0»285394£ -00 0.221937E -00 0« 181564E -00 0>153619E -00

2 0.328'»01£-01 0.733518E -02 0.324162E -02 0.179503E -02 0.112254E -0 2 0.758280E -03 0>540553£ -03 0,168246E-02 0.297491E -03 0 • 107209E -03 0i497892E -04 0i266201E -04 0.156080E -04 0.977624E -05

6 0.139326E-03 0.206778E -04 0.637633E -05 0.257265E -05 0.120976E -0 5 0.630230E -06 0.353757E -06

8 0. 154738E-0'» 0.199540E -05 0.541229E -06 0. 194040E -06 0.817767E -0 7 0.384619E -07 0«196154E -07

10 0.211138E-05 0»241952E -06 0.588189E -07 0 1 190388E -07 0t729033E -08 0.313277E -08 Oi 146691E -08

12 0.336599E-06 0»348270E -07 0.769281E -08 0.227507E -08 0>799866£ -09 0>316962£ -09 0« 137402E -09

M£V = 0. 70 zoaz •

0 0 0.190429E 01 0.6U6462E 00 0.425935E -00 0.310020E -00 0»244060£ -00 0.201378E -00 0.171461E -00

2 0.317921E-01 0.791503E -02 0.370649E -02 Q.213839E -02 0.137824E -02 0>953063£ -03 0>692326E -03

h 0. 16'i978£-02 0t328727E -03 0« 127998E -03 0«629108E -04 0a351542E -04 0«2 13623E -04 0«137B49E -04

6 0.137813E-03 0.232506E -04 0.783967E -05 0.338812E -05 0.168422E -05 0.918967E -06 0.536574E -06

8 0. 153900E-04 0i227O0O£ -05 0.679365E -06 0.263410E -06 0.1 18464E -06 0«588845E -07 0<315048£ -07

10 0.210611E-05 0.277345E -06 0.749275E -07 0»264360E -07 0« 108885E -07 0>498350£ -08 0<246640£ -08

12 0.401029E -07 0.990174E -08 0.321299E -08 0 • 122333E -08 0«519821E -09 0«239751E -09

MEV = 1, 00 Z»82

0 0 0>181863E 01 0.705370E 00 0«451625£ -00 0.33466eE -00 0«266572E -00 0<221789£ -00 0>190018E -00

2 0.315889E-01 0.tj&3861£ -02 0.427977E -02 0.256099E -02 0.169580E -02 0«119761E -02 0.884910E -03 0.169680E-02 0.376899E -03 0.157176E -03 0.812126E -04 0.471855E -04 0.295962E -04 0«196104E -04

6 0.145990E-03 0>276802E -04 0.101026E -04 0.463831E -05 0.242100E -0 5 0.1375B9E -05 0>831804E -06

6 0.167264E-04 0>27e880E -05 0.910832E -06 0.378356E -06 0»180141E -06 0.939919E -07 0»524503E -07

10 0.234107E-05 0»350034E -06 0. 103876E -06 0.395406E -07 0«173618E -0 7 0.839768E -08 0«4362e5£ -08

12 0«381039E~06 0«318154E -07 0 • 141294E -07 0.497580E -08 0*203182E -08 0.917824E -09 0t446939E -09 MEV= 2a 00 Z»82

0 0 0.165215E 01 0.745919E 00 0«509848E 00 0.392598E-00 0«320882E -00 0.272013E-00 0.236395E -00

2 0.337757E-01 0.11253OE -01 0.&18643E -02 0.397881E-02 0.278011E -02 0.204818E-02 0>1566S0£ -02 0»21009eE-02 0a3U124&E -03 0.277055E -03 0.157715E-03 0»988444£ -04 0.659546E-04 0.460 345E-04

6 0.206011E-03 0.494502E -04 0.210500E -04 0.108571E-04 0.622450E -05 0.382647E-05 0.247449E -05

8 0»263638E-0^ 0.567501E -.05 0.219634E -05 0.104140E -05 0«552968E -06 0.316611E-06 0.191556E -06 10 O.'fl'tS^SE-OS 0«80116SE -06 0.285406E -06 0,125678E -06 0.623546E -07 0.335144E -07 0.191055E -07

12 0.745462E-06 0.132073E -06 0.437048E-07 0.180105E -07 0.840556E -08 0>426649E -08 0i230422E-08

MEV = 4« 00 Z=82 •

0 0 0al'>49<»2E 01 0«8038S9E 00 0.600905E 00 0.488873E-00 0.415259E-00 0«362359E -00 0<322168E -00

2 0.376061E-01 0.163267E-01 0.103370E-01 0.733190E-02 0.552182E -02 0«432214£ -02 0.347740E -02 0.28b659E-02 0.107738E-02 0.612198E -03 0.396305E -03 0.275136E -03 0.199917E-03 0.150109E -03

6 0.340194E-03 0.112925E -03 0.588505E-04 0.353791E-04 0.229827E-04 0.157092E -04 0.111414E -04

a 0.517003E-0't 0.155679E-04 0.753816E-05 0.425300E-05 0.260884E-05 0.169120E-05 0.114140E -05 10 0«936000E~03 0.259106E-05 0.117620E-05 0.627381E--06 0«365729E -06 0<226153E-06 0.146012E-06

12 0«193120E-05 0.496270E-06 0.212607E-06 0.107804E-06 0.600109E-07 0.355512E-07 0.220456E--07

MEV = 0* 025 Air

0 0 0.201025E 01 0.664624E 00 0.397379E -00 0.283291E-00 0.220065E -00 0.179899E-00 0.152127E -00

2 0.191918E-00 0.332702E -01 0.122010E -01 0.587097E -02 0.328322E -02 0.202376E-02 0«133619E -02 0.'t791aOE-01 0.589477E -02 0.161166E -02 0.600080E-03 0.267288E -03 0.134293E-03 0»736496E -04

6 0.165278E-01 0.159400E -02 0.350845E-03 0.107433E-03 0<400500£ -04 0. 170e92E-04 0.805872E -05

8 0.679527E-02 0.541449E -03 0.100143E -03 0.261361E-04 0>e40485£ -05 0.312581E-05 0.129633E-05

10 0.31309'tE-02 0.213050E -03 0.340512E -04 0.775836E -05 0.219746E-05 0.725411E-06 0.268871E -06 12 0« 156476E-02 0.930497E -04 0.131104E -04 0.265363E -05 0.672254E -06 0.199697E-06 0«669673£ -07

M£V = 0» 05 Air

0 0 0»196193£ 01 0.674383E 00 0.409994E-00 0.295011E -00 0.230532E-00 0.189232E-00 0.160504E-00

2 0.186748E-00 0.341924E -01 0.129702E-01 0.6J8905E -02 0.363530E-02 0.227088E -02 0.151534E -02 0.464103E-01 0.607313E -02 0.173417E-02 0.667327E-03 0« 3050e6E -0 3 0.156567E-03 0.873901E--04

6 0. 159093E-01 0.163909E -02 0.379187E -03 0. 120819E-03 0.465378E -04 0.204114E-04 0.985433E--05

8 3.649552E-02 0.554481E -03 0.108275E -03 0.295539E-04 0.987124E-05 0.379295E-05 0.161839E--05 10 C.297072E-02 0.21701&E -03 0.367447E-04 0.879046E-0? 0.259683E-05 0.889427E-06 0.340589E--06

12 0. 147334E-02 0.942065E -04 0. 140989E-04 0.300584E -05 0.796944E-06 0.246491E-06 0.857022E -0 7

52
Table 2. Spatial Moments, Plane Isotropic Source — Continued

p P '/2 1 /o 72 3/0 5/2 '/2 y 2

11/4 "/Z

0 •1 1

0

Ai'r

0 00 UaHU? /7UC —00 U • £ 7 1 UC"wU 0«^c IU21 L—UU w • 1 eoU 7 7C — 00 u« 19 roo4t —00

2 0. 191636E-00 0»3'f3062E -01 0. 128361E -01 0.626377E-02 0.353951E-02 0.219937E -02 0«146147E -02

<* 0.614250E -02 0.172244E -02 0.653941E-03 0.29b843E-a3 0.150545E -03 0.8 34449E -04

6 0.16675itE-Ul 0»166879E -02 0.37B026E -03 0. 118499E-03 0.450466E-04 0.195426E -04 0.934806E -05

8 0.68&7ieE-02 0«5b763IE -03 0.108312E -03 0,290232E-04 0.954706E-05 0.362126E -05 0.152804E -05

1

0

—03 — 04 O * 9 m 07aF—0 0 . n A7AO Rp — 06 U# j£WHjWL "06

X 2 — 04 W* ±*r ±9 J C.C —04 W»^757y^t \iO n . 7 7 0A0AF—OA 0« 9 3AR9A.P'— 06 OV .• ROAOAAFi OU*fvHO t —0 7 MtV- 0 • 20 Mil Air

0 1^ 00 — 00 0.w«i75i'0UC 9o^QflOF—onwU O-99QA07P —O A OU

.•1X AOOQ AOAF *rUOL —00 Oil U 4 X97KO7A0P' 1 owe —00

2 0. 192't97E-00 0.348191E -01 0.131132E -01 0t642847E-02 0.364509E-02 0.227104E -02 0.1S1234E -02

<t 0.'»67*61E-01 0.627951E -02 0.177502E -02 0.678131E-03 0.308336E-03 0.157556E -03 0<876366E -04

6 0.169338E-01 0.171391E -02 0.391767E -03 0.123727E-03 0.473315E-04 0<206449E -04 0i992161E'-05

8 0.698299E-02 0.584757E -03 0.112674E -03 0.304464E-04 0.100886E-04 0.385129E -05 0«163435E'-05 10 -03 n ^ "xa /.c. J c, c

,

U • ^a*tOc PL'—04 w»7UVOlOL—U5 J • i004U3L.—y 3 A A A C T Q O P . U • 9Ut} r 03t -06 0 • 34* / wVt'-06

12 -03 n iziQiOAP —04 0»312244E—05 0 • 8 19959E—06 0*251 586E -06 0 • 8&6774E'-07

MEV = 0« 40 Air Air

0 Q 00 U^fi i*tucst —00 U • 30 ly o3 t~00 0 • 2 Jo7o 3 1—00 Q* 194833E -00 0* 169548E'-00

2 0.1921't5E-00 0.3538HE'-01 0.137837E -01 0.685147E-02 0»392527E-02 0«246&30E -02 0<165228E'-02 0.'t9212tE-01 0.65643'fE'-02 0.190210E -02 0.740609E-03 0»34l880E-03 0«176a76£ -03 0.994075E'-04

6 0.172<f23E-01 0.1810<f3E -02 0.425645E'-03 0.137517E-03 a.5360e6E-04 0.237593E -04 0.11S762E'-04

8 0.715799E-02 0.622651E'-03 0.123704E'-03 0»342930£-04 0»11614lE-04 0.431833E -05 0<194947E'-05

1

0

n » 5 ZlA AQ 1 P "03 —04 0. 1 0'3*i*;ft F—OZi O A ^ 1 O A7 AP —O (^ O - 1 070 1 <iF . U • X U f 7

1

—— Oc; UP 0<418&«3E -06

12 O. 1 ASil f^ZiP.—04 nU*700^^0u aOAActonP —ouoA — OAUo 0«107053E-06

MEV= 0« 70 Air

0 0 U • bO U U J 3

1

00 A./ii 7/in(iP. U • *f 1 / *f UO f"00 U t jU 1 703 1—UO U* l74'039C'"00 0.1&»54eE-00

2 0.192922E-00 0.359868E'-01 0.138157E'-01 0.686464E-02 0.393170E-02 0*246883£--02 0.16543eE-02

0.494984E-01 0.659264E'-02 0.190863E'-02 0t742722E-03 0.342714E-03 0.1772&3E'-03 0<99»95SE -04

6 0.173535E-01 0.181893E'-02 0.427196E'-03 0*l37922E-03 0.537399E-04 0#23e087£'-04 0.11S970E-04

8 0.720't20E-02 0.625464E'-03 0.124116E'-03 0t343e0lE-04 0.n6370E-04 0.432&31E--05 0.195185E'-05

1

0

n . 9 ft 7 7 P ."03 0.426815E--04 U» IUj »H/t— U*t A « Q 1 1 A A A P kA K y» lw79y It'-05 0.41S712E'-06

^2 0.10865'fE'-03 0.165461E'-04 OU

.

• O700P AAA 5ULOP—OAwO 0«303445E'-06 0.106979E--06

ME V' 00 Air

Q Q 0.70't500£ 00 0.450422E-00 o.^'^'i^oi F—no O M. 9ASAQfiP—OO 0«220810E'-00 0.189124E--00

2 0.186279E-00 0.394339E-01 0.163580E-01 0.857957E-02 0.511664E-02 0.331589E-02 0.227919E--02 0.491333E-01 C.753406E'-02 0.240526E'-02 0. 100805E-02 0.493388E-03 0<267803E'-03 0>136682E--03

6 0.176428E-01 0.21't872E-02 0.564296E-03 0.199120E-03 0.834817E-04 0.393432E-04 0i202076E--04

8 0.747898E-02 0.759373E-03 0.170240E-03 0.521291E-04 0.192050E-04 0.803377E-05 0.36932SE-05

10 0.3529't3E~02 0.308074E-03 0.604069E'-04 0« 163798E-04 0«539574£-05 0«203424E-05 0«848437E--06

12 0, 179791E-02 0.13784'tE-03 0.240552E-04 0»5e6199E-05 0* 174894E~05 0«601042E-06 0»229760E-06

MtV* 2 • 00 Air

0 0 u • loo / 5**t u i 0.741988E 00 0.504011E 00 U • JOOOO£ c uu 0>266723E-00 0<231#«3E--00

2 0.175920E-00 0.451362E-01 0.210061E-01 0.119437E-01 0.757135E-02 0.514951E-02 0i36ai86E--02

4 0.482984E-01 0,919118E-02 0.339463E-02 0.158825E-02 0.84e698E-03 0.495263E-03 0.308041E-03

6 0.179694E-01 0.275856E--02 0.856301E-03 0.344746E-03 0.16H13E-03 0.832369E-04 0.462794E--04

8 0.785902E-02 0.101717E-02 0.273960E-03 0.973710E-04 0.406685E-04 0.189545E-04 0.957903E-05

1

0

U • 3o 1 J / IE U2 0.427968E--03 0.102121E-03 0 • 1 t34S5t—'04 0.525785E-05 0.244307E-05

12 U • l7 7^^ It U£ 0tl97714E'-03 0.424296E-04 A. A 97(il 7P •O H 0.167964E-05 0«723715E-06

4*00 Air

Q 0 0*148027E 01 0.794306E 00 0.5B5224E 00 f)Wv?7wXWX& . 9 OA 1 A 1 F —onWW 0.345717E-00 0.30615*E-00

2 0.161451E-00 0.540810E--01 0.293733E-01 0.186297E-01 0.128445E-01 0.934763E-02 0.707019E--02 0.<f67705E-01 0,120556E-01 0.541884E-02 0.293889E-02 0.176809E-02 0.113892E-02 0.770775E-03

6 0,182931E-01 0.389930E-02 0.151819E-02 0.729354E-03 0.394250E-03 0.230518E-03 0»142721E--03

8 0.836919E-02 0.153215E-02 0.529941E-03 0.230075E-03 0.113651E-03 0.612196E-04 0«351381E-04

1

0

0.423029E-02 0.681277E-03 0.212814E--03 0 .RAA007P—OA O . OftA97RP—OA 0il93612E-04 0.103950E-04

12 0.229413E-02 0.330549E-03 0.943643E-04 0 > "^^AR 7 R F —OA. O * 1 A.7K7 5F—0 A 0.693291E-05 0>390486E-0$

MEV=10. 00 Air

0 0 0>12'>0'»2E 01 0.877859E 00 0.732230E 00 O.A'aOOaAF OA U«7 /J1^7C Uw 0«521417E 00 0.479696E-00

2 0.137570E-00 0.708955E-01 0.488896E-01 0 • 368079E—01 0»290469E—01 0.2363&4E-01 0<19«606E-01 0.427443E-01 0.182523E-01 0.111437E-01 0.760442E-02 0«551207E-02 0<415678E-02 0«322583E-02

6 0.179803E-01 0.668055E--02 0.371383E-02 0»234723E-02 0»l59134E-02 0.112997E-02 0.829778E-03

8 0.881183E-02 0.292446E-02 0.150375E-02 0.B91152E-03 0«5710it4E-03 0.386353E--03 0.27O032E-03

10 0.'t75029£-02 0.143243E-02 0.688493E--03 0.385811E-03 0.235381E-03 0.15195ie-03 0«10222SE--03 12 0.27't325E-02 0.761565E--03 0.345134E-03 0. 184204E-03 0*l07696E-03 0.669143E-04 0.434715E-04

53
Table 2. Spotial Moments, Plane Isotropic Source — Continued

n 1/2 V2 V2 9/2 11^2

MEV« Oa 025 Polystyrene

0 0»2010&0E 01 OaSbifSSSE 00 0a397290E -00 Oa283208E -00 0a219992£ -00 0al79834E-00 0al52069£ -00

2 0.219909E-00 0.366989E -01 0al31708E -01 0a625006E -02 0a346145E -02 0a211840E--02 0«139101E -02 0.620303E-01 0.722793E -02 Oa 190943E -02 0a694030E -03 0.303631E -03 Oa 130436E-03 0adl5831E -04

6 0.238070E-01 0.2153B2E -02 0a<.549dlE-03 Oal35100E -03 0.491790E -04 0a205874E-04 0a955671E -05

8 0,107687E-01 0.e01132E -03 0.1'tl356E -03 0a356101£ -04 0alll353£-04 0a404741E-05 Oa 164657E -05

10 0.541218E-02 0.342490E -03 0a52O289E-04 0all4034E -04 Oa313079E -0 5 0al00715E-05 0.363195E -06

12 0«29306'tE-02 Oa 161373E -03 0a215769E -04 0a419007£ -05 Oa 102638E -0 3 0a296425£-06 Oa970360E -07

MEV = Ot 05 Polystyrene

0 0il9S33^E 01 0«676108E 00 0a4122't8E -00 0a297120E -00 0a232425£ -00 0al90926E-00 0al62028E -00

2 0. 212687E-00 0>378800E -01 Oal41550E-01 0,690776£ -02 0a390552£ -02 0a242849£-02 0al61489E -02

it 0.597297E-01 0.74902BE -02 0.208407E -02 Oa 7e7901£ -03 Oa355577£ -0 3 Oa 180677E-03 Oa 100058E -03

6 0.228004E-01 0.22331'.E -02 Oa500116E -03 Oal5570BE -03 0a589341E -04 0a254926£-04 0al21693E -04

a 0.102519E-01 0.82770&E -03 Oa 155796E -03 0.413994E -04 0al35435E -04 0a511769E-05 0a215361E-05

10 0.512015E-02 0.352473E -03 0.373485E -04 0.133205E -04 0a384498£ -0 5 0al29231£-05 0a487115E -06

12 0.275469E-02 Oa 163319E -03 0.237468E -04 0a490524E -05 Oa 126840E -05 0a384336E-06 0al31336E -06

MEV = 0« 10 Polystyrene

0 0«198d31E 01 0a669579E 00 0a403755E -00 0a289198E -00 0a225329£ -00 0al84586£-00 0.156329E -00

2 0»220300E-00 0a37641'tE -01 0al37137E -01 0a657693£ -02 0a367127E -02 Oa226056E-02 0al4913eE -02

It 0.626532E-01 0a7'fU866E -02 0a201586E -02 Oa 7435 15E -03 0a329119E -03 0al64642E-03 Oa900089E -04

6 OtZ'tl'f'taE-Ol 0.22't538E -02 0a484100£ -03 0al46295E -03 0a540459E -04 0a229107E-04 0.107510E -04

8 0.109394E-01 OabSb'i^TE -03 0al51036E -03 0a3880»3£ -04 0al23449£ -04 0a455467E-05 0.187750E -05 10 0.5'»9ei4E-02 0a357784E -03 0a556961£ -04 0al24723E -04 0a348996E -0 5 0.114184E-05 0a4203S4£ -06

12 0«297399£-02 Oa 168677E -03 0.231057E -04 0a459056E -05 0all4782E -0 5 0a337704E-06 0all2424£ -06

MEV» 0< 20 Polystyrene

0 0«196823E 01 0a673091E 00 0aA0831O£-00 0a293439E-00 0.229123E-00 0al87973E- 00 0tl59371£-00

2 0.219506E-00 0.381810E -01 0al40673£-01 0a679966£-02 0a381777E-02 0a236138E- 02 0.156371E--02

It 0.6259*8E-01 0.763043E-02 0a208344£-02 0a776883E-03 Oa346898E-03 0al74775£- 03 0a961173E--04

6 0.241'»50E-01 0a229262E-02 0a502355E-03 0al53821£ -03 0a574507E-04 0a245804E- 04 Oall6263£--04

8 0.109386E-01 0.85'i619E-03 0al57057E-03 0.409575E-04 0al31947E -04 0a492200E- 05 Oa20483&£ -05 10 0.5'»9382E-02 0a365'.91E-03 0.579669E-04 0.131914E--04 0a374345E -0 3 0al24008E-05 0a461594£--06 12 0»296822E-02 0al72161E-03 0a240'»93E-04 0a486053£-05 0al23394£-05 0a36a015£- 06 0.124027£^-06

MEV = 0« to Polystyrene

0 0al937&6E 01 0a679408E 00 Oa416582E-00 0.301188E-00 0a236082E-00 0al94204E- 00 Oal64982E -00

2 0«218261E-00 0.391898E-01 0al47299£ -01 0a722OOO£-O2 Oa409610E-02 0a255401£- 02 0al70220E--02 0»627574E-01 0.792111E-02 0a221757E-02 0a842919E--03 0a382184E-03 0al94978£- 03 0al08354E--03

6 0.2'f3562£-01 0a239909E-02 0.5'.0813E-03 0al69442E-03 0a645026£-04 0a280462£- 04 0al34507E-04

8 0. 110860E-01 0a899668E-O3 0.170507E-03 0a456270£-04 0al50264E -04 0a571325E- 05 0.241794E--05 10 0.558835E-02 0a3865'»lE-03 0.633389E-04 Oa 148236E-04 0a431067E -05 Oa 145905E- 05 0a553598E--06 12 0.302822E-02 0al82768E -03 0a264128£-04 0a549981£-05 0al43360E -05 0a437767E- 06 0al50699E--06

MEVa 0« 70 Polystyrene

0 0«18e873E 01 0a689809E 00 0a430416£-00 0.314279E--00 0a247924E-00 0a204863£- 00 0al74618E--00

2 0.215270E-00 0a407720E -01 0.158417E-01 0a794732£-02 0a458742£-02 0a289910£- 02 0.195315E^02

0i626699E-01 0a838907£-02 Oa244854E-02 0a960810E-03 Oa446810£ -03 0a232721£- 03 0al3138e£^-03

6 0.245756E-01 0a257604E-02 0a608860£-03 0al98154E-03 0a778431E -04 0a347582E- 04 Oal70543E^-04

8 0.1128'f6£-01 0a976854E -03 Oal94914£ -03 0a544359E-04 0al85905£ -04 Oa729358£- 05 0a317261E--05 10 0.573187E-02 0a423645E-03 0.733158E-04 Oa 179747E-04 0a544182E-05 0al90822E- 05 0a747098E--06 12 0.312693E-02 0.201931E-03 0.308969E-04 0a675996E -05 0al84052E-05 0a584229E- 06 0a208233£--06

MEV= !• 00 Polystyrene

0 0.ie'tO'»8E 01 0<700'»36E 00 0.444834E-00 0a328097E-00 0a260535£-00 0a216291£- 00 0al83003£--00

2 0.211703E-00 0.'»23657E-01 0al70285£-01 0a874766£-02 0a51?972£-02 0a329342£- 02 Oa224369E-02

0«623553E-01 0.887136E-02 0.270213E-02 Oa 109529E-02 0a522667E-03 0a278033£- 03 0al60O32£--03

6 0.247074E-01 Oa276277E-02 0a685465E-03 0a231899£-03 Oa940610£-04 0a431500E- 04 0t216689£-04

8 0.114492E-01 0,106003E-02 0a222990£-03 0a650511£-04 Oa230510E-04 0a933610E- 05 0a417573£-05

10 0.586319E-02 .Oa464386E-03 0a850096£-04 0.218542E--04 0a689282E-05 0a250531E- 05 0.101255E-05

12 0.32223'»E-02 0a22332BE -03 0a3624OeE -04 0a834057E-05 0a237375E-05 0a783703E- 06 0a289343E-06

MEV = 2> 00 Polystyrene

0 0«168928E 01 0.736399E 00 0a495786£-00 0a378345E-00 Oa307342E-00 0a259366E- 00 0a224624£-00

2 0» 197669E-00 0.477535E -01 0a215027E-01 Oall9607E--01 0a746158E--0 2 0a501246E- 02 0.354e51£-02

0 • 599089E~0

1

0.105252E -01 0a370237E-02 0al67337E-02 0a870871E--03 0a497573£- 03 0>304123E-03

6 0.2'»3673E-01 0.341351E-02 0a998604£-03 0a384848E-03 0al73778£-03 0a872888E- 04 0a473965E-04

8 0.115575E-01 0al35438£-02 0.341179E-03 0.115282E--03 0a462352E-04 0a208338£- 04 0al02299£--04 10 0.60't3'f7E-02 0.610544E-03 0al3547lE -03 Oa408845£-04 0al47959£-04 Oa606431E- 05 0a272616E-05

12 0.336<tVlE-02 0.301042E-03 0.597951E -04 0al6335eE-04 0a539667E-05 0a203258E- 05 0a844244E-06

54
Table 2. Spatial Moments, Plane Isotropic Source — Continued

n D=- 1 /9 1/9 / c Vz 5/2 1/9 9/9 11,2

MEV= 4« 00 Polystyrene

0 0.151748E 01 0. 783171E 00 0.567284E 00 0. 'f52523E-00 0< 379038E'-00 0.327244E- 00 0>28B489E-00

2

A laiQA'SC _A A U • io IJ U J t wU 0 • &&7602E -01 0.289184E'-01 0 • 17771'tE'-01 Ot 119649E'"01 0» 854434E- 02 0.&36265E'-02 0.57370bE-01 0. 132't2'*E -01 0.557353E'-02 0. 288344E'-02 0. 167210E -02 0.104523E-02 0.689710E'-03

^ 0 • 457095E'-02 0.16't333E'-02 0* 744208E'-03 0 • i9 O J O V X t -03 03 0.12923XE-03

8 0.119923E-01 Oi 191323E -02 0.604591E.-03 0. 245128E-03 0> 114568E'-03 0.589070E- 04 0.324796E'-04

10 0.6*952eE-02 0< 903853E -03 0.255779E-03 0. 942419E-04 0« 404271E'-04 0.192193E- 04 0.9a5495£'-05

i2 0.375781E-02 0> '>64.68 7E -03 0.1193'tlE'-03 0. 403929E--04 0< 160510E'-04 0«711324E- 05 0>341694E -05 MEV=10a 00 Polystyrene

0 0.131041E 01 0« 851004E 00 0.682<t'61E 00 0. 580966E 00 0> 510111E 00 0.456785E- 00 0>41473eE'-00

2 0.158946E-00 0. 6»4258E'-01 0.'f38542E-01 0. 31021tE-01 0« 233106E'-01 0.182148E-01 0«146364E'-01 0.535286E-01 0. lb5185E'-01 0.100261E-01 0. 626536E-02 0* 423216E'-02 0.300793E- 02 0.221759E'-02

6 0.2425ieE-01 0. 707503E'-02 0.340310E-02 0. 193030E-02 0> 119862E -02 0.7899b9£- 03 0<343»61E-03

8 0.127343E-01 0> 32't029E--02 0.141318E-02 0. 739111E--03 0< 427491E'-03 0>264276E-03 0.171*74E--03

XO 0.731976E-02 0. 165969E-02 0.665135E-03 0. 324127E-03 0* 176166E'-03 0.102950E-03 0>634292E'-04

12 0«Vi775'tE-02 0« 918293E'-03 0.3'»1420e-03 0> 156194E-03 0> 802865E'-04 0«446046E-04 0«262294E-04

55
p=-l/2

Table 2. Spatial Moments, Plone Perpendiculor Source

1/2 3/2 5/2 V2 9/2

MEV« 0.025

MEV- 0.05

MEV» 0.10

MEV= 0.20

MEV= 0.<»0

11/2

0 0. 200623E 01 0. 663'>23E 00 0. 398't03E -00 0. 284237E -00 0.220907E -00 0. 180648E -00 0. 152797E-00

1 0. 77587e£ 00 0. 185371E -00 0. 8b6827£ -01 0. 507241E -01 0.334119E -01 0. 237070E -01 0. 177082E -01

2 0. 40369'»E -00 0. 747'»8 IE -01 0. 287182E -01 0. 143033E -01 0 •821343E -02 0. 516994E -02 0. 347193E -02

3 0. 229335E -00 0. 3501<.0E -01 0. 114897E -01 0. 500519E -02 0.255752E -02 0. 145139E -02 0. 8S7905E -03

0. 1'>23&0E -00 0. 184342E -01 0 • 327029E -02 0 « 203848E -02 0.937970E -03 0 * 4d4612E -03 0. 272287E -03

5 0. 920't<i9E -01 0. 103813E -01 0. 263'»27E -02 0. 917319E -03 0.384246E -0 3 0. 182340E -03 0. 9«7a66E -04

6 0. 623239E -01 0. 622012E -02 0. 141788E -02 0. 448735E -03 0.172427E -0 3 0. 756312E -04 0. 365705E -04

7 0. 432490E -01 0. 387725E -02 0. 803079E -03 0. 233087E -03 0.8276476 -04 0. 337604E -04 0. 152630E -04

8 0. 30895*E -01 0. 251355E -02 0. 476938E -03 0. 127801E -03 0.421687E -04 0. 160719E -04 0. 6e2128E -05

9 0. 22'Kf27E -01 0. 167291E -02 0. 293062E -03 0. 729669E -04 0.224929E -04 0. 804692E -05 0. 321890E -05

10 0. 166376E -01 0. ll't't32E -02 0. 18616i.E -03 0. 432825E -04 0.123182E -04 0. 421921E -05 0. 159583E -05 11 0. 124a60£ -01 0. 797676L -03 0. 121189E -03 0. 264364E -04 0.720328E -05 0. 229550E -05 0. 823527E -06 12 0. 951'»41E -02 0. 567480E -03 0. 808b98C -04 0. 166152E -04 0.427937E -0 5 0. 129320E -05 0. 441210E -06

0 0. 195082E 01 0. 676671E 00 0. 412986E- 00 0. 297812E -00 0. 233046E -00 0.191482E- 00 0.162529E -00

1 0. 760494E 00 0. 191484E -00 0. 921155E- 01 0. 548962E -01 0. 366282E -01 0.262398E- 01 0.197468E -01

2 0. 394309E -00 0. 775606E -01 0. 309137E- 01 0. 157929E -01 0. 924108E -0 2 0.590229E- 02 0.401032E -02

3 0. 223980E -00 0. 364855E -01 0. 124927E- 01 0. 561305E -02 0. 293711E -02 0.169870E- 02 0.10S546E -02

4 0. 13e547E -00 0. 192ie8E -01 0. 576276E- 02 0. 231042E -02 0. 109364E -02 0.578218E- 03 0.331179E-03

5 0. 894289E-01 0. 108325E -01 0. 289427E- 02 0. 104896E -02 0. 453771E -03 0.221152E- 03 0.1i7581E-03

6 0. 6033e3E -01 0. 648362E -02 0. 156162E- 02 0. 516276E -03 0. 205608E -03 0.929351E- 04 0.4610S5E -04

7 0. 4i7639E -01 0. 403896E -02 0. 886444E- 03 0. 269600E -03 0. 995276E -04 0.419620E- 04 0.195196E -04

3 0. 297334E -01 0. 261353E -02 0. 526813E- 03 0. 148343E -03 0. 510346E -04 0.201609E- 04 0.8a2780E -05

9 0. 215393E-01 0. 173697E -02 0. 323937E- 03 0. 849627E -04 0. 273776E -04 0.101775E- 04 0.421045E -05

10 0. 159118E-01 0. 118540E -02 0. 205702E- 03 0. 504929E -04 0. 153012E -04 0.537155E- 05 0.210&04E -05

11 0. 119066E -01 0. 824739E -03 0. 133876E- 03 0. 308939E -04 0. 883852E -0 5 0.293995E- 05 0.109565E -05 12 0. 904111E -02 0. 585221E -03 0. 892424E- 04 0. 194316E -04 0. 526512E -0 5 0.166408E- 05 0.590951E -06

0 0.198330E 01 0.670026E 00 0. 404333E-00 0. 289734E -00 0 .225809E-OO 0. 185014E -00 0. 156713E -00

1 0.784967E 00 0.190559E -00 0. e98725E-01 0. 52e804E-01 0 .349676E-01 0. 248829E -01 0. ia6286E -01

2 0.409145E -00 0,772044E -01 0. 300110E-01 0. 150702E -01 0 .870698E-02 0. 550685E -02 0. 371242E -02 0.234077E -00 0.364165E -01 0. 121050E-01 0. 532441E -02 0 .274136E-02 0. 156531E -02 0. 962493E -03

4 0.145405E -00 0.192068E -01 0. 557148E-02 0. 217955E -02 0 .101213E-02 0. 526925E -03 0. 297973E-03

5 0.943347E -01 0.108528E -01 0. 279656E-02 0. 986006E -03 0 •417302E-03 0. 199763E -03 0. 104626E-03

6 0.638747E -01 0.650659E -02 0. 150771E-02 0. 483700E -03 0 .188013E-03 0. 832861E -04 0. 40619SE -04

7 0.443950E -01 0.406278E -02 0. 855987E-03 0. 252062E-03 0 .906213E-04 0. 373670E -04 0. 170549E-04

8 0.316988E -01 0.263353E -02 0. 508690E-03 0. 138419E-03 0 .462873E-04 0. 178503E -04 0. 765544E -05

9 0.230394E -01 0.175403E -02 0. 312966E-03 0. 791847E-04 0 .247576E-04 0. 896903E -05 0. 362825E-05

10 0.170647E -01 0.119907E -02 0. 198e01E-03 0. 470035E-04 0 .137991E-04 0. 471348E -05 0. 180434E -05

11 0.128054E -01 0.835883E -03 0. 129479E-03 0. 287402E -04 0 .795419E-05 0. 257069E -05 0. 934063E-06

12 0.974589E -02 0.594066E -03 0. a63562£-04 0. 180644E-04 0 .472895E-05 0. 145030E -05 0. 501499E -06

0 0.196614E 01 0.6735ieE 00 0. 408867E -00 0. 293959E -00 0 .229589E -00 0.188389E -00 0. 159745E -00

1 0.785821E 00 0.193501E -00 0. 919621E -01 0. 543781E -01 0 .360837E -01 0.257442E -01 0. 193125E -01

2 0.409596E -00 0.785816E -01 0. 308582E -01 0. 156056E -01 0 .906392E -02 0.575615E -02 0. 38932eE -02

3 0.234950E -00 0.371874E -01 0. 125044E -01 0. 554697E -02 0 .287482E -02 0.165023E -02 0. 101914E -02

4 0.145910E -00 0.196283E -01 0. 576784E -02 0. 227881E -02 0 .106661E -02 0.558899E -03 0. 317777E -03

6 0.947531E -01 0.111066E -01 0. 290192E -02 0. 103441E -02 0 .441714E -03 0.213034E -03 0. 1122e8E -03

6 0.641268E -01 0.66594aE -02 0. 156617E -02 0. 508500E -03 0 .199626E -03 0.891787E -04 0. 438099E -04

7 0.445800E -01 0.416058E -02 0. 890291E -03 0. 265533E -03 0 .964986E -04 0.401599E -04 0. 184776E -04

8 0.318095E -01 0.269621E -02 0. 529301E -03 0. 145994E -03 0 .493890E -04 0.1923e6£ -04 0. 832379E -05

9 0.231152E-01 0.179589E -02 0. 325842E -03 0. 836225E -04 0 .264679E -04 0.969214E -05 0. 395814E -05

10 0.171068E -01 0.122705E -02 0. 206983E -03 0. 496696E -04 0 .147717E -04 0.510358E -05 0. 197360E -05

11 0,128309E-01 0.S55161E -03 0. 134830E -03 0. 303915E -04 0 .852569E -05 0.278867E -05 0. 102421E -05 12 0.975629E-02 0.607344E -03 0. 899001E -04 0. 191068E -04 0 .507274E -0 5 0.157543E -05 0. 550971E -06

0 0. 193695E 01 0. 679556E 00 0. 416776E -00 0. 301370E -00 0 .236247E -00 0. 194352E-00 0.165115E -00

1 0. 787531E 00 0. 198716E -00 0. 956697E -01 0. 570650E -01 0 .380952E -01 0. 273023E- 01 0.205536E -01

2 0. 412566E-00 0. 813962E -01 0. 325102E -01 0. 166354E -01 0 .974684E -0 2 0. 623204E- 02 0.423S22E -02

3 0. 238355E -00 0. 388541E -01 0. 133212E -01 0. 599382E -02 0 .314064E -02 0. 181870E- 02 0.113131E -02

4 0. 148560E -00 0. 206183E -01 0. 619256E -02 0. 248748E -02 0 .117967E -02 0. 624810E- 03 0.3S8449E-03

5 0. 96906&E -01 0. 117309E -01 0. 313823E -02 0. 113948E -02 0 .493919E -03 0. 241194E- 03 0.12a478E -03

6 0. 657633E-01 0. 706029E -02 0. 170289E -02 0. 564187E-03 0 .225217E -0 3 0. 102037E- 03 0.507353E-04

7 0. 458646E-01 0. 442e20£ -02 0. 973035E -03 0. 296575E-03 0 .109758E -03 0. 463928E- 04 0.216343E -04

8 0. 327963E-01 0. 287777E -02 0. 580825E -03 0. 163942E -03 0 .565573E -04 0. 224063E- 04 0.983853E-05

9 0. 238909E-01 0. 192250E -02 0. 358965E -03 0. 943803E -04 0 .305009E -04 0. 113732E- 04 0.471939E-05

10 0. 177115E-01 0. 131647E -02 0. 228736E -03 0. 562951E-04 0 .171136E -04 0. 602778E- 05 0.237119E-05

11 0. 133104E-01 0. 9196ieE -03 0. 149461E -03 0. 345e41E-04 0 .992710E -0 5 0. 331369E- 05 0.123931E-05

12 0. 101352E-01 0. 654289E -03 0. 999038E -04 0. 218158E-04 0 .593207E -0 5 0. 188197E- 05 0.670S7eE-06

56
Table 2. Spatial Moments, Plane

n p=-l/2 1/2 3/2

MEV = 0« 70 Z =

0 0«188794E 01 0.689981E 00 0«43064eE-00 0

1 0.784723E 00 0.206911E -00 0.102020E-00 0

2 0»'»152'»6£-00 0.861150E -01 0.354420E-01 0

3 0.2'»2517E-00 0.416984E -01 0.148013E-01 0

<» 0.152262E-00 0.223617E -01 0.698296E-02 0

5 0.100060E-00 0.128459E -01 0.358506E-02 0 6 0.682933E-01 0.779107E'-02 0.196619E-02 0

7 0.'f79040E-01 0.492193E -02 0

8 0»3'»'tl80E-01 0,32131 3E'-02 0

9 0.251921E-01 0i216238E -02 0

10 0.187527E-01 0.148820E'-02 0.272736E-03 0 11 0.141507E-01 0.104465E'-02 0.179333E-03 0 12 0.108140E-01 0.746457E'-03 0» 120543E—03 0

MEV = 1< 00 Z

= 6 •

0 0.183977E 01 0.700595E 00 0a'f4303lE-00 0

1 0«779331E 00 0.215034E'-00 0. 108&34E-00 0 2 0.417028E-00 0.910255E'-01 0.386246E-01 0 3 0>2<»6111E-00 Of'f47124E'-01 0.164440E-01 0 0.155778E-00 0.242547E'-01 0.788124E-02 0

5 0.103138E-00 0.140729E-01 0.410124E-02 0 6 0.708484E-01 0.860829E-02 0.227544E-02 0

7 0.f99951E-01 0.548004E'-02 0« 132630E-02 0 8 0i36C752E'-02 0«805497E-03

9 0.265698E-01 0.2'f3929£'-02 0#505761E—03 0

10 0.198720E-01 0« 168844E'-02 0.326855E-03 0 11 0.150629E-01 0.119158E'-02 0.216399E-03 0 12 0.115599E-01 0.855703E'-03 0«T*6382E-03 0

MEV = 2. 00 Z = 6 •

0 0.168836E 01 0.736579E 00 0.496049E-00 0

1 0.749S20E 00 0.2'tl766E'-00 0.132702E-00 0

2 0.itl3272E-00 0.107601E'-00 0.506534E-01 0

3 0.250831E-00 0t551496E'-01 0,228826E-01 0

<• 0.162281E-00 0,309520E'-01 0.11512eE-01 0

5 0.109636E-00 0.164990E'-01 0.624697E-02 0

6 0.766172E-01 0.116030E'-01 0.359178E-02 0

7 0.5't9'.61E-01 0.755515E'-02 0.216089E-02 0

8 0.307326E -02 0.134940E-02 Q

9 0.300307E-01 0.349374E'-02 0.a68966E-03 0

10 0.227i.20E-01 0.245857E'-02 0.574496E-03 0 11 0. 17'f461E-01 0.176216E'-02 0.388430E-03 0 12 0.135382E-01 0.128357E'-02 0,267849E-03 0

MEV = 00 Z = 6 «

0 0.15170itE 01 0.783300E 00 0.567490E 00 0

1 0.710917E 00 0.279926E'-00 0.170542E-00 0

2 0.i»10'»31E-00 0,133749E'-00 0.716391E-01 0 3 0.259722E-00 0,728698E'-01 0 • 33 1120E-01 0

<> 0.174128E-00 C.430710E'-01 0.ia9379L-01 0

5 0tl21«81E-00 0.269368E'-01 0 6 0.373658E-01 0.175828E -01 0.662226E-02 c 7 0.643352E-01 C.118674E -01 C.417909E-02 0 3 C«483073E~01 0.O23189E'-02 0.272446E-02 Q

9 0.368607E-01 0.3340e6E -02 0.132481E-02 0

10 0.285174E-01 0.422512E -02 0.125073E-02 0 11 G.223250E-01 0,310731E -02 0.o744lOE-03 0 12 0.176605E-01 0.231660E -02 C.522020E-03 0

MEV=10. 00 z= 6 •

0 0 0.131270E 01 0.3501&eE 00 0.680953E 00 0

1 C.631212E 00 0.340514E'-00 0.240074E-00 0 2 0.401648E-00 0.180575E'-00 0.115752E-00 0

3 0.270937E-00 0. 103034E'-00 0.6'40418E-01 0 4 0.192561E-00 0.693910E'-01 0.384454E-01 0

5 0. 141749E-00 0.467645E -01 0.243967E-01 0 6 0.107094E-00 0.326570E -01 C.1O1320E-01 c

7 0.323615E-01 0i234445E -01 0.110147E-01 0 8 0.647000E-01 3.172120E -01 C.771869E-02 0 9 0.513956E-01 0.123731E -01 0.552705E-02 0

10 J.413020E-01 3.978104E -02 0.403102E-02 0 11 0.325225E-01 0.7i>3319E -02 0.298680E-02 0 12 i.27446eE-01 0.5a7122E -02 0.224396E-02 0

Perpendiculor Source — Continued

5/2 V2 9/2 11/2

.314500E'-00 0.248124E-00 0« 205044E-00 0<17^782E-00

.617800E'-01 0i416952E-01 0« 301287E-•01 0>22a276E-01

.183161E'-01 0»110177E-01 0« 712989E-•02 0>489600E'-02 .682984E'-02 0»364885E-02 0* 214605E-•02 0.135206E'-02

• 288844E'-02 0. 140191E-02 0. 756665E-03 0«4409»4E^-03 .134511E-02 0.598676E-03 0< 298827E-03 0«1421S5E-03

.675240E--03 0.277611E-03 0. 128929E-03 0«*547M£-04

.359360E-03 0.137339E-03 0> 596600E-04 0«284«60E-04

.200772E'-03 0.717020E-04 0« 292636E-04- Otl3184«E-04

.116713E'-03 0 • 1 50646E— 04 0.6^«77E-05

.702153E-04 0«221898E-04 0. 808&42E- 05 0.327744E-05 •434808E-04 Otl29981E-04 0« 4*9677E-05 0«l.T34)4E-05 .2762*2E-04 0«7835e5E-05 0. 2S80a6E-05 0.99UA0E-06

•32e306E-00 0>260727E-00 0> 21*4ME- 00 0* 1*5142 E-00 .668357E-01 0«4M213E-01 0> 332497E-•01 0. 253428 E-01 .206105E-01 0.12*593£-01 0> eit322E- 02 0«5441<9E-02

.778555E-02 0.424274E-02 0. 253532E- 02 0.16U34E--02 •335869E-02 0«166e99E-02 0« 918299E-03 0.543855E-03

.159102E-02 0.727419E-03 0* 371273E-03 0.205305E-03

.810530E-03 0.343356E-03 0> 163&21E- 03 0«84«524E'-04 .437000E-03 0.172556E-03 0. 770669E-04 0.3748»eE-04

.246979E-03 0.913580E-04 0. 384269E-04 0«177744E-04

• 145074E-03 0«504928E-04 0. 200773E-04 O.S«1454E-OS .881021E-04 0>2e9*16E-04 0* X09220E-04 Ot454374E-05

.550297E-04 0.171436E-04 0. 6149e2E-0S O.245207E-O5

•352399E-04 0<104349E-04 0> 3S4995E-OS 0.134139E--05

.378611E-00 0 .307593E'-00 0>259600E-00 0i224a41E'-00 .862225E-01 0 • 612275E^-01 0.459963E-01 0.359423E-01

.290584E-01 Q • 1855 19E^-0

1

0.126912E-•01 0.911811E--02 .118254E-01 0 • 689727E^-02 0.435412E-•02 0<290902£'-02 .542854E'-02 0 • 292266E'-02 0.171751E-•02 0.107514E-02

.271340E-02 0 .135897E^-02 0.748298E-03 Oa441400E'-03 tl44779E-02 0 .678622E'-03 0.351934E-•03 0>196492E'-03 .813281E'-03 0 .358568E'-03 0.175886E-•03 0.932969E-04

.476614E'-03 0 • 19848eE^-03 0.924242E-04 0t467231E--04 t289301E'-03 0 .114220E^-03 0.506465E-•04 0«244^6E-04

.180963E-03 0 .679481E^-04 0.287693E-•04 0tl33153E-04

•116148E-03 0 .415924E^-04 0>168566E-•04 0t7*9013E-05

.762512E-04 0 • 261061E^-04 0.101494E-•04 0i^33a05E-05

.452743E-00 0 .379255E'-00 0.327453E-•00 0«28a4«9E-00

.118835E-00 0 .883722E'-01 0.695287E-•01 0.S61510E-01

.450107E-01 0 .308126E^-01 0.222955E-•01 0<167826E-01

.202348E--01 0 .128563E'-01 0.a70521E-•02 0>61498aE-02

.101192E'-01 0 .602040E^-02 0>384385E-•02 0«258240E-02

.545210E-02 0 .305706E'-02 0<18506a£-•02 g 0<118432E-02

.310843E'-02 0 .165078E^-02 0.951600E-03 0.582254E-03

.135301E'-02 0 .935792E^-03 0.515454E-•03 0t302485E-03

.114572E-02 0 .552061E'-03 0.291406E-03 0«164430E-03

.730310E--03 0 t336714E^-03 0.1707*6E-•03 0t92a45iE-04

.477781E'-03 0 .211303E'-03 0.103159E-•03 0«541592E--04 .319653E'-03 0 .135902E'-03 0.63997aE-•04 0>324955E-04

.218101E'-03 0 .893129E^-04 0.406374E-•04 0«199862E--04

.579212E 00 0 •508263E 00 0.454913E-•00 0>412875E-00

. 184960E^-00 0 .149337E^-00 0<124268E-00 0il05652E-00

.826969E^-01 0 • 626065E^-01 0.492114E-01 0.397375E--01 .429708E'-01 0 .308235E^-01 0.230931E-01 0«178513E--01 .244235E'-01 0 .167112E^-01 0.120030E-01 0>892856E-02

.147578E--01 0 .967788E -02 0.669197E-02 0<480799E--02 .933191E'-02 0 .588644E'-02 0.393082E-02 0.273551E-02

.611394E'-02 0 .372020E^-02 0.240513E-02 0il62486E-02

.412260E'-02 0 .242546E^-02 0.152125E-02 0.999541E-03

.284718E^-02 0 .162283E^-02 0.989158E-03 0«633085E-03

.200680E^-02 0 .111002E^-02 0.658494E-03 0.4H079E--03 .143953E^-02 0 .773857E^-03 0.447377E-03 0.272730E--03

• 104863E^-02 0 .348588E -03 0.309423E-03 0«184395£--03

57
Table 2. Spatial Moments, Plone

n p=-l/2 1/2 3/2

MEV» Oa 025 Z" 13 a

0 0.203906E 01 0a6&89SBE 00 0a390161E-00 0

1 0.S60891E 00 Oal41344E-00 0.6e3960£-01 0

2 0.246525E-00 0a482409E-01 0. 192809E-01 0 3 0«1144e9£-00 Oa 188148E-01 0a649958E-02 0 0a616319E-01 0ae61956£-02 0«259981E-02 0

5 0.341734E-01 0a419965E-02 Oa 113096E-02 0 6 0.204383E-01 Oa223083E-02 0a540876£-03 0

7 0.124584E-01 0al22910E-02 0.271904E-03 0

s 0« 796245E-02 0a715314£-03 Oa 145291E-03 0

9 0t515980£-02 0a426662£-03 0a802685E-04 0

10 0.345534E-02 0a2644ieE-03 0.46i930E-04 0 11 0.233e70E-02 Oal66829E-03 Oa273483E-04 0 12 0. 162208E-02 Oa 108302E-03 Oa 166841E-04 0 MEVs Oa 05 Z" 13 a

0 0.198057E 01 0a670578E 00 0.405047E-00 0

1 0.S43576E 00 Oa 144826E-00 0«722112£-01 0

2 0,235139E-00 0a491161E-01 0a204189E-01 0

3 0.10e350E-00 Oa 190939E-01 0.690198E-02 0 4 0.575659E-01 Oa867334E-02 0a275356E-02 0

5 0.3i6229E-01 0a420O53E-02 0.119570E-02 0 6 0.186833E-01 0a22ill4E-02 0a569007£-03 0

7 0.112824E-01 0al20945E-02 0a284673E-03 0

8 0. 712875E-02 0a69737faE-03 Oal51273E-03 0 9 0.457603E-02 0a412695E-03 0a831181E-04 0

10 0.303116E-02 0a253392E-03 0.476028E-04 0 11 0.203234E-02 Oa 1&8&66E-03 0.279456E-04 0 12 0«139488E-02 0al01989£-03 0.169223E-04 0 MEV = Oa 10 Z« 13a

0 0.198161E 01 0a670368E 00 Oa40477fcE-00 0

1 0iSS0135E 00 0al46071E-00 0a726769E-01 0

2 0«2376l2E-00 0a494515£-01 0a205123E-01 0

3 Oa 110031E-00 Oa 192869E-01 0a694764E-02 0 4 0«^84098E~01 0a875133£-02 0.276787E-02 0

5 0.3217406-01 0a424612E-02 0al20324E-02 0 6 0« 189949E-01 0a223310E-02 0a571952E-03 0

7 0.114879E-01 0al22268E-02 0a2a6502E-03 0

8 0. 725261E-02 0a704343E-03 0al51973E-03 0

9 0.465897E-02 0a4l6987E-03 Oa835109E-04 0

10 0.308322E-02 0a255764E-03 0.477732E-04 0 11 0.206768E-02 0al60047£-03 0a280388E-04 0 12 0.141764E-02 0al02825E-03 0al69581E-04 0 MEV = Oa 20 Z» 13a

0 0>19&899E 01 0a672936E 00 Oa40810eE-00 0

1 0«33i017E 00 Oal48675E-00 Oa742974E-01 0

2 0»239490E-00 0a503902E-01 0a210347E-01 0

3 0.111623E-00 Oal97707E-01 Oa716893E-02 0 4 0.592385E-01 0a897652E-02 Oa286094E-02 0

5 0.327506E-01 Oa437081E-02 0al24e48E-02 0

6 0.193308E-01 0a229936E-02 0a594068E-03 0

7 0.117170E-01 0al26173E-02 0a298325E-03 0

a 0i739470E-02 0a72&838E-03 0al58328E-03 0

9 0.475657E-02 Oa430890E-03 Oa871440E-04 0

10 0«31462eE-02 0a264225E-03 0a498591E-04 0 11 Oa 2111d3E-02 0al65470£-03 0a292923£-04 0 12 Oa 144681E~02 0al06261E-03 0al77138E-04 0 MEV" Oa 40 Z>13t

0 Oal9363&E 01 0a6796eiE 00 0a416941E-0O 0

1 0a3609&2E 00 Oal54196E-00 0a780799£-01 0 2 0a242860E-00 Oa527236E-01 0a224113E-01 0

3 0all4620E-00 Oa209646E-01 Oa775758£-02 0 4 0a610421E-01 0a957624E-02 0.312403E-02 0

5 0a340165E-01 0a470361£-02 0al37756E-02 0 6 0a201408E-01 0a248i77E-02 0a659831E-03 0

7 0al22778E-01 Oal37266E-02 0.333884E-03 0

6 0»776954E-02 0a793614£-03 Qal78104E-03 0

9 0a501960E-02 0a472766E-03 0a986062E-04 0 10 0a332794E-02 0a29O76'»E-03 0a566463E-04 0 11 0a224127E-02 0al82797E-03 Oa33436&E-04 0 12 0.153875E-02 0all7678E-03 0a202871E-04 0

58

Perpendicular Source — Continued V2 7/« '/2 a/2 11/2

•276646E -00 0a214169E -00 Oa 174667E- 00 0al47448E -00

• ^09663E -0

1

0 •274409E -0

1

Oa 197177E- 01 0 a 146737E -0

1

•989262E -02 0a581444E -02 0 a 372930E- 02 0a254360E -02

• 29^300 E -02 Oa 153048E "0 2 0 a 902158E- 03 0 • 7639 rob -03

-02 Ua4V(Tr# fc. —0 3 0 a 264381E- 03 A Ift^ATTC -03

• <»ll97'tE -03 Oal78912E -03 Oa 874901E- 04 0«'»66616E -04

a 1793b0t -03 —04 0 a 323736E-04 A 1 i A "T TA C —04 a829333E -04 0 • 306396E —04 0 a 129173E- 04 A - £. f\/\ £^AO C U* oUUo9oL -05 a409782E -04 0«140e49E -04 Oa 555349E- 05 0*242633E -05 .210862E -04 0«&78366E -05 0. 2 5 1428E* 05 0tl03656E -05

.113733E -04 0«343691E -05 Oa 120121E- 05 0«4683aeE -06 a631683E -05 A lOAlllC U* I0UI2IC. -0 5 0 • 595965E- 06 Ua 220 1 4UL -06 a363468E -05 A 0 a A ~T C T C 0 •you r 3 / t —06 0 • 307991E- 06 U a 1 0 8 794 c -06

a2S0399£-00 0*226403E -00 Oa 185544E- 00 0al57189E -00 a440978E -01 0 •299<>7&£ -01 Oa 217424E- 01 Oa 165342E -01 al07667E -01 0 •643 70dE -02 0 • 420734E- 02 0a290635E -02 a322972£-02 0 1 7*»5 1 5E -02 0 a 103621E- 02 0a658197E -03 all5278£-02 0 •364912E -03 0 a 307396E- 03 0 a 180432E -03 a454567£ -03 0.204304E -03 0. 102783E- 03 Oa561486£ -04 al97737E -03 0 •S 19546E -04 C a 382939E- 04 Oa 195449E -04 a913700E -04 0 •351922E -04 Oa 153692E- 04 0 a 736759E -05 .450122E -04 0.i618l7E -04 Oa 662984E- 05 0a299472£ -05 •230983E -04 0^779375E -05 Oa 300991E- 05 0al28632£ -05 al24039E -04 0.394X83E -05 Oa 143930E- 05 0a583511E -06 •6e6113E -05 0 • 206218E -0 5 0 a 714502E- 06 0a275673E -06 a392693E-05 0 • 1 11938E -05 0 a 368934E- 06 0 a 135766E -06

a290147E-00 0#226177E -00 Oa ie5342E- 00 0al57008E -00 .443178E-01 A -aAA^CAC -01 0 • 218099E- 01 U • I 63 /46c -0

1

a 107985E-01 u • o*toy p 7

1

-02

A* 421200E- 02 v^^yU A . 'DQn7<.OP / OOt -02 a324320E-02 A IT/iO^ICT U • 1 * HVa It -02 0 • 103727E- 02 A AtiJlTAC "0 3 .115563E-02 U • 3 07 i 7 0 • 307041E- 03 u • 1 / 77 7 0 c -03 a455908E-03 0a2043eiE -03 Oa 102614E- 03 0a559646£ -04 al98054£-03 0a8ia578E -04 0 a 381633E- 04 Oal94427E -04 a915287E-04 0a351426E -04 0 a 153084E- 04 0a732291£ -05 a450344E-04 0al61363E -04 0 a 659334E- 05 0a297149E -05 a231056E-04 0a776e55E -05 0. 299136E- 05 0al27522E -05 al23922E-04 0.392369E-05 Oa 142829E- 05 0a57754eE-06

a685163E-05 0.205140E-05 Oa 70e469E- 06 0a272592E -06 a391635E-05 0allll96E-05 Ca 365271E- 06 0al34036E -06

a293251E-00 0 a228954E -00 Oa 187822E-00 Oa 159235E -00 a454302E-01 0 a308786E -01 Oa 224321E-01 Oa 170666E -01 alll216£-01 0 a668455£ -02 Oa 436283E-02 Oa 301786E -02 a336249E-02 0 al82037E -02 Oa 108263E-02 Oa 688660E -03 al20140E-02 0 a590237E -03 Oa 321881E-03 Oa 189298E -03

a475995E-03 0 a214468E -03 Oa 108135E-03 Oa 591898E -04 a207149E-03 0 a361119E -04 Oa 403435E-04 Oa 206403E -04 a960106E-04 0 a370931E -04 Oa 162445E-04 Oa 7e0699E -05 .472922E-04 0 al70608E -04 Oa 701237E-05 Oa 317678E -05 .243120E-04 0 a823316E -0 5 Oa 319035E-05 Oa 136769E -05

al30472E-04 0 a416292E -05 Oa 152571E- 05 Oa 620696E -06 a722320E-05 0 a218007E -05 Oa 75e322£- 06 Oa 293660E -06 a412972E-05 0 all8247E -05 Oa 391386E- 06 Oa 144606E -06

a301525E-00 0 a236386E -00 Oa 194477E- 00 Oa 165228E -00 a481457£-01 0 a329191E -01 Oa 240213E- 01 0. ie3397E -01 all9960£-01 0 a727566E -02 0. 478199E- 02 Oa 332642E -02 .369189E-02 0 a202106E-02 Oa 121270E- 02 Oa 777031E -03 .133484E-02 0 a6647e4E-03 Oa 366564E- 03 Oa 217569E -03 .535408E-03 0 a244996£ -03 Oa 125117E- 03 Oa 692283E -04 a235037E- 03 0 a99424e£-04 Ca 472672E- 04 Oa 24486eE--04

a 109937E-03 0 .432884E-04 0. 192663E- 04 Oa 938923E--05 .545151E- 04 0 a200739E -04 Oa 839901E- 05 Oa 386409E--05 a282250E- 04 0 a976999E -0 5 0. 385851c- 05 Oa 168197e--05 al52279E- 04 0 a497282E -05 0. 185994E- 05 Oa 770391E--06 a847e66E- 05 0 a262196£-05 Oa 931790E- 06 Oa 367789E--06 a486857E- 05 0 al42988E-05 0. 484068E- 06 Oa 182498E--06
Table 2. Spatial Moments, Plane Perpendicular Source — Continued

n p=-l/2 1/2 3/2

MEV= 0.70 Z=13.

0 0«187981£ 01 0«691746E 00 0« 433023E -00

1 0.566164E 00 0.163275E -00 0. 8'»7*7eE'-01

2 0.247399E-00 0.568825E -01 0« 2'f9941E -01

3 0»118898E'-00 0.231038E'-01 0. 888019E -02

<» 0.638515E'-01 0.106904E'-01 0. 364211E -02

5 0.360121E-01 0t332622E'-02 0. 163500E'-02

6 0.21'f784E-01 0.2b4287E'-02 0. 793844E -03

7 0.132138E-01 0.138684E'-02 0. 'f071't9E'-03

8 0«8i»1563E-02 0.9249*2£'-03 0. 219538E'-03

9 0.5't7805E-02 0.55581'tE'-03 0. 122864E'-03

10 0.365262E-02 0.3'»'»2ieE'-03 Ot 712154E'-04

11 0.2't7578£-02 0.217995E'-03 0> t24153E'-04

12 0.1708<»7E-02 0.1fH88E-03 0. 259320E'-04

MEV= 1.00 2=13.

0 0. 182231E 01 0. 704539E 00 0. 450476E'-00

1 0. 568399E 00 0. 172613E -00 0. 920220E'-01

2 0. 251021E'-00 0. 613611E'-01 0. 27928bE'-01

3 0. 122626E'-00 0. 254381E'-01 0. 101839E'-01

4 0. 664483E'-01 0. 119342E'-01 0. 423868£.-02

5 0. 378910E'-01 0. 602870E'-02 0. 194641E'-02

6 0. 227731E -01 0. 325195E'-02 0. 958771E'-03

7 0. 141308E'-01 0. 183443E'-02 0. 498477E -03

8 0. 906012E'-02 0. 107853E'-02 0. 271885E'-03

9 0. 593989E'-02 0. 6&3716E -03 0. 153840E'-03

10 0. 398422E'-02 0. 407839E'-03 0. 900253E'-04

11 0. 271736E'-02 0. 260189E'-03 0. 541147E'-04

12 0. 18e526E'-02 0. 169606E'-03 0. 333569E'-04

MEV= 2.00 2«13.

0 0 0. 167676E 01 0.739576E 00 0. 500452E 00

1 0. 573559E 00 C.200308E -00 0. 114760E -00

2 0. 263196E'-00 0.7S)7799E -01 0. 378565E'-01

3 0. 134599E'-00 0.333040E -01 0. 148548E -01

4 752097E'-01 S.lo320aE -01 0. 658325E'-02

5 0. 442924E-01 0.858878E'-02 0. 317009E'-02

6 0. 27313CE'-01 0.479173E'-02 0. 163183E'-02

7 0. 173932E'-01 0.279099E'-02 0. 833537E'-03

8 0. 114034E-01 0.168730E'-02 0. 499391E'-03

9 0. 764399E--02 0. 105039E'-02 0. 292161E'-03

10 0. 523013E--02 0.671234E'-03 0. 176193E'-03

11 0. 36378i!E-02 C.438254E'-03 0. 108974E'-03

12 0. 2b6976E--02 0.29180eE'-03 0. 689538E'-04

M£V= 4.00 2^13.

0 0. 150159E 01 0 .787877E 00 0. 574821E 00

1 0. 572468E 00 0 .242184E'-00 0. 153087E -00

2 0. 279520E'-00 0 .100374E'-00 0. 567412E -01

3 0. 151933E'-00 0 .478173E -01 0. 24625bE -01

4 0. 890286E'-01 0 .250165E'-01 0. 118575E -01

5 0. 548428E'-01 0 .139612E'-01 0. 615493E -02

6 c. 351621E'-01 0 .al9614E'-02 0. 338047E'-02

7 0. 232361E'-01 0 .300322E'-02 0. 194146E'-02

8 0. 157540E'-01 0 .315537E'-02 0. 115725E -02

9 0. 109048E'-01 0 .204368E'-02 0. 711219E -03

10 0. 768693E--02 0 .135458E'-02 0. 448805E'-03

11 w • 550226E--02 0 .915562E'-03 0. 289656E -03

12 0. 399315E'-02 3 .&29695E'-03 0. 190709E'-03 M£V=10.C0 Z=13.

0 0. 129644E 01 0.a56174£ 00 0.691847E 00

1 0. 562491E 00 0.311597E'-00 0.226015E'-00

2 0. 304a50E'-00 0.14d861£'-00 0.996151E'-01

3 0. 182307E -00 0.a03939E -01 0.503201E'-01

4 0. 115994E -00 0.4<>a72a£'-01 0.i76734E.-01

5 0. 770350E -01 0.288250E'-01 0.161496E'-01

6 0. 528664E -01 0.1d4611£'-01 0.936044E'-02

7 0. 372220E -01 0.122067E'-01 0.623876£'-02

d 0. 267668E'-01 0.328365E -02 0.406438E'-02

9 0. 1958d5£ -01 0.574a02£'-02 0.271350E'-02

10 3. 145526E'-01 0.40=i27B£'-02 0.184981£.-02

11 b. 109i26£ -01 O.^SlalcE--02 0.1283y9£'-02

12 0. 833801E'-02 0.212600E'-02 0.905541E--03

5/2

7 / '/2 3/2 11/2

0.316764E'-00 0.250183E -00 0. 206905E-•00 0.176469E-00

0.530956E'-01 0.367175E -01 0. 270240E-'01 0.207720E'-01

0. 136837E'-01 0.843e63E -02 0. 561854E-•02 0.394917E'-02 0.434277E'-02 0.242742E -02 0. 148091E-02 0.961912E--03 0.160714E'-02 0.820864E -03 0. 462003E-03 0.27073Dt -03

0.658760E'-03 0.310268E -03 0. 162275E-'03 0.916139E'-04 0.294236E'-03 0.128368E -03 0. 628046E- 04 0.332986E'-04 0.139913E--03 0.570772E -04 0. 261776E-•04 0.130920E--04 0.703323E'-04 0.269114E -04 0. 116341E-•04 0.550729E'-05 0.368973E'-04 0.133030E -04 0. 544225E-05 0.244676E--05

0.201312E-04 0.&86330E -05 0. 266537E-•05 0.114122E--05 0.113319E'-04 0 . 3666 16£ -05 0 . 1 35558E-'05 0.554242E--06 0.656889E-05 0.202232E -0 5 0 • 713744E-'06 0.279283E'-06

0.333553E-00 0.265546E -00 0. 220853E-00 0.189164E--00 0.586621E-01 Uc'tiU lolL'-0

1

0 * JU u dc~'0

1

0.236372E--01 0.156635E-01 -0 2 0 * 6640 1 2E'''02 0.472041E--02 0.512814E-02 0 •29315 IE -02 0 . 02 0.120043E'-02 0.194497E-02 0 • 102063E -0 2 0 • 587229E-03 0.361127E'-0 3 0.815038E-03 0«39&928E -03 0. 212445E-03 0.122564E'-03 0.370771E-03 0 • 167716E -03 0 • 84341 7E"'04 0.458414E'-04 0.179308E--03 0 • 759680E -04 0. 359775E" 04 0.184984E'-04 0.914531E-04 0 * ^043

1

-04 0 • iO J i. VUC"'04 0.796371E--05 0.486342E-04 0.183139E -04 0. 777896E-05 0.361441E--05 0.268546E-04 0.958640E'-0 5 0. 387473E-05 0.171864E--05 0.152892E-04 0.319061E'-05 0. 200203E-05 0.849811E'-06 0.895362E--05 0.289859E'-05 0. i06937E-05 0.435313E--06

0. 383056E -00 0 .31ie04E-00 0. 263525E-00 0.2284«8E -00

0. 767045E -01 0 .555952E-01 0<I424243E-01 0.335660E -01

0. 226402E -01 0 .149184E -01 0. 104654E-01 0.767603E -02

0. 808553E -02 0 .490912E -02 0. 320142E-02 0.219772E -02

0. 329292E -02 0 .ia5678E -02 0, 113323E-02 0.732391E'-03

0. 146995E -02 0 .775147E -03 0. 445326E-03 0.272305E -03

0. 70593eE -03 0 .349963E -03 0. 190096E-03 0.110401E<-03

0. 358662E -03 0 .167945E -03 0. 865998E-04 0.479341E'-04

0. 191098E -03 0 .848442E -04 0. 416671E-04 0.220449E'-04

0. 105824E'-03 0 .447031E -04 0. 209714E-04 0.1063Z9E-04

0. 606147E^-04 0 .244329E -04 0. 1097695-04 0.534S60E-05

0. 357178E -04 0 .137744E -04 0. 594012e-05 0.278417E-05

0. 215891E^-04 0 .798358E -05 0. 331135E-05 0.1496ME-0S

04460590E'-00 0 .387016E -00 0. 334933E-00 0.295627E-00

0. 109311E'-00 0 .832301E -01 0. 660300E-01 0.539302E-01

0. 370087E'-01 0 .2&0649E -01 0. 192938E-01 0.1«7989£-01

0. 148771E-01 0 .980345E -02 0. 683761E-02 0.496803E-02

0. 669737E'-02 0 .415842E -02 0. 27*958E-02 0.190268E-02

0. 326654E--02 0 • 192162E^-02 0. 121023E-02 0.800937E-03

0. 169584E'-02 0 .949215E -03 0. 571506E-03 0.362899E--03

0. 924638E-03 0 .494222E'-03 0. 285357E-03 0.174336E-03

0. 52511BE-03 0 • 268831E'-0 3 0. 149240E-03 0.879265E-04

0. 308446E'-03 0 .151640E^-0 3 0. 811244E-04 0.461S56E--04

0. 186523E--03 0 .882584E'-04 0. 455913E-04 0.251259E--04

0. 115633E-03 0 .527675E'-04 0. 263660E-'04 0.1408e2E--04

0. 732801E-04 0 .323069E'-04 0. 156386E-04 0.811301E-0S

0. 591925E 00 0 .521688E 00 0. 468547E- 00 0.426%65E-00

0. 177511E--00 0 . 145425E-00 0. 122432E- 00 0.105105E--00

0. 733261E--01 0 .568037E-01 0. 454927E-01 0.373167E-01

0. 350854E--01 0 .259311E-01 0. 199102E-01 0.15714*E-01

u. 183964E-01 0 .130437E'-01 0. 964849E-02 0.735938E--02

0. 102838E-01 0 .702292E-02 0. 502220E-02 0.371367E-02

0. 603619E-02 0 .398226E-02 0. 276043E-02 0.198360E--02 0. 368207E-02 0 .235247E-02 0. 158407E-02 0.110831E--02 0. 231832E--02 0 .143730E-02 0. 941840E- 03 0.&42644E-03

0. 149878E--02 0 .903245E-03 0. 576865E- 03 0.384389E-03

0. 991167E-03 0 .581508E-03 0. 362440E-03 0.236133E-03

0.668443E-03 0 .382286E-03 0. 232804E-03 0.148455E-03

0. 458665E--03 0 .256005E-03 0. 152486E- 03 0.952661E-04

59
Table 2. Spotiol Moments, Plone Perpendicular Source — Continued

n P=-l/2 1/2 Vz

MEV= 0.025 2-29«

0 0« 216947E 01 0> 634619E 00 0. 360036E -00

1 0. 353260E -00 0> a73889E -01 0. 425694E -01

2 0, 13'»71*E -00 0 • 2't9'»86E -01 Oa 978854E -02

3 0» 452376E -01 0» 725027E -02 0 • 249685E -02

* 0 • 2107 1 IE -01 0 •

t u "3 a ^ ~J c 20303 ft -02 0 • 842541E — 03

5 0. 914676E -02 0. 110081E -02 0. 294128E -03

6 0. '.755'.7E -02 0. 306332E -03 0. 121046E -03

7 0. 237059E -02 0. 230472E -03 0. 505317E -04

8 0. 1326^0E -02 0. 117323E -03 0* 233438E -04

9 0. 7225'»7E -03 0. 592318E -04 0. llp487E -04

10 0* '»267'>0E -03 0. 323820E -04 0. 56H93E -05

11 0. 247482E -03 0> 175945E -04 0. 286252E -05

12 0. 152419E -03 0. 101499E -04 0. 155053E -05

MEV- 0.05 Z=29.

0 0 0.203129E 01 0.660473E 00 0. 392086E -00

1 0.314083E -00 0.a81791£ -01 0. 4598e3E -01

2 0.113059E -00 0.243071E -01 0. 104363E -01

3 0.361477E -01 0.&b0550E -02 0. 2&0233E -02

4 0.159719E -01 0.255940E -02 0. 856186E -03

i 0.661714E -02 0.954830E -03 0. 290564E -03

6 0.327440E -02 0.421401E -03 0. 115949E -03

7 0.156060E -02 0.184406E -03 0. 469011E -04

8 0.833313E -03 0.900864E -04 0. 211330E -04

9 0.434610E -03 0.437273E -04 0. 959228E -05

10 0.245461E -03 0.229565E -04 0. 470638E -05

11 0.136475E -03 0.1i996ciE -04 0. 231988E -05

12 0.805204E -04 0.665139E -05 0. 121335E -05

MEV= 0.10 Z«29.

0 0. 201498E 01 0. 663686E 00 0. 396179E -00

1 0. 306929E -00 0. 876050E -01 0. 461053E -01

2 0. 10a722E -00 0. 237994E -01 0. 103308E -01

3 0. 343618E -01 0. 659808E -02 0. 255529E -02

4 0. 149447E -01 0. 244577E -02 0. 830007E -03

5 0. 612762E -02 0. 904007E -03 0. 279441E -03

6 0. 298559E -02 0. 393261E -03 0. 110064E -03

7 0. 140886E -02 0. 170514E -03 0. 441543E -04

8 0. 7410&6E -03 0. 821247E -04 0. 196362E -04

9 0. 382742E -03 0. 394957E -04 0. 883720E -05

10 0. 213044E -03 0. 204491E -04 0. 427988E -05

11 0. 117311E -03 0. 105876E -04 0. 209135E -05

12 0. 682457E -04 0. 579123E -05 0. 107990E -05

MEV= 0.20 Z=29.

0 0.198355E 01 0.669975E 00 0.404267E -00

1 0.304265E -00 0.892455E -01 0.476253E -01

2 0.10&473E -00 0.240893E -01 0.106583E -01

3 0.337182E -01 0.669993E -02 0.265032E -02

4 0.145119E-01 0.246560E -02 0.857732E -03

5 0.594742E -02 0.9il746E -03 0.2e93B5E -03

6 0.287024E -02 0.393665E -03 0.113417E -03

7 0.135170E -02 0.170461E -03 0.454976E -04

8 0.704666E -03 0.814840E -04 0.201195E -04

9 0.362e33E -03 0.390863E -04 0.904120E -05

10 e.200252E -03 0>2008e0E -04 0.435234E -05

11 0.109a32E -03 0.103659E -04 0.212144E -05

12 0.63M61E -04 0.562834E -05 0.108862E -05

MEV« 0.40 2«29 •

0 0 0. 194377E 01 0.678134E 00 0.414906E -00

1 0. 308599E-00 0.934421E -01 0.506347E -01

2 0. 107369E-00 0,252966E -01 0.114497E -01

3 0. 346926E-01 0.717876E -02 0.290973E -02

4 0. 148883E-01 0.26458eE -02 0.947585E -03

5 0. 618472E-02 0.991991E -03 0.32460aE -03

6 0. 298005E-02 0.428761E -03 0.127759E -03

7 0. 141706E-02 0.187522E -03 0.518281E -04

8 0. 73a027£-03 0.897074E -04 0.229881E -04

9 0. 382755E-03 0.433581E -04 0.104ie7E -04

10 0. 211104E-03 0.222939E -04 0.502663E -05

11 0. 116443E-03 0.115709E -04 0.246640E -05

12 0. 671510E-04 0.62a471£ -05 0.126773E -05

60

5/2 V2 11/9

0.249416E-00 0.190304E -00 0. 153676E- 00 0. 128804E -00 0.257620E-01 0 .174285E -01 0. 126330E- 01 0.960132E -02 0.499731E-02 0 .293967E -02 0. 189206E- 02 0. 129652E -02 0.113522E-02 0 •602184E -03 0. 363154E- 03 0.222411E -03 0.337188E- 03 0 . 160047E -03 0 • 850763E- 04 0.490673E -04 0,106868E-03 0 .464263E -04 0. 227507E- 04 0.121730E -04 0.397805E-04 0 . 157797E -04 0. 711788E- 05 0.352992E -05 0.153127E-04 0 • 563064E -05 0. 236616E- 05 0« 1098 16E -05 0.657178E- 05 0 •223917E -05 0. 876580E- 06 0.380805E -06 0.287711E- 05 0 •917935E -06 0. 337689E- 06 0.138317E -06 0.136334E- 05 0 .407429E -06 0. 140919E-06 0.544550E -07 0.654549E-06 0 . 184610E -06 0. 604238E- 07 0.221516E -07 0.333856E-06 " -07 0. 275609E-07 0.959262E -08

0.278414E-00 0 .215735E -00 Oi 176055E- 00 0. 14868eE -00 0.291046E-01 Q -01 0. 151092E- 01 0.117108E -01 0.566974E-02 Q • 34930 7£ -02 0. 233101E-02 0.164478E -02 0.127636E-02 0 .717715E -03 0. 441031E-03 0.288659E -03 0.374699E-03 0 .190783E -03 0. 107358E- 03 0.649239E -04 0.116695E-03 0 .549336E —04 0 . 287620E- 04 0. 162720t -04 0.425680E-04 • lOHOU^C -04 0. 898814E-05 0.475217E -05 0.160115E- 04 0 -0 5 0. 296785E- 05 0.147955E -05 0.670055E-05 0 -05 0. 108934E- 05 0.512067E -06 0.285643E- 05 0 •102 104E -0 5 0. 414258E- 06 0.184815E -06 0.131605E-05 0 .443587E -06 0. 170328E- 06 0.721495E -07 0.613908E-06 0 • 1 96'tl2E -06 0. 717814E-07 0.290112E -07 0.303953E-06 0 -07 0. 321374E- 07 0« 123997E -07

0.282183E-00 0 •219080E -00 0. 179024E- 00 0.151343E -00 0.293570E- 01 0

o n ^ A c r\ c

• 2UoU7 UL -01 0. 153626E-01 0.119409E -01 0.565612E-02 0 -02 0. w ^ 0. 166532E -02 0.126500E-02 0 .716516E -03 0. 442915E- 03 0.291344E -03 0.367197E- 03 0 .188582E -03 0. 106879E- 03 0.650259E -04

0. H3591E-03 0 .539961E -04 0. 285018E- 04 0.162369E -04 0.409537E-04 0 . 179765E -04 0. 882476E- 05 0.470323E -05

0. 15292aE-04 0 -0 5 0. 289817E- 05 0.145762E -05 0.632353E-05 •242895E -05 0. 105336E- 05 0.500040E -06 0.267495E-05 0 .969532E -06 0. 398119E- 06 0.179500E -06

0. 121764E- 05 0 .416549E -06 0. 162029E- 06 0.694237E -07 0.563442E- 06 0 • 18308 IE -06 0. 678260E- 07 0.277463E -07 0.275631E- 06 0 * 3 5 1 1 56E -07 0. 300513E- 07 0.117451E -07

0.289673E-00 0 .225754E -00 0. 184965E- 00 0. 15&669E -00 0.30596HE- 01 0 .2i6125E -01 0. 161925E- 01 0.126348E -01 0.591156E- 02 0 •369910E -0 2 0. 249902E- 02 0.178119E -02 0.133195E- 02 0 .763150E -03 0 • 476084E- 03 0.315535E -03 0.386452c- 03 0 .201315E -03 Oa 115416E- 03 0.708955E -04

0. 120015E- 03 0 .579681E -04 0. 310029E- 04 0.178582E-04

0.431630E- 04 0 .192954E -04 0. 961747E- 05 0.519246E -05 0.161409E- 04 0 .676164E -05 0. 317243E- 05 0.161859E -05 0.664945E- 05 0 .261001E -05 0. 115296E- 05 0.566140E -06 0.281203E- 05 0 . 104284E -0 5 0. 436753E- 06 0.200341E -06

0. 127430E- 05 0 •446724E -06 0* 177494E- 06 0.774828E -07 0.588781E- 06 0 .196263E -06 0. 743519E- 07 0.310230E -07 0.286592E- 06 0 .909065E -07 0. 328627E- 07 0.131166E -07

0.299613E- 00 0 .234665E-00 0. 192933E- 00 0.163836E -00 0.328402E- o: 0 .233523E -01 0. 175836E- 01 0.137742E -01 0.644699E- 02 0 .407845E -02 0. 277845E- 02 0. 199360E -02 0. 148737E- 02 0 .863157E -03 0. 543928E- 03 0.363476E -03 0.43604a£- 03 0 .230885E -03 0. 134112E- 03 0.832737E -04 0.137738E- 03 0 .677439E -04 0. 367719E- 04 0.214458E--04 0.49e989E- 04 0 .227780E -04 0. 115520E- Ci. 0.632932E -05 0. 188985E- C4 0 .809702E-05 0. 387160E- 05 0.200764E--05 0.782717E- 05 0 .314927t-05 0. 142078E- 05 0.697914E--06 0.334267E- 05 0 .127245E -05 0. 545018L- 06 0.254950E--06 0.152091E- 05 0 .548286E-06 0. 223190E- i6 0.995268E--07 0.708166E- 06 0 .243041E -06 0. 944475E- 07 0.403057E--07 0.345779E- 06 0 .113095E-C6 0. 420009E- 07 0.171710E-"u 7
Table 2. Spatial Moments, Plane Perpendicular Source — Continued

n P- '/2 vz

? /n V2

M 'V- 0 • 7 ,0 2 = 29 •

0 0 0. 1863486 01 0.69051ifrE 00 0.431365E-00

1 A aiTHii.ic—nA U • iUUoJ^C —00 Ci &s77ly. c f\ ^ 2 U • ^ ' 3 7** f u "01

3 U* Joo^ J ic. W i. U • O iU Lc^t. "02 U*^U133aL "02

5 0.115807E -02 0.396687E-03

6 0 • 3263 36£~02 0 • 3U*f733t "03

7 0* 158 04-2 E~02 0 • 224946E "03 n tfiClAOC A/. 8 0.827667E-03 0»10d476E -03 0.293865E-04

9 0.435365E-03 0,332130E'-04 0»135403E-04

10 0«2^i<»7bE-03 0«27&63bt'-04 0.659720E-05

1

1

UftXJH/ / ft Uj w • lH**Of DC 12 U • f 0 13 33 C W** 0.792114E'-05 n* 1 7A1 77?— OS

MEV = 1«00 Z = 29 •

0 0 0*ie2ai2E 01 0.703219E 00 0.448657E-00

1 0 • 32'fr857E~00 0.10a204E-00 0»613753£—01

2 0» li3196£-00 0.301428E'-01 0 • 146006E—0

1

3 0 t JVUt 1 ?c"y

1

0.914074E-02 A '^QOOTOC A") 0.344476E-02 0 • 1346'»^E"02

5 0.734395E-02 0.135347E-02 0.if85892£-03

6 U • j30 1 £**C. U t 0.596591E-03

7 0 • 1762 l^£—02 0.270496E-03

0tl31730E-03

9 0.495588E-03 0.fc55566E-04 0.176936E-04

10 0.276873E-03 0.342647E-04 0.372014E"05

11 0fl5629'»E-03 0.182268E-04 0.439863E-05

12 0.912673E-04 0.100507E-04 0«230420E-03

MEV = 2.00 £•29 •

0 0 0tl67823E 01 0.739201E 00 0* 499899E "00

1 0.347708E"00 0.132451E'"00 0. 801521E'"01

2 0.123808E-00 0.390436E "01 0. 207407E "01

3 0.464463E-01 0.129530E'-01 0. &26346E -02

4 O.206823£"01 0.3106&3E'-02 0. 224971E -02

3 0.953182t"02 0.21392fe£'-02 0. 873181E'-03

6 0.478427C-02 0.980303E'-03 0. 372067E'-03

7 Oa246480E-02 0.467550E'-03 0. 166476E'-03

a 0.133729E-02 2.235732E'-03 0. 790241E'-04

9 0.7407!eE"03 :.122371E'-03 0. 388310E'"04

10 0«4250>^2£"03 0.660179E'-04 0. 198863E'-04

11 0.247993£-03 0.364157E'-04 0. 104547E'-04

12 Cii46512E-03 0.206721E'-04 56686eE'-05

McV = 4*00 Z = 29 •

0 0 0.149518E 01 0.78979OE 00 0« 577916E 00

1 0.3765o3£"00 0.172750E'-00 0> 114444E'-00

2 0.141657E"00 0.561377E'"01 0. 336913E'"01

3 0t590344E-01 C.209533E "01 0. 116325E "01 0.277876E-01 0.a91719£'"02 0. 460396E'"02

5 0.137946E"01 0<40o&9&E'-02 0« 197291E.-02

6 0.728703E-02 0.198967E'-02 0. 910123E'-03

7 0,39e612£-02 3.101640E'-02 0. 441124E -03

8 S.226662C-02 a.542470£'-03 3. 224140E'-03

9 0.132163E-02 3.296541£'-03 0. 117877E'-03

10 0.791603E-03 0.169442E -03 0. 640970E'-04

11 0.48356SE-03 0.9a4120E'-04 0. 357624E'-04

12 0.30i40sE-03 0.5830&2E'-04 0. 204628E'-04

ilEVilO.OO Z = 29.

0 0 0. 128370E 01 0.a60967£ 00 0. 70063CE 00

1 0. 418644E'-00 0.2481S5E'-00 0. 186629E'-00

2 0. 180140E'-00 0.964691E'-01 0. 679755E'-01

3 0. 07C162E'-01 0.428992E -01 0. 2B6279E'-01

4 0. 457815E'-01 0.20986CE'"01 0. 133397E'"01

5 0. 25455SE'-01 0tl09453£ -01 0. 666056E'-02

6 0. 148127E'-01 0.601090E'-02 C. 351476E--02

7 0« 691t>35£'-02 0.343290E -02 0. 193493E'-02

8 0. 5526S5E'-02 0.202721E -02 3. 110417E.-02

9 0. 35069OE--02 0.i22Sa7£ -02 0. 648771E -03

10 c. 22724iE'-02 &.764162E'-03 0. 391123E'-03

11 0. 149a44£'-02 0.404450E -03 3. 2409ti7E -03

12 G • 10u40o£'-02 C.312799E -03 0. 151446E'"03

5/9 7/5 / C 9/2 II/?

0. 315182E -00 0a248745E -00 0a205605E-00 0.175290E--00

0« 366803E -31 0a263397£ -01 3al99798E"01 0 • 157i>25£--31

0 • 743820E "02 3a478232E -02 0a329e61£-02 0 • 239031E'-02

0 • 178563E -02 Oa 1 35633E "02 3a675839£-33 0 •457256E -33

0< 535598E "03 0a29O59OE -03 Sal72132£-•03 0 • 108626E'-33

0. 174199E -03 0aa80385E -34 0a488664E-04 0i290389£'-04

Ot 642378E'"04 0a302539E "04 Ba 157471E-34 Oi 8 820 14E'-35

0 • 248902E -04 Oa 1 1 0?99E "34 Ba542600E-05 -35

0. 104604E -04 0a436707E "05 0a203310£"35 0al32626£'-35

0. 455083E -05 Oal80141E "05 3a797948E"06 0a384383E'-06

0. 209654E'"05 0a787976E "0 6 Ba332558E-36 Oal53083E'-36

0> 991492E -06 0a355426E "06 3al43475E-36 0a633242E^-37

0> 489400E'-06 0. 167557E "06 Sa647776E-07 0a274463E^-37

0. 331791E'-00 0a263926E "00 0a219377E-00 0al87816E'-00

0 • 409593E*-01 0a297185E "0

1

0a227209E-01 Oa 160145E--01

0« 360064E'-02 0 a 567?5 1

E

"02 0a392830E-02 0 a 287607E*-02

0» 214718E'-02 0 • 129582E "02 0a842343E-03 0 a 577395E'-03

0 • 660304E'-03 0 a367316E "03 0a222024E-03 0 a 142486E'-03

0< 221027E'-03 Oall48e4E "03 0a652582E-04 0a395439E'-04

0« 831215E-04 Oa404197£'"04 0a216073E-04 0al23809£^-04

0, 329433E-04 Oa 151132E'-34 3a765552£-05 0a417177E'-05

0. 140727E-04 0a61014OE "3 5 3a293353£-05 0al52278E'-05

0. 623712E'-05 0a256987E "35 0all7830E-05 0a584993E-36

0. 291407E'-05 0all4297E'"0 5 0a500549E-06 0a238335E'-06

0> 139998E-05 0a524771E "06 Oa220256E-06 Oal00&26E'-06

0« 699625E-06 0a251008E'-06 Oal01112£-06 0a444373E^-07

0. 382497E'-00 0a311274E -00 0.263030E-00 0«22e02eE^-00

0» 557530E'-01 0 a4 1&798E'"0

1

0.326084E-01 0a263371E'-01

0. 130027E'-01 Oa890195E'"02 Oa644847E-02 0.486177E'-02

0< 362522E'-02 0a231305E -02 0al57244E-02 0alX186<>E'-02

Oa 120409E"02 0a717321E'"0 3 3a458532c-03 0a308411E-03

0. 437418E--03 0a245595E'-03 0al48733£-03 0.951706E--04

0« 174976E-03 0 a 928427E'"04 0a534012£-04 0a325e25£'-04

0 • 740229E-04 \i * 3 t SULZ. 0a204935£-'04 0.119725£"04

0. 333123E-04 0al60080£'-04 3a840472E-05 0»471083£'-05

3. 155909E--04 0a716625E'-0 5 3a361072E"05 0al94734E-05

0. 762200E-05 0a335772E'-0 5 3a 162646E-05 Oa845441E--06

0, 383770E-05 Oa 162485E'-0 5 3a758524E-06 0i3S0838E-06

0 • 199660E"05 0a613792E'"06 0a366669E- 06 0al78062E-06

0. 463916E-00 0a390316E'-00 0a338120£- 00 0»298876E-00

Oa a45172£-01 0a660563£'-01 Oa535272£-01 Oa444974E--01 Oa 229764E--01 0 a 167702E'-01 0al27887E"01 Oal00622E"01

Oa 743410E'-02 0a512532E -02 0a371259E"02 0a278&60£--02

Oa 276938E'-02 0 a 1 8 1039E'-02 0al24995£-02 0a897826E-03

3a 112514E--02 0a701505£'-03 3a463925E- 03 0a320242£-03

Oa 493893E--03 0 a 294613E'-03 0al87139£-03 0al2*454E"03

Oa 228801E-03 0al31062E'-03 0a802174E" 04 Oa515404E--04

3a 111423E-03 Oa614364E'-04 0a363092£- 04 0.225819E-04.

3. 563312E-04 0 a299737E'-04 0al71436E- 04 Oal0341*E-04

Oa 295077E-04 0al51796E'-04 3a841586E- 05 0.493123E--05

Oa 158946E-34 0a791992E'-0 5 0a426344E- 05 0a243024E"05

3a 879480E"05 0 a425078£'-05 0a222468E" 05 0al23508E--05

Oa 602247E 00 0a532648E 00 0a479729E- 00 0a437653E--00

0 a 150390E-00 0al25706E'-00 0al07591£- 00 0a936628E--01

C a 519592E"01 Oa414805E'-01 0a340653E" 01 Oa285521E--01 Oa 209275E--01 Oa 160666E'-01 3al27366E- 01 0al03338E--01 Oa 936815E-02 0a694326£-02 Sa533147E- 02 0a420042£--02

Oa 451140E--02 0a323867£'-02 0a241585£- 02 0al85306£--02 Ca 230266E--02 0al60506£'-02 Oall6560E- 02 0a872151E--03 Oa 122921E-02 0a833722E'-0 3 0a590554E" 03 0a431787E--03 0a681535£--03 0.450571E'-03 0a311776E- 03 0a223060E--03

Oa 389766E--03 0a251548E"03 0al7O267E" 33 0all9349E--03

3a 229049E--03 0al44491£-03 0a957821E- 04 0a658472E--04

Ca 137752E-03 0a850389E--04 0a552655£- 04 0a372992E--04 846000E--04 0a511634E--04 0a326295E- 04 0a216393£--04

61
Table 2. Spatiol Moments, Plane Perpendicular Source — Continued

n D= - 1/9 1/5 3/?

M£V = 0<05 Z = 50t

0 0>2119&<tE 01 0 •643694E 00 0«371104E -00

1 0.233'.16£-00 0.637946E -01 0.330460E -01

2 0>813438E-01 0>16'>232E -01 0.684021E -02

3 0.206691E-01 0.372254E -02 0.139850E -02

<» 0.86'»823E-02 0,130823E -02 0.424379E -03

0«298817E"02 0«41241dE -03 0*1226B4E -03

6 0.13902eE-02 0.1699e3E -03 0.453723E -04

7 0.5703iOE-03 0.643869E -04 0< 160209E -04

e 0.285624E-03 0.294815E -04 0.&71315E -05

9 0* 131006E'~03 — 04 •J • £ I \Jt3£.^ L —05

10 0«6937'»2E-0* 0 abZ 1967E -05 0* 1236&3E -05

11 0.344513E-04 0.29i6l7E -05 0»549239E -06

12 0.190751E-04 0«131552£ -05 0«26d707E -06

MEV = 0*10 2» 50*

0 U«2UDO90t Ul 00 — 00

1 0.215043E-00 0.613067E -01 0.326594E -01

2 0.716962E-01 0>132843E -01 0.658869E -02

3 0.172138E-01 0.330374E -02 0.129371E -02 0.692665E-02 0.112116E -02 0.38104eE -03

3 0a228122E-02 0>338<»51E -03 0* 106042E -03

6 0.102035E-02 0.134489E -03 0.379585E -04

7 0.400554E-03 0.'>90381E -04 0.129177E -04

8 0.192885E-03 0.215788E -04 0.523181E -05

9 0<846891E-0't 0>a91'>00E -05 0.203461E -05

10 0.432491E-0'. 0.'t21981E -05 0.e99540E -06

11 0.206'»97E-04 0.190575E -05 0.385i44E -06

12 0.110076E-04 0«954e4&E -06 0*182020E -06

MEV« 0.20 2 = 50

0 0 0. 201897E 01 0. 662898E 00 0. 395172E -00

1 Ot 205269E-00 0. 610985E -01 0. 332872E -01

2 0, 666747E-01 0> 149597E -01 0. 664435E -02

3 0. 156733E-01 0. 317794E -02 0. 123812E -02

4 0< 614624E-02 0. 105628E -02 0. 373615E -03

5 0. 198453E-02 0. 313343E -03 0. 102531E -03

6 0. 865731E-03 0. 121807E -03 0. 360451E -04

7 0. 333278E-03 0. 436546E -04 0. 120839E -04

8 0. 156613E-03 0. 187789E -04 0. 460027E -05

9 0» 676175E-04 0. 762095E -05 0. 183773E -05

10 0. 336375E-04 0. 352e43E -05 0. 796462E -06

11 0. 157601E-04 0. 156544E -05 0. 335555E -06

12 0. 820766E-05 0. 767291E -06 0. 155424E -06

MEV = 0.40 Z = 50

0 0« 1960b8E 01 0. 674639E 00 0.410328E -00

1 0.204177E -00 0. 638034E -01 0.355919E -o:

2 0.650598E -01 0. 155235E -0.1 0.713892E -02

3 0.155116E -01 0. 334919E -02 0.140991E -02

4 0.598905E -02 0. 110327E -02 0.408327E -03

5 0.194989E -02 0. 330466E -03 0.113425E -03

6 0.838945E -03 0. 127244E -03 0.397003E -04

7 0.324ba2E -03 0. 468694E -04 0.134133E -04

8 0.130637E -03 0. 195444E -04 0.529767E -05

9 0.651971E -04 0. 795661E -05 0.203783E -05

10 0.320623E -04 0. 364950E -05 0.877453E -06

11 0.150313E -04 0. i62110E -05 0.370623E -06

12 0.774398E -05 0. 7b7323E -06 0.170484E -06

MEV= 0.70 2-50.

0 0. 188653E 01 0.6902e6E 00 0. 431057E -00

1 0. 209573E -00 0.696077E -01 0. 399547E -01

2 0. 658805E -01 0.170208E -01 0. 8ie054E -02

3 0. 163973E -01 0.383367E -02 0. 169110E -02

4 0. 628417E -02 0.126567E -02 0. 495752E -03

5 0. 211121E -02 0.391314E -03 0. 142474E -03

6 0. 904831E -03 0. 15097bE -03 0. 503065E -04

7 0. 35SS85E -03 0.557725E -04 0. 174530E -04

8 0. 166118E -03 0.23ttl55E -04 0. 694183E -05

9 0. 732789E -04 0.9b8654E -05 0. 272770E -05

10 0. 360169E -04 0.454514E -05 0. 118156E -05

11 0. 171487E -04 0.205146E -05 0. 507887E -06

12 0. 883675E -05 0.99a685E -06 0. 234854E -06

62

5/2 / c 9/2

U«2593Z6t -00 0.198934E —00 0 . 161231E- 00 0. 135490E -00 0.209325E -01 0.146746E -01 0. 109466E-01 C.351898E -02 0.365b03E -02 0.223484E -02 0. 148490E- 02 0.104569E -02 0.680999E -03 0.382068E -0 3 0. 234a42E-03 0.153959E -03 0.182391E -03 0.918464E -04 0. 513369E-04 0.309221E -04

n./. tii.y. o"7P U*^Z f £.7 sc. —0 if 118508E- 04 f\ ^ f».e^or\ z ^ F U • OO 1 5 c -0 5 0.163292E -04 0.699312E -0 5 0. 336b95E-05 0.176931E -05 0.538011E -05 0.2158&8E -0 5 0. 978053E- 06 0.484789E -06 0.208381E -05 0.777598E -06 0. 329437E- 06 0.153409E -06 0.790811c -06 0.278640E -06 0. 111785E- 06 0.494265c -07

0.338723E -06 0.11217OE -06 0. 424551E- 07 0.177709E -07

0. 142391E -06 0.448011E -07 0. 161470E-•07 0.644977E -08 0.657872E -07 0. 196068E -07 0. 671263E-08 0.255361E -08

-00 u t o oy xc —00 0 • 169821E-•00 U. L** J i — 00 0.210845E -01 0.149928E -01 0. 113103E-01 0.S8833OE -02 0.360913E -02 0.224544E -02 0. 151379E- 02 0.107896E -02 0.649382E -03 0.373058E -03 0. 233763E- 03 0.155745E -03

0.16961.5E -03 0.878185E -04 0. 502161E- 04 0.3O8323E -04 0.437678E -04 0.211251E —04 0 • 113153E-04 0.653587c -05 0.142780E -04 0.634019E -0 5 0. 314877E-05 0.169732E -05 0.455198E -05 0.190102E -0 5 0. 891120E- 06 0.454869E -06 0.170966E -05 0.666197E -06 0. 292915E-06 0.140881E -06 0.627880E -06 0.231740E -06 0. 967779E-C7 0.443237E -07 0.260501E -06 0.906106E -0 7 0. 357964E- 07 0.155609E -07 0.105997E -06 0.351205E -0 7 0. 132456E- 07 0.550843E -08 0.474131E -07 0.149154E -07 0. 535609E-0B 0.212619E -08

0.281254E -00 0.218255E -00 0. 178291E-00 0. 150687E -00 0.218090E -01 0.156768E -01 0. 119267E-01 0.943213E -02 0.371445E -02 0.234611E -02 0. 160048E- 02 0.115182E -02 0.662748E -03 0.388029E -03 0. 246877E-03 0.166573E -03 0.171296E -03 0.907638E -04 0. 528834E-04 0.329822E -04

0 . 437438 E -04 0.216OU3C —04 0 • H8694E-04 U.6903 / jC -05 0.140692E -04 0.643827E -0 5 0. 327886E-05 0.ie0569E -05 0.443109E -05 0.191240E -05 0. 921730E-06 0.481890E -06 0.163736E -05 0.661321E -0 6 0. 299816E-06 0.148084E -06 0.593312E -06 0.227504E -06 0. 981S79E- 07 0.462823E -07

0.241899E -06 0.876321E -07 0. 358647E-07 0. 160830E -07 0.970339E-07 0.335503E -07 0. 131343E- 07 0.564536E -08 0.426257E-07 0.140223E -0 7 0. 523757E- 08 0.215330E -08

0.295324E -00 0.2 30 8 13E -00 0 • 189483E- 00 U • i oU 1 ^UC. "00 0.236670E-01 0.171922E -01 0. 131851E- 01 0.104943E -01 0.408446E -02 0.262356E -02 0. 181303E- 02 0.131834E -02 0.744653E -03 0.444883E -0 3 0. 287550E- 03 0.196536E -03 0.193489E-03 0.105168E -03 0. 625426E- 04 0.396708E -04

0.501562E-04 0.255725E -04 0 * 143287E- 04 0.859626E -05 0.161404E-04 0.763257E -0 5 0. 399438E- 05 0.225106E--05 0.513525E-05 0.229589E -05 0. 113988E- 05 0.611276E -06 0.189380E-05 0.795254E -06 0. 372654E- 06 0.189391E--06 0.690872E-06 0.276007E -06 0. 123388E- 06 0.599714E--07 0.280692E-06 0.106260E-06 0. 451754E- 07 0.209458E--07 0.113073E-06 0.409292E-07 0. 166757E- 07 0.742470E--08 0.494502E-07 0.170725E-07 0. 665280E- 08 0.283996E--08

0.314890E-00 0.248479E-00 0. 205364E- 00 0.175072E--00 0.270382E-01 0.198835E-01 0. 153905E- 01 0.123395E--01 0.481897E-02 0.316132E-02 0. 222016E- 02 0.163520E-02

0.922786E-03 0.564705E-C3 0. 372054E- 03 0.258296E-03

0.244739E-03 0.137291E-03 0. 837387E- 04 0.542364E--04 0.658275E-04 0.347442E-04 200264E- 04 0.123030E-04

0.215059E-04 0.105884E-04 0. 572961E- 05 0.332170E-05 0.704391E-05 0.328777L-05 0. 169242E- 05 0.936146E--06 0.262e75£--05 0.115772E-05 0. 564869t- 06 0.297273E-06

0.981791E-06 0.412358E-06 0. 192415E- 06 0.970784E-07

0.402820E-06 0.160916E-06 0. 716613E- 07 0.346057E--07 0. 165459E-06 0.633350E-07 0. 270899E- 07 0.125902E-07

0.729663E-07 0.267221E--07 0. 109648E- 07 0.490000E-08
Table 2. Spatial Moments, Plane Perpendiculor Source — Continued

n = — i/o 1 /1 3/0 7/9 9/> 11/,

MEV = 1«00 Z = 50 •

0 0.182016E 01 0. 70502eE 00 0. 451152E -00 0. 334208E'-00 0 .266149E -00 0. 221403E-00 0« 189666E'-00

1 0.216277E-00 0. 759749E -01 0. 447614E-01 0. 307823E'-01 0 .228941E -01 0« 178731E-01 0. 144275E -01

2 0.67508'(-E-01 0> 187673E -01 0. 93893aE -02 0. 568044E'-02 0 .379942E -02 0. 270839E-02 0> 201871E'-02

3 0.175624E-01 0. 441848E -02 0. 203380E -02 0. 114304E'-02 0 .715244E -03 0« 479632E-03 0> 337839E'-03 0.672288E-02 0. 147006E -02 0. 606190E -03 0. 310589E'-03 0 .179310E'-03 0. 111932E-03 0> 739030E'-04

5 0.233309E-02 0« 469695E'-03 0> 180437E'-03 0. 867562E'-04 0 .472562E -04 0. 279522E-04 0> 175607E'-04

6 0.100198E-02 0, 182575E'-03 Oi 645765E'-04 0. 288898E'-04 0 •147534E -04 0. 822968E-05 0( 489601E'-05

7 0.407229E-03 0. 69209bE'-04 0. 230354E'-04 0. 975259E'-05 0 .473339E'-05 0< 251802E-05 Oi 143275E'-05

8 0.189366E-03 0« 297735E'-04 0. 927092E'-05 0. 369861E-05 0 .170061E -05 0. 860687E-06 0> 467542E'-06

9 0.852592E-04 0« 126232E-04 0« 372704e'-05 0. 141629E-05 0 .622436E'-06 0« 301953E-06 0< 157601E'-06

10 0.421024E-04 0> -05 0. 163172E'-05 0. 589308E--06 0 •247143E -0 6 Oi 114781E-06 0> 575100E'-07

11 0.2039ieE-04 0. 268572E--05 0. 715037E'-06 0. 247236E-06 0 .995533E'-07 0« 444984E- 07 Ot 215013E-07

12 0.105623E-04 0. 1316e2E--05 0, 333890E-06 0. 110405E-06 0 • 426301E'-07 0. 183370E- 07 0< 854136E-03

MEV = 2,00 Z= 50 •

0 0 0.166229E 01 0.743289E 00 0. 505939E 00 0<388619E-00 0.317090E-00 0.268463E-00 0<233065E-00

1 0.239573E-00 0.968341E-01 0« 608830E-01 0.436085E-01 0.333873E-01 0.266494E-01 0.2X8973E-01

2 0.750472E-01 0.250330E-01 0< 138126E-01 0.892260E-02 0.626340E-02 0.463613E-02 0.356242E-02

3 0«220783E-01 0«667265£-02 0> 340934E-02 0.206088E-02 0« 136316E-02 0.955672E-03 0»698394E-03

4 0«860304E-02 0»230878E-02 0« 107869E-02 0.604927E-03 0«374710E-03 0.247695E-03 0»171575E-03

5 0.326758E-02 0.809187E-03 0> 354403E-03 0.187812E-03 0.110529E-03 0.696982E-04 0>462063E-04

6 0. 143778E-02 0.326514E-03 0« 133521E-03 0.666869E-04 0.372207E-04 0«223644E-04 0.141797E-04

7 0.627508E-03 0.133259E-03 0* 515694E-04 0.245288E-04 0.130945E-04 0.755019E-05 0«460592E-05

8 0.299775E-03 Of 594201E-04 0. 217351E-04 0,983870E-05 0.502193E-05 0.277841E-05 0.163095E-05

9 0. 14317eE-03 0.267931E-04 0. 933993E-05 0.404991E-05 0.198726E-05 0.105986E-05 0.601074E-06

10 0.727000E-04 0.128411E-04 0. 426562E-05 0.177193E-05 0.836035E-06 0.429951E-06 0<235666E-06

11 0.370406E-04 0.622060E-05 0. 197989E-05 0.791379E-06 0.360375E-06 Otl79290E-06 0.952512E-07

12 0.197269E-04 0.315160E-05 0. 961416E-06 0.369923E-06 0.162654E-06 0.783202E-07 0i403490E-07

MEV = 4.00 Z= 50«

0 0 0.147129E 01 0.797057E 00 0. 589712E 00 0.476666E-00 0.403018E-00 0.350432E- 00 0a310&82E-00

1 0.272545E-00 0.133502E-00 0. 918895E-01 0.698177E-01 0.558315E-01 0.461187E-01 0.389763E-01

2 0.888482E-01 0.37748bE-01 0. 236636E-01 0.166827E-01 0.125132E-01 0.976718E-02 0<784291E-02

3 0.303306E-01 0.117744E-01 0. 691871E-02 0.461884E-02 0.330087E-02 0.246552E- 02 0<190086E-02

4 0.124397E-01 0.440065E-02 0. 242025E-02 0.152896E-02 0. 104090E-02 0.744115E-03 0.551047E-03

5 0.526459E-02 0.173289E-02 0. 903447E-03 0.545271E-03 0.356354E-03 0.245392E-03 0.175512E-03

6 0.244442E-02 0i750038E-G3 0. 371146E-03 0.214262E-03 0.134580E-03 0.893743E-04 0.6X8097E-04

7 0.116332E-02 0.336296E-03 0. 159038E-03 0.882917E-04 0.535379E-04 0.344199E- 04 0.230947E-04

8 0.585946E-03 0.159954E-03 0. 724046E-04 0.387069E-04 0.226867E-04 0.141365E- 04 0.921270E-05

9 0.301124E-03 0t781168E-04 0. 339902E-04 0.175570E-04 0.997527E-05 0.503964E-05 0.383152E-05

10 0.160863E-03 0.397454E-04 0. 166478E-04 0.831877E-05 0i458668E-05 0.270111E-05 0>166968E-0S

11 0.874C41E-04 0.206493E-04 0. 835013E-05 0.404593E-05 0.216920E-05 0.124472E-05 0.750911E-06

12 0.488658E-04 0. 110602E-04 0. 432326E-05 0t203337E-05 0. 106108E-05 0.593781E-06 0.349881E-06 MEV=10.00 Z=50.

0 0.125340E 01 0.872687E 00 0« 722447E 00 0. 628176E 00 0t560420£ 00 0. 508263E 00 0>466373£ -00

1 0.327278E^-00 0.208403E -00 0. 162842£^-00 0. 134966E^-00 0.115397E -00 0« 100671E-00 0«891002E -01

2 0.121946E'-00 0.711676E -01 0. 526326E^-01 0. 417175E -01 0»343079E -01 0. 288989E-01 0«247667E -01

3 0.508175E^-01 0.277170E -01 0. 196126E^-01 0. 149889E^-01 0.119370E -01 0. 976560E-02 0<814«10E -02

4 0.236335E^-01 0.121182E'-01 Oa 823256E^-02 0. 608339E'-02 0.470297E -02 0. 374500E-02 0<30M86E'-02

5 0.116337E'-01 0.565588E'-02 0. 370732E^-02 0. 265901E'-02 0.200198E^-02 Ot 155614E-02 0.123796E-02

6 0.606391E'-02 0.280738E^-02 0. 178013E'-02 0. 124185E'-02 0.912238E'-03 0. 693290E-03 0«540103E-03

7 0.327652E'-02 0.145156E -02 0. 893005E'-03 0. 607349E'-03 0.436163E'-03 0. 324674E-03 0«248095E-03

8 0.183605E'-02 0.780766E^-03 0. 466905E'-03 0. 310063E--03 0.217979E'-03 0« 159124E-03 Otll9400E'-0 3 9 0.105530E'-02 0.432222E'-03 0. 251752£^-03 0. 163508E-03 0.112688E'-03 0> 807753E-04 0<595890E'-04

10 0.622ai6E'-03 0.24617aE'-03 0. 139872£^-03 0. 889583E'-04 0.601710E'-04 0. 423961E- 04 0.307795E--04

11 0.374914E'-03 0.143399E -03 0. 796084E^-04 0. 4964B4E-04 0.329999E'-04 0. 228822E-04 0>163671E--04

12 0.230459E'-03 0.854826E^-04 0. 464375E'-04 0. 284362E-04 0.185957E'-04 0. 127044E- 04 0.894317E-05

MEV = 0<10 Z = 82«

0 0 0«215598E 01 0.637042E 00 0.362973E -00 0. 252034E-00 0.192578E -00 0< 155663E -00 0, 130559E -00

1 0.145450E-00 0.399781E -01 0.212012E -01 0. 137484E-01 0«984798E -02 0. 748935E -02 0. 592969E -02

2 0.475773E-01 0.945426E -02 0.394269E -02 0. 212383E-02 0.131041E -02 0. 880286E -03 0. 626953E -03

3 0.810198E-02 0.148787E -02 0.5'74647£ -03 0. 287948E-03 0.166049E -03 0. 104720E -03 0> 703060E^-04

4 0.313144E-02 0»47b640£ -03 0.157015E -03 0> 6e7455E-04 0.352988E -04 0. 201167E^-04 0« 123482E'-04

5 0.773991E-03 0.110047E'-03 0.33a981£'-04 0. 139162E-04 0.672167E -05 0. 361509E^-05 0< 210067E'-05

6 0.328149E-03 0>410248£<-04 0.112572£^-04 0. 416878E-05 0.183603E -05 0. 908617E^-06 Oi 489538E--06

7 0.100658E-03 0.1ie577£ -04 0.306801E'-05 0. 107335E-05 0«447636E^-06 0. 210272E'-06 0. 107787E--06

8 0.455790E-04 0,487253E'-05 0.115210E^-05 0. 371075E-06 0.143438E'-06 0. 628257E'-07 0. 301867E'-07

9 0.161539E-04 0tl63826E^-05 0.367667E^-06 0. 112559E-06 0.414285E^-0 7 0< 173100E--07 Ot 794881E-08

10 0.770234E-05 0,722688E^-06 0.150683E^-06 0. 430609E-07 0.148618E'-0 7 0< 584708E'-08 Ot 253777E--08

11 0.303136E-05 0.271286E^-06 0.539713E'-07 0. 147332E-07 0.486389E^-08 0. 183319E-08 Ot 763318E--09

12 0.150822E-05 0.126499E^-06 0.236501E.-07 0. 608648E-03 0.190044E'-08 0. 679484E-09 Ot 269157E--09

63
Table 2. Spotiol Moments, Plane Perpendicular Source — Continued

n P=-l/2 1/2 VZ

MEV= 0.20 Z'82t

0 0 • 206&03E 0

1

0 • 650 14 IE 00 —00

1 0. 129397E -00 0. 378541E -01 0.207433E -01

2 0. 't05122E -01 0. U66059e -02 0.377005E -02

3 0. 6'>0't91E -02 0. 127430E -02 0.517870E -03

0. 236493E -02 0. 392324E -03 0.i37012E -03

5 0. 5't609'tE -03 0. 850667E -04 0.279536E -04

6 0. 220857E -03 0. 303625E -04 0.893498E -05

7 0. 63Sa71E -04 0. ti26^y54E -05 0.230574E -05

8 0. 274'»45E -04 0. 324725E -05 0.830644E -06

9 0. 9162b6E -05 0. 103163E -05 0.251432E -06

10 0. '»16290£ -05 0. 434481E -06 0.986783E -07

11 0« 1547 786 -05 0« i54459E -06 0.335769E -07

12 0. 733784E -06 0> 667369E -07 0.140762E -07

MEV> 0>40 Z'B2b

0 0. 200135E 01 0>666398E 00 0. 399654E -00

1 0. 123079E -00 0.386056E -01 0. 218630E -01

2 0, 370955E -01 0>86561bE -02 0< 396087E -02

3 0. 5793a8E -02 0.126244E -02 0. 542024E -03

4 0> 206347E -02 0.378532E -03 0» 141196E -03

5 0> 469783E -03 0.811198E -04 0« 2e5853£ -04

6 0. 183513E -03 0.281352E -04 0. 894626E -05

7 0. 520154E -04 0>755804E -05 0. 228426E -05

8 0. 217093E -04 0>28ai96E -05 0. 803549E -06

9 0« 712748E -05 0.901714E -06 0. 240162E -06

10 0. 313455E -05 0.368745E -06 0. 919126E -07

11 0> 114513E -05 0«128961E -06 0> 308329E -07

12 0. 525960E -06 0.557353E -07 0. 125961E -07 MEV» 0.70 Z»82.

0 0 0.190429E 01 0.686462E 00 0.425935E -00

1 0.124255E-00 0.422318E -01 0.248427E -01

2 0,362491E-01 0.939300E -02 0.455604E -02

3 0.591669E-02 0.143236E -02 0.653853E -03

4 0.205193E-02 0.423803E -03 0.170447E -03

5 0.483367E-03 0.940092E -04 0.358066E -04

6 0.1846 56E-03 0.321566E -04 0.111604E -04

7 0.537625E-04 0.8e7634E -05 0.293419E -05

8 0.220120E-04 0.333989E -05 0.102589E -05

9 b.73a256E-05 0.106788E -05 0.313892E -06

10 0.319240E-05 0.431261E -06 0.119294E -06

11 0.118630E-05 0.153472E -06 0.407845E -07

12 0.536695E-06 0.655528E -07 0.165393E -07

MEV» 1.00 .2 = 82 .

0 0 0.18i865E 01 0.705370E 00 0.451625E -00

1 0.128040E-00 0.468159E -01 0.284706E -01

2 0.365076E-01 0.104137E -01 0.532366E -02

3 0.631034E-02 0.168145E -02 0.810674E -03

4 0.21536eE-02 0.495763E -03 0.213264E -03

5 0.530928E-03 0.115085E -03 0.469732E -04

6 0.200546E-03 0.392370E -04 0.147224E -04

7 0.605889E-04 0.112404E -04 0.402398E -05

8 0.246079E-04 0.421917E -05 0.141273E -05

9 0.851047E-05 0.139141E -05 0.446534E -06

10 0.365895E-05 0.561020E -06 0.170295E -06

11 0.139535E-05 0.204950E -06 0.598519E -07

12 0.628667E-06 0.874612E -07 0.243484E -07

MEV = 2.00 Z = 82.

0 0.165215E 01 0. 745919E 00 0. 509848E 00

1 0,146382£-00 0. 620839E -01 0. 403520E -01

2 0.408400E-01 0. 141726E -01 0. 804347E -02

3 0.d37800£-02 0. 27101<)E -02 0. 145459E -02

4 0.284931E-02 0. 817193E -03 0. 401014E -03

5 0.805298E-03 0. 217301E -03 0. 101487E -03

6 0.306551E-03 0. 759179E -04 0. 331570E -04

7 0. 103708E-03 0. 243530E -04 0. 101797E -04

8 0.427448E-04 0. 9385655 -05 0. 371664E -05

9 0. 162757E-04 0. 340932E -05 0. 129795E -05

10 0.713232E-05 0. 141335E -05 0. 514022E -06

11 0.295694E-05 0. 561719E -06 0. 197126E -06

12 0.136165E-05 0. 246650E -06 0. 831772E -07

5/2 V2 9/2

1 1 ^ 11/2

0.266540E -00 0.205256E-00 0. 166792E-00 0.140429E -00

0. 137474E -01 0. 100086E-01 0. 771089E-02 0.617124E -02 0.2O9057E -02 0. 131774E -0 2 0. 900110E- 03 0.649a76E -03 0.269181E -03 0. 159681E -0 3 0. 103034E- 03 0.705094E -04 0.626458E -04 0.332769E -04 0. 194941E-04 0.122444E -04

0. 120603E -04 0.606263E -0 5 0. 337048E-05 0.201437E -05

0. 349600E -05 0.161048E -0 5 0. 827566E-06 0.460441E -06 0.856624E -06 0.375535E -06 0. 184045E- 06 0.9786605 -07 0.285307E -06 0.116413E -06 0. 534094E-07 0.267195E -07 0.824235E -07 0.321552E -0 7 0. 141301E- 07 0.678226E -08 0.302989E -07 0.111226E -07 0. 461811E-08 0.210202E -08 0.98ei46E -08 0.348186E -08 0. 138967E-08 0.608890E -09 0.391646E -08 0. 13090eE -08 0. 497125E- 09 0.207821E -09

0.285394E -00 0.221937E -0 0 0. 181564E- 00 0.153619E -00 0.148 141

E

-01 0. 109507E -01 0. 853667E-02 0.6897aOE -02 0.227020E -02 0.146553E -02 0. 101951E-02 0.746886E -03 0.292742E -03 0.17874bE -03 0. 118009E-03 0.822904E -04 0.677305E -04 0.373337E -04 0. 225291E-04 0.145013E -04 0.129961E -04 0.680938E -05 0. 391629E-05 0.240826E -05 0.371592E -05 0.179621E -0 5 0. 960596E-06 0. 5528415 -06 0.904164E -06 0.417488E -06 0. 213734E-06 0.117987E -06 0.295743E -06 0.127797E -0 6 0. 615607E-07 0.321224E -07 0.846157E -07 0.350715E -07 0. 162338E-07 0.815316E -08 0.304704E -07 0.119378E -07 0. 52436aE-0e 0.250765E -08 0.982206E -08 0.370384E -08 0. 156831E- 08 0.724014E -09 0.3e07eOE -08 0.136725E -08 0. 552899E-09 0.244407E-09

0.310020E -00 0.244060E -00 0. 201378E-00 0.171461E -00 0.172010E -01 0.129161E -01 0. 10ia87E- 01 0.83104aE -02 0.271366E -02 0. 18Q096E -02 0. 127955E-02 0.953191E -03 0.368301E -03 0.232044E -0 3 0. 157014E-03 0.111707E-03

0.863191E -04 0.496027E -04 0. 309460E- 04 0.204722E-04 0.172408E-04 0.944918E -0 5 0. 563743E-05 0.357462E -05 0.495474E -05 0.252608E -0 5 0. 141171E- 05 0.843250E-06

0.124478E -05 0.60e02&E -06 0. 326280E-06 0.187509E-06

0.40756eE-06 0.187560E -06 0. 952a83E- 07 0.520550E -07 0.119663E -06 0.529605E -07 0. 259257E- 07 0.136697E -07 0.430348E -07 0.181025E -0 7 0. 845321E-08 0.426470E -08 0.141677E -07 0.574981E -08 0. 259470E- 08 0.126&89E -08 0.547754E-08 0.212647E -08 0. 920522E- 09 0.432191E-09

0.334668E-00 0.266572E -00 0. 221789E- 00 0.190018E--00 0,201156E-01 0.153189E -01 0. 122129E- 01 0.1004SeE -01 0.328317E-02 0.223467E -02 0. 161879E- 02 0.122471E-02 0.474076E -03 0.307187E -03 0. 212514E- 03 0.153956E -03 0.113353E-03 0.676095E -04 0. 434620E- 04 0.294736E--04

0.237965E -04 0.135731E -04 0. 836629E- 05 0.545236E--05 0.693319E-05 0.370558E -05 0. 215345E- 05 0.132970E--05 0.iei487£-05 0.931610E -06 0. 52H58E- 06 0.310375E--05 0.600478E-06 0.292113E -06 0. 155546E- 06 0.884934E--07 0. 182498E-06 0.355729E -07 0. 440078E- 07 0.242212E--07 0.661961E-07 0 .296443E-07 0. 146087E- 07 0.772609E--08 0.224449E-07 0.971749E -08 0. 463773E- 08 0.237889E--08 0.874139E-08 0.363496E-08 0. 167062E- 08 0.827060E-09

0.392598E-00 0.320882E -00 0. 272013E- 00 0.23A395E--00 0.296927E-01 0.232637E-01 0. 1894a6E- 01 0.158531E-01 0.531817E-02 0.380957E -02 0. 287132E- 02 0.224289E-02

0.915541E-03 0.627006E-03 0. 453262E- 03 0.340461E-•03 0.234226E -03 0.150285E -03 0. 102490E- 03 0.730148E--04 0.567293E-04 0.349620E-04 0. 229648E- 04 0.157922E-04

0.174973E--04 0.102443E-04 0. 642229E- 05 0.423055E--05 0.516554E--05 0.291725E -05 0. 176828E- 05 0.112837E-•05 0.179883E-05 0.973424E-06 0. 567319E- 06 0.349036E-•06 0.606382E--06 0.317602E-06 0. 179527E- 06 0.107304E-06

0.230615E--06 0.116412E-06 0. 635915E- 07 0.368121E--07 0.856344E-07 0.419557E-07 0. 222a51E- 07 0.125622E- 07 0.348690E-07 0.165342E-07 0. 851882E- 08 0.466651E- 08

64
n

Table 2. Spatial Moments, Plane Perpendicular Source — Continued

p=-l/2 1/2 3/2 5/2 7/2 9/2 11/2

MEV= 4.00 Z=82. i=0 0 0, 01 0«e03859E 00 0«600905E 00 0«488873E-00 0 .415259E -00 0. 362359E -00 0»322168E'-00

1 0, 175290E -00 0,9117a7E -01 0.650525E'-01 0.508133E-01 0 .415816E -01 0. 350395E -01 0t30i395E--01

2 0, *83544E'-01 0.220284E -01 0.143264E'-01 . 0.103941E-01 0 •798688E -02 0» 636705E -02 0.520992E--02

3 Q^ 1246B't£'-01 0.525701E -02 0.325720t'-02 0.226721E-02 0 •167836E -02 0> 129275E -02 0>10243SE'-02

0 • '32734E-02 0.166951E -02 0.972066E'-03 0 • 642 5 64 E—03 0 •4&4p8St -03 0 • 336094E'-03 0«25648eE'-03

5 0. 14^980E'-02 0.52846'tE -03 0.295044E'-03 0.188108E-03 0 .128802E -03 0. 923970E -04 0>6e5'»52E'-04

6 0. 569255E'-03 0.194395E -03 0.103490E'-03 0.633727E-04 0 .41860&E -04 0. 290585E -04 0.209101E--04

7 0. 221't69E-03 0.720346E'-04 0.369676E'-04 0.219292E-04 0 .140741E'-04 0. 951257E -05 0.667575E-05

0. 9'f6449E-04 0.292140E'-04 0.144161E'-04 0.826854E-05 0 • 514848E'-0 5 0. 338423E -05 0.231406E--05

9 0. 405929E'-04 0.12006&E'-04 0.573452E'-05 0.319694E-05 0 .193983E -0 5 0. 124487E -05 0.832227E--06

10 0. 184882E-04 0.523197E'-05 0.241592E-05 0.130e03E-05 0 .772953E'-06 0< 484050E -06 0.316267E'-06

11 0. 850554E-05 0.231722E'-05 0.103891E-05 0.548i63e-06 0 .316399E -06 0> 193853E -06 0<124076E'-06 12 0. 0.106303E-05 0.464743E-06 0.238899E-06 0 • 134662E'-06 0. 807107E -07 0«506027E'-07

MEV= 0.025 Air

0 0 0.201025E 01 0. 664624E 00 0. 397379E'-00 0. 283291E-00 0 .220065E -00 0.179899E-00 Oi 152127E--00

1 0.718231E 00 0. 174648E -00 0. 825087E'-01 0. 486035E-01 0 .321643E -01 0.229003E-01 0. 171509E'-01

2 0.357447E'-00 0. 675555E'-01 0. 263011E'-01 0. 132235E-01 0 .764741E -02 0.484052E-02 0. 326534E -02

3 0.193674E'-00 0. 303174E'-01 0. 101140E'-01 0. 445910E-02 0 .229969E -02 0.131480E-02 0. 809282E^-03 4 0.115974E'-00 0. 154210E'-01 0. 448773E'-02 0. 175879E-02 0 .817693E -03 0.426054E-03 0. 241085E'-03

5 0.723178E'-01 0. 839313E'-02 0. 217138E.-02 0. 767127E-03 0 .325029E -03 0.155697E-03 0. 815818E^-04

6 0,474855E-01 0. 4B8290E'-02 0. 113583E'-02 0. 364972E-03 0 .141947E -03 0.628874E-•04 0. 306678E^-04

7 0.319594E-01 0. 295650E'-02 0. 625594E'-03 0. 184516E-03 0 .663636E -04 0.273596E-04 0> 124817E--04

8 0.222188E-01 0. lB671bE'-02 0. 362222E-03 0. 986955E-04 0 .330026E -04 0.127186E- 04 0. 544937E--05

9 0.157lilE-01 0. 121108E'-02 0. 217099E.-03 0. 550025E-04 0 .171931E -04 0.622256E-05 0. 251388E'-05

10 0.113640E-01 0. 808958E'-03 0. 134760E-03 0. 318987E-04 0 .935952E -0 5 0.319260E- 05 0> 121997E^-05

11 0.832331E--02 0. 530847E'-03 0> 857570E-04 0. 190574E-04 0 .527059E'-0 5 0.170057E-05 0. 616603E--06 12 0>620031E'-02 0. 383374E'-03 0. 560159E-04 0. 117299E-04 0 .306772E'-05 0.938956E-06 0< 323870E--06

MEv= 0.05 Air

0 0 0. 196193E 01 0.67<>3e3E 00 0.409994E -00 0. 295011E-00 0 .230532E -00 0. 189232E-00 0. 160504E-00

1 0. 705657E 00 0.179575E'-00 0.869395E -01 0. 520278E-01 0 .348157E'-01 0. 249951E-01 0. ie8411E-01

2 0. 348996E'-00 0<695371E'-01 0.279540E -01 0. 143694E-01 0 .844785E -0 2 0. 541585E-02 0. 369102E-02

3 0. 188819E-00 0.312723E'-01 0.108252E'-01 0. 490269E-02 0 .258131E^-02 0. 150041E- 02 0. 936134E-03

4 0» 1124^6E'-00 0.158762E'-01 0.481387E'-02 0. 194729E-02 0 .927948E'-03 0. 493322E-03 0. 283870E-03

5 0. 698961E'-01 0.863278E'-02 0.233574E -02 0. 854352E-03 0 .372267E -03 0. 182511E-03 0. 975266E-04

6 0. 456573E^-01 0.500728E'-02 0.122192E'-02 0. 407821E-03 0 .163626E -03 0. 744112E-04 0. 371073E-04

7 0. 306120E'-01 0.302496E'-02 0.673128E'-03 0. 206768E-03 0 .769235E^-04 0. 326370E-04 0. 152630E-04

8 0. 211749E'-01 0.190367E'-02 0.389250E^-03 0. 110733E-03 0 .383970E'-04 0. 152659E-04 0. 672055E-05

9 0. 149114E^-01 0.123109E'-02 0.233039E'-03 0. 617733E-04 0 .200677E'-04 0. 750918E-05 0. 312367E-05

10 0. 107323E-01 0.819174E'-03 0.144350E^-03 0. 358209E-04 0 .109456E'-04 0. 386816E-05 0. 152503E-05

11 0. 782718E--02 0.555917E'-03 0.916832E -04 0. 213963E-04 0 .617376E'-05 0. 206760E- 05 0. 774902E-06

12 0. 580240E'-02 0.385352E'-03 0.597286E -04 0. 131558E-04 0 .359586E'-0 5 0. 114439E-05 0. 408722E-06

MEv= 0.10 Air

0 0 0. 197775E 01 0.671i51E 00 0 .405790E'-00 0. 291090E-00 0.227021E -00 0. 186095E-•00 0. 157684E--00

1 0. 721772E 00 0.160139E'-00 0 .862902E'-01 0. 512850E-01 0.341521E'-01 0. 244297E-•01 0. 183629E'-01

2 0. 358245E'-00 0.698270E'-01 0 .277014E'-01 0. 141107E-01 0.824038E'-02 0. 525554E-•02 0. 356698E-02

3 0. 195105E'-00 0.315178£^-01 0 .107372E'-01 0. 480773E-02 0.250954E^-0 2 0. 144878E-•02 0. 898931E^-03

4 0. 116541E^-00 0.16022eE^-01 0 .477434E'-02 0. 190529E-02 0j6r8725E'-03 0. 473892E-•03 0. 270857E^-03

5 0. i27640E -01 0.873662E'-02 0 .231779E'-02 0. e36291E-03 0,35* 716E'-03 0. 174680E-•03 0. 926010E'-04

6 0. 476509E'-01 0.5O7tiOE^-02 0 .121268E'-02 0. 338236E-03 0.157715E^-03 0. 709576E-•04 0. 350663E-04

7 0. 3205S2E^-01 0.307278E'-02 0 .b68713E<-03 0. 201856E-03 0.740357E'-04 0. 310410E-•04 0. 143707E--04

8 0. 222199E'-01 0.193642E -02 0 • 386849E'-03 0. 108033E-03 0.368945£^-04 0. 144812E-•04 0. 630515E--05

9 0. 1568e4£ -01 0.125465E'-02 0 .231829E'-03 0. 602680E-•04 0.192640E^-04 0. 710974E- 05 0. 292246E--05

10 0. 113115E'-01 0.335869E'-03 0 .143670E'-03 0. 349368E-04 0.104952£^-04 0. 365523E-•05 0. 142288E--05

11 0. 826711E^-02 0.568151E'-03 0 .913331E'-04 0. 208709E-04 0.591590£^-05 0. 195102E- 05 0. 721430E--06 12 0. 613760E -02 0.394253E'-03 0 .595297E'-04 0. 128308E-04 0.344280E'-05 0. i07823E- 05 0. 379686E--06

MEv= 0.20 Air

0 0. 196606E 01 0.673536E 00 0.408889£^-00 0. 293980E-00 0 .229607E -00 0. 188406E-00 0. 159760E-00

1 0. 726624E 00 0.162837E'-00 0.879590E'-01 0. 524210E^-01 0 .349766E -01 0. 250560E-01 0. 188551E-01

2 0. 360996E^-00 0.710537E^-01 0.283556E'-01 0. 145037£^-01 0 .849604E -02 0. 543166E-02 0. 369367E-02

3 0. 197482£^-00 0.322106E^-01 0.110444E'-01 0. 496906E^-02 0 .260353E -02 0. 150763E-02 0. 937821E-03

4 0. 118047E'-00 0.163968E^-01 0.492170E'-02 0. 197527E-02 0 .936000E -03 0. 495417E-03 0. 284067E-03

5 0. 738788E'-01 0.896200£^-02 0.239608E^-02 0. 868875E^-03 0 .376101E -03 0. 183428E-03 0. 976007E-04

6 0. 484020E'-01 0.520982£^-02 0.125532E'-02 0. 415063E-03 0 .165327E -03 0. 747482E-04 0. 370975E-•04

7 0. 326056E^-01 0.315908E'-02 0.693473E^-03 0. 210857E-03 0 .778189E -04 0. 328033E-•04 0. 152584E-04

8 0. 226054E'-01 0.199159E'-02 0.401501E -03 0. 112998E^-03 0 .388498E -04 0. 153385E- 04 0. 671324E-05

9 0. 159734E'-01 0.129153E^-02 0.240888E'-03 0. &31336E-04 0 .203240E -04 0. 754829E-•05 0. 312016E-•05

10 0. 115i64E^-01 0.860546E'-03 0.149351E^-03 0. 366285E--04 0 .110866E'-04 0. 388720E-•05 0. 152232E-•05 11 0. 842039E^-02 0.5o520eE'-03 0.950121E^-04 0. 219039E-04 0.625780E -05 0. 207843E- 05 0. 773463E-•06 12 0. 625008E'-02 0.406053E'-03 0.619380£^-04 0. 134724E--04 0 .364482E'-0 5 0. 115002E- 05 0. 407711E-•06

65
Table 2. Spotial Moments , Plane Perpendicular Source — Continued

n P=-l/2

i-o

0 •

0 0«193466E 01

I 0«729&b6E 00

2 0.36'»3*8E-00

3 0.201019E-00

0» 120635E-00

5 0.759028E-01

6 0.<.98807E-01

7 0.337314E-01

e 0.23'»'»3'tE-01

9 0 • 166 148 E~0

1

1

0

1 1 0»879712E-02

12 0.654068E-02

MEV = o«

0 0>193466E 01

1 0>732494E 00

2 0.365447E-00

3 0.201790E-00

0< 121007E-00

5 0.761462E-01

6 0.500051E-01

7 0.338087E-01

8 0.234800E-01

9 0 • 166341 E^O

1

10 Oa 120078E-01

11 0»879600E-02

12 0.653464E-02

MEVc 1,

0 0 A 1 A? 74fi F 01 0.73? 00^ F 00

2 0,368356£-00

3 0>208128E-00

^

6 0.81i430E-01

6 0.539961E-01

7 0.369786E-01

8 0.259710E-01

9 0« 186006E-01

10 0«133601E-01

11 0»100286E-01

12 0»7516&2E-02

MEVe 2«

0 0«166734E 01

1 0.700656E 00

2 0.370237E-00

3 0.216259E-00

4 0» 135288E-00

6 0.886039E-01

6 0.601780E-01

7 0.420102E-01

8 0.300170E-01

9

1

0

0 ft 16 1 7 ? 0

1

1

1

0*171 34 1 F—0

1

12 0.921784E-02

4»

0 0«148027E 01

1 0,663454E 00

2 0.366655E-00

3 0.225379E-00

*

5 0«992995E"'01

6 0.695327E-01

7 0.499307E-01

8 0.366088E-01

9 0.273060E-01

10 0.206703E-01

11 0.158462E-01

12 0.122844E-01

66

1/2 3/2

40 Air 0.6e003&E 00 0.417408E

0«188407E -00 0.918987E 0,739031E -01 0.300292E

0»338395£ -01 U • 1 1 0444t

Otl73285>E -01 0.532376E

0.953196E -02 0.261331E

0*5^6471E -02 0« 13 7744E 0.338977E -02 0.765483E

0*21439&E -02 0 •445 2 HE

0.139521E -02 0.268329E

0.932019E -03 0.16695BE

0.635579E -03 0.106596E

0.441928E -03 0.696892E

70 Air 0i6e0033E 00 0.417408E

0>188953E -00 0.921103E

0.740506E -01 0.300728E

0 • Loct — 0

1

0.173527E -01 0.532606E

0.954376E -02 0.261346E

0«556719E -02 0. 137632E 0.339006E -02 0.764492E

0»214247E -02 0»444265E

0,139357E -02 0.267608E

0.930183E -03 0.166371E 0«633960E -03 0.106154E

0.440441E -03 0«693420E

00 Air

0.704500E 00 0.450422E

0>206761E -00 0.106559E

0.841037E -01 0.366584E

0.397848E -01 0.151071E

0»20866:3E -01 0.702612E 0.117319E -01 0.355394E

0<696998E -02 0« 192002E 0.431607E -02 0.109110E

lb i 04t "02 0<182513E -02 0.396790E

0«123332E -02 0.250745E

0>S30431E -03 0.162442E

0.597184E -03 0.107594E

00 Air

0.7419fe8E 00 0.504011E

0.235285E -00 0.131882E

0.101296E -00 0.490618E

-01 0.274205E -01 0.105973E

0.159477E -01 0.561555E

U*9fdl9Jc -02 0.619795E -02 0.1fe5906£

0 « 40673 3E -02 U*113/J1E

0.273993E -02 0.717930E

0.188775E -02 0.465613E

0.132555E -02 0.303970E

0.946632E -03 0.209225E

00 Air 0.794306E 00 0.585224E

0.277876E -00 0.174712E

0.129566E -00 0.723667E 0«688764E -01 0»348872E

0.397651E -01 0. 183006E 0.243153E -01 0. 104877E 0.155340E -01 0.625575E

0.102700E -01 0.388379E

0.698359E -02 0.249177E

0.486066E -02 0.164293E

0.345112E -02 0.110886E

0.249246E -02 0.763562E

0.18272BE -02 0.53513bE

5/2

-00 0.301965E-00 0*

— 01 0 • —01 0 • — 01 0 a 54095 2 E~02 0 • — 02 0 • 2 1 744 9 E—02 0 • -02 0.966381E-03 0«

-*02 0 • 465 338 £—03 0 • — 03 0 • -03 0.12e413E-03 0> -03 0.721627E-04 0. -03 0.420654E-04 0. —03 0 • — 04 n. 1 RAn'snF—Ha, 0»

-00 0.301965E-00 0* "01 0 • 553644E—0

1

0 • -01 0*155695£-0l 0 • -01 0»541415E— 02 0 • -02 0« 2 174 lOE-02 0 •

-02 0.965685E-03 0«

— 02 0 • —03 0 • -03 0.128011E-03 0< -03 0«7ia9l4E-04 0« -03 0.418712E-04 0* —03 0 • 25 1 375 £—04 0 • —04 0 • 1 55070E—Oa 0 •

-00 0.333501E-00 0*

— 00 —01 0 • — 01 U# / jJ.Oo4t — 0 • —02 U • f J ( 4t— 0 • -02 ©•141920E-02 0« —02 0 • —02 n-i7i 71 "jF—ni 0 • -03 0.205445E-03 0« -03 0. liei04E-03 Oi -03 0.702427E-04 0« -03 0»429937E—04 0 • -03 0«269941E-04 0 •

00 0.386662E-00 0> -00 0*868731 E—0

1

0 • —0

1

0 • 287047E—0

1

0 • -01 0*1 14320E-01 0 • -01 0.513855E-02 0 •

-02 0.251615E-02 0. -02 0» 131641E-02 0 • —02 0 • 725489E—03 0 • -02 0.417424E-03 0. -03 0.248871E-03 0. -03 0.152992E-03 0.

n. Q^iCi '^AA F—nil 0 • — 03 0 •

00 0.471801E-00 0* —00 0 •12433 7 E—00 0 • —01 0 • -01 0«208389E— 01 0 • —0

1

0 •

-01 0.548393E-02 0* —n 0 w t 0 • —02 0 - 1 Qi 7Q7F—no —02 0 • -02 0.698801E-03 0. -02 0.4&1516E-03 0> -03 0.298360E-03 0. -03 0.201082E-03 0>

7 / 9/2

236783E -00 0. 194833E- 00

3 7 1 03 7E — 0

1

n. OATOArtF- n 1 9 1 946 OE —0 2 n»^^c•>^^SftF- U» P7^U3ot n 0 2 86724E -0 2 0 • 1 67 57 5£" 02 104482£ — 0 2 03 424984E -03 0.210012E- 03

1 8866 3E -0 3 0 • 86 5806E'~ 04

0 QA 1 A —04 04 450780E -04 0» 181196E- 04 237503E -04 0.899219E- 05 130331E -04 0.466430E- 05 739848E -0 3 n»7<^inQAF- U»£5iU70w 05

4 3 30 1 2 E -0 3 0 » 1 39 75 7£- 05

236783E -00 0.194833E- 00 371642E -0

1

0« 267440E- 0

1

9202e9E -02 0 • 592501E- 02 286e67E -02 0. 16761 7E- 02 104420E -0 2 0 • 558832E- 03 424450E -03 0.209668E- 03

1 8 8 2 3 7 E —03 04

8 9 3 5 30E —0 4 04 4490 39E -04 0« 160395E" 04 236420E -04 0.894571E- 05 129621E -04 0.463592E- 05 735290E -0 5 0.249378E- 05 429964E -0 5 0.138676E- 05

265498E -00 0. 220810E-00

457469E -01 0« 335712t- 01

1 22 1 59E -0

1

0* 809147E- 02 405930E -02 0 • 246027E- 02

1 5 5 90 7 E —02 872290E- 03 663947E -03 0< 345354E- 03 306528E -03 0« 149057E- 03 150793E -03 0. 688854E- 04 782093E -04 0> 337010E- 04 423712E -04 0« 172855E- 04 238363E -04 Of 923520E- 05 138452E -04 0< 510912E- 05 827305E -0 5 0. 291500E- 05

315229E -00 0. 266723E- 00 623038E -01 0. 471615E- 01 185996E -01 0. 128738E- 01 679401E -02 0. 435432E- 02 28278aE -02 0. 169190E- 02 129167E -02 0. 725893E- 03 633977E -03 0. 336280E- 03 329358E -03 0« 165569L- 03 179354E -03 0. 857427E- 04 101b61£ -03 0. 463124E- 04 594777E -04 0« 259387E- 04 358493E -04 0« 149871E- 04 221641E -04 0> 890077E- 05

398161E -00 0> 345717E- 00 944591E -01 0. 748193E- 01 327759E -01 0, 241486E- 01 136159E -01 0. 943322E- 02 633362E -02 0. 41549Ct- 02 319053E -02 0. 199190E- 02 170800E -02 0. 101879E- 02 959441E -03 0* 548518E- 03 560727E -03 0. 308075E- 03 33e732E -03 0. 179262E- 03 210510E -03 0. 107521E- 03 134064E -03 0. 662044E- 04 872349E -04 0. 417152E- 04

1 1 / 11/2

0< 165548E -00

0 • 20 1 7 1 3£ -01

0 • *t U 7 *» 1 C -02

0 • 1 05 0 34£ -02

0 • 32 3756E -0 3

Oi 112996c -03

0» 43 522 1

£

-04

0 • 181 194E -04

0» 805560E -05

0. 37B051E -05

0. 186013E -05

0 • 95261 1

£

"06

0 • 50565 2 E -06

0> 165548E -00

Oa 201 968E -0 1 Oa 405 198E -02

0 a 105043E "02

Oa 323411E -03

Oa 112780E -03

0 a 43 3 9 08 £ -04

0 a 1 80497 E -04

0. 801653E -05

Oa 375915E -05

Oa 184787E -05

0 a 945578E -06

0 a 501456E -06

Oa 189124E -00

0 a 2 5 746 1

£

-01

0 a 566190E -02

0 a 1 58 893 £ -02

0 a 5238 95 £ -03

Oa 194054E -03

0 a 787 324E -04

0 a 04

Oa 159ie0£ -04

Oa 775892E -05

Oa 395041E -05 Oa 208 792 E""05

0 a 114063E""05

Oa 231463E -00

0 a 370761E -0

1

Oa 933841E -02

Oa 29460 1

E

-02

0 a 107524E -02

Oa 435661E--03

Oa 191406E--03

0 a 896930E*-04

Oa 443415E -04

Oa 229242E -04

Oa 123179E -04

0 • 68422 2 E'"05

0 • "05

0% 306154E--00

0 • 610377E-01

0 • 1845 32 E""01

0 • A Q 1 Ait p F-"02

0 • 285655E*"02

Oa 130a83E--02

0 • AionnziF- O 4 ^ UU H' C "03

0 « 332439E""0 3 0 • 1 BOOOOE -03 0« 101178E-"03

0« -04 0* 350484E--04 0« 214346E--04
Table 2. Spatial Moments, Plane Perpendicular Source — Continued

n p=-l/2 1/2 3/2

MEv=io.oo Air

c 0. 124042E 01 0, 877859E 00 0. 732230E 00

0 • 589641E 00 0 • 351734E — 00 0

1

2650O1E'-00

2 0 • 350544E'-00 1 A R n A ^ r X o 7 U o C — 00 0 • 129313E'-00

3 Q ( 22875CE'-00 0 • 10950aE -00 0» 718858E'-01

4 0< 157693E'-00 Ot 69455fcE -01 0> 431920E'-01

3 0. 112a24E--00 0. 461852E'-01 0. 273657E'-01

6 c. 829849E--01 0. 318110E'-01 0. ltiC372E'-01

7 0. 623676E-0i 0> 225206E'-01 0. 122619E'-01

b c. 477C36E-0i 0. 163049E--01 0. 854884E--02

9 0. 370230E-01 0. i20285E'-01 0. 60d600E'-02

10 3. 29il07E--01 0« 901976E'-02 0. 44i6b3£-02

11 0. 23150SE-01 0. 6fc6417E'-02 Oi 325857E'-02

12 0« 186125E-01 0> 529781E-02 0. 244347E'-02 MEv= 0.025 Polystyrene

0 0.201060E 01 0 .664555E 00 0. 397290E'-00

1 0<823196E 00 0 .192682E -00 0> 890a26E -01

2 0.443707E'-00 0 .601637E -01 0. 303328E -01

3 0<261138E'-00 0 .367507E'-01 0> 124828E -01

4 0>166713E'-00 0 .209460E'-01 0> 386328E -02

5 0.110812E-00 0 .121017E'-01 0. 300419E'-02

6 0.768367E'-01 0 .741666E'-02 0. 165203E'-02

7 0.5457a5E--01 0 .472610E'-02 0. 955440E'-03

8 0.39B179E'-01 0 .3i2595E'-02 0. 5784C6E'-03

9 0.295273E-01 0 .212182E'-02 0. 362143E'-03

10 0.223107E-01 0 .147814E'-02 0. 234113E'-03

11 0. 170599E-0i 0 .104903E'-02 0. 155050E'-03

12 0.132297E-01 0 t759006E'-03 0» 105162E'-03

MEv- 0.05 Polystyrene

0 0. 1953&5E 01 0. 676108E 00 0. 412248E -00

1 0. 803e74E 00 0. 198790E'-00 0. 946863E -01

2 0. 431432E-00 0. 830220E'-01 0. 326475E -01

3 0. 253508E-00 0. 402355E -01 0. 135597E -01

4 0. 161.1ME-00 0. 217559E -01 0. 640719E -02

5 0. 106820E-00 0. 125691E'-01 0. 329339E -02

6 0. 737640E-01 0. 769029E'-02 0. iei453E -02

7 0. 522256E-01 0. 489374E -02 0. 105106E -02

8 0. 379467E-01 0. 322913E'-02 0. 636430E -03

9 0. 280437E-01 0. 218735E'-02 0. 398529E -03

10 0. 211050E-01 0. 151957E'-02 0. 257431E'-03

11 0. 160819E-01 0. 107580E'-02 0. 17036eE -03

12 0. 124222E-01 0. 776040E'-03 0. 115385E'-03

MEv= 0.10 Polystyrene

0 0. 198551E 01 0 .669579E 00 0.403755E'-00

1 0. 828097E 00 0 .197590E -00 0.923083E'-01

2 0. 446433E'-00 0 .824925E -01 0.316549E'-01

3 0. 263871E-00 0 .400675E -01 0.131122E'-01

4 0. 168325E'-00 0 .216669E'-01 0.617353E'-02

5 0. 112019E-00 0 .125381E'-01 0.317168E -02

6 0. 775700E'-01 0 .767892E -02 0.174508E'-02

7 0. 550934E'-01 0 .469421E -02 0.101032E'-02

8 0. 401240E'-01 0 .323303E -02 0.611391E'-03

9 0. 297287E'-01 0 .219319E -02 0.382325E'-03

10 0. 224174E'-01 0 .152530E -02 0.24723eE'-03

11 0. 171185E'-01 0 .108130E -02 0.16364SE'-03

12 0. 132454E'-01 0 .780812E -03 0.110336E -03 MEv= 0.20 Polystyrene

0 0 0. 196823E 01 0 .673091E 00 0. 408310E-00

1 0. 82743AE 00 0 .200379E'-00 0. 943671E-•01 2 0. 445861E'-00 0 .838140E -01 0. 325044E-•01

3 0. 263931E'-00 0 .408071E -01 0. 135166E-•01 4 0. 16&248E'-00 0 .220726E -01 0. 637996E-•02

5 0. 111992E'-00 0 .127821E -01 0. 328074E-•02 6 0. 774780E'-01 0 .782573E'-02 0. 180621E-•02 7 0. 550076E'-01 0 .498778E -02 0. 104647E-02

8 0. 400185E'-01 0 .329266E -02 0. 633287E-03

9 0. 296299E-01 0 .223273E -02 0. 39b593E-03

10 0. 223166E-01 0 .155145E'-02 0. 256043E-•03 11 0. 170262E'-01 0 .10990BE -02 0. 169437E-•03 12 0. 131575E-01 0 .792850E'-03 0. 114689E-03

5/2 Vz 9/2 11/2

0. 639936E 00 0 .573129E 00 0. 521417E 00 0.479695E'-00

0. 213940E-00 0 .179097E -00 0. 153517t-00 0. 133842E'-00

0. 982693E-•01 0 .781190E -01 0. 639498E-01 0.534688E--01

0. 519597E--01 0 .395578E -01 0. 311558E-01 0.251471E^-01

0. 298836E-01 0 .219055E -01 166772E-•01 0. 130497E--01

0. 182047E-01 0 •128973E -01 0. 952315E-02 0.724582E--02

0. 115759E-01 0 .794876E -0 2 0. 570669E-02 0.423165E'-02

0. 761225E-02 0 .507780E -02 0. 355170£-02 0.257141E^-02

0. 514511E--02 0 .334038E -02 0. 228014E-02 0.161425E'-02

0 . 355904E-02 0 • 22I?264E -02 0 « 150283E-02 U. iU4ioiL "02

0. 251239E--02 0 .15526fcE-02 0. 101381E-02 0.689095E'-03

0. 180681E-02 0 . 109195E -02 0. 698835t-03 0.466380E^-03

0. 132303E-02 0 •783226E-0 3 0. 492083E-03 0. 322934E'-03

0. 283208E-00 0 .219992E -00 0. 179834E-00 0.152069E'-00

0. 517516E-01 0 .339174E -01 0. 239768E-01 0.178590E--01

0. 149483E-01 0 .851668E -02 0. 532833E-02 0.356096E'-02

0. 536575E-02 0 .2713S3E -02 0. 152771E-02 0.928411E'-03

0. 223399E-02 0 .101685E -02 c. 520390E-03 0.290082E'-03

0. 102902E-02 0 .425436E -0 3 0. 199730E-03 0.102892E--03

0. 513737E-03 0 .194645E -0 3 0. 843864E-04 0.404019E--04

c. 272199E-03 0 .952123E -04 0. 383544E-04 0.171555E--04

0. 152009E-03 0 .493709t -04 0. 185695E-04 Oi 779232E'-05

0 * 833601E-04 0 • 945232E-05 -0 5

0. 533032E-04 0 .151541E -04 0. 503402E-05 Oil88029E--05

0. 331001E-04 0 .885996E -0 5 0. 278115E-05 0.984788E'-06

0. 211319E-04 0 .534380E -05 0. 158985E-05 0.535113E--06

0. 297120E-00 0 .232425E -00 0. 190926E-00 0.162028E-00

0. 560715E-01 0 .372474E -01 0. 265964E-01 0.199649E'-01

0. 165233E-01 0 .960152E'-02 0. 609947E-02 0.412637E--02

0. 602114t-02 0 .312238E'-02 0. 179293E-02 0. 110747E'-02

0. 253499E-02 0 .118758E -0 2 0. 622633E-03 0.354127E^-03

0. 117636E-02 0 .503059E'-0 3

^ 0. 242867E-•03 0.128102E-03

0. 590653E-03 0 .232333E'-03 0. 103944E-03 0.511205E--04

0. 314452E-03 0 .114563E^-0 3 0. 477731E-04 0.220154E--04

0. 17ei54E-03 0 .597669E^-04 0. 233381E-•04 0.101179E--04

0 • 102669E-03 119739E-•04 O.490194E--05

0. 620279E-04 0 .185147E'-04 0. 641745E-05 0.248367E--05

0. 385676E-•04 0 .108622E'-04 0. 356557E-05 0.131369E--05

0. 246329E-•04 0 .656731E'-05 0. 204740t-05 0.718506E--OS

0. 289198E-•00 0 .225329E-00 0. 184586E-00 0.156329E-00

0. 539872E-•01 0 .355506E'-01 0. 252203E- 01 0.188366E--01 0. 157539E-•01 0 .904172E'-02 0. 568919E-02 0.381958E--02 0. 570307E-•02 0 .291121E-02 0. 165097E- 02 0.100949E--02

0. 238678E-•02 0 .109750E-02 0. 566823E- 03 0.318407E--03

0. 110295E-•02 0 .461731E-03 0. 219061E- 03 0.113871E--03

0. 551700E-•03 0 .211948E-03 0. 929839E- 04 0.449779E--04 0. 292931E-•03 0 . 104011E-03 c. 424452E-04 0.192027E--04

0. 163693E-•03 0 .540278E'-04 0. 206090E- 04 0.875624E--05

0 . 952399E-•04 0 .293730E--04 c • 105197E- 04 0.421364E--05

0. 574443E-•04 0 .166265E'-04 0. 561181E-05 0.212623E--05 0. 356760E-•04 0 .972956E--05 0. 310567E-05 0. 111642E--05 0. 227597E-•04 0 .586842E-05 0. 177681E- 05 0.607615E--06

0. 293439E-•00 0 .229123E-00 0. 187973E- 00 0.159371E--00 0. 554782E-•01 0 .366664E-01 0. 260830E- 01 0.195225E-01

0. 162966E-01 0 .940471C-02 0. 594293E- 02 0.400362E-02

0. 593157E-02 0 .304885E-02 0. 173864E- 02 0.106796E--02 0. 249026E-•02 0 .115459E-02 0. 600364E- 03 0.339170E-03

0. 115403E-•02 0 .487656E-03 0. 233176E- 03 0.122017E-03

0. 578210E-•03 0 .224452E-03 0. 993397E- 04 0.4S4175E-04

0. 307488E-•03 0 .110416E-03 0. 454968E- 04 0.207562E-04

0. 171971E-03 0 .574497E-04 0. 221447E- 04 0.949543E-•05 0. 100138E-•03 0 .312811E-04 0. 113290E- 04 0.458305E-05

0. 604167E-•04 0 .177238E-04 0. 605356E- 05 0.231792E-05

0. 375338E-•04 0 .103811E--04 0. 335524E- 05 0.121967E-•05 0. 239432E-04 0 .626448ti--0 5 0. 192165E- 05 0.664909E-06

67
Table 2. Spatial Moments, Plane Perpendicular Source — Continued

n P=-l/2 1/2 Vz

MEv= o.*o Polystyrene

0 0.1937666 01 0«67940aE 00 0>4165a2E -00

1 0.826759E 00 0.205567E -00 0.982038E -01

2 0 • 447505 E*"00 U«<>ooo4oL — 01 U»34/3Vi;t — 01

3 0 1 2665 32 £"00 -01 U»i430OdL — 0

1

0,170411E-00 0.231196E -01 0i6642l4E -02

5 0. 113849E-00 0.134529E -01 0.354210E -02

6 0.789362E-01 0.B26359E -02 0. 195993E -02

7 0 • 56 ld66E''0

1

0«528440E -02 0. 114089E -02

6 0*40944 2 £"01 0 • 34968 3E -02 0.692953E -03

9 0* 3037 31£~0

1

-02 0.435476E -03

10 0.229059E-01 0.165469E -02 0.281925E -03

11 0.175015E-01 0.117443E -02 0.187067E -03

12 0« 1353fcl5£-01 0*348400E -03 0.126a95E -03

MEV = Oa 70 Polystyrene

0 0«186673E 01 0»689809E 00 0.430416E -00

1 0»821698E 00 0.213622E -00 0. 104538E -00

2 0«449039E-00 0i914614E -01 0.372402E -01

3 0»270091£-00 0«454823E -01 0.159361E -01

4 0. 173874E-00 0.249697E -01 0.768627E -02

5 0.116949E-00 0.146605E -01 0.402856E -02

6 0«315179E-01 0«907091E -02 0.225193E -02

7 0 • 58 3284E—0

1

0»583969E -02 0.132290E -02 0«426917E"01 0,3S8627E -02 0.809806E -03 0«318064E-01 0.265591E -02 0.512575E -03

10 0.240770E-01 0.ia5751E -02 0.333934E -03

11 0. 184644E-01 0.13242eE -02 0.222882E -03

1

2

0« 143304£"'01 0 • 96046 7E -03 0.151986E -03

MEV = 1. 00 Polystyrene

0 0«184048£ 01 0.700436E 00 0.444a34E -00

1 0.814119E 00 0.221640E -00 C.lllia6E -00

2 0«449603£-00 0«964364E -01 0.405036E -01

3 0«273043E-00 0 t486097E -01 0.176562E -01 0.177121E-00 0.269796E -01 0.864620E -02

5 0.119976E-00 0.159932E -01 0.459163E -02

6 0.841304E-01 0.997559E -02 0.259537E -02

7 0 • 605445E—01 0»646998E -02 0.154000E -02

5 0 * 445362E~01 0 • 433343E -02 0.950908E -03

9 0 333450E-0

1

0,297970£ -02 0.606766E -03

10 0.253519E-01 0.209518E -02 0.398109E -03

11 0.195277E-01 0.150161E -02 0.267522E -03

-02 0.ia3525E -03

MEV = 2< 00 Polystyrene

0 0.168928E 01 0.736399E 00 0.495786E -00

1 0.777972E 00 0.248071E -00 0.135372E -00

2 0»441878E-00 0tll3219£ -00 0.528241E -01

3 0»275416£-00 0«594207E -01 0.243a31E -01

0« 182396E-00 0.340732E -01 0.125158E -01

5 0.125e93E-00 0.207742E -01 0.691972E -02

6 0.a97232E-01 0.132727E -01 0.404876E -02

7 0«655413E-01 0.879372E -02 0.247640E -02

3 0«488675E"01 0«600246E -02 0.157077E -02

9 0« 370507E-01 0.419a72E -02 0.102674E -02

10 0.285008E-01 0.299906E -02 0.688570E -03

11 0.221948E-01 0.2ia062E -02 0.472010E -03

12 U • i * ** / Ji>C wl 0.161047E -02 0.329832E -03

MEV = 4>00 Polystyrene

0 0.1517<ie£ 01 0.783171E 00 0t3672a4E 00

1 0.731808E 00 0.285635E -00 0.173290E -00

2 Ot433623E~00 0.139439E -00 0.74J694E -01

3 0 • 280941E~00 0.775528E -01 0.370364E -01 0.467274E -01 0.203334E —01

5 0.136871E-00 0.2975ieE -01 0.119217E -01

6 0. 100227E-&0 0. 197485E -01 0.734549E -02

7 0.750644E-01 0. 135414E -01 0.470536E -02

a 0.572692E-0i 0.953477E -02 0.311150E -02

9 0.443653E-01 0«686253£ -02 0.2112b5E -02

10 0.348226E-01 0.503245E -02 0.146695E -02

11 0.276409E-01 0.374996E -02 0.103852E -02

12 0.221586E-01 0.283378E -02 0.747765E -03

68

5/2 9/2

1 1 J

0.30H8aE-00 0*236082£ -00 0« 194204E-00 0«1649e2E -00 0.582699E-01 0 • 3 8 7641E -0 1 0 • 277105E-01 Ot 208 196E -01 0.173861E-01 -0 1 0 • 644774E- 02 0 •436940E -02 0.641235E- 02 0 • 3 33540E -02 0 • 192022E- 02 0 • 1 1 88 7^E -02 0.271894E-02 U • i 2 ' 003L —02 0 • 672630E-03 U

•

3o3o9hc "03

0,127108E- 02 cs^fSeyTE -03 0. 264548E-03 0*140018E -03 0.641266E-03 U • ^ 7 J4P4t —03 113892E-03 u a 30£i flu -04 0.343167E-03 0 • 12766tic -03 0 • 526551E-04 0a243724t -04 0.192904E-03 0.658159E -04 0. 258352E- 04 Oall2552£ -04 0.112a59E-03 0.360529E -04 0. 133142E- 04 0a547934£ -05 0.683580E- 04 0.205322E -04 0. 715949E-05 0a279217£ -05 0.426238E- 04 0»120833E -04 0* 399151E-05 Oa 147947E -05 0.272738E-04 0»732143E -05 0 • 229777E- 05 0aail517E -06

0.314279E-00 0.247924E -00 0. 204863E- 00 0al746iaE -00 0,630050E- 01 0«423ai9E -0

1

0 • 305505E- 01 0a231039£ -01 0.193127E- 01 0 • 1 14292E -01 0 • 736498E-02 0 a 504030E -02 0.728596E-02 0 • 386524E -02 0« 226061E- 02 Oa 141770E -02 0.314638E- 02 0»15147aE -02 Oa 812234E-03 0a470784E -03

0. 14943aE-02 0.659iaiE -03 0. 326625E-03 Oal7614a£ -03 0.764017E- 03 0*31 1 lOOE -03 0 * 143340E-03 0a723099E -04 0.413720E-03 0.156505E -03 0» 674124E-04 0a319565£ -04 0.234954E-03 0.830115E -04 0. 3357aOE-04 Oal50160E -04

0. 138742E-03 0.459971E -04 0> 175423E-04 0a742635E -05 0.847272E-04 0t264641E -04 Oa 954904E-05 0a383a44E -05 0.532317E-04 0» 157209E -04 Oa 538375E-05 Oa 20&054E -05 0.342937E- 04 0«960641E -0 5 Oa 313090E- 05 Oa 114375E -05

0.32a097E-00 0.260535E -00 Oa 216291E-00 Oal85003E -00 0.681030E- 01 0»463432E -01 Oa 3369a9E- 01 0a256603E -01 0.214627E-01 0 • 129077E -01 Oa 842320E-02 Oa 5a2346E -02 0.828626E-02 0»448550E -02 Oa 266615E-02 Oa 1&9445E -02 0.364806E-02 0tl79881E -02 Oa 983549E-03 Oa 579466E -03 0.176189E-02 0.798673E -03 Oa 404798E-03 Oa222530E -03 0.913742E-03 0»383527E -03 0 a 181273E-03 Oa93462eE -04 0.501177E- 03 0 • 1 97 768L -03 0 a 868iaOE-04 0a42167aE -04 0.287810E-03 0.105370E -03 Oa 439439E- 04 Oa20iai&£ -04 0.171710E-03 0.591225E -04 Oa 232991E- 04 Oal01S12E-04

0.105814E-03 0.343958E -04 Oa 12a508E- 04 0a532697E -05 0.67050aE-04 —04 0 a 733497E-05 0a290041E -05 0.435264E-04 U • i ^ ( J«fOt -04 Oa 431311E- 05 0«163068E -05

0.3783A5Er 00 0.307342E -00 Oa 259366E- 00 Oa22462'»E-00 0.876350E- 01 0 • 620705E -01 Oa 465399E- 01 0a363124E-01

0.301218E- 01 0 • 1 91457E -01 Oa 130522E- 01 0a9351*3E-02

0.125041E-01 0 • 72507 IE -02 0 a 455605E- 02 Oa303235E -02 0.5a4913E- 02 0 • 3 12760E -02 Oa 1827aiE- 02 0all3894E-02

0.297612E- 02 0tl47918E -02 Oa B09425E- 03 Oa47^964E -03 0.161471E-02 0»750589E -03 Oa 386612E- 03 0a21^16£ -03 0.921521E- 03 0«4026a7E -03 Oa 196087E- 03 0al03368E-03

0.54a213E- 03 0.226163E -03 Oa 104496E- 03 0a524782E-04

0,337576E- 03 0.131965E -0 3 Oa 580376E- 04 0.278*48E-04

0.2140a5E- 03 0.795564E -04 Oa 333967E- 04 0«153444E-04

0.139242E- 03 0 •493279E -04 0 • 198137E- 04 0.873713E-05

0,925913E- 04 0 • 3 134a2E -04 0 • 120747E- 04 0.512015E-0S

0.452523E- 00 0.379038E -00 0* 3272*4E- 00 0a2S84a9E-00

0.120430E- 00 0»89e954E -01 0* 702288E- 01 0a566523E-01

0.463857E- 01 0«316462E -0

1

0 • 22a3eoE- 01 0tl71540E--01 0.212141E- 01 0 • 134169E -01 0* 905172E- 02 0«639625E--02 0.107867E- 01 0.638226E -0 2 0 • 405691E- 02 0.271551E--02

0.590457E- 02 0.329014E -02 0« 198172E- 02 0>126281E-02

0.341742E- 02 0.180244E -02 0 a 103323E- 02 0a629230£--03 0.206655E- 02 0.103592E -02 0 a 567158E- 03 0a331128E-03

0.129530E- 02 0.619219E -03 Oa 324745E- 03 0al82241E-03

0.836494E- 03 0t382465E-03 Oa 192621E- 03 0al04133E--03

0.554150E- 03 0.242940E-03 Oa 117752E- 03 0a61M36E-04

0.375251E- 03 0«15a086E-03 Oa 738855E- 04 0a372763E--04 0.259044E- 03 0tl05074E-03 Oa 474345E- 04 0.231737E-04
Table 2. Spatial Moments, Plane Perpendicular Source — Continued

n p=-l/2 1/2 3/2 5/2 7/2 V2 '1/2

MEV=10« 00 Polystyrene

Q Ot 85 lOO^E 00 0.682<»&1£ 00 0 • 580966E 00 Q •510111E 00 0 • 4b6785E- 00 0

1

4147 38 E*-00

1 0«661394£ 00 0 • 3^5512E -00 0.243552E' 0 • 1876<(0E--00 Q • 151512E'-00 0 • 126091E- 00 0

1

1072 15E*-00

2 0.i»13490E-00 Oi ia6092E -00 0«119109E'-00 0. 850245E-01 0 .643354E'-01 0. 505b32£-01 0. 408114E--01

3 0i2a5277E-00 0. 113084E -00 0 &&8&26 E'-01 0. 447947E-01 0 .320986E'-01 0. 240306E-01 Ot 185656i--01 0«2Q6i'+6£-00 0< 73733'>E -01 0»407113£'-01 0 • 258085E--01 0 • 1 7&332E'-01 0 • 1265 17!i-01 Ot Q /. n "3 T o c

.

94U j23t'-02

. U • X3»ti. J U t wU 0 • 50it078E'-01 0.261891E'-0

1

0 • 158013E-01 0 • 103435E'-0

1

0, 7 14256E-02 0 t 5 12630E--02

6 0ill8165E-C0 0. 356836E'-01 0.17544ifE'-01 0. 101189E--01 0 .636947E'-02 0. 424663E-02 Ot 295163E--02

7 0.923637E-01 0. 259515E'-01 0.121292E'-01 0. 671038E-02 0 .407355E'-0 2 0> 262891E-02 Ot 177355E--02

6 0.733366E-01 0« 192895E'-01 0.860163E--02 0. 457.767E-02 0 t26B631E'-02 0« 168159E-02 Ot 110319E--02

9 0i589888E-01 0. l'.5985E'-01 0.623010E'-02 Of 319697E--02 0 I181719E--0 2 0. 110531E-•02 Ot 706255E--03

XO 0.479735E-01 Oi 112186E'-01 0.459397E'-02 0. 227768E-02 0 .123617E'-02 0< 743534E-03 Ot 463352E--03 11 O.393866E-01 Ot 873530E'-02 0.344016E'-02 0. 165086E--02 0 .884721E'-03 0. 510269E-03 Ot 310494E'-03 12 0.326062E-01 Oi 688028E-02 0.261113E'-02 0. 121470E--02 0 .633399E'-03 Ot 356380E-03 Ot 211966E--03

69
4. References

[1] L. V. Spencer, Phys. Rev. 98, 1597 (1955).

[2] Ann T. Nelms, NBS Circ. 577 (1956).

[3] Ann T. Nelms, Supplement to NBS Circ. 577 (July 30, 1958).

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'

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