**3. FILE 3, REACTION CROSS SECTIONS**

**3.1. General Description**

Reaction cross sections and auxiliary quantities are given in File 3 as
functions of energy E, where E is the incident energy in the laboratory
system. They are given as energy-cross section (or auxiliary quantity)
pairs. An interpolation scheme is given that specifies the energy
variation of the data for incident energies between a given energy point
and the next higher point. File 3 is divided into sections, each
containing the data for a particular reaction (MT number); see Section
0.5 and Appendix B. The sections are ordered by increasing MT number. As
usual, each section starts with a HEAD record and ends with a SEND
record. The file ends with a FEND record.

**3.2. Formats**

The following quantities are defined

+----------+-----------------------------------------------------------+
| **       | Standard material charge and mass parameters.             |
| ZA,AWR** |                                                           |
+----------+-----------------------------------------------------------+
| **QM**   | Mass-difference Q value (eV): defined as the mass of the  |
|          | target and projectile minus the mass of the residual      |
|          | nucleus in the ground state and masses of all other       |
|          | reaction products; that is, for a+A→b+c+\...+B,           |
|          | QM=\[(m~a~+m~A~)-(m~b~+m~c~+\...+m~B~)\](9.315016x10^8^)  |
|          | if the masses are in amu. (See paragraph 3.3.2).          |
+----------+-----------------------------------------------------------+
| **QI**   | Reaction Q value for the (lowest energy) state defined by |
|          | the given MT value in a simple two-body reaction or a     |
|          | breakup reaction. Defined as QM for the ground state of   |
|          | the residual nucleus (or intermediate system before       |
|          | breakup) minus the energy of the excited level in this    |
|          | system. Use QI=QM for reactions with no intermediate      |
|          | states in the residual nucleus and without complex        |
|          | breakup (LR=0). (See paragraph 3.3.2.)                    |
+----------+-----------------------------------------------------------+
| **LR**   | Complex or \"breakup\" reaction flag.                     |
|          |                                                           |
|          | Indicates that additional particles not specified by the  |
|          | MT number will be emitted. See Sections 0.5.5 and 3.4.4.  |
+----------+-----------------------------------------------------------+
| **NR,NP, | Standard TAB1 parameters.                                 |
| E~int~** |                                                           |
+----------+-----------------------------------------------------------+
| **σ(E)** | Cross section (barns) for a particular reaction (or the   |
|          | auxiliary quantity) given as a table of NP energy-cross   |
|          | section pairs.                                            |
+----------+-----------------------------------------------------------+

The structure of a section is

> \[MAT, 3, MT/ ZA, AWR, 0, 0, 0, 0\] HEAD
>
> \[MAT, 3, MT/ QM, QI, 0, LR, NR, NP/ E~int~ / σ(E)\] TAB1
>
> \[MAT, 3, 0/ 0.0, 0.0, 0, 0, 0, 0\] SEND

**3.3. General Procedures**

**3.3.1. Cross Sections, Energy Ranges, and Thresholds**

For incident neutrons, the cross-section data must cover an energy range
up to a common upper limit of at least 20 MeV, and the data must extend
to a lower limit of the reaction threshold or 10^-5^ eV whichever is
higher. For other reactions, the cross section should start at the
reaction threshold energy (with a value of 0.0 barns) and should
continue up to a **common upper energy limit**.

In the case where there is a change in the representation above a given
energy, *e.g.*, a change from separate reactions to MT=5 (sum of
reactions not given separately in other sections), the following
procedure should be used. For the cross sections in the lower energy
region, there should be a duplicate point with a value of zero at the
last energy for a which a non-zero cross section is given, and a point
with a value of zero at the common upper energy limit. Similarly, for
the cross sections in the upper energy region, there should be a
duplicate point with a value of zero at the first energy for a which a
non-zero cross section is given, and a zero value at the low energy
limit. The evaluator should document the change in representation in the
File 1 comments.

For charged-particle emission, the cross section is usually very small
from the threshold (or lower limit) up to an ***effective threshold***
defined by a noticeable cross section (for example, 10^-10^ barns). The
evaluator should tabulate a cross section of 0.0 in such a range in
order to avoid interpolation problems.

Sometimes ENDF reactions have an apparent upper limit lower than the
upper limit for the material due to changes in representation in
different sections. For example, there might be a change from discrete
levels to a continuum rule, or from separate reactions to MT=5. Such
cross sections must be ***double valued*** at the highest energy for
which the cross section is nonzero. The second cross section at the
discontinuity must be zero, and it must be followed by another zero
value at the upper limit. This will positively show that the cross
section has been truncated. For such reactions, there will be another
reaction with an artificial threshold at the discontinuity. The cross
sections must be chosen in such a way that their sum is continuous.

The limit on the number of energy points (NP) to be used to represent a
particular cross section is given in Appendix G. The evaluator should
not use more points than are necessary to represent the cross section
accurately. When appropriate, resonance parameters can be used to help
reduce the number of points needed. The evaluator should avoid sharp
features such as triangles or steps (except for the required
discontinuities at the limits of the resonance ranges or where reactions
change representation), because such features cannot be realistically
Doppler broadened.

**3.3.2. Q Values**

Accurate Q values should be given for all reactions, if possible. If QI
is not well defined (as for a range of levels in MT=91, 649, 699, 749,
799, or 849), use the value of QI which corresponds to the threshold of
the reaction. Similarly, if the value of QM is not well defined (as in
elements or for summation reactions like MT=5), use the value of QM
which gives the threshold. If there is no threshold, use the most
positive Q value of the component reactions. Note that these ill-defined
values of QM cannot be relied on for energy-release calculations.

As an example to clarify the use of QM and QI, consider the reaction
α+^9^Be→n+X. After the neutron has been emitted, the compound system is
^12^C with QM=5.702 MeV and energy levels (E~x~) at 0.0, 4.439, 7.654,
and 9.641 MeV. The ground state is stable against particle breakup, the
first level decays by photon emission, and the higher levels decay with
high probability by breaking up into three alpha particles (7.275 MeV is
required). This pattern can be represented as follows.

  -------------------- ------------- ------------- ------------- -------------
  **Reaction**         **QM**        **QI**        **EX**        **MT**

  9Be(a,n~0~)12C       5.702         5.702         0.000         50

  9Be(a,n~1~)12C       5.702         1.263         4.439         51

  9Be(a,n~2~)12C(3α)   -1.573        -1.952        7.654         52

  9Be(a,n~3~)12C(3α)   -1.573        -3.939        9.641         53

  9Be(a,n~C~)12C(3α)   -1.573        -1.573                      91
  -------------------- ------------- ------------- ------------- -------------

The gamma for the second reaction is not written explicitly in this
notation. The last reaction

includes the contributions of all the levels above 9.641 MeV, any missed
levels, and any direct

four-body breakup; therefore, the threshold for MT=91 may be lower than
implied by the fourth level of ^12^C. Note the value used for QI.

**3.3.3. Relationship Between File 3 and File 2**

If File 2 (Resonance Parameters) contains resolved and/or unresolved
parameters (LRP=1), then the cross sections or self-shielding factors
computed from these parameters in the resonance energy range for elastic
scattering (MT=2), fission (MT=18), and radiative capture (MT=102) must
be combined with the cross sections given in File 3. The resonance
contributions must also be included in any summation reactions that
involve the three resonance reactions (for example, MT=1, 3, or 5). The
resonance energy range is defined in File 2. Double-valued energy points
will normally be given in File 3 at the upper and lower limits of the
unresolved and resolved resonance regions.

Some materials will not have resonance parameters but will have a File 2
(LRP=0) that contains only the effective scattering radius. This
quantity is sometimes used to calculate the potential scattering cross
section in self-shielding codes. For these materials, the potential
scattering cross section computed from File 2 *must not* be added to the
cross section given in File 3. The File 3 data for such materials
comprise the entire scattering cross section.

In certain derived libraries, the resonance cross sections have been
reconstructed and stored in File 3. Such files may have LRP=0 as
described in the preceding paragraph. Alternatively, they may have LRP=2
and include a full File 2 with complete resonance parameters. In this
case, resonance cross sections or self-shielding factors computed from
File 2 *are not* to be combined with the cross sections in File 3.

**3.4. Procedures for Incident Neutrons**

Cross section data for non-threshold reaction types must cover the
energy range from a lower limit of 10^-5^ eV to an upper limit of ***at
least*** 20 MeV for all materials. For non-threshold reactions, a cross
section value must be given at 0.0253 eV. The limit on the number of
energy points (NP) to be used to represent a particular cross section is
50,000. The evaluator should not use more points than are necessary to
represent the cross section accurately.

The choice of data to be included in an evaluation depends on the
intended application. For neutron sublibraries, it is natural to define
\"transport\" evaluations and \"reaction\" evaluations. The transport
category can be further subdivided into \"low-energy transport\" and
\"high-energy transport.\"

A ***reaction evaluation*** will contain File 1, File 2, File 3, and
sometimes File 32 and/or File 33. File 2 can contain resonance
parameters. If radioactive products must be described, Files 8, 9, 10,
39, and/or 40 may be present. File 3 may tabulate one or more reaction
cross sections. The total cross section is not usually well defined in
reaction evaluations since they are incomplete. Examples of this class
of evaluations include activation data and dosimetry data. A
***low-energy transport evaluation*** should be adequate for calculating
neutron transport and simple transmutations for energies below about
6-10 MeV. Photon production and covariance data should be included when
possible. Typical evaluations will include Files 1, 2, 3, 4, 5, and
sometimes Files 8, 9, 10, 12, 13, 14, 15, 31, 32, 33, 34, 35, 39, and/or
40. Resonance parameters will usually be given so that self shielding
can be computed. Charged-particle spectra (MT=600-849) and neutron
energy-angle correlation (MF=6) will usually not be given. File 3 should
include all reactions important in the target energy range, including
the total (MT=1) and elastic scattering (MT=2). Other reactions commonly
included are inelastic scattering (MT=4,51-91), radiative capture
(MT=102), fission (MT=18,19-21,38), absorption (MT=103,104,105,\...),
and other neutron emitting reactions such as MT=16,17,22,28,\....
Specific procedures for each reaction are given below. Examples of this
class of evaluations include fission-product data and actinide data.

A ***high-energy transport evaluation*** should be adequate for
calculating neutron transport, transmutation, photon production, nuclear
heating, radiation damage, gas production, radioactivity, and
charged-particle source terms for energies up to at least 20 MeV. In
some cases, the energy limit needs to be extended to 40-100 MeV. These
evaluations use Files 1, 2, 3, 4, 5, 6, 12, 13, 14, 15, and sometimes 8,
9, 10, 31, 32, 33, 34, 35, 39, and/or 40. Once again, File 3 should give
cross sections for all reactions important in the target energy range,
including MT=1 and 2. This will normally include many of the reactions
mentioned above plus the series MT=600-849. At high energies, some
reactions may be combined using the \"complex reaction\" identifier
MT=5. File 6 will normally be needed at high energies to represent
energy-angle correlation for scattered neutrons and to give particle and
recoil energies for heating and damage calculations. Special attention
to energy balance is required. High-energy evaluations are important for
materials used in fusion reactor designs, in shielding calculations, and
in medical radiation-therapy equipment (including the components of the
human body).

**3.4.1. Total Cross Section (MT=1)**

The total is often the best-known cross section, and it is generally the
most important cross section in a shielding material. Considerable care
should be exercised in evaluating this cross section and in deciding how
to represent it.

Cross section minima (potential windows) and cross section structure
should be carefully examined. Sufficient energy points must be used in
describing the structure and minima to reproduce the experimental data
to the measured degree of accuracy.

The total cross section, as well as any partial cross section, must be
represented by 50,000 incident-energy points or fewer. The set of points
or energy mesh for the total cross section must be a union of all energy
meshes used for the partial cross sections. Within the above
constraints, every attempt should be made to minimize the number of
points used. The total cross section must be the sum of MT=2 (elastic)
and MT=3 (nonelastic). If MT=3 is not given, then the elastic cross
section plus all nonelastic components must sum to the total cross
section.

The fact that the total cross section is given at every energy point at
which at least one partial cross section is given allows the partial
cross sections to be added together and checked against the total for
any possible errors. In certain cases, more points may be necessary in
the total cross section over a given energy range than are required to
specify the corresponding partial cross sections. For example, a
constant elastic scattering cross section and a 1/v radiative capture
cross section could be exactly specified over a given energy range by
log-log interpolation (INT=5), but the sum of the two cross sections
would not be exactly linear on a log-log scale. If a precise total cross
section is required between the energy points provided, it is
recommended that the total be calculated from the sum of the partials
rather than interpolated directly from MT=1.

**3.4.2. Elastic Scattering Cross Section (MT=2)**

The elastic scattering cross section is generally not known to the same
accuracy as the total cross section. Frequently, the elastic scattering
cross section is obtained by subtracting the nonelastic cross section
from the total cross section. This procedure can cause problems. The
result is an elastic scattering cross section that contains unreal
structure. There may be several causes. First, the nonelastic cross
section, or any part thereof, is not generally measured with the same
energy resolution as the total cross section. When the somewhat poorer
resolution nonelastic data are subtracted from the total, the resolution
effects appear in the elastic cross section. Second, if the evaluated
structure in the nonelastic cross section is incorrect or improperly
correlated with the structure in the total cross section (energy-scale
errors), an unrealistic structure is generated in the elastic scattering
cross section.

The experimental elastic cross section is obtained by integrating
measured angular distributions. These data may not cover the entire
angular range or may contain contributions from nonelastic neutrons.
Such contamination is generally due to contributions from inelastic
scattering to low-lying levels that were not resolved in the experiment.
Care must be taken in evaluating such results to obtain integrated cross
sections. Similarly, experimental angular distribution data can also
cause problems when used to prepare File 4.

**3.4.3. Nonelastic Cross Section (MT=3)**

The nonelastic cross section is not required unless any part of the
photon production multiplicities given in File 12 uses MT=3. In this
case, MT=3 is required in File 3. If MT=3 is given, then the set of
points used to specify this cross section must be a union of the sets
used for its partials.

**3.4.4. Inelastic Scattering Cross Sections (MT=4,51-91)**

A total inelastic scattering cross section (MT=4) must be given if any
partials are given; that is, discrete level excitation cross sections
(MT=51-90), or continuum inelastic scattering (MT=91). The set of
incident energy points used for the total inelastic cross section must
be a union of all the sets used for the partials.

Values should be assigned to the level excitation cross sections for as
many levels as possible and extended to as high an energy as possible.
Any remaining inelastic scattering should be treated as continuum. In
particular, low-lying levels with significant direct interaction
contributions (such as deformed nuclei with 0^+^ ground states) should
be extended to the upper limit of the file (at least 20 MeV) in
competition with continuum scattering. The secondary energy distribution
for such neutrons resembles elastic scattering more than an evaporation
spectrum.

Level excitation cross sections must start with zero cross section at
the threshold energy. If the cross section for a particular level does
not extend to the upper limit for the file (*e.g.*, 20 MeV), it must be
***double-valued*** at the highest energy point for which the cross
section is non-zero. The second cross section value at the point must be
zero, and it should be followed by another zero value at the upper
limit. This will positively show that the cross section has been
truncated.

If LR=0, a particular section (MT) represents (n,n\'gamma). The angular
distribution for the scattered neutron must be given in the
corresponding section of File 4 or 6. The associated photons should be
given in a corresponding section of File 6 or 12, if possible. If the
inelastic photons cannot be assigned to particular levels, they can be
represented using MT=4 in File 6, 12 or 13. When inelastic photons
cannot be separated from other nonelastic photons, they can be included
in MF=13, MT=3.

A LR flag greater than zero indicates inelastic scattering to levels
that de-excite by breakup, particle emission, or pair production rather
than by photon emission (see Section 0.6)[^1] . If LR=1, the identities,
yields, and distributions for all particles and photons can be given in
File 6. If LR\>1, angular distributions for the neutron must be given in
File 4, and distributions are not available for the emitted particles.
In this case, photon production is handled as described above for LR=0.

If a particular level decays in more than one way, then File 6 can be
used or several sections can be given in File 3 for that level. Consider
the case in which an excited state sometimes decays by emitting a
proton, and sometimes by emitting an alpha particle. That part of the
reaction that represents (n,n\'α) would use LR=22, and the other part
would be given the next higher section number (MT) and would use LR=28
(n,n\'p). The angular distribution for the neutron would have to be
given in two different MT numbers in File 4, even though they represent
the same neutron. The sections must be ordered by decreasing values of
QI (increasing excitation energy).

**3.4.5. Fission (MT=18,19-21,38)**

The total fission cross section is given in MT=18 for fissionable
materials. Every attempt should be made to break this cross section up
into its various parts:first-chance fission (n,f), MT=19; second-chance
fission (n,n\'f), MT=20; third-chance fission (n,2nf), MT=21; and
fourth-chance fission (n,3nf), MT=38. The data in MT=18 must be the sum
of the data in MT=19, 20, 21, and 38. The energy grid for MT=18 must be
the union of the grids for all the partials.

If resolved or unresolved resonance parameters are given in File 2, the
fission cross section computed from the parameters must be included in
both MT=18 and MT=19.

The Q value for MT=18, 19, 20, 21, and 38 is the energy released per
fission minus the neutrino energy. It should agree with the
corresponding value given in MT=458 in File 1.

Secondary neutrons from fission are usually stated to be isotropic in
the laboratory system in File 4. Energy distributions are given in File
5. The complex rules associated with the partial fission reactions are
described in Section 5.

**3.4.6. Charged-Particle Emission to Discrete and Continuum Levels
(MT=600-849)**

The (n,p) reaction can be represented using a summation cross section,
discrete levels, and a continuum (MT=103, 600-648, and 649) in the same
way that the (n,n\') reaction is represented using MT=4, 51-90, and 91
(see Section 3.4.4). Similarly, (n,d) uses MT=104 and 650-699, and so on
for t, ^3^He, and α. Of course, MT=600, 650, 700, *etc*., represent the
ground state and would not have corresponding sections in the photon
production files, unless the flag LR\>0 (such as in the ^10^B(n,t)^8^Be
reaction).

**3.5. Procedures for Incident Charged Particles and Photons**

See Table 0.1 for sublibrary numbers for incident charged particles and
photons. Procedures for incident charged particles are generally the
same as for neutrons as given in section 3.4. The exceptions are noted
below.

**3.5.1. Total Cross Sections**

The total cross section is undefined for incident charged particles.
MT=1 should be used for the photonuclear total cross section, while
MT=501 is used for the total atomic photon interaction cross section.

**3.5.2. Elastic Scattering Cross Sections**

As discussed in detail in Section 6.2.6, it is not possible to construct
an integrated cross section for charged-particle elastic scattering
because of the Coulomb term. Therefore, σ is either set to 1.0 or to a
\"nuclear plus interference\" value using a cutoff angle. This value may
in theory be 0.0, and, in this case, should be set to epsilon, *e.g.*,
10^-38^. The first and last energy points used for MT=2 in File 3 define
the range of applicability of the cross section representation given in
File 6. The cross section need not cover the complete range from 10^-5^
eV to 20 MeV. MT=2 is used for the elastic scattering cross section for
all incident particles and photons (resonance fluorescence). For
photons, MT=502 and 504 are used for coherent and incoherent atomic
scattering, respectively.

**3.5.3. Inelastic Scattering Cross Sections**

The procedure for inelastic cross section for incident charged particles
and photons is the same as for neutrons. The following MT combinations
should be used.

  ---------------------- ------------------------ ------------------------
  **Incident Particle**  **MT\'s for Excited      **MT\'s for Total
                         States**                 Inelastic σ**

  γ                      undefined                102

  n                      51-91                    4

  p                      601-649                  103

  d                      651-699                  104

  t                      701-749                  105

  ^3^He                  751-799                  106

  α                      801-849                  107
  ---------------------- ------------------------ ------------------------

**3.5.4. Stopping Power**

The total charged-particle stopping power in eV×barns is given in MF=3,
MT=500. This is basically an atomic property representing the shielding
of the nuclear charge by the electrons, but it should be repeated for
each isotope of the element. It is a \"total\" stopping power in that
most tabulations implicitly include large-angle coulomb scattering which
is also represented here in File 6. In practice, this contribution is
probably small enough to keep double counting from being a problem. At
low particle energies, mixture effects are sometimes noticeable. They
are not accounted for by this representation.

[^1]: LR=31 is still allowed, however, to uniquely define the γ-decay
    when using MF=3, and MF=12 (or 15) and MF=4.