IR 87-3547

NEVER PUBLISHED

NBSIR 87-3548

Calculated Response of A 5.5 x 5.5 cm

High-Purity Ge Detector to Gamma Rays

With Energies Up to 20 MeV

Stephen M. Seltzer

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Measurement Laboratory

Center for Radiation Research

Gaithersburg, MD 20899

April 1987

Prepared for: Office of Health and Environmental Research

Department of Energy

Washington, DC 20545

NBSIR 87-3548

CALCULATED RESPONSE OF A 5.5 x 5.5 cm

HIGH-PURITY Ge DETECTOR TO GAMMA RAYS

WITH ENERGIES UP TO 20 MeV

Stephen M. Seltzer

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Measurement Laboratory

Center for Radiation Research

Gaithersburg, MD 20899

April 1987

Prepared for: Office of Health and Environmental Research

Department of Energy

Washington, DC 20545

U.S. DEPARTMENT OF COMMERCE. Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director

CALCULATED RESPONSE OF A 5.5 x 5.5 cm HIGH-PURITY Ge DETECTOR

TO GAMMA RAYS WITH ENERGIES UP TO 20 MeV*

Stephen M. Seltzer

National Bureau of Standards

Gaithersburg, MD 20899

Monte Carlo calculations have been done of the energy and angular

response of a 5.5 x 5.5 cm, high-purity Ge detector, for gamma rays

incident with energies from 0.1 to 20 MeV. Results are given for

the absolute probabilities of total energy absorption and of single

and double annihilation escape, which relate the areas of the peaks

in the measured pulse-height distribution to the intensities of

incident gamma-ray lines.

Keywords: detection efficiency; escape peaks; gamma rays;

Ge detectors; response function; total absorption peak.

1. Introduction

Because of their good energy resolution, high-purity Ge detectors are

preferred in many applications of gamma-ray spectroscopy. A 5.5 x 5.5 cm

cylindrical detector, among the largest of such detectors which are presently

available with good energy resolution, has been selected in the design of the

Gamma-Ray Remote Sensing Spectrometer to be flown on NASA's Mars Observer

Mission, scheduled for 1990. This experiment will measure from orbit the

gamma-ray line emission induced in the Martian surface by incident cosmic

rays, solar protons, and* secondary neutrons, as well as that due to the

presence of natural radioactivity. Measurement of these line emissions will

provide the basis for the elemental analysis and geochemical mapping of the

Martian surface.

The conversion of the measured pulse-height distributions to the actual

gamma-ray line fluxes incident on the detector requires knowledge of the

detector response as a function of the incident photon energy, particularly

the absolute probabilities of the delta-function features in the absorbed

energy spectrum (i.e., the total -absorption and the single- and doubleannihilation-escape peaks) which largely determine the multi-peaked pulseheight signature of an incident gamma ray. The work reported here was done to

provide this information. Using a fully coupled photon/electron Monte Carlo

code used in an earlier study [l] 1 of 3" x3" Nal detectors, calculations were

done for gamma rays incident on the Ge detector with energies from 0.1 to

*This work was carried out with support from the Department of Energy (Office

of Health and Environmental Research).

lumbers in brackets indicate the literature references at the end of the

paper.
20 MeV. Calculations for various angles of incidence confirmed the anticipated result that, by appropriate scaling, the angular dependence of the

response function can be effectively eliminated. The main results are given

in a table of scaled total -absorption, single-annihilation-escape and doubleannihilation-escape probabilities vs. energy, along with a table giving the

energy and angular dependence of the detection efficiency which is used as the

scaling parameter.

2. Method of Calculation

For a monoenergetic, monodi recti onal photon beam, the spectrum of energy

absorbed in the detector, D(E;E 0 ,e 0 ), can be written as the sum of a continuum, C(E;E 0 ,e 0 ), and a line spectrum:

D(E;Eq,9q) = C(E;E o ,0q) + Po(E 0 >e

0

) “ E

0

> + P^Eq. 00) 6 (E “ E

o + mc2 ) + P

2 (E

o

, 0

o

) 6(E - E

0 + 2 me 2

) + P

3 (Eo

, 0

o

) «(E - ek

) , (1)

where E

0 is the energy of the incident photon, 0

Q

is its angle with respect to

the axis of the cylindrical detector, E is the energy absorbed in the

detector, 6 is the delta function, and me 2 is the electron rest mass. P

0 is

the probability that the entire energy of the incident photon is deposited in

the detector, and can be interpreted as the area under the total -absorption

peak. P, and P

2 are the probabilities that all of the incident energy is

deposited with the exception of the amounts me 2 and 2 me 2

, respectively, which

are carried out of the detector by one or two unscattered annihilation quanta.

Pj_ and P

2 are then the areas under the single- and double-escape peaks,

respectively. P

3 is the probability that the all of the incident energy is

deposited except that carried away by unscattered Ge K x rays (with a weighted

average energy EK

). Because P

3 is relatively unimportant for photon energies

above 0.1 MeV, it will be ignored in the remainder of this report.

The detection efficiency, n(E o ,0 o ), is the probability that the incident

photon will have at least one interaction in^the detector leading to the

deposition of energy, and is thus equal to /

0 D(E;E o ,0 o

) dE. However, the

evaluation of the detection efficiency can be accomplished independently

through the solution of the geometrical problem, without knowledge of the

absorbed-energy spectrum (see, e.g., ref. [2]). For example, for the case of

a monoenergetic photon beam incident along the axis of a right-ci rcul ar cylinder, the detection efficiency is simply

n(E 0 ,0°) = 1 - exp[-y(E

0 )z] , (2)

where y is the photon attenuation coefficient and z is the height of the

detector.

2
The Monte Carlo calculations of the absorbed-energy spectra were carried

out using the ETRAN code [3]. The Monte Carlo model treats in rather full

detail the processes involved in the production and transport of all components of the photon-electron cascade initiated by the incident gamma rays.

Compton scattering, photoelectric absorption and pair production are taken

into account in tracing the histories of the primary gamma rays as well as of

secondary photons (bremsstrahl ung, annihilation quanta, fluorescence x rays).

The methods used to simulate the trajectories of electrons and positrons that

are set in motion in photon interactions (electron-positron pairs, Compton

electrons, photoelectrons, Auger electrons) take into account elastic and

inelastic angular deflections, energy loss (including fluctuations) due to

atomic excitation and ionization (knock-on production) and to bremsstrahl ung

production, and the production of characteristic x-rays and Auger electrons in

K-shell ionization events. Positrons are treated as electrons, except for the

emission of two annihilation quanta when the positron stops in the target.

The pertinent distributions, cross sections, and related data used in the

calculation of electron transport are discussed in some detail elsewhere

[1,4-10]. Data on photon interaction cross sections were taken from the

compilations of Hubbell [11]; some auxiliary atomic data used for Ge can be

found in ref [12].

The detector was assumed to be a right-ci rcul ar cylinder, 5.5 cm high and

5.5 cm diameter, of uniformly distributed Ge (density of 5.323 g/cm 3 ). No

surrounding material, such as mechanical and thermal encapsulation or a charged-particl e anti -coincidence mantle, was taken into account. The

distribution of such material is not yet accurately known. Moreover, it

should be adequate to correct for the effect of such material on the baredetector peak probabilities by means of a simple attenuation factor, thereby

avoiding the introduction of any extrinsic angular dependence.

A broad, monoenergetic, monodi recti onal beam of photons was assumed

incident on the endface and/or sides of the detector at an angle e

0 with

respect to the detector axis. The histories of the incident gamma rays and

all generations of secondary photons and electrons were followed until they

either escaped from the detector or reached a cut-off energy of 1 keV.

Electron histories were also terminated within the detector if their energy

fell below 10% of the incident photon energy, provided the shortest distance

to any boundary was greater than the residual electron range. This greatly

speeded up the calculations, at the expense of the neglect of only a small

amount of low-energy bremsstrahl ung. For each cascade from a sample of 20,000

incident gamma rays, the energy deposited E was scored as the difference

between the incident energy E

0 and the energy carried out of the detector by

escaping electrons, positrons or photons. Dividing the scores by the incident

number provided estimates of the spectrum of absorbed energy, normalized to one incident gamma ray.

3
3. Results

Preliminary to analyzing the Monte Carlo results, detection efficiencies

were calculated using the analytical /numerical methods developed by Trombka

et al [2]. Table 1 gives the detection efficiency as a function of e

0 for

monodi recti onal gamma rays incident with energies from 0.1 to 20 MeV. Table 1 also includes the detection efficiency for an isotropic flux of gamma rays,

and gives as a function of e

0 the projected area of the detector by which an incident flux should be multiplied to determine the count rate. The results

in Table 1 indicate that for this detector the detection efficiency at any

energy or angle is greater than about 40%, and the maximum variation with

angle at a given energy is typically about a factor of 1.5.

The photon attenuation coefficient, also given in Table 1, is close to

its minimum value at 5 MeV. Judging that at this energy the incident photon

can perhaps best probe the shape of the detector, 5 MeV was chosen to study

the angular variations of the peak probabilities, P

0

, P, and P

2

, in the

absorbed-energy spectrum. The results are shown in Table 2 which gives the

calculated values of the scaled peak probabilities P^/n, and estimates of

their standard deviation, for angles of incidence e

0 from 0 to 90°. The

standard deviation of the individual values of P^ is

o(?^) = [P

i (l-P

i )/NDi/2 , ( 3 ) with N=20000. No discernable trends with e

0 are evident in the P^ values, and — with the exception of the anomalously low value for P

: at 15° (judged a statistical fluke) — the scatter in the values is consistent with their

standard deviations. In the earlier similar study [1] for a 3"x3" Nal

detector (also a cylinder whose height equals its diameter), no significant

angular dependence for the scaled peak probabilities P^/n was found for gammaray energies of 0.661, 6.13 and 12.0 MeV. Therefore, the angular dependence

of the peak probabilities can to a good approximation be accounted for through

the use of the appropriate values of the detection efficiencies. Table 2 also

gives values of the detection efficiency from the Monte Carlo calculations 2. The good agreement with the corresponding values from Table 1 provides a useful check on the Monte Carlo sampling procedures.

For incident gamma-ray energies of 20, 10, 2, 1.6, 1, 0.5, 0.2 and

0.1 MeV, Monte Carlo calculations were done for e

Q = 0 and 90°. After finding

agreement generally within statistical limits between the values of P^/n for

the two incident angles, the average of the two results was adopted for each

energy. The scaled peak probabilities were smoothed as a function of energy

by means of a least-squares cubic-spline algorithm [13], and interpolated to

intermediate energies. The results are shown in Fig. 1 and listed in Table 3.

Combined estimated uncertainties (due to statistical fluctuations, averaging

over incident angles, and smoothing), are less than ~ 2% for P^* greater than

0.2 and grow to ~ 5% for P^* = 0.02 and - 10% for P^ = 0.005.

2 The statistical errors associated with the values of the detector

efficiencies from the Monte Carlo calculations can be estimated using Eq (2)

with n|vic

TM

P^ ace Pi*

4
REFERENCES

1. M.J. Berger and S.M. Seltzer, Nucl . Instr. and Meth. 104 (1972)317.

2. J.I. Trombka, J.I. Vette, F.W. Stecker, E.L. Eller and W.T. Wildes,

Nucl. Instr. and Meth. 117(1974)99.

3. M.J. Berger and S.M. Seltzer, National Bureau of Standards Reports 9836

and 9837 (1968); also Oak Ridge Radiation Shielding Information Center,

Computer Code Collection 107/ETRAN (1968).

4. M.J. Berger, Methods of Computational Physics, Vol 1 (Academic Press, New

York, 1963) p. 135.

5. S.M. Seltzer, National Bureau of Standards Publ . NBSIR 74-457 (1974).

6. S.M. Seltzer, Nucl. Instr. and Meth. 119 (1974)157.

7. S.M. Seltzer and M.J. Berger, National Bureau of Standards Publ. NBSIR

82-2572 (1982).

8. M.J. Berger and S.M. Seltzer, National Bureau of Standards Publ. NBSIR

82-2550-A (1983).

9. S.M. Seltzer and, M.J. Berger, Nucl Instr. and Meth. B12 ( 1985)95.

10. S.M. Seltzer and M.J. Berger, At. Data Nucl. Data Tables 35(1986)345.

11. J.H. Hubbell , Int. J. Appl . Radiat. Isot. 33(1982)1269.

12. S.M. Seltzer, Nucl. Instr. and Meth. 188(1981)133.

13. M.J .D. Powell, Atomic Energy Research Establishment (Harwell, England)

Report TP 307 (1967).

5
Table 1. Detection efficiencies n(E 0 ,e

0

) for a cylindrical 5.5 x 5.5 cm highpurity Ge detector. Results, for broad beams of gamma rays incident

with energies E

0 (attenuation coefficients y) , are given as a function of Qp, the angle of incidence with respect to the detector

axis. Detection efficiencies are given in the last column for the

case of an isotropic incident flux. Entries at the bottom give, for

each incident angle, the projected area of the detector by which an incident gamma-ray flux should be multiplied to determine the count

rate.

E

o (MeV) (cm 2/g)

o o

it o

CD 15° 30° 45° cn o

o 75° <X) Oo iso

20.0 0.0353 0.644 0.519 0.458 0.435 0.441 0.474 0.543 0.466

15.0 0.0334 0.624 0.502 0.442 0.420 0.425 0.457 0.524 0.449

10.0 0.0316 0.603 0.484 0.426 0.404 0.409 0.440 0.505 0.432

8.0 0.0310 0.597 0.478 0.421 0.399 0.404 0.435 0.499 0.427

6.0 0.0311 0.597 0.479 0.421 0.399 0.405 0.435 0.499 0.428

5.0 0.0316 0.603 0.484 0.426 0.404 0.409 0.440 0.505 0.432

4.0 0.0327 0.616 0.495 0.436 0.,414 0.419 0.451 0.517 0.443

3.0 0.0352 0.643 0.518 0.457 0.434 0.440 0.473 0.542 0.465

2.0 0.0407 0.696 0.565 0.500 0.476 0.483 0.519 0.592 0.509

1.5 0.0463 0.742 0.606 0.539 0.514 0.522 0.560 0.637 0.549

1.0 0.0567 0.810 0.669 0.599 0.574 0.583 0.624 0.706 0.612

0.8 0.0633 0.843 0.702 0.631 0.606 0.616 0.659 0.743 0.645

0.6 0.0729 0.882 0.741 0.671 0.646 0.657 0.701 0.786 0.686

0.5 0.0797 0.903 0.764 0.695 0.670 0.682 0.727 0.812 0.711

0.4 0.0896 0.927 0.792 0.725 0.701 0.714 0.758 0.843 0.742

0.3 0.107 0.956 0.829 0.765 0.744 0.757 • 0.801 0.883 0.784

0.2 0.152 0.988 0.885 0.833 0.817 0.829 0.869 0.941 0.852

0.15 0.224 0.999 0.925 0.887 0.876 0.887 0.919 0.975 0.904

0.1 0.502 1.000 0.967 0.950 0.945 0.951 0.968 0.995 0.959

Projected

Detector

Area (cm 2

) 23.76 30.78 35.70 38.19 38.08 35.37 30.25 35.64

6
Table 2. Scaled peak probabilities P

0

, ?

l and P~, and the detection

efficiency n^c from the Monte Carlo calculations for broad beams

of 5-MeV gamma rays incident at an angle 8p with respect to the

detector axis. Numbers in parentheses indicate the estimated

statistical uncertainty in the last significant figures.

0

O nMC

P

0/t1 P: /

n

P

2 /n

0° 0.603 0.0847(26) 0.0551(21) 0.0?70(17)

15° 0.482 0.0858(29) 0.0433(21) 0.0408(20)

30° 0.424 0.0844(31) 0.0539(25) 0.0398(21)

45° 0.403 0.0810(31) 0.0560(26) 0.0392(22)

60° 0.405 0.0889(33) 0.0567(26) 0.0389(22)

75° 0.438 0.0854(31) 0.0577(25) 0.0374(20)

90° 0.506 0.0807(28) 0.0545(23) 0.0385(19)

7
Table 3. Calculated values of the peak probabilities for total absorption,

P

0

, single-annihilation escape, P 1# and double-annihilation escape,

P

2

, for the 5.5 x 5.5 cm Ge detector irradiated by broad beams of

gamma rays incident with energy E

0

. The results have been scaled by

the detection efficiency to remove dependence on the angle of

i ncidence.

E

0 (MeV) P0/n E

0 (MeV) p

0/i Pj/n P

2 /n

0.1 0.964 1.2 0.248 0.000709 0.000644

0.15 0.898 1.5 0.220 0.00253 0.00206

0.2 0.791 2.0 0.187 0.00868 0.00661

0.3 0.592

• 3.0 0.142 0.0267 0.0199

0.4 0.478 4.0 0.109 0.0431 0.0316

0.5 0.411 5.0 0.0836 0.0539 0.0388

0.6 0.367 6.0 0.0648 0.0598 0.0419

0.8 0.310 8.0 0.0398 0.0611 0.0403

1.0 0.274 10.0 0.0255 0.0540 0.0341

15.0 0.00971 0.0290 0.0181

20.0 0.00434 0.0122 0.00853

8
Scaled

Probability

10~ 3

10~ 2

10

"

Figure 1. Peak probabilities for total absorption, P

Q

, single-annihilation

escape, P 1# and double-annihilation escape, P

2

, for the 5.5 x 5.5 cm

Ge detector irradiated by broad beams of gamma rays incident with

energy E

0

. The results have been scaled by the detection efficiency

n to remove dependence on the angle of incidence.

9
NBS-114A (REV. 2-8C) U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publication Date S

BIBLIOGRAPHIC DATA

REPORT NO.

NBSIR 87-3548 APRIL 1987

SHEET (See instructions

)

4. TITLE AND SUBTITLE

CALCULATED RESPONSE OF A 5.5 x 5.5 cm HIGH-PURITY Ge

OETECTOR TO GAMMA RAYS WITH ENERGIES UP TO 20 MeV

5. AUTHOR(S)

Stephen M. Seltzer

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

national bureau of standards

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

10. SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a si gnificant

bi bliography or literature survey, mention it here)

Monte Carlo calculations have been done of the energy and angular response of

a 5.5 x 5.5 cm, high-purity Ge detector, for gamma rays incident with energies

from 0.1 to 20 MeV. Results are given for the absolute probabilities of total

energy absorption and of single and double annihilation escape, which relate

the areas of the peaks in the measured pulse-height distribution to the

intensities of incident gamma-ray lines.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons

)

detection efficiency; escape peaks; gamma rays; Ge detectors; response function;

total absorption peak

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