Copy Right (c) 2001 Los Alamos National Laboratory, USA. All rights reserved.

 

LA-UR-02-016

DOUBLE-DIFFERENTIAL GAMMA-RAY PRODUCTION: CROSS SECTIONS AND SPECTRA OF Al, Si AND Fe

FOR 8.51, 10.00, 12.24 AND 14.24 MeV NEUTRONS

 

M. Drosg

Institut für Experimentalphysik

University of Vienna

Boltzmanngasse 5

A-1090 Vienna, Austria

 

D. M. Drake and R. C. Haight

Los Alamos National Laboratory

Los Alamos, NM 87545, USA

January 8, 2002

 

Abstract

Neutron-induced gamma-ray production cross sections for Al, Si and Fe have been measured for neutron energies of 8.51, 10.00, 12.24 and 14.24 MeV at angles of 35, 55, 75 and 90 degrees for gamma-ray energies up to 5 MeV. Similar to experiments with pulsed white neutron sources, the time-of-flight method was applied to select the monoenergetic portion of the 3H(p,n)3He neutron source spectrum so that data in the "gap" region (8 to 14 MeV) could be measured. A measurement with a threefold smaller iron sample taken under otherwise identical conditions was used to check the computer codes extracting cross-section data from the measured data. This resulted in substantial improvements in the corrections for neutron and gamma-ray interactions in the sample. For 28Si the new neutron-gamma reaction cross sections in the middle of the gap are about 15 % lower than the evaluated ENDF/B-VI values. For aluminum, the present results are higher than those of one previous evaluation but in agreement with another.

(27Al, Si, Fe, cross section, gamma-ray production, NaI detector, tandem accelerator, Monte Carlo, neutron transport, gamma transport)

 

 

1. Introduction

Neutron-induced gamma-ray production cross sections are needed for many applications, e.g. for controlled thermonuclear reactor design calculations, for nondestructive determination of the elemental composition of materials, etc. Data in the "gap" region between 8- and 14-MeV neutron energy are especially sparse. The data presented here cover the energy range between 8.51 MeV and 14.24 MeV for the materials iron, aluminum and silicon in an angular range between 35 and 90 degrees. It is shown that, in the two iron samples (differing in mass by about a factor of three), the correction factors for the finite sample size effect deviate from each other by as much as 80 %.

This report documents the experimental procedure, data reduction and results of these measurements.

 

2. Experimental Procedure

2.1 Neutron Source

Disregarding the preferred 1H(t,n)3He source, which was not available at the time of the experiment (and which is no longer available), there is no monoenergetic neutron source available for making (n,x gamma) experiments over the energy range between 8.5 and 14.2 MeV. Therefore, the neutron source reaction 3H(p,n)3He, which we used in this experiment, had to be combined with the "white neutron" technique to suppress events caused by background neutrons from both the reaction itself as well as those stemming from the beam stop. Compared to a "real" white neutron source, such "monoenergetic" sources have the advantage of a much higher counting rate in the energy range of interest even when using a relatively small neutron energy width [1,2]. The energy spread of the monoenergetic neutron beam was about 85 keV for the 8.51 MeV source and smaller for the higher energies. At the same time smaller samples may be used reducing the finite sample size corrections drastically.

As was pointed out before [2,3], the p-T reaction has several advantages over the d-D reaction. Although the specific neutron yield in the required energy range is practically the same for these two reactions [3], the signal-to-(intrinsic) background ratio is much better for p-T [4]. Besides, the neutron background from the beam stop can be kept small in the p-T case by using materials with a high (p,n)-threshold [4]. Finally because the neutrons and the proton beam have very nearly the same velocity, transit time differences for protons and neutrons through the target are small compared to other considerations of time resolution, and hence the improved time resolution can be used to improve the signal-to-background with the p-T source reaction.

 

2.2 Experimental Set-up

Bunched protons from the tandem accelerator of the Ion Beam Facility (IBF) at Los Alamos were directed through a 5.3 mg/cm2 molybdenum window into a 3 cm long gas cell filled with 2.9 atmospheres of tritium and with a beam stop made of 58Ni. The samples (upright cylinders) were placed at 0 degrees at a distance of 96.1 cm from the neutron target. Their properties are given in Table 1.

Table 1. Sample Properties

Material

Mass

Diameter x Height

 

[mole]

[cm]

 

 

 

Al

2.513

1.6 x 3.0

Fe

3.464

3.0 x 3.0

Fe, hollow

1.254

(3.0-2.4) x 3.0

Si

1.877

1.6 x 3.0

The samples are relatively small to make systematic errors small. To check the effect of the sample size, a tubular cylinder of iron with the same outer dimensions was used. Fig.1 shows this set-up.

 

 

 

 

 

 

 

Figure 1- Layout of the experiment showing the proton beam and tritium target which serve as the neutron source, sample, NaI(Tl) gamma-ray detector with anti-Compton annulus, shield, and shadow bar.

 

The choice of the flight path length between source and sample was a compromise between a big enough solid angle to enhance the counting rate and a sufficient energy separating power to discriminate against background events by neutrons produced by tritium break-up (Q = -6.26 MeV; threshold = 8.35 MeV) and by (p,n) reactions on the 58Ni beam stop (Q = -9.35 MeV; threshold = 9.51 MeV). Thus gamma rays stemming from the interaction of the monoenergetic neutrons alone could be recorded.

For each measurement the relative neutron output of the source was recorded by means of a neutron monitor and by a beam current integrator. At each neutron energy the absolute calibration of the neutron flux was measured in a side experiment. A proton recoil counter telescope was placed at 0 degrees at a distance of 67.4 cm from the neutron target and its proton yield converted into neutron fluence using YALE phase shift predictions for the differential 180 degree n-p scattering cross sections at the four energies (see Table 2).

Table 2. Data relevant to the calibration of the set-up

n-Energy

n-p Sigma(180)

p-T lab Sigma(0)

[MeV]

[mb/sr]

[mb/sr]

8.51

88.48

26.49

10.00

77.64

29.00

12.24

65.43

36.09

14.24

57.32

41.99

The energy dependence of the absolute counter telescope measurements and that of the calculated relative neutron yields using collected beam charge and known neutron production cross sections [5] agreed to better than 1% rms.

The gamma-ray spectrometer was a cylindrical NaI crystal (6 cm diam x 15 cm long) located 98 cm from the center of the sample. It was centered inside a NaI annulus detector (25 cm diam x 30 cm long) surrounded by a large shield-collimator. To improve the peak-to-tail ratio of the response of the spectrometer, the annulus detector was used in the anticoincidence mode suppressing Compton and escape events.

Recording both the arrival time and the pulse-height not only allows the selection of the "monoenergetic" events but also allows the subtraction of time-independent background and of background from neutrons scattered into the detector [6].

 

3. Data Reduction

3.1 Calibration of the Gamma Detector and Spectrum Unfolding

To obtain the response functions and the efficiency of the spectrometer, spectra of discrete gamma-rays of known intensity in the energy range from 0.28 to 4.4 MeV were measured with the sources at the same position as the scattering sample.

After corrections for the background, the gamma-ray spectra were unfolded by using the response functions, and the full-energy-peak detection efficiency was applied to the spectra.

3.2 Corrections

Originally, the data of the two iron samples that differed strongly in mass (but not in outside dimensions) could not be made to agree [6] reasonably because of the strongly differing neutron and gamma-ray attenuation and scattering. After an appropriate Monte Carlo code had been written [7], attenuation and multiple scattering of both the neutrons and the gamma rays could be properly corrected using ENDF/B-VI as data base for Al and Si, and ENDF/B-V for Fe.

The largest corrections were expected for the iron samples because of the size and density of the samples and because they had the heaviest nuclei of the three elements investigated. Therefore, these samples were used to check the effectiveness of the calculated corrections. At 14.24 MeV and 90 degrees the correction factors of the 0.847 MeV iron gamma ray for the full and the hollow cylinder were 1.4935 and 0.8365 respectively, i.e. they differ by 80%! The largest correction factor obtained in this experiment was 1.724 for the full iron cylinder (at 8.51 MeV and 35 degrees, 0.847 MeV peak). The correction necessary for the other two samples was typically a factor of three to four less than that for the larger iron sample.

From the good agreement between the corrected spectra of the full and the hollow iron sample (see [7], Fig. 1), it was concluded that the calculated correction had an uncertainty of about 5%. This uncertainty was included in the individual errors given with the individual differential cross sections.

 

4. Results

4.1 Double-differential Cross-Section Spectra

For all three samples (Al, Fe, Si) cross section data at neutron energies of 8.51, 10.00, 12.24 and 14.24 MeV have been extracted at 35 degrees (8.51 and 10.00 MeV only), at 55 degrees, at 75 degrees and at 90 degrees. For 6 spectra (10 MeV at 35 degrees, and 14 MeV at 55 degrees) sample-out runs were available. In these cases more reliable information on gamma-ray continua could be obtained (see e.g. [7], Fig. 2). For the differential cross section data of the more pronounced peaks, very little improvement was obtained using sample-out runs.

All 42 double-differential gamma-ray cross section spectra are given graphically, without uncertainties, in the Appendix. The results are available numerically from the National Nuclear Data Center a Brookhaven National Laboratory where they are presented as triplets of gamma energies in MeV units, of double differential cross section data and their uncorrelated uncertainties in units of mb/(sr*MeV).

 

4.2 Differential Cross Sections

Even though this experiment was aimed at getting information on the continuous gamma-ray background, the double differential cross sections have been integrated over several peaks to obtain differential cross sections. The individual errors of the present data as given in the tables include statistical errors, background subtraction errors and uncertainties in the finite sample size corrections.

4.2.1 Iron (0.847 MeV gamma ray)

Table 3. Peak-integrated elemental differential gamma production cross sections (iron, 0.847 MeV). Present data compared with preliminary, uncorrected data [6].

Angle:

90deg

75deg

55deg

35deg

Integrated

n-Energy

Elemental

Differential

Gamma

Production

Cross Sections

[MeV]

[mb/sr]

[mb/sr]

[mb/sr]

[mb/sr]

[mb]

8.51

75.9 4.1

82.0 3.4

86.3 3.7

97.0 4.5

1099 26

[6]

77.5 9.3

79.7 9.6

85.810.3

91.6 11.0

 

 

 

 

 

 

 

10.00

67.4 3.3

70.6 4.0

81.5 3.8

87.9 4.6*)

994 27

[6]

68.4 8.2

74.6 8.9

83.010.0

84.5 10.2

 

 

 

 

 

 

 

12.24

64.7 2.2

66.0 2.9

67.2 3.2

 

847 40

[6]

62.4 7.5

64.7 7.8

66.1 7.9

 

 

 

 

 

 

 

 

14.24

42.1 2.6

47.5 2.3

50.13.0*)

 

642 39

[6]

49.2 5.9

52.6 6.3

54.9 6.6

 

 

 

 

 

 

 

 

14.24 hollow

38.4 1.8

 

 

 

 

*) measured background subtracted

 

Table 3 compares preliminary data as given in [6] with the final ones, which were corrected for neutron and gamma ray attenuation and multiple scattering. The individual errors of the present data include statistical errors, background subtraction errors and uncertainties in the finite sample size corrections, only.

Comparing the preliminary data [6] with the present ones it can be seen that, except for one case (14.24 MeV, 90deg), the errors of the preliminary data were estimated properly including the uncertainties due to the incomplete corrections for the sample size which are their dominating error contributions.

4.2.2 Silicon (1.779 MeV gamma ray)

Table 4. Peak-integrated elemental differential gamma production cross sections (silicon, 1.779 MeV)

Angle:

90deg

75deg

55deg

35deg

Integrated

n-Energy

Elemental

Differential

Gamma

Production

Cross Sections

[MeV]

[mb/sr]

[mb/sr]

[mb/sr]

[mb/sr]

[mb]

8.51

35.5 1.6

40.1 1.7

45.8 1.8

50.7 1.8

562 11

10.00

36.1 1.9

37.4 1.6

38.6 2.3

40.4 2.5*)

489 15

12.24

32.4 2.4

32.5 2.0

35.9 2.1

 

448 26

14.24

29.3 2.5

30.2 1.3

32.9 1.6*)

 

415 20

*) measured background subtracted

 

Table 4 gives elemental energy (and angle) integrated cross sections for the 1.779 MeV gamma ray production of silicon (corrected for neutron and gamma ray attenuation and multiple scattering). The individual errors include statistical errors, background subtraction errors and uncertainties in the finite sample size corrections, only.

Unfortunately the peak of the 1.779 MeV gamma ray is not well separated from a peak that corresponds to gamma rays between 1.44 and 1.47 MeV. Although there are some potential candidates for such lines (see Table 5), the various contributions to this satellite peak have not been completely identified.

Table 5. Gamma rays in the energy range from 1.443 to 1.473 MeV that could contribute to the satellite peak in the silicon spectrum.

Reaction

Threshold

Gamma

Level

Gamma

Type

Energy

Energy

Energy

Intensity

 

[MeV]

[MeV]

[MeV]

[%]

28Si(n,n')

 

 

 

 

 

9.722

1.44805

9.38155

3.14

 

10.796

1.4479

10.9440

7.3

 

11.341

1.4730

10.41825

5.9

28Si(n,d)27Al

 

 

 

 

 

13.513

1.4692

3.6804

<0.16 *)

29Si(n,n')

 

 

 

 

 

6.604

1.446234

6.380836

6

29Si(n,p)29Al

 

 

 

 

 

5.693

1.4675

2.8656

78.6

 

6.797

1.4476

3.6717

<15

29Si(n,d)28Al

 

 

 

 

 

13.035

1.47251

2.4861

<3.3 *)

30Si(n,n')

 

 

 

 

 

8.978

1.460

8.684

11

 

10.918

1.449

10.561

44

 

11.631

1.472

11.250

17

30Si(n,4He)27Mg

 

 

 

 

 

9.047

1.4433

4.5528

10

 

9.538

1.4684

5.028

41

 

10.366

1.430

5.829

35

*) although energetically possible, this transition contributes only a negligible amount to the peak.

At 8.51 MeV the peak position is about 1.47 MeV and slightly higher than at the higher energies (1.45 MeV). This suggests that the (n,p) reaction on 29Si is involved. The intensity of the satellite peak is typically a factor of five less than that of the 1.779 MeV peak. It seems reasonable to assume that the background subtraction uncertainty under the main peak introduced by double-peak fitting of both peaks was 7% of the intensity of this lower energy satellite.

4.2.3 Aluminum (1.72, 2.21 and 3.00 MeV gamma rays)

Table 6. Peak-integrated differential gamma production cross sections for aluminum, (1.692&1.719&1.809), (2.21&2.30) and (2.980 to 3.001) MeV)

Angle:

 

90deg

75deg

55deg

35deg

Integrated

n-Eng.

g-Eng.

Experimental

Differential

Gamma

Production

Cross Sections

[MeV]

[MeV]

[mb/sr]

[mb/sr]

[mb/sr]

[mb/sr]

[mb]

8.51

2.2

20.4 2.0

22.7 1.1

23.1 1.6

24.6 1.7

291 10

 

3.0

12.6 1.5

13.2 1.7

14.7 1.3

15.5 1.2

179 9

10.00

2.2

17.8 1.4

20.2 1.3

22.3 1.3

27.8 1.1*)

289 8

 

3.0

11.5 1.6

13.5 1.6

12.2 1.6

16.6 1.6

170 11

12.24

2.2

13.0 2.1

16.9 1.5

17.6 1.7

 

227 29

 

3.0

9.5 1.1

11.6 1.8

11.3 1.4

 

145 18

14.24

1.7

14.4 1.5

14.7 1.3

19.4 1.5*)

 

244 30

 

2.2

10.7 1.5

12.7 1.0

15.8 1.3*)

 

201 25

 

3.0

7.8 1.1

8.7 1.7

11.0 1.1*)

 

138 17

*) measured background subtracted

 

 Table 6 gives energy (and angle) integrated cross sections for the production of 1.7, 2.2 and 3.0 MeV gamma rays of aluminum (corrected for neutron and gamma ray attenuation and multiple scattering). The individual errors include statistical errors, background subtraction errors and uncertainties in the finite sample size corrections, only.

4.2.4 Data comparison at 14.24 MeV, 90 degrees

Table 7. Comparison of peak-integrated differential cross sections of one gamma-ray line of each sample at 90 degrees and 14 MeV with previous data. The present data and that of [7] are based on the same experimental data!

Sample

Gamma-Ray

Elemental

Differential

Cross

Sections

 

Energy

Present data

[7]

[8]

[9]

 

 

 

 

 

 

 

[MeV]

[mb/sr]

[mb/sr]

[mb/sr]

[mb/sr]

Al

3.00

7.81.1

8.11.0

7.91.6

7.30.9

Fe

1.24

28.81.8

28.82.0

23.02.3

28.23.4

Fe hollow

1.24

27.71.7

 

 

 

Si

1.78

29.32.5

32.82.8

29.0 7.

27.53.3

 

Table 7 compares the present 90 degree data at 14.24 MeV of the three samples with literature values. Because of the relatively poor gamma energy resolution of the NaI(Tl) spectrometer, weak neighboring lines are included in the data. The individual errors of the present data include statistical errors, background subtraction errors and uncertainties in the finite sample size corrections, only.

4.2.5 Neutron-gamma reaction cross sections of 28Si

Taking the abundance of 28Si as 0.9223 and the gamma emission probability per reaction as 0.917, one can use the integrated values of Table 4 to calculate the neutron-gamma reaction cross section for 28Si. These results are shown in Table 8.

Table 8. Neutron-Gamma Reaction Cross Sections of 28Si

n-Energy

present data

ENDF/B-VI

[MeV]

[b]

[b]

8.51

0.665 0.013

0.650

10.00

0.578 0.018

0.665

12.24

0.530 0.031

0.622

14.24

0.490 0.024

0.503

 

These data have a common scale error of 4.2%. The individual (uncorrelated) errors stem from the individual uncertainties at each angle. Whereas the agreement with ENDF/B-VI is excellent at 8.51 and 14.24 MeV, the new data in the middle of the gap are typically lower by 15%.

5. Sources of Error

Errors given with the data do not include correlated uncertainties. When one compares differential cross sections at various neutron energies but for the same gamma ray energy, the correlated uncertainty of all such data comprises the (practically energy independent) neutron flux calibration error of 3 % and the gamma ray efficiency error of 3 to 5 % (see below), so that, depending on the gamma ray energy, neutron-energy-independent scale errors between 4.2 and 5.8 % are obtained.

Within each double differential cross-section spectrum only the calibration error of 3 % can be regarded as scale error.

5.1 Correlated uncertainties

Measuring the three samples under as identical conditions as possible gives a strong correlation between their scale uncertainty at each energy. In addition, the scale uncertainty at different energies is rather strongly correlated, as well, because the identical set-up was used each time, so that mainly the uncertainties in the n-p reference cross sections contribute to the uncorrelated portion. Finally, the uncertainty in the gamma-ray counting efficiency is correlated at each gamma-ray energy. Obviously, the uncertainty in the mass of each sample is correlated for all energies. Its contribution to the total (correlated) uncertainty is negligible anyway, due to the quadratic error summation.

The absolute uncertainty of the neutron flux measurements is 3%. This scale uncertainty has a correlation factor of 0.94 among the four energies. The uncertainty in the gamma-ray counting efficiency is less than 3% below 3 MeV, increasing to about 5% at 5 MeV.

5.2 Uncorrelated uncertainties

The statistical error (from the foreground and background runs) ranges from about 1% for peak integrals to about 0.2 mb/(sr MeV) for continua. These errors (bin by bin) are given in the Appendix together with the data.

The individual errors given in the tables for the peak-integrated differential gamma-ray production cross sections were obtained by adding quadratically the statistical error, the background subtraction error and the uncertainty of the finite sample size correction. The uncertainty in the (linear) background subtraction was assumed to be 10 to 20 % of the correction, depending on its size. In the case of the 1.779 MeV line of silicon the separation from the neighboring low energy lines was uncertain by about 7% of the intensity of these lines. This uncertainty was added quadratically to the uncertainty in the subtraction of the flat background. The uncertainty of the finite sample size correction was assumed to be 5% of this correction (see discussion in 3.2). Only in the case of iron did this uncertainty contributed noticeably to the combined uncertainty.

The correction factors for dead time losses (up to 2%) and for the beam heating in the tritium gas target (up to 5%) had uncertainties that could be neglected when added quadratically. The uncertainty introduced by the unfolding procedure cannot be assessed quantitatively. It is negligible for intense peaks, and appreciable for the continuum.

6. Conclusions

This set of 42 double differential gamma production cross sections for the materials Al, Fe and Si bridges the difficult "gap" region where only few data are available. For the 846.8 keV line of iron there is a perfect agreement with the evaluation of Savin et al. [10] at 8.51 and 14.24 MeV. In the gap the new data are about 5 % lower. As discussed above there is also very good agreement for the silicon sample with ENDF/B-VI both at 8.51 and 14.24 MeV.

For aluminum the gamma production cross sections of all three peaks in Table 6 are higher (up to 40 %) than the evaluated data of Zvenigorodskij et al. [11]. However, at 14 MeV the agreement with the data of Hlavac et al. [12] is good to very good. Because all three samples have been measured under identical conditions in the same experiment (at each angle and energy they were measured one after the other) there cannot be such a pronounced sample dependence, unless the mass was wrong or the multiple scattering correction was wrong. The first can be ruled out because such a mistake is utterly unlikely (density!!) and the deviation would be the same at all neutron and gamma energies. Using too low input cross sections for the multiple scattering corrections makes the corrections too small and consequently the cross sections too small and not too big. Therefore the most likely explanation is that the evaluated data [11] are too small.

7. References

[1] J. K. Dickens and F. G. Perey, Nucl. Instr. Meth. 82, 301 (1970).

[2] M. Drosg, Nucl. Sci. Eng. 106, 279 (1990).

[3] M. Drosg and O. Schwerer, Production of Monoenergetic Neutrons Between 0.1 and 23 MeV: "Neutron Energies and Cross Sections," in Handbook on Nuclear Activation Data, K. Okamoto, Ed., IAEA Tech. Rep. Ser. 273, (Vienna 1987).

[4] M. Drosg and G. F. Auchampaugh: "Signal-to-Background Ratio for Neutron Production Between 10 and 14 MeV by the Reactions 3H(p,n)3He, 1H(t,n)3He, and 2H(d,n)3He", Nucl. Instr. Meth. 140, 515 (1977).

[5] M. Drosg, DROSG-2000, Codes and database for 57 neutron source reactions, documented in the IAEA report IAEA-NDS-87 Rev. 6 (January 2001), available cost-free from IAEA, A-1400 Vienna, Austria.

[6] D. M. Drake, L. R. Veeser, M. Drosg, and G. Jensen: "Differential Cross Sections for the 0.847-MeV Gamma Ray from Iron for Incident Neutrons of 8.5, 10.0, 12.2 and 14.2 MeV", Bull. Am. Phys. Soc. Ser.2, 20, 168 (1975) and Proc. Conf. on Nuclear Cross Sections and Technology, Wash. D.C. 1975, p.813 (NBS-SP-425).

[7] M. Drosg, D. M. Drake, K. Hasegawa, S. Chiba, and M. Mizumoto: "Double-differential gamma-ray production cross sections of Al, Fe and Si for neutrons between 8.5 and 14.2 MeV", Proc. International Conf. on Nucl. Data for Sci. and Techn., Juelich, May 1991, p.304 in S.M. Qaim (Editor): " Nuclear Data for Science and Technology", Springer Verlag Berlin/Heidelberg (1992).

[8] F. C. Engesser and W. E. Thompson, J. Nucl. Energy, 21, 487 (1967).

[9] D. M. Drake, E. D. Arthur and M. G. Silbert, Nucl. Sci. Eng. 65, 49 (1978).

[10] M. V. Savin, A. V. Livke, and A. G. Zvenigorodskij, translation from Yadernye

Konstanty 2 (1999), report INDC(CCP)-426, p.95 (February, 2000).

[11] A. G. Zvenigorodskij, M. S. Shvetsov, A. M. Shvetsov, M. V. Savin, Yu. A.

Nefedov, and V. A. Zherebtsov, translation from Yadernye Konstanty 2 (1999),

Report INDC(CCP)-426, p.27 (February, 2000).

[12] S. Hlavac, L. Dostal, and I. Turzo, Nucl. Sci. Eng. 125, 196 (1997).

 

 

Appendix

 

The results of this work are presented in the following graphs without uncertainties. Double-differential cross sections in mb sr-1 MeV-1 are plotted versus the gamma-ray energy in log-log format. Numerical values for all of these results with the uncertainties can be obtained from the National Nuclear Data Center in Brookhaven National Laboratory in the EXFOR format.