Angular distributions of gamma rays produced by neutron bombardment of Al, Mg and Si

I 2.B:2.D I

Nuclear Physics 73 (1965) 561 --578; (~) North-Holland Publishing Co., Amsterdam

!

Not to be reproduced by photoprint or m i c r o f i l m without written permission from the publisher

A N G U L A R D I S T R I B U T I O N S OF G A M M A RAYS

PRODUCED BY NEUTRON BOMBARDMENT OF AI, Mg and Si s. c. MATHUR, W. E. TUCKER, R. W. BENJAMIN and I. L. MORGAN Texas Nuclear Corporation, Austin, Texas t

Received 20 April 1965

Abstract: The angular distributions of gamma rays produced by inelastic scattering of neutrons with magnesium, aluminium and silicon have been measured in the neutron energy range of 3.0-4.5 MeV. An attempt has been made to determine the validity of the statistical assumption in the compound nucleus formation with 27A1, 24Mg, 26Mg and zsSi nuclei. In order to do so, the angular distributions and differential cross sections have been calculated on the basis of the Satchler formalism and comparisons made with the experimental results.

E

I NUCLEAR REACTIONS 24Mg, 26Mg, Z7A1,~sSi (n, n'y), E = 3-4.5 MeV; measured or(E; E~,, 0). Z4Mg,26Mg,~A1, 2sSideduced levels, J, ~r. Natural targets.

1. Introduction The measurement of angular distributions of gamma rays produced in the inelastic scattering of neutrons with nuclei is one of the important experimental means of studying the nuclear level schemes. Moreover, such a systematic study over the various regions of the periodic table can lead to an insight into the nuclear reaction mechanisms. In particular, a comparison of the experimental excitation functions and angular distributions with the Hauser-Feshbach 1) and Satchler 2-4) formalisms, provides valuable information regarding the extent of validity of the statistical assumption in the compound nucleus formation. The study of nucleon interactions with light nuclei is of great interest in this direction. In recent years, a large number of nucleon inelastic scattering experiments have been undertaken with this aim in view. In the present experiment, the angular distributions of gamma rays produced in the inelastic scattering of neutrons with Mg, A1 and Si have been measured in the neutron energy range 3.0--4.5 MeV. The energy levels of light nuclei have been surveyed comprehensively by Endt and van der Leun 5). The odd mass nucleus 27A1 has a ground state spin of ~+. The light nuclei 24Mg, 26Mg and 2ssi are even with 0 + ground states. Recently, Ophel and Lawergren 6) have studied the low-lying levels of 27A1 by measuring the gamma ray spectrum produced in the 27Al(p, p'y)27A1 reaction. They have also determined the branching ratios for the de-excitation of the 2.212, 2.73 and t This work was supported in part by the U.S. Atomic Energy Commission. 561

562

s.c.

MATHUR e t al.

2.976 MeV levels. The decay of the 2.976 MeV and 3.00 MeV levels has been studied by Lawergren 7) by measuring the gamma radiation produced by proton inelastic scattering with 27A1. These measurements led to a spin assignment of J = 2 + for the 2.976 MeV level and J = -~+ for the 3.00 MeV level. Perkin 8) has measured the gamma ray production cross sections at 90 ° in the neutron inelastic scattering with Mg, A1 and Si in the neutron energy range 3.5-8.5 MeV. A three crystal pair spectrometer was used in their work. Earlier, Hosoe and Suzuki 9) had measured the gamma ray production cross sections at 90° in aVA1with neutrons in the energy range 2.85-3.0 MeV. They also measured the angular distribution of the 1.37 MeV gamma ray from the 2aMg(n, n'y)24Mg reaction. The angular distributions for this gamma ray have also been measured by Boring and McEllistrem lo) and Donahue and Roberts 11). In other related experimental work, Thomson et aL 12) have measured the angular distributions for the scattering of fast neutrons by 24Mg. The angular distributions for inelastic scattering of neutrons leading to the first level in 28Si have been measured by Tsukada et al. 13). Lind and Day 14) have measured the excitation functions of the gamma rays produced by neutron inelastic scattering in silicon. Sheldon is) has surveyed the experimental work on angular correlations in the inelastic nucleon scattering with 24Mg and 28Si. This brief survey indicates the interest in the nucleon interactions with magnesium, aluminium and silicon. In the present work, the experimental results on the angular distributions and differential cross sections of the gamma rays produced in the neutron inelastic scattering have been compared with theoretical calculations based on the Satchler formalism 2--4). Comparisons have also been made with the results of previous experiments of other workers.

2. Experimental Procedure The experimental system has been described in a Texas Nuclear Corporation Report 16) and by Ashe et al. 1~). The equipment consists of a two-crystal total absorption gamma ray spectrometer of the type developed by Trail and Raboy 18), used in conjunction with a conventional pulsed beam time-of-fright spectrometer, based on the Los Alamos design 19). The neutron beams in the energy range 3.0 to 4.5 MeV were provided by Texas Nuclear Corporation's 3 MeV Van de Graaff accelerator. A deuterium target cell 1 cm long and filled with 2 atm pressure of deuterium gas was used to produce neutrons in the D(d, n)aHe reaction. The aluminium scatterer was in the form of a hollow cylinder, 2.54 cm outer diam., 1.25 cm inner diam., and 5.1 cm long. The magnesium scatterer was in the form of a solid cylinder, 2.54 cm in diam. and 5.08 cm long. The scattering samples were positioned at 0 ° with respect to the incident deuteron beam direction. The distance between the front face of the gas cell and the centre of the scattering samples was of

ANGULAR DISTRIBUTIONS

563

the order of 4-6 cm in the various experimental runs. For magnesium and aluminium experiments, the background runs were made with the "scatterer out". In the case of silicon, the background runs were made with an empty plastic container in the scatterer position. The "scatterer in" and the "scatterer out" runs were usually made for periods of 30-40 min. During the course of each run, the neutron flux was continuously monitored by means of a calibrated long counter of the Hanson-McKibben type 20) set at 90 ° with respect to the deuteron beam direction. The charge collected at the target cell was also integrated simultaneously. All the data runs were made for a constant integrated charge. The analysis of the spectral data for obtaining the angular distributions and the differential cross sections is described in detail in a Texas Nuclear Corporation report 16). The estimated errors are displayed as error bars on the experimental data points presented in the following section. The errors in the angular distribution data are mainly the errors propagated through the statistical deviations in the scatterer in and scatterer out counts, the subtraction of the Compton distribution from the gammaray photopeaks in the spectra, and the statistical error in the long counter counts used for the normalization of data runs. However, the errors quoted on the absolute differential cross sections also include the errors involved in the determination of the long counter efficiency, the efficiency of the N a I detector, the self-absorption of g a m m a rays due to the scatterer itself and the error caused by the Compton distribution due to scattering in the sample. The upper limit on the errors in the determination of the cross sections has been estimated to be 20 ~ .

3. Results and Discussion 3.1. THE ~Al(n, n'y)27A1 REACTION Fig. 1 shows a typical gamma-ray spectrum produced in the 27Al(n, n'7)27Al reaction. The g a m m a ray peaks at 0.84, 1.01, 1.72, 2.21, 2.73 and 3.0 MeV ale clearly resolved. The origin of these g a m m a rays can be seen with reference to the level scheme for 27A1 as shown in fig. 2. The information given in this diagram has been obtained from several sources 5 -7, 25), including the results of the present experiment. The multipolarities indicated for the g a m m a rays are the ones most probable on the basis of the present spin assignments. The angular distributions of the g a m m a rays have been measured at the incident neutron energies of 3.57, 4.07 and 4.57 MeV. The spread in the neutron beam energy has been calculated to be 150 keV about the median energy. The angular distributions and the differential cross sections have also been calculated theoretically on the basis of Satchler formalism 2-4). In these calculations the angular m o m e n t u m of the neutrons has been restricted to l < 4 in the entrance channel and l < 3 in the exit channel.

8. C. MATHUR e t al.

564

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Fig, 1. G a m m a ray s p e c t r u m p r o d u c e d in the n e u t r o n b o m b a r d m e n t o f =rA1. T h e scatterer o u t b a c k g r o u n d h a s been subtracted. 4400

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5/2*

ANGULAR DISTRIBUTIONS

565

The numerical evaulation of the angular distribution functions was carried out using the transmission coefficients calculated by Beyster et al. 21) and Auerbach and Perey 22). The latter have calculated the transmission coefficients using the optical model potentials of Bjorklund and Fernbach 23) (henceforth referred to as B and F) and Perey and Buck 24) (henceforth referred to as P and B). A computer code TRANSEC in FORTRAN-63 language has been developed to carry out theoretical calculations based on the Satchler formalism. The code is sufficiently versatile to take into account multiple exit channels, gamma-ray cascades, mixed multipolarities and branching Iatios of various excited levels in the computation of the angular distributions and the differential cross sections of gamma rays. TABLE 1 Experimental excitation functions do'(90°)/d.Q (mb/sr) En Er 0.84 1.01 1.72 2.21 2.73 3.00(doublet)

2.95 MeV a)

3.57 MeV

4.07 MeV

4.57 MeV

8±2 20±2

9.5±2.6 18.1!3.4 7.0±1.5 17.0~2.9 2.4~0.6 8.0±1.4

9.9±2.3 19.5±3.7 8.0~1.6 16.8i2.8 3.4i0.7 13.6±2.3

8.8~2.5 18.6±3.7 5.1il.5 14.6~2.6 3.9i0.9 12.0±2.2

7±1

~) These are the differential cross sections at 90° measured by Hosoe and Suzuki ~). A first orientation towards the experimental results can be obtained from the differential cross sections for the production of gamma rays at 90 °, presented in table 1. The cross sections obtained by Hosoe and Suzuki 9) at E n --- 2.95 MeV are also listed for comparison. The experimental and the calculated distributions for the production of 0.842, 1.013, 1.72, 2.212, 2.73 and 3.0 MeV gamma rays are shown in figs. 3-8. The distributions are represented on an absolute cross section scale for the sake of clarity. The observed gamma ray at 3.0 MeV is an incoherent mixture of two gamma rays produced in the ground state transitions of the doublet levels at 2.976 and 3.000 MeV, respectively. The work of Towle and Gilboy 25) and Lawergren 7) indicate spin assignments of 3 + for the 2.976 MeV level and 9+ for the 3.000 MeV level. The good agreement between the experimental and the calculated distributions of the 3.0 MeV gamma ray (fig. 8) lends further support to the assumed spin assignments for the doublet levels. In general, a comparison between the experimental and the calculated differential cross sections for the production of the various gamma rays in the 27Al(n, n'y)27A1 reaction (figs. 3-8) shows a good agreement in the shapes of the distributions and the anisotropies. Further quantitative comparisons can be made by an examination of

566

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e t al.

MATHUR

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567

ANGULAR DISTRIBUTIONS

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ANGULAR DISTRIBUTIONS

569

level excitations i n 27A1. T a b l e 2 lists the experimental a n d the calculated cross sections integrated over all angles for the p r o d u c t i o n o f various g a m m a rays. It can be seen that for most cases, there is excellent quantitative agreement between the experim e n t a l results a n d the cross sections calculated with the Beyster 2t) a n d the Bjorkl u n d a n d F e r n b a c h 2z) t r a n s m i s s i o n coefficients. I n general, the cross sections calculated with the t r a n s m i s s i o n coefficients o f Perey a n d Buck 22) are higher t h a n t h e experimental results. TABLE 2

Integrated cross sections for the production of gamma rays in the ~Al(n, n'~,)27A1reaction Neutron energy (MeV)

3.57

4.07

4.57

Experiment or calculation Present experiment Beyster B and F P and B Present experiment Beyster B and F P and B Present experiment Beyster B and F P and B

Integrated cross sections for gamma ray production (mb) 0.84 MeV 1.01 MeV 1.72 MeV 2.21 MeV 2.73 MeV 3.0 MeV doublet 1204-32 86 79 102

2274-43 244 225 271

884-18 83 87 100

2144-36 230 212 259

304-7 28 29 33

1114-20 109 132 147

1254-29 97 89 113

2464-47 225 203 255

1014-20 89 88 104

2124-36 228 196 244

444-9 30 29 35

1824-31 177 180 215

1114-22 110 102 128

2344-47 223 188 238

654-13 96 86 103

1914-38 219 190 239

32 28 34

1664-28 193 190 230

TABLE 3 Cross sections for the excitation of levels in ~Al(n, n'y)~TA1reaction Incident neutron energy (MeV)

Integrated cross sections for level excitation (rob) 0.842+1.013 2.21 2.73 2.976+3.000 MeV MeV MeV MeV levels level level levels

Towle and Gilboy 25)

3.99

2174-13

1934-8

1274- 8

2264-9

Present experiment

4.07

2454-58

1864-3

1454-22

2074-31

Experiment

As m e n t i o n e d earlier, Towle a n d G i l b o y 25) have measured the spectrum of neutrons inelastically scattered f r o m 27A1. It is possible to c o m p a r e their experimental results with the present experiment by a n e x a m i n a t i o n o f table 3. This table lists the cross sections for level excitations in 27A1 o b t a i n e d by Towle a n d G i l b o y 2s) from

570

s.c. MATHURet

al.

neuuon time-of-flight spectra of the inelastically scattered neutrons at an incident neutron energy of 3.99 MeV. Table 3 also contains the cross sections for level excitations in 27A1 calculated from the gamma-ray cross sections measured in the present experiment. In these calculations, the cascade gamma rays from various levels and their branching ratios have been taken into account to obtain the level excitations. It can be stated that there is a good quantitative agreement between the results of the present experiment and that of Towle and Gilboy 25). Recently Ciuffolotti and Demichelis 26) and Vasil'ev e t a L 27) have reported two levels in 27A1 at 1.65 and 1.83 MeV. However, the gamma-ray spectra obtained in the present experiment do not show any evidence that these levels are significantly excited by neutron bombardment of 27A1. A theoretical calculation on the basis of Satchler formalism gives a level excitation of the order of 160 mb for each of these levels. However, these level excitations are completely incompatible with the results of the present experiment. It is possible to draw some conclusions from a comparison of the results of the present experiment and the calculations based on Satchler 2-4) formalism. It can be seen from an examination of cross sections listed in table 2 that the theoretical calculations predict the ratios between the production cross sections of the various gamma rays rather closely within the limits of experimental errors. As Lind and Day 14) have pointed out, the correct prediction of the cross section ratios lends support to the validity of the statistical assumption in case of 27A1 for the incident neutron energy region under consideration. A similar conclusion has been drawn by Towle and Gilboy 25) from the measurement of elastic and inelastic scattering of neutrons by 27A1. 3.2. THE ~4Mg(n,n'y)~4Mg REACTION In the present experiment, the angular distributions of the 1.37 MeV gamma ray produced in the 24Mg(n, n'~)24Mg reaction have been measured at incident neutron energies of 3.0, 3.5, 4.0 and 4.35 MeV. A typical gamma ray spectrum obtained with natural magnesium (78.7 % 24Mg) at incident neutron energy of 4.0 MeV is shown infig. 9. Fig. 10 shows the angular distributions of the 1.37 MeV gamma ray obtained in the present experiment. The solid curves are the distributions calculated with the use of Beyster's 21) transmission coefficients. Figs. 11 and 12 show the experimental and the calculated differential cross sections for the production of the 1.37 MeV gamma rays. These cross sections are also presented in table 4 along with the results of other authors for comparison. An examination of the angular distributions (fig. 10) shows that the experimental data are fitted reasonably well by Satchler calculations. However, it can be seen from figs. 11 and 12 that the differential cross sections are consistently higher than the experimental results. The cross sections calculated with the penetrabilities of Percy and Buck 22) have the largest disagreement. However, the differential cross sections cal-

ANGULAR DISTRIBUTIONS

0.5

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Fig. 9. G a m m a - r a y s p e c t r u m f r o m n a t u r a l m a g n e s i u m at En = 4.0 MeV. The scatterer out backg r o u n d has been subtracted. En =4.35 MeV

Mg24

I.E

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4.0 MeV

1.2 o

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1.2 1.0 1.0

0,5

0

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- 1.0

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Fig. 10. A n g u l a r d i s t r i b u t i o n of the 1.37 MeV g a m m a r a y f r o m =4Mg(n, n'?)24Mg reaction. The ,curves are d i s t r i b u t i o n s c a l c u l a t e d w i t h the use o f Beyster's penetrabilities. The e rror bars represent relative errors.

572

s . c . MATHUR e t al.

culated with the penetrabilities of Beyster et al. 21) and Bjorklund and Fernbach 22) are in reasonable agreement with the experiment. 80 70

En = 3 . 5

MeV

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t

t

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0

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i

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l

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Fig. 11. The experimental and calculated differential cross sections for the production of 1.37 MeV g a m m a ray at incident n e u t r o n energies of 3.0 and 3,5 MeV. The solid error bars represent relative errors and the dotted error bars the absolute errors. 80

Mg?-4

En = 4,55 MeV

7O 60 50 ":

40

1

i

r

'

z

--g -o 70

1

L

En= 4.0 MeV P&B

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£

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1

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Fig. 12. The experimental and calculated differential cross sections for the production of 1.37 MeV" g a m m a ray at incident neutron energies of 4.0 and 4.35 MeV. The solid error bars represent relative errors and the dotted error bars the absolute errors.

573

ANGULAR DISTRIBUTIONS

It is significant to remark here that although the calculated differential cross sections are consistently higher in absolute magnitude, the shapes of the angular distributions are still reproduced fairly well. This may be taken as an indication that the compound nucleus formation is the predominant mechanism in case of 2#Mg at the neutron energies under consideration. A similar inference is drawn by Hosoe and Suzuki 9) from their measurement of the angular distribution of 1.37 MeV gamma ray and by Thomson et al. 12) with the measurement of inelastically scattered neutrons from 24Mg. TABLE 4 The 90 ° differential cross sections and the integrated cross sections for the production of 1.37 MeV gamma ray in the ~4Mg(n, n'y)24Mg reaction Incident neutron energy (MeV)

3.0

3.5

4.0

4.35

Experiment or calculation

da(90 °) d£2 (rob/st) 39.34-7.8

Integrated cross section (rob)

Present experiment Thomson et al. 1~) Hosoe and Suzuki Beyster B and F P and B

592-4-118 6104-60

44q-4 42.6 42.3 49.0

650 638 743

Present experiment Beyster B and F P and B

38-4-7 44.6 42.5 49.8

5684-113 679 637 754

Present experiment Thomson et aL 12) Beyster B and F P and B

364-7 44.7 41.9 50.5

5464-109 770:k 77 673 625 759

Present experiment Beyster B and F P and B

374-7 44.6 41.4 50.8

5594-112 672 617 760

3.3. THE ~Mg(n, n'~,)2~Mg REACTION

The isotopic abundance of 26Mg in natural magnesium is 11.7 ~ . Fig. 13 shows the energy level diagram for the 26Mg nucleus. At the incident neutron energies under consideration, the first level at 1.81 MeV is strongly excited, resulting in a gamma ray of 1.81 MeV as shown in fig. 9. The differential cross sections for the production of the 1.81 MeV gamma ray have been obtained from the spectral data for incident neutron energy of 3.0 MeV. The 90 ° cross section has also been obtained for neutron energies of 3.5, 4.0 and 4.35 MeV.

574

s.c.

MATHUR et al.

The differential cross sections for the 1.81 MeV g a m m a ray have also been calculated on the basis of Satchler formalism. The cascade contributions to the 1.81 MeV g a m m a ray due to de-excitation of the 2.94, 3.58 and 3.94 MeV levels have been taken into account in these calculations. 4.83 4.32 4.33

4.35

/-2*

5.94 5.58

2.94 I

ii

'

1.8i

2* I0% 0÷ Mg26

Fig. 13. Energy level d i a g r a m for ~6Mg. 90 E n -- 5.0 MeV

so !

Mg 26

7C c~ 6C

T

Be

5C 4C

q,,

I

I

I

I ol.

31.',.'

I

i

I

I

I 0

i

I

I

i --

I 0.~

I

i

I

I --1.0

COS 0

Fig. 14. T h e experimental and. calculated differential cross sections for the p r o d u c t i o n o f 1.81 M e V g a m m a ray in t h e ~nMg(n, n'y)~6Mg reaction at En = 3.0 MeV. T h e solid error bars represent relative errors a n d the dotted error bars the absolute errors.

The experimental and the calculated differential cross sections for incident neutron energy of 3.0 MeV are shown in fig. 14. The 90 ° differential cross sections at neutron energies of 3.5, 4.0 and 4.35 MeV are shown in table 5. It may be pointed out that due to the low isotopic abundance of 26Mg, the reaction yield is small and the experimental data do not possess sufficient statistical accuracy to permit a definite determination of the anisotropy in the gamma-ray angular distribution. However, it can be seen from the results that there is a reasonable agreement between the experimental and the calculated values of the absolute differential cross sections. 3.4. T H E ~aSi(n, n'~)2~Si R E A C T I O N

The angular distributions for the 1.77 MeV g a m m a ray resulting from the 2SSi (n, n'7)2aSi reaction were measured for the incident neutron energies of 3.0, 3.5 and

575

ANGULAR DISTRIBUTIONS

4.0 MeV. The g a m m a ray spectrum obtained with natural silicon (92.2 % ~ssi) is shown in fig. 15. The g a m m a ray spectrum consists o f a single peak at 1.77 MeV with a small first escape peak at 1.25 MeV. The escape peak also includes a small contribution f r o m the first excited state o f 2Zsi (4.7 %) at 1.28 MeV. TABLE 5

The 90° differential cross section for the production of 1.81 MeV gamma ray in the 26Mg(n, n'7)26Mg reaction da(90°)/d.Q (mb/sr) E~ Present experiment Beyster e t al. B and F P and B

E~ 4.0 MeV

47.4i9.5 43.8 40.5 47.0

63.6~12.7 50.5 45.6 55.0

70.4±14.1 62.2 52.6 64.9

i

1.0

Ey(MeV) 1.5 2.0

I

i

i

150

25(

4.35

MeV

69.4:k13.9 61.9 62.1 68.7

2.5

3.0

i

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1.77

4.61

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3.5 M e V

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1.77-0.51

t

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t

I00 CHANNEL NUMBER

o Si

150

200

Fig. 15. Gamma-ray spectrum fromnaturalsilicon a t E n = 4 . 1 M e V . The scatterer out background has been subtracted.

The experimental distributions and angular distributions calculated with the use o f Beyster's 22) transmission coefficients are shown in fig. 16. It m a y be pointed out that Beyster's 21) tabulation does not list the transmission coefficients for silicon. F o r the present calculations, therefore, the transmission coefficients listed for aluminium were used. In view o f this, the agreement between the experimental and the calculated distributions is gratifying.

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ANGULAR DISTRIBUTIONS

577

Fig. 17 shows the differential cross sections obtained in the present experiment and by Satchler calculations using various penetrabilities. These cross sections are also presented in table 6 along with the results o f other authors for comparison. TABLE 6

The 90° differential cross sections and the integrated cross sections for the production of 1.77 MeV gamma ray in the 3sSi(n, n'y)2sSi reaction Incident neutron energy (MeV)

3.0

3.5

4.0

4.2

Experiment or calculation

dcr(90°) d.Q (mb/sr)

Present experiment Lind and Day 14) Beyster B and F P and B

35.8 38.5 45.6

Present experiment J. L. Perkin 8) Tsukada e t aL 13) Beyster B and F P and B

30~:6 54~16 27~: I0 42.2 39.4 48.2

455.74-91

Present experiment Beyster B and F P and B

39±8 44.1 39.5 50.1

628+126 674 601 769

Tsukada

57:~7

690~90

e t al.

13)

32~6

Integrated cross section (mb) 510:~ 102 280±28 548 589 712

320:~80 647 607 743

It can be seen f r o m table 6 that there is a large disagreement between the cross section measured by Lind and D a y 14) and the present experiment at a neutron energy o f 3.0 MeV. This diagreement m a y be explained by the presence o f a resonance p e a k at 2.85 M e V obtained by Lind and D a y 14) in their measurement o f the excitation function for the p r o d u c t i o n o f the 1.77 M e V g a m m a ray. I n their experiment, the n e u t r o n b e a m energy spread was o f the order o f 36 keV, whereas the energy spread in the present experiment was in the order o f 200 keV at incident neutron energy o f 3.0 MeV. However, the results o f the present experiment agree closely with the calculated results. We wish to express our thanks to Dr. D. O. Nellis for his assistance in the experiment and to Mrs. Patricia S. B u c h a n a n for her assistance in the analysis o f the experimental data and c o m p u t e r programming.

578

s . c . MATHUR et al.

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