Elastic and inelastic scattering of 14.2 MeV neutrons from 31P

Nuclear Physics 68 (1965) 369--377; (~) North-Holland Publishing Co., Amsterdam blot to be reproduced by photoprint or microfilm without written permission from the publisher

E L A S T I C A N D I N E L A S T I C S C A T T E R I N G O F 14.2 MeV N E U T R O N S F R O M Sip G. C. BONAZZOLA and E. CHIAVASSA Istituto di Fisica della Universit~ di Torino Istituto Nazionale di Fisica Nucleare, Sezione di Torino t

Received 21 October 1964 Abstract: The angular distribution of the elastic scattering of 14.2 MeV neutrons and of the inelastic scattering from the two first excited states in alp was measured by means of a time-of-flight spectrometer from 30° to 160°. The differential cross sections for elastic scattering and for (n, n') reactions with Q = -1.26 MeV and Q = -2.23 MeV are given. A comparison between the sum of these two inelastic differential cross sections and. the differential cross section for the scattering to the first excited level in s2S is made.

E I

I

NUCLEAR REACTIONS alP(n, n), (n, n'), E = 14.2 MeV; measured a(Eu,, 0). alp deduced levels, J, ~.

1. Introduction

Recent improvements o f the time-of-flight technique allow measurements o f neut r o n spectra in which a high energy resolution is obtained. I n this way the angular distribution o f fast neutrons inelastically scattered f r o m individual levels o f a nucleus can be studied 1,2). Clarke and Cross 1), for instance, for light even nuclei such as 12C, 2 4 M g 2sSi, 32S, measured the differential cross-sections for inelastic scattering o f 14.1 M e V neutrons f r o m the first excited level. I n this paper we report on the measurement o f the angular distribution o f 14.2 M e V neutrons inelasticaUy scattered f r o m the first two excited levels in 31p. Thus, results obtained for phosphorous, an odd-mass nucleus, can be c o m p a r e d with similar results for 32S, which is the neighbouring even nucleus. 2. Experimental Method

The experimental procedure was based on the use o f a time-of-flight spectrometer previously described a,4). The block diagram o f the electronic apparatus is given in fig. 1. In this experiment we varied the scattering angle by rotating a r o u n d the deuteron b e a m the s-counter and the sample holder rigidly assembled. See fig. 2. I n this way the n e u t r o n counter is m o v e d only a few centimeters to maintain the length o f flight path constant and it is tilted a few degrees to remain aimed at the scatterer; t This work has been done under the Euratom/CNEN contract. 369

370

G. C. BONAZZOLA A N D E. CHIAVASSA

furthermore the shadow bar which shields the neutron counter from direct neutrons always remains in the same place: this experimental situation gives a background nearly independent of the scattering angle. The ~ detector was a sheet of plastic scintillator 0.1 mm thick coupled to a 56 AVP photomultiplier. The neutron detector was a cylinder of NE 102A plastic scintillator 110 mm in diameter and 50 mm in

[LDETECTO~' N E L r r RON

~

Anode

~

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,

,

,

FAST D/node

Fig. 1. Block diagram of the time-of-flight apparatus

Torget

NeUtron detector Neutron source

7

/

~

7/

"~"~ OOse

'~

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// / r

Fig. 2. Experimental set-up. The neutron source is consists of a tritium target on which the deuteron beam impinges perpendicularly to the plane of the figure. The 0~-detector and the 8xp target are assembled together and rotate around the deuteron beam. The neutron detector can be shifted along a straight line passing through the neutron source. The drawing is not in scale.

height coupled to a XP 1040 photomultiplier. The bias in the neutron channel during this experiment was 7.5 MeV. The time of resolution of the spectrometer (full width at half maximum) for 14.2 MeV neutrons was 1.8 nsec, allowing, over the flight path of 3.50 meters chosen for the experiment, an energy resolution of about 5 ~ . The linearity of the spectrometer, as tested by measuring the time-of-flight of 14.2 MeV neutrons for different base

371

NEUTRON SCATTERING

lengths, was 1%. The target was composed of red phosphorous contained in a cylinder o f 10 cm diameter and 3.5 cm height, the axis of the cylinder forming an angle o f 45 ° with the direction o f the incident neutron beam. The target intercepted completely the neutron beam as defined by the ~ counter and its thickness was such that Q=-3,3

0=-2.23

Q=-1.28

Q=O

~16C U ~'= 4 0 " 31p

C

z 1,4o

o

120

100

80

60

40

20

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80

90

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100

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110

120

130 CHANNEL

Fig. 3. Time-of-flight spectrum of fast neutrons scattered from "P.

the beam attenuation was 18 %. During the experiment the neutron flux in the whole solid angle was maintained at a constant value o f 107 neutron • see -1, which is in our case the maximum permissible for an acceptable background situation. The angular distribution was measured from 30 ° to 160 ° , at each point the counting period lasted some 80 hours. The neutron output monitoring was accomplished by counting the 0c particles by means of a solid state junction detector.

372

O. C. BONAZZOLA AND E. CHIAVASSA

3. R e s u l t s

In fig. 3 we report a typical spectrum for 31p obtained at a scattering angle of 40 °. Besides the peaks due to ~-rays and to elastically scattered neutrons, the two inelastic peaks due respectively to the levels 1.26 MeV and 2.23 MeV are quite evident. Similar spectra were obtained at each angle. While the structure of the spectrum is well recQ--4.43

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Fig. 4. Time-of-flight spectrum o f 14.2 MeV neutrons scattered f r o m C 12.

ognizable, a certain overlapping of adjacent peaks is still present. Therefore a suitable numerical procedure for the determination of the number of counts pertaining separately to each neutron peak was needed. For this purpose two important features of our spectrometer had to be known, namely the background characteristic and the shape of a peak due to monochromatic neutrons. The background v e r s u s time-of flight turned out to be flat and constant at each angle; for each run it was then evaluated from parts of the spectrum where no true events could have been counted, i.e., between the peaks due to elastically scattered neutrons and to y-rays, and in the part of the spectrum corresponding to neutron energies lower than the actual bias. The characteristic shape of a monoenergetic peak was determined from measurements taken on 12C in which the peak due to elastic neutrons is completely separated from the nearest inelastic peak. As can be seen in fig. 4 the actual shape is nearly symmetrical. At this point the required correction was easily made; a really significant overlapping of the two peaks was found only at forward angles. In the useful energy range

373

NEUTRON SCATTERING

TABLE 1 Differential elastic and inelastic cross section for 14.2 MeV neutrons on 8zp (deg., c.m.)

da/d'~(mb) Q = - 1 . 2 6 MeV

30 ° 40 ° 50 ° 60 ° 70 ° 80 ° 90 ° 105 ° 125 ° 145 ° 160 °

dtr/d#'(mb) Q = 0 MeV

10 -t-1 6.44-0.6

118 4-11 15:1:1 26 4- 5 51 -4- 1 28 4- 3 19 4- 2 12 4- 0.5 15 4- 0.7 9.34- 1 6.54- 0.8 7.24- 0.5

13.64-3 4.94-0.5 4.04-0.5 3.34-0.7 1.44-0.4 1.64-0.6 2.94-0.6 1.24-0.3 1.94-0.2 1.4:5:0.3 0.5 d:O.4

200 I

I

I 1 I

'

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4.44-0.4 5.5+0.6 3.55:0.5 2.04-0.2 2.94-0.4 1.54--0.2 2.2:d:0.2 2.7-4-0.2 1.54-0.2

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5. Differential elastic cross-section for mp as measured in this experiment. For a comparison, theoretical curves for =~AI and 3=S are given.

374

O. C. BONAZZOLA AND E. CHIAV/h.~A

the efficiency of the spectrometer was proven to be constant. For each angle the absorption of neutrons entering and leaving the target was accounted for and the double scattering contribution was calculated. Our values have been normalized to known

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Fig. 6. Differential cross-section for inelastic scattering to the 1.26 MeV level in sxp. At 160° we obtain for do/dee a value of 0.54-0.4 mb which is not plotted. l

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Fig. 7. Differential cross section for inelastic scattering to the 2.23 MeV level in sip.

results f o r elastic scattering o n 12C. T h e n the differential cross-sections were calc u l a t e d by t a k i n g i n t o a c c o u n t three c o n t r i b u t i o n s to the error. Th e first is due t o c o u n t i n g statistics. T h e second c o n t r i b u t i o n t o the er r o r is due to the p r o b a b l e e r r o r

NEtrrRoN SCATTERING

375

in setting the scattering angle and is proportional to the first derivative of the resulting angular distribution. The third is due to the fact that, having a finite angular resolution, we integrated the angular distribution over some degrees. In assigning the final value to the centre of the interval of integration an error is made which is proportional to the second derivative of the angular distribution. From a rigorous point of view this last term is more properly a corrective one; we nevertheless considered it as an error because its exact evaluation was practically impossible. The formula used for error evaluation was A(dtr Id:)) = 17[Nt q- N s + e2Nb -I- (dNp/dO) 2(d 1 tg)2 -I- (sin~d 2 Np/d,92) 2(2-~-A2 0) 2 ]~, (1) where ~/ is the coefficient of proportionality between the differential cross-sections and Np, N t is the number of counts in the channels occupied by each peak, Ns is the number of counts estimated as falling in the same channels and due to the neighbouring peaks, Nb is the sum of the counts in the channels used for background determination, e is the ratio between the number of channels utilized in the determination of each peak and the number of channels used for background determination measurement, Np = N t - N~-eNb is the number of counts attributed to each peak, A~I is the probable error in setting the scattering angle, and A92 is the angular interval in which the scattering angle ranges because of the finite extension of both target and detector. In the given errors an uncertainty of 6 ~o due to normalization is not included. Double scattering contribution was evaluated by a Monte Carlo calculation. Corrections were not important except for the first minimum of the elastic distribution where they amounted to about 15 ~o. The results are given in table 1 and plotted in figs. 5, 6 and 7. 4. Discussion The angular distribution for elastic scattering obtained in this experiment is plotted in fig. 5 together with the theoretical curves calculated 1, 5) for 32S and 27A1 which are typical in this region of atomic number. The agreement between the experimental points and the theoretical calculation is good. The integrated elastic cross-section is 0.87_ 0.02 b which is in good agreement with the value 0.84 +0.45 b, ref. 6), obtained by subtracting the non-elastic cross-section, 1.13 + 0.03 b, from the total cross-section 1.97-1-0.03 b, ref. 7). The angular distributions of neutrons due to inelastic scattering to the two first excited states are similar. In fig. 8 we give the angular distribution obtained by summing the two measured inelastic angular distributions. The data of Clarke and Cross for inelastic scattering to the first level in S 32 are also plotted. The two angular distributions agree within the experimental errors. This fact can be explained by a model in which the two levels in 31p are considered to be due to weak coupling of a 2s~r hole to the core 2 + level, as can be inferred by the work of deShalit a). In this hypothesis, the following formula must apply 9), relating the in-

376

O.

C. BONAZZOLA

AND

E. CHIAVASSA

tegrated cross sections for the two investigated reactions to the integrated cross section for the scattering to the 2 + level in 32S,

2J+ 1

o'(31P, J ) =

(2)

0"(32S, Ore).

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Fig. 8. A comparison between the inelastic scattering differential cross section to the 2.24 MeV state in s2S and the sum of the differential cross sections for the two first levels in sxp. TABLE 2 Experimental and calculated cross sections for inelastic scattering to the first levels in 81p and a2S or(alp, J ) experimental values (present work)

(mb) o'(siP, ~)

a(slP, t )

25.94-2.6

33.44-2.8

(x(slP, ~)-}-o'(sxP, ~)

59.34-3.8

t~(ssS, J ) experimental values from Clarke and Cross (mb)

tT(axP, J ) calculated values

(rob)

o'(ssS, 2)

o.(sxp, ~_)

if(sip,/~)

59.8

23.9

35.9

Here J is the angular momentum of the excited level, g(31p, j ) is the cross section for the inelastic scattering to the J state of alp, Jo is the angular momentum of the odd nucleon, Jo is the angular momentum of the first excited state of the core, and g( a2s, Je) is the cross section for the inelastic scattering to the Jo a2S level. In our case we have Je = 2, Jo = ½ and J = ½ and ~, respectively.

NEUTRON SCATTERING

377

Substituting in formula (2) for o'(32S, 2) the value found by integrating the data of Clarke and Cross from 30 ° to 150 ° degrees, we obtained the cross sections given in table 2. In the same table we report our experimental values. The good agreement seems to confirm the given hypothesis about the origin of the two levels in 31p, notwithstanding the fact that the centre of mass of the two levels is lower than expected. Moreover it is to be recalled that Jacmart et aL 1 o) came to the same conclusions by studying (with 155 MeV protons) the (p, p') reaction on 31p at forward angle. We wish to thank Prof. P. Brovetto for his interest in this work and Mr. G. Venturello his valuable cooperation. References I) 2) 3) 4) 5) 6) 7) 8) 9) I0)

R. L. Clarke and W. G. Cross, Nuclear Physics 53 (1964) 177 R. Bouchez, J. Duclos and P. Perrin,Nuclear Physics 43 (1963) 628 (3. C. Bonazzola and E. Chiavassa, Nucl. Instr.27 (1964) 41 (3. C. Bonazzola and E. Chiavassa, Atti Accad. Sci.Torino 9 (1964) F. (3. Percy and B. Buck, Nuclear Physics 32 (1962) 353 N. N. Fleroy and V. M. Talyzin, J. Nucl. Energ. 4 (1957) 529 J. H. Coon, E. R. Graves and H. H. Barschall,Phys. Rev. 88 (1952) 562 A. dc-Shalit,Phys. Rev. 122 (1961) 1530 N. Cindro, Nuclear Physics 57 (1964) 542 J. C. Jacmart, M. Liu, R. A. Ricci, M. Riou and C. Ruhla, Phys. I_ctt.8 (1964) 273