The energy and angular distribution of protons from 14.8 MeV neutron reactions with Al27 and Co59

Nuclear Physics 44 (1963) 597-606; Not

THE

to

be reproduced

ENERGY

FROM

AND

by photoprint

or

ANGULAR

14.8 MeV NEUTRON

North-Holland

microfilm

without

of Physics Muslim

Publishing

written

permission

DISTRIBUTION

REACTIONS

R. K. MOHINDRA Department

@

OF

Co., Amsterdam from

the

publisher

PROTONS

WITH A12’ AND

Co59

and H. S. HANS 7 University, Aligarh,

Received 26 October

U.P. India

1962

Abstract: The energy and angular distribution of protons from AI%’and CoSQwhen bombarded by 14.8 MeV neutrons has been studied by using a triple coincidence and an anticoincidence proton scintillation spectrometer. The observed spectra have been compared to the calculated ones, on the basis of the volume direct interaction and the statistical models. Various level density formulae based on the Fermi gas model of the nucleus have been tried and it has been noted that the level density formulae of Lang-LeCouteur and Newton give the best results. The agreement between the theory and experiment is only qualitative. The behaviour of the nuclear temperature is studied at various angles.

1. Introduction

The problem of nuclear reactions at moderate energies has aroused a great interest during the last few years. One of the most important points of interest has been the presence of two different kinds of mechanisms in these reactions, i.e. the statistical evaporation and the direct interaction. The contribution due to both mechanisms has been established. Recently much work on the energy spectra of protons emitted from medium weight nuclei has been carried out by several groups ’ -“) to test the validity of the statistical theory of nuclear reactions and to estimate the contribution of the direct effects. ++ 2. Experimental

Technique

The experimental set up has been described earlier “), henceforth referred to as I. It consists essentially of a telescope containing two proportional counters in coincidence with a CsI(T1) scintillation counter plus a proportional counter in anticoincidence. These particle defining proportional counters share a common gold-lined gas chamber having a tungsten target wheel. This set up is similar to that of Marcazan et al. “). The target of A12’(100%) was 18.4 mg/cm2 and of Co” (100%) was 34.2 mg/cm’ thick and of 3 cm diameter made from spectroscopically pure foils. The distance between the tritium target and the elemental target under study was kept 12 cm in all the observations. The deuteron beam was defocussed over an area of about 1 cm2 of the tritium target. The intensity of emitted neutrons was monitored by a Hornayak button. The measurements consist in detecting successively a) the spectrum of the recoil 7 Present address: Physics Deptt. Texas A & M, College station, Texas. +t Ref. I) contains

additional

references. 597

598

R. K. MOHINDRA AND H. S. HANS

protons from 1 cm and 3 cm diameter polythene radiators, b) the spectrum of the background using a blank target holder and c) that of the element under study. The maximum spread in the reaction angle is ___17° at zero degree position including the maximum possible extension of the source of neutrons. Before, during and after each observation, the calibration of the energy scale was carried cut by measuring the 14.5 MeV (14.8 less the energy loss in half the thickness of the radiator) recoil proton spectrum from an 1 cm diameter and 13.8 mg/cm 2 thick polythene radiator using a CsI(T1) crystal known to exhibit linear reponse in the range 0-18 MeV for protorts 13). The resolution of the proton spectrum was 12~, the full width at half maximum. Also, the recoil proton peak was taken from a polythene radiator of exactly the same size as the elemental target under study. The number of protons under this peak along with the calibration of the monitor has been used for calculating the differential cross-sections. The spectrum of the particular element under study and the background spectra were taken at 0 °, 45 °, 105 ° and 135 ° while the recoil proton spectra were taken only in the forward direction. As discussed in I and ref. 14), the detailed analysis of the response curves of protons, deuterons and alphas in CsI (Tl) and the behaviour of atomic stopipng cross sections for these particles in argon (the counter gas) has been carried out. This analysis along with the calibration of the CsI(Tl) crystal and one of the proportional counters with 5.3 MeV P o 21 o alphas and 14.5 MeV recoil protons can be used for determining the values of the higher as well as the lower bias of the blocking circuit for checking the pulses of various energy deuterons and alphas. According to our estimates, the alphas of 0-14 MeV and deuterons of 0-8 MeV should not be counted. 3. Results The energy spectra of protons from A127 and C o 5 9 at 0 °, 45 °, 105 ° and 135 ° are shown in figs. 1 and 2. The inset in each of these figs. shows the conventional, •statistical theory' plot to obtain the nuclear temperature. While drawing these straight lines, maximum weight has been given to points between 5.5 to 7 MeV as this region is free from (n, np) contamination and also here the direct effects are not serious. In figs. 1 and 2 the dotted curves are the calculated spectra and are obtained by adding up the various calculated partial differential cross sections both due to the statistical evaporation and direct interaction as discussed in the next section. Figs. 3 and 4 show the calculated and experimental angular distribution of protons in different energy ranges for A127 and Co sg, respectively. The cross sections for the energy intervals 5-7 MeV, 7-9 MeV and > 9 MeV are obtained by graphical integration over the respective regions. 4. Calculation of Energy Spectra and Angular Distributions In a previous paper 15), henceforth referred to as II, the authors reported the detailed calculations of the energy spectra of protons, neutrons and alphas from A127

AT 45" AT 0~

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i

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AT 135"

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7

9

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>~

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O0

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}½

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14

L Proton energy C.M.S.(MeV)

0

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4 6 8 10 12 - Proton energy C.WtS. (MeV)

14

Fig. 1. Energy spectra of protons from AI 2Tat various angles. The inset of each figure is the conventionat statistical theory plot where the abscissa is the channel energy sp and the ordinate is the logarithm of the observed yield divided by the energy and cross section for the compound nucleus formation. The dotted curves are the calculated spectra. (a) Calculated curves. Dot-and-dash line comp. only with Newton's formula; dashed line comp. q- dir. (b) Calculated curves. Dot-and-dash line LangLeCouteur formula with odd even effects; dashed line Newton's formula. (c) Dashed line represents calculated curve with Newton's formula. (d) Dashed line represents curve calculated with Newton's formula

AT

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0 =1.65 MeV

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i !il

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30 !

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~=1,8 MeV

3.6

Co5~

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(MeV)

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1

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AT 135~ 2.5

Co 59

A T 105" (¢)

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7

9

11

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9 11 13 15 Proton e ~ e r g y C,M.S.(MeV)

Fig. 2. Energy spectra of protons from Co B9 at various angles. Inset in each figure is the conventional 'statistical theory' plot. The dotted curves are the calculated spectra. (a) Calculated curves. Dot-anddash line comp. only with Newton's formula; dashed line ¢ompt. + dir. (h) Calculated curves; dashed line with Lang.LeCouteur formula with odd even effects, dot-and-dash line Lang-LcCoutenr formula without odd-even effects; dotted line Newton's formula. (c)Dot-and-dashline represents curve calculated curve with Newton's formula. (d) Dot-and-dashline represents curve calculaw,d with Newton's formula.

601

ENERGY AND ANGULAR DISTRIBUTION

due to the interaction of 14.8 MeV neutrons. The c o n t r i b u t i o n of direct interaction has been c o m p u t e d on the basis of a model of volume p r o d u c t i o n as proposed by B r o w n a n d M u i r h e a d s). 40

~12 I 8

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5-7 MeV

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, o°

• A n g l e (C M S.)

40 --

8o ~Angle(C

~2o

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Fig. 3. The angular distribution of protons from AP7 for the various energy intervals. The smooth curves are the calculated angular distributions. 10 r L

I

8L/

8

:

{

eV

{

~ 6! ,

7-9 Mev

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0

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Fig. 4. The angular distribution of protons from Co59 for the various energy intervals. The smooth curves are the calculated angular distributions. F o r the Statistical theory calculations, ~ve used a square well potential 16) with R = 1.5 A ~ fm. The formulae for the spectra of p r i m a r y a n d secondary particles as given by H a y a k a w a et al. 4) have been used. As described in II the calculations o f the energy spectra o f p r o t o n s from A127 were carried out for the following well k n o w n level density formulae of the statistical model:

602

R.

K.

MOHINDRA

AND

H.

S.

HANS

The simple Fermi gas model level density formula 16) w(U) = CezJz, The constant temperature formula ‘) W(Q) = Ce’“@, where 8 is the nuclear temperature. Newton’s shell dependent formula D, = & = A’(2& + 1)*(2jN+ 1)*(2 U + 3t)‘exp {8.75 - 0.4982& +jN + l)A* t?} , where Ia and IN are the effective values of j for a nucleus of 2 protons and N neutrons and are listed by Newton I’), t = [~x-~G-‘U]~,

where G = 2cr(3,+9,+1)A*, 2a = 0.03772,

U is the excitation energy and A is the mass number, Lang and LeCouteur’s formula ia) DO = & = 0.11AZ(U+t)2 exp-

2 Ary *+&(lIIJ)+

((

)

, 1

where t = (lO.SU/A)*- (7.9/A). It has been found that the rigorous level density formulae of Newton and LangLeCouteur give similar results in the case of Al ” . In the case of the simple Fermi gas model and the constant temperature formulae, the calculated (n, n’) and hence the (n, np) yield is exaggerated if one uses the same value of the parameter a or 0 for the (n, n’) process as for the (n, p). The various calculated partial differential cross sections for Al” are given in II, obtained by using various level density formulae. The sum of these various partial differential cross sections which we call the calculated proton spectra has been compared with the experimental ones in fig. 1. I 12 -

Dotted CWV~S are Wlttl odd even effects

Oo

2 4 -Proton

6

8 energy

10

-----+Protm

6

8 10 energy

12

Fig. 5. Various calculated partial differential cross sections for Co60 obtained by using (a) Newton’s and (b) Lang and LeCouteur’s level density formulae. Dashed cunm are with odd-even effects.

ENERGY AND ANGULAR DISTRIBUTION

603

Fig. 5 describes the detailed spectra for C o s9 o b t a i n e d b y using N e w t o n ' s level density f o r m u l a , a n d fig. 5(b) is for L a n g - L e C o u t e u r ' s f o r m u l a . Fig. 6 shows the v o l u m e direct i n t e r a c t i o n c o n t r i b u t i o n at v a r i o u s angles calculated b y using eq. (7) o f B r o w n a n d M u i r h e a d 5).

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Fig. 6. The volume direct interaction contribution at four angles. The dotted curve on the left hand side is due to the compound nucleus formation only. T h e a n i s o t r o p y in the calculated spectra is only due to the direct interaction coni t r i b u t i o n as the resultant spectra due to the c o m p o u n d nucleus p a r t have been a s s u m e d to be isotropic. T h e values o f the v a r i o u s constants used for the calculations in the case o f A1z7 a n d C o '9 are listed in table 1. TABLE 1 Separation energies Nucleus Na 2a Na 2' Mg26 Mgs7 AP AIs~ Mn 56 Fess Co 6' V = 42 MeV (re£ as)),

Xnp/Xnn =

Sp(MeV) ref. ~1)

S.2t)(MeV) ref. m)

San)(MeV) ref. n)

8.8 10.6 14.0 14.3 6.3 8.3 9.3 12.0 7.4

12.5 7.0 11.1 6.5 11.3 13.0 7.3 6.6 10.5

10.6 11.1 10.2 11.0 9.7 8 ~) 8.0 8.0 7.2

0.3 (ref. 16)) ~z(AI,~) = 900 mb, O'I(CO 61) = 1500 mb (both cross sections are from ref. u)). 5. Discussion

T h e shape o f the s p e c t r u m due to A127 at 45 ° is in fair a g r e e m e n t with the s m o o t h e d s p e c t r u m at 40 ° o f G l o v e r a n d W e i g o l d 6) except t h a t in the present e x p e r i m e n t the l o w energy yield is slightly higher. T h e Q value o f the A127(n, d ) r e a c t i o n is - 5 . 7

604

R.K.

M O H I N D R A A N D H . S. H A N S

MeV and deuterons of 8.6 MeV can contaminate the proton spectrum but in the present experiment by using the blocking circuit, it is estimated that 0-8 MeV deuterons can not contaminate the observed proton spectrum. Glover and Weigold have separated the deuterons from the proton spectrum. The agreement between their results and our spectra shows that deuteron contamination is not serious in our spectra. The observed spectrum of Co s9 at the extreme forward angle follows the general trend of Jack and Ward's lo) spectrum. Their spectrum shows a clear peak at about 13 MeV. In the present spectrum also, there is a slight trend of a similar type. Such a peak could be due to hydrogen contamination of the target but in the present experiment care was taken to avoid any such contamination. Further, the spectrum of A117 taken under similar conditions does not show such a peak. Recently, Colli et al. 9) have reported only the energy distribution of Co 59 at 15~"and tried to separate the deuteron spectrum. The Q value of Co(n, d) reaction is - 5 . 2 MeV so that the m a x i m u m possible deuteron energy is 9.5 MeV. According to our estimates, these deuterons can contaminate the proton spectrum below 7 MeV only, because of the blocking circuit. The yield in the present experiment is quite high as compared to the yield of Colti et al. and it is difficult to explain this difference as due to deuteron contamination. 5.1. LOW ENERGY PART In the low energy region the shape of the observed A127 spectrum differs remarkably from the shape expected due to a primary (n, p) reaction. The low energy yield is attributed to an (n, np) reaction. In the case of Co 59, the yield of low energy protons is less than that for the case of A127 even though the total (n, p) cross section is nearly the same for the two cases. This difference is due to different contributions from the (n, np) reaction in the two cases which is readily understood in terms of the separation energies of neutron (An) and proton (Sp) in the residual nuclei A1z7 and Co 59 left after the (n, n') reaction. For Co s9, S n - S p = 3.1 MeV and for A127 it is 4.7 MeV. 5.2. ANGULAR DISTRIBUTION Figs. 3 and 4 show our experimental and calculated angular distribution plots for the various energy intervals in the case of A127 and Co 59. The solid line curves are the calculated ones. In the interval 5-7 MeV, the observed angular distributions are fairly isotropic showing that in this region, the contribution of direct protons or deuterons is not serious as (n, d) is a type of pick-up reaction and is mostly forwarddirected. In the range 7-9 MeV, there is a slight anisotropy arid it is further enhanced in the energy interval > 9 MeV. For Co 59, the anisotropy is higher than for A1zT. This suggests that direct effects are more pronounded for Co 59. Such a behaviour of Co 59 may be expected due to its higher mass number and also due to its position near a doubly closed shell nucleus. Brown and Muirhead's 5) calculations for a large number of cases show that the direct effects increase with mass number. The calculated angular distribution plots are highly forward directed compared to the experimental

605

ENERGY AND ANGULAR DISTRIBUTION

ones. T h i s is d u e to t h e fact t h a t the c o n t r i b u t i o n p r e d i c t e d d u e to direct i n t e r a c t i o n t h e o r y is t o o h i g h at t h e e x t r e m e f o r w a r d a n g l e . . B e y o n d 45 ° t h e a g r e e m e n t is q u a l i t a t i v e l y fair. 5.3. N U C L E A R TEMPERATURES

The values of nuclear temperature at various angles are listed in table 2. The value of the nuclear temperature decreases as we go to backward angles. This is easily TABLE 2 Nuclear temperatures at varions angles in MeV \X~ent Angle

A127 x~

0° 45 ° 105 °

135 °

Present values 1.68 1.62 1.55

1.52

Earlier values

Co s. Ref.

1.75 s) 1.55 b)

10) e)

1.5 b)

x)

1.16 b) 1.1 b)

Present values

Earlier values

Ref.

1.80 1.65 1.55

1.6(15 °)

9)

1.2 b)

9)

1.59 s)

lo)

e) so)

1.47

a) Corresponds to the integrated energy spectrum. b) Corresponds to the backward angle.

understood as due to direct effects. The difference in the value at the forward and backward directions is more pronounced for Co s9 than for A127. This shows that direct effects are more prominent for Co 59. 5.4. V A L U E OF THE LEVEL DENSITY PARAMETER a

The experimental value of the parameter a of the simple Fermi gas model level density formula [w(U) = Ce 2¢~v] has been found from the relation a.xpt = Up.ak/O2 as suggested by Allan 1). Here U is taken as the excitation energy corresponding to the peak of the proton spectrum. We have taken Upcak = E l . - - Q . p - 6 o - E p , where 6~ is the pairing energy as given by Cameron 19) and Ep (corresponding to the peak of proton spectrum) for A12T and Co 59 is 4 MeV and 5 MeV, respectively. The values TABLE 3 Values of A/a Element

0135 ° (MeV)

~e (MeV)

Q.p (MeV)

Upesk (MeV)

A127 Co •

1.52 1.47

--2.1 -- 1.45

-- 1.78 --0.78

5.9 7.4

aexpt = 2.55 3.43

U ~ / O = A/a 10.6 17.2

606

R.K.

MOHINDRA A N D H. S. HANS

o f A / a a r e g i v e n in t a b l e 3 a n d are c l o s e to t h e a v e r a g e v a l u e o f A / a = 11.5 ___3 M e V - 1 as g i v e n b y A l l a n 1) f o r 15 nuclei in t h e r a n g e Z = 15 t o 30. T h e a u t h o r s are h i g h l y g r a t e f u l to P r o f e s s o r P. S. G i l l f o r his k e e n i n t e r e s t a n d kind encouragement.

O n e o f t h e a u t h o r s ( R . K . M . ) is t h a n k f u l to t h e D e p a r t m e n t

o f A t o m i c E n e r g y , G o v e r n m e n t o f I n d i a f o r t h e a w a r d o f a s e n i o r scientific r e s e a r c h assistantship. References

1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 1 I) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25)

D. L. Allan, Nuclear Physics 24 (1961) 274 L. Colli et aL, Nuovo Cim. 13 (1959) 730 N. Austern et al., Phys. Rev. 92 (1953) 350 S. Hayakawa, M. Kawai and K. Kikuchi, Prog. Theor. Phys. 13 (1955) 415 G. Brown and H. Muirhead, Phil. Mag. 2 (1957) 473 R. N. Glover and E. Weigold, Nuclear Physics 24 (1961) 630 G. Brown et al., Phil. Mag. 2 (1957) 785 R. K. Hailing, R. A. Peck and H. P. Eubank, Phys. Rev. 106 (1957) 971 L. Colliet al., Nuovo Cim. 21 (1961) 966 W. Jack and A. Ward, Proc. Phys. Soc. 75 (1.960) 833 R. K. Mohindra and H. S. Hans, Ind. J. Phys. 36 (1962) 93 G. Marcazan, A. Sona and M. Pignanelli, Nuovo Cim. 10 (1958) 155 Bhaskin et aL, Phys. Rev. 109 (1958) 434 R. K. Mohindra, P h . D . Thesis, Aligarh Muslim University (1962) unpublished R. K. Mohindra and H. S. Hans, Ind. J. Phys., in the press J. M. Blatt and V. F. Weisskopf, Theoretical nuclear physics (Wiley and Sons, New York, 1952), chapt. VIII T. W. Newton, Can. J. Phys. 34 (1956) 804 J. M. B. Lang and K. J. LeCouteur, Proc. Phys. Soc. 67 (1954) 856 A. G. W. Cameron, Can. J. Phys. 36 (1959) 1040 Nair, Iyenger and Ramanna, Nuclear Physics 26 (1961) 193 D. M. Van Patter and W. Whaling, Revs. Mod. Phys. 26 (1954) 402; Masami Yamada and Z. Matumoto, J. Phys. Soc. Jap. 16 (1961) 1497 P. A. Seeger, Nuclear Physics 25 (1961) 1 A. G. W. Cameron, AECL Report No. 433 (1958) E. Erba et al., Nuovo Cim. 22 (1961) 1237 I. Kumabe et aL, Phys. Rev. 106 (1957) 155