Angular distribution of neutrons from the 55Mn(α,n)58Co reaction at Eα = 14 and 17 MeV

Nuclear Physics 72 (1965) 209--217; (~) North-Holland Publishing Co., Amsterdam Not to

be reproduced by photoprint or microfilm without written permission from the publisher

ANGULAR DISTRIBUTION OF NEUTRONS FROM THE 5SMn(~, n)SSCo REACTION AT Eet = 14 AND 17 MeV A. ALEVRA, R. DUMITRESCU, I. R. LUKAS, M. T. MAGDA, N. MARTALOGU, D. PLO~TINARU, D. POENARU, E. TRUTIA, I. V]LCOV and N. V$LCOV

Institute for Atomic Physics, Bucharest, Rumania Received 24 March 1965 Abstract: The angular distribution of neutrons from the 6bMn(u, n)SSCo reaction was measured at two bombarding energies E~ = 14 and 17 MeV and for various intervals of the excitation energy E* in the residual nucleus bSCo. The angular distribution in the range E* = 1--4 MeV shows a forward peak, indicating a direct interaction contribution to the reaction. The angular distributions in the ranges E* = 4-5 MeV, 5-6 MeV and 6-7 MeV were treated in the frame of the compound nucleus statistical theory and were used to calculate the ratio ~ = J/Jrigla for 5sCo. The data are completed by the angular distribution of the apparent temperature of the 5sCo nucleus. N U C L E A R REACTIONS ~SMn(cqn), E = 14, 17 MeV; measured tr(E;En, O). 5sCo deduced nuclear temperature Tn(O), moment of inertia.

1. Introduction

The variation of the nuclear temperature with bombarding energy in the SSMn (~, n)SSCo reaction was reported in a previous paper 1). This effect was observed in many experiments (see Bodansky 2)) and some attempts have been made to explain it either by a more rigorous analysis of the evaporation spectra 3-5) or by the contribution of the non-compound processes 1.6). Thomas 3) studied the influence of the angular momentum dependence of the level densities on the analysis of neutron evaporation spectra and has shown that its neglect is not responsible for the observed dependence of the level density parameters on the bombarding energy. The same result was obtained by Hurwitz et al. 4) by means of a similar analysis of proton spectra from (a, p) reactions. The energy dependence of the inverse reaction cross-section was also taken into account 5) in the analysis of the evaporation spectra but the temperature variation with the bombarding energy has not been removed. The contribution of non-compound processes could also produce the appearance of such a dependence of statistical parameters (temperature, level density parameter) on the bombarding energy, thus a more detailed study of the reaction could improve the understanding of this phenomenon. 209

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A. ALEVRAet al.

For this purpose we have studied energy and angular distribution of the neutrons emitted from the 55Mn(0~, n)SSCo reaction at two bombarding energies, 14 and 17 MeV.

2. Experimental Method The alpha-particle beam from the IAP cyclotron was collimated by a system of carbon, bismuth and tantalum slits to give a 4 x i0 mm 2 spot at the target position. The targets were of spectroscopically pure manganese deposited on 0.1 mm thick tantalum backings. Target thicknesses were of 200-300 keV for the respective bombarding energies. The neutrons were detected with a stilbene scintillator (3 x 2 cm) and a 56 AVP photomultiplier placed in a heavy shielding against neutrons and gamma-rays. Neutron energy was determined by a classical time-of-flight method. The time spectrum, corresponding to the energy spectrum of neutrons, was converted into a pulse-height spectrum by means of a time-to-pulse-height converter. The marking signals consisted of pulses synchronized with the r.f. voltage, but of half frequency, so that a total display of the spectrum was obtained. DETECTO/2 ! /FAr~_ST

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Fig. 1. Block diagram of electronics. A flight path of 1.8 m was chosen, the energy resolution being sufficiently good as not to change the shape of the evaporation spectra. Each spectrum was corrected for the converter linearity (which was better than 5 70) and for the spectrometer efficiency. Corrections for background were also made by subtracting the spectra obtained by irradiating the target backing for the same monitor from the actual spectra. The monitor was a current-integrator with negligible losses. I n order to obtain the angular distribution, a correct system of monitoring was necessary. The current-integrator was not adequate for this purpose because it could not take into account such effects as the destruction of the target after some irradiation time or the shifting of the beam into an inhomogeneous part of the target. The gamma-peak from the time-of-flight spectrum taken as a monitor would remove the above-mentioned difficulties in the case of self-supporting targets. In our case the target backing also gives a contribution to the prompt gamma-rays, so that

6~Mn(ot,n)58Co REACTION

21 ]

this monitor is not sutticiently good. In addition the change in the absorption of gamma-rays at various angles in the target device can alter the indication of the chosen monitor. F o r the above-mentioned reasons, we have employed as monitor a fixed detector of neutrons, which was placed at 90 ° against the incident beam, and which was well shielded so as to "see" only the target. This second time-of-flight spectrometer was identical to the first one, and their electronics had many c o m m o n elements as can be seen from fig. 1. This block diagram has the advantage of employing one time-topulse-height converter, whose instability is manifest in an identical manner on both spectrometers. The time spectra from both detectors were gated by the linear chains of the spectrometers and the signals entering into the SA-40 analyser in A and C allowed the separate storage of these time spectra; each of them was on a group of 200 channels. The two simultaneously stored spectra had the same dead time so that for the angular distribution no dead time correction was necessary. The energy discrimination on the linear chains was verified for every run using gamma-ray sources of known energy, and we found that it remained within good limits of stability; the obtained values were employed to calculate the efficiencies of the spectrometers. The time-pulse-height response of the converter was also controlled for every run with a time uncorrelated source. I

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Fig. 2. A n g u l a r variation o f the a p p a r e n t temperature at E~ = 14 a n d 17 MeV. T h e s m o o t h curves are visual fits to the data. T h e y have no theoretical significance. T h e abscissa represents the emission angle o f the n e u t r o n in the centre-of-mass system.

3. Results and Discussion The spectra of neutrons were transformed from the time scale into the energy scale and corrected for the efficiency of the time-of-flight spectrometer and centre-of-mass motion. The calculations were partly performed with an electronic computer.

212

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A. ALEVRA

The neutron energy spectra at different emission angles were studied and apparent temperatures were calculated for the 4-7 MeV range of excitation energy, in the same manner as in our previous paper ~). (We call "apparent temperature" the values obI

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tained in this simple manner, without taking into account in the calculations the angular momentum dependence of nuclear level density.) The results are shown in fig. 2. The angular distribution of the apparent temperature at E~ = 14 MeV appears

55Mn(~, n)SgCo REACTION

213

to be symmetrical about 90 °, as a consequence of the limitation on the angular momentum due to the spin dependence of nuclear level density. Although the experimental values are more spread at E= = 17 MeV, the same angular variation of the

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apparent temperature seems to take place. This effect was observed in heavy-ion reactions where high angular momenta are also involved 7). Angular distributions of the neutrons corresponding to various excitation energies in the residual nucleus are represented in figs. 3 and 4. The differential cross-sections

214

A. ALEVRAet aL

are given in arbitrary units a n d the errors o n i n d i v i d u a l points represent only the statistical ones. The a n g u l a r distributions o f the n e u t r o n s leading to excitation energies u p to 4 M e V are strongly peaked forward, showing the presence of direct i n t e r a c t i o n processes. The other groups o f n e u t r o n s c o r r e s p o n d i n g to excitation energies of 4-5, 5 - 6 a n d 6-7 M e V are symmetrical a b o u t 90 °, or isotropic. The solid curves f r o m figs. 3 a n d 4 represent the least-squares fits of the experimental points with the following expression: W ( ~ ) = (x0 + i x 2 c o s 2 9 .

(1)

Firstly the expression W(3) = ~0 + ~i cos 3 + ~2 COS2~ was employed in the leastsquares fit to the data. The term s t cos3 was i n t r o d u c e d i n order to verify that the a n g u l a r distributions are symmetrical a b o u t 90 ° . The result was that the thus obtained ~lwere negligible within the error limits. The least-squares fit was p e r f o r m e d by the m e t h o d of Rose 8) e m p l o y i n g the statistical weighting factors. Rose's m e t h o d was used to calculate the error in the coefficients ~o, a l a n d cz2; b o t h statistical errors a n d residuals of least-squares fit were the same. The least-squares fit expressions o b t a i n e d for the a n g u l a r distributions are given in table 1.

TABLE 1 The coefficients of the angular distribution of neutrons from SSMn(u,n)SSCo reaction at two bombarding energk and for different intervals of excitation energies E* = 4-5 MeV, 5-6 MeV and 6-7 MeV

E~

E*

Set of measuremerits first

4-5 14 MeV

17 MeV

first

6-7

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5-6

(1 ± 0.04)-- (0.006±0.035)cos # + (0.11+0.045)cos~ ~

second

5-6

4-5

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1+0.129 cos~& 1+0.073 cos2

(14-0.01)-- (0.05±0.03) cos ~ + (0.094-0.03) cos2&

1+0.042 cos2

practically isotropic

first

(1 4-0.02)+ (0.024-0.04) cos ~ + (0.45 4-0.05) cos2 ~

1+0.474 cos2

second

(1 ±0.06) + (0.06±0.06) cos # + (0.34+0.11) cos2 ~

1+0.309 cos2 ~

first

(1+ 0.02) + (0.05 4-0.04) cos ~ + (0.354-0.05) cos2 #

1+0.399 cos2 ~

second

(1 4-0.05) --(0.07±0.05) cos ~ + (0.36±0.05) cos2~

1+0.320 cos2

first 6-7

W(~) = 0~o+~2cos2

second

1+0.396 cos2 (1±0.04)-- (0.21 ±0.11) cos ~ + (0.42:k0.14) cos2 ~

The coefficients were normalized to an ~0 coefficient equal to unity.

1+0.188 cos~ ~

SSMn(~,n)58Co REACTION

215

The obtained angular distributions were compared to the theoretical distribution which was calculated by Ericson and Strutinsky 9) in a semiclassical approximation (which is valid in our ease because max(Icfe, lcfr) < 202) W(#) = 1 + a cos2# + . . . .

(2)

where the coefficient a is given by the expression: a = ½ ( ~ f f 12),

(3)

and ~f = h2/2JT (T is the nuclear temperature of the residual nucleus, ,8" is the moment of inertia of the residual nucleus); 12 and 12 represent the means of the squares of angular momenta of compound nucleus and emitted neutrons with the weighting factors IT~(I) and lT2(l). In the sharp cut-off approximation for the transmission coefficients TI(I) and T2(l), 12 and l 2 are given by the relations (17) and (18) of Ericson and Strutinsky 9). We employed in the calculations a parameter of the interaction radius r 0 = 1.45 fm and for the neutron and the ~-particle we took R n = 0 and R~ = 1.2 fm, respectively. With these values the Ericson-Strutinsky formulae lead to the following expression: .~ _

17.561212 1 A°

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(4)

T dt'

where ~ = .:/J~i,,ia, A is the atomic number of the residual nucleus and d is the anisotropy defined as W(0 °) - W(90 °) W(90 °) From the angular distribution data we calculated the moment of inertia of the residual nucleus s SCo in the excitation energy ranges 4-5 MeV, 5-6 MeV and 6-7 MeV and compared it to the moment of inertia of a rigid spherical nucleus. The values we obtained for the ratio ~ = J / J r i g i d are given in table 2, and are shown in fig. 5. Our results are in agreement with ~ = 0.3 determined by Iwata 1o) from the isomeric cross-section ratios for 55Mn(c~, n)SSm'gCo reaction. They also agree, in the limit of experimental errors, with the value ~ ,~ 0.5 given by Malishev 1~) for a little higher energies at the binding energy of the nucleon. The low value ~/Jrigid, as suggested by existing data ~ ) , is explained by the vicinity of the nucleus 5 SCo with the magic number 28. Concerning the calculation of the ~ values which are given in table 2 and fig. 5, we should like to comment on the temperature values used in the formula (4). Our measurements indicate at the two bombarding energies two different values of the nuclear temperature. This variation of the temperature with the bombarding energy does not agree with the compound nucleus statistical theory, at least in the manner

216

A. ALEVRAe t al.

in wh i ch this t h e o r y led to the f o r m u l a (4). In o r d e r to a v o i d that the change o f the t e m p e r a t u r e should be reflected artificially in increasing the ~ v al u e at E , = 14 M e V a nd r e d u c i n g the values at E , = 17 M e V , we i n t r o d u c e d in the f o r m u l a (4) a single TABLE 2 The ~ = J/Jrtgla ratio for the 5sCo nucleus = J/J,l~la

E* I

II

4-5 5-6 6--7

0.26+0.07 0.404-0.08

0.344-0.09

14 MeV

17 MeV

4-5 5-6 6--7

0.25-4-0.03 0.25-[-0.03 0.234- 0.05

0.31 +0.06 0.284-0.03 0.344- 0.07

The data from the last column were obtained by repeating the experiment at a later date (called in fig. 5 the second set of measurements). I

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Fig. 5. The ~ = JJ'/J~rlgld ratio for the 6aCo nucleus. The closed points are calculated from data at 14 MeV and the open ponts are calculated from data at 17 MeV. Circles are derived from the first set of measurements, triangles are derived from the second set of measurements. The error bars indicate statistical errors only. va lu e o f the t e m p e r a t u r e f o r b o t h b o m b a r d i n g energies, n a m e l y the m e a n v al u e o f those o b t a i n e d in o u r m e a s u r e m e n t s . A l t h o u g h , this c a u t i o n was taken, the @2 values at 14 M e V b o m b a r d i n g energy seem to be slightly higher t h a n the values at 17 M e V .

5tiMn(~, n)SSCo REACTION

217

Because of the small number of ~ data and their statistical errors and also because a simple analysis of data in the frame of the semi-classical approximation was made, we cannot consider this difference significant and consequently a discussion on it is premature. We mention that in heavy-ion reactions, the determination of the ratio J / J r i g i d related to a given range of excitation energies for various bombarding energies has led to identical values, as is expected for reactions taking place by compound nucleus formation 1,). In conclusion, our data on the SSMn(~, n)SSCo reaction show that the predominant process is of statistical nature, except for neutrons corresponding to the excitation energies in the residual nucleus E* = 1-4 MeV. These neutrons are probably emitted in a direct-interaction process. The authors wish to express their sincere thanks to Felicia Stan and to the cyclotron crew for their cooperation. They also thank Dr. M. L. Halbert for kindly sending us his paper before publication.

References 1) 2) 3) 4) 5) 6) 7)

8) 9) 10) 11)

A. Alevra et al., Nuclear Physics 58 (1964) 108 D. Bodansky, Ann. Revs. Nucl. Sci. 12 (1962) 105 T. Darrah Thomas, Nuclear Physics 53 (1964) 558 C. Hurwitz et aL, Nuclear Physics 54 (1964) 65 C. H. Holbrow and H. H. Barschall, Nuclear Physics 42 (1963) 264 V. A. Sidorov, Nuclear Physics 35 (1963) 253 M. L. Halbert and F. E. Durham, paper submitted to third Conf. on Reactions between Complex Nuclei, Asilomar, April 1963; A. Ghiorso, R. M. Diamond and H. E. Conzett, Proc. Conf. on Reactions between Complex Nuclei, p. 223 M. E. Rose, Phys. Rev. 91 (1953) 610 T. Ericson and V. Strutinsky, Nuclear Physics 9 (1958) 689, 8 (1958) 284 S. Iwata, J. Phys. Soc. Japan 17 (1962) 1323 A. V. Malishev, JETP 45 (1963) 316