Protons from 32S bombarded by 14.6 MeV neutrons

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Nuclear Physics 44 (1963) Not

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NEUTRONS

B. ANTOLKOVIC Institute “Ruder Received

BoSkovid”, Zagreb

18 December

1962

Abstract: Protons from 14.6 MeV neutron induced reactions on YS have been studied. The proton energy and angular distributions are consistent with the statistical model predictions and from the shapes of the distributions the level density parameters have been derived. A small contribution only from a direct interaction of incident neutrons with protons has been found. The cross sections for the reactions involved have been determined and compared to the existing data.

1. Introduction

There exists quite a large discrepancy between the results on the values of the cross section for the 32S(n, P)~~P reaction thus far ‘) published. Cross sections obtained by the activation method (Paul and Clarke 2, and Allen “)) are cross sections of the pure (n, p) reaction leading to the residual nucleus 32P. Cross sections measured by proton counters, such as proton telescopes (Colli et al. 4), Eubank et al. “) and Hassler et al. “)) or nuclear emulsions (Allan ‘)> are essentially a mixture of (n, p), (n, np) and (n, pn) cross sections and cannot be directly compared to the values obtained by the activation method. In the case of sulphur the double particle emission - when 14.6 MeV neutrons are used - is energetically possible even at a proton energy as large as 4.9 MeV. Thus by taking the proton telescope technique with the usual lowere energy limit at w 3 MeV one measures, besides protons from the (n, p) reaction, also a certain fraction of’the protons from the reactions prpceeding via a double particle emission. So far an estimate of the (n, np) cross section for sulphur has been made 7, based on the level density parameters of nuclei having mass number in the vicinity of 32. A measurement has been made in an energy region not comprising protons below 2.8 MeV (ref. “)). In the present experiment the 14.6 MeV neutron induced reactions on 32S resulting in proton emission were studied using nuclear plates as the proton detector. Some preliminary results of this experiment have already been published *). The present paper deals with the results based on improved statistics and with the angular distribution extended to backward angles. From the energy and angular distributions which have been studied through the whole range of energies of emitted protons it is possible to establish the contribution of the double particle emission processes, such as (n, np) and (n, pn) reactions. From the measured distributions it is also possible to determine or at least evaluate the contributions of the direct and the compound nucleus processes as well as some statistical model parameters. 123

124

a. ANTOLKOVIt~

2. Experimental Technique The experimental arrangement is shown in fig. 1(a). The target chamber is an evacuated brass cylinder of 1 m m wall thickness lined internally with a 1 m m thick tin foil. The target and the plates are placed in a holder, which can be fixed in a desired position. The plates are placed normal to the target at the vertical level of its lower and upper edge. The mounting of the target and of only one of the two plates placed symmetrically above and below the central line are shown in figs. 1(a) and (b), respectively. On the lower side there are two 2.5 cm × 7.6 cm C2 200 l~m plates with the emulsion upwards, and on the upper side there are two 2.5 cm × 7.6 cm K O 200/~m plates with the emulsion downwards. The sulphur target of 13 mg/cm z

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thcikness evaporated on the gold foil surrounds the plates on one side of the central line and the bare gold foil on the other side. This geometry of exposition makes it possible to record protons from the whole angular distribution both for run and background on the same plate. The iron collimator 20 cm long has a prismatical opening, which allows the neutrons to strike the target but prevents them from striking the plates. Neutrons of 14.6 MeV were obtained from a Cockcroft-Walton accelerator using the T(d, n)4He reaction. We defined the neutron energy by measuring the proton recoil tracks in the nuclear emulsion. The neutron flux was monitored by the detection of alpha particles generated from the T(d, n)4He reaction and by the measurement of recoil protons in the nuclear emulsions. The time integrated flux on the front farget was 1.3 × 10 9 neutrons/cm 2. The scanning of the tracks consists in measuring the position coordinates, range, and horizontal and dip angle of traversal of all proton tracks entering the emulsion surface. Each track is then virtually prolonged to the target and the position of its starting point determined. The position of the starting point was the indication whether the track belongs to protons from the reaction or to protons from the back-

PROTONS FROM 31S

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ground. The total number of about 5000 tracks accepted was measured on an area of 1.4 cm 2 on the two C2 200/2m plates. The arrangement which employs an extended target and an extended detector, as in the case of our experiment, has a large detection efficiency, but this efficiency is strongly dependent on the angle that the emerging protons form with the incident neutrons and on the distance of the scanned area to the target. The analytical expressions for the solid angles as functions of the n-p angle and the position of the scanned area on the plate have been calculated 9) and are shown in a graphical form in fig. 2.

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parallel to the target.) 3. Results

3.1. ENERGY DISTRIBUTION It has been shown 8) that in the 14.0 MeV neutron energy region the main feature of the energy distribution of protons emitted from 32S is its MaxweUian distribution shape. In the statistical theory plot, however, the influence of direct interaction products is much more pronounced. At small angles of emission there appear some bumps in the high energy part of the energy distribution caused by direct interaction protons 8). There appears also a constant departure of the experimental points from the lines indicating the compound nucleus processes in the region about 5 MeV, where deuterons from the 32S(n, d)31P reaction are expected (as mentioned in ref. 8) deuterons could not be separated from protons by the nuclear plate method). To minimize the direct interaction contribution, in the present analysis the energy distribution is plotted containing only the protons with an angle of emission larger

126

B. ANTOLKOVIC

than 45 ° (fig. 3). Above 5 MeV, i.e., in the energy region where the (n, np) reaction is energetically impossible, the experimental points are compared with the theoretical curves using the relations (a) p = Ce -e~/r and (b) p = C'e 2 " / ~ for the level density (Ep is the proton energy, E* is the excitation energy of the residual nucleus and T and a are the level density parameters). The Z2 test was a check that the latter o f these two expressions gives a much better agreement with the experimental points. The best fit for case (a) is obtained by using the parameter T = 1.38-t-0.08 MeV for the nuclear temperature of the residual nucleus from the 32S(n, p)a2p reaction (fig. 3a) while for case (b) a value o f a = 2.13 MeV -1 gives a best fit (fig. 3b).

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theoretical angular distribution 11,12) leads then to the evaluation of the parameter a of the level density formula or even of a moment of inertia of the residual nucleus with which it is in a close connection. The 1 + A cos 2 0 fit to the experimental angular distribution for the (n, p) reaction in the energy region above 5 MeV (the experimental points at small angles of emission are excluded because of the direct reaction contributions) was carried out. Due to the large statistical errors the coefficient o f the cos 4 0 term was found to be quite uncertain. Thus from the .4 value compared to the first order anisotropy coefficient of the theoretical angular distribution ~2), the lower limit of the spin dependent parameter a was estimated. In order to determine the averages of the squares of the compound nucleus angular momenta and the orbital angular m o m e n t u m of emitted

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Fig. 4. Angular distribution of protons. The upper diagram shows all emitted protons. The lower diagram presents only the protons of an energy larger than 7.0 MeV. particle occurring in the theoretical expression, the transmission coefficients are calculated by means of Coulomb wave functions with a radius R = rA ~, r = 1.5 fm. The parameter a was found to be a ~, 1.9 and from this value the moment of inertia of the excited nucleus 32p was deduced to be I ~ 0.4/rigid body. 3.3. CROSS SECTION The forward peaking of the angular distribution for the high energy protons is ascribed to direct reactions, and the estimate of the cross section for this process leads to a value of the order of magnitude of 10 mb. The total cross section for the part o f ' t h e reaction proceeding via the compound nucleus formation is found to be 380+19 mb. The calculations were performed to evaluate the contributions of the particular reactions in the total compound nucleus process leading to the proton emission. By means of the shape o f the energy spectrum of first emitted protons the separation of the (n, p) + (n, pn) reaction f r o m the (n, np) reaction is possible, but not until some behaviour of the angular distribution of these reactions is known. In order to

128

B. ANTOLKOVI(~

determine the angular anisotropy o f these two processes, the calculations o f the ratios of differential cross sections at the angles 4 5 ° + 10 °, 90°+__10 ° and 135°+ 10 ° were carried out. The theoretical energy spectrum was normalized to the experimental points in the energy region above 5 MeV for each angular interval separately. The values a(.,p)+~.,p.)/a~.,np) were obtained from the ratio of the n u m b e r o f protons which were confined by the theoretical energy distribution curve to the n u m b e r o f protons not confined by it. It turns out that for all angular intervals in question these ratios are equal inside the 2 0 ~ statistical error, which means that the anisotropics o f both processes are similar to each other within the mentioned range o f error. The ratio of (n, p ) + ( n , pn) to (n, rip) cross section strongly depends on the expression used for the description o f the level density of the residual nucleus left after the emission o f the first proton. The a(n,p)+(n, pn)/a(~.np) values obtained for the level density parameters a = 2.13 MeV -1 and T -- 1.38 MeV are 1.56 and 3.18, respectively, giving for the cross section o f the (n, p ) + ( n , pn) and (n, np) processes the values presented in table 1. On table 1, the results o f other authors are also listed as well as the detection method (column two) and the energy region studied (column three). To make possible the comparison between the different sulphur data, the last column contains the values extrapolated to the protons f r o m the low energy region not included in the measurements performed by the p r o t o n TABLE 1 S u m m a r y o f cross section d a t a o f 14 M e V n e u t r o n induced reactions o n s2S resulting in p r o t o n emission

Ref. 2) z) 4) 5) 6) 7) Present results

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PROTONS FROM 8~S

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telescope method. These extrapolations were calculated on the basis of the energy spectrum shape obtained in the present experiment. After the extrapolation procedure the values for the total cross section of proton yielding reactions on sulphur, derived from the proton telescope and nuclear emulsion techniques appear to be in reasonable agreement. The comparison of the results obtained by the activation method and the (n, p) + (n, pn) cross section derived from the measurements performed by the proton counter technique gives an insight into the (n, pn) reaction cross section. It should be mentioned that the direct reaction contribution, as shown by CoUi et al. 4) and by the present work is rather small and comparable to the statistical error of the total compound nucleus reaction cross section. It is therefore not necessary to take direct contributions into account in the discussion of the activation results. By the rough assumption that the (n, pn) reaction always proceeds when it is energetically possible, a cross section of only 114 mb is atributed to the (n, p) reaction. However, an inspection of the values cited in table 1 clearly shows that the above assumption overestimates the (n, pn) reaction contribution and that in the competition between neutron and y-ray emission the latter is much more favoured. This is a further support to the fact 7, 13,14) that the pairing effects play an important role in selecting the reaction leading to the odd nucleus rather than to the odd-proton nucleus. The author wishes to express her thanks to Professor M. Paid for initiating the problem and for his great interest and valuable advice in the course of this work. Thanks are also due to Mrs. M. Turk and Mr. B. Eman for many helpful discussions.

References 1) 2) 3) 4)

Donald G. Gardner, Nuclear Physics 29 (1962) 373 E. B. Paul and R. L. Clarke, Can. J. Phys. 31 (1953) 267 L. Allen, Jr., W. A. Biggers, R. S. Prestwood and K. Smith, Phys. Rev. 107 (1957) 1363 L. Colli, I. Iori, G. Marcazzan, F. Merzari, A. M. Sona and P. G. Sona, Nuovo Cim. 17 (1960) 634 5) H. P. Eubank, R. A. Peck, Jr. and F. L. Hassler, Nuclear Physics 9 (1958) 273 6) F. L. Hassler and R. A. Peck Jr., Phys. Rev. 125 (1962) 1011 7) D. L. Allan, Nuclear Physics 24 (1961) 274 8) B. Antolkovi6, Nuovo Cim. 22 (1961) 853 9) B. Antolkovid, Thesis 10) H. A. Bethe, Revs. Mod. Phys. 9 (1937) 84 11) T. Ericson and V. Strutinski, Nuclear Physics 8 (1958) 284 12) T. Ericson, Phil. Mag. Suppl. 9 (1960) 425 13) J. Kumabe and R. W. Fink, Nuclear Physics 24 (1960) 316 14) R. N. Glover and E. Weigold, Nuclear Physics 24 (1957) 630