Proton total reaction cross sections at 9.1 MeV

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2.A.1

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Nuclear Physics Alll (1968) 315--320; (~) North-HollandPublishin.q Co., Amsterdam

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N o t to be reproduced by photoprint or microfilm without written permission from the publisher

P R O T O N T O T A L R E A C T I O N C R O S S S E C T I O N S AT 9.1 M e V P. J. BULMAN ~ and J. A. R. GRIFFITH Department of Physics, University of Birminyham, Enyland Received 1 February 1968 Abstract: Proton total reaction cross sections have been measured at 9.1 MeV for Mg, Ti, ~'~Cu,~sCu,

natural Cu and Zr using a counter anti-coincidence technique. These and earlier results have been compared with the predictions of the nuclear optical model. Good agreement has been found in the case of medium-weight nuclei. NUCLEAR REACTIONS Mg, Ti, 63Cu, 65Cu, Cu, Zr (p) E = 9.1 MeV; m e a s u r e d O'removal, d e d u c e d O'non.elastl e reaction.

1. Introduction

The continuing interest in the optical model for nuclear interactions has led to measurements of differential cross sections, polarizations and reaction cross sections for a wide range of nucleides, for m a n y incident particles and at many energies. In particular, values of the total reaction cross sections for protons of about 9 MeV have recently been measured both at this laboratory 1) and by Bearpark z). More complete lists of references to earlier work may be found in refs. 1,7). Other proton total reaction cross sections have been reported by Pollock 3) and by Dicello 4). Measurements with 26.5 MeV deuterons have been published by Mayo s) and with 29 MeV 3He particles by Balcarcel 6). Recently the determination of 24.7 MeV alpha particle reaction cross sections and elastic differential cross sections have been reported by Budzanowski 7). During the last few years an accurate set of measurements of the differential scattering cross sections for protons of about 9.5 MeV and many target nucleides has been made in this laboratory 8). A detailed optical-model analysis of the results 8) offers good fits to the experimental data and also gives predictions of total reaction cross sections. The measurements of this quantity reported in ref. 8) for an energy of 8.8 MeV have therefore been extended and the precision of some of the earlier data improved with the object of making a closer comparison with the optical analysis. 2. Apparatus

A detailed description of the experimental arrangement is given in ref. t); the counter-anticoincidence-attenuation method was used. A schematic diagram of t Present address: Royal Radar Establishment, Malvern, England. 315

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the counter arrangement is shown in fig. 1. The geometry of the incident proton beam from the Birmingham University Nuffield cyclotron was defined by two thin plastic scintillators (AEI and A E2) and an antiscattering detector (AS). An incident proton was specified by the logic (AE1 and AE2 and not AS). These detectors were similar to those previously described 1), but the antiscattering cylinder was halved in length and was viewed by a single photomuitiplier. This relaxation in the geometry, besides simplifying the counter, reduced its singles counting rate, while not resulting in any significant loss of experimental accuracy. The target and the full energy (E) counter followed the antiscattering counter as previously described 1). A tantalum stop was interposed between the antiscattering detector and the target. The effect of this was to reduce the magnitude of the backward hemisphere inelastic scattering correction to the final measurement. The elastic scattering correction is of course increased, but elastic differential cross sections are usually known more accurately than inelastic cross sections, and a gain in over-all precision results. MASK

E

AE~

'NC'OENT, I1

BEAM AXIS

f

TARGET

Fig. 1. Schematic diagram (not to scale) of the detector arrangement used in the present work. Each passing counter absorbed about 160 keV of energy from the incident protons. The beam line was as described in ref. 1). An important feature was that all collimation of the cyclotron beam was performed before the beam bending magnet, so that low-energy contamination was removed from the beam. The dummy target was used to reduce the beam energy during "target out" runs and so maintain a constant energy in the E-counter; it was also placed before the magnet. The nuclear magnetic resonance field stabilizer of the bending magnet re-set automatically for the dummy target runs. 3. Procedure

As described in ref. 1), the incident proton condition defined above was placed in anticoincidence with the E-detector signal. The anticoincidence rate, which measured the attenuation of the incident beam, was measured both for "target in " and "target out", the difference being almost entirely the attenuation due to the target. The use of the dummy target, however, causes a slight change in the behaviour of the passing counter system. This effect was measured as described in ref. ~) by reducing the Edetector discriminator bias to about 2 700 so that all inelastic events in that detector

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would register. The attenuation rates were then measured for both " d u m m y - i n " and " d u m m y - o u t " conditions, with the main target held out. The difference between these rates gavethe necessary correction. The correction runs were made part oftheautomatic counting sequence. The relative portions of a complete cycle spent on normal counting and low bias counting were chosen so that the two terms contributed approximately equal statistical errors to the final results. The counting cycle repeated at the rate of about 30 cycles/h, which was fast enough to average out the effects of systematic fluctuations that may occur in the equipment. A full measurement occupied about 24 h continuous running.

4. Treatment of experimental data The attenuation rate measured as described above combined with the target composition gave a value of the removal cross-section O'rem which was called the " r a w " cross section in ref. 1). Two corrections were applied to this number. Protons elastically scattered into the angular region between the acceptance cones of the E- and AS-detectors caused unwanted attenuation events, which had to be subtracted from the measured value. This correction Aael was calculated by integrating experimental differential cross sections between the relevant angles, which were approximately TABLE 1 Experimental results showing the size o f the corrections Target

Mg Ti ~3Cu nsCu Cu Zr

Energy (MeV) 9.15 9.15 9.10 9.10 9.05 9.2

Crrem

592±12 783 ± 18 883 ± 21 9224-23 913 ± 19 1283 t-43

ZlO'el

/I o'laei

130120 102 "- 3 2 0 6 !: 10 212~10 208 4-10 427 4- 20

140q-10 69 :~-:15 74 ,-R17 44! 8 63 ~_ 12 25 -:- 10

(O'r-- O'C.E.) (mb) 602 750 751 754 768 880

i-uncertainty (rob) 25 24 29 27 25 50

The total energy spread introduced by the target thicknesses was --400 keV.

63 ° and 123 °. In the case of Mg, 63Cu, 65Cu and Cu, the elastic scattering data of Rolph and Scarrott 8) were used. For Zr, their data on the neighbouring nucleide a 9 y were used and for Ti the data of Hintz 9). Where necessary, corrections for small energy differences were made assuming that Acre, was proportional to E -2 and were checked using optical-model calculations. In no case, was the magnitude of any such correction factor large enough to increase appreciably the over-all uncertainty of the measurement. The inelastic correction A~ri,~t comprised the integration of the differential cross sections for inelastic groups lying above the E-detector threshold (53 ~o) and the antiscattering detector threshold. The integrations were performed over the appro-

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priate regions of space. The data of Hintz 9) were used for Cu and its isotopes and the data of Rolph and Scarrott 8) for Mg. The Zr correction was small and was inferred from their results on a9y. After allowing for reaction Q-values and the response of the NE102 scintillator 1o), no other charged-particle producing reactions contributed to the inelastic corrections. The errors introduced by the integration of the differential cross sections were in most cases small. For the inelastic correction, however, some uncertainty surrounded the value of the discriminator bias, particularly in the backward hemisphere correction. Account has been taken of this in assessing the quoted experimental uncertainty. In every case except Mg, the largest single contribution to the uncertainty came from counting statistics. The final experimental results for the total inelastic plus reaction cross sections less the unknown amounts of the compound elastic cross sections are displayed in table 1 with the values of the applied correction terms. The elastic correction includes an allowance for the effect of the finite size of the beam spot, though the magnitude of this effect is only about 3 mb. Comparison of the results for Cu with those of ref. 1) shows the reduction of the inelastic correction previously mentioned. 5. Discussion

The values for 63Cu, 65Cu and Cu agree well with the previous i) measurements at 8.8 MeV. The separated-isotope results are consistent with the natural-mixture data within statistical errors alone. Comparison with the measurements of Bearpark 2), which span the same energy range, shows that there is a tendency for the present work to give higher values than the direct-beam charge-loss method. The magnitude of the discrepancy is only of the order of the uncertainties in applying the scattering corrections, to which both methods are susceptible. There is greater certainty in the smaller elastic corrections in the present work, but this is largely offset by the poorer statistical accuracy of the counter method. The present measurements have been compared with the predictions of the nuclear optical model. The parameters found by Rolph and Scarrott s) in fitting differential elastic cross sections were used to predict at, allowance being made only for the slight change in energy. In the fitting procedure of ref. 8), all the geometrical parameters and the spin-orbit potential were fixed; a search was made for a fit by changing the real central potential V and the imaginary surface-peaked potential Ws only. No volume absorption was used. The geometrical parameters were those of Perey 11). The radius parameters were set at 1.25 fm, the diffuseness of the real potential was 0.65 fm and that of the imaginary potential, 0.47 fm. The spin-orbit potential was taken to be 6 MeV. Table 2 shows the values of V and Ws obtained s) for the different elements together with the predictions (arcazc) and the experimental values (a~--ac.e.) of the reaction cross sections. Some values taken from ref. 1) have also been included. It is clear that in all cases of medium-weight nuclei (80 > A > 40), where the parameters

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have been derived from good fits to elastic data, an excellent prediction of a r results. The fits to the differential cross sections for SSNi showed that approximately 3 m b • sr-1 of isotropic compound elastic scattering helped to give a good fit and that slightly less helped in the case of Fe. I f a total compound elastic cross section of about 40 mb is added to ar-trc.r, for SSNi and about 30 mb for Fe, then the agreement with the prediction is again reasonable. To give a quantitative assessment of the agreement, table 2 contains values of X 2 = (O'rexp--O"r talc) 2(Aarcxp) -2 for each point. The sum total of these X2-values with the exception of Mg and Zr gives 10.4 from ten values. TABLE 2

Comparison of the experimental results with optical-model calculations Parameters N u c l e u s Energy (MeV)

V

WB

O'rcale (mb)

tTr- C.E.ex p (mb)

:!:error (rob)

~3Cu 6~Cu Cu Ti Mg Zr

9.1 9.1 9.05 9.15 9.15 9.2

53.7 54.3 54.1 51.6 49.0 53.8

13.4 13.3 13.4 8.2 9.0 13.0

749 775 757 784 770 660

751 754 768 750 602 880

V Fe Co 5SNi 6°Ni Zn

8.8 8.9 8.8 8.8 8.8 8.75

51.9 50.6 52.3 52.8 52.8 53.7

8.2 13.9 13.9 13.6 13.6 13.5

770 770 753 730 730 713

730 680 825 728 728 726

(MeV)

7.2

Ref.

29 27 25 24 25 50

0.0 0.6 0.2 2.0 45.0 19.4

~) a) ~) a) a) a)

30 50 40 55 55 35

1.8 1.4 3.2 1.0 0.0 0. I

4) 4) b) b) 4) 4)

F o r V and Ti, different optical-model geometrical parameters were used (see text). In calculating g ~ for Fe a n d 58Ni, c o m p o u n d elastic c o n t r i b u t i o n s o f 30 m b a n d 40 m b , respectively, have been a d d e d to the experimental results [see text a n d ref. 1)]. a) Present work. b) Ref. 1).

The predictions for V and Ti were calculated from an optical model with different geometrical parameters. Berovic t2) found in fitting the elastic data for V and Sc that it was essential to vary the diffuseness parameters. He used a value of 0.58 fm for both. It is interesting to note that good predictions only result when parameter sets found for the same or very near nucleides are used. Predictions for Ti and V based on parameters extrapolated from Fe, Ni and Co come out approximately 100 mb too high. The two nuclei for which the agreement between the observed and calculated cross sections is poor are Mg and Zr. In the case of M g there appears to be resonant behaviour in the experimental elastic and inelastic scattering data 1a, 14) near 9 MeV, and this makes the present elastic and inelastic corrections somewhat uncertain. For the same reason, the optical-model predictions may be unreliable and the analysis of this case has not been pursued further.

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In the case of Zr, it is unlikely that the discrepancy can be due to resonances. The experimental value, however, is found to be substantially larger than a prediction based on a parameter set which have a good fit to the elastic data for the neighbouring n u c l e i d e 8 9 y . Similarly the values found by Bearpark 2) for silver and indium at 9.5 MeV are again about 150 mb higher than optical-model predictions obtained from the data of ref. 8). There thus appears to be a systematic discrepancy for the heavier nuclei. In the case of silver, extra information has been obtained in the form of polarization data 15) at 9.4 MeV. However the potentials indicated by fitting these data with the differential cross section did not yield reaction cross sections nearer to the experimental value. Since the disagreement between experiment and calculation is confined to the heavier nuclei, it is possibly due to Coulomb barrier effects. At about 9 MeV proton energy, a, increases with mass number up to A ~ 70 mainly because of increasing nuclear size. For A > 70, the Coulomb barrier causes a levelling off and finally a decrease beyond about A > 90. It is therefore possible that slight miscalculation of the shape of the Coulomb barrier in the optical analysis, brought about by inadequacy of the parameter set used, could cause serious errors in the predictions of a r for heavier nuclei. Preliminary calculations have been performed on the silver data at 9.4 MeV [refs. 2,15)] and at 17.8 MeV [ref. 16)], in which the diffuseness parameters were increased to place more of the absorptive potential beyond the influence of the Coulomb barrier. The results were encouraging, suggesting that good fits to all the data could be found. We acknowledge with thanks the invaluable work of the Nuffield Cyclotron operating staff. We are also indebted to Drs. Hodgson and Hill of the University of Oxford for making available their optical-model parameter-searching computer programme. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16)

P. J. Bulman, G. W. Greenlees and M. J. Sametband, Nucl. Phys. 69 (1965) 536 K. Bcarpark, W. R. Graham and G. Joncs, Nucl. Phys. 73 (1965) 206; Nucl. Instr. 35 (1965) 235 R. E. Pollock and G. Schrank, Phys. Rev. 130 (1965) B575 J. F. Dicello, G. J. Igo and M. L. Roush, Phys. Rev. 157 (1967) 1001 S. Mayo, W. Schimmerling and M. J. Sametband, Nucl. Phys. 62 (1965) 393 R. Balcarcel and J. A. R. Griffith, Phys. Left. 26B (1968) 213 A. Budzanowski et al., Nucl. Phys. 106 (1968) 21 S. M. Scarrott, P h . D . thesis, University of Birmingham; R. M. Rolph and S. M. Scarrott, to be published N. M. Hintz, private communication (1964) T. J. Gooding and H. G. Pugh, Nucl. Instr. 7 (1960) 189 E. G. Perey, Phys. Rev. 131 (1959) 1099 N. Berovic, Ph. D. thesis, University of Birmingham G. W. Greenlees, Proc. Phys. Soc. A70 (1957) 331 K. Matsuda et al., Nucl. Phys. 27 (1961) 1 J. A. R. Griffith and S. Roman, Phys. Lett. 19 (1965) 410 D. J. Baugh, J. A. R. Griffith and S. Roman, Nucl. Phys. 83 (1966) 481