Elastic scattering of 4–20 MeV alpha particles by Be9

I 2.B:2.L I

Nuclear Physics 65 (1965) 318--328; (~) North-Holland Publishing Co., Amsterdam

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Not to be reproduced by photoprint or microfilm without written permission from the publisher

ELASTIC SCATTERING OF 4-20 MeV ALPHA PARTICLES BY Be9 R. B. TAYLOR, t N. R. FLETCHER and R. H. DAVIS

Department of Physics, Florida State University, Tallahassee, Florida tt Received 26 October 1964 The scattering of alpha particles by Be9 has been studied in the bombarding energy range 4-20 MeV. Eight excitation functions and sixteen angular distributions were measured. Angular distributions were analysed with an optical model which included a term coupling the target spin 1 to the orbital angular momentum l. The optical model parameters varied smoothly with energy over the entire range, and the value of the spin-orbit parameter Vso varied from 1.6 to 2.7 MeV. Real well depths of about 55 MeV were used. Optical model fits without the I . 1 term were poor especially at back angles. A smooth cut-off model analysis was also attempted with little success.

Abstract:

El

N U C L E A R REACTIONS Beg(~, u), E = 4-20 MeV; measured a(E; 0).

1. Introduction

Although a large number of experimental and theoretical investigations of the Be 9 target nucleus and the C 13 compound nucleus have been reported, information about the elastic scattering of alpha particles by Be 9 is very limited. Only three angular distributions have been published: one at 18.4 MeV by Lucas et aL 1), one at 23.8 MeV by Gregoire et al. 2) and one at 48 MeV by Summers-Gill z). The two lowenergy distributions were analysed using a Blair diffraction model 4). Since small angle scattering is assumed in this model it is not surprising that agreement between theory and experiment was obtained at extreme forward angles only. Measurements o f the inelastic scattering have been made 1, 2) and these are complicated by alpha particles resulting from the four body break up of the compound nucleus C la ( a = - 1 . 6 6 7 MeV). In this paper the experimental results of the elastic scattering of alpha particles by Be 9 are presented. Eight excitation functions in the laboratory energy region 4-20 MeV and sixteen angular distributions at various energies between 9.5 and 20 MeV were measured. The angular distributions have been analysed using an optical model which includes a term proportional to I • l, the coupling of the target spin I = ~ to the relative orbital angular momentum l of the He 4 and Be 9 nuclei. t Present Address: AERE Harwell, U.K. tt Work supported in part by the Air Force Office of Scientific Research. 318

ELASTIC SCATrERING

319

There were three interrelated objectives. The first was to assess the applicability of the optical model to the alpha particle plus Be 9 nucleus system in the bombarding energy region of 10-20 MeV. The second was to investigate the variation of the optical model parameters as a function of energy, and third to determine the importance o f an I • l term in the optical model potential. Previous investigations have indicated that the spin-orbit term of primary importance is the l . s term coupling the projectile spin s and the orbital angular momentum and that terms due to I • s and I • I couplings are small. The polarization of protons scattered by M g ( ! = 0) and A I ( / = ~) at similar energies are almost identical 5). Perey 6) found that both the elastic scattering and the polarization o f protons could be fitted using the same optical model parameters which included only an l . s spin-orbit potential term. An l . s term was suggested by Seth 7) in connection with anomalies in S wave neutron strength functions. A recent calculation by Robson s) shows that if the spin-orbit potential is treated as a perturbation, the first order effect of an I • s or I • I interaction on the projectile polarization is zero. It follows from this result that the analysis of projectile polarization data is not a good test of the existence of an interaction involving the target spin. In effect, the random orientation of the target spin leads to a cancellation of its effects on the projectile polarization. A measurement of the I . I interaction strength may be performed by scattering a zero spin projectile (I-Ie4) from a non-zero spin target and looking for either the polarization o f the target nucleus or anomalies in the angular distribution which can be attributed to the I • 1 interaction. Light target nuclei provide the best opportunity to investigate this interaction since the I • l term is presumed to have an A-1 dependence 9). The possibility of doing a polarization measurement was ruled out in this experiment because of low beam intensities and small cross sections. The present investigation was limited to studying the elastic scattering cross section, and while the results are not conclusive, they suggest that the I • ! interaction is important for light target nuclei.

2. Experimental Procedure The alpha particle beam was obtained from the Florida State University tandem Van de Graaffaccelerator by the use o f negative helium ion injection. After momentum analysis with a 90 ° magnet the beam was deflected and focussed on the target position o f a 45.7 cm diameter target chamber 1o). The 90 ° magnet was calibrated by a measurement o f the A127(p, n) threshold energy which was found to differ by less than 10 keV from a previous calibration ~1). Over the entire energy range of the machine, the beam has a nominal energy spread o f less than 2 keV. Alpha particle beam currents o f 4 to 25 nA were used and the bombarding energy was continuously variable in the range 4~20 MeV. The scattered alpha particle yield was measured with silicon surface-barrier detectors placed behind two defining slits. The front slit was 0.254 cmx0.381 cm

320

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TAYLOR

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and the back slit was 0.127 cm x 0.381 cm. Detectors were mounted on two rotating plates situated at the top and bottom of the chamber and on the wall. All counter apertures subtended angles less than 2 °, and for measurements at small scattering angles this upper limit was reduced to 1° . The observation angle could be set with an accuracy of _+_0.1°. With this geometry the effects of finite detector apertures were small. Self-supporting Be targets 130 pg/cm 2 thick were obtained by condensing Be vapor from a hot tantalum boat on glass. The Be foils were subsequently floated in water and picked up by an aluminium target frame. Target contaminants consisted of carbon ( < 0.1 ~ ) , oxygen ( ~ 1 ~o) and tantalum ( < 1 ~o), but these did not effect the measurements except at very forward angles. These impurities were estimated by the use of previously measured C12(0q ~o) and O16(0q Cto) data 12,13) and by assuming that the Ta(0~, ~o) cross section was Rutherford. The absolute cross section was determined by performing a Beg(~, ~o)Be 9 normalization experiment in which the target thickness was established by a subsidiary Be9(p, po)Be 9 experiment. In the proton energy range 10 to 12 MeV there are three independent measurements of the absolute Be9(p, po)Be 9 cross section 3,14,15). Measurements showed that these Beg(p, po)Be 9 cross sections were in agreement to better than 10 ~ and within the quoted experimental errors, Absolute Be9(~, 0%)Be9 differential cross sections measured at 18.4 MeV agreed within 5 ~ with the results of Lucas et al. 1). An estimated error of 10 ~ is assigned to the cross sections with a relative error in the angular distributions of less than 5 ~ . To make the best possible use of the low beam intensity, four detectors were used simultaneously in the excitation curve experiment. Certain regions of the excitation functions were measured with a target 50 pg/cm 2 thick to check the possibility that fine structure was averaged over by the heavier targets. Angular distributions were measured in 2.5 ° steps from 15 ° to 90 ° and 5 ° steps from 90 ° to 165 ° . 3. Results The eight excitation functions (figs. 1 and 2) show considerable resonance structure despite the high excitation energy (12.8 to 23.8 MeV in the C 13 compound system). These variations are most prominent below I0 MeV but still persist at 20 MeV. Although the exact nature of these anomalies was not ascertained, the moderate success of the optical model analysis of the angular distribution suggests that the structure at higher energies m a y be an optical model resonance phenomenon. Excitation functions do not exhibit single 1 value resonance behaviour, and no resonance terms were included in the analysis of the angular distributions. The 16 angular distributions are shown in fig. 3. There are two general features. The distributions vary slowly with energy; peak intensity and position change smoothly over the range of alpha-particle bombarding energy. The number of maxima in the angular distributions monotonically increases as the incident energy increases in contrast with the scattering of alpha particles by carbon 12).

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Secondly, the diffraction pattern, although pronounced at back angles, does not show the large peak-to-valley ratios observed in other light nuclei 12, 13,16). This can be readily explained by the spin-orbit coupling term used in the nuclear potential. Amplitudes due to the discrete couplings shift out of phase as the angle increases and the summed contribution smoothes the angular distributions at back angles.

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ELASTIC SCATTERING

323

4. Analysis of the Data Above 20 MeV bombarding energy, considerable success has been achieved in the fitting of alpha particle elastic scattering data for medium weight and heavy target nuclei with both the optical model 16) and the semi-classical smooth cut-off model4' 17). The success of the smooth cut-off model has been attributed to the fact that alpha particles have a very short mean free path inside the nucleus. Both models were used in attempts to fit the data obtained from this experiment. Differential cross sections computed with the smooth cut-off model failed to fit the experimental values at large angles. This may be due to the breakdown of the assumption regarding the absorptive nature o f the nucleus or the absence o f nuclear spin effects. No attempts were made to improve the fits by the inclusion of resonant phase shifts in either the smooth cut-offmodel or the optical model since the excitation curves did not exhibit sharp compound nucleus resonances. The optical model potential used is given by

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where Vc, U, W, W' and Vso are the Coulomb, real, volume imaginary, surface imaginary and spin-orbit parts of the potential, respectively. The quantities R and a are the radius and diffuseness parameters associated with the potential terms, and r is the projectile-target separation distance. The mass m~ is that of the rc meson. The quantity I is the spin of the target nucleus, which in the case of Be 9 is ~. 2 Calculations were performed on the F S U IBM 709 computer using a computer code written by Robson, Snover and Thompson is). The spin-orbit term was programmed to permit an arbitrary choice of the nuclear spin, and the radial dependence was that customarily used in ! • s coupling analysis 19). A spin ½ program written by Perey 2o) served to check the code. Initially the data were fitted by varying all the parameters under the restrictions that the same value was used for all of the diffuseness parameters (a r = ai = as), and the nuclear radius parameters were also set equal ( R r = .R i ~-- Rs). The Coulomb

324

R.B. TAYLOR et aL

radius R c was fixed. Removal of these restrictions did not improve the fits appreciably, but radically changed the value of some of the other parameters. The best set of parameters is given in table 1 and the parameters show considerable variation with energy. Any systematic trend with energy is masked by the variations. TABLE 1 R r =

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(MeV)

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(fm)

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3.30 3.10 3.37 3.84 3.84 4.00 3.84 3.84 3.62 3.76 4.04 4.22 4.00 3.84 3.84 4.31

0.64 0.67 0.72 0.55 0.58 0.54 0.55 0.58 0.60 0.60 0.55 0.51 0.50 0.56 0.53 0.48

2.5 2.4 2.9 2.5 2.6 2.5 4.2 4.8 5.0 5.4 4.2 4.6 4.6 5.0 4.5 4.2

TABLE 2 Optical model parameters for best fits, Rr ---- Rt = RB = 3.84 fin, ar = ai = as, Re = 2.91 fm, W ' = 0 E~ (MeV) 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 14.05 14.86 15.7 16.55 17.5 18.4 19.47 20.0

u (MeV)

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45.0 46.5 50.7 50.0 51.2 52.0 54.0 54.1 57.0 58.0 60.0 60.1 60.7 61.0 60.9 61.0

2.0 2.2 2.4 2.5 2.6 2.7 3.3 4.2 4.8 4.8 4.2 5.0 4.7 5.0 4.5 4.6

1.5 1.8 1.8 1.8 1.8 2.0 2.7 2.6 2.4 2.2 1.5 1.6 1.6 2.1 2.4 1.9

0.52 0.61 0.63 0.55 0.58 0.55 0.55 0.58 0.58 0.60 0.59 0.58 0.54 0.56 0.53 0.58

ELASTIC

325

SCATTERING

In order to reduce the variation o f the parameters with energy the radius parameters ( R , , R i , R s) were fixed at a value o f 3.84 fro. This further restriction yielded a new

set of parameters which are given in table 2 and the corresponding theoretical fits to the experimental data are shown in fig. 3. Fixing the radius parameters significantly changed other parameters, but not the quality o f the fits. The energy dependence o f the parameters is shown in fig. 4. The real potential well depth varies smoothly f r o m 45 MeV (E, = 9.5 MeV) to 61 MeV (E, = 20 MeV), a range of values which is consistant with Igo's 16) fitting parameters for 40 MeV alpha particle elastic scattering data. The imaginary potential depth also shows a significant increase with the bombarding energy. A volume imaginary potential has been used since this gave a slightly better fit than a surface imaginary potential. i

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Ec~(MeV) Fig. 4. Energy dependence of optical model parameters with a fixed radius parameter of 3.84 fro. The values are listed in table 2. Parameter symbols are as follows: • - real potential U, o - imaginary potential W and + - spin-orbit potential Vso. The diffuseness and spin-orbit parameters remain essentially constant over the entire energy range. The question o f uniqueness was investigated. It was found that with a radius parameter of about 3.84 f m it was possible to obtain fits to the data using real potentials in the vicinity of 55, 95 and 125 MeV. Above 16 MeV bombarding energy, the real potential o f 125 MeV gave slightly better fits to the angular distributions, mainly in the vicinity o f the last maxima. However, below 15 MeV this real potential gave very poor fits. A real potential o f about 95 MeV gave poor fits at all energies. Although the use of a real potential well depth in the vicinity of 60 MeV does not give the best fit at all energies it does lead to the best overall fit of the data (fig. 3). In several o f the angular distributions, the last maxima are not well reproduced by the optical model. This difference can be reduced by removing the restriction on the diffuseness parameter.

326

R.B. TAYLORe t

al.

A n u m b e r o f attempts were m a d e to fit the data using no spin-orbit interaction. A l t h o u g h a large range o f potentials were tried, no satisfactory fits were obtained. The difficulty lay in matching both peak and valley intensities at large angles. Also, at some energies, the peak positions were displaced by as m u c h as 20 degrees f r o m observed locations. I

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3

Optical model parameters for the best fit at 14.05 MeV with and without a spin orbit potential U

W

Rr

ar

Vso

(MeV)

(MeV)

(fro)

(fm)

(MeV)

57.0

4.8

3.84

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2.4

57.7

5.6

3.84

0.60

0.0

Between 13 and 15 MeV, the best optical model fits with zero spin-orbit coupling have an extra peak which is n o t seen in the experimental data. This extraneous peak is removed by the addition o f the spin-orbit potential. The best fits with and without the spin-orbit potential at 14.05 M e V are shown in fig. 5. A t all the other energies b o t h the zero and spin ~r spin-orbit potentials gave the correct n u m b e r o f maxima. 5. Discussion While the justification for an optical model analysis o f the Be9(o~, 00Be 9 data is not clear in view o f the failure to fit similar data for other light nuclei, the low binding

327

E L A S ~ C SCATTER/NO

energy of the Be 9 nucleus m a y be important. Reaction cross sections, especially those leading to four-body breakup are large compared with the elastic scattering cross section. A process in which the elastically scattered alpha particle predominantly interacts with the Be 9 nucleus as a whole is consistent with an optical model analysis. In the bombarding energy range of 4 to 10 MeV the reaction Be9(~, n]))C 12 has been studied 21), and apart f r o m the broad anomaly between 4 and 6 MeV, no correlation was established between the elastic scattering and (~, ny) reaction results. Inclusion of the I • l term decisively improved the quality of the optical model fits. To confirm the existence and magnitude of the I • ! coupling, a polarization I

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Fig. 6. Comparison of optical model calculations for two spin-orbit coupling terms. The solid line is for I = ½and Vso = 4.4 MeV. The points are for I = ~ and Vso= 2.4 MeV. Except for Vso,the same parameter values are used in both. The spin ] curve is the best fit to the 14.05 MeV angular distribution data. measurement should be performed on the recoil Be 9 nucleus. Much larger beam currents are required than were available for the present experiment. It is interesting to note that if the spin-orbit potential is treated as a perturbation, the spin ½ result is the same, to first order, as that for spin ½ except that a smaller spin-orbit potential value is required s) for spin 3. A comparison o f / = ½ and I = ½ calculations is shown in fig. 6. An optical model calculation with a deformed potential m a y reproduce the data more accurately and further reduce the energy dependence of the parameters. Satchler 22) has discussed a deformed optical model potential, and his results show that even for weakly deformed nuclei, the deformation effects should be observable at large angles. To the extent that the geometric relationship between the deformation

328

R.B. TAYLORet aL

symmetry axes a n d the spin axis are d e t e r m i n e d b y the intrinsic structure o f the nucleus, the two effects are related. N o a t t e m p t was m a d e to incorporate n u c l e a r d e f o r m a t i o n i n this work, a n d the relative i m p o r t a n c e o f the d e f o r m a t i o n a n d I • l coupling was n o t assessed. The authors are i n d e b t e d to Dr. D. R o b s o n , K . A. Snover a n d W. S. T h o m p s o n for writing the spin ½ optical m o d e l p r o g r a m a n d to Dr. R o b s o n for his p e r t u r b a t i o n calculations o n the nuclear spin orbit potential. One o f the a u t h o r s (R. B. T a y l o r ) wishes to t h a n k the U n i t e d States E d u c a t i o n a l F o u n d a t i o n for a F u l b r i g h t Scholarship.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) II) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22)

B. T. Lueas, S. W. Cosper and O. E. Johnson, Phys. Rev. 133 (1964) B 963 G. Gregoire and P. C. Macq., Phys Lett. 8 (1964) 328 R. G. Summers-Gill, Phys. Rev. 109 (1958) 1591 J. S. Blair, Phys. Rex,. 108 (1957) 827 L. Rosen, Proc. Kingston Conference (University of Toronto Press, 1960) p. 185 F. C. Percy, Phys. Rev. 131 (1963) 745 K. K. Seth, Nuclear Physics 24 (1961) 169 D. Robson, private communication P. E. Hodgson, The optical model of elastic scattering (Oxford University Press, 1963) p. 58 E. J. Feldl, P. B. Weiss and R. H. Davis, Nucl. Instr. 28 0964) 309 J. W. Nelson, H. S. Plendl and R. H. Davis, Phys. Rev. 125 (1962) 2005 E. B. Carter, G. E. Mitchell, and R. H. Davis, Phys. Rev. 133 (1964) B 1421 M. K. Mehta, W. E. Hunt and R. H. Davis, Plays Rev., to be submitted H. R. Blieden and G. M. Temmer, Proc. Padua Conf. (Gorden and Breach, New York, 1963) p. 155 S. W. Rasmussen, Phys. Rev. 103 (1956) 186 G. lgo and R. M. Thaler, Phys. Rev. 106 (1957) 126 N. S. Wall, I. R. Rees and K. W. Ford, Phys. Rev. 97 (1955) 726 D. Robson, W. J. Thompson and K. A. Snorer, private communication ref. 9), p. 19 F. G. Percy, ORNL-3429, Oak Ridge National Laboratory Report J. B. Seaborn, G. E. Mitchell, N. R. Fletcher and R. H. Davis, Phys. Rev. 129 (1963) 2217 G. R. Satchler, Nuclear Physics 45 (1963) 197