Mechanism of the Li7 (p, α) He4 reaction

r-l 2.A.l: 2.B

Nuclear Physics 44 (1963) 205-211; Not

to be reproduced

MECHANISM N. SARMA,

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OF THE Li’ (p, a) He4 REACTION K. S. JAYARAMAN

Atomic Energy

Establishment,

Received 18 February

and C. K. KUMAR Trombay, India

1963

The reaction Li’(p, cc)He4 has been investigated with a view to determine the contribution of direct interaction processes to the cross section. Excitation functions at angles 8,, = 60, 80, 100 and 150 degrees and the angular distributions at incident energies ED = 3.0, 3.5, 4.0, 4.5, 4.88, 5.0 and 5.5 MeV were measured. Resonant processes predominate in the reaction, and an analysis was made to determine the spins of the compound-nucleus states in Be” at 19.9 and 22.2 MeV.

Abstract:

1. Introduction

The reaction Li’(p, cr)He4 has been intensely studied during the last few years rd4). These investigations were made primarily to label the excited states of the compound nucleus Be’, which even at an excitation of about 20 MeV has level widths less than their spacing. There have been attempts to estimate the contribution from direct interaction processes to the cross section, but these have not been very successful. The target nucleus Li’ is predominantly in the cluster state, alpha + triton, with a binding energy of only 2.466 MeV, as against a separation energy of 1.25 MeV for the Li6 + nucleon cluster. The binding energies, ordering and spacing of the ground and excited states of Li’ have been calculated “) for the alpha + triton cluster model and the calculations have shown good agreement with experiment. The validity of the cluster model is also supported by a comparison of the reduced widths for the reactions H3(~, y)Li’ and Li6(n, y)Li’, which shows that the alpha + triton cluster predominates 6). The low binding energy of this cluster implies a large intercluster distance. These considerations predict a direct interaction process for the reaction Li’(p, cz)He4, particularly at energies large compared to the Coulomb barrier (1.8 MeV). The high Q-value for the reaction (17.35 MeV), on the other hand, requires the extraction of large momentum from the target wave function and so may work against the direct interaction process. 2. Experimental

Techniques

The apparatus and the instrumentation used for the determination of the differential cross section is shown in fig. 1. The angular-distribution chamber was a brass cylinder of internal diameter 36 cm 205

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THE LiT(p, or)Pie4 REACTION

207

and height 6 cm, sealed on both sides with O-ring gaskets by two flat plates 1.25 cm thick and of diameter 42 cm. Two observation ports, 2 cm in diameter, were located at 90 ° to the direction of the beam. The angle of observation was read on a circular scale outside the vacuum; it was changed by rotation of this scale. A vacuum interlock arrangement was provided, by which targets could be changed without breaking the vacuum in the chamber. Electrical connections to within the chamber were made using standard subminiature coaxial connectors modified as vacuum seals. The target was centred at the axis of a wheel, on whose periphery were mounted two semiconductor detectors of the diffused P-Si type. The detectors were 20 m m 2 in area, and their energy resolution was measured to be about 1 percent for 5.0-MeV alpha particles; these instruments were used to detect the alpha particles from the reaction. A second wheel, whose axis was coincident with the first, carried a third detector, which was used as a monitor in the experiment. The solid angle and circular angle subtended by the detectors at the target were 8.65 x l0 -4 sr and 1°, respectively. All three detectors were calibrated for energy and were checked for stability and linearity of response to energy in the desired energy region. Observations could be made from zero to almost 180 ° , but practical considerations limited the range of observation from 10° to 170 °. Pulses from the detectors were amplified by low-noise, charge-sensitive transistorized preamplifiers. The preamplifiers were mounted close to the detectors within the Scattering chamber. The output from the preamplifiers was fed through 6AC76AG7 amplifier-cathode followers to single-channel analysers and scalers. The detector bias voltage was adjusted to keep the proton pulse-height much lower than the pulseheight caused by the alphas. The targets were made by evaporating natural lithium metal onto self-supporting carbon films of thickness about 20 #g/cm 2. The target thickness was estimated by measuring the Coulomb scattering of protons in a forward direction at 2.0 MeV; the thickness used in the experiments was about 40 pg/cm z. The proton beam from the T r o m b a y 5.5-MeV Van de Graaff accelerator was collected in a Faraday cup after passing through the target. A ring negatively charged to 180 V provided electron suppression. The charge arriving at the Faraday cup was measured using a current integrator. The current integrator was calibrated and found to be accurate and stable to within 1 percent to a minimum current of 0.15 pA. Counts were taken at 10-degree intervals from 10° to 170 ° with each detector for a monitor count of 2500. This gave a statistical accuracy of about 3 percent in each reading. The error is reduced by the fact that each reading is repeated by a second detector, thereby reducing the error to about 2 percent at best. A further check was obtained because of the identity of the two reaction products; the angular distribution of the alpha particles must have fore-and-aft symmetry in centre-of-mass coordinates for an unpolarized beam. The readings at 90 ° were obtained by rotating the target through a small angle and normalizing the counts over an angular range to the rest of the angular distribution.

N. SARMAet al.

208

3. Results Excitation functions were taken for proton energy intervals of l0 keV. The results are shown in fig. 2 for laboratory angles of 60, 80, 100 and 150 degrees. The counts per 24/~C have been converted into absolute cross sections by estimating the target thickness and the solid angle subtended by the detectors. The differential cross sections measured at energies 3.0, 3.5, 4.0, 4.5, 5.0 and 5.5 MeV are shown in fig. 3. Only statistical errors are indicated. Systematic errors in the cross sections are esti-

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Fig. 2. Excitation functions for the LiT(p,~)He4 reaction. mated to be less than 5 percent. The total cross section for the reaction, calculated from the excitation function at 60 °, and the angular distributions are shown in fig. 4. The angular distributions were analysed in terms of a series of Legendre polynomials up to P8 (cos 0). Because of the identity of the two emergent particles in the reaction, odd polynomials do not exist. The coefficients of the even polynomials in the expansion 8

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as a function of energy, are shown in fig. 5.

THE Li?(p,

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209

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210

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Energy (MeV)

Fig. 5. Coefficients of the Legendre polynomials as a function of incident proton energy. 4. Discussion The excitation functions s h o w t w o resonances at energies Ep = 3.1 M e V and 5.6 M e V o f widths 800 k e V and about 600 keV, respectively. The identity o f the excitation curves at the four angles seems to indicate that there is little interference between the t w o resonances. Contribution f r o m non-resonant processes appears to be small, and it is estimated that the contribution to the total cross section is about 0.5 m b ,

THE LiT(p, ~.)He "t REACTION

211

as against the peak cross section for the 3.1 MeV resonance of 21 mb. There is no sign of any resonance at 4.9 MeV as reported by Macklin and Gibbons 7) in the measurement of the LiV(p, n) reaction. Coefficients of polynomials of order greater than P4(cos 0) are not statistically significant at the two resonances. The theorems governing the complexity of the angular distributions, therefore, indicate that both the compound nucleus states have J = 2 +. Angular distributions for this spin value, at energies of 3.1 and 5.6 MeV, were computed accordingly, taking into account the interference of p and f incident waves and admixtures of channel spins. For the 3.1 MeV resonance, E(Be 8) = 19.9 MeV, admixture of 33 percent channel s p i n - - 1 and 67 percent channel spin = 2 gives a good fit to the experimental data. A variation with energy of the admixture or the penetrability of the f waves could account for the local variation of A 2. There is no evidence for the very broad overlapping resonance of spin 0 ÷ or 2 + that has been proposed 1, 8). At 5.5 MeV, calculations give a reasonable agreement with experiment if the reaction is assumed to go entirely through channel spin = 2. The small cross section near 4.8 MeV indicates that the interference between the two resonances is small. In any case, interfering 2 + states will not give the observed large values of A 6 and A8; neither will there be such a sharp anomaly. For dispersion theory to explain the data, a narrow state of width 200 keV and spin J = 6 + is required. This is not observed in the LiV(p, n) or the LiV(p, 7) reactions nor in the LiV(p, ~)He 4 reaction. A direct interaction process, however, can give the observed distribution. Large amplitude resonances predominate the angular distribution at higher and lower energies and reduce the relative contribution of the higher order polynomials. Interference between the direct interaction and compound nucleus processes is possible, and this may account for the fluctuations in the coefficients of the P2(cos O) and P4 (cos O) terms. We are grateful to K. M. L. Jha for his assistance in the experiment and also to the operational staff of the Van de Graaff accelerator. We also thank Dr. R. Ramanna for his advice and Professor H. A. Enge, of the Massachusetts Institute of Technology, for several helpful discussions.

References 1) N. P. Heydenburg, C. M. Hudson, D. R. Inglis and D. Whitehead, Phys. Rev. 73 (1948) 241, 74 (1948) 405 2) F. L. Talbot, A. Busala and G. D. Weiffenbach, Phys. Rev. 82 (1951) 1 3) I. B. Teplov, I. S. Dmitriev, Ya. A. Teplova and O. P. Shevchenko, JETP (Soviet Physics) 15 (1962) 243 4) Y. Cassagnou, J. M. F. Jeronymo, G. S Mani and F. Sadeghi, Nuclear Physics 33 (1962) 499 5) R. K. Sheline and K. Wildermuth, Nuclear Physics 21 (1960) 196 6) T. A. Tombrello asad G. C. Phillips, Phys. Rev. 122 (1961) 224 G. C. Phillips and T. A. Tombrello, Nuclear Physics 19 (1960) 555 7) J. H. Macklin and R. L. Gibbons, Phys. Rev. 114 (1959) 571 8) R. F. Christy and S. Rubin, Phys. Rev. 71 (1947) 275A