The electric-dipole radiative capture reaction of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ by $\alpha$, leading to the ground and first excited states of ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$, is considered. The wave functions used are the result of a single-channel ${}_{}{}^3{}_{}{}^{}\mathrm{He}+\alpha$ resonating-group calculation which yields not only correct ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ separation energies in both of these ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ bound states, but also a satisfactory description of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}+\alpha$ scattering angular distributions in the low-energy region. As in our previous ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ charge-form-factor study, the present investigation is entirely microscopic and has the following important characteristics: (i) totally antisymmetric wave functions are used, (ii) the c.m. motion is correctly accounted for, (iii) bound-state and continuum wave functions are obtained in a unified manner, and (iv) the wave functions used have correct asymptotic behavior. With no adjustable parameters, it is found that quite reasonable agreement with experiment can be obtained. In particular, the behavior of the branching ratio is satisfactorily reproduced. The only discrepancy is that the calculated total capture cross section is about 20-30% too large, which is very likely related to the fact that, for simplicity, only the dominant ${}_{}{}^3{}_{}{}^{}\mathrm{He}+\alpha$ cluster configuration has been included in the calculation.

[NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{He}(\alpha ,\gamma )$, $E=0.1\mathrm{}-4.0$ MeV; calculated capture cross section and branching ratio with resonating-group wave functions.]

• Received 3 October 1980

DOI:https://doi.org/10.1103/PhysRevC.23.645