Study ofα+dandα+d*Systems with the Resonating-Group Method

Abstract

The resonating-group method with a one-channel approximation is used to examine the $\alpha +d$ elastic scattering and bound-state problems. The nucleon-nucleon potential employed is the same as that used in previous resonating-group calculations and fits the low-energy scattering data satisfactorily. The deuteron wave function, which is given by a sum of two Gaussian functions, yields nearly correct values for the binding energy and the rms radius. For the bound and resonant states in ${\mathrm{Li}}^6$, it is shown that a careful consideration of the distortion effect on the deuteron cluster is essential. The calculated excitation energy of the ${}_{}{}^3{}_{}{}^{}D$ level is 4.6 MeV, which is rather close to the value of 3.8 MeV obtained by averaging the excitation energies of the experimentally found ${}_{}{}^3{}_{}{}^{}D_3^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}D_2^{}{}_{}{}^{}$, and ${}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ levels. Phase shifts are calculated in the energy region of 0-20 MeV and, in general, they agree quite well with those determined phenomenologically. In particular, the result shows that in the excitation region below 10 MeV, the $P$-wave phase shifts are small and show no resonance behavior. The $T=1\mathrm{}$ levels in the isobaric triad ${\mathrm{He}}^6$, ${\mathrm{Li}}^6$, and ${\mathrm{Be}}^6$, which have predominantly a structure of an $\alpha$ cluster plus a two-nucleon cluster in a ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ configuration ($d^{*}$ cluster), have also been studied. Here it is found that with a two-Gaussian function for the $d^{*}$ cluster, the calculated energy spacings between the ${}_{}{}^1{}_{}{}^{}S$ and the ${}_{}{}^1{}_{}{}^{}D$ levels are too large by about 1 MeV.