We have implemented a dynamical microscopic α+p+n model for the description of the ground state (g.s.) of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ in an attempt to achieve the perfection of macroscopic α+p+n three-body models. We use a generator-coordinate approach, which includes (pn)α,(αn)p, and (αp)n partitions with all angular-momentum components of any significance. The trial function is constructed out of 0s and a set of 0s,0p,0d harmonic-oscillator (h.o). eigenfunctions of the α intrinsic and of intercluster Jacobi coordinates, respectively, with the generator coordinates being the h.o. size parameters. The effective nucleon-nucleon force used contains tensor and spin-orbit terms. We have determined its parameters by fitting to the properties of the subsystems. We found that the description of the subsystems is less perfect than with central forces, and explained this by the inconsistency of the use of a tensor force with describing the α g.s. by 0s oscillator states. The binding of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ with this force was found to be about 1 MeV too weak. After readjusting the force to yield the correct energy, we calculated some properties of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$. The radius obtained is somewhat too large, and the tiny quadrupole moment has the wrong sign. The results for the weights of the components of summed nucleon spin and orbital momentum (S,L)=(1,0), (1,1), (1,2), and (0,1) are 94.6%, 0.2%, 3.9%, and 1.3%, respectively.

The (1,2) component comes predominantly from clusterization (pn)α; the others can be attributed to any of the highly overlapping partitions. The α+d and ${}_{}{}^5{}_{}{}^{}\mathrm{He}$+p spectroscopic factors were calculated with a new formula, which expresses them in the generator-coordinate basis directly, without resort to integral transformations. The estimates for the α+d spectroscopic factor, ∼0.9, are realistic, but those for ${}_{}{}^5{}_{}{}^{}\mathrm{He}$+p are a factor of 2 too high. This is understood to be a consequence of the model’s tendency to compress the low-energy continuum, which appears to be a general defect of forces that are constrained to reproduce the bulk properties of the α particle in terms of 0s states. Thus a radical remedy would require an improvement of the description of the cluster internal motion.

• Received 13 January 1992

DOI:https://doi.org/10.1103/PhysRevC.46.576