Abstract
We apply the hyperspherical method to the -body Schrödinger equation and solve for the bound states of with the center of mass motion correctly treated. It is shown how to construct antisymmetric hyperharmonic polynomials of definite , , , and from Slater determinants with shell model coordinates. A set of coupled one dimensional differential equations are obtained and solved in approximation. A super-soft- core potential that provides a good fit to the two-nucleon scattering phase shifts is given a slight state dependence and is used for the two-nucleon potential. The proper handling of the potential energy matrix element with the center of mass motion excluded is detailed. A prescription for obtaining effective interactions for shell model calculations is presented. The difference in the potential energy matrix element of four nucleons in a nucleus or in a nucleus is shown not to be zero. A , state of is calculated to have a binding energy of 15.245 MeV. This state may resemble a nuclear molecule of and .
NUCLEAR STRUCTURE Many-body problem, hyperspherical method, bound states.
- Received 3 February 1978
DOI:https://doi.org/10.1103/PhysRevC.18.2395
©1978 American Physical Society