Gaussian Overlap Approxomation for the quadrupole collective states

TL;DR

This paper applies the Gaussian Overlap Approximation within the Generator Coordinate Method to derive a differential form of the Bohr Hamiltonian for nuclear quadrupole states, improving the understanding of collective nuclear motion.

Contribution

It introduces a method to derive the differential Bohr Hamiltonian from the GCM with GOA using the full five-dimensional quadrupole tensor as generator coordinates, reducing the Hill-Wheeler integral equation.

Findings

Derived a differential equation for the Bohr Hamiltonian from GCM with GOA.

Compared the derived Hamiltonian with the traditional approach, highlighting differences.

Showed that moments of inertia at quadrupole rotations align with Yoccoz's type.

Abstract

The Generator Coordinate Method (GCM) in the Gaussian Overlap Approximation (GOA) is applied to a description of the nuclear quadrupole collective states. The full five-dimensional quadrupole tensor is used as a set of the generator coordinates.The integral Hill-Wheeler equation is reduced to a differential equation by using the Fourier transforms of the overlap and energy kernels. The differential Bohr Hamiltonian obtained this way is compared with that derived by the usual approach to the collective Hamiltonian in the GOA which does contain an additional approximation. The method of calculating the quantities which determine the Bohr Hamiltonian from the set of deformation-dependent intrinsic states is demonstrated. In particular, it appears that the moments of inertia at the quadrupole rotations are of the type of that of Yoccoz.