Adiabatic hyperspherical approach to large-scale nuclear dynamics

Abstract

We formulate a fully microscopic approach to large-scale nuclear dynamics using a hyperradius as a collective coordinate. An adiabatic potential is defined by taking account of all possible configurations at a fixed hyperradius, and its hyperradius dependence plays a key role in governing the global nuclear motion. In order to go to larger systems beyond few-body systems, we suggest basis functions of a microscopic multicluster model, propose a method for calculating matrix elements of an adiabatic Hamiltonian with use of Fourier transforms, and test its effectiveness.

Correlated-Gaussian approach to linear-chain states: Case of four α particles

“…We examine the energy of the LC configuration with J π = L + (even L) by changing H or equivalently the root-mean-square (rms) radius. It is important to get a global change of the system's energy with respect to that key parameter [46,47]. …”

Computing an orthonormal basis of symmetric or antisymmetric hyperspherical harmonics

“…[15][16][17], antisymmetrical HH functions are obtained in terms of combinations of Slater determinants of the oscillator translation-invariant shell model. Recently, another approach has been developed where hyperspherical calculations are performed using correlated Gaussian basis functions constrained at fixed values of the hyperradius [18][19][20][21][22]. Alternatively, one can use directly the non-symmetrized HH basis, exploiting the fact that the exact eigenvectors of the Hamiltonian matrix belongs to well defined irreducible representations of the symmetric group.…”