Vibrational modes of light nuclei

Lorenzo Fortunato,Yang Sun

doi:10.1051/epjconf/201817802017

Abstract

A potential energy surface is constructed for various light nuclei, 3,4He with the Argonne V18 potential and then for alpha- conjugate nuclei like 12C,16O, 20Ne with α – α potentials. Despite the nucleons have large momenta and large fluctuations around the equilibrium points, the minimization suggests the underlying geometric structure. We calculate the Hessian matrix determining the normal modes of vibration. This approach might lead to a new way of fitting the alpha-alpha interactions on the spectroscopic data available for alpha-conjugate nuclei, rather than on scattering phase shift.

Highlights

Molecular models of nuclei are fundamentally dierent from models used in molecular physics, where the Born-Oppenheimer approximation is valid and one can think of nuclear motion as a small vibration, happening only close to the minimum of a very deep potential[1]
Energy Surface (PES, for short) is a large fraction of the well depth, there are large uctuations around the equilibrium points and we should not expect that the vibrational levels are deeply lying in the potential well as it happens in molecules
It is instructive to look at the normal modes, nd the best internal coordinates to express symmetry-adapted vibrational motio and calculate the energy scale and structure of the vibrational levels

Summary

Introduction

Molecular models of nuclei are fundamentally dierent from models used in molecular physics, where the Born-Oppenheimer approximation is valid and one can think of nuclear motion as a small vibration, happening only close to the minimum of a very deep potential (in molecular energy scales)[1]. Energy Surface (PES, for short) is a large fraction of the well depth, there are large uctuations around the equilibrium points and we should not expect that the vibrational levels are deeply lying in the potential well as it happens in molecules. At most they can be weakly bound states, close to threshold, or more probably resonances in the continuum. Despite this fact, it is instructive to look at the normal modes, nd the best internal coordinates to express symmetry-adapted vibrational motio and calculate the energy scale and structure of the vibrational levels

Light nuclei

Alpha-conjugate nuclei