Collective model for cluster motion in $^8$Be, $^{12}$C, and $^{16}$O systems

TL;DR

This paper develops a collective model for cluster motion in light nuclei like $^8$Be, $^{12}$C, and $^{16}$O, based on microscopic calculations, to better understand their excited states and dynamics.

Contribution

It introduces a novel collective model incorporating microscopic inputs and dynamical effects to describe cluster motion in light nuclei.

Findings

The collective model reproduces energies and radii accurately.

It captures large-amplitude cluster excitations.

The model aligns well with microscopic generator coordinate method results.

Abstract

A microscopic $n\alpha$ cluster model was applied to $^{8}$Be, $^{12}$C, and $^{16}$O systems to investigate cluster motion in the ground state and radial excitation. In the microscopic calculation of $^{12}$C and $^{16}$O using the generator coordinate method with the coordinate $D$ of the $\alpha$-$\alpha$ distance, excited states were obtained as the large-amplitude mode built on the ground state. A collective model was constructed to describe the cluster motion of these states by utilizing inputs from the microscopic cluster model such as the norm kernel and energy expectation values. Furthermore, the cluster model was extended by introducing the imaginary part of the coordinate $D$ to incorporate the dynamical effects on the collective mass. The collective wave function obtained with the collective model was found to be in reasonable agreement with the results of the generator coordinate method for energies, root-mean-square radii, and amplitude functions.