Search for three alpha states around an $^{16}$O core in $^{28}$Si

TL;DR

This study explores the existence of gas-like three-alpha particle states around an oxygen-16 core in silicon-28, identifying specific excited states with large monopole strengths and radii indicative of a layer of loosely bound alpha particles.

Contribution

The paper introduces a multi-configuration cluster model combined with THSR wave functions to identify and characterize gas-like three-alpha states in $^{28}$Si, revealing their coexistence with traditional cluster states.

Findings

Identification of states with large overlap with THSR wave functions.

Observation of significant isoscalar monopole strengths.

Evidence of a layer of gas-like alpha particles around the $^{16}$O core.

Abstract

We investigate the existence of weakly coupled gas-like states comprised of three $\alpha$ particles around an $^{16}$O core in $^{28}$Si. We calculate the excited states in $^{28}$Si using the multi-configuration mixing method based on the $^{16}$O + 3$\alpha$ cluster model. We also include the $^{16}$O + $^{12}$C and $^{24}$Mg + $\alpha$ basis wave functions prepared by the generator coordinate method. To identify the gas-like states, we calculate the isoscalar monopole transition strengths and the overlap of the obtained states with the geometrical cluster wave function and the Tohsaki-Horiuchi-Schuck-R\"{o}pke (THSR) wave function. The results show that the obtained fourth and twelfth states significantly overlap with the THSR wave function. These two states clearly coexist with the $^{16}$O + $^{12}$C cluster states, emerging at similar energies. The calculated isoscalar monopole strengths between those two states are significantly large, indicating that the states are members of the excitation mode. Furthermore, the calculated root-mean-squared (RMS) radii for these states also suggest that a layer of gas-like three $\alpha$ particles could exist around the surface of the $^{16}$O core, which can be described as a "two-dimensional gas" in the intermediate state before the Hoyle-like three $\alpha$ states emerge.