$\alpha+\alpha+{}^{3}$He cluster structure in ${}^{11}$C

TL;DR

This study investigates the cluster structure of ${}^{11}$C using a microscopic model, revealing dilute gaslike states and potential linear chain configurations, with results aligning well with experimental spectra.

Contribution

It provides a detailed microscopic analysis of ${}^{11}$C's cluster states, identifying new gaslike and linear chain structures, and suggesting candidates for Hoyle-analog states.

Findings

Reproduces energy spectra for negative and positive parity states.

Identifies dilute gaslike cluster states near the threshold.

Suggests certain states as Hoyle-analog and linear chain structures.

Abstract

We study the $\alpha + \alpha + {}^{3}$He cluster structure of ${}^{11}$C within the microscopic cluster model. The calculations essentially reproduce the energy spectra for both negative and positive parity states, particularly the $3/2_3^-$ state near the $\alpha+\alpha$+${}^{3}$He threshold. We also calculate the isoscalar monopole, electric quadrupole transition strengths, and root-mean-square radii for the low-lying states. These results suggest that the $3/2_3^-$, $1/2_2^-$, and $5/2_3^-$ states have a well-developed $\alpha + \alpha$ + ${}^{3}$He cluster structure. The analysis of the generator coordinate method wave functions indicates the dilute gaslike nature for the $3/2_3^-$, $1/2_2^-$, and $5/2_3^-$ states, suggesting that they could be candidates for the Hoyle-analog state. Furthermore, it is found that the $5/2_2^+$ and $5/2_3^+$ states may possess a linear chain structure.