# Correlated-Gaussian approach to linear-chain states -Case of four $\alpha$-particles-

## TL;DR

This paper demonstrates that correlated Gaussian basis functions effectively model linear-chain states of four alpha particles, revealing specific rotational states and deformation parameters through analytical calculations.

## Contribution

It introduces a novel application of correlated Gaussians with angular momentum and parity to study linear-chain alpha states, providing analytical evaluation of matrix elements.

## Key findings

- Possible chain states for J=0+, 2+, 4+, 6+ with energies around 33 MeV from ground state.
- No chain states with J≥8 found.
- Quadrupole deformation parameters increase with spin from 0.59 to 1.07.

## Abstract

We show that correlated Gaussians with good angular momentum and parity provide flexible basis functions for specific elongated shape. As its application we study linear-chain states of four-alpha particles in variation-after-projection calculations in which all the matrix elements are evaluated analytically. We find possible chain states for $J=0^+$, $2^+$, $4^+$ and perhaps $6^+$ with the bandhead energy being about 33 MeV from the ground state of $^{16}$O. No chain states with $J\geq 8$ are found. The nature of the rotational sequence of the chain states is clarified in contrast to a rigid-body rotation. The quadrupole deformation parameters estimated from the chain states increase from 0.59 to 1.07 for $2^+$ to $6^+$. This work suggests undeveloped fields for the correlated Gaussians beyond those problems which have hitherto been solved successfully.