Novel approach to the removal of the Pauli-forbidden states in the orthogonality condition model: A case of multi-$\alpha$ systems

TL;DR

This paper introduces a new basis function approach based on the microscopic cluster model to efficiently and accurately remove Pauli-forbidden states in multi-cluster systems, demonstrated on the $^{12}$C nucleus.

Contribution

The authors develop an analytical basis function using correlated Gaussian functions for multi-cluster systems, improving computational efficiency and stability over traditional methods.

Findings

Significantly reduces the number of basis functions needed.

Includes small components of Pauli-forbidden states.

Enables simple discussion of the Hoyle state structure.

Abstract

We propose to use a basis function constructed based on the microscopic cluster model for an efficient description of multi-cluster systems with the orthogonality condition originating from the Pauli principle. The basis function is expressed analytically by a superposition of correlated Gaussian functions. We demonstrate the power of this approach by taking an example of a $3\alpha$ system, $^{12}$C. A comparison with the conventional pseudopotential method using the projection operator is made. The present method offers efficient and numerically stable computations as the number of basis functions is significantly reduced compared to the conventional method. We show that the present basis function includes reasonably small components of the Pauli-forbidden states, allowing us to discuss simply the structure of the first excited $0^+$ state, Hoyle state.