# Laplace expansion method for the calculation of the reduced width amplitudes

## TL;DR

This paper introduces the Laplace expansion method, a new approach for calculating reduced width amplitudes in nuclear models with Gaussian wave packets, demonstrated through numerical examples involving specific nuclear cluster configurations.

## Contribution

The paper presents a novel Laplace expansion method for exact calculation of RWA in deformed and various-sized clusters within Gaussian wave packet models.

## Key findings

- Accurately calculates RWA without approximation.
- Applicable to deformed and various-sized clusters.
- Demonstrated on ${}^{20}{
m Ne}$ and ${}^{28}{
m Si}$ examples.

## Abstract

We derive the equations to calculate the reduced width amplitudes (RWA) of the different size clusters and deformed clusters without any approximation. These equations named Laplace expansion method are applicable to the nuclear models which uses the Gaussian wave packets. The advantage of the method is demonstrated by the numerical calculations of the ${}^{16}{\rm O}+\alpha$ and ${}^{24}{\rm Mg}+\alpha$ RWAs in $^{20}{\rm Ne}$ and $^{28}{\rm Si}$.