# Large-amplitude quadrupole shape mixing probed by the $(p,p^\prime)$ reaction : a model analysis

## TL;DR

This paper investigates large-amplitude quadrupole shape mixing in nuclei using a collective model and microscopic coupled-channel calculations to analyze proton scattering, highlighting the significance of shape mixing in inelastic cross sections.

## Contribution

It introduces a simple five-dimensional quadrupole collective Hamiltonian model to simulate shape phase transitions and assess their impact on proton scattering observables.

## Key findings

- Large-amplitude shape mixing influences inelastic scattering cross sections.
- The inelastic cross section of the 2_2^+ state indicates quadrupole shape mixing.
- Model results suggest shape softness affects scattering outcomes.

## Abstract

To discuss a possible observation of large-amplitude nuclear shape mixing by nuclear reaction, we employ a simple collective model and evaluate transition densities, with which the differential cross sections are obtained through the microscopic coupled-channel calculation. Assuming the spherical-to-prolate shape transition, we focus on large-amplitude shape mixing associated with the softness of the collective potential in the $\beta$ direction. We introduce a simple model based on the five-dimensional quadrupole collective Hamiltonian, which simulates a chain of isotopes that exhibit spherical-to-prolate shape phase transition. Taking $^{154}$Sm as an example and controlling the model parameters, we study how the large-amplitude shape mixing affects the elastic and inelastic proton scatterings. The calculated results suggest that the inelastic cross section of the $2_2^+$ state tells us an important role of the quadrupole shape mixing.