# Kinetic energy in the collective quadrupole Hamiltonian from the experimental data

## TL;DR

This paper investigates how the kinetic energy term in the collective quadrupole Hamiltonian, especially the fourth order in collective momentum, significantly affects nuclear excitation energies and quadrupole matrix elements, emphasizing the need for detailed experimental data.

## Contribution

It demonstrates the impact of fourth order collective momentum terms on nuclear models and highlights the importance of comprehensive experimental quadrupole matrix element data.

## Key findings

- Fourth order momentum terms significantly affect excitation energies.
- Results are sensitive to quadrupole matrix element values.
- Experimental data on low-lying states are crucial for accurate modeling.

## Abstract

Dependence of the kinetic energy term of the collective nuclear Hamiltonian on collective momentum is considered. It is shown that the fourth order in collective momentum term of the collective quadrupole Hamiltonian generates a sizable effect on the excitation energies and the matrix elements of the quadrupole moment operator. It is demonstrated that the results of calculation are sensitive to the values of some matrix elements of the quadrupole moment. It stresses the importance for a concrete nucleus to have the experimental data for the reduced matrix elements of the quadrupole moment operator taken between all low lying states with the angular momenta not exceeding 4.