Quantization of the kinetic energy of a deformed nucleus in curvilinear coordinates

TL;DR

This paper develops a new Hamiltonian formulation for the kinetic energy of deformed nuclei undergoing octupole oscillations, extending previous quadrupole models to include more complex nuclear surface deformations.

Contribution

It introduces a quantization method for the kinetic energy of deformed nuclei in curvilinear coordinates, specifically addressing octupole oscillations and providing explicit forms for various nuclear symmetries.

Findings

Derived a new Hamiltonian form for octupole oscillations

Extended previous quadrupole models to include octupole deformations

Provided explicit kinetic energy expressions for different nuclear symmetries

Abstract

The quantization of the kinetic energy of a deformed nucleus in curvilinear coordinates in the case of octupole oscillations of its surface firstly has been carried out. The obtained form of the Hamiltonian differs from the previously obtained Hamiltonian for quadrupole oscillations only by factors in front of the derivatives $\partial/\partial\gamma$ and $\partial/\partial\eta$. An explicit form of the kinetic energy of the Hamiltonian of even-even nuclei with free and effective triaxiality, as well as for axially symmetric even-even nuclei, is given.