Description of Collective Motion in Two-Dimensional Nuclei; Tomonaga's Method Revisited

TL;DR

This paper revisits Tomonaga's theory of collective motion in two-dimensional nuclei, providing exact canonical variables and analyzing the structure of the collective subspace with subsidiary conditions.

Contribution

It introduces exact canonical conjugate momenta for quadrupole-type collective coordinates and studies the structure of the collective subspace under subsidiary conditions.

Findings

Derived exact canonical variables for collective coordinates.

Analyzed the structure of the collective subspace.

Revisited and extended Tomonaga's original theory.

Abstract

Four decades ago, Tomonaga proposed the elementary theory of quantum mechanical collective motion of two-dimensional nuclei of N nucleons. The theory is based essentially on the neglect of 1/sqrtN against unity. Very recently we have given exact canonically conjugate momenta to quadrupole-type collective coordinates under some subsidiary conditions and have derived nuclear quadrupole-type collective Hamiltonian. Even in the case of simple two-dimensional nuclei, we have a subsidiary condition to obtain exact canonical variables. Particularly the structure of the collective subspace satisfying the subsidiary condition is studied in detail. This subsidiary condition is important to investigate what is a structure of the collective subspace.