Nuclear Scissors with Pairing and Continuity Equation

TL;DR

This paper extends the Wigner Function Moments method to include pairing correlations, deriving equations of motion for nuclear collective modes like scissors and giant quadrupole resonances within a TDHFB framework.

Contribution

It introduces a generalized Wigner Function Moments approach that incorporates pairing and ensures the continuity equation, applied to nuclear collective excitations.

Findings

Derived equations of motion for collective variables with pairing.

Analyzed coupled dynamics of giant quadrupole and scissors modes.

Ensured the continuity equation in the extended model.

Abstract

The coupled dynamics of the isovector and isoscalar giant quadrupole resonances and low lying modes (including scissors) are studied with the help of the Wigner Function Moments (WFM) method generalized to take into account pair correlations. Equations of motion for collective variables are derived on the basis of the Time Dependent Hartree-Fock-Bogoliubov (TDHFB) equations in the harmonic oscillator model with quadrupole-quadrupole (QQ) residual interaction and a Gaussian pairing force. Special care is taken of the continuity equation.