Equations of motion of test particles for solving the spin-dependent Boltzmann-Vlasov equation

TL;DR

This paper derives equations of motion for test particles to solve the spin-dependent Boltzmann-Vlasov equation, providing a foundation for studying spin dynamics in heavy-ion collisions and related nuclear phenomena.

Contribution

It presents a consistent derivation of test particle equations of motion incorporating spin, aligning with quantum mechanics and enabling improved modeling of spin effects in nuclear collisions.

Findings

Derived EOMs similar to Hamiltonian dynamics

Separated EOMs for spin-up and spin-down nucleons

Identified key elements influencing spin dynamics

Abstract

A consistent derivation of the equations of motion (EOMs) of test particles for solving the spin-dependent Boltzmann-Vlasov equation is presented. The resulting EOMs in phase space are similar to the canonical equations in Hamiltonian dynamics, and the EOM of spin is the same as that in the Heisenburg picture of quantum mechanics. Considering further the quantum nature of spin and choosing the direction of total angular momentum in heavy-ion reactions as a reference of measuring nucleon spin, the EOMs of spin-up and spin-down nucleons are given separately. The key elements affecting the spin dynamics in heavy-ion collisions are identified. The resulting EOMs provide a solid foundation for using the test-particle approach in studying spin dynamics in heavy-ion collisions at intermediate energies. Future comparisons of model simulations with experimental data will help constrain the poorly known in-medium nucleon spin-orbit coupling relevant for understanding properties of rare isotopes and their astrophysical impacts.