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

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.

5 pages

References in corpus (4)

• Spin Hall Effect
• Production of spin-controlled rare isotope beams
• Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling: I. Kinetic equation and anomalous Hall and spin-Hall effects
• Comment on "Dynamics of nuclear fluid. VIII. Time-dependent Hartree-Fock approximation from a classical point of view"

Cited by in corpus (8)

• Extended Skyrme interactions for transport model simulations of heavy-ion collisions
• Simulating chiral anomalies with spin dynamics
• Nucleon spin polarization in intermediate-energy heavy-ion collisions
• Spin dynamics in intermediate-energy heavy-ion collisions with rigorous angular momentum conservation
• Simulating spin dynamics with spin-dependent cross sections in heavy-ion collisions
• Probing properties of nuclear spin-orbit interaction with nucleon spin polarization in intermediate-energy heavy-ion collisions
• Origins and Impacts of High-Density Symmetry Energy
• Is nucleon spin thermalized in intermediate-energy heavy-ion collisions?