Time-Dependent relativistic mean-field model

Relativistic mead field models which are based on the quantum hadrodynamics have been successfully applied in the description of various nuclear phenomena. In this work the time-dependent variant of relativistic mean-field theory (TDRMFT) is used in order to describe monopole giant resonances in spherical nuclei. In the TDRMFT[3] the nucleus is described as a system of Dirac nucleons which interact through exchange of virtual mesons and photons. The Lagrangian density of relativistic mean field model is

$${\cal L} = \bar\psi\left(i\gamma\cdot\partial-m\right)\psi ~+~\frac{1}{2}(\partial\sigma)^2-U(\sigma )$$

$$-~\frac{1}{4}\Omega_{\mu\nu}\Omega^{\mu\nu} +\frac{1}{2}m^2_\omeg... ...frac{1}{2}m^2_\rho\vec\rho^{\,2} ~-~\frac{1}{4}{\rm F}_{\mu\nu}{\rm F}^{\mu\nu}$$

$$-~g_\sigma\bar\psi\sigma\psi~-~ g_\omega\bar\psi\gamma\cdot\omega... ...a\cdot\vec\rho\vec\tau\psi~-~ e\bar\psi\gamma\cdot A \frac{(1-\tau_3)}{2}\psi\;$$ (1)

with notation corresponding to Ref.[3]. By using variational principle, we can derive Dirac equations for the nucleons, and Klein-Gordon equations for the meson fields[3]. In the mean-field approximation the meson degrees of freedom are described by classical fields which are defined by the nucleon densities and currents. The sources of the fields in the Klein-Gordon equations are calculated in the no-sea approximation [3]. Evolution of the system starts from the self-consistent ground state solution, with initial conditions which are defined to simulate excitations of giant resonances. The Dirac Hamiltonian depends on the nucleon densities and currents through the solutions of the Klein-Gordon equations. Therefore, equations of motion are nonlinear, and for a specific set of initial conditions, the nuclear system and corresponding collective variables could enter into chaotic regime [2].

Nils Paar, 1999.