Semiclassical expansions up to }4-order in relativistic nuclear physics
نویسندگان
چکیده
We present the first calculation of the }4 Wigner–Kirkwood corrections to a relativistic system of fermions in the presence of external scalar and vector potentials. The method we propose allows the efficient computation of semiclassical corrections to one-body operators such as mean energies and local densities. It also preserves gauge invariance and produces explicitly convergent results despite some apparent divergences at the classical turning points. As a byproduct we obtain the }4 corrections stemming from the polarization of the Dirac sea. We apply our results to the relativistic σ–ω Lagrangian in the Hartree valence approximation. We compare the semiclassical expansion with the exact result and with the Strutinsky average whenever it can be obtained. We find that the }4 corrections are much smaller than typical shell effects. Our results provide convincing arguments for neglecting higher than second order } effects in the Wigner–Kirkwood scheme on relativistic nuclear physics in the mean field approximation.
منابع مشابه
SEMICLASSICAL EXPANSIONS UP TO h̄-ORDER IN RELATIVISTIC NUCLEAR PHYSICS
We present the first calculation of the h̄-Wigner–Kirkwood corrections to a relativistic system of fermions in the presence of external scalar and vector potentials. The method we propose allows to compute efficiently semiclassical corrections to one body operators such as mean energies and local densities. It also preserves gauge invariance and produces explicitly convergent results despite som...
متن کاملNuclear curvature energy in relativistic models.
The difficulties arising in the calculation of the nuclear curvature energy are analyzed in detail, especially with reference to relativistic models. It is underlined that the implicit dependence on curvature of the quantal wave functions is directly accessible only in a semiclassical framework. It is shown that also in the relativistic models quantal and semiclassical calculations of the curva...
متن کاملNuclear Mean Fields through Selfconsistent Semiclassical Calculations
Semiclassical expansions derived in the framework of the Extended ThomasFermi approach for the kinetic energy density τ(~r) and the spin-orbit density ~ J(~r) as functions of the local density ρ(~r) are used to determine the central nuclear potentials Vn(~r) and Vp(~r) of the neutron and proton distribution for effective interactions of the Skyrme type. We demonstrate that the convergence of th...
متن کاملExact Semiclassical Evolutions in Relativistic and Nonrelativistic Scalar Quantum Mechanics and Quantum Cosmology
The necessary and sufficient conditions for the exactness of the semiclassical approximation for the solution of the Schrödinger and Klein-Gordon equations are obtained. It is shown that the existence of an exact semiclassical solution of the Schrödinger equation determines both the semiclassical wave function and the interaction potential uniquely up to the choice of the boundary conditions. T...
متن کامل