The dynamics of systems composed of a classical sector plus a quantum sector is studied. We show that, even in the simplest cases, (i) the existence of a consistent canonical description for such mixed systems is incompatible with very basic requirements related to the time evolution of the two sectors when they are decoupled. (ii) The classical sector cannot inherit quantum fluctuations from the quantum sector. And, (iii) a coupling among the two sectors is incompatible with the requirement of physical positivity of the theory, i.e., there would be positive observables with a non positive expectation value.
We present the first calculation of theh 4 -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 some apparent divergencies at the classical turning points. As a byproduct we obtain theh 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 theh 4 corrections are much smaller than typical shell effects. Our results provide convincing arguments to neglect higher than second orderh effects in the Wigner-Kirkwood scheme to relativistic nuclear physics in the mean field approximation.
We fit the 1 S 0 ΛΛ interaction in the nuclear medium to the masses of the experimentally known double−Λ hypernuclei: 6 ΛΛ He, 10 ΛΛ Be and 13 ΛΛ B. We derive this effective interaction from OBE Jülich ΛΛ-type potentials and using both HartreeFock and variational approaches. We find that the inclusion of ΛΛ correlations in the variational scheme leads to significant differences and a better understanding of the dynamical features of the system. We investigate the sensitivity of the binding energies and the mesonic decay widths of the above double−Λ hypernuclei to the ωΛΛ coupling and the form factor at the σΛΛ vertex. We also use this effective interaction to predict binding energies and pionic decay widths of heavier double−Λ hypernuclei, not discovered yet. Finally, we discard the existence of 1 S 0 ΛΛ bound states provided the ΛΛ − ΞN coupling can be neglected.
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