5,907 research outputs found
Finite size mean-field models
We characterize the two-site marginals of exchangeable states of a system of
quantum spins in terms of a simple positivity condition. This result is used in
two applications. We first show that the distance between two-site marginals of
permutation invariant states on N spins and exchangeable states is of order
1/N. The second application relates the mean ground state energy of a
mean-field model of composite spins interacting through a product pair
interaction with the mean ground state energies of the components.Comment: 20 page
Solitons in relativistic mean field models
Assuming that the nucleus can be treated as a perfect fluid we study the
conditions for the formation and propagation of Korteweg-de Vries (KdV)
solitons in nuclear matter. The KdV equation is obtained from the Euler and
continuity equations in nonrelativistic hydrodynamics. The existence of these
solitons depends on the nuclear equation of state, which, in our approach,
comes from well known relativistic mean field models. We reexamine early works
on nuclear solitons, replacing the old equations of state by new ones, based on
QHD and on its variants. Our analysis suggests that KdV solitons may indeed be
formed in the nucleus with a width which, in some cases, can be smaller than
one fermi.Comment: 15 pages, 1 figur
Pairing gaps from nuclear mean-field models
We discuss the pairing gap, a measure for nuclear pairing correlations, in
chains of spherical, semi-magic nuclei in the framework of self-consistent
nuclear mean-field models. The equations for the conventional BCS model and the
approximate projection-before-variation Lipkin-Nogami method are formulated in
terms of local density functionals for the effective interaction. We calculate
the Lipkin-Nogami corrections of both the mean-field energy and the pairing
energy. Various definitions of the pairing gap are discussed as three-point,
four-point and five-point mass-difference formulae, averaged matrix elements of
the pairing potential, and single-quasiparticle energies. Experimental values
for the pairing gap are compared with calculations employing both a delta
pairing force and a density-dependent delta interaction in the BCS and
Lipkin-Nogami model. Odd-mass nuclei are calculated in the spherical blocking
approximation which neglects part of the the core polarization in the odd
nucleus. We find that the five-point mass difference formula gives a very
robust description of the odd-even staggering, other approximations for the gap
may differ from that up to 30% for certain nuclei.Comment: 17 pages, 8 figures. Accepted for publication in EPJ
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