Abstract
We develop a Dirac-Hartree-Fock-Bogoliubov description of nuclear matter pairing in ¹S0 and ³S¹-³ D¹ channels. Here we investigate the density dependence ot the ¹S0 and ³S¹-³ D¹ pairing fields in asymmetric nuclear matter, using a Bonn meson-exchange interaction between Dirac nucleons. In this work, we present preliminary results.
A Dirac description of 1S0+3 S13 D1 pairing in nuclear matter
B. Funke Haas; B. V. Carlson; Tobias Frederico
Departamento de Física, Instituto Tecnológico de Aeronáutica 12228-901, São José dos Campos, SP, Brazil
ABSTRACT
We develop a Dirac-Hartree-Fock-Bogoliubov description of nuclear matter pairing in 1S0 and 3S13D1 channels. Here we investigate the density dependence ot the 1S0 and 3S13D1 pairing fields in asymmetric nuclear matter, using a Bonn meson-exchange interaction between Dirac nucleons. In this work, we present preliminary results.
1 Introduction
Nonrelativistic calculations of 1S0 + 3S13D1 in symmetric nuclear matter, using standard nucleon-nucleon interactions, yeald a 1S0 pairing gap of about the expected size, but an extremely large pairing gap, of the order of 10 MeV, in the 3S13D1 channel [1, 2, 3, 4, 5]. It has been suggested that relativistic effects substantially reduce this pairing gap [6], as is the case for 1S0 pairing at densities near saturation [7]. However, the size of the pairing gap has also been found to be related to the energy of the virtual/bound state in the vacuum of the channel under consideration [7]. This would imply a much larger pairing gap in the 3S13D1 channel, corresponding to the deuteron in the vacuum, than that in the 1S0 channel, which corresponds to the two-nucleon virtual state in the vacuum.
2 The Formalism
We take the hamiltonian form of the HFB equation to be
where
and
with
The index n denotes the 16 solutions to the HFB equation.
The self-consistency equations may be written as
and
where the index j refers to the different mesons exchanged and the indices a and b are their Lorentz/isospin indices. The normal and anomalous densities, g(q) and f(q) , respectively, are given by
with the sum over n running over the appropriate set of solutions of the HFB equation.
We take for the Dirac and isospin structure of the mean fields
and
where the rank two tensor Y2() is given by
The densities can be decomposed similarly, where the component densities can be obtained with the appropriate traces,
The vertices and propagators of the mesons are given in Table 1, where we have defined
We will neglect retardation effects in the following so that the composite form-factor/reduced propagator will take the form
We will denote the remaining factors of the vertices as the bare vertices.
To obtain the reduced self-consistency equations, we substitute these decompositions in the unreduced equations, calculate and take traces. The equations for the components of 1S0 pairing field that result are uncoupled integral equations of the form
The equations for the l = 0 and l = 2 components of 3S13D1 pairing field reduce to coupled equations. To uncouple these further, we make an additional approximation - we replace the components of the mean field and pairing field by their (spherically symmetric) angular averages.
3 Results and Conclusions
In Figs. 1 and 2 we show the pairing gap for the pp and nn pairs as a function of asymmetry and density, calculated numerically for pure standard pairing in nuclear matter. In Figs. 3 to 5, we show pp, nn and quasi-deuteron pairings gaps for standard plus quasi-deuteron pairing. We have found that pairing in these two channels coexists in asymmetric nuclear matter. This mixed state is the ground state of nuclear matter in the region in which it exists.
Received on 7 October, 2003
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Publication Dates
-
Publication in this collection
26 Oct 2004 -
Date of issue
Sept 2004
History
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Accepted
07 Oct 2003 -
Received
07 Oct 2003