exotic nuclei structure and reaction noyaux exotiques ... - IPN - IN2P3

Pairing properties in nuclei and in neutron stars
IPNO Participation: J. Margueron, E. Khan
Collaboration : University of Aizu-Wakamatsu, Tohoku University, Institut d'Astronomie et d'Astrophysique
de Bruxelles, NIPNE Bucharest.
Les propriétés d’appariement des noyaux ainsi que des étoiles à neutrons sont étudiés dans des modèles
de champ moyen Hartree-Fock-Bogoliubov. Pour cela, nous proposons une interaction d’appariement de
portée nulle et dépendante de la densité, non-empirique (non-ajusté sur des noyaux), qui reproduit la longueur
de diffusion dans le canal 1 S 0 ainsi que les calculs ab-initio de gap dans la matière uniforme. Pour
reproduire à la fois la matière symétrique et la matière de neutrons, nous avons du introduire une dépendance
en isospin dans la force d’appariement. Nous discutons aussi les effets de polarisation du milieu audelà
du premier ordre BCS. D’une étude systématique sur des noyaux semi-magiques (chaines isotopiques
et isotoniques) nous avons montré que l’interaction d’appariement au premier ordre BCS reproduit très bien
les données expérimentales. Nous avons montré l’impact des différent modèles d’appariement sur le refroidissement
des étoiles à neutrons.
The pairing gap is an important quantity to understand
the cooling of neutron stars, as it modifies
the specific heat as well as neutrino emission processes
(1). It is also important to understand the
Glitches of neutron stars. A precise and well constrained
theory for pairing in neutron stars is thus
necessary.
Among these constrains are those given by nuclei.
In a marked contrast with electronic systems, the
nuclear interaction is already attractive in the first
order approximation (BCS). Nevertheless, it has
been shown that higher order contributions, such
that medium polarization, may lead to important
corrections to the nuclear interaction in the particle
-particle channel and therefore to the pairing gap in
uniform matter as well as in finite nuclei.
We have proposed an effective density-dependent
pairing interaction that reproduces both the neutron-neutron
scattering length in the 1 S 0 channel
and the neutron pairing gap in uniform matter (2).
In order to simultaneously describe the density
dependence of the neutron pairing gap for both
symmetric and neutron matter, it was necessary to
include an isospin dependence in the effective
pairing interaction. Depending on whether the medium
polarization effects on the pairing gap calculated
in Ref.(3) are taken into account or not, we
have proposed two different density dependences
in the pairing interaction (hereafter named Bare
and Induced). The comparison of the predictions of
these interactions with the odd-even mass staggering
(OEMS) in semi-magic nuclei is shown in Fig.1
(for isotopic chain) and Fig.2 (for isotonic chain).
The HFB calculations based on the IS+IV Bare
pairing force well account for the experimental
OEMS (similar comparison for the binding energy
and the two neutrons separation energy are shown
in Ref.(4)). This result suggests that a global nonempirical
pairing interaction depending on both the
IS and IV densities can be adjusted to be used for
a wide range of the nuclear chart. In contrast, the
IS Bare force, which is adjusted only in symmetric
matter, fails to correctly reproduce isotopic and
isotonic systematic, and the IS+IV induced pairing
force, which includes medium polarization, under
estimate the OESM.
In Ref.(4) it has also been shown, with the local
density approximation (LDA), that the pairing field
deduced from the pairing gaps in infinite matter
reproduces qualitatively well the pairing field for
finite nuclei obtained with the HFB method.
Despite the differences between finite nuclei and
neutron stars matter, self-consistent mean field
models could be extrapolated to infinite matter under
the extreme conditions realized in stars (1,5).
The crust of neutron stars is made of nuclear clusters
where the HFB model is applicable within the
Wigner-Seitz approximation. In Ref.(5), a comparison
between band theory and mean field approximation
has sheld light on the domain of application
of mean field models. A systematic calculation of
the neutron specific heat in the crust of neutron
stars has therefore been performed and has been
used in a model for the cooling of neutron stars (1).
The effects of the clusters are moderated, but nonnegligeable.
Larger effects induced by the pairing
force have been observed. These results motivate
the comparison of the different pairing interactions
in finite nuclei, such as in Ref.(4), with an improved
description of medium polarization.
References:
(1) M. Fortin, F. Grill, J. Margueron,and N. Sandulescu,
submitted to Phys. Rev. C,
ArXiv/0910.5488(nucl-th).
(2) J. Margueron, H. Sagawa, and K. Hagino,
Phys. Rev. C 76, 064316 (2007).
(3) L. G. Cao, U. Lombardo, and P. Schuck, Phys.
Rev. C 74, 064301 (2006).
(4) J. Margueron, H. Sagawa, and K. Hagino,
Phys. Rev. C 77, 054309 (2008).
(5) N. Chamel, J. Margueron, E. Khan, Phys. Rev.
C 79, 012801 (2009).
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