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

Extended Skyrme interaction in the spin channel
IPNO Participation: J. Margueron, M. Grasso
Collaboration : Institut d'Astronomie et d'Astrophysique de Bruxelles, Dipartimento di Fisica Università
di Milano, University of Aizu-Wakamatsu.
Les interactions de type Skyrme prédisent une phase ferromagnétique au-delà de la densité de saturation
de la matière nucléaire (Fig. 1), ce qui est contraire aux prédictions de modèles ab-initio. Ce désaccord
limite l’utilisation des forces de Skyrme pour prédire les propriétés des étoiles à neutrons. Nous proposons
donc une correction des interactions de type Skyrme pour reproduire les résultats ab-initio (1). En outre,
l’analyse des propriétés de la matière permet de définir des restrictions sur les paramètres du nouveau terme.
Dans les noyaux impairs, nous proposons une approximation pour extraire la densité de spin (OSPA)
qui fourni une estimation maximale de l’effet de ce nouveau terme (2). Nous montrons que ce nouveau terme
a un effet très modéré. En conclusion, la correction que nous proposons modifie très peu les états fondamentaux
des noyaux impairs, mais a un impact beaucoup plus important sur l’interaction résiduelle particule-trou.
Cette dernière peut donc être ajustée sur les modes collectifs de spin.
Despite many theoretical and experimental investigations,
the spin and the spin-isospin channels in
either the ground and the excited states of nuclei
are still widely open for future study. Since the
ground states of nuclei are non spin-polarized in
the case of even-even nuclei and weakly spinpolarized
in odd nuclei, it is indeed difficult to probe
the spin and the spin-isospin channels of the nuclear
interaction. Dense matter in neutron stars
could however give some global constraints. For
instance the ferromagnetic phase predicted by all
the Skyrme interactions beyond the saturation density
0 (see Fig.1) might not be realistic.
A modification of the standard Skyrme interaction
has therefore been proposed such that the ferromagnetic
instability is removed (1). Being added in
perturbation on top of existing forces, the new term
retains the simplicity and the good properties of
0
Fig.1: Ferromagnetic phase diagram for various Skyrme
forces (BSk16: diamond, RATP: down-triangle, SkMS: lefttriangle,
SLy5: circle, SGII: up-triangle, LNS: square) The
horizontal axis shows the critical density at which the asymmetric
matter becomes unstable while the vertical axis
shows the proton fraction. On the l.h.s., matter is not polarized
while on the r.h.s., matter is made of domains where
spin are aligned.
original Skyrme force for nuclear matter and the
ground states of even-even nuclei. From the analysis
of the properties of nuclear matter, restrictions
on the parameters governing the new term could
be obtained (2).
We have also studied the effects of the new term
on the ground state properties of odd nuclei, in
particular the total binding energy and the density
distribution (2). To provide an approximate maximal
estimate of the effects while keeping our model
simple, we have performed HF calculations
and we introduced the one-spin polarized approximation
(OSPA): we use the equal filling approximation,
so that the time-reversal symmetry is not
broken, but to get the spin density we assumed for
the last occupied state that the spin-up state is
completely filled while the spin-down state is empty
between the two possible spin orientations (or,
equivalently, the opposite). The OSPA is therefore
an approximation which overestimate the spin density,
and therefore the effect of the new term. However,
from the OSPA we have shown that the
new term has only a negligible contribution to the
ground-state of odd nuclei (few tens of KeV).
We conclude that with an extended Skyrme interaction
including the new term that we propose (1),
the binding energies and the mean field of odd nuclei
remains nearly unchanged but the residual
particle-hole interaction could be tuned with a large
flexibility (2).
References:
(1) J. Margueron and H. Sagawa, J. Phys. G: Nucl.
Part. Phys. 36, 125102 (2009).
(2) J. Margueron J., S. Goriely, M. Grasso, G. Colo,
H. Sagawa, J. Phys. G: Nucl. Part. Phys. 36,
125103 (2009).
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