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

Pygmy resonance and torus mode within Vlasov dynamics
IPNO Participation: M. Urban, P. Schuck
Dans des noyaux riches en neutrons, des modes collectifs qui n’ont pas d’équivalent dans des noyaux N=Z
apparaissent. Un exemple en est la resonance pygmée dans la réponse dipolaire électrique. Nous étudions
cette resonance dans le cadre de l’équation de Vlasov que nous résolvons par la méthode des pseudoparticules,
avec la fonctionelle d’énergie BCP (qui décrit les masses des noyaux stables et l’équation d’état de
la matière asymétrique) comme interaction. Nous obtenons des résultats très raisonnables pour la réponse
dipolaire. L’existance de la resonance pygmée est donc un phénomène générique qui ne depend pas de la
structure en couches des noyaux. En analysant le champ de vitesse correspondant, il semble que la resonance
pygmée n’est pas seulement une oscillation de la peau à neutrons contre le cœur N=Z, mais elle
ressemble beaucoup au mode toroïdal qui a été prédit comme mode isoscalaire aussi dans les noyaux
N=Z.
In neutron-rich nuclei, the rms radius of the neutrons
is larger than that of the protons. Hence, the
surface region of these nuclei consists mainly of
neutrons. The existence of this ‘’neutron skin’’
leads to the existence of new excitation modes. A
famous example for such a mode is the ’’pygmy
resonance’’.
In order to learn more about the character of this
mode, we study it in the framework of the semiclassical
Vlasov equation, which we solve numerically
employing the pseudo-particle method (as in
the simulation of heavy-ion collisions). The particles
propagate in a mean field which is calculated
from a slightly modified version of the so-called
BCP energy-density functional, which was fitted to
the masses of some finite nuclei and to Brückner
calculations for symmetric and asymmetric nuclear
matter. The ground state is computed within the
Thomas-Fermi approximation in order to be
consistent with the Vlasov dynamics. We excite the
nucleus at t=0 and then let it evolve until the oscillation
is sufficiently damped. The response function
is obtained by calculating the Fourier transform
of the resulting time-dependent electric dipole
moment.
Results for the electric dipole response of different
tin isotopes are shown in Fig. 1. The response is
dominated by the giant dipole resonance, but with
increasing neutron excess some strength at lower
energies builds up, which in the case of 132 Sn is
concentrated in a well localised peak at 8.6 MeV,
corresponding to the pygmy resonance. Although
our semiclassical theory does not take into account
any shell effects, the results for the electric dipole
response are in reasonable agreement with fully
quantum mechanical RPA calculations. We thus
conclude that the main features of the pygmy resonance
are independent of the shell structure of the
nucleus.
We also calculate the velocity fields of protons and
neutrons corresponding to the pygmy resonance
(see Fig. 2). We see that not only the neutron skin
is moving against the core, but the motion resembles
that of the isoscalar torus mode which was
predicted to exist even in N=Z nuclei.This confirms
a result obtained earlier for 208 Pb within a completely
different approach [Ryezayeva et al., Phys.
Rev. Lett. 89, 272502 (2002)].
Figure 1: electric dipole response of
different tin isotopes.
Figure 2: proton and neutron velocity
fields of the pygmy resonance in 132 Sn.
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