Finite-size effects and collective vibrations in the inner crust of neutron stars

Abstract

We study the linear response of the inner crust of neutron stars within the Random Phase Approximation, employing a Skyrme-type interaction as effective interaction. We adopt the Wigner-Seitz approximation, and consider a single unit cell of the Coulomb lattice which constitutes the inner crust, with a nucleus at its center, surrounded by a sea of free neutrons. With the use of an appropriate operator, it is possible to analyze in detail the properties of the vibrations of the surface of the nucleus and their interaction with the modes of the sea of free neutrons, and to investigate the role of shell effects and of resonant states.

Anderson-Bogoliubov phonons in the inner crust of neutron stars: Dipole excitation in a spherical Wigner-Seitz cell

“…These models have been applied extensively to explore equilibrium crust configurations and to study pairing properties and the heat capacity of the matter [11][12][13][28][29][30][31][32][33][34][35][36]. Collective excitation of inner crust matter has been studied also using the (quasiparticle) random phase approximation (RPA, QRPA) formulated on the ground of the HF/HFB models [24,[37][38][39][40]. However, the AB phonon mode in the inner crust has been investigated very little except in Ref.…”

“…We adopt the Wigner-Seitz approximation so that the calculation can be performed in a single spherical Wigner-Seitz cell. In contrast to the previous works along the same line [37][38][39][40], we pay special attention to the neutron pair correlation and we intend to reveal the properties of the AB phonon mode realized in the inner crust. As a first step of the study, we focus on the dipole excitation in the present paper since this multipolarity is responsible for the coupling to the the small amplitude displacement motion of the cluster, and hence to the lattice phonon degrees of freedom.…”

Pairing properties of the inner crust of neutron stars at finite temperature

“…The HFB (BCS ) equations are solved using a Skyrme zero range interaction, SLy4 [14], for the ph-channel, and a Gogny D1 interaction in its separable form [15,16] for the pp-channel. Higherorder pairing correlations are expected to play a role in WS cells, where the exchange of collective vibrations [17] lead to a suppression of the pairing gap [18]. This is clearly an important effect, but at present there is no clear method on how to include such effects in a consistent way in a mean-filed description.…”

Quantum size effects in the inner crust of neutron stars

“…It is found (see ref. [9]) that the strength evolves in a rather continuous fashion going from atomic nuclei into the inner crust. These results should be contrasted with those obtained making use of the operator r λ , which heavily weight the free neutron part of the cell.…”

“…Some calculations have used a density functional obtained interpolating between a functional adopted in neutron matter and a functional used in atomic nuclei [30]. Only exploratory calculations have directly addressed medium renormalization effects in the inner crust [31,32]. They have explicitly included the coupling with the vibrations of the systems in the WS cell (cf.…”