ELSEVIER Nuclear Physics A73 1 (2004) 401-408 www.elsevier.comllocate/npe Excitation modes and pairing interaction in the inner crust of a neutron stars. G. Goriaatl, F. Ramponi a,b, F. Barranco ‘, R.A. Broglia a,b,d, G.L. Co16 B;b, D. Sarchi a.b and E. Vigezzi ” B Dipartimento di Fisica, Universit6 degli Studi di Milano, via Celoria 16, 20133, Milano, Italy “INFN, Sezione di Milano, via Celoria 16, 20133, Milano, Italy “Departamento de Fisica Aplicada III, Escuela Superior de Ingenieros, Camino de 10s Descubrimientos s/n, 41092 Seville, Spain. “The Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen 0, Denmark We perform a detailed calculation of the pairing properties of the inner crust of a neu- tron star. We focus on a specific density, and take into account the coexistence of a nuclear lattice with a superfluid gas of neutrons. The Hartree-Fock-Bogoliubov (HFB) equations are solved adding the matrix elements of the direct nucleon-nucleon interaction and those of the interaction induced by medium-polarization effects. The latter are obtained after a detailed calculation of the excited states of the system, within the random phase approxi- mation. It is concluded that for the density considered, polarization processes reduce the pairing gap of about a factor of 2. 1. THE INNER CRUST OF A NEUTRON STAR. In the interior of a neutron star there exists a region, the so called inner crust, where nuclei are placed at the vertices of a Coulomb lattice, in order to minimize the Coulomb repulsion. These nuclei are surrounded by a sea of free neutrons that, due to the low temperature (T M 0.1 MeV), are superfluid. The properties of this lattice were firstly investigated in detail by Negele and Vautherin [l]: they treated the lattice within the Wigner-Seitz method, namely they studied the properties of an elementary cell which represents the building block of the whole lattice. For different regions of the inner crust, each characterized by a given density, they determined the lattice step and the number of protons and neutrons in the elementary cell which minimize the energy of the system. The energy was calculated within the framework of the Hartree-Fock theory by using an effective interaction. Approaching the center of the star, the step of the lattice reduces while the density of free neutrons increases. The inner crust plays an important role in many models which try to connect the electromagnetic radiation emitted from neutron stars with their internal structure. One 0375-9474/$ - see front matter 0 2004 Published by Elsevier B.\! doi:10.1016/j.nuc1physa.2003.11.052