Superfluid and Finite-Temperature Extensions of Self-Consistent Band Theory for the Inner Crust of Neutron Stars

Neutron star is regarded as a very unique system with various physical properties of nuclear matter. In the inner area of “crust” of neutron stars, a Coulomb lattice of neutron-rich nuclei and uniform dripped neutrons coexist under the β equilibrium condition. At the bottom layer of inner crust, nuclei form diverse non-uniform crystalline structures, and are thought to provoke a very controversal phenomenon, called “entrainment effect”. The entrainment is characterized as the gain of effective masses of dripped neutrons, and it may disrupt the present interpretation of neutron stars’ astronomical phenomena, such as pulsar glitches.

For the comprehension of this phenomenon, self-consistent microscopic calculations combined with the band theory is strongly desired. This trend just started from 2005[1][2], and there is still a lot of room for progress and improvement.

In our research, we realized the Time-Dependent Density Functional Theory (TDDFT) extended for superfluid systems (TDSLDA) combined with the band theory, and calculations were performed for 1 dimensional (slab) crystalline structures, imposing β equilibrium condition[3]. In this presentation, we will first show the scheme and formulation of our calculations. We then discuss the results obtained for the slab phases and present possible progress towards further applications.

[1] B. Carter, N. Chamel, and P. Haensel, Nucl. Phys. A 748, 675 (2005)

[2] N. Chamel, Nucl. Phys. A 747, 109 (2005)

[3] K. Yoshimura and K. Sekizawa, arXiv:2306.03327