How accurately can the Extended Thomas-Fermi method describe the inner crust of a neutron star?

Abstract

We perform a systematic comparison between the results obtained by solving fully self-consistently the Hartree-Fock-Bogoliubov equations, and those obtained using the semi-classical Extended Thomas-Fermi method, for various Wigner-Seitz cells within the inner crust of a neutron star. The lack of pairing correlations in the semi-classical approach leads to a large discrepancy between the two approaches. This discrepancy is well beyond the error of the quantum-mechanical calculation, and is related to spurious shell effects in the neutron gas.

Comparison between the Thomas–Fermi and Hartree–Fock–Bogoliubov Methods in the Inner Crust of a Neutron Star: The Role of Pairing Correlations

“…From ρ b = 0.013 fm −3 , when the neutron gas contribution starts to become more important, there is a remarkable agreement between the full HFB calculation and the ETFSI+pairing. This result confirms our previous hypothesis concerning the discrepancy observed between the two methods in reference [37]. At this density, the total energy difference between the two methods is less than 10 keV per particle.…”

“…The main reason for this disagreement is probably related to the properties of the functional used to perform the calculations. In previous work [37], we compared the structure of some WS cells performing both ETFSI and HFB calculations using the same functional. We observed an energy discrepancy far larger than the estimated error of the HFB method [29], and we identified the cause as a lack of neutron pairing correlations [38] in the ETFSI approach [35].…”

Analytical determination of the structure of the outer crust of a cold nonaccreted neutron star

“…An alternative approach, originally developed for finite nuclei [41] and later adapted to neutron-star crusts [42][43][44], is to employ the extended Thomas-Fermi method with consistent shell corrections added perturbatively. This semiclassical approach provides a fast and fairly accurate approximation of the Hartree-Fock-Bogoliubov equations [45], thus opening the door to systematic studies of neutron-star crusts, treating consistently both the outer and inner parts. I.…”