The compressible liquid drop model with curvature included algebraically for the pasta phases in neutron stars

Abstract

In the compressible liquid drop model (CLDM), the curvature energy term has been included in many works in the literature, and its effects on the presence of pasta phases have also been extensively investigated. However, the analytical part of the inclusion used to cease once a 4-order algebraic equation for the optimized size of the nucleus was written. In this paper, an optimization is suggested to the analytical part of the solution of the CLDM equations. Solving analytically the 4-order algebraic equation proves to be helpful for a straightforward identification of the denied parameter ranges in which the CLDM has no real-root solutions. Using a particular nuclear force derived from the chiral effective field theory, I investigate effects on the ground state of the nucleus curvature. Surprisingly, the inclusion has lead to a significant modification of the range of baryon density in which the bubble phases are found, disfavoring the bubble phases from the ground state. This shows a strong difference between the predictions of the CLDM with the nucleus size obtained when including the curvature term and that obtained from the $w_{\mathrm{s}}=2w_{\mathrm{C}+\mathrm{L}}$ approximation. The importance of the curvature energy in the CLDM is linked with its ability to change qualitatively the ground state. This paper presents an analytical extension to the CLDM solution, which is ready to be used with any other nuclear model in the future, in order to optimize the inclusion of the nuclear curvature energy, and is not limited to one nuclear model.

Comments: 21 pages, 10 figures