Curvature effect on nuclear “pasta”: Is it helpful for gyroid appearance?

Abstract

In supernova cores and neutron star crusts, nuclei are thought to deform to rodlike and slablike shapes, which are often called nuclear pasta. We study the equilibrium properties of the nuclear pasta by using a liquid drop model with curvature corrections. It is confirmed that the curvature effect acts to lower the transition densities between different shapes. We also examine the gyroid structure, which was recently suggested as a different type of nuclear pasta by analogy with the polymer systems. The gyroid structure investigated in this paper is approximately formulated as an extension of the periodic minimal surface whose mean curvature vanishes. In contrast to our expectations, we find from the present approximate formulation that the curvature corrections act to slightly disfavor the appearance of the gyroid structure. By comparing the energy corrections in the gyroid phase and the hypothetical phases composed of d-dimensional spheres, where d is a general dimensionality, we show that the gyroid is unlikely to belong to a family of the generalized dimensional spheres.

Equations of state for supernovae and compact stars

“…(Baym, Bethe, and Pethick, 1971;Lattimer, 1981;Lamb et al, 1983;Ravenhall, Pethick, and Wilson, 1983;Lattimer and Swesty, 1991;Lorenz, Ravenhall, and Pethick, 1993;Watanabe, Iida, and Sato, 2000;Douchin and Haensel, 2001;Oyamatsu and Iida, 2007;Nakazato, Oyamatsu, and Yamada, 2009;Furusawa et al, 2011;Nakazato, Iida, and Oyamatsu, 2011;. They depend on the size of the heavy nucleus and the density of the surrounding gas of nucleons.…”

“Parking-garage” structures in nuclear astrophysics and cellular biophysics

“…The impact of such an A 1/3 term on nuclear pasta shapes was considered in ref. [11]. The curvature energy could be important for nuclear fission where a nucleus dramatically changes shape.…”

Topological characterization of neutron star crusts

“…More recently, shape characterizations were attempted both in dynamical simulations and with static models; the former use topological measures such as the Minkowski functionals and the Euler characteristics [23], while the latter modified the liquid drop model with a curvature correction to detect structure shape changes [28].…”