Exotic nuclear rod formation induced by superfluid vortices in neutron star crusts

The inner crust of a neutron star consists of a lattice of nuclei, relativistic degenerate electrons, and a neutron superfluid. Since the star is rotating, there are a number of quantized vortices in the superfluid. Mochizuki & Izuyama pointed out that such vortex lines may induce nuclear matter rods along the vortex cores. The exotic nuclear structure is possible in a very limited region of the inner crust. However, the short nuclear rod can completely pin the vortex line and can be an origin of vortex accumulation. The accumulation goes on until the local Magnus force among the accumulated vortices reaches a critical magnitude for unpinning of the trapped vortices. The unpinning at this stage, which must be collective, leads to pulsar glitches. In this paper, we first reconsider the energetics of this vortex-induced nuclear matter rod given by Mochizuki & Izuyama. We present a picture in which the nuclear rod is constructed by successive captures of certain neighboring nuclei into the vortex core, and subsequent fusion reactions of the captured nuclei with those inside the vortex core. We found that the marginal region, where the induced nuclear rods are stable, is not trivial. As the next step, the possibility of nuclear rod formation should be warranted by dynamical analysis. The crucial part of the dynamics is the Coulomb potential barrier, which seems at first sight to prohibit fusion if one neglects the screening due to electrons. Then we also report our theoretical estimate of this Coulomb barrier, i.e., the energy increase when a nucleus deviates form its equilibrium site to the onset position of nuclear fusion. The screening of nuclear charge by the background electrons is accurately taken into consideration. We found that the Coulomb barrier against the rod formation is of the order of 1 MeV throughout the marginal region. The obtained barrier is only several times as large as the zero-point energy of the nuclei-forming crystalline lattice. This result suggests that pycnonuclear reactions for the rod formation are feasible.