The structure of a vortex in low density neutron matter

A. Bulgac and Y. Yu

We have studied in a fully self consistent approach the structure of a vortex in low density superfluid neutron matter [8]. The fact that we were able to develop a theoretically consistent description of pairing correlations in nuclear systems allowed us to address this question in an unambiguous manner. It is fair to say that the quality of the description of the vortex structure is better than anything else available in literature so far. We determined that the matter density profile of a vortex shows a significant depletion in the region of the core, a feature never reported for a vortex state in a Fermi superfluid. The existence of a strong density depletion in the vortex core is going to affect appreciably the energetics of a neutron star crust. One can obtain a gross estimate of the pinning energy of a vortex on a nucleus as $E^V_{pin}=[\varepsilon(\rho_{out}) \rho_{out} - \varepsilon(\rho_{in}) \rho_{in}]V$, where $\varepsilon(\rho)$ is the energy per particle at density $\rho$, $\rho_{in}$ and $\rho_{out}$ are the densities inside and outside the vortex core and $V$ is the volume of the nucleus. Naturally, this simple formula does not take into account a number of factors, in particular surface effects and the changes in the velocity profile and the pairing field. However, if the density inside the vortex core and outside differ significantly one expects $E^V_{pin}$ to be the dominant contribution. In the low density region, where $\varepsilon(\rho_{out})\rho_{out}/\varepsilon(\rho_{in})\rho_{in}$ is largest, one expects a particularly large anti-pinning effect $(E^V_{pin}>0)$. The energy per unit length of a simple vortex is expected to be significantly lowered when compared with previous estimates by $\approx [\varepsilon(\rho_{out}) \rho_{out} - \varepsilon(\rho_{in}) \rho_{in}]\pi R^2$, where $R$ is an approximate core radius.