Role of the vacuum energy in the thermodynamics of neutron matter

The only way neutron matter can couple to the electromagnetic field is through an anomalous coupling, which plays an important role in the thermodynamics of pure neutron matter. Such theories are, however, perturbatively non-renormalizable, which presents a difficulty in terms of the unambiguous treatment of the divergencies in a perturbative approach. Here, we show that despite this, an unambiguous expression can be obtained for the vacuum energy contribution to the grand canonical potential in the case of a constant magnetic field. We find that this contribution is quite small, which justifies the no-sea approximation usually made. We also discuss the density and temperature dependence of the full grand canonical potential.

Figure 1

The unambiguous vacuum contribution to $\mathrm{\Omega }$ as a function of $x=\frac{gB}{m}$. We note that it is a very small contribution at typical values of $x\approx {10}^{-3}$.

Figure 2

(a) $\mathrm{\Omega }$ at zero temperature with and without vacuum corrections and at $\rho ={\rho }_s$ (solid and dashed lines) and $\rho =2{\rho }_s$ (dashed and dot-dashed lines). (b) Same as in (a), but now for $\beta =20$ fm. The vacuum corrections are not discernible on these graphs as they are very small.

Figure 3

(a) $\epsilon$ at zero temperature with and without vacuum corrections and at $\rho ={\rho }_s$ (solid and dashed lines) and $\rho =2{\rho }_s$ (dashed and dot-dashed lines). (b) Same as in (a), but now for $\beta =20$ fm. The vacuum corrections are not discernible on these graphs as they are very small.

Figure 4

$M$ as a function of the applied magnetic field $H$ at (a) zero temperature and $\rho =2{\rho }_s$ with (dashed line) and without (solid line) the vacuum energy contribution. (b) Same as in (a), but now for $\beta =20$ fm.

Figure 5

Longitudinal pressure without (solid line) and with (dashed line) the vacuum energy contribution as a function of the magnetic field. Also shown is the transverse pressure without (dotted line) and with (dot-dashed line) the vacuum energy contribution. (a) At zero temperature and (b) at $\beta =20$ fm with constant density $\rho =2{\rho }_s$.