### 11.6 Cooper pairing of neutrons

For temperatures , the free neutrons in the inner crust are superfluid (see Section 8).
The elementary excitations in the superfluid neutron gas, denoted by , are fermions. They
have a specific energy spectrum, as discussed in Section 8.3.1. The elementary excitations are
called (Bogoliubov) quasiparticles. The simplest excitation in a superfluid is a quasiparticle pair.
Annihilation of a quasiparticle pair can go via an emission of a neutrino-antineutrino pair,
Such a process was first considered by Flowers et al. [148]. Neglecting for simplicity the presence of the
nuclear clusters and considering a uniform superfluid (see Section 8.2), the temperature dependence of the
neutrino emissivity from these processes is given by
where and . Detailed derivations and formulae can be found
in [428].
The actual value of the numerical prefactor in Equation (272) has recently become a topic of lively
discussion. Recent calculations have shown that previous results may severely overestimate (see, e.g.,
[368, 245], and references therein). However, the actual reduction of is still a matter of
debate.