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11.6 Cooper pairing of neutrons

For temperatures T < Tcn, the free neutrons in the inner crust are superfluid (see Section 8). The elementary excitations in the superfluid neutron gas, denoted by ^n, 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,
^n + ^n − → νℓ + ¯νℓ, ℓ = e,μ, τ . (271 )
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 CP Qν from these processes is given by
CP 7 Qν ∝ T F (T ∕Tcn) , (272 )
where F (x ≥ 1) = 0 and F (x −→ 0) = 0. Detailed derivations and formulae can be found in [428Jump To The Next Citation Point].

The actual value of the numerical prefactor in Equation (272View Equation) has recently become a topic of lively discussion. Recent calculations have shown that previous results may severely overestimate QCP ν (see, e.g., [368Jump To The Next Citation Point245Jump To The Next Citation Point], and references therein). However, the actual reduction of CP Q ν is still a matter of debate.


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