Stars as Laboratories for Fundamental Physics - MPP Theory Group

Processes in a Nuclear Medium 153
reactions after a casino in Rio de Janeiro. It must have been as easy
to lose money there as it is to lose energy in reactions which produce a
neutrino whether the electron is in the initial or final state.
Fig. 4.11. The URCA processes. For the modified versions, there are obvious
other graphs with the leptons attached to other nucleon lines, and exchange
amplitudes.
However, in a neutron star the direct URCA processes can be highly
suppressed by energy-momentum conservation. Because all participating
degenerate fermions are close to their Fermi surface one must require
p F,p + p F,e > p F,n . Because the proton and electron concentration
is small in a neutron star, it was thought that this “triangle condition”
could not be satisfied. However, the equilibrium proton concentration
depends on details of the equation of state—even in a naive model with
free fermions it is a sensitive function of the effective nucleon mass (Appendix
D). Therefore, it is conceivable that the direct URCA processes
actually do take place in neutron stars (Boguta 1981; Lattimer et al.
1991), in which case they provide a cooling mechanism much faster
than all other proposed possibilities.
If the triangle condition is fulfilled, the energy-loss rate is (Lattimer
et al. 1991)
Q URCA = 457π
10080 G2 F cos 2 θ C (1 + 3C 2 A) m 2 N p F,e T 6 , (4.76)
where θ C ≈ 0.24 is the Cabbibo angle and C A is the charged-current
axial-vector constant which is −1.26 in vacuum while in nuclear matter
it is suppressed somewhat (Appendix B).