where R\ and R2 are the classical turning points at which G(R) = G*. The integral over G* can be evaluated using the saddle point approximation.
The expressions for W are simplified in the thermal and quantum regimes. These regimes are separated by a characteristic temperature Tq , which depends on P. At T » Tq the quantum tunneling is negligible and W = Gmax/kBT. On the contrary, at T ^ Tq the quantum tunneling dominates and W can be approximated by its T = 0 value which corresponds to G* = 0:
These ideas have been applied for describing the nucleation of exotic phases (pion condensate, kaon condensate, quark matter) in a supercompressed neutron star core. However, the neutron star matter is more complicated than liquid helium for which the original Lifshitz-Kagan theory was developed. Additional complications are introduced by the multicomponent structure of the matter, by the slowness of weak interaction processes, and by Coulomb interactions between charged particles.
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