Effective Free Energy for Solidification of Superfluid 4He Under Pressure

Effective free energy for the solidification of the superfluid 4 He under pressure is presented. Since this free energy is a function of two parameters, the density change (zeta)and the translational symmetry breaking parameter (eta), it is expected to describe over both the superfluid phase and the solid phase. The experimentally established values below and equal to the melting pressure Pm are successfully reproducible by the free energy. For P>Pm, where the superfluid is metastable, the free energy predicts that the instability for (eta) should occur first and then (zeta) accompanies. That is, (eta)-nucleation is essential for the solid nucleation in the superfluid 4 He.