Theory of the Superfluid-Solid Transition ofHe4

We investigate the pressure-induced superfluid-solid transition of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at $T=0\mathrm{}$. Neglecting the accidental instability against nucleation, we find a definite stability limit at which the superfluid phase becomes intrinsically unstable against a density fluctuation number $Q_L$. We find that the roton minimum with frequency $\omega \left(Q_L\right)$ is the soft mode associated with this stability limit. This interpretation reflects the observed pressure dependence both of the roton minimum and of the first maximum of the structure factor at $Q_L$.