  The anharmonic soft modes studied in recent numerical work in the glass phase
of simple liquids have an unstable core, stabilized by the positive restoring
forces of the surrounding elastic medium. The present paper formulates an
unstable core version of the phenomenological soft potential model for the low
temperature anomalies of glasses, relates a new numerical finding on
low-barrier relaxations to old soft potential model results, and discusses
experimental evidence for an unstable core of the boson peak modes.
