Energy spectrum of vacancies and nanobubbles in condense matter: Crystal melting

The quantized energy spectra of the oscillating spherical voids in solids and liquids are calculated within the continuum matter model. It is suggested that the ground state of the oscillating void corresponds to the vacancy in real crystals or nanobubble in liquids. The dependence of the oscillating void formation energy on the density, surface tension, pressure and shear modulus is determined. The obtained results are used to estimate properties of vacancies in solid Ar and nanobubbles in liquid Ar. The possibility to use the obtain results for the development of the vacancy or hole theory of melting is discussed.