Vibrational spectrum of isolated impurity of hydrogen and its isotopes in aluminium

The problem on calculation of the vibrational crystal spectrum with interstitial impurities in case when the perturbation of force parameters of dynamic interatomic interaction is spread only onto the nearest to the defect coordination spheres is considered. Presentation for scattering T- matrix through minors of perturbation matrix of near-impurity force parameters (φ) and Green function matrix of ideal lattice (α) determined in the defect subspace is obtained. The calculation procedure of φ and α matrix elements is discussed.Expressions for spectrum of impurity, located in T- and O-sites of hcc lattice are shown as an example