Elimination of Spurious States of Oscillator Shell Model
  A new method for elimination of the 'spurious' states comprising reguirement of translational invariance and simplicity of the enumeration scheme of antisymmetric A-particle states has been developed. The method presented enables one to project off the space of purely spurious antisymmetric A-particle oscillator functions with singled out dependence on intrinsic coordinates of two last particles onto the subspace of the nonspurious motion. The method is based on constructing the matrix elements of the centre-ofmass Hamiltonian and spectral decomposition of the corresponding real symmetric matrix. The obtained coefficients of the expansion of the antisymmetric A-particle oscillator functions in terms of the ones with singled out dependence on intrinsic coordinates of two last particles and with eliminated spurious states are required for calculation of two-particle oscillator intrinsic density matrices. Software tools based on root rational fraction expression of numbers for the theoretical formulation presented have been developed. 
A. Deveikis, G. Kamuntavicius