Application of a variational method to three-particle systems

The possibilities of the method of oscillator functions applied to small-nucleon nuclei are investigated. A new method of construction of the oscillator base of translation-invariant envelope model for the three-particle system is suggested. In the example of 3H, 3He and 12C (α - cluster model) the suggested base construction correctness is investigated. The energy of the ground and first O+ excited states of 12C nuclei up to excitation quantum No. 24 Ali-Bodmer potential inclusively is calculated. The dependence of these characteristics on excitation quantum and hω oscillator parameter is studied. It has been shown that considering all excitation quanta up to No. 24 inclusively in the expansion base, the stability is observed for the ground state of 12C relative to the hω oscillator parameter. Numerical values for the ground and first O+ excited states are equal to E1=-2.16 MeV and E2=+2.57 MeV with account of Coulomb interaction and to E1=-7.39 MeV and E2=-1.89 MeV taking no account of the Coulomb interaction. The results obtained make it possible to suppose that the wave function for 12C can be successfully used to describe other characteristics of 12C