A variational study of the ground and excited states of light nuclei in a three-body model on the complete basis. I. General formalism

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Abstract
The variational method proposed recently is used to develop a formalism for calculating the structure of light nuclei in terms of the multi-cluster model. The technique is developed to calculate all the matrix elements of the Hamiltonian on a multi-dimensional gaussian basis (MGB) including the central, spin-orbit and tensor forces. The basis constructed is shown to give rise to convenient pure analytical formulae for all the matrix elements of the Hamiltonian and, moreover, for all the observables of practical interest such as the RMS radius, the quadrupole and magnetic moments, the electromagnetic form factors etc. A method to take account of the Pauli principle in the composite-particle system based on the introduction of a projecting addend in the Hamiltonian is described. Essential advantages of the projection technique described are demonstrated.