Perturbation Expansion of the Ground State Energy of Solid Helium

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Abstract
The ground state energy of solid helium is expanded in powers of a non-singular effective potential, i.e., the reaction matrix, which is defined by a self-consistent equation of an interacting pair of atoms in the solid. Two alternative schemes are given by taking advantage of arbitrariness in introducing the reaction matrix. One, in the first approximation, leads to the formula of ground state energy proposed by the authors previously. The other is a modified scheme which results in a vanishing second order term. In both scheme the expansion of the energy is explicitly written up to the third order in the reaction matrix.

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