The approximate energy expression for the variational calculation of nuclear matter is refined by taking into account three-body cluster terms with tensor correlations. In this variational method, the energy expression is constructed as an explicit functional of various two-body distribution functions which are regarded as variational functions. Then, the Euler-Lagrange equations are derived and fully minimized energies are obtained. The previous energy expression does not include the kinetic-energy terms caused by noncentral correlations sufficiently, and the obtained energy of nuclear matter is too low. Therefore, in this study, the energy expression is improved by taking into account important missing three-body-cluster kinetic-energy terms caused by tensor correlations. In this refinement, necessary conditions on tensor structure functions play important roles. The obtained energy per neutron for neutron matter with the v6' potential is considerably higher than that of the old energy expression.
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