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Based on the general calculation of the tetrad formalism in a 4-dimensional space-time, we have shown that the deviation from the Riemannian geometry to the non-Riemannian geometry depends on the torsion case. In the absence of the torsion case, one is naturally confined to the Riemannian geometry, while for the nonzero torsion case, our formalism uses the Einstein-Cartan geometry which is a basis in the spinor space and is incorporated with the gauge transformation for the zero rest mass Dirac field. After constructing the Lagrangian density of the Dirac particle in this spinor space, deriving the corresponding Heisenberg-Pauli type field equations, using V-A weak interaction model for the coupling term, and solving the Klein-Gordan equation, we obtain a nonzero oscillatory mass due to the torsion-contortion term of the field equation. This agrees, both in magnitude and range, approximately with those reported by F. Reines.{dollar}\\sp{lcub}(15){rcub}{dollar} We then suggest this mass to be a candidate for the solution to the "missing mass" problem of the closed universe model in the cosmology.