Possible Spin - Singlet Superconductivity in ( TMTSF ) 2 X : Superconducting Transition Temperature in a Magnetic Field

We study the transition temperature Tc(H) of a quasi-one-dimensional (Q1D) superconductivity which is derived from the quantum effect of an electron motion in a strong magnetic field. We calculate Tc(H) of both isotropic and anisotropic superconductivity by taking account of the optimal momentum of the Cooper pairs and the effect of higher harmonic terms along second conducting axis in the tight-binding model. We find that, although Tc(H) of the spin-singlet superconductivity is suppressed strongly by the Zeeman effect, the suppression of Tc(H) is not very severe if we take the optimal pair-momentum and the higher harmonic terms into account. The obtained Tc(H) for the spin-singlet superconductivity is consistent with the experimental results in TMTSF salts.