  In this paper, a microscopic theory of magnetic-interaction-induced pairing
in superconductivity of metals was developed on the basis of four idealized
assumptions: (1) only a small number of electrons are involved in
superconductivity; (2) magnetic interactions between electron spins lead to
superconductivity; (3) there are different electronic states, i.e.,
doubly-occupied, singly-occupied (spin up or down) and empty states; (4) the
average kinetic energy of electrons complies with the equipartition theorem of
energy. A formula to estimate T_C was thus derived. It was found that, T_C is
not only related to the electron density and the critical magnetic field, but
also to the degrees of freedom of electrons. The T_C values calculated from
this formula are in good agreement with the experimental results for most
metals. According to this theory, T_C generally increases with decreasing
dimension of metals. For example, T_C in the 3-dimensional (3D) Al metal is
1.19K, but increases to 1.46K in 2D and 2.06K in 1D.
