  For a given crystal structure, say body-centred-cubic, the many-body
Hamiltonian in which nuclear and electron motions are to be treated from the
outset on the same footing, has parameters, for the elements, which can be
classified as (i) atomic mass M, (ii) atomic number Z, characterizing the
external potential in which electrons move, and (iii) bcc lattice spacing, or
equivalently one can utilize atomic volume, Omega. Since the thermodynamic
quantities can be determined from H, we conclude that Tc, the superconducting
transition temperature, when it is non-zero, may be formally expressed as Tc =
Tc^(M) (Z, Omega). One piece of evidence in support is that, in an atomic
number vs atomic volume graph, the superconducting elements lie in a well
defined region. Two other relevant points are that (a) Tc is related by BCS
theory, though not simply, to the Debye temperature, which in turn is
calculable from the elastic constants C_{11}, C_{12}, and C_{44}, the atomic
weight and the atomic volume, and (b) Tc for five bcc transition metals is
linear in the Cauchy deviation C* = (C_{12} - C_{44})/(C_{12} + C_{44}).
Finally, via elastic constants, mass density and atomic volume, a correlation
between C* and the Debye temperature is established for the five bcc transition
elements.
