Theory of isotope exponent for high critical temperature superconductors

We calculate the isotopic exponent alpha for a Hubbard Hamiltonian with the presence of local Coulomb interaction U and an attractive BCS type potenti al V by using a normal state one-particle Green function, G(N)((k) over bar , i omega (n)), which is renormalized by the interactions. The BCS type pai ring interaction V acts within a region h omega (D) around the Fermi energy and it is appropriate to study alpha as function of the hole density rho. Our results for alpha vs rho for relevant U and V values for some high temp erature superconductors reproduce the general main features and are in very good agreement with the experimental data. (C) 2001 Elsevier Science B.V. All rights reserved.