208 Bulletin of Magnetic Resonance Green's Function Calculation of Effective Nuclear Relaxation Times in Metals and Disordered Metals M. Martin-Landrovc and J A . Moreno Departamento de Fisica and Centro de Resonancia Magnetica, Facultad de Cicncias, Universidad Central de Venezuela, Apartado 47586, Caracas 1041-A, Venezuela. 1 Introduction The theoretical derivation of expressions for die magnetic nuclear relaxation times at very low temperatures and the description of the beha- viour with temperature for such relaxation times, has been of major interest among the researchers in the field, specially because of the recent expe- rimental possibility to obtain measurements of nuclear magnetic properties at such low tempera- tures. There has been a considerable amount of work in the area of nuclear magnetism [1], but a comprehensive theoretical interpretation of NMR relaxation times, at arbitrary temperatures, is still lacking. Recently, Sbibata et al. has pub- lished a series of papers [2], [3] concerning the theoretical determination of the nuclear spin lat- tice relaxation time for a system of nuclear spins interacting with conduction electrons ina a metal. Using a theory of nonlinear spin relaxation [4], [5] they predicted a multicxponential spin-lattice re- laxation behaviour. In the case of disordered metals and high tempe- ratures, where a Korringa law is aplicable, Wa- rren [6] predicted an enhancement of the relaxa- tion rate, which in some cases [7] could be as large as 6,500. More recently [8], Gdtze and Ketterle derived expressions for die Warren enhancement factor by means of normalized Kubo response functions [9]. ED the present work, we make use of the two-ti- mes Green's function formalism in the regime of the Linear Response Theory to derive the tempe- rature behaviour of nuclear relaxation times [10] for nuclei in metals and disordered metals. The results obtained are in complete agreement with those derived by Sbibata in the assumption of an effective unique relaxation time [2], [3] and with experimental evidence [11], [12]. Also, there is agreement between our results and those derived by Gdtze and Ketterle [8] in the high temperature regime, where Korringa law is valid but additio- nally we obtained expressions for the enhanced relaxation rate which are valid in the whole tem- perature range. The organization of this paper is as follows, in section 2, the general formalism is derived, in section 3, we work out the Hamilto- nian of die systemfromwhich the equation for the Green's function < < I°/I°> > to, which con- tains all the information relevant to the spin-lat- tice relaxation, is derived. This equation is then solved including terms up to second order in the electron nucleus interaction and the disorder pa- rameters. Finally in section 4 we discuss the rela- xation times formulas. 2 Green's Functions and the Relaxation Rate We will consider a system which can be mode- lled by the total Hamiltonian: H = Hs + HSL + HL (1) where Hs represents the nuclear spin Hamilto- nian, HL is the Hamiltonian for the heat bath and HSL represents the couplig between both systems, usually under the condition HL > Hs > HSL which occurs commonly in NMR experiments. In order to consider the evolution of