We consider the problem of ion neutralization scattering from surfaces. For large kinetic energies, the motion of the ion can be treated classically. The electronic part is assumed to be described by a time-dependent Newns-Anderson Hamiltonian. The ion is supposed to have a closed-shell structure with one empty orbital outside the shell, which can take up, at the most, two electrons from the metal. One can obtain a time-dependent Hartree-Fock (TDHF) solution for this using a procedure suggested earlier. [T. B. Grimley, V. C. Jyothi Bhasu, and K. L. Sebastian, Surf. Sci. 124, 305 (1983)]. We show that this solution is defective in that it predicts that the probability that the ion comes back as a neutral species is always less than 0.5, thus illustrating that one has to include electron correlation in order to describe the process correctly.

For this we make use of the time-dependent version of the coupled-cluster approach. In this, one assumes the wave function to have the form exp[$T_0$(t)+$T_1$(t)+$T_2$(t)+. . .]‖${\Phi }_0$〉 where ‖${\Phi }_0$〉 is a Slater determinant and $T_n$(t) can create n-particle hole excitations in it. We take $T_1$(t) as a linear combination of all possible single-particle hole-excitation operators while $T_2$(t) is taken as a linear combination of just those two-particle hole-excitation operators which transfer two electrons to the orbital of the ion from the solid, neglect $T_n$(t) for n>2, and derive differential equations for the matrix elements of the operators $T_1$(t) and $T_2$(t). These differential equations are solved numerically to obtain the wave function at any time t.

New theorems which enable us to calculate all the expectation values that arise in our treatment of the problem are presented. Also, we have derived expressions for the excitation spectrum, produced as a result of the collision, by particles which come back as ions and also by those which have taken up one or two electrons from the solid. The method is applied to the scattering of lithium ions from the Ni(100) surface and also from a Ni surface contaminated with alkali atoms. The calculations show that TDHF theory is not a bad approximation if one is concerned just with the approach of the ion to the surface. But, in treating an ion which leaves the surface, TDHF fails. The predicted values of charge-transfer probabilities are considerably different in the two theories. Also, calculation of the excitation spectrum produced as a result of the collision show that the spectra are much broader for a contaminated surface having a lower work function than for the clean surface.

• Received 12 December 1984

DOI:https://doi.org/10.1103/PhysRevB.31.6976