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By investigating the differential reflection coefficient for one-phonon transition, various properties of the scattering of the He-Ag(111) system are studied. The formulation employed here is based on the distorted-wave Born approximation of an ab initio time-independent scattering theory. In the formulation, an arbitrary pair potential between the projectile and the crystal atoms together with the dispersion relation and the polarization vectors can be input. A model of a 69-layer slab is chosen for the computation of the vibrational modes. The plate modes are then mapped onto the Rayleigh modes. Using a pair potential proposed by others we calculated the differential reflection coefficient for one-phonon transitions corresponding to the Rayleigh modes. The phonon wave vectors are chosen along the (112) direction with magnitude ranging from 0.10 to 0.90 A −1 . The shape of the differential reflection coefficient is in agreement with experiment by other workers if we choose the amplitude of the Rayleigh modes to be proportional to the square root of the phonon wave vectors. We find that the projectile mainly interacts with the vibrational motion of the atoms in the first layer of the crystal, and the interaction reaches the third layer for small parallel momentum transfer and no deeper than the surface for phonon wave vectors greater than 0.6 A −1 . We also find that the effect of the Debye-Waller factor is small as temperature increases from 60 to 300 K. The differential reflection coefficient increases with temperature due to the Bose-Einstein distribution of the phonons and is larger for phonon annihilation than for phonon emission as determined by the density of the final states of the projectile, the incident flux and the kinematic conditions of the scattering.

Ionization probabilities of the hydrogenic ions, with atomic number between 4 and 9, impinging upon a crystal at grazing angle are calculated. It is found that the transition probability from the ground state nlm = (100) to the continuum states is negligible. For incident ions at near-resonance velocity, transition probabilities from 2 lm and 3 lm states to the continuum states exhibit high peaks. As a result of ionization, the efficiency of coherent excitation of the ions by a crystal is greatly reduced. Based on the present ionization data, we point out some possible methods to enhance stimulated emission of soft X-rays by a crystal surface.

Coherent excitation of fast hydrogenic ions with velocity near 10 9 cm/s by a periodic crystal surface is investigated. Electronic transitions of the ion induced by the crystal potential are calculated for both the cases that nucleus of the ion travels above and below the surface. It is found that the transition matrix elements between the hydrogenic (1, 0, 0) and (3, l, m ) states depend strongly on whether the nucleus of the ion is above or below the surface and on the value of l and m . It is estimated that the Rabi distance for complete excitation of the Be 3+ ion lies between 1 and 300 A and the fractional energy loss ΔE loss / E ion is of the order of 10 −6 to 10 −4 . From estimating the collision time between ions, the excitation time of ionic electrons, the spontaneous and the stimulated lifetimes, we calculate the upper and lower limits of the incident ion current density for which stimulated emission of soft X-ray occurs. The distance beyond which the surface effect becomes insignificant and the confinement of ions over the crystal are discussed.

The total ionization rates R 100 → k μ from the ground state to the continuum, via coherent excitation to the first excited state, of a fast hydrogenic ion impinging upon a thin film of gold are computed for ions with atomic number between 6 and 9. Since the inclusion of the relativistic factor makes the analytical manipulation of the total ionization rate and the numerical computations extremely difficult, we adopt the approximation of treating the crystal as one-dimensional in the numerical computations. For incident ions at the calculated resonance velocity, R 100 → k μ exhibits a narrow peak. Further, we found that the resonances are asymmetric with respect to the velocity of the ions and the total ionization rate decreases as the atomic and/or harmonic number increases. These results are qualitatively in agreement with the experiments. Since the ions do not follow exactly the same paths in the channel, they experience different electrostatic potentials. As a result the energy levels of the ions are broadened by approximately 1 eV, The effect of this broadening on the total ionization rate is also discussed.

The selectively adsorbed compound states for H2 + Cu rigid surface scattering, which are the quasibound states embedded in the continuum, are computed employing quantum mechanical method. With a semi-empirical molecule-flat surface interaction potential, we diagonalize the total Hamiltonian of the system including the rotational and vibrational states of the molecular projectile. Our emphases here are to study the vib-rotational and vibrational components that are proportional to the scattering amplitude of the Feshbach type internal excitation associated with selectively adsorbed resonance states, to study the relative importance between the rotational and vibrational mediations for selective adsorption, and to make comparison with quasiclassical trajectory results obtained in the preceeding paper. For incident energy below ∼ 0.3 eV, rotation mediations are found to be dominant in the resonance scattering, whereas the resonance states that arise from the vibrational mediation often appear above that energy. Good agreement between the quantal and the classical trajectory results is obtained regarding the energies of the selectively adsorbed quasibound states and other related physical quantities in the energy region above the potential barrier. Below this barrier, the quantum mechanical tunneling effect is important.