Kinetic theory of gas-surface interaction

The kinetics of particle and energy exchange between gas and surface is treated in analogy to the transport of particles and energy in solutions using Onsager's theory of nonequilibrium thermodynamics. In addition to the coefficients of sticking and thermal accommodation a third kinetic coefficient is introduced describing the coupling of particle and energy transport. This coupling turns out to be particularly important at low temperatures reducing the accommodation coefficient from 2 to 1.The Onsager coefficients are then expressed in terms of the scattering properties of the surface. A simple model is treated to illustrate the general results and to provide estimates for the kinetic coefficients.Extract from doctoral thesis of H.M. submitted to Fachbereich Physik, Techn. Universität München, 1978     

Current trends in the theories of gas-surface interaction

Studies on gas-surface dynamics have acquired considerable importance recently not only for their intrinsic scientific interest but also for their technological potential. This article first briefly describes various experimental techniques and a number of interesting recent observations resulting from these techniques. It then discusses certain important theoretical methodologies being extensively used nowadays. There arethree broad overlapping streams of theoretical works, viz classical, semi-classical and quantum-mechanical. There are alsothree basic problems in gas-surface interaction, viz (i) the interface presents a manybody problem; (ii) the solid surface is “rough”; (iii) the number of diffractive and inelastic channels is enormously large. The semi-classical approaches appear to dominate over the others in variety and quantity. But the sources of benchmark theoretical results are still the rigorous classical-trajectory and close-coupling quantum-mechanical calculations. The coming years are likely to witness not only increased numerical accuracy through refinements in semi-classical and quantum-mechanical approaches, but also certain special approximate methods designed to yield deeper physical insights into the nature of gas-surface interaction. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion. An erratum to this article is available at .     

On the use of a Debye-Waller-type factor in gas-surface scattering theory

The status of the use of a Debye-Waller-type factor, in the theory of gas-surface inelastic (phonon) scattering to describe the attenuation of diffracted beams, is considered, and several conclusions are made; for example, it is concluded that the commonly-used Debye-Waller-type relation, which in the literature seems to be generally accepted as established, has no firm basis. In the context of such a relation, the role of the gas atom-solid interaction potential well is discussed; it is concluded that methods generally used in the literature for taking account of the presence of this well are arbitrary. No suggestions are made as to how the present situation may be improved.     

Microscopic theory of particle-hole states

A self-consistent procedure for calculating the particle-hole states of nuclei is given. This has been applied to the levels of¹⁶O nucleus. The particle-hole interaction is derived using Landau theory. The basis states are generated using the Brueckner many-body theory, and used in the random-phase-approximation calculation. The sensitivity of the 3- state at 6.13 MeV with the interaction is discussed, the other states being reasonably insensitive to such a choice. The effect of renormalization of the particle-hole interaction, on various states is also discussed.     

Microscopic theory of particle-vibration coupling

A microscopic theory of the coupling between collective vibrations and independent-particle excitations is developed, in which generator coordinates are used in order to describe the collective modes. Formulae for the coupling are derived and compared with the standard theory. The method applies to any Hamiltonian with two-body interactions that has a stable Hartree-Fock solution. It is found that the strength of some of the coupling terms depends on energy, and that second-order coupling, which does not figure in the standard treatment, can be important.     

Microscopic theory of memory functions

We define a sequence of microscopic dynamical variables by decomposing a Hilbert space into orthogonal subspaces, and construct for them a new hierarchy of equations which is particularly useful for highly correlated systems. A formal solution is shown to give a microscopic expression of Mori's generalized Langevin equation. With a classical liquid as an example, we demonstrate that the theory facilitates a first-principles calculation of memory functions.     

Microscopic theory of cluster radioactivity

Recent developments in the dynamical microscopic theories of cluster decay are reviewed with special emphasis on the nuclear structure aspects and physical interpretation of the models. What we call dynamical microscopic theories are those in which the decay width is derived from the nucleonic structures, of the participating nuclei, which are deduced through the solution of their equations of motion. After a brief review of the various expressions for the decay width, we turn to the nuclear-structure aspects of the problem. We thoroughly discuss the treatment of the Pauli effects in models involving macroscopic elements. We settle the long-standing controversy over the cluster-core norm operator that relates microscopic and macroscopic relative-motion wave functions in the transition amplitude. We conclude that the way the norm operator was originally introduced in the mid-1970s is in principle correct. The main part of the paper is a detailed review, in which the approaches considered are categorized according to the structure models used for the parent nucleus. The approaches discussed are the ordinary shell models, the cluster-like shell models and the Bardeen-Cooper-Schrieffer (BCS) approach. By discussing these diverse calculations, it is concluded that the most essential prerequisite for a realistic model of the mother nucleus is that it should correctly describe the cluster correlation in the surface region. This implies that the proton-neutron interaction is indispensable, and the moderate success of ordinary shell models is accounted for by their failure to include both proton-neutron interaction and large enough bases. For the special case of a doubly-closed-shell residual state, cluster-like models are able to cope with this problem, because their bases are more economical, and, for these cases, they provide a fully satisfactory decay theory. The BCS approach, on the other hand, is widely applicable, and is the only one that has been applied to heavy-cluster decay with reasonable success. We point out, however, that the formation amplitude calculated in this model still contains approximations. We explain the success of the BCS theory by showing that, in spite of appearance, it does include proton-neutron interaction, in an effective manner. In discussing the results for the widths, we address the problem of the preformation probability of a cluster-core pair in the parent nucleus. One can be fairly confident that in the ground state of ²¹²Po the amount of core-α-clustering is as high as 20–30%, but, in respect of other cluster-decaying nuclei, the theory is not yet conclusive. We conclude that a satisfactory understanding of heavy-cluster radioactivity requires the application of both more sophisticated cluster models and improved BCS approaches.     

Microscopic theory of network glasses

A theory of the glass transition of network liquids is developed using self-consistent phonon and liquid state approaches. The dynamical transition and entropy crisis characteristic of random first-order transitions are mapped as a function of the degree of bonding and density. Using a scaling relation for a soft-core model to crudely translate the densities into temperatures, theory predicts that the ratio of the dynamical transition temperature to the laboratory transition temperature rises as the degree of bonding increases, while the Kauzmann temperature falls explaining why highly coordinated liquids are "strong" while van der Waals liquids without coordination are "fragile."     

Microscopic theory of strong superfluidity

Various forms of superfluidity in nuclei and nuclear and neutron matter are characterized by the relevance of strong nucleon-nucleon correlations, as well as by gap values, which can be a substantial fraction of the Fermi energy. We present a microscopic many-body theory of nuclear superfluidity. The influence of various physical effects is analyzed within the Green's function formalism and the Bethe-Brueckner-Goldstone expansion. In particular, dispersive effects are discussed in detail. We point out open problems that must be solved before a full understanding of nuclear superfluidity can be achieved.     

Laser-induced gas-surface interactions

Chemical reactions in homogeneous systems activated by laser radiation have been extensively investigated for more than a decade. The applications of lasers to promote gas-surface interactions have just been realized in recent years. The purpose of this paper is to examine the fundamental processes involved in laser-induced gas-surface chemical interactions. Specifically, the photon-enhanced adsorption, adsorbate-adsorbate and adsorbate-solid reactions, product formation and desorption processes are discussed in detail. The dynamic processes involved in photoexcitation of the electronic and vibrational states, the energy transfer and relaxation in competition with chemical interactions are considered. These include both single and multiple photon adsorption, and fundamental and overtone transitions in the excitation process, and inter- and intra-molecular energy transfer, and coupling with phonons, electron-hole pairs and surface plasmons in the energy relaxation process. Many current experimental and theoretical studies on the subject are reviewed and discussed with the goal of clarifying the relative importance of the surface interaction steps and relating the resulting concepts to the experimentally observed phenomena. Among the many gas-solid systems that have been investigated, there has been more extensive use of CO adsorbed on metals, and SF₆ and XeF₂ interactions with silicon as examples to illustrate the many facets of the electronically and vibrationally activated surface processes. Results on IR laser stimulated desorption of C₅H₅N and C₅D₅N molecules from various solid surfaces are also presented. It is clearly shown that rapid intermolecular energy exchange and molecule to surface energy transfer can have important effects on photodesorption cross sections and isotope selectivities. It is concluded that utilization of lasers in gas-surface studies not only can provide fundamental insight into the mechanism and dynamics involved in heterogeneous interactions, but also offer the possibility for technical innovation for practical applications.     

Microscopic theory of the two-proton radioactivity

We formulate a theory of the two-proton radioactivity based on the real-energy continuum shell model. This microscopic approach is applied to describe the two-proton decay of the 1(-)(2) state in 18Ne.     

Microscopic transport theory of heavy-ion collisions

Drift and diffusion coefficients for the variables of mass fragmentation and excitation energy are studied for deeply inelastic collisions. The transport coefficients are obtained in closed form as functions of the parameters of the interaction matrix elements between nucleonic states and as functions of the binding energy of the intermediate rotating quasimolecular configuration. Drift and diffusion coefficients for excitation and mass transfer are related (dissipation fluctuation theorem). In good approximation these relations take the simple form of Einstein's relation between the mobility and the diffusion coefficient of a particle in a medium. For the total mass numbers 100, 250 and 500 the results are discussed in detail. The transport coefficients are compared with experimental results. Within the uncertainties of determination from experimental data, the drift and diffusion coefficients are well described by two previously adjusted parameters of the mean interaction matrix elements. Consequences for the production of superheavy elements in deeply inelastic collisions of U on U or Cf are discussed.     

Microscopic theory of charge-density wave systems

An effective action (in imaginary time) for the phase of the order parameter is derived using the path integral formulation of the microscopic theory. After analytic continuation, the classical equation of motion is derived. Dissipation is found to arise from impurity scattering and from the screened Coulomb interaction with normal electrons. Similarities to a recent theory of Josephson junctions are discussed.     

Microscopic theory of liquid 4He

A finite temperature theory is given of the temperature variation of the sound velocity and of the structure factor of liquid helium. The sound velocity is found to decrease slightly as the temperature is increased from absolute zero. The first peak of the structure factor is higher for higher temperature below the λ point. The internal energy is characterized by the quasiparticle distribution function with the Bogoliubov-Zubarev type excitation energy. The structure factor and the energy are determined by the effective interaction which depends on the average density, the density of the excited particles, and temperature in addition to the interaction potential.     

Microscopic transport theory of heavy-ion collisions

Analytical expressions for the diffusion coefficients for the transfer of neutrons and protons in a heavy-ion collision are derived. The mass diffusion coefficient implied by these two coefficients is compared with previous theoretical calculations and the values extracted from experiment for a variety of systems. Drift coefficients are related to the diffusion coefficients and the driving potential by the usual Einstein relations. On approximating the driving potential by a second-order form, the Fokker-Planck equation is solved analytically by the moment expansion method. A comparison of the predictions of this theory with a variety of recent experimental data gives generally good agreement. Thus we conclude that the experimental data currently available can be interpreted in purely statistical terms. Some deviations between theory and experiment indicate a possible influence of shell effects and/or direct transfer processes in the early stages of the reaction.     

Microscopic transport theory of heavy-ion collisions

Transport equations of the Fokker-Planck type are derived from a master equation for deeply inelastic collisions. Using the method of spectral distributions, the transport coefficients are calculated for symmetric fragmentations. Analytic formulas are given for the memory time, for the energy-drift coefficient and for the diffusion coefficients which correspond to the excitation of the fragments and the transfer of nucleons. These expressions contain parameters of the basic interaction matrix elements only, which describe excitations and transfers. Agreement with experimental data is obtained for reasonable values of these interaction parameters. Production cross-sections are predicted for superheavy nuclei in the deeply inelastic collisions U+U and U+Cf.     

Microscopic transport theory of heavy-ion collisions

Effects from shell structure on mass transport coefficients are studied in a schematic model. The diffusion coefficient is slightly reduced by shell effects, the reduction being less than 20% for realistic cases and reasonably high excitation energies. A much stronger effect results for the drift coefficient. This is due to the rapid variation of the shell correction energy as function of the fragmentation variable. The influence of shell effects on the time-dependent mass distributions is illustrated.