[en] A theory describing the autoionization of inner atomic shells in nuclear β decay has been developed. It is shown on the basis of diagram technique that in first order in Z^-1 the matrix element of the process is represented in the form of the sum of two terms, one of which corresponds to ionization of an electron shell of an atom with sudden change of the charge of the nucleus, and the other to direct interaction of a β particle with the electrons of the atomic shell. Specific calculations are carried out in the nonrelativistic approximation with use of electron wave functions and a Green's function constructed with a Teitz screened Coulomb potential, the systematic inclusion of the contribution of the direct mechanism being carried out for the first time. For the case of β decay of the isotopes ³⁵S, ⁴⁵Ca, ⁶³Ni, ¹⁴⁷Pm, and ¹⁵¹Sm we have calculated the shape of the spectrum of shakeup electrons and the integrated probability of autoionization of the K shell. It was found that the contribution of the direct mechanism in all cases considered is significant

[en] We propose a new parameter for verifying the validity of sudden approximation at any given time by using power series expansion with respect to time. Through a rigorous definition of an infinite potential well and applying the parameter to the problem of sudden compression of the well, we show sudden approximation is still valid in this situation as long as the compression process is fast enough, which differs from previous conclusions (2005 Eur. J. Phys. 26 121). By introducing scattering states in the inifinite well, the wave function outside the well could be explained reasonably. The theory presented in this paper is tested against finite difference time domain (FDTD) numerical results. (paper)

[en] The general theory of atomic processes stimulated by the nuclear β^- decay is considered. The final-state probabilities are determined for a number of β^-decaying light atoms (He-Ar) with the use of sudden approximation

[en] The recently developed (energy) sudden representation of the Schroedinger propagator is examined in conjunction with the path integral method. The perturbation expansion of the propagator in this representation (with the sudden approximation as the zeroth order term) is easily understood using Feynman diagrams. The zeroth order term is a form involving only sudden paths (i.e., paths resulting from the sudden approximation). Each higher order term is a series of sudden paths which are connected to one another due to the nonsudden effects of the dynamics. The sudden representation, and in particular its perturbation expansion, is also used to study the bath effects in many body systems which are expressed in the form of influence functionals in the path integral formalism. In our treatment, the bath coordinates are assumed to be the slow coordinates. The zeroth order (sudden approximation) influence functionals are expressed in a very simple form; they involve only an ordinary integral over the bath coordinates. Finally, to illustrate the approach, a harmonic oscillator coupled linearly to an unspecified primary system is used as a simple model bath. The reduction of the exact influence functional to the sudden approximation form is also considered

[en] Performing the classical limit of the coordinate-representation-sudden approximation of Gerber et al. [J. Chem. Phys. 73, 4397 (1980)], we discuss rainbow effects in diatom-surface scattering. Under special conditions, which are stated in this article, rainbows can be classified into surface rainbows and rotational rainbows. The latter are expected to be common features of diatom-surface scattering provided: (i) the collision is impulsive and (ii) many rotational states are energetically open. Simple analytic expressions for the rainbow states are derived using a repulsive model potential and the dependence on collision and potential parameters is discussed. The predictions are all substantiated by calculations performed within the sudden approximation and using this model potential

[en] The probabilities of single, double, triple and quadruple shake processes upon inner-shell K-, L-, M- and N-ionization are calculated in the sudden perturbation approximation for the atoms with 3 ≤ Z ≤ 55. Multiple shake processes make 10 to 30% of all the shake processes involving a given nl outer subshell depending on the orbital quantum number l, on the subshell occupation, and on the initial inner-shell vacancy

[en] The time-independent energy sudden (ES) representation is defined through application of the energy shift operator S = exp[-(h-#betta#/sub n/)partial/partialepsilon], where h is the internal (molecular) Hamiltonian. Our introduction of S follows from an earlier study by Chang, Eno, and Rabitz where exp[-iht], which ''factors out'' internal motion, was used to define the time-dependent ES representation. Exact integral equations for the scattering wave function within the ES representation are derived, the leading terms being the approximate ES wave function. Corrections to the ES wave function are nonsingular and involve the generalized potential increment V = S^-₁VS-V, where V is the interaction potential. Boundary conditions and transition amplitudes are discussed, as is the connection between wave functions in the ES and the original representations

[en] We have recently demonstrated that the energy corrected sudden (ECS) scaling law of De Pristo et al. when conbined with the power law assumption for the basis rates k/sub l/→0proportional[l(l+1)]/sup -g/ can accurately fit a wide body of rotational energy transfer data. We develop a simple and accurate approximation to this fitting law, and in addition mathematically show the connection between it and our earlier proposed energy based law which also has been successful in describing both theoretical and experimental data on rotationally inelastic collisions

[en] It is shown that atom--surface interaction potentials can be recovered from the diffraction peak intensities measured in beam scattering experiments by a direct, simple inversion method. The potential is determined uniquely, apart from a term depending only on the coordinate perpendicular to the surface. The method does not assume any parametrized functional form for the potential. The results are obtained for a rigid surface, using the sudden approximation for the scattering dynamics. Application to a test case using simulated data for Ne/W (110) yielded an inverted potential of remarkable accuracy

[en] A semiclassical multichannel branching model is developed and applied to various dynamical phenomena in polyatomic molecular systems. The model is based on the reaction path Hamiltonian of Miller, Handy, and Adams [J. Chem. Phys. 72,99 (1980)] and also utilizes the semiclassical perturbation-infinite order sudden approximation of Miller and Shi [J. Chem. Phys. 75, 2258 (1981)] for describing vibrational inelasticity along the reaction path. Specific applications of the model are made to state-specific unimolecular decomposition, energy level splitting in multidimensional double-well potentials, and to reaction probabilities along reaction paths with multiple transition states