Effects of complex-valued electronic wave functions on nuclear motions

Moleculer species and colliding groups of atoms are considered for which the electronic wave functions are complex-valued, having arguments that depend parametrically on the nuclear coordinates. The effective Hamiltonian for nuclear motions in the adiabatic approximation that arises in the present case differs from the ordinary Born–Oppeneheimer Hamiltonian, the latter being obtained when restriction to real-valued electronic functions is made. The asymptotic boundary conditions imposed in collision theory lead to in- and out- states [8], and hence to complex-valued wave functions in the coordinate representation. The study of the influence of electron–molecule scattering on nuclear motions therefore necessitates the use of the new effective Hamiltonian, which leads to results differing from those predicted on the basis of the Born–Oppenheimer operator. It is shown that momentum-dependent potentials occurring in the new Hamiltonian might cause “distortions” to the vibrational patterns of some electron–molecule metastable states. Also, these terms can give rise to non-Born–Oppenheimer resonances when motions in an internuclear coordinate become unbounded. We derive expressions for the relevant level widths and line shapes, showing them to be subject to an isotope effect. Even when real-valued electronic functions may be used, the selections of complex-valued functions in their linear span is still optional. Although exact treatments lead to the same results in both real and complex cases we show how the choice of the argument of the electronic function to be non-zero and dependent on nuclear coordinates may be useful for the application of certain approximation schemes. It is demonstrated that for certain systems a suitable choice of the argument assures convergence when the related Lippmann–Schwinger Equation is iterated. It is also shown that in this way an nth order term in the series expansion of the T matrix [8] for moleculer systems can be made negligibly small.     

Different chemical dynamics for different conformers of biological molecules: photoionization of glycine

Single-photon ionization dynamics of two conformers of glycine is studied by classical trajectory simulations using the semiempirical PM3 potential surface in "on the fly" calculations. Initial conditions for the trajectories are weighted according to the Wigner distribution function computed for the initial vibrational ground state. Vertical ionization in the spirit of the classical Franck-Condon principle is assumed. The dynamics of the two conformers are compared during the first 10 ps. The comparison shows very different dynamical behavior for the two conformers. In particular, the chemical fragmentation pathways differ in part. Also, one of the conformers gives much higher rates of conformational transitions, while the other conformer gives larger chemical fragmentation yields. The example shows significantly different chemical dynamics for two conformers close in energy and separated by a low barrier.     

Extraction of interaction potentials from the elastic scattering amplitudes: an accurate quantum mechanical procedure

A quantum-mechanical method for obtaining the interaction potential from the elastic scattering amplitude is described. We present two examples in which nonmonotonic potentials possessing deep wells and strong repulsions are accurately determined.     

A semiclassical self-consistent field (SC SCF) approximation for eigenvalues of coupled-vibration systems

The self-consistent-field (SCF) approximation for coupled-vibron systems in the semiclassical limit yields Hartree-type equations, in which only the eigenenergies and turning points are self-consistently evaluated. Calculations yield vibrational energies in excellent agreement with quantum SCF and exact quantum results. Applications and extensions are briefly discussed.     

Spin-dimensionality dependence of critical parameters

High-temperature series expansions for the susceptibility of isotropic classicaln-vector models are examined with special emphasis on the global dependence on the dimensionalityn of the spin field. The usual fixed-spin model and an incomplete-Gaussian model, which allows for analytic continuation to arbitrary negativen, are considered. A method of examining trends in successive estimates is employed which allows to obtain improved estimates for the extremely slowly setteling sequences as obtained for highn-values. The estimates for the two models obey the universality principle. An approximate function for the critical exponent(n) is obtained in the range –4<n. Reasonable agreement with-expansion results and 1/n-expansion values is found.     

Cross sections of the interactions of He nuclei with protons

⁴He-p collisions at two values of⁴He momenta 8.6 GeV/c and 13.6 GeV/c as well as the³He-p collisions at 13.5 GeV/c have been studies using the one-meter JINR hydrogen bubble chamber. Total, elastic, topological and reaction cross sections have been measured. The cross sections have been determined on a sample of minimum biased events.     

Can projectiles traversing solids bind electrons at all velocities?

PAC measurements on the 4.43 MeV ¹²C(2⁺) state on recoil in magnetized iron at velocities υ_ion = 0.058c, 0.071c yield integral nuclear precession angles of Φ = ?0.18 (30), +0.17 (39) mrad respectively. Evidently, the high electron-spin-polarization transfer to the innermost carbon orbits implied by a previous measurement (υ_ion = 0.03c, Φ = +0.85 (14) mrad) is suppressed at higher ion velocities.