Electron spin resonance of photolytically reduced pyrazine

A mapping between the exactly soluble forced oscillator and the general vibrationally inelastic scattering problem is shown to yield a new uniform approximation based on generalized Laguerre polynomials. Computations are reported for collinear He-H₂ collisions in which H₂ is represented by harmonic and Morse oscillators. The results show that the Laguerre approximation avoids the known failings of the existing Airy and Bessel uniform approximations.     

On the semiclassical impulse approximation for electron capture in asymmetric ion-atom collisions

A derivation of the impulse approximation for the capture of a targetK-shell electron by a light projectile in ion-atom collisions is given in the framework of the semiclassical approximation. The impact-parameter dependence of the capture probability is calculated numerically without further approximations, and shows good agreement with recent experimental results for protons colliding with Ne and Ar. The validity of several peaking approximations and the relation to ionisation theories is briefly discussed.     

Semiclassical and quasiclassical calculation of reaction probabilities for collinear X + F2→XF + F (X = Mu,H, D,T)

Semiclassical calculations of reaction probabilities have been carried out for the collinear H + F₂ (n = 0, 1) reaction using the best extended LEPS surface No. II of Jonathan et al. Both real and complex valued classical trajectories have been included in the calculations for an energy range where the quasiclassical total reaction probability is unity. Comparison with quantum results shows the semiclassical reaction probabilities are accurate to about ± 0·05 provided only two real or complex stationary phase points make an important contribution to the S matrix element, so that the uniform Airy or integer Bessel approximations are valid. Real semiclassical calculations are also reported for the collinear Mu, D, T + F₂ (n = 0) reactions. For the D and T reactions, the semiclassical reaction probabilities are estimated to be accurate to ± 0·05, except close to the reaction threshold, but for the Mu reaction the estimated errors are much larger. In addition, quasiclassical calculations for the reaction probabilities have been carried out using half integer boxing and smooth sampling methods to quantize the product distributions. For the H + F₂ reaction, there are usually systematic deviations from the quantum reaction probabilities and the same is expected to be true for the Mu, D and T reactions.     

Dynamically based fitting law for cross-sections of vibrational energy transfer

A three-dimensional semiclassical analytical model for cross-sections of vibrational energy transfer in collisions between an atom and a diatomic molecule has been developed. The model is based on the Bessel uniform approximation for transition probabilities valid for highly excited states of a molecule represented by the Morse oscillator. Three fitting parameters of the model are expressed in terms of the features characterizing the anisotropic intermolecular potential. The accuracy and validity of this law are tested by comparison with large Δn transitions and isotope effects in the crossed beam inelastic scattering of I₂ from He, H₂ and D₂.     

Application of a uniform semiclassical theory to the multiple Coulomb excitation of heavy ions

Transition probabilities of classically allowed multiple Coulomb excitation of deformed heavy nuclei induced by heavy ions are calculated within a uniform semiclassical approximation. It is found that a Bessel uniform approximation is necessary and that caustics have to be treated carefully.     

Multiphonon excitations in heavy ion grazing collisions

A semiclassical model is used to study the excitation of giant resonances in heavy ion grazing collisions. The projectile is described as a moving Woods-Saxon potential with a fixed shape, and the evolution of the target state is calculated by time-dependent perturbation theory. Using random phase approximation wave functions, probabilities to excite various resonances are obtained. Multiple phonon excitations appear as the possible mechanism for the structures observed in heavy ion collisions.     

Relativistic coulomb collisions and the virtual radiation spectrum

We evaluate the Coulomb-excitation cross sections in relativistic heavy-ion collisions by means of the plane-wave Born approximation. The final total cross section is shown to be equal to that obtained by a semiclassical method. As a byproduct the virtual photon spectrum for similar electromagnetic processes is derived. Comparison with other methods is performed.     

Relativistic coulomb collisions and the virtual radiation spectrum

We evaluate the Coulomb-excitation cross sections in relativistic heavy-ion collisions by means of the plane-wave Born approximation. The final total cross section is shown to be equal to that obtained by a semiclassical method. As a byproduct the virtual photon spectrum for similar electromagnetic processes is derived. Comparison with other methods is performed.     

Generalized semiclassical optical model and velocity-dependent potentials

A procedure is developed for the construction of a complex potential in a generalized semiclassical optical model for molecular collisions involving internal nuclear degrees of freedom. The procedure involves a local approximation on the exact quantum optical potential, which is an integral operator over an energy-dependent, non-local kernel. The resulting potential for the model is velocity-dependent. The classical limit of transition amplitudes is obtained from complex-valued classical trajectories whose equations of motion are derived with this potential. The potential contains coordinate integrals over the kernel, and various approximations for the kernel are discussed. Sample calculations are carried out for collinear atom-diatom collisions.     

Calculated ionization cross sections for proton-fullerene ion collisions

A simple jellium model is constructed in order to obtain one-electron wave functions for the valence electrons of the fullerene. With this jellium wave function we have calculated ionization cross sections for proton-C₆₀ ⁺ collisions in the semiclassical approximation. For higher projectile velocities, for which the semiclassical approximation is valid also for electron impact, theoretical cross sections fit satisfactorily the experimental data of Völpel et al. [Phys. Rev. Lett. 71 (1993) 3439].     

Semiclassical approximation of path integrals on and near caustics in terms of catastrophes

A semiclassical approximation of Feynman's path integral is derived which, in contra-distinction to conventional formulae, remains finite in conjugate (focal) points and on caustics, exhibits the experimentally observed oscillatory behavior near these and reduces to familiar approximations far away. The approximative path integral is proportional to a generalized Airy integral governed by a Thom catastrophe polynomial whose bifurcation properties correspond to those of the solutions of Euler-Lagrange equations. The result is illustrated by computing the propagator of the quantized anharmonic oscillator.     

Photon production in nucleon-nucleon collisions

We calculate the differential cross section for nucleonnucleon bremsstrahlung in covariant way based on a realistic meson-exchange approximation for the NN-scattering amplitude. The results are discussed in comparison to semiclassical approximations and with respect to the role of internal radiation diagrams. The influence of the anomalous magnetic moment on the proton-neutron bremsstrahlung is found to contribute up to 50% for specific kinematical conditions. Recent measurements on the elementary differential cross sectionpnpn are found to be quite accurately reproduced. Furthermore, for use in proton-nucleus and nucleus-nucleus collisions, we present a parametrization of thepn cross section within a broad kinematical range.Work supported by BMFT, GSI Darmstadt and a NATO science grant     

Phase-integral calculation of quantal matrix elements between unbound states,without the use of wavefunctions

The paper deals with the calculation of diagonal as well as off-diagonal matrix elements between unbound states pertaining to a radial Schrödinger equation. For the case that the effective potential, i.e. the potential with the centrifugal barrier included, is real and that only a single generalized classical turning point exists, we derive, on the basis of a phase-integral method, a new, general formula for the calculation of such matrix elements without the use of wavefunctions. The formula applies to an arbitrary order of the phase-integral approximations used. While conventional methods may present difficulties when the radial wavefunctions oscillate rapidly in space, this formula, in which the wavefunctions do not appear, is expected to be more accurate the more rapidly the wavefunctions oscillate. The formula is tested numerically for a Lennard-Jones potential and is found to yield extremely accurate results.

When specialized to the first-order approximation, our formula goes over into a formula derived previously by other authors. They derived the formula by introducing the first-order JWKB approximation for the wave-functions in the integral defining the matrix element and simplifying the resulting expression by using simple qualitative arguments. The remarkably good accuracy of this first-order formula has puzzled previous authors. So has also the fact that attempts to improve it, by including quantities neglected on the basis of the simple qualitative arguments, and by using Airy functions or uniform approximations for the wavefunctions through the turning points, have failed. Our derivation throws light on the question of the accuracy to be expected, and it explains why already the first-order formula is remarkably accurate and why no improvement is gained in the attempts mentioned.     

On the effect of off-shell wavefunctions onK andL shell charge transfer in fast,asymmetric collisions

Within the semiclassical strong potential Born approximation (SPB) we have calculated the electron capture from theK andL shell of a heavy target atom by protons using two different peaking approximations. Both total capture cross sections and impact parameter distributions are compared with the impulse approximation (IA) and in the case of transfer from the ArK-shell also with an exact evaluation of the SPB and with experimental data. While for theK shell, all theories give a similar impact-parameter dependence, there is a substantial difference between IA and SPB results for the 2s subshell.     

Quantum mechanical treatment of electron-positron excitations in heavy ion collisions with nuclear contact

A general theory is formulated of electron-positron excitations in heavy ion collisions with nuclear contact, treating the nuclear relative motion quantum mechanically. A set of coupled channel equations for the electronic occupation amplitudes is derived, which is formally very similar to the semiclassical theory based on a classical nuclear trajectory, and reduces to the latter in the JWKB approximation. The new coupled equations contain all the quantum mechanical information on the details of the nuclear scattering during nuclear contact. The importantce of this formulation for a quantitative theory of spontaneous positron creation in supercritical systems with nuclear time delay is pointed out. The possibility of line structures in the positron spectrum, as predicted semiclassically and recently discovered experimentally, is discussed in the framework of the DWBA approximation. For light-particle scattering off a nuclear resonance, the Blair formula for vacancy production is recovered in the same approximation.     

Soliton-antisoliton pair production in particle collisions

We propose a general semiclassical method for computing the probability of soliton-antisoliton pair production in particle collisions. The method is illustrated by explicit numerical calculations in a (1+1)-dimensional scalar field model. We find that the probability of the process is suppressed by an exponentially small factor which is almost constant at high energies.     

Semiclassical approach to the three-body muon-transfer collisions

Muon-transfer rates in collisions of hydrogen-like atoms or with light nuclei t, ³He, ⁴He, ⁶Li or ⁷Li, are calculated in a semiclassical approximation to the Faddeev-Hahn equations. The two nuclei involved are treated classically, while the motion of the muon in their Coulomb field is considered from the quantum mechanical point of view. The experimentally observed strong dependence on the charge of the nuclei is reproduced. Received: 1st November 1997 / Revised: 26 March 1998 / Accepted: 18 August 1998