DWBA approach to inelastic scattering at medium energies

Medium energy proton elastic and inelastic scattering to states of ⁵⁸Ni and ²⁰⁸Pb, and ⁴He elastic and inelastic scattering to states of ⁴⁰Ca, are analyzed using the partial wave approach, by solving the Schrödinger equation with relativistic kinematics and using the distorted wave Born approximation. Our results can be compared with results of several previous analyses of the nucleon inelastic data using the Glauber approximation. Our calculations are absolute, using nuclear collective parameters obtained from a survey of a large number of low-energy analyses of inelastic scattering of electrons, nucleons and nuclei from ⁴⁰Ca, ⁵⁸Ni and ²⁰⁸Pb.     

Elastic and inelastic scattering of nucleons from 16O

Measurements of differential elastic and inelastic cross sections for neutron scattering from ¹⁶O at incident energies 18 to 26 MeV are presented. In addition to cross sections for neutron scattering differential cross sections for proton scattering up to 66 MeV are described in terms of phenomenological optical model potentials. At 24.5 MeV incident energy inelastic scattering up to 11.5 MeV excitation was measured. The elastic and inelastic compound nucleus contributions were examined. Direct inelastic scattering from the normal parity states was calculated using the DWBA and coupled-channel formalisms. The inelastic scattering cross section from non-normal parity state 2⁻ was calculated using the coupled-channel formalism via multi-step processes. Cross sections due to inelastic scattering from some of the states, which are thought to be members of an excited state rotational band were calculated using both vibrational and rotational approaches and were compared.     

Electron scattering off simple atoms for large momentum transfer collisions

In a previous paper this author examined the Born expansion and isolated those parts of the expansion that contribute most significantly to the scattering amplitude for large momentum transfer collisions in inelastic collisions from the ground state of both hydrogen and helium. It turned out that certain terms where the scattering electron interacts once with the nucleus and once with the other electron dominate. The physical reason is that large momentum transfer collisions require the nucleus to take the bulk of the incident momentum but require an interaction with the one of the bound electrons to change the state of the atom. The arguments are quite general and this paper will extend this analysis by comparing the inelastic results obtained by this method for hydrogen and helium to a close coupling calculation with many intermediate states. Further, we will extend this analysis to the correction to the 1st Born result for elastic electron-hydrogen and electron-helium collisions and provide some results for scattering from the initial metastable states of hydrogen for large momentum transfer collisions. A comparison of the results of this analytic approach will be made to the numerical close coupling approach and experiments where available. The agreement is remarkable.     

Closed-form quantal description of inelastic heavy ion scattering

The amplitude for inelastic heavy ion scattering, given by the distorted-wave theory for excitation of low-lying collective states, is evaluated in closed form. Use is made of the Austern-Blair relation and of other approximations appropriate for strongly absorptive interaction to express the inelastic partial-wave amplitude entirely in terms of the elastic S-matrix elements in the initial and final channels. The resulting formulae display explicitly the various contributions to the transition amplitude, whose superposition gives rise to the variety of interference patterns observable in the angular distributions and excitation functions of inelastic heavy ion scattering. It is shown that, as for elastic scattering, the dominant mechanism in inelastic heavy ion collisions near and above the Coulomb barrier is diffractive scattering of Fresnel type.     

Multiphonon atomic scattering by solid surfaces

A multiphonon solution for the problem of atom-surface scattering at thermal energies is proposed. The scattering equations are solved using the assumption of low inelastic scattering intensities, and the theoretical formalism is basically an improvement of a previous work on one-phonon scattering. Present results reduce to the one-phonon expression of the previous work when the appropriate limit is taken.     

The effect of inelastic electron scattering on the conductivity of very thin wires

The behaviour of the conductivity of a thin wire is calculated in the regime in which inelastic scattering between localized states is beginning to limit the metallic conductivity apparent at higher temperatures. The implications of this for the experiments of Giordano et al. and of Chaudhari and Habermeier, and the possibility of using it to detect inelastic scattering of electrons when elastic scattering is dominant, are discussed.     

Elastic and inelastic scattering of 18O by 16O and 18O

Angular distributions have been measured for the elastic and inelastic scattering of ¹⁸O by ¹⁶O and ¹⁸O at laboratory bombarding energies of 42 and 52 MeV. The inelastic scattering data are analyzed in terms of collective excitations using a coupled channel approach. Deformation parameters are obtained for the strongly excited states. The relationship between the strength of inelastic scattering and the amount of structure in the elastic scattering distributions is discussed.     

Spatial quantum beats in vibrational resonant inelastic soft x-ray scattering at dissociating states in oxygen

Resonant inelastic soft x-ray scattering (RIXS) spectra excited at the 1σ(g) → 3σ(u) resonance in gas-phase O2 show excitations due to the nuclear degrees of freedom with up to 35 well-resolved discrete vibronic states and a continuum due to the kinetic energy distribution of the separated atoms. The RIXS profile demonstrates spatial quantum beats caused by two interfering wave packets with different momenta as the atoms separate. Thomson scattering strongly affects both the spectral profile and the scattering anisotropy.     

Raman scattering from plasmon-polaritons in a nipi superlattice

Linear response-function theory is used to determine Green functions describing plasmon-polaritons in superlattices consisting of n- and p-doped semiconductors intercalated by an insulator. Applications are made to inelastic light scattering of Raman type off these excitations, and we compare our results with previous works on the subject.     

Fine structure of the cross section of contact inelastic scattering of an X-ray photon by an atom

The analytical structure of the double differential cross section of contact inelastic scattering of an X-ray photon by a free atom is established by the methods of the theory of irreducible tensor operators beyond impulse approximation. For the example of an Ne atom in the energy region of the ionization threshold of the 1 s shell, the existence of a fine structure of the cross section caused by transitions of electrons of the atomic core to excited states of the discrete spectrum is predicted theoretically. The results of the calculation with the effects of radial relaxation, inelastic scattering via the formation of intermediate states, and elastic Rayleigh scattering taken into account are predictive in character and, at the incident photon energy of 22 keV, are in good agreement with the results of the synchrotron experiment. Original Russian Text ? A.N. Khoperskiĭ, A.M. Nadolinskiĭ, A.S. Kasprzhitskiĭ, 2008, published in Optika i Spektroskopiya, 2008, Vol. 105, No. 1, pp. 5–10.     

Transverse beam spin asymmetries at backward angles in elastic electron-proton and quasielastic electron-deuteron scattering

We have measured the beam-normal single-spin asymmetries in elastic scattering of transversely polarized electrons from the proton, and performed the first measurement in quasielastic scattering on the deuteron, at backward angles (lab scattering angle of 108°) for Q2 = 0.22 GeV2/c2 and 0.63 GeV2/c2 at beam energies of 362 and 687 MeV, respectively. The asymmetry arises due to the imaginary part of the interference of the two-photon exchange amplitude with that of single-photon exchange. Results for the proton are consistent with a model calculation which includes inelastic intermediate hadronic (πN) states. An estimate of the beam-normal single-spin asymmetry for the scattering from the neutron is made using a quasistatic deuterium approximation, and is also in agreement with theory.     

Resonant inelastic contact scattering of X-ray photons on atoms and ions

The existence of an extended resonance structure outside the X-ray emission regions is theoretically predicted in the total double differential cross section for the scattering of linearly polarized photons on free atoms (ions). This structure is almost entirely determined by inelastic photon scattering of the contact type. The amplitude of the inelastic contact scattering probability is described using an analytical expression for a non-relativistic transition operator, which was previously obtained by the author outside the dipole and momentum approximations. The resonant inelastic contact scattering of X-ray photons on a neon atom and neonlike ions of argon, titanium, and iron has been studied. Calculations were performed in a nonrelativistic approximation for the wave functions of the scattering states, with allowance for many-body effects of the radial relaxation of one-electron orbitals in the Hartree-Fock field of a deep 1s vacancy and (for neon atom) the double excitation/ionization of the ground atomic state.     

Bound states and scattering resonances induced by spatially modulated interactions

We study the two-body problem with a spatially modulated interaction potential using a two-channel model, in which the interchannel coupling is provided by an optical standing wave and its strength modulates periodically in space. As the modulation amplitudes increase, there will appear a sequence of bound states. Part of them will cause a divergence of the effective scattering length, defined through the phase shift in the asymptotic behavior of scattering states. We also discuss how the local scattering length, defined through short-range behavior of scattering states, modulates spatially in different regimes. These results provide a theoretical guideline for a new control technique in the cold atom toolbox, in particular, for alkaline-earth(-like) atoms where the inelastic loss is small.     

Multi-step processes in high-energy elastic and inelastic nuclear scattering

Multi-step processes in elastic and inelastic nuclear scattering at intermediate and high energies are investigated using a formulation whereby a finite number of channels are explicitly treated while all the other channels are approximately accounted for through a “second-order potential matrix”. Within the framework of the eikonal approximation the problem reduces to a finite system of first-order coupled integro-differential equations with non-local potentials which depend on the two-body density matrix of the target nucleus. The relationship of the above formulation to the DWIA, the close-coupling method, and the Glauber multiple scattering model is examined. This approach is applied to the elastic and inelastic (2⁺, 4.43 MeV) scattering of 1 GeV nucleons by ¹²C. The corrections to the DWIA are sizeable, and the inelastic scattering appears to be very sensitive to the multi-step contributions and the nuclear structure.     

Unitarity relation for deep inelastic scattering

Saturating the multiparticle states in the unitarity relation for virtual Compton scattering by two-particle states consisting of an infinite set of high mass vector mesons and a nucleon leads to a non-linear integral equation the solution of which determines the behaviour in the scaling limit and the non-forward scaling functions for deep inelastic scattering.     

Multiphonon resonances in the Debye-Waller factor of atom surface scattering

He atom surface scattering by dispersionless phonons is treated employing coupled channel (CC) calculations. At low energies, they predict a behavior opposite to perturbative Born or "exponentiated" Born approximation: strong resonant phonon stimulated elastic and inhibited inelastic scattering. The corresponding resonances have not been observed in earlier CC results since these have considered only the temperature dependence of the Debye-Waller factor at higher energy or omitted the attractive well. The resonances can be interpreted in terms of bound states in the attractive well with several excited vibrational quanta. They may be observable for, e.g., He scattering by a cold Xe/Cu surface.     

Microscopic and macroscopic aspects of 135 MeV proton scattering from 16O

Differential cross sections have been measured for the scattering of 135 MeV protons from ¹⁶O and data from the transitions to 13 states (up to 19.5 MeV excitation) have been analysed using microscopic and macroscopic nuclear reaction models. Extensive collective model calculations have been made of the transitions to all natural-parity states. The deformation parameters for the 4p4h rotational band are in good agreement with theoretical models. The inelastic scattering data from the excitation of the negative-parity states have also been analysed in the distorted-wave approximation using microscopic (shell and RPA) models of nuclear structure and with density-dependent two-nucleon t-matrices. For positive-parity states, we report the first shell-model calculation using the complete 2?ω basis space and find that the triplet of 2p2h states (4⁺, 2⁺, 0⁺) around 11 MeV excitation is quite well described by this model, as may be a 1⁺ state which is observed for the first time by proton scattering from ¹⁶O.