Low Partial Waves Research Articles

Threshold law for electron-atom impact ionization: towards the inside contribution of the Coulomb-dipole theory

The author has previously derived an ionization threshold law on the basis of the Coulomb-dipole theory, but including only the contribution from the outer (semi-asymptotic) region of configuration space to the relevant matrix element. Here the author initiates a study of the (overwhelmingly dominant) inside contribution. The main part of this paper is devoted to a detailed analysis of the asymptotic form to which the inside function must be attached. The author returns to an older approach of deriving the ionization yield by extrapolating excitation cross sections of excited states (N) (because the asymptotic form there is known to be dipole configurations of degenerate (l) states for each N excited by the incoming electron) into the continuum. Here the author concentrates on the dipole matrix from which the dipole configurations are obtained; it is derived analytically; its eigenfunctions and eigenvalues are evaluated numerically to very high N (for several of the lower partial waves L). A key parameter emerges, JC(N,L), which specifies the number of coherent, attractive, dipole states as a function of N and L.

Rainbow-shift mechanism behind discrete optical-potential ambiguities.

Some years ago, Drisko et al. suggested that the discrete ambiguity often encountered for elastic scattering optical potentials could be understood as being due to the interior or small-l S-matrix elements for two ``equivalent'' potentials differing in phase by 2\ensuremath{\pi}, l-by-l. We point out that the absence of this phase change for peripheral partial waves is equally essential, and suggest that a deeper understanding of the ambiguity may be achieved by viewing it as a consequence of a farside interference between interior and peripheral partial waves. It is this interference which produces the broad ``Airy maxima'' of a nuclear rainbow, and we show that a Drisko-type phase-shift increment ${\mathrm{\ensuremath{\delta}}}_{\mathit{l}}$\ensuremath{\rightarrow}(${\mathrm{\ensuremath{\delta}}}_{\mathit{l}}$+\ensuremath{\pi}) for low-l phases relative to the high-l ones is exactly what is needed to shift a farside rainbow pattern by one Airy maximum, thus providing an equivalent ``rainbow-shift'' interpretation of the discrete ambiguity. The physical importance of both interpretations lies in the fact that the existence of discrete ambiguities (as well as of nuclear rainbows) is explicit evidence for low-l transparency in nucleus-nucleus collisions. The essential role played by low partial waves explains why peripheral reactions have generally not proven helpful in resolving this ambiguity.

Hybrid approach to electron scattering from polar molecules.

Electron scattering from polar molecules is studied in a hybrid approach that uses the recently introduced algebraic-eikonal approach to describe the forward-angle scattering and the results of, for example, a close-coupling calculation for larger angles. The two calculations are matched by making a partial-wave expansion and combining the high partial waves of the algebraic-eikonal approach with the low partial waves obtained in a full close-coupling calculation. The method is illustrated by applying it to electron scattering from a rigid-rotor molecule with a large dipole moment.

Elastic scattering ofα-particles from20Ne

A relatively simple procedure using nuclear interaction calculated microscopically from two-nucleon potential employing equivalence of resonating group method and generator coordinate method has been used to calculate the differential cross-sections (DCS) forα +20Ne elastic scattering atElab=18.0, 20.2, 21.9, 23.0 and 27.2 MeV. The absorption effects due to the opening of the non-elastic channels are taken into account approximately by the sharp cut-off of lower partial waves. The anomalous large oscillations of the DCS at backward angles atElab=18.0 and 27.2 MeV are reproduced. The calculated results are in fair agreement with the experimental data.

Relativistic potential model of proton-proton scattering spin observables.

A model has been constructed of the interaction between two protons and applied to the calculation of spin-dependent elastic-scattering parameters over a range of beam momenta from 3 to 24 GeV/c. The interaction is one-boson exchange, augmented by a zero-range core and an imaginary potential to model absorption into inelastic channels. The model provides excellent agreement with experimental measurements of the unpolarized differential cross section, and reproduces the qualitative features of the transverse asymmetry and spin correlation. The absorptive potential is found to dominate the real potential, greatly attenuating the low partial waves. This suggests that perturbative quantum chromodynamics does not apply to elastic scattering at the energy scale examined here, since absorptive effects prevent the quarks from approaching to appropriately small separations.

The theoretical treatment of low-energy e+-H2 scattering using the Kohn variational method

The authors present calculations of e+-H2 scattering below the positronium formation threshold at 8.63 eV for the Sigma g+, Sigma u+, Pi u and Pi g symmetries using the generalized Kohn method. Mixing of the two lowest partial waves is allowed for in the Sigma g+, Sigma u+ and Pi u symmetries, using a two channel K-matrix. Comparisons with Kohn calculations of the lowest partial waves of these symmetries show that mixing of partial waves has a relatively small effect on the contributions to the total scattering cross section at the energies considered. The Pi g calculation includes only the lowest partial wave. As well as separable short-range correlation functions, the trial functions used in these calculations include Hylleraas-type functions containing the positron-electron distance as a linear factor and functions appropriate for taking into account long-range polarization of the hydrogen molecule.

Quantum molecular dynamics study of fusion and its fade out in the 16O+16O system.

The quantum molecular dynamic method is used to study the fusion reaction in the $^{16}\mathrm{O}$${+}^{16}$O system and its fade out with the increase of the incident energy. It is shown that without two-nucleon collisions there appears the so-called fusion window, as in the time-dependent Hartree-Fock approach, while with the inclusion of two-nucleon collisions the low partial wave cutoff in fusion disappears. The fade out of the fusion process with the increase of the incident energy is found to be due to the increase of the cross sections mainly of the incomplete fusion process in the whole range of the impact parameter and partly of the deep-inelastic-collision--like process in the peripheral region. The calculated fusion cross section as a function of incident energy is shown to be in good accordance with experiments.

Phase shift analysis of all proton-proton scattering data below Tlab=350 MeV.

As a continuation of our 0--30 MeV analysis we present a multienergy phase shift analysis of all {ital pp} scattering data below {ital T}{sub lab}=350 MeV. In the description of all partial waves we take exactly into account the long-range potential consisting of the improved Coulomb potential (including the magnetic moment interaction), the vacuum polarization potential, and the tail of the one-pion-exchange potential. To describe the short-range interaction in the lower partial waves we use a {ital P}-matrix parametrization. The intermediate partial waves are treated either by optimal mapping techniques or by using the Nijmegen soft-core potential. The latter gives a better description of the data. The final data set comprises 1626 scattering observables. The best fit to this final data set results in {chi}{sup 2}/{ital N}{sub df}=1.117, where {ital N}{sub df}=1576 is the number of degrees of freedom. The {ital pp}{pi}{sup 0} pseudovector coupling constant is determined to be {ital f}{sub 0}{sup 2}=(74.9{plus minus}0.7){times}10{sup {minus}3}. Single-energy phase shifts and errors are also given.

Hyperon resonances in SU(3) soliton models

Hyperon resonances excited in kaon-nucleon scattering are investigated in the framework of an SU (3) soliton model in which kaon degrees of freedom are treated as small fluctuations around an SU (2) soliton. For partial waves l ⩾ 2 the model predicts correctly the quantum numbers and average excitation energies of most of the experimentally observed Λ and Σ resonances. Some disagreement are found for lower partial waves.

Positron-hydrogen scattering including short- and long-range correlations

An integral form of the close-coupling approximation has been employed to investigate positron-hydrogen scattering. Two coupling schemes (1s-2s-2p-Ps and 1s-2s-2p-Ps) are employed and the present method includes the short- and long-range correlations partially. The calculations have been carried out for low (<or=3) partial waves and up to the incident energy 10.0 eV. The effect of the positronium formation channel is found to be significant in the energy region considered. Low-order elastic phaseshifts and ground-state capture cross sections are found to be very encouraging. The model proves to be a systematic way to attack the e+-H system.

Symmetry analysis of accurate H+H 2 resonances for low partial waves

We have performed accurate quantum mechanical three-dimensional reactive scattering calculations for both parities of the J = 1 partial wave of the H + H 2 system up to total energies of 1.75 eV. The collision lifetime resonance spectra for both J = 0 and J = 1 are discussed in terms of the characteristics of the system's potential energy surface and of a simple physical model involving its symmetry properties.

Hamiltonian hierarchy and the Hulthén potential.

We deal with the Hamiltonian hierarchy problem of the supersymmetry quantum mechanics for the Hulth\'en potential and find that the associated ``supersymmetric partners'' belong to the Eckart class of potentials. The partner potentials, on the one hand, simulate the effect of the centrifugal barrier fairly accurately at least for few lower partial waves and, on the other hand, provide a natural basis for writing expressions for higher partial wave Jost functions. We present specific results for the p and d waves and examine their Coulomb limits.

Phase shift analysis of 0-30 MeV pp scattering data.

A multienergy phase shift analysis of all published proton-proton (pp) scattering data in the energy range ${T}_{\mathrm{lab}\mathrm{\ensuremath{\le}}30}$ MeV is presented. In the description of all partial waves the well-known long-range interaction is included: the improved Coulomb, the vacuum polarization, and the one-pion-exchange potential. In the lower partial waves the energy-dependent analysis uses a P-matrix parametrization for the short-range interaction. Special attention is paid to the electric interaction, the definition of the phase shifts, and the selection of the data. The fit to the final data set comprising 360 scattering observables results in ${\ensuremath{\chi}}^{2}$/${N}_{\mathrm{df}=1.0}$, where ${N}_{\mathrm{df}}$ is the number of degrees of freedom. The pp${\ensuremath{\pi}}^{0}$ coupling constant is determined to be ${\mathit{g}}_{\mathrm{pp}}$${\mathrm{\ensuremath{\pi}}}_{^{2}}^{0}$/4\ensuremath{\pi}=14.5\ifmmode\pm\else\textpm\fi{}1.2, but there are several indications for a lower value. The optimum value for the P-matrix radius b\ensuremath{\approxeq}1.4 fm is satisfying. Single-energy phase shifts with second derivative matrices, and effective range parameters are given.

Extension of the Bonn meson exchange NN potential above pion production threshold: Nucleon renormalization and unitarity

Nucleon self-energy diagrams, which are necessary to satisfy unitarity in NN scattering above pion production threshold, are studied for a realistic one-boson-exchange model. It is demonstrated that, in the framework of noncovariant perturbation theory, the independent iteration of (lowest order) bubble diagrams at both nucleon lines leads to dressing factors which provide well-defined off-shell corrections to the meson exchange contributions. It turns out that nucleon dressing yields additional attraction in lower partial waves. A slight readjustment of meson parameters (especially a reduction of the cutoff mass in the \ensuremath{\pi}NN vertex) leads to a reproduction of the empirical NN data below pion threshold which is of the same quality as before. The resulting inelasticities are, however, much too small, which clearly establishes the need for using a NN potential model containing the \ensuremath{\Delta} isobar explicitly.

Baryon resonances as soliton excitations from an effective meson Lagrangian

The replacement of the higher order Skyrme terms by explicit vector meson fields improves the results for the baryon resonances. For the low partial waves the situation is still unsatisfactory. In the case of the S11 channel a great improvement is aceived by inclusion of an isoscalar-scalar glueball field.

The theoretical treatment of low-energy e+-H2scattering using Kohn trial functions containing Hylleraas-type functions

The lowest partial wave is calculated for low-energy e+-H2 scattering using a Kohn trial function which includes basis functions containing the positron-electron distance as a linear factor, i.e. Hylleraas-type functions. All the necessary matrix elements are accurately evaluated using, at the most, one-dimensional numerical integration. The inclusion of Hylleraas-type functions has a very significant effect on the low-energy phaseshift; and total cross section, bringing the cross section into agreement with experiment for incident positron energies less than about 2 eV. The authors have already reported the dramatic effect the inclusion of Hylleraas-type functions has on the calculated value of Zeff, the effective number of electrons per molecule available to the positron for annihilation. As far as they are aware, this is the first time that Hylleraas-type functions have been used in a molecular scattering calculation.

The inclusion of $\pi$ functions in the treatment of low-energy positron - hydrogen-molecule scattering by a generalisation of the Kohn method

In the application of a generalisation of the Kohn method to low-energy positron-hydrogen-molecule scattering which was described in a recent letter, up to 31 short-range correlation functions, made up of one-particle functions of sigma symmetry, were included in the trial function. In the calculation described in this paper, the flexibility of the trial function is greatly improved by the inclusion of up to 64 short-range correlation functions of which 32 contain products of one-particle functions of pi symmetry. The inclusion of the pi functions has a very big effect on the calculated results, especially at very low energies. The behaviour of the phaseshift values with increasing incident energy is qualitatively similar to the behaviour of the corresponding S-wave phaseshifts in low-energy positron-helium scattering. Comparison with experiment indicates that the results reproduce qualitatively the experimental trend at very low energies but higher partial waves must make a significant contribution to the total cross section above about 0.1 eV. The improved results can be attributed to the much more satisfactory description of the polarisation of the hydrogen molecule made possible by the inclusion of pi functions.

Elastic scattering of positrons and electrons by argon

Differential and integrated cross sections for the elastic scattering of low- and intermediate-energy (3--300 eV) positrons and electrons by argon atoms are calculated. Higher transport cross sections, representing moments of 1-(costheta)/sup n/, for these systems are also obtained for n = 1--4. Model potentials are used to represent the interactions between positrons or electrons and argon atoms. For each impact energy, the phase shifts of the lower partial waves are obtained exactly by numerical integration of the radial equation. The Born approximation is used to obtain the contribution of the higher partial waves to the scattering amplitude. The phase shifts of the seven lowest partial waves are tabulated for various impact energies of positrons and electrons.

Electron-impact excitation of inelastic transitions in C V.

The collision strengths for the inelastic transitions among the lowest eleven LS states of C v are presented. Configuration-interaction wave functions are used to represent the eleven target states which are included in the calculation. The calculation for the lower partial waves (l\ensuremath{\le}11) are carried out using the R-matrix method. The contribution from higher partial waves is obtained in the close-coupling approximation with exchange terms omitted. The effective collision strengths have been calculated assuming a Maxwellian distribution of electron energies. Results are also presented for calculations in which the five lowest states were included. The present results are compared with the previous calculation of Pradhan, Norcross, and Hummer. Some significant differences are noted, particularly at lower temperatures for some transitions.

Partial wave cross sections for 34S + 130Te fusion

Angular and multiplicity distributions for the γ-decay of 164Er compound nuclei have been measured with the Darmstadt-Heidelberg Crystal Ball. Combining this information with the fusion cross section of (500 ± 50)mb, a compound nuclear spin distribution has been derived which almost exhausts the unitarity limit for lower partial waves. Near the limiting angular momentum of (52 ± 2)ℏ the distribution of partial wave cross sections exhibits a steeper fall-off than predicted by barrier fluctuation and coupled channel calculations.