H.J. Weber

Romanovski polynomials in selected physics problems

We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.

Pion production in two-body pd collisions

Abstract The reactions d(p, π + )t and d(p, π o ) 3 He are analyzed in terms of the pp → π + d sub-process. The exclusion principle induces an additional exchange contribution involving the π d scattering amplitude. Acceptable deuteron and tritron ( 3 H) wave functions which reproduce the charge form factors yield results consistent with experimental angular distributions at 470, 590, 754 and 1192 proton lab. energies. The forward peak is not sensitive to details of the wave functions. Both the direct and exchange form factors develop a zero which is imposed by the dip in the 3 He charge form factor. The associated interference pattern governs the backward cross section.

Theorie der Riesenresonanzen in sphärischengg-Kernen

The “Dynamic Collective Theory” ofDanos andGreiner has been extended to spherical nuclei. For the coupling of giant resonances with surface quadrupole-vibrations a systematical theory is developed by computing the dipole-quadrupole interactionK1(α2α1α1)0+K0 (α2α2)0 (α1α1)0+K2 ((α2α2)2 (α1α1)2)0. The dipole-quadrupole hamiltonian is solved by establishing the energy matrix with the 1-dipole-many-quadrupole phonon states as a basis.

Zur Klassifikation der Zustände des 5-dimensionalen harmonischen Oszillators

A classification of the eigenstates of the harmonic quadrupole oscillator is given within the framework of the Lie-AlgebraB2 ofR(5). There still exists the problem of complete classification, since the multiplicitydv(l2) for seniority numbersv≧6 may be greater than one. For these multiplicitiesdv(l2) easily managable recursion formulae are derived and therefore their explicit calculation for arbitraryv andl2 is easily possible.

Relativistic quark spin coupling effects in the nucleon electromagnetic form-factors

Abstract We investigate the effect of different forms of relativistic spin coupling of constituent quarks in the nucleon electromagnetic form factors. The four-dimensional integrations in the two-loop Feynman diagram are reduced to the null-plane, such that the light-front wave function is introduced in the computation of the form factors. The neutron charge form factor is very sensitive to different choices of spin coupling schemes, once its magnetic moment is fitted to the experimental value. The scalar coupling between two quarks is preferred by the neutron data, when a reasonable fit of the proton magnetic momentum is found.

Exclusion principle effects in pion-nucleus scattering in the region of the 3,3 resonance

Abstract Chew-Low theory for pion scattering is examined for a nucleon immersed in a Fermi sea. All exclusion principle effects, including those internal to the pion-nucleon scattering amplitude, are considered, and the modifications of the 3, 3 resonance in nuclei are studied. An optical model is constructed in a local density approximation. Results are compared with recent data on pion scattering from 12C.

Relativistic corrections of the electromagnetic current in a one-pion exchange model☆

Abstract Photon absorption or emission in nucleon-nucleon collisions is studied in the one-pion exchange approximation. A gauge-invariant expansion in 1/ m is obtained for the isoscalar electro-magnetic current. Kinematic and dynamic relativistic corrections are discussed.

BAG MODEL QUANTUM CHROMODYNAMICS AT LOW-ENERGY

Gluon-exchange mediating quark-exchange scattering is the mechanism of lowest order in perturbative QCD that contributes to the strong interactions at low energy. When it is dressed with long-range quark-gluon correlations by means of bag-model wavefunctions, this quark interchange force becomes bilocal in the quark-gluon sector involving the whole bag and non-perturbative. When it is Fierz-rearranged, the quark-interchange amplitude takes on the usual local form for each hadron that is expected from the wealth of empirical knowledge at low energy. This quark interchange is calculated here in the MIT bag model, which is supplemented by tunneling rules, and then applied to elastic NN scattering, and subsequently toπN andππ scattering. For each reaction the OBE interaction is obtained in agreement with meson theoretic models. Repulsive axial-vector meson exchanges are predicted for NN scattering at short range. The chiral structure of the quark interchange force in conjunction with its tunneling aspects suggest an interpretation of the strong interactions at low energy as Josephson currents of non-Abelian superconductivity.

Theorie der Riesenresonanzen in sphrischen Kernen: II. Theorie und Experiment

The dynamic collective theory has been developed for vibrational nuclei in a previous paper. Here the details are studied and compared with experiments. For this purpose the structure of the dipole operator has been established, the energy matrix of the dipole-quadrupole interaction has been diagonalized and the various approximations are discussed quantitatively in detail. It is interesting that this systematic theory gives the details of theγ-absorption cross section in many nuclei.The dynamic collective theory has been developed for vibrational nuclei in a previous paper. Here the details are studied and compared with experiments. For this purpose the structure of the dipole operator has been established, the energy matrix of the dipole-quadrupole interaction has been diagonalized and the various approximations are discussed quantitatively in detail. It is interesting that this systematic theory gives the details of theγ-absorption cross section in many nuclei.

Are there bound A=2 hyperon states?

Abstract One-boson-exchange potentials for ΛN , Σ + p , ΛΛ and Ξ N elastic scattering at E lab ≲ 150 MeV are calculated including renormalizations due to two-boson exchanges. The model is derived from a quark pairing mechanism that has previously been tested for elastic NN scattering. The resulting phase shifts and effective range parameters are compared with data and other phenomenological potentials for Λ N and Σ + p systems, and reasonable agreement is achieved. In the ΛΛ and Ξ N channels, deuteron-like bound states may exist.