Sensitivity of neutron radii in the ""sup208Pbnucleusandaneutronstartonucleon−"" sup 208_Pb nucleus and a neutron star to nucleon- sigma_-$ rho_ coupling corrections in relativistic mean field theory

We study the sensitivity of the neutron skin thickness, $S$, in a $^{208}$Pb nucleus to the addition of nucleon-sigma-rho coupling corrections to a selection (PK1, NL3, S271, Z271) of interactions in relativistic mean field model. The PK1 and NL3 effective interactions lead to a minimum value of $S$ = 0.16 fm in comparison with the original value of $S$ = 0.28 fm. The S271 and Z271 effective interactions yield even smaller values of $S$ = 0.11 fm, which are similar to those for nonrelativistic mean field models. A precise measurement of the neutron radius, and therefore $S$, in $^{208}$Pb will place an important constraint on both relativistic and nonrelativistic mean field models. We also study the correlation between the radius of a 1.4 solar-mass neutron star and $S$.Comment: 40 pages 13 figures. to be published in Physical Review

Energy-dependent Lorentz covariant parameterization of the NN interaction between 50 and 200 MeV

For laboratory kinetic energies between 50 and 200 MeV, we focus on generating an energy-dependent Lorentz covariant parameterization of the on-shell nucleon-nucleon (NN) scattering amplitudes in terms of a number of Yukawa-type meson exchanges in first-order Born approximation. This parameterization provides a good description of NN scattering observables in the energy range of interest, and can also be extrapolated to energies between 40 and 300 MeV.Comment: 18 pages, 7 figures, Final version accepted by Physics Review

Nuclear medium modifications of the NN interaction via quasielastic (p⃗,p⃗′\vec p,\vec p ') and (p⃗,n⃗\vec{p},\vec{n}) scattering

Within the relativistic PWIA, spin observables have been recalculated for quasielastic ($\vec p,\vec p '$) and ($\vec p,\vec n$) reactions on a $^{40}$Ca target. The incident proton energy ranges from 135 to 300 MeV while the transferred momentum is kept fixed at 1.97 fm^{-1}. In the present calculations, new Horowitz-Love--Franey relativistic NN amplitudes have been generated in order to yield improved and more quantitative spin observable values than before. The sensitivities of the various spin observables to the NN interaction parameters, such as (1) the presence of the surrounding nuclear medium, (2) a pseudoscalar versus a pseudovector interaction term, and (3) exchange effects, point to spin observables which should preferably be measured at certain laboratory proton energies, in order to test current nuclear models. This study also shows that nuclear medium effects become more important at lower proton energies ($\leq$ 200 MeV). A comparison to the limited available data indicates that the relativistic parametrization of the NN scattering amplitudes in terms of only the five Fermi invariants (the SVPAT form) is questionable.Comment: 10 pages, 6 Postscript figures, uses psfig.sty and article.sty, submitted to Phys. Rev.

Polarization transfer observables for quasielastic proton-nucleus scattering in terms of a complete Lorentz invariant representation of the NN scattering matrix

For the calculation of polarization transfer observables for quasielastic scattering of protons on nuclei, a formalism in the context of the Relativistic Plane Wave Impulse Approximation is developed, in which the interaction matrix is expanded in terms of a complete set of 44 independent invariant amplitudes. A boson-exchange model is used to predict the 39 amplitudes which were omitted in the formerly used five-term parameterization(the SPVAT form) of the nucleon-nucleon scattering matrix. Use of the complete set of amplitudes eliminates the arbitrariness of the five-term representation.Comment: 29 pages, 2 figure

Sensitivity of exclusive proton knockout spin observables to different Lorentz invariant representations of the NN interaction

Within the framework of the relativistic plane wave impulse approximation, we study the observable consequences of employing a complete Lorentz invariant representation of the NN scattering matrix in terms of 44 independent amplitudes, as opposed to the previously-employed, but ambiguous, five-term Lorentz invariant parametrization of the NN scattering matrix, for the prediction of complete sets of exclusive ($\vec{p},2 \vec{p}$) polarization transfer observables. Two kinematic conditions are considered, namely proton knockout from the $3s_{1/2}$ state of $^{208}$Pb at an incident energy of 202 MeV for coplanar scattering angles ($28.0^{\circ}, -54.6^{\circ}$), as well as an incident energy of 392 MeV for the angle pair ($32.5^{\circ}, -80.0^{\circ}$). The results indicate that certain spin observables are ideal for discriminating between the two representations.Comment: 19 pages, 5 figures, Revtex, To be published in Phys. Rev.

Relativistic descriptions of polarization transfer observables for quasielastic proton scattering

Thesis (PhD)--University of Stellenbosch, 1999.ENGLISH ABSTRACT: This thesis is devoted to the development of relativistic Dirac-based models for describing complete sets of quasielastic (p,p') and (p, ii) polarization transfer observables at medium energies. The original relativistic-plane-wave-impulse-approximation (RPWIA) model of Horowitz and Murdock is modified to include the phenomenological Horowitz-Love-Franey meson-exchange (HLF) model for the NN amplitudes, and new HLF parameter sets are generated between 80 and 200 MeV. Medium effects are incorporated by replacing free nucleon masses in the Dirac plane waves with more refined effective projectile and target nucleon masses. For a 4°Ca target at a fixed momentum transfer of 1.97 fm-1, and incident energies between 135 and 300 MeV, the sensitivity of complete sets of quasielastic (P,p') and (P, ii) polarization transfer observables is investigated with respect to nuclear medium effects, ambiguities in 1rNN coupling, exchange contributions to NN amplitudes, and spin-orbit distortions. It is seen that, (1) compared to (p,p 1 ) scattering, the (p, ii) polarization transfer observables are more sensitive to pseudoscalar versus pseudovector forms of the 1rNN coupling, (2) as the incident proton energy is lowered, nuclear medium effects and spin-orbit distortions become more important, (3) nuclear medium effects are extremely sensitive to the type of pion coupling, (4) contrary to the original RPWIA, exchange contributions cannot be neglected at energies as high as 500 MeV. For an optimal study of nuclear medium effects, this investigation stresses the urgent need for measurements of complete sets of quasielastic polarization transfer observables for both (p,p') and (p, n) reactions at energies lower than 200 MeV. Comparison of RPWIA predictions with the small amount of available data yields an inconsistent picture: The (P, p') data favour a pseudoscalar coupling for the pion, whereas the limited (P, n) data suggest a pseudovector form. Our poor treatment of distortions is considered to be the main source for this inconsistency. The issue of distortion effects on polarization transfer observables is addressed by developing the theoretical framework for the relativistic distorted wave impulse approximation. As an additional improvement over the RPWIA, models of nuclear structure (relativistic Fermi-gas model, relativistic mean-field approximation, and local-density-approximation) are developed, whereby the nuclear structure information is contained in a large set of nuclear responAFRIKAANSE OPSOMMING: Hierdie proefskrif handel oor die ontwikkeling van relatiwistiese modelle, gebaseer op die Diracformalisme, vir volledige stelle parameters vir spinpolarisasie-oordrag in die geval van kwasielastiese (p, p ') en (p, ii) verstrooiing by medium energiee. Die oorspronklike Relatiwistiese Vlakgolf-Impulsbenadering (RVI) van Horowitz en Murdock is gewysig om ook die fenomenologiese meson-uitruilmodel van Horowitz, Love en Franey (HLF-model) vir die nuckleon-nukleon (NN) amplitudes in te sluit. Hiervoor is 'n nuwe stel HLF-parameters vir die energiegebied 80- 100 MeV bereken. Om effekte van die omringende kernmedium in te sluit, is effektiewe nukleon massas tans vir beide die projektiel- en die teikennukleon op 'n nuwe, verfynde wyse bereken. Vir die kwasi-elastiese reaksies (p,p ') en (p, ii) met 4°Ca as teikenkern, invallende energiee tussen 135 en 500 MeV en 'n (vaste) momentum-oordrag van 1,97 fm-1, is volledige stelle polarisasie-parameters bereken. Laasgenoemde se gevoeligheid is ondersoek ten opsigte van effekte van die kernmedium, dubbelsinnighede ten opstigte van die 1r NN-interaksie, die bydraes van uitruilterme tot die NN-interaksie en die golfvervorming as gevolg van spin-baan koppeling. Die volgende is bevind: (1) Die polarisasieveranderlikes van die (p, ii)-reaksie is meer gevoelig ten opsigte van die keuse tussen 'n pseudoskalare of 'n pseudovektor term in die 1rNN-interaksie, as die van die (P,p ') reaksie; (2) Effekte van die kernmedium en spin-baan vervorming word belangrik by lae energiee; (3) Die effekte van die kernmedium is uiters gevoelig vir die tipe pion-koppeling; ( 4) In teenstelling met die oorspronklike RVI, kan uitruileffekte nie by hoer energiee, byvoorbeeld 500 MeV, verontagsaam word nie. Hierdie ondersoek beklemtoon dat, vir 'n behoorlike studie van effekte van die kernmedium, veral vir energiee laer as 200 MeV, volledige stelle van polarisasie-veranderlikes van beide (P,p') en (if, ii) reaksies gemeet moet word. Vergelykings met die beperkte beskikbare data (hoofsaaklik vanaf onvolledige stelle veranderlikes) lewer 'n onsamehangende prentjie: Die (p, ii)polarisasieveranderlikes gee voorkeur aan 'n pseudovektor term in die 1rNN-interaksie, waar die (if, p ') veranderlikes egter 'n pseudoskalare-term verkies. Die oorsaak van hierdie niekonsistensie kan moontlik aan die weglating van vervorming van die invallende golf deur die kernmedium gewyt word

Analytic continuation of single-particle resonance energy and wave function in relativistic mean field theory

Single-particle resonant states in spherical nuclei are studied by an analytic continuation in the coupling constant (ACCC) method within the framework of the self-consistent relativistic mean field (RMF) theory. Taking the neutron resonant state $\nu 1g_{9/2}$ in $^{60}$Ca as an example, we examine the analyticity of the eigenvalue and eigenfunction for the Dirac equation with respect to the coupling constant by means of a \pade approximant of the second kind. The RMF-ACCC approach is then applied to $^{122}$Zr and, for the first time, this approach is employed to investigate both the energies, widths and wave functions for $l\ne 0$ resonant states close to the continuum threshold. Predictions are also compared with corresponding results obtained from the scattering phase shift method.Comment: 19 pages, 9 figure

Electromagnetic production of hypernuclei

A formalism for the electromagnetic production of hypernuclei is developed where the cross section is written as a contraction between a leptonic tensor and a hadronic tensor. The hadronic tensor is written in a model-independent way by expanding it in terms of a set of five nuclear structure functions. These structure functions are calculated by assuming that the virtual photon interacts with only one bound nucleon. We use the most recent model for the elementary current operator which gives a good description of the experimental data for the corresponding elementary process. The bound state wave functions for the bound nucleon and hyperon are calculated within a relativistic mean-field model. We calculate the unpolarized triple differential cross section for the hypernuclear production process e + 12C --> e + K+ + 12_Lambda{B} as a function of the kaon scattering angle. The nuclear structure functions are calculated within a particle-hole model. The cross section displays a characteristic form of being large for small values of the kaon scattering angle with a smooth fall-off to zero with increasing angle. The shape of the cross section is essentially determined by the nuclear structure functions. In addition, it is found that for the unpolarized triple differential cross section one structure function is negligible over the entire range of the kaon scattering angle.Comment: 33 pages, 13 figure