arXiv subjects
Publications and source records attributed to H. V. von Geramb.
Quantum information entropy is calculated from the nucleon nucleus forward scattering amplitudes. Using a representative set of nuclei, from $^4$He to $^{208}$Pb, and energies, $T_{lab} < 1$\,[GeV], we establish a linear dependence of quantum information entropy as functions of logarithm nuclear mass $A$ and logarithm projectile energy $T_{lab}$.
We investigate $K^{+}$-nucleus elastic scattering at intermediate energies within a microscopic optical model approach. To this effect we use the current $K^{+}$-nucleon {\it (KN)} phase shifts from the Center for Nuclear Studies of the George Washington University as primary input. First, the {\it KN} phase shifts are used to generate Gel'fand-Levitan-Marchenko real and local inversion potentials. Secondly, these potentials are supplemented with a short range complex separable term in such a way that the corresponding unitary and non-unitary {\it KN} $S$ matrices are exactly reproduced. These {\it KN} potentials allow to calculate all needed on- and off-shell contributions of the $t$ matrix,the driving effective interaction in the full-folding $K^{+}$-nucleus optical model potentials reported here. Elastic scattering of positive kaons from $^{6}$Li, $^{12}$C, $^{28}$Si and $^{40}$Ca are studied at beam momenta in the range 400-1000 MeV/{$c$}, leading to a fair description of most differential and total cross section data. To complete the analysis the full-folding model, three kinds of simpler $tρ$ calculations are considered and results discussed. We conclude that conventional medium effects, in conjunction with a proper representation of the basic {\it KN} interaction are essential for the description of $K^{+}$-nucleus phenomena.
The formalism of two coupled Dirac equations within constraint instant form dynamics is used to study the nucleon-nucleon interaction. The salient features and the final Schroedinger type equation is given. Explicitly energy dependent coupled channel potentials, for use in partial wave Schroedinger like equations, with nonlinear and complicated derivative terms, result. We developed the necessary numerics and study np and pp scattering phase shifts for energies 0-3 GeV and the deuteron bound state. The interactions are inspired by meson exchange of pi, eta, rho,omega and sigma mesons for which we adjust coupling constants. This yields, in the first instant, high quality fits to the Arndt phase shifts 0-300 MeV. Second, the potentials show a universal, independent from angular momentum, core potential which is generated from the relativistic meson exchange dynamics. Extrapolations towards higher energies, up to 3 GeV, allow to separate a QCD dominated short range zone as well as inelastic nucleon excitation mechanism contributing to meson production. A local and/or nonlocal optical model, in addition to the meson exchange Dirac potential, produces agreement between theoretical and data phase shifts. Third, the 1S0, 3P0 and 3P1 partial waves elicit a fusion/scission, for T-Lab<1GeV, and a fusion/fission, for T-Lab>1 GeV, mechanism for intermediate dibaryon formation.
The nonrelativistic full-folding optical model approach for nucleon-nucleus scattering is extended into the relativistic regime. In doing so, kinematical issues involving the off-shell Lorentz boost of the colliding particles between the two nucleons and the projectile-nucleus center-of-mass reference frames have been taken into account. The two-body effective interaction is obtained in the framework of the nuclear matter g-matrix using nucleon-nucleon optical model potentials that fully account for the inelasticities and isobar resonances in the continuum at nucleon energies up to 3 GeV. Diverse nucleon-nucleon potential models were constructed by supplementing the basic Paris, Nijmegen, Argonne or Gel'fand-Levitan-Marchenko inversion potentials with complex separable terms. In each case the additional separable terms ensured that the combination led to NN scattering phase shifts in excellent agreement with experimental values. With each phase shift fitting potential nuclear matter g-matrices have been formed and with each of those relativistic full-folding optical potentials for nucleon-nucleus elastic scattering determined. Application to such scattering for projectile energies to 1.5 GeV have been made. Good and systematic agreement is obtained between the calculated and measured observables, both differential and integrated quantities, over the whole energy range of our study. A moderate sensitivity to off-shell effects in the differential scattering observables also is observed.
The relativistic light-front dynamics (LFD) method has been shown to give a correct description of the most recent data for the deuteron monopole and quadrupole charge form factors obtained at the Jefferson Laboratory for elastic electron-deuteron scattering for six values of the squared momentum transfer between 0.66 and 1.7 (GeV/c)$^{2}$. The good agreement with the data is in contrast with the results of the existing non-relativistic approaches. In this work we firstly make a complementary test of the LFD applying it to calculate another important characteristic, the nucleon momentum distribution $n(q)$ of the deuteron using six invariant functions $f_{i}$ $(i=1,...,6)$ instead of two ($S$- and $D$-waves) in the nonrelativistic case. The comparison with the $y$-scaling data shows the decisive role of the function $f_{5}$ which at $q\geq$ 500 MeV/c exceeds all other $f$-functions (as well as the $S$- and $D$-waves) for the correct description of $n(q)$ of the deuteron in the high-momentum region. Comparison with other calculations using $S$- and $D$-waves corresponding to various nucleon-nucleon potentials is made. Secondly, using clear indications that the high-momentum components of $n(q)$ in heavier nuclei are related to those in the deuteron, we develop an approach within the natural orbital representation to calculate $n(q)$ in $(A,Z)$-nuclei on the basis of the deuteron momentum distribution. As examples, $n(q)$ in $^{4}$He, $^{12}$C and $^{56}$Fe are calculated and good agreement with the $y$-scaling data is obtained.
Within the key issues of hadronic physics one of the interesting issues in nuclear physics is whether there is a transition region between meson-nucleon and quark-gluon degrees of freedom in the NN interaction. This question is relevant for pairs of free nucleons as well as for nucleon pairs immersed in nuclear matter. From NN phase shifts we deduce a dibaryonic scale of 1 GeV for the soft core NN potential strengths at nucleon separation r equal 0.25 to 0.5 fm. A short range intermediate transition, with fusion and fission of the two scattered nucleons into a dibaryon with prevailing quark-gluon dynamics, is conjectured from NN optical models for T-lab greater 1.5 GeV. From efforts and progress of nucleon-nucleus scattering analysis in the GeV region some results are presented. This is our first step for an in-medium search for transitions from the meson-nucleon into the quark-gluon sector using NA optical models.
Several nucleon-nucleon potentials, Paris, Nijmegen, Argonne, and those derived by quantum inversion, which describe the NN interaction for T-lab below 300$ MeV are extended in their range of application as NN optical models. Extensions are made in r-space using complex separable potentials definable with a wide range of form factor options including those of boundary condition models. We use the latest phase shift analyses SP00 (FA00, WI00) of Arndt et al. from 300 MeV to 3 GeV to determine these extensions. The imaginary parts of the optical model interactions account for loss of flux into direct or resonant production processes. The optical potential approach is of particular value as it permits one to visualize fusion, and subsequent fission, of nucleons when T-lab above 2 GeV. We do so by calculating the scattering wave functions to specify the energy and radial dependences of flux losses and of probability distributions. Furthermore, half-off the energy shell t-matrices are presented as they are readily deduced with this approach. Such t-matrices are required for studies of few- and many-body nuclear reactions.
Several boson exchange potentials, describing the NN interaction $T_\ell\le 300$ MeV with high quality, are extended in their range of applicability as NN optical models with complex local or separable potentials in r-space or as complex boundary condition models. We determine in this work the separable potential strengths or boundary conditions on the background of the Paris, Nijmegen-I, Nijmegen-II, Reid93, AV18 and inversion potentials. Other hadronic systems, $π$N, KN and $ππ$, are studied with the same token. We use the latest phase shift analyzes SP00, SM00 and FA00 by Arndt {\em et al.} as input and thus extent the mentioned potential models from 300 MeV to 3 GeV . The imaginary parts of the interaction account for loss of flux into direct or resonant production processes. For a study of resonances and absorption the partial waves wave functions with physical boundary conditions are calculated. We display the energy and radial dependences of flux losses and radial probabilities. The results lend quantitative support for the established mental image of intermediate elementary particle formation in the spirit of fusion.
Solutions SP00, SM00 and FA00 of nucleon-nucleon (NN) phase shift analyzes by Arndt et al. are used in optical model studies. The partial waves, single channels J.leq.7 and coupled channels J.leq.6, are scrutinized. The radial probability distributions and losses of flux are used to identify the known Delta and N* resonances as well as anticipated other structures. The energy interval extends to 3 GeV.
We analyse the SM97 partial wave amplitudes for nucleon--nucleon (NN) scattering to 2.5 GeV, in which resonance and meson production effects are evident for energies above pion production threshold. Our analyses are based upon boson exchange or quantum inversion potentials with which the sub-threshold data are fit perfectly. Above 300 MeV they are extrapolations, to which complex short ranged Gaussian potentials are added in the spirit of the optical models of nuclear physics and of diffraction models of high energy physics. The data to 2.5 GeV are all well fit. The energy dependences of these Gaussians are very smooth save for precise effects caused by the known $Δ$ and N$^\star$ resonances. With this approach, we confirm that the geometrical implications of the profile function found from diffraction scattering are pertinent in the regime 300 MeV to 2.5 GeV and that the overwhelming part of meson production comes from the QCD sector of the nucleons when they have a separation of their centres of 1 to 1.2 fm. This analysis shows that the elastic NN scattering data above 300 MeV can be understood with a local potential operator as well as has the data below 300 MeV.
The one solitary boson exchange potential (OSBEP) is used to evaluate observables of NN elastic scattering below pion threshold. In this approach, we use a nonlinear model of self-interacting mesons as a substitution for the commonly used phenomenological form factors. NN data support an empirical scaling law between the pion and other meson fields, which suggests a link to QCD and significantly reduces the number of parameters in the boson exchange potential. The analysis of np and pp observables distinguishes the model by its fit and few adjustable parameters. An outlook to apply OSBEP in pi-N systems is given.
Low energy scattering and bound state properties of the πN, ππand Kπsystems are studied as coupled channel problems using inversion potentials of phase shift data. In a first step we apply the potential model to explain recent measurements of pionic hydrogen shift and width. Secondly, predictions of the model for pionium lifetime and shift confirm a well known and widely used effective range expression. Thirdly, as extension of this confirmation, we predict an unexpected medium effect of the pionium lifetime which shortens by several orders of magnitude. The σmeson shows a narrow resonance structure as a function of the medium modified mass with the implication of being essentially energy independent. Similarly, we see this medium resonance effect realized for the Kπsystem. To support our findings we present also results for the ρmeson and the Δ(1232) resonance.
Motivated by the success of models based on chiral symmetry in NN interactions we investigate self-interacting scalar, pseudoscalar and vector meson fields and their impact for NN forces. We parametrize the corresponding nonlinear field equations and get analytic wavelike solutions. A probability amplitude for the propagation of particle states is calculated and applied in the framework of a boson-exchange NN potential. Using a proper normalization of the meson fields makes all self-scattering amplitudes finite. The same normalization is able to substitute for the phenomenological form factors used in conventional boson exchange potentials and thus yields an phenomenological understanding of this part of the NN interaction. We find an empirical scaling law which relates the meson self-interaction couplings to the pion mass and self-interaction coupling constant. Our model yields np phase shifts comparable to the Bonn B potential results and deuteron properties, in excellent agreement with experimental data.
Two-body interactions of elementary particles are useful in particle and nuclear physics to describe qualitatively and quantitatively few- and many-body systems. We are extending for this purpose the quantum inversion approach for systems consisting of nucleons and mesons. From the wide range of experimentally studied two-body systems we concentrate here on $πN$, $ππ$, $K^+N$, $K π$ and $K\bar{K}$. As input we require results of phase shift analyses. Quantum inversion Gelfand-Levitan and Marchenko single and coupled channel algorithms are used for Schrödinger type wave equations in partial wave decomposition. The motivation of this study comes from our two approaches: to generate and investigate potentials directly from data by means of inversion and alternatively use linear and nonlinear boson exchange models. The interesting results of inversion are coordinate space informations about radial ranges, strengths, long distance behaviors, resonance characteristics, threshold effects, scattering lengths and bound state properties.
The notion of interacting elementary particles for low and medium energy nuclear physics is associated with definitions of potential operators. In principle, this potential carries the rich substructure consisting of quarks and gluons and thus may be deduced from some microscopic model. In this spirit we propose a boson exchange potential from a nonlinear quantum field theory. Essentially, the meson propagators and form factors of conventional models are replaced by amplitudes derived from the dynamics of self-interacting mesons in terms of solitary fields. Contrary to deduction, we position the inversion approach. Using Gel'fand-Levitan and Marchenko inversion we compute local, energy-independent potentials from experimental phase shifts for various partial waves. Both potential models give excellent results for on-shell NN scattering data. In the off-shell domain we study both potential models in PP Bremsstrahlung, elastic nucleon-nucleus scattering and triton binding energy calculations. It remains surprising that for all observables the inversion and microscopic meson exchange potentials are equivalent in their reproduction of data. Finally, we look for another realm of elementary interactions where inversion and meson exchange models can be applied with the hope to find more sensitivity to discern substructure dynamics.
The sensitivity of nucleon-nucleus elastic scattering to the off-shell behavior of realistic nucleon-nucleon interactions is investigated when on-shell equivalent nucleon-nucleon potentials are used. The study is based on applications of the full-folding optical model potential for an explicit treatment of the off-shell behavior of the nucleon-nucleon effective interaction. Applications were made at beam energies between 40 and 500 MeV for proton scattering from 40Ca and 208Pb. We use the momentum-dependent Paris potential and its local on-shell equivalent as obtained with the Gelfand-Levitan and Marchenko inversion formalism for the two nucleon Schroedinger equation. Full-folding calculations for nucleon-nucleus scattering show small fluctuations in the corresponding observables. This implies that off-shell features of the NN interaction cannot be unambiguously identified with these processes. Inversion potentials were also constructed directly from NN phase-shift data (SM94) in the 0-1.3 GeV energy range. Their use in proton-nucleus scattering above 200 MeV provide a superior description of the observables relative to those obtained from current realistic NN potentials. Limitations and scope of our findings are presented and discussed.
Characteristic properties of pionium $A_{2π}$ and associated low energy s--wave cross sections $σ(π^0π^0\to π^0π^0)$, $σ(π^+π^-\toπ^0π^0)$ and $σ(π^0π^0\to π^+π^-)$ are investigated with a coupled channels potential model. Some experimental results and conclusions are to be reconsidered.
NN and Pi-N partial wave radial potentials have been generated using the latest SM94-VPI(NN) and FA93-VPI(Pi-N) phase shifts. The potentials are used to determine the deuteron properties and to compute the 3H and 3He binding energies. The e_1 mixing angles of SM94-VPI and NY93-Nijmegen differ significantly and inversion potentials yield a P_d of 6.37% and 5.78%, respectively. Underbinding of 3H and 3He is enhanced by SM94, which signals more nonlocality and/or three-body potential effects than predicted from Nijmegen phase shifts and boson exchange models. The local pion-nucleon S_31, P_31 and P_33 channel potentials have been generated for guidance and to obtain a quantitative impression in r-space of what the Pi-N FA93-VPI phase shifts imply.