arXiv subjects

H. Müther

Publications and source records attributed to H. Müther.

At least 55 records · Page 3Linked to original sources

arXiv2001

$Δ(1232)$ Isobar Excitations in Nuclear Many-Body Systems derived from various NN Interactions

$Δ$ isobar components in the nuclear many-body wave function are investigated for the deuteron, light nuclei (${}^{16}O$) and infinite nuclear matter within the framework of the coupled-cluster theory. The predictions derived for various realistic models of the baryon-baryon interaction are compared to each other. These include local ($V28$) and non-local meson exchange potentials (Bonn$_{2000}$) but also a model recently derived by the Salamanca group accounting for quark degrees of freedom. The characteristic differences which are obtained for the $NΔ$ and $ΔΔ$ correlation functions are related to the approximation made in deriving the matrix elements for the baryon-baryon interaction.

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arXiv2000

Charge symmetry breaking of the nucleon-nucleon interaction: $ρ$-$ω$ mixing VERSUS nucleon mass splitting

We investigate three models for the charge symmetry breaking (CSB) of the nucleon-nucleon ($NN$) interaction (based upon $ρ$-$ω$ mixing, nucleon mass splitting, and phenomenology) that all reproduce the empirical value for the CSB of the $^1S_0$ scattering length ($Δa_{CSB}$) accurately. We reveal that these models make very different predictions for CSB in $^3P_J$ waves and examine the impact of this on some observable quantities of $A\geq 3$ nuclear systems. It turns out that the $^3$H-$^3$He binding energy difference is essentially ruled by $Δa_{CSB}$ and not very sensitive to CSB from $P$ waves. However, the Coulomb displacement energies (which are the subject of the Nolen-Schiffer anomaly) receive about 50% of their CSB contribution from $NN$ partial waves beyond $^1S_0$. Consequently, the predictions by the various CSB models differ here substantially (10-20%). Unfortunately, the evaluation of the leading Coulomb contributions carry a large uncertainty such that no discrimination between the competing CSB models can presently be made. To decide the issue we suggest to look into nuclear few-body reactions that are sensitive to CSB of the nuclear force.

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arXiv2000

Final State Interaction in Exclusive $(e,e'NN)$ Reactions

Contributions of nucleon-nucleon (NN) correlations, meson exchange currents and the residual final state interactions (FSI) on exclusive two-nucleon knock-out reactions induced by electron scattering are investigated. All contributions are derived from the same realistic meson exchange model for the NN interaction. Effects of correlations and FSI are determined in a consistent way by solving the NN scattering equation, the Bethe-Goldstone equation, for two nucleons in nuclear matter. One finds that the FSI re-scattering terms are non-negligible even if the two nucleons are emitted back to back.

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arXiv2000

Correlations and the Dirac Structure of the Nucleon Self-Energy

The Dirac structure of the nucleon self-energy in symmetric nuclear matter as well as neutron matter is derived from a realistic meson exchange model for the nucleon-nucleon (NN) interaction. It is demonstrated that the effects of correlations on the effective NN interaction in the nuclear medium can be parameterized by means of an effective meson exchange. This analysis leads to a very intuitive interpretation of correlation effects and also provides an efficient parametrization of an effective interaction to be used in relativistic structure calculations for finite nuclei.

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arXiv2000

Two-Body Correlations in Nuclear Systems

Correlations in the nuclear wave-function beyond the mean-field or Hartree-Fock approximation are very important to describe basic properties of nuclear structure. Various approaches to account for such correlations are described and compared to each other. This includes the hole-line expansion, the coupled cluster or ``exponential S'' approach, the self-consistent evaluation of Greens functions, variational approaches using correlated basis functions and recent developments employing quantum Monte-Carlo techniques. Details of these correlations are explored and their sensitivity to the underlying nucleon-nucleon interaction. Special attention is paid to the attempts to investigate these correlations in exclusive nucleon knock-out experiments induced by electron scattering. Another important issue of nuclear structure physics is the role of relativistic effects as contained in phenomenological mean field models. The sensitivity of various nuclear structure observables on these relativistic features are investigated. The report includes the discussion of nuclear matter as well as finite nuclei.

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arXiv1999

Nucleon-Nucleon Correlations and Two-Nucleon Currents in Exclusive ($e,e'NN$) Reactions

The contributions of short-range nucleon-nucleon (NN) correlations, various meson exchange current (MEC) terms and the influence of $Δ$ isobar excitations (isobaric currents, IC) on exclusive two-nucleon knockout reactions induced by electron scattering are investigated. The nuclear structure functions are evaluated for nuclear matter. Realistic NN interactions derived in the framework of One-Boson-Exchange model are employed to evaluate the effects of correlations and MEC in a consistent way. The correlations correlations are determined by solving the Bethe-Goldstone equation. This yields significant contributions to the structure functions W_L and W_T of the (e,e'pn) and (e,e'pp) reactions. These contributions compete with MEC corrections originating from the $π$ and $ρ$ exchange terms of the same interaction. Special attention is paid to the so-called 'super parallel' kinematics at momentum transfers which can be measured e.g. at MAMI in Mainz.

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arXiv1999

Correlations derived from Modern Nucleon-Nucleon Potentials

Various modern nucleon-nucleon (NN) potentials yield a very accurate fit to the nucleon-nucleon scattering phase shifts. The differences between these interactions in describing properties of nuclear matter are investigated. Various contributions to the total energy are evaluated employing the Hellmann - Feynman theorem. Special attention is paid to the two-nucleon correlation functions derived from these interactions. Differences in the predictions of the various interactions can be traced back to the inclusion of non-local terms.

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arXiv1999

Exploring Nucleon-Nucleon correlations in ($e,e'NN$) reactions

Correlations in the nuclear wave-function beyond the mean-field or Hartree-Fock approximation are very important to describe basic properties of nuclear structure. Attempts are made to explore details of these correlations in exclusive nucleon knock-out by electron scattering experiments. Basic results of $(e,e'p)$ experiments are reviewed. The role of correlations in $(e,e'NN)$ experiments is discussed. Special attention is paid to a consistent description of the competing effects due to final state interaction, meson exchange current and isobar currents. Results are discussed for systematic studies of these features in nuclear matter as well as for specific examples for the finite nucleus $^{16}$O.

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arXiv1999

Correlation effects in single-particle overlap functions and one-nucleon removal reactions

Single-particle overlap functions and spectroscopic factors are calculated on the basis of the one-body density matrices (ODM) obtained for the nucleus $^{16}O$ employing different approaches to account for the effects of correlations. The calculations use the relationship between the overlap functions related to bound states of the (A-1)-particle system and the ODM for the ground state of the A-particle system. The resulting bound-state overlap functions are compared and tested in the description of the experimental data from (p,d) reactions for which the shape of the overlap function is important.

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arXiv1999

Short-range and tensor correlations in the $^{16}$O(e,e$'$pn) reaction

The cross sections for electron induced two-nucleon knockout reactions are evaluated for the example of the $^{16}$O(e,e$'$pn)$^{14}$N reaction leading to discrete states in the residual nucleus $^{14}$N. These calculations account for the effects of nucleon-nucleon correlations and include the contributions of two-body meson exchange currents as the pion seagull, pion in flight and the isobar current contribution. The effects of short-range as well as tensor correlations are calculated within the framework of the coupled cluster method employing the Argonne V14 potential as a model for a realistic nucleon-nucleon interaction. The relative importance of correlation effects as compared to the contribution of the meson exchange currents depends on the final state of the residual nucleus. The cross section leading to specific states, like e.g. the ground state of $^{14}$N, is rather sensitive to the details of the correlated wave function.

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arXiv1999

Modern nucleon-nucleon interactions and charge-symmetry breaking in nuclei

Coulomb displacement energies, i.e., the differences between the energies of corresponding nuclear states in mirror nuclei, are evaluated using recent models for the nucleon-nucleon (NN) interaction. These modern NN potentials account for breaking of isospin symmetry and reproduce $pp$ and $pn$ phase shifts accurately. The predictions by these new potentials for the binding of $^{16}O$ are calculated. A particular focus of our study are effects due to nuclear correlations and charge-symmetry breaking (CSB). We find that the CSB terms in the modern NN interactions substantially reduce the discrepancy between theory and experiment for the Coulomb displacement energies; however, our calculations do not completely explain the Nolen-Schiffer anomaly. Potential sources for the remaining discrepancies are discussed.

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arXiv1998

Photoinduced Two-Nucleon Knockout: A Kinematical Study in Nuclear Matter

The contributions of short-range nucleon-nucleon correlations, meson exchange current (MEC) corrections and the influence of Delta isobar excitations (isobaric currents, IC) on photon induced two-nucleon knockout reactions are investigated. The nuclear structure functions are evaluated for the system of infinite nuclear matter. This allows a systematic investigation of the relative importance of the various contributions (MEC, IC and correlations) in different kinematical regions. Nucleon-nucleon (NN) correlations derived from a realistic NN interaction by solving the Bethe-Goldstone equation yield significant changes in the structure functions W_L and W_T of the (e,e'pn) and (e,e'pp) reactions. This is true in particular for the so-called 'super parallel' kinematics at momentum transfers which can be measured e.g. at MAMI in Mainz.

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arXiv1998

Pauli exclusion operator and binding energy of nuclear matter

Brueckner-Hartree-Fock calculations are performed for nuclear matter with an exact treatment of the Pauli exclusion operator in the Bethe-Goldstone equation. The differences in the calculated binding energy, compared to the angle-average approximation, which is commonly used, are non-negligible. These difference exhibits a specific density dependence, which shifts the calculated saturation point towards smaller densities. This effect is observed for various versions of modern models for the NN interaction.

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arXiv1998

Study of relativistic bound state wave functions in quasielastic (e,e'p) reactions

The unpolarized response functions of the quasielastic $^{16}O(e,e^\prime p)^{15}N$ reaction are calculated for three different types of relativistic bound state wave functions. The wave functions are obtained from relativistic Hartree, relativistic Hartree-Fock and density dependent relativistic Hartree calculations that reproduce the experimental charge radius of $^{16}$O. The sensitivity of the unpolarized response functions to the single particle structure of the different models is investigated in the relativistic plane wave impulse approximation. Redistributions of the momentum dependence in the longitudinal and transverse response function can be related to the binding energy of the single particle states. The interference responses $R_{LT}$ and $R_{TT}$ reveal a strong sensitivity to the small component of the relativistic bound state wave function.

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arXiv1997

Phaseshift equivalent NN potentials and the deuteron

Different modern phase shift equivalent NN potentials are tested by evaluating the partial wave decomposition of the kinetic and potential energy of the deuteron. Significant differences are found, which are traced back to the matrix elements of the potentials at medium and large momenta. The influence of the localisation of the one-pion-exchange contribution to these potentials is analyzed in detail.

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arXiv1997

Correlations and the relativistic structure of the nucleon self-energy

A key point of Dirac Brueckner Hartree Fock calculations for nuclear matter is to decompose the self energy of the nucleons into Lorentz scalar and vector components. A new method is introduced for this decomposition. It is based on the dependence of the single-particle energy on the small component in the Dirac spinors used to calculate the matrix elements of the underlying NN interaction. The resulting Dirac components of the self-energy depend on the momentum of the nucleons. At densities around and below the nuclear matter saturation density this momentum dependence is dominated by the non-locality of the Brueckner G matrix. At higher densities these correlation effects are suppressed and the momentum dependence due to the Fock exchange terms is getting more important. Differences between symmetric nuclear matter and neutron matter are discussed. Various versions of the Bonn potential are considered.

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arXiv1997

Selectivity of the 16O(e,e'pp) reaction to discrete final states

Resolution of discrete final states in the $^{16}$O(e,e$'$pp)$^{14}$C reaction may provide an interesting tool to discriminate between contributions from one- and two-body currents in this reaction. This is based on the observation that the $0^+$ ground state and first $2^+$ state of $^{14}$C are reached predominantly by the removal of a $^1S_0$ pair from $^{16}$O in this reaction, whereas other states mostly arise by the removal of a $^3P$ pair. This theoretical prediction has been supported recently by an analysis of the pair momentum distribution of the experimental data. In this paper we present results of reaction calculations performed in a direct knock-out framework where final-state interaction and one- and two-body currents are included. The two-nucleon overlap integrals are obtained from a calculation of the two-proton spectral function of $^{16}$O and include both long-range and short-range correlations. The kinematics chosen in the calculations is relevant for recent experiments at NIKHEF and Mainz.

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arXiv1997

Relativistic Structure of the Nucleon Self-Energy in Asymmetric Nuclei

The Dirac structure of the nucleon self-energy in asymmetric nuclear matter cannot reliably be deduced from the momentum dependence of the single-particle energies. It is demonstrated that such attempts yield an isospin dependence with even a wrong sign. Relativistic studies of finite nuclei have been based on such studies of asymmetric nuclear matter. The effects of these isospin components on the results for finite nuclei are investigated.

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