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H. Müther

Publications and source records attributed to H. Müther.

At least 73 records · Page 4Linked to original sources
arXiv1997

Correlations and the Cross Section of Exclusive ($e,e'p$) Reactions for $^{16}$O

The reduced cross section for exclusive ($e,e'p$) reactions has been studied in DWIA for the example of the nucleus $^{16}$O using a spectral function containing effects of correlations. The spectral function is evaluated directly for the finite nucleus starting from a realistic nucleon-nucleon interaction within the framework of the Green's function approach. The emphasis is focused on the correlations induced by excitation modes at low energies described within a model-space of shell-model configurations including states up to the $sdg$ shell. Cross sections for the $p$-wave quasi-hole transitions at low missing energies are presented and compared with the most recent experimental data. In the case of the so-called perpendicular kinematics the reduced cross section derived in DWIA shows an enhancement at high missing momenta as compared to the PWIA result. Furthermore the cross sections for the $s$- and $d$-wave quasi-hole transitions are presented and compared to available data at low missing momenta. Also in these cases, which cannot be described in a model without correlations, a good agreement with the experiment is obtained.

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arXiv1997

On the Dirac Structure of the Nucleon Selfenergy in Nuclear Matter

The relativistic structure of the self-energy of a nucleon in nuclear matter is investigated including the imaginary and real components which arise from the terms of first and second order in the NN interaction. A parameterized form of Brueckner $G$ matrix is used for the NN interaction. The effects of the terms beyond the DBHF approximation on quasiparticle energies and the optical potential for nucleon-nucleus scattering are discussed.

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arXiv1996

Deep Inelastic Lepton Scattering in Nuclei at x > 1 and the Nucleon Spectral Function

The nuclear structure function F_2A(x) has been studied in the Bjorken limit for (l, l') scattering on nuclei in the region of x > 1 and was found to be very sensitive to the information contained in the nucleon spectral function in nuclei, particularly the correlations between momenta and energies in the region of large momenta. Calculations were done in a local density approximation using two different spectral functions for nuclear matter. Results are compared to those obtained for a spectral function which has been evaluated directly for the finite nucleus, ^{16}O, under consideration. For values of x around 1.5 and larger the quasiparticle contribution is negligible, thus stressing the sensitivity of the present reaction to the dynamical properties of nuclei beyond the shell model approach. Several approximations which are usually employed in studies of the EMC effect have been analyzed and their inaccuracy in this region is demonstrated. The results stress the fact that the nuclear structure function contains important information on nuclear dynamical correlations. Therefore further measurements of F_2A(x) in that region and for many nuclei would be most welcome.

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arXiv1996

Lepton Scattering on Nuclei at x > 1 and the Nucleon Spectral Function

We analyze the processes of deep inelastic and quasielastic scattering in the region of x > 1. These processes are found to be very sensitive to the information contained in the nucleon spectral function in nuclei, particularly to the correlations between energy and momentum. Calculations are done using two spectral functions for nuclear matter and one for finite nuclei, ^{16}O. Several approximations are also analyzed and are shown to be inaccurate in this region. These results stress the fact that the region of x > 1 contains important information on nuclear dynamical correlations.

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arXiv1996

A Microscopic Energy- and Density-Dependent Effective Interaction and its Test by Nucleus-Nucleus Scattering

An effective nucleon-nucleon interaction calculated in nuclear matter from the Bonn potential has been parametrized in terms of a local density- and energy-dependent two-body interaction. This allows to calculate the real part of the nucleus-nucleus scattering potential and to test this effective interaction over a wide region of densities ($ρ\leq 3ρ_0$) produced dynamically in scattering experiments. Comparing our calculations with empirical potentials extracted from data on light and heavy ion scattering by model-unrestricted analysis methods, we find quantitative agreement with the exception of proton scattering. The failure in this case may be traced back to the properties of the effective interaction at low densities, for which the nuclear matter results are not reliable. The success of the interaction at high overlap densities confirms the empirical evidence for a soft equation of state for cold nuclear matter.

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arXiv1996

Long-Range Correlations and the Momentum Distribution in Nuclei

The influence of correlations on the momentum distribution of nucleons in nuclei is evaluated starting from a realistic nucleon-nucleon interaction. The calculations are performed directly for the finite nucleus $\,^{16}$O making use of the Green's function approach. The emphasis is focused on the correlations induced by the excitation modes at low energies described within a model-space of shell-model configurations including states up to the sdg shell. Our analysis demonstrates that these long-range correlations do not produce any significant enhancement of the momentum distribution at high missing momenta and low missing energies. This is in agreement with high resolution $(e,e'p)$ experiments for this nucleus. We also try to simulate the corresponding effects in large nuclei by quenching the energy-spacing between single-particle orbits. This yields a sizable enhancement of the spectral function at large momenta and small energy. Such behavior could explain the deviation of the momentum distribution from the mean field prediction, which has been observed in $(e,e'p)$ experiments on heavy nuclei like $^{208}$Pb.

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arXiv1996

Realistic effective interactions for halo nuclei

We study halo nuclei using a two-frequency shell-model approach employing wave functions of two different oscillator constants $\hbarω_{in}$ and $\hbarω_{out}$, the former for the inner orbits and the latter for the halo (outer) orbits. An initial application has been made for the halo nuclei $^6$He and $^6$Li, with $0s_{1/2}$ taken as the inner and ( $0p_{3/2}$, $0p_{1/2}$) as the halo orbits. Starting from the Paris NN interaction, we have derived a G-matrix folded-diagram effective interaction for this two-frequency model space, using an essentially exact treatment for the Pauli exclusion operator for the G-matrix. While keeping $\hbarω_{in}$ fixed, we have performed calculations with different choices for $\hbarω_{out}$, treating it as a variation parameter. For $\hbarω_{in}=19.7 MeV$ and $\hbarω_{out}=8.2 MeV$, our calculated valence energies for $^6$He and $^6$Li are -2.77 and -3.55 Mev, respectively, both in good agreement with experiments. The importance of certain three-body-force diagrams is discussed.

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arXiv1995

Momentum Distribution in Nuclear Matter and Finite Nuclei

A simple method is presented to evaluate the effects of short-range correlations on the momentum distribution of nucleons in nuclear matter within the framework of the Green's function approach. The method provides a very efficient representation of the single-particle Green's function for a correlated system. The reliability of this method is established by comparing its results to those obtained in more elaborate calculations. The sensitivity of the momentum distribution on the nucleon-nucleon interaction and the nuclear density is studied. The momentum distributions of nucleons in finite nuclei are derived from those in nuclear matter using a local-density approximation. These results are compared to those obtained directly for light nuclei like $^{16}O$.

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arXiv1995

Short-Range Correlations and the One-Body Density Matrix in Finite Nuclei

The effects of short-range correlations derived from a realistic meson-exchange potential on the single-particle density matrix in finite nuclei are investigated by analyzing the one-body density in terms of the natural orbits. Basic features of these natural orbits and their spectral distributions are discussed. For many observables it seems to be sufficient to approximate the one-body density matrix in terms of those natural orbits, which exhibit the largest occupation probabilities. For the investigation of the high-momentum components in the single-particle density, however, it is important to take into account natural orbits with small occupation probabilities, originating from the single-particle Green function at large negative energies.

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arXiv1994

Momentum and Energy Distributions of Nucleons in Finite Nuclei due to Short-Range Correlations

The influence of short-range correlations on the momentum and energy distribution of nucleons in nuclei is evaluated assuming a realistic meson-exchange potential for the nucleon-nucleon interaction. Using the Green-function approach the calculations are performed directly for the finite nucleus $^{16}$O avoiding the local density approximation and its reference to studies of infinite nuclear matter. The nucleon-nucleon correlations induced by the short-range and tensor components of the interaction yield an enhancement of the momentum distribution at high momenta as compared to the Hartree-Fock description. These high-momentum components should be observed mainly in nucleon knockout reactions like $(e,e'p)$ leaving the final nucleus in a state of high excitation energy. Our analysis also demonstrates that non-negligible contributions to the momentum distribution should be found in partial waves which are unoccupied in the simple shell-model. The treatment of correlations beyond the Brueckner-Hartree-Fock approximation also yields an improvement for the calculated ground-state properties.

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arXiv1994

Auxiliary potential in no-core shell-model calculations

The Lee-Suzuki iteration method is used to include the folded diagrams in the calculation of the two-body effective interaction $v^{(2)}_{\rm eff}$ between two nucleons in a no-core model space. This effective interaction still depends upon the choice of single-particle basis utilized in the shell-model calculation. Using a harmonic-oscillator single-particle basis and the Reid-soft-core {\it NN} potential, we find that $v^{(2)}_{\rm eff}$ overbinds $^4\mbox{He}$ in 0, 2, and $4\hbarΩ$ model spaces. As the size of the model space increases, the amount of overbinding decreases significantly. This problem of overbinding in small model spaces is due to neglecting effective three- and four-body forces. Contributions of effective many-body forces are suppressed by using the Brueckner-Hartree-Fock single-particle Hamiltonian.

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arXiv1994

On the Momentum Dependence of the Nucleon - Nucleus Optical Potential

The momentum dependence of the mean-field contribution to the real part of the optical model potential is investigated employing realistic nucleon-nucleon interactions. Within a non-relativistic approach a momentum dependence originates from the non-locality of the Fock exchange term. Deducing the real part of the optical model from a relativistic Dirac Brueckner Hartree Fock approximation for the self-energy of the nucleons yields an additional momentum dependence originating from the non-relativistic reduction of the self-energy. It is demonstrated that large Fock terms are required in the non-relativistic approach to simulate these relativistic features. A comparison is made between a local density approximation for the optical model and a direct evaluation in finite nuclei.

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arXiv1993

Long-Range Correlations in Closed Shell Nuclei

The effects of correlations on the bulk properties of nuclei are investigated in large model spaces including up to 21 single-particle orbits. The evaluation of the single-particle Green function is made feasible by means of the BAGEL approximation. The spectral function for single-nucleon pick-up and removal is investigated for the nuclei $^{16}O$ and $^{40}Ca$ . Special attention is paid to the effects produced by correlations on the calculated ground state properties of closed shell nuclei. It is observed that correlations beyond the Brueckner Hartree Fock approximation tend to improve the results obtained using realistic nucleon nucleon interactions.

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arXiv1993

NN Correlations and Relativistic Hartree Fock in Finite Nuclei

Two different approximation schemes for the self-consistent solution of the relativistic Brueckner-Hartree-Fock equation for finite nuclei are discussed using realistic One-Boson-Exchange potentials. In a first scheme, the effects of correlations are deduced from a study of nuclear matter and parameterized in terms of an effective $σ$, $ω$ and $π$ exchange. Employing this effective interaction relativistic Hartree-Fock equations are solved for finite nuclei \osi , \caf\ and \cafe . In the second approach the effect of correlations are treated in the Brueckner-Hartree-Fock approximation directly for the finite nuclei, but the modifications of the Dirac spinors in the medium are derived from nuclear matter assuming a local-density approximation. Both approaches yield rather similar results for binding energies and radii in fair agreement with experimental data. The importance of the density dependent correlation effects is demonstrated and different ingredients to the spin-orbit splitting in the shell-model of the nucleus are discussed.

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arXiv1993

Width of the $Δ$ resonance in nuclei

In this work we evaluate the imaginary part of the isobar $Δ$ self-energy $Σ_Δ$ from the two-body absorption process $Δ+N\rightarrow 2N$. This contribution is calculated using a recently developed non-relativistic scheme, which allows for an evaluation of the self-energy with a basis of single-particle states appropriate for both bound hole states and for particle states in the continuum. In order to test the medium dependence of the self-energy, we calculate the two-body absorption term $Σ_Δ^{A2}$ for several finite nuclei with $N=Z$, i.e.\ $^{16}$O, $^{40}$Ca and $^{100}$Sn. The resulting self-energy, which is energy dependent and non-local, is compared with a simple parameterization derived from nuclear matter.

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arXiv1993

On the Analytic Structure of the Quark Self-Energy in Nambu-Jona- Lasinio Models

The self-energy of quarks is investigated for various models which are inspired by the Nambu--Jona-Lasinio (NJL) model. Including, beyond the Hartree-Fock approximation, terms up to second-order in the quark interaction, the real and imaginary parts of scalar and vector components of the self-energy are discussed. The second-order contributions depend on the energy and momentum of the quark under consideration. This leads to solutions of the Dirac equation which are significantly different from those of a free quark or a quark with constant effective mass, as obtained in the Hartree-Fock approximation.

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arXiv1993

The Single-Particle Spectral Function of $^{16}{\rm O}$

The influence of short-range correlations on the $p$-wave single-particle spectral function in $^{16}{\rm O}$ is studied as a function of energy. This influence, which is represented by the admixture of high-momentum components, is found to be small in the $p$-shell quasihole wave functions. It is therefore unlikely that studies of quasihole momentum distributions using the $(e,e'p)$ reaction will reveal a significant contribution of high momentum components. Instead, high-momentum components become increasingly more dominant at higher excitation energy. The above observations are consistent with the energy distribution of high-momentum components in nuclear matter.

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