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R. Machleidt

Publications and source records attributed to R. Machleidt.

104 records · Page 6Linked to original sources

Comment on "Phase-Shift Analysis of NN Scattering Below 160 Mev: Indication of a Strong Tensor Force"

In his recent publication of a NN phase shift analysis below 160 MeV, Henneck reports relatively large values for the mixing parameter $ε_1$. Based on these results, Henneck suggests that the strength of the $ρ$-meson tensor coupling to the nucleon may be weaker than used in present day NN interactions, like the Paris or Bonn potentials. We point out that at low energies ( < 100 MeV ) there is very little sensitivity to the strength of the $ρ$ coupling, due to the compensating effect of the second order tensor term. In order to establish sensitivity, one has to go to energies > 200 MeV, where the second order contribution has gone out. As it happens, the $ε_1$ mixing parameter is well determined in the region of energies 200--300 MeV, and there is agreement with the predictions by the Paris and Bonn potentials; whereas the weak-$ρ$ model is about 50\% above the data. This and additional considerations in triplet $P$-waves re-confirm that NN scattering requires the strong $ρ$, consistent with the $ππ-N\bar{N}$ partial-wave analysis by Höhler and Pietarinen.

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Constraints on the $πNN$ Coupling Constant from the $NN$ System

The sensitivity of the deuteron and of $pp$ scattering to the $πNN$ and $ρNN$ coupling constants is investigated systematically. We find that the deuteron can be described about equally well with either {\it large $π$ and $ρ$} or {\it small $π$ and $ρ$} coupling constants. However, $pp$ scattering clearly {\it requires} the strong $ρ$, but favors the weak $π$ (particularly, in $^3P_0$ at low energies). This apparent contradiction between bound-state and scattering can be resolved by either assuming charge-dependent $πNN$ coupling constants or by adding a heavy pion to the NN model. In both cases, the neutral-pion coupling constant is small ($g^2_{π^0}/4π= 13.5$).

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Self-Consistent Relativistic Calculation of Nucleon Mean Free Path

We present a fully self-consistent and relativistic calculation of the nucleon mean free path in nuclear matter and finite nuclei. Starting from the Bonn potential, the Dirac-Brueckner-Hartree-Fock results for nuclear matter are parametrized in terms of an effective $σ$-$ω$ Lagrangian suitable for the relativistic density-dependent Hartree-Fock (RDHF) approximation. The nucleon mean free path in nuclear matter is derived from this effective Lagrangian taking diagrams up to fourth-order into account. For the nucleon mean free path in finite nuclei, we make use of the density determined by the RDHF calculation in the local density approximation. Our microscopic results are in good agreement with the empirical data and predictions by Dirac phenomenology.

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Microscopic Calculation of in-Medium Proton-Proton Cross Sections

We derive in-medium PROTON-PROTON cross sections in a microscopic model based upon the Bonn nucleon-nucleon potential and the Dirac-Brueckner approach for nuclear matter. We demonstrate the difference between proton-proton and neutron-proton cross sections and point out the need to distinguish carefully between the two cases. We also find substantial differences between our in-medium cross sections and phenomenological parametrizations that are commonly used in heavy-ion reactions.

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Momentum-Dependent Mean Field Based Upon the Dirac-Brueckner Approach for Nuclear Matter

A momentum-dependent mean field potential, suitable for application in the transport-model description of nucleus-nucleus collisions, is derived in a microscopic way. The derivation is based upon the Bonn meson-exchange model for the nucleon-nucleon interaction and the Dirac-Brueckner approach for nuclear matter. The properties of the microscopic mean field are examined and compared with phenomenological parametrizations which are commonly used in transport-model calculations.

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Microscopic Calculation of in-Medium Nucleon-Nucleon Cross Ssections

We derive in-medium nucleon-nucleon (NN) cross sections in a microscopic model. Our calculations are based upon the Bonn NN potential and the Dirac-Brueckner approach for nuclear matter. We consider energies up to 300 MeV (in the laboratory frame) and densities up to twice nuclear matter density. Our results deviate substantially from cross section parametrizations that are commonly used in the nuclear medium.

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Comment on "Comparison of Potential Models with the PP Scattering Data Below 350 Mev"

We point out two flaws in the recent test of nucleon-nucleon (NN) potentials conducted by Stoks and de Swart. First, in some cases, the neutron-proton ($np$) version of an NN potential was compared to the proton-proton ($pp$) data, which is improper and yields (large) $χ^2$ that are essentially meaningless. Second, for a proper test of the quantitative nature of a NN potential, it is insufficient to compare to $pp$ data only, since this leaves the T=0 potential untested. Thus, it can happen that the $pp$ version of a potential predicts the $pp$ data accurately, while the $np$ version of that same potential is poor in $np$ (where also the T=0 potential is involved). An example for this is the Nijmegen potential, which predicts the $pp$ data well with a $χ^2$/datum of 2.0, but yields a $χ^2$/datum of 6.5 in $np$.

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Comment on Neutron-Proton Spin-Correlation Parameter A_{ZZ} at 68 Mev

We present two arguments indicating that the large value for the $ε_1$ mixing parameter at 50 MeV, which the Basel group extracted from their recent $A_{zz}$ measurement, may be incorrect. First, there are nucleon-nucleon (NN) potentials which predict the $ε_1$ at 50 MeV substantially below the Basel value and reproduce the Basel $A_{zz}$ data accurately. Second, the large value for $ε_1$ at 50 MeV proposed by the Basel group can only be explained by a model for the NN interaction which is very unrealistic (no $ρ$-meson and essentially a point-like $πNN$ vertex) and overpredicts the $ε_1$ in the energy range where it is well determined (150--500 MeV) by a factor of two.

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Dirac Hartree-Fock for Finite Nuclei Employing realistic Forces

We discuss two different approximation schemes for the self-consistent solution of the {\it relativistic} Brueckner-Hartree-Fock equation for finite nuclei. In the first scheme, the Dirac effects are deduced from corresponding nuclear matter calculations, whereas in the second approach the local-density approximation is used to account for the effects of correlations. The results obtained by the two methods are very similar. Employing a realistic one-boson-exchange potential (Bonn~A), the predictions for energies and radii of $^{16}$O and $^{40}$Ca come out in substantially better agreement with experiment as compared to non-relativistic approaches. As a by-product of our study, it turns out that the Fock exchange-terms, ignored in a previous investigation, are not negligible.

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Nucleon-Nucleon Potentials in Comparison: Physics or Polemics?

Guided by history, we review the major developments concerning realistic nucleon-nucleon (NN) potentials since the pioneering work by Kuo and Brown on the effective nuclear interaction. Our main emphasis is on the physics underlying various models for the NN interaction developed over the past quarter-century. We comment briefly on how to test the quantitative nature of nuclear potentials properly. A correct calculation (performed by independent researchers) of the $χ^2$/datum for the fit of the world NN data yields 5.1, 3.7, and 1.9 for the Nijmegen, Paris, and Bonn potential, respectively. Finally, we also discuss in detail the relevance of the on- and off-shell properties of NN potentials for microscopic nuclear structure calculations.

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Relativistic Ring-Diagram Nuclear Matter Calculations

A relativistic extension of the particle-particle hole-hole ring-diagram many-body formalism is developed by using the Dirac equation for single-particle motion in the medium. Applying this new formalism, calculations are performed for nuclear matter. The results show that the saturation density is improved and the equation of state becomes softer as compared to corresponding Dirac-Brueckner-Hartree-Fock calculations. Using the Bonn A potential, nuclear matter is predicted to saturate at an energy per nucleon of --15.30 MeV and a density equivalent to a Fermi momentum of 1.38 fm$^{-1}$, in excellent agreement with empirical information. The compression modulus is 152 MeV at the saturation point.

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Relativistic Corrections to the Triton Binding Energy

The influence of relativity on the triton binding energy is investigated. The relativistic three-dimensional version of the Bethe-Salpeter equation proposed by Blankenbecler and Sugar (BbS) is used. Relativistic (non-separable) one-boson-exchange potentials (constructed in the BbS framework) are employed for the two-nucleon interaction. In a 34-channel Faddeev calculation, it is found that relativistic effects increase the triton binding energy by about 0.2 MeV. Including charge-dependence (besides relativity), the final triton binding energy predictions are 8.33 and 8.16 MeV for the Bonn A and B potential, respectively.

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Saturation in the Nuclear Matter Problem

Once density-dependent meson masses are introduced into the nuclear many-body problem, conventional mechanisms for saturation no longer operate. We suggest that a loop correction, essentially the introduction of the axial vector coupling $g_A(ρ,k)$ as function of density $ρ$ and momentum $k$, can bring about saturation, and present schematic calculations to illustrate this. We find that a very small density-dependence in $g_A$ gives rise to a very large saturating effect on nuclear matter. In fact, this new saturation mechanism turns out to be more powerful than any of the conventional mechanisms.

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