Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

The Bonn Meson Exchange Model for the Nucleon Nucleon Interaction

Nuclear forces can be systematically derived using effective chiral Lagrangians consistent with the symmetries of QCD. I review the status of the calculations for two- and three-nucleon forces and their applications in few-nucleon systems. I also address issues like the quark mass dependence of the nuclear forces and resonance saturation for four-nucleon operators.

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Modern theory of nuclear forces

Nowadays it has become customary in nuclear physics to denote by “tradition” the approach that considers nucleons and mesons as the relevant degrees of freedom. It is the purpose of this chapter to review this “traditional” approach in the area of nuclear forces and their applications to nuclear structure.

The Meson Theory of Nuclear Forces and Nuclear Structure

Neutron star observations: Prognosis for equation of state constraints

A low momentum nucleon-nucleon (NN) potential $V_{low-k}$ is derived from meson exhange potentials by integrating out the model dependent high momentum modes of $V_{NN}$. The smooth and approximately unique $V_{low-k}$ is used as input for shell model calculations instead of the usual Brueckner $G$ matrix. Such an approach eliminates the nuclear mass dependence of the input interaction one finds in the $G$ matrix approach, allowing the same input interaction to be used in different nuclear regions. Shell model calculations of $^{18}$O and $^{134}$Te using the {\bf same} input $V_{low-k}$ have been performed. For cut-off momentum $\Lambda$ in the vicinity of 2 $fm^{-1}$, our calculated low-lying spectra for these nuclei are in good agreement with experiments, and are weakly dependent on $\Lambda$.

A new approach to shell model effective interactions based on low momentum nucleon-nucleon potential

Linked diagram expansions for the nuclear transition matrix and the normalization of model-space wave functions

Using two-nucleon force alone is usually inadequate to interpret nuclear systems’ experimental data. We adopt a chiral N 3 LO two-nucleon potential V 2N with the inclusion of an in-medium three-nucleon (NNN) force V 3N to calculate binding energies of closed-shell nuclei. The matrix elements of low momentum nucleon-nucleon potential Vlow−k obtained from integrating the high momentum part of a realistic potentials is inputted in the particle-particle hole-hole ring diagram calculation to study nuclear properties. Nuclear binding energies are accurately reproduced. Without this three-nucleon force, the nuclear binding energy is too weak, as already known. The correction from ring diagrams of order higher than 1 can not be ignored.

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Contributions of chiral two- and three-nucleon interactions to closed shell nuclei

We have calculated the ground-state energy of the doubly-magic nucleus Ca within the framework of the Goldstone expansion using the CD-Bonn nucleon-nucleon potential. The short-range repulsion of this potential has been renormalized by integrating out its high-momentum components so as to derive a low-momentum potential Vlow−k defined up to a cutoff momentum Λ. A simple criterion has been employed to establish a connection between this cutoff momentum and the size of the two-nucleon model space in the harmonic oscillator basis. This model-space truncation approach provides a reliable way to renormalize the free nucleon-nucleon potential preserving its many-body physics. The role of the 3p − 3h and 4p − 4h excitations in the description of the ground state of Ca is discussed.

0 61 20 12 v 3 2 3 A pr 2 00 7 Study of the ground-state energy of 40 Ca with the CD-Bonn nucleon-nucleon potential

We have studied p-shell nuclei using a two-frequency shell-model approach with an effective interaction derived from the Bonn-A nucleon-nucleon potential by means of a G-matrix folded-diagram method. First, we briefly describe our derivation of the effective interaction in a model space composed of harmonic hoscillator wave functions with two different length parameters, b_in and b_out, for the core and the valence orbits, respectively. Then we present some selected results of our calculations. We show that a good agreement with experiment is obtained, which is definitely better than that provided by a standard one-frequency calculation. A comparison with results obtained from large-basis shell-model calculations is also made.

T.T.S. Kuo

Papers

A new approach to shell model effective interactions based on low momentum nucleon-nucleon potential

Linked diagram expansions for the nuclear transition matrix and the normalization of model-space wave functions

Contributions of chiral two- and three-nucleon interactions to closed shell nuclei

0 61 20 12 v 3 2 3 A pr 2 00 7 Study of the ground-state energy of 40 Ca with the CD-Bonn nucleon-nucleon potential

p-Shell Nuclei and Two-Frequency Shell Model with a Realistic Effective Interaction