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The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory

The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory

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2 1. Introduction<br />

nuclear force of Yukawa type due to exchange of particles with the mass m is proportional to<br />

exp (-mr)/(mr), where r denotes the distance between two nucleons, exchanges of the heavier<br />

particles are, <strong>in</strong> general, of shorter range. While the long range part of the nuclear force is<br />

dom<strong>in</strong>ated by one-pion exchange, two-pion exchange as well as exchanges of heavier mesons<br />

become important <strong>in</strong> the <strong>in</strong>termediate region. In the core region nucleons are overlapp<strong>in</strong>g with<br />

each other. So, the "classical" meson-exchange picture of the nuclear force is not adequate any<br />

more. Taketani and the co-workers proposed a phenomenological treatment of the short-range<br />

nuclear force.<br />

After, <strong>in</strong> the 1950s, the long-range part of the nuclear <strong>in</strong>teractions due to the one-pion exchange<br />

became well established, more attention has been paid to the two-pion exchange contributions.<br />

Various approaches have been proposed to attack this problem [19], [20]. Soon it became clear<br />

that the two-pion exchange itself can not account for a sufficiently strong sp<strong>in</strong>-orbit force, whose<br />

evidence was transparent from the data.<br />

<strong>The</strong> situation has changed after the experimental discovery of heavy mesons <strong>in</strong> 1969s, which has<br />

motivated developments of the one-boson exchange models (OBE) of the nuclear force. One assumed<br />

<strong>in</strong> such models that the two- and more-pion exchanges can be parametrized <strong>in</strong> terms of<br />

multi-pion resonances. With only few parameters one could achieve a quite remarkable quantitative<br />

agreement with the exist<strong>in</strong>g nucleon-nucleon scatter<strong>in</strong>g data [21], [22], [23].<br />

Apart from the one-boson exchange models other concepts like dispersion relations and field theoretical<br />

approaches were suggested to describe the nucleon-nucleon <strong>in</strong>teraction. In particular,<br />

dispersion theory was applied to calculate the two-pion exchange contributions to the N N amplitude<br />

start<strong>in</strong>g from 7r N and 7r7r scatter<strong>in</strong>g data. <strong>The</strong> most detailed work <strong>in</strong> this direction was<br />

performed by the Stony Brook [24], [25] and the Paris [26], [27] groups. <strong>The</strong> short range part<br />

of the nuclear force <strong>in</strong> these models was parametrized by OBE and by some phenomenological<br />

terms. <strong>The</strong> nucleon-nucleon <strong>in</strong>teraction developed by the Paris group became known as the Paris<br />

potential. <strong>The</strong> field theoretical approach to the 27r-exchange contributions us<strong>in</strong>g the technique of<br />

Feynman diagrams was considered by Lomon and collaborators [28].<br />

One of the most detailed and successful works with<strong>in</strong> the meson-exchange models was performed<br />

by the Bonn group. Start<strong>in</strong>g from the OBE model [23] based on relativistic time-ordered perturbation<br />

theory, Erkelenz, Hol<strong>in</strong>de, Machleidt and Elster calculated two- and some of the threeand<br />

four-pion exchange diagrams and extended the model to take <strong>in</strong>to account effects of virtual<br />

isobar excitations. <strong>The</strong> so constructed Bonn-potential, which <strong>in</strong>cludes apart from these terms<br />

exchanges of heavy mesons, allows for an accurate description of the nucleon-nucleon scatter<strong>in</strong>g<br />

data. Recently, few attempts have been undertaken by the J ülich group to <strong>in</strong>corporate also<br />

correlated meson exchanges (like 7r7r, 7rp) [30], [31], [32].<br />

A series of modern high-quality potentials based on the pure one-boson exchange model was<br />

constructed by the Nijmegen group [33], who also performed a partial-wave analysis (PWA) l of<br />

all pp and np scatter<strong>in</strong>g data [36].2 With 15 free parameters they were able to achieve with the<br />

Nijmegen 93 potential a X2 / Ndata of about two. Fitt<strong>in</strong>g some of the free parameters <strong>in</strong> each partial<br />

wave separately <strong>in</strong> the case of the Nijmegen I,II potentials allows to describe the data perfectly<br />

with X2 / Ndata rv l.<br />

Another quite successful modern high-quality N N force is the so-called CD-Bonn potential,<br />

[36].<br />

1 Another partial-wave analysis has been performed by Arndt and collaborators [34], [35].<br />

2 <strong>The</strong> Nijmegen database consists of 1787 pp and 2514 np scatter<strong>in</strong>g date <strong>in</strong> the energy range from 0 to 350 MeV

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