Relativistic $O(q^4)$ two-pion exchange nucleon-nucleon potential: configuration space

Details Relativistic $O(q^4)$ two-pion exchange nucleon-nucleon potential: configuration space Relativistic $O(q^4)$ two-pion exchange nucleon-nucleon potential: configuration space

2003-10-02

arxiv.org/abs/nucl-th/0310011v1

Phys.Rev. C69 (2004) 034009

Physics

Nuclear Physics

Nuclear Theory

27 pages, 33 figures

Scientific paper

10.1103/PhysRevC.69.034009

We have recently performed a relativistic $O(q^4)$ chiral expansion of the two-pion exchange $NN$ potential, and here we explore its configuration space content. Interactions are determined by three families of diagrams, two of which involve just $g_A$ and $f_{\pi}$, whereas the third one depends on empirical coefficients fixed by subthreshold $\pi N$ data. In this sense, the calculation has no adjusted parameters and gives rise to predictions, which are tested against phenomenological potentials. The dynamical structure of the eight leading non-relativistic components of the interaction is investigated and, in most cases, found to be clearly dominated by a well defined class of diagrams. In particular, the central isovector and spin-orbit, spin-spin, and tensor isoscalar terms are almost completely fixed by just $g_A$ and $f_{\pi}$. The convergence of the chiral series in powers of the ratio (pion mass/nucleon mass) is studied as a function of the internucleon distance and, for $r>$ 1 fm, found to be adequate for most components of the potential. An important exception is the dominant central isoscalar term, where the convergence is evident only for $r>$ 2.5 fm. Finally, we compare the spatial behavior of the functions that enter the relativistic and heavy baryon formulations of the interaction and find that, in the region of physical interest, they differ by about 5%.

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