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Correlated two-pion exchange and large-N(C) behavior of nuclear forces

Murat M. Kaskulov·Heinz Clement
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Abstract

The effect of correlated scalar-isoscalar two-pion exchange (CrTPE) modes is considered in connection with central and spin-orbit parts of the NN force. The two-pion correlation function is coupled directly to the scalar form factor of the nucleon which we calculate in the large-N(C) limit where the nucleon can be described as a soliton of an effective chiral theory. The results for the central NN force show a strong repulsive core at short internucleon distances supplemented by a moderate attraction beyond 1 fm. The long-range tail of the central NN potential is driven by the the pion-nucleon sigma term and consistent with the effective $σ$ meson exchange. The spin-orbit part of the NN potential is repulsive. The large-N(C) scaling behavior of the scalar-isoscalar NN interaction is addressed. We show that the spin-orbit part is O(1/N^2(C)) in strength relative to the central force resulting in the ratio $\simeq 1/9$ suggested by the 1/N(C) expansion for N(C)=3. The latter is in agreement with our numerical analysis and with the Kaplan-Manohar large-N(C) power counting. Unitarization of the $ππ$ scattering amplitude plays here an important role and improves the tree level results. Analytical representations of the CrTPE NN potential in terms of elementary functions are derived and their chiral content is discussed.

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Murat M. Kaskulov, Heinz Clement. 2004-06-06. Correlated two-pion exchange and large-N(C) behavior of nuclear forces. https://doi.org/10.1103/physrevc.70.014002

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