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Spin-isospin stability of nuclear matter

N. Kaiser
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Abstract

We calculate the density-dependent spin-isospin asymmetry energy $J(k_f)$ of nuclear matter in the three-loop approximation of chiral perturbation theory. The interaction contributions to $J(k_f)$ originate from one-pion exchange, iterated one-pion exchange, and irreducible two-pion exchange with no, single, and double virtual $Δ$-isobar excitation. We find that the approximation to $1π$-exchange and iterated $1π$-exchange terms (which leads already to a good nuclear matter equation of state by adjusting an emerging contact-term) is spin-isospin stable, since $J(k_{f0})\simeq 24 {\rm MeV}>0$. The inclusion of the chiral $πNΔ$-dynamics, necessary in order to guarantee the spin-stability of nuclear matter, keeps this property intact. The corresponding spin-isospin asymmetry energy $J(k_f)$ stays positive even for extreme values of an undetermined short-distance parameter $J_5$ (whose possible range we estimate from realistic NN-potentials). The largest positive contribution to $J(k_f)$ (a term linear in density) comes from a two-body contact-term with its strength fitted to the empirical nuclear matter saturation point.

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N. Kaiser. 2006-01-31. Spin-isospin stability of nuclear matter. https://doi.org/10.1103/physrevc.72.014007

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