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Analysis of zero-frequency solutions of the pion dispersion equation in nuclear matter

V. A. Sadovnikova
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Abstract

In this paper we consider instability of nuclear matter which takes place when the frequencies of the collective excitations turn to zero. We investigate collective excitations with pion quantum numbers J^π=0^-. We study the dependence of zero-frequency solutions of the pion dispersion equation on the value of the spin-isospin quasiparticle interaction G'. The solutions of the pion dispersion equation describe the different types of the excitations in the matter, ω_i(k). At the critical density ρ=ρ_c one of solutions of the definite type turns to zero: ω_{i0}(k_c)=0. When ρ>ρ_c, the excitations ω_{i0}(k) become amplified. It is shown that there is such a "transitional" value of G'=G'_{tr} that for G' G'_{tr} they pertain to the type ω_c. The solutions of the type ω_{sd} correspond to instability to small density fluctuations of the nuclear matter at G'\le -1. On the other hand, ω_c is responsible for the "pion condensation" at G'\approx 2. For the stable nuclear matter the branches of solutions ω_{sd}(k) and ω_c(k) are located on the unphysical sheets of the complex plane of frequency.

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V. A. Sadovnikova. 2005-10-25. Analysis of zero-frequency solutions of the pion dispersion equation in nuclear matter. https://arxiv.org/abs/nucl-th/0510076

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