Scalar quanta in Fermi liquids: zero sounds, instabilities, Bose condensation, and a metastable state in dilute nuclear matter

TL;DR

This paper explores scalar excitation modes in Fermi liquids, revealing conditions for zero sound instabilities, Bose condensation formation, and metastable states in nuclear matter, with implications for heavy-ion collisions.

Contribution

It introduces a detailed analysis of scalar-mode excitations in Fermi liquids, deriving an effective Lagrangian, and demonstrates how instabilities can lead to Bose condensates and metastable nuclear states.

Findings

Scalar Landau parameter influences zero sound spectrum and stability.

Bose condensation of scalar modes can stabilize instabilities.

Metastable states may occur in nuclear matter at subsaturation density.

Abstract

Spectrum of bosonic scalar-mode excitations in a normal Fermi liquid with a local scalar interaction is investigated for various values and momentum dependence of the scalar Landau parameter $f_0$ in the particle-hole channel. For $f_0 >0$ the conditions are found when the phase velocity on the spectrum of the zero sound acquires a minimum at a non-zero momentum. For $-1<f_0 <0$ there are only damped excitations, and for $f_0<-1$ the spectrum becomes unstable against a growth of scalar-mode excitations. An effective Lagrangian for the scalar excitation modes is derived after performing a bosonization procedure. We demonstrate that the instability may be tamed by the formation of a static Bose condensate of the scalar modes. The condensation may occur in a homogeneous or inhomogeneous state relying on the momentum dependence of the scalar Landau parameter. We show that in the isospin-symmetric nuclear matter there may appear a metastable state at a subsaturation nuclear density owing to the condensate. Then we consider a possibility of the condensation of the zero-sound-like excitations in a state with a non-zero momentum in Fermi liquids moving with overcritical velocities, provided an appropriate momentum dependence of the Landau parameter $f_0 (k)>0$. We also argue that in peripheral heavy-ion collisions the Pomeranchuk instability may occur already for $f_0 >-1$.