Eur. Phys. J. A (2016) 52: 362
https://doi.org/10.1140/epja/i2016-16362-0

Regular Article - Theoretical Physics

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

¹ Matej Bel University, SK-97401, Banska Bystrica, Slovakia
² National Research Nuclear University (MEPhI), 115409, Moscow, Russia

^* e-mail: E.Kolomeitsev@gsi.de

Received: 9 September 2016
Accepted: 24 November 2016
Published online: 15 December 2016

Abstract

The spectrum of bosonic scalar-mode excitations in a normal Fermi liquid with local scalar interaction is investigated for various values and momentum dependence of the scalar Landau parameter in the particle-hole channel. For the conditions are found when the phase velocity on the spectrum of zero sound acquires a minimum at non-zero momentum. For there are only damped excitations, and for the spectrum becomes unstable against the 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 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 . We also argue that in peripheral heavy-ion collisions the Pomeranchuk instability may occur already for .