English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study self-consistent approximations such as the $\Phi$-derivable andvirial approaches to dilute strongly interacting systems in equilibrium. Weconsider a system of non-relativistic fermions of one kind interacting via apair potential Thermodynamical quantities are expressed in terms of variousspectral functions. We review the $\Phi$ derivable approximation schemedemonstrating the exact conservation of the Noether and the Botermans-Malflietfermion number densities, and then for $\Phi$ described by the tadpole andsandwich diagrams we show the coincidence of these two number densities. Asexamples of test pair potentials, we consider the Yukawa centralnucleon-nucleon potentials within Walecka, CD Bonn, and Reid parameterizations,and the corresponding classical Lennard-Jones potentials. Expressions for thesecond and third virial coefficients are derived and analyzed for $\Phi$described by the tadpole and sandwich diagrams. Next, we focus on the virialapproach to the equation of state. Classical, semiclassical, and purely quantumapproaches are studied in detail. Then, different extrapolations of the virialequation of state are considered including the van~der~Waals form andexcluded-volume models. We derive the expression for the second virialcoefficient using the effective range approximation for the scatteringamplitude and compare the result with the purely quantum result using theexperimental phase shifts. Attention is focused on the problem of anomalouslylarge value of the nucleon-nucleon scattering length appearing due to thepresence of the quasi-bound state in nucleon-nucleon scattering, which can bedestroyed in the matter because of the action of the Pauli blocking. We presentresults for the second virial coefficient subtracting this term. We discuss thevalidity of such a procedure to describe the equation of state of the nuclearmatter in the virial limit.

Conserving approximations to dilute equilibrium systems. Pair interaction potential