Real-time Kadanoff-Baym approach to nuclear response functions

• Published in: arXiv.org
• Main Authors: Köhler, H S, Kwong, N H
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 20.01.2016
• Subjects: Approximation; Bethe-Salpeter equation; Born approximation; Collision dynamics; Correlation; Density; Electron gas; Green's functions; Mathematical analysis; Nuclear matter; Nucleons; Particle theory; Physics - Nuclear Theory; Plasma oscillations; Real time; Response functions; Time dependence; Variations
• DOI: 10.48550/arxiv.1601.05463

Linear density response functions are calculated for symmetric nuclear matter of normal density by time-evolving two-time Green's functions in real time. Of particular interest is the effect of correlations. The system is therefore initially time-evolved with a collision term calculated in a direct Born approximation as well as with full (RPA) ring-summation until fully correlated. An external time-dependent potential is then applied. The ensuing density fluctuations are recorded to calculate the density response. This method was previously used by Kwong and Bonitz for studying plasma oscillations in a correlated electron gas. The energy-weighted sum-rule for the response function is guaranteed by using conserving self-energy insertions as the method then generates the full vertex-functions. These can alternatively be calculated by solving a Bethe -Salpeter equation as done in some previous works. The (first order) mean field is derived from a momentum-dependent (non-local) interaction while \(2^{nd}\) order self-energies are calculated using a particle-hole two-body effective (or 'residual') interaction given by a gaussian \it local \rm potential. We present numerical results for the response function \(S(\omega,q_0)\) for \(q_0=0.2,0.4\) and \(0.8 {\rm fm}^{-1}\). Comparison is made with the nucleons being un-correlated i.e. with only the first order mean field included, the 'HF+RPA' approximation. We briefly discuss the relation of our work with the Landau quasi-particle theory as applied to nuclear systems by Sj\"oberg and followers using methods developped by Babu and Brown, with special emphasis on the 'induced' interaction.