Mean field, occupation numbers and spectral functions in nuclear matter

J. Lehr, H. Lenske, S. Leupold +1 more

J. Lehr A, H. Lenske, Stefan Leupold +1 more

Quantum transport theory is used to calculate the nucleon spectral function in infinite nuclear matter. A self-consistent description is obtained by utilizing the relations between collision rates and correlation functions. Static and dynamical self-energies are taken into account in the single particle propagators. The real parts of the non-static self-energy contributions are calculated by dispersion theory thus conserving the analyticity of momentum distributions. The transport theoretical spectral functions, momentum distributions, occupation probabilities and responce functions are in close agreement with results of variational and other many-body theoretical calculations. The results indicate that the nucleon spectral functions are determined only by the average short-range correlation strength.

Sergey A. Ponomarenko, Manolo E. Sherrill, David P. Kilcrease +1 more

We develop a statistical mean-field theory of finite quantum systems in thermal equilibrium. Our formulation employs the canonical ensemble of statistical mechanics, and it enables us to analytically determine the occupation number distributions of interacting particles obeying Bose–Einstein or Fermi–Dirac statistics. We have also developed a numerical procedure that enables us to obtain a universal scaled occupation number distribution that, for a given total number of interacting particles in a finite system, makes it possible to determine the occupation number distribution for any temperature. The developed mean-field theory is applicable to a wide range of atomic, nuclear and condensed matter systems for which finite-size effects can play an important role. In particular, the present approach makes it possible to formulate a finite temperature mean-field theory for a specific ion in a dense plasma.

P. Grangé, J. Cugnon, A. Lejeune

Y Chen, Wei‐jie Fu, Yang-yang Tan

Hossein Mahzoon, Paweł Danielewicz, Arnau Rios

Computational difficulties aside, nonequilibrium Green's functions appear ideally suited for investigating the dynamics of central nuclear reactions. Many particles actively participate in those reactions. At the two energy extremes for the collisions, the limiting cases of the Green's function approach have been successful: the time-dependent Hartree-Fock theory at low energy and Boltzmann equation at high. The strategy for computational adaptation of the Green's function to central reactions is discussed. The strategy involves, in particular, incremental progression from one to three dimensions to develop and assess approximations, discarding of far-away function elements, use of effective interactions and preparation of initial states for the reactions through adiabatic switching. At this stage we concentrate on inclusion of correlations in one dimension, where relatively few approximations are needed, and we carry out reference calculations that can benchmark approximations needed for more dimensions. We switch on short-range interactions generating the correlations adiabatically in the Kadanoff-Baym equations to arrive at correlated ground states for uniform matter. As the energy of the correlated matter does not quite match the expectations for nuclear matter we add mean field to arrive at the match in energy. From there on, we move to finite systems. In switching on the correlations we observe emergence of extended tails in momentum distributions and evolution of single particle occupations away from 1 and 0.