Many-body perturbation theory of the effective interaction in nuclei

Mikaël Frosini, T. Duguet, J.-P. Ebran +1 more

Mikaël Frosini, T. Duguet, J.-P. Ebran +6 more

BRUCE R. BARRETT

A brief review of the history of many-body perturbation theory (MBPT) and its applications in nuclear physics is given. Problems regarding its application to nuclear-structure calculations are discussed and analysed. It is concluded that the usefulness of nuclear MBPT in terms of an expansion in the nuclear reaction matrix G for the calculation of effective interactions in shell-model investigations is severely challenged and restricted by the problems and uncertainties connected with this approach. New methods based on unitary transformation approaches have proven to be more accurate and reliable, particularly for light nuclei.

Kailash Kumar, Robert T. Folk

Zhen Li, A. Tichai, A. Schwenk +1 more

We advance the many-body perturbation theory (MBPT) calculations of the ground-state energy and radius of closed-shell nuclei beyond third order. Using automated diagram generation and evaluation up to fifth order, we present ground-state properties of selected closed-shell nuclei up to $^{78}$Ni with two- and three-nucleon interactions derived from chiral effective field theory. A clear convergence trend is observed for the ground-state energy enabling calculations at improved accuracy. We further investigate in detail the decomposition of the fourth-order contributions. For the ground-state energy, the magnitude of the fourth-order contribution is typically less than half of the third order, and a typical cancellation among different classes of diagrams is observed. Finally, we perform a comprehensive comparison between MBPT and non-perturbative in-medium similarity renormalization group (IMSRG) calculations, with the goal to provide insight into many-body uncertainties associated with the IMSRG(2) truncation.

Morten Hjorth-Jensen

Various perturbative and non-perturbative many-body techniques are discussed in this work. Especially, we will focus on the summation of so-called Parquet diagrams with emphasis on applications to finite nuclei. Here, the subset of two-body Parquet equations will be discussed. A practical implementation of the corresponding equations for studies of effective interactions for finite nuclei is outlined.