Self-consistent Green's function method for nuclei and nuclear matter

Abstract

Recent results obtained by applying the method of self-consistent Green's functions to nuclei and nuclear matter are reviewed. Particular attention is given to the description of experimental data obtained from the (e,e ′ p) and (e,e ′ 2N) reactions that determine one and two-nucleon removal probabilities in nuclei since the corresponding amplitudes are directly related to the imaginary parts of the single-particle and two-particle propagators. For this reason and the fact that these amplitudes can now be calculated with the inclusion of all the relevant physical processes, it is useful to explore the efficacy of the method of self-consistent Green's functions in describing these experimental data. Results for both finite nuclei and nuclear matter are discussed with particular emphasis on clarifying the role of short-range correlations in determining various experimental quantities. The important role of long-range correlations in determining the structure of lowenergy correlations is also documented. For a complete understanding of nuclear phenomena it is therefore essential to include both types of physical correlations. We demonstrate that recent experimental results for these reactions combined with the reported theoretical calculations yield a very clear understanding of the properties of all protons in the nucleus. We propose that this knowledge of the properties of constituent fermions in a correlated many-body system is a unique feature of nuclear physics.

Infrared extrapolations for atomic nuclei

“…As seen in the right panel, these frequencies are much larger than the naive estimate Ω min ≈ 2 Λ χ /(mR) that minimizes the energy for a nucleus of radius R and interaction with cutoff Λ χ [17]. The exponential extrapolation (6) to all solid data points is shown as a dashed line, and the asymptote E ∞ as a full line.…”

“…Figure 5 shows the CCSD groundstate energies for 22 O (left) and 24 O (right) as a function of L eff . The exponential extrapolation (6), and the extrapolated ground-state energies E ∞ = −148.41±0.60 MeV (for 22 O) and E ∞ = −155.38 ± 0.83 MeV (for 24 O) are also shown. These results employ model spaces with N = 8, 10, 12.…”

“…The solid lines are fits of Eq. (6) for fixed N to only the solid points. The arrow marks the minimum energy E Ω min that is obtained when varying the oscillator spacing Ω for N max = 12.…”

“…Wave-function based methods for computing atomic nuclei, such as exact diagonalization [1,2], coupled cluster [3,4,5], self-consistent Green's functions [6], or in-medium similarity renormalization group (SRG) [7,8], require a computational effort that depends strongly on the size of the Hilbert space used. Truncating this model space introduces systematic errors that must be quantitatively analyzed for a given Hamiltonian and nucleus.…”

Chiral three-nucleon forces and the evolution of correlations along the oxygen isotopic chain

“…The concept of correlations is fundamental to a deep understanding of nuclear phenomena [1]. These are generally defined as characteristics of the nucleus that cannot be explained in terms of a simple mean field picture (i.e., a wave function of Slater determinant type).…”