Nuclear structure in the framework of the Unitary Correlation Operator Method

Abstract

Correlations play a crucial role in the nuclear many-body problem. We give an overview of recent developments in nuclear structure theory aiming at the description of these interactioninduced correlations by unitary transformations. We focus on the Unitary Correlation Operator Method (UCOM), which offers a very intuitive, universal and robust approach for the treatment of short-range correlations. We discuss the UCOM formalism in detail and highlight the connections to other methods for the description of short-range correlations and the construction of effective interactions. In particular, we juxtapose UCOM with the Similarity Renormalization Group (SRG) approach, which implements the unitary transformation of the Hamiltonian through a very flexible flow-equation formulation. The UCOM-and SRG-transformed interactions are compared on the level of matrix elements and in many-body calculations within the no-core shell model and with Hartree-Fock plus perturbation theory for a variety of nuclei and observables. These calculations provide a detailed picture of the similarities and differences as well as the advantages and limitations of unitary transformation methods.

In-medium similarity renormalization group for closed and open-shell nuclei

“…Slater determinants that are variationally optimized through a Hartree-Fock (HF) procedure have been shown to be reasonable reference states for interactions with low resolution scales around λ = 2.0 fm −1 (see, e.g., Refs. [33,51,53,58,62,115] and references therein), allowing post-HF methods like MBPT, CC, or the IMSRG discussed below to converge rapidly to the exact FCI result. Starting from such a HF reference state |Φ HF , we can obtain a basis consisting of the state itself and up to A-particle, A-hole (ApAh) excitations:…”

Density dependence of quasifree single-nucleon knockout reactions

“…where g(r 12 ) is the so-called Jastrow correlation function [31] and γ ( r) a function which guarantees the proper normalization of ρ [2] A . The γ ( r) can be numerically obtained as (12) and (17).…”

Proton Radius of 14Be from Measurement of Charge-Changing Cross Sections

“…Strong mixings of sd configurations are important for 12 Be and 14 Be. Although the general trend for the radii in different isotopes is properly reproduced, the charge radii are smaller than the experimental values obtained from isotope-shift measurements [27,28].…”