1,171 research outputs found
The Shell Model, the Renormalization Group and the Two-Body Interaction
The no-core shell model and the effective interaction can
both be derived using the Lee-Suzuki projection operator formalism. The main
difference between the two is the choice of basis states that define the model
space. The effective interaction can also be derived using
the renormalization group. That renormalization group derivation can be
extended in a straight forward manner to also include the no-core shell model.
In the nuclear matter limit the no-core shell model effective interaction in
the two-body approximation reduces identically to . The same
considerations apply to the Bloch-Horowitz version of the shell model and the
renormalization group treatment of two-body scattering by Birse, McGovern and
Richardson
Projection Operator Formalisms and the Nuclear Shell Model
The shell model solve the nuclear many-body problem in a restricted model
space and takes into account the restricted nature of the space by using
effective interactions and operators. In this paper two different methods for
generating the effective interactions are considered. One is based on a partial
solution of the Schrodinger equation (Bloch-Horowitz or the Feshbach projection
formalism) and other on linear algebra (Lee-Suzuki). The two methods are
derived in a parallel manner so that the difference and similarities become
apparent. The connections with the renormalization group are also pointed out.Comment: 4 pages, no figure
In-Medium Similarity Renormalization Group for Nuclei
We present a new ab-initio method that uses similarity renormalization group
(SRG) techniques to continuously diagonalize nuclear many-body Hamiltonians. In
contrast with applications of the SRG to two- and three-nucleon interactions in
free space, we perform the SRG evolution "in medium" directly in the -body
system of interest. The in-medium approach has the advantage that one can
approximately evolve -body operators using only two-body machinery
based on normal-ordering techniques. The method is nonperturbative and can be
tailored to problems ranging from the diagonalization of closed-shell nuclei to
the construction of effective valence shell-model Hamiltonians and operators.
We present first results for the ground-state energies of He, O and
Ca, which have accuracies comparable to coupled-cluster calculations.Comment: 4pages, 4 figures, to be published in PR
Density Matrix Expansion for Low-Momentum Interactions
A first step toward a universal nuclear energy density functional based on
low-momentum interactions is taken using the density matrix expansion (DME) of
Negele and Vautherin. The DME is adapted for non-local momentum-space
potentials and generalized to include local three-body interactions. Different
prescriptions for the three-body DME are compared. Exploratory results are
given at the Hartree-Fock level, along with a roadmap for systematic
improvements within an effective action framework for Kohn-Sham density
functional theory.Comment: 50 pages, 10 figure
From low-momentum interactions to nuclear structure
We present an overview of low-momentum two-nucleon and many-body interactions
and their use in calculations of nuclei and infinite matter. The softening of
phenomenological and effective field theory (EFT) potentials by renormalization
group (RG) transformations that decouple low and high momenta leads to greatly
enhanced convergence in few- and many-body systems while maintaining a
decreasing hierarchy of many-body forces. This review surveys the RG-based
technology and results, discusses the connections to chiral EFT, and clarifies
various misconceptions.Comment: 76 pages, 57 figures, two figures updated, published versio
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