The Unitary Correlation Operator Method from a Similarity Renormalization Group Perspective

We investigate how the Unitary Correlation Operator Method (UCOM), developed to explicitly describe the strong short-range central and tensor correlations present in the nuclear many-body system, relates to the Similarity Renormalization Group (SRG), a method to band-diagonalize Hamiltonians by continuous unitary transformations. We demonstrate how the structure of the UCOM transformation, originally motivated from the physically intuitive picture of correlations in coordinate space, arises naturally from the SRG flow equation. Apart from formal considerations we show that the momentum space matrix elements of the effective interactions obtained in both schemes agree extremely well.Comment: 5 pages, 2 figures, using REVTEX4; v2: references adde

Mean-field instability of trapped dilute boson-fermion mixtures

The influence of boson-boson and boson-fermion interactions on the stability of a binary mixture of bosonic and fermionic atoms is investigated. The density profiles of the trapped mixture are obtained from direct numerical solution of a modified Gross-Pitaevskii equation that is self-consistently coupled to the mean-field generated by the interaction with the fermionic species. The fermions which in turn feel the mean-field created by the bosons are treated in Thomas-Fermi approximation. We study the effects of different combinations of signs of the boson-boson and the boson-fermion scattering lengths and determine explicit expressions for critical particle numbers as function of these scattering lengths.Comment: 4 pages, 2 figures (using RevTeX4

Quasiparticle Random Phase Approximation with Interactions from the Similarity Renormalization Group

We have developed a fully consistent framework for calculations in the Quasiparticle Random Phase Approximation (QRPA) with $NN$ interactions from the Similarity Renormalization Group (SRG) and other unitary transformations of realistic interactions. The consistency of our calculations, which use the same Hamiltonian to determine the Hartree-Fock-Bogoliubov (HFB) ground states and the residual interaction for QRPA, guarantees an excellent decoupling of spurious strength, without the need for empirical corrections. While work is under way to include SRG-evolved 3N interactions, we presently account for some 3N effects by means of a linearly density-dependent interaction, whose strength is adjusted to reproduce the charge radii of closed-shell nuclei across the whole nuclear chart. As a first application, we perform a survey of the monopole, dipole, and quadrupole response of the calcium isotopic chain and of the underlying single-particle spectra, focusing on how their properties depend on the SRG parameter $\lambda$. Unrealistic spin-orbit splittings suggest that spin-orbit terms from the 3N interaction are called for. Nevertheless, our general findings are comparable to results from phenomenological QRPA calculations using Skyrme or Gogny energy density functionals. Potentially interesting phenomena related to low-lying strength warrant more systematic investigations in the future.Comment: 18 pages, 17 figures, 3 tables (RevTeX 4.1), v2: fixed typos & figures, as publishe

Density functional theory for hard-sphere mixtures: the White-Bear version Mark II

In the spirit of the White-Bear version of fundamental measure theory we derive a new density functional for hard-sphere mixtures which is based on a recent mixture extension of the Carnahan-Starling equation of state. In addition to the capability to predict inhomogeneous density distributions very accurately, like the original White-Bear version, the new functional improves upon consistency with an exact scaled-particle theory relation in the case of the pure fluid. We examine consistency in detail within the context of morphological thermodynamics. Interestingly, for the pure fluid the degree of consistency of the new version is not only higher than for the original White-Bear version but also higher than for Rosenfeld's original fundamental measure theory.Comment: 16 pages, 3 figures; minor changes; J. Phys.: Condens. Matter, accepte

Nuclear Structure in the UCOM Framework: From Realistic Interactions to Collective Excitations

The Unitary Correlation Operator Method (UCOM) provides a means for nuclear structure calculations starting from realistic NN potentials. The dominant short-range central and tensor correlations are described explicitly by a unitary transformation. The application of UCOM in the context of the no-core shell model provides insight into the interplay between dominant short-range and residual long-range correlations in the nuclear many-body problem. The use of the correlated interaction within Hartree-Fock, many-body perturbation theory, and Random Phase Approximation gives access to various nuclear structure observables throughout the nuclear chart.Comment: 9 pages, 3 figures, invited talk at the 2nd Int. Conf. on "Collective Motion in Nuclei under Extreme Conditions" (COMEX 2), Sankt Goar, German

Nuclear Structure and Response based on Correlated Realistic NN Interactions

Starting from the Argonne V18 nucleon-nucleon (NN) interaction and using the Unitary Correlation Operator Method, a correlated interaction v_UCOM has been constructed, which is suitable for calculations within restricted Hilbert spaces. In this work we employ the v_UCOM in Hartree-Fock, perturbation-theory and RPA calculations and we study the ground-state properties of various closed-shell nuclei, as well as some excited states. The present calculations provide also important feedback for the optimization of the v_UCOM and valuable information on its properties. The above scheme offers the prospect of ab initio calculations in nuclei, regardless of their mass number. It can be used in conjunction with other realistic NN interactions as well, and with various many-body methods (Second RPA, QRPA, Shell Model, etc.).Comment: 3 pages, incl. 2 figures; Proc. Int. Conf. on Frontiers in Nuclear Structure, Astrophysics and Reactions (FINUSTAR), Kos, Greece, Sept.200