Density-functional theory for fermions in the unitary regime

In the unitary regime, fermions interact strongly via two-body potentials that exhibit a zero range and a (negative) infinite scattering length. The energy density is proportional to the free Fermi gas with a proportionality constant $\xi$. We use a simple density functional parametrized by an effective mass and the universal constant $\xi$, and employ Kohn-Sham density-functional theory to obtain the parameters from fit to one exactly solvable two-body problem. This yields $\xi=0.42$ and a rather large effective mass. Our approach is checked by similar Kohn-Sham calculations for the exactly solvable Calogero model.Comment: 5 pages, 2 figure

Chaos in fermionic many-body systems and the metal-insulator transition

We show that finite Fermi systems governed by a mean field and a few-body interaction generically possess spectral fluctuations of the Wigner-Dyson type and are, thus, chaotic. Our argument is based on an analogy to the metal-insulator transition. We construct a sparse random-matrix ensemble ScE that mimics that transition. Our claim then follows from the fact that the generic random-matrix ensemble modeling a fermionic interacting many-body system is much less sparse than ScE.Comment: 8 figures, 8 pages, amplified and corrected, main conclusion unchange

Medium-mass nuclei from chiral nucleon-nucleon interactions

We compute the binding energies, radii, and densities for selected medium-mass nuclei within coupled-cluster theory and employ the "bare" chiral nucleon-nucleon interaction at order N3LO. We find rather well-converged results in model spaces consisting of 15 oscillator shells, and the doubly magic nuclei 40Ca, 48Ca, and the exotic 48Ni are underbound by about 1 MeV per nucleon within the CCSD approximation. The binding-energy difference between the mirror nuclei 48Ca and 48Ni is close to theoretical mass table evaluations. Our computation of the one-body density matrices and the corresponding natural orbitals and occupation numbers provides a first step to a microscopic foundation of the nuclear shell model.Comment: 5 pages, 5 figure

Computation of spectroscopic factors with the coupled-cluster method

We present a calculation of spectroscopic factors within coupled-cluster theory. Our derivation of algebraic equations for the one-body overlap functions are based on coupled-cluster equation-of-motion solutions for the ground and excited states of the doubly magic nucleus with mass number $A$ and the odd-mass neighbor with mass $A-1$. As a proof-of-principle calculation, we consider $^{16}$O and the odd neighbors $^{15}$O and $^{15}$N, and compute the spectroscopic factor for nucleon removal from $^{16}$O. We employ a renormalized low-momentum interaction of the $V_{\mathrm{low-}k}$ type derived from a chiral interaction at next-to-next-to-next-to-leading order. We study the sensitivity of our results by variation of the momentum cutoff, and then discuss the treatment of the center of mass.Comment: 8 pages, 6 figures, 3 table

Complex coupled-cluster approach to an ab-initio description of open quantum systems

We develop ab-initio coupled-cluster theory to describe resonant and weakly bound states along the neutron drip line. We compute the ground states of the helium chain 3-10He within coupled-cluster theory in singles and doubles (CCSD) approximation. We employ a spherical Gamow-Hartree-Fock basis generated from the low-momentum N3LO nucleon-nucleon interaction. This basis treats bound, resonant, and continuum states on equal footing, and is therefore optimal for the description of properties of drip line nuclei where continuum features play an essential role. Within this formalism, we present an ab-initio calculation of energies and decay widths of unstable nuclei starting from realistic interactions.Comment: 4 pages, revtex