Low-momentum interactions for nuclei

We show how the renormalization group is used to construct a low-momentum nucleon-nucleon interaction V_{low k}, which unifies all potential models used in nuclear structure calculations. V_{low k} can be directly applied to the nuclear shell model or to nucleonic matter without a G matrix resummation. It is argued that V_{low k} parameterizes a high-order chiral effective field theory two-nucleon force. We use cutoff dependence as a tool to assess the error in the truncation of nuclear forces to two-nucleon interactions and introduce a low-momentum three-nucleon force, which regulates A=3,4 binding energies. The adjusted three-nucleon interaction is perturbative for small cutoffs. In contrast to other precision interactions, the error due to missing many-body forces can be estimated, when V_{low k} and the corresponding three-nucleon force are used in nuclear structure calculations and the cutoff is varied.Comment: 10 pages, 5 figures, talk at INT workshop on Nuclear Forces and the Quantum Many-Body Problem, Seattle, October 200

Three-body forces and proton-rich nuclei

We present the first study of three-nucleon (3N) forces for proton-rich nuclei along the N=8 and N=20 isotones. Our results for the ground-state energies and proton separation energies are in very good agreement with experiment where available, and with the empirical isobaric multiplet mass equation. We predict the spectra for all N=8 and N=20 isotones to the proton dripline, which agree well with experiment for 18Ne, 19Na, 20Mg and 42Ti. In all other cases, we provide first predictions based on nuclear forces. Our results are also very promising for studying isospin symmetry breaking in medium-mass nuclei based on chiral effective field theory.Comment: 5 pages, 4 figures, minor changes, published versio

Supernova matter at subnuclear densities as a resonant Fermi gas: Enhancement of neutrino rates

At low energies nucleon-nucleon interactions are resonant and therefore supernova matter at subnuclear densities has many similarities to atomic gases with interactions dominated by a Feshbach resonance. We calculate the rates of neutrino processes involving nucleon-nucleon collisions and show that these are enhanced in mixtures of neutrons and protons at subnuclear densities due to the large scattering lengths. As a result, the rate for neutrino pair bremsstrahlung and absorption is significantly larger below 10^{13} g cm^{-3} compared to rates used in supernova simulations.Comment: 5 pages, 4 figures, published version, NORDITA-2014-2

Two-neutrino double electron capture on 124^{124}Xe based on an effective theory and the nuclear shell model

We study the two-neutrino double electron capture on $^{124}$Xe based on an effective theory (ET) and large-scale shell model calculations, two modern nuclear structure approaches that have been tested against Gamow-Teller and double-beta decay data. In the ET, the low-energy constants are fit to electron capture and $\beta^{-}$ transitions around xenon. For the nuclear shell model, we use an interaction in a large configuration space that reproduces the spectroscopy of nuclei in this mass region. For the dominant transition to the $^{124}$Te ground state, we find half-lives $T^{2\nu{\rm ECEC}}_{1/2}=(1.3-18)\times 10^{22}$ y for the ET and $T^{2\nu{\rm ECEC}}_{1/2} = (0.43-2.9)\times 10^{22}$ y for the shell model. The ET uncertainty leads to a half-life almost entirely consistent with present experimental limits and largely within the reach of ongoing experiments. The shell model half-life range overlaps with the ET, but extends less beyond current limits. Our findings thus suggest that the two-neutrino double electron capture on $^{124}$Xe has a good chance to be discovered by ongoing or future experiments. In addition, we present results for the two-neutrino double electron capture to excited states of $^{124}$Te.Comment: 5 pages, 2 figure

Three-nucleon forces and spectroscopy of neutron-rich calcium isotopes

We study excited-state properties of neutron-rich calcium isotopes based on chiral two- and three-nucleon interactions. We first discuss the details of our many-body framework, investigate convergence properties, and for two-nucleon interactions benchmark against coupled-cluster calculations. We then focus on the spectroscopy of 47-56Ca, finding that with both 3N forces and an extended pfg9/2 valence space, we obtain a good level of agreement with experiment. We also study electromagnetic transitions and find that experimental data are well described by our calculations. In addition, we provide predictions for unexplored properties of neutron-rich calcium isotopes.Comment: 15 pages, 22 figures, published versio

How should one formulate, extract, and interpret `non-observables' for nuclei?

Nuclear observables such as binding energies and cross sections can be directly measured. Other physically useful quantities, such as spectroscopic factors, are related to measured quantities by a convolution whose decomposition is not unique. Can a framework for these nuclear structure `non-observables' be formulated systematically so that they can be extracted from experiment with known uncertainties and calculated with consistent theory? Parton distribution functions in hadrons serve as an illustrative example of how this can be done. A systematic framework is also needed to address questions of interpretation, such as whether short-range correlations are important for nuclear structure.Comment: 7 pages. Contribution to the "Focus issue on Open Problems in Nuclear Structure", Journal of Physics

Nuclear forces and their impact on neutron-rich nuclei and neutron-rich matter

We review the impact of nuclear forces on matter at neutron-rich extremes. Recent results have shown that neutron-rich nuclei become increasingly sensitive to three-nucleon forces, which are at the forefront of theoretical developments based on effective field theories of quantum chromodynamics. This includes the formation of shell structure, the spectroscopy of exotic nuclei, and the location of the neutron dripline. Nuclear forces also constrain the properties of neutron-rich matter, including the neutron skin, the symmetry energy, and the structure of neutron stars. We first review our understanding of three-nucleon forces and show how chiral effective field theory makes unique predictions for many-body forces. Then, we survey results with three-nucleon forces in neutron-rich oxygen and calcium isotopes and neutron-rich matter, which have been explored with a range of many-body methods. Three-nucleon forces therefore provide an exciting link between theoretical, experimental and observational nuclear physics frontiers.Comment: 28 pages, 13 figures, 1 tabl

Dynamical Symmetries in q-deformed Quantum Mechanics

The dynamical algebra of the q-deformed harmonic oscillator is constructed. As a result, we find the free deformed Hamiltonian as well as the Hamiltonian of the deformed oscillator as a complicated, momentum dependent interaction Hamiltonian in terms of the usual canonical variables. Furthermore we construct a well-defined algebra SU$_q$(1,1) with consistent conjugation properties and comultiplication. We obtain non lowest weight representations of this algebra.Comment: 19 pages, latex, no figure