Nuclear Physics from Lattice QCD

We review recent progress toward establishing lattice Quantum Chromodynamics as a predictive calculational framework for nuclear physics. A survey of the current techniques that are used to extract low-energy hadronic scattering amplitudes and interactions is followed by a review of recent two-body and few-body calculations by the NPLQCD collaboration and others. An outline of the nuclear physics that is expected to be accomplished with Lattice QCD in the next decade, along with estimates of the required computational resources, is presented.Comment: 56 pages, 39 pdf figures. Final published versio

Chiral dynamics of the nuclear equation of state

We present a new chiral power expansion scheme for the nuclear equation of state. The scheme is effective in the sense that it is constructed to work around nuclear saturation density. The leading and subleading terms are evaluated and are shown to provide an excellent equation of state. As a further application we considered the chiral quark condensate in nuclear matter. Already at nuclear saturation density we predict a substantially smaller reduction of the condensate as compared to conventional approaches.Comment: 7 pages, 4 figures, talk given at: "QCD at Finite Baryon Density", Bielefeld (April 1998

Radial vibrations of BPS skyrmions

We study radial vibrations of spherically symmetric skyrmions in the BPS Skyrme model. Concretely, we numerically solve the linearised field equations for small fluctuations in a skyrmion background, both for linearly stable oscillations and for (unstable) resonances. This is complemented by numerical solutions of the full nonlinear system, which confirm all the results of the linear analysis. In all cases, the resulting fundamental excitation provides a rather accurate value for the Roper resonance, supporting the hypothesis that the BPS Skyrme model already gives a reasonable approximate description of this resonance. Further, for many potentials additional higher resonances appear, again in agreement with known experimental results.Comment: Latex, 41 pages, 22 pdf figures; v2: minor change

Shell-model calculations and realistic effective interactions

A review is presented of the development and current status of nuclear shell-model calculations in which the two-body effective interaction is derived from the free nucleon-nucleon potential. The significant progress made in this field within the last decade is emphasized, in particular as regards the so-called V-low-k approach to the renormalization of the bare nucleon-nucleon interaction. In the last part of the review we first give a survey of realistic shell-model calculations from early to present days. Then, we report recent results for neutron-rich nuclei near doubly magic 132Sn and for the whole even-mass N=82 isotonic chain. These illustrate how shell-model effective interactions derived from modern nucleon-nucleon potentials are able to provide an accurate description of nuclear structure properties.Comment: 71 pages, to be published in Progress in Particle and Nuclear Physic

Techniques in Analytic Lamb Shift Calculations

Quantum electrodynamics has been the first theory to emerge from the ideas of regularization and renormalization, and the coupling of the fermions to the virtual excitations of the electromagnetic field. Today, bound-state quantum electrodynamics provides us with accurate theoretical predictions for the transition energies relevant to simple atomic systems, and steady theoretical progress relies on advances in calculational techniques, as well as numerical algorithms. In this brief review, we discuss one particular aspect connected with the recent progress: the evaluation of relativistic corrections to the one-loop bound-state self-energy in a hydrogenlike ion of low nuclear charge number, for excited non-S states, up to the order of alpha (Zalpha)^6 in units of the electron mass. A few details of calculations formerly reported in the literature are discussed, and results for 6F, 7F, 6G and 7G states are given.Comment: 16 pages, LaTe

Toward ab initio density functional theory for nuclei

We survey approaches to nonrelativistic density functional theory (DFT) for nuclei using progress toward ab initio DFT for Coulomb systems as a guide. Ab initio DFT starts with a microscopic Hamiltonian and is naturally formulated using orbital-based functionals, which generalize the conventional local-density-plus-gradients form. The orbitals satisfy single-particle equations with multiplicative (local) potentials. The DFT functionals can be developed starting from internucleon forces using wave-function based methods or by Legendre transform via effective actions. We describe known and unresolved issues for applying these formulations to the nuclear many-body problem and discuss how ab initio approaches can help improve empirical energy density functionals.Comment: 69 pages, 16 figures, many revisions based on feedback. To appear in Progress in Particle and Nuclear Physic