High-resolution probes of low-resolution nuclei

Renormalization group (RG) methods used to soften Hamiltonians allow large-scale computational resources to be used to greater advantage in calculations of nuclear structure and reactions. These RG transformations lower the effective resolution of the nuclei, which raises questions about how to calculate and interpret high-momentum transfer probes of nuclear structure. Such experiments are conventionally explained in terms of short-range correlations, but these disappear with the evolution to low-momentum scales. We highlight the important issues and prospects in the context of recent developments in RG technology, with guidance from the analogous extraction of parton distributions.Comment: Contribution to the proceedings of the International Conference on Nuclear Theory in the Supercomputing Era 2013, Iowa State University, May 13-17, 2013, Ames, Iowa. 10 pages, 18 figure

Building Atomic Nuclei with the Dirac Equation

The relevance of the Dirac equation for computations of nuclear structure is motivated and discussed. Quantitatively successful results for medium- and heavy-mass nuclei are described, and modern ideas of effective field theory and density functional theory are used to justify them.Comment: 9 pages, REVTeX 4.0 with 12pt.rtx, aps.rtx, amssymb.tex, bm.sty, ntgdefs.tex. Contribution to the Dirac Centennial Symposium (FSU, 12/6-7/02

Neutron matter based on consistently evolved chiral three-nucleon interactions

We present the first results for the neutron matter equation of state (EOS) using nucleon-nucleon and three-nucleon chiral effective field theory interactions that are consistently evolved in the framework of the Similarity Renormalization Group (SRG). The dependence of the EOS on the SRG resolution scale is greatly reduced when induced three-nucleon forces (3NF) are included and the residual variation, which in part is from missing induced four-body interactions, is comparable to estimated many-body perturbation theory truncation errors. The relative growth with decreasing resolution of the 3NF contributions to the energy per neutron is of natural size, but it accelerates at the lowest resolutions where strong renormalization of the long-range 3NF matrix elements is also observed.Comment: 6 pages, 5 figure

Comment on: "Nucleon-nucleon scattering lengths in QCD sum rules,"

In a recent Physical Review Letter, Kondo and Morimatsu present a QCD sum rule calculation of nucleon-nucleon scattering lengths. They also relate the empirical scattering lengths to the nucleon mass shift in nuclear matter to cast doubt on the "linear density approximation." In this Comment, we point out flaws in both parts of their analysis and draw very different conclusions.Comment: 4 pages in RevTeX, OSU-0901/UTHEP-26

Universality in Similarity Renormalization Group Evolved Potential Matrix Elements and T-Matrix Equivalence

We examine how the universality of two-nucleon interactions evolved using similarity renormalization group (SRG) transformations correlates with T-matrix equivalence, with the ultimate goal of gaining insight into universality for three-nucleon forces. With sufficient running of the SRG flow equations, the low-energy matrix elements of different realistic potentials evolve to a universal form. Because these potentials are fit to low-energy data, they are (approximately) phase equivalent only up to a certain energy, and we find universality in evolved potentials up to the corresponding momentum. More generally we find universality in local energy regions, reflecting a local decoupling by the SRG. The further requirements for universality in evolved potential matrix elements are explored using two simple alternative potentials. We see evidence that in addition to predicting the same observables, common long-range potentials (i.e., explicit pion physics) is required for universality in the potential matrix elements after SRG flow. In agreement with observations made previously for Vlowk evolution, regions of universal potential matrix elements are restricted to where half-on-shell T-matrix equivalence holds.Comment: 13 pages, 16 figure

The Gluon Condensate and Running Coupling of QCD

An expression for the photon condensate in quantum electrodynamics is presented and generalized to deduce a simple relation between the gluon condensate and the running coupling constant of quantum chromodynamics (QCD). Ambiguities in defining the condensates are discussed. The values of the gluon condensate from some Ans\"{a}tze for the running coupling in the literature are compared with the value determined from QCD sum rules.Comment: 10 pages, RevTex, No figure

Effective Field Theory and Nuclear Mean-Field Models

The implications of an effective field theory (EFT) interpretation of nuclear mean-field phenomenology are reviewed.Comment: Contribution to PANIC99 conferenc

Quantum Hadrodynamics: Evolution and Revolution

The underlying philosophy and motivation for quantum hadrodynamics (QHD), namely, relativistic field theories of nuclear phenomena featuring manifest covariance, have evolved over the last quarter century in response to successes, failures, and sharp criticisms. A recent revolution in QHD, based on modern effective field theory and density functional theory perspectives, explains the successes, provides antidotes to the failures, rebuts the criticisms, and focuses the arguments in favor of a covariant representation.Comment: 18 pages, RevTeX; references added and minor editorial changes; submitted to Comments on Modern Physic

Describing Nuclear Matter with Effective Field Theories

An accurate description of nuclear matter starting from free-space nuclear forces has been an elusive goal. The complexity of the system makes approximations inevitable, so the challenge is to find a consistent truncation scheme with controlled errors. The virtues of an effective field theory approach to this problem are discussed.Comment: 4 pages, 2 figures, Contribution to the Proceedings of the 15th Particles and Nuclei International Conference (PANIC 99), Uppsala, Sweden, June 10-16, 1999; minor change to Eq.

Covariant RPA in Effective Hadronic Field Theory

In an effective hadronic theory constructed to describe long-range nuclear physics, the dynamics of the vacuum can be expanded in terms with zero or a finite number of derivatives acting on the fields. Thus vacuum dynamics can always be absorbed in the (infinite number of) counterterm parameters necessarily present in the effective lagrangian. These finite parameters, which at present must be fitted to data, encode the empirical vacuum physics as well as other short-range dynamics into the effective lagrangian; in practice, only a small number of parameters must be fitted. The strength of the effective field theory (EFT) framework is that there is no need to make a concrete picture of the vacuum dynamics, as one does in a renormalizable hadronic theory. At the one-loop level, the most convenient renormalization scheme requires explicit sums over long-range (``valence'') nucleon orbitals only, thus explaining the so-called ``no-sea approximation'' used in successful covariant mean-field theory (MFT) calculations of static ground states. When excited states are studied in the random-phase approximation (RPA), the same EFT scheme dictates the inclusion of both familiar particle-hole pairs and contributions that mix valence and negative-energy single-particle Dirac wave functions. The modern EFT strategy therefore justifies and explains the omission of some explicit contributions from the negative-energy Dirac sea of nucleons, as was done to maintain conservation laws in earlier pragmatic calculations of the nuclear linear response.Comment: 19 pages, 3 figures, REVTeX4, minor correction