Recent studies have shown that concepts of effective field theory such as naturalness can be profitably applied to relativistic mean-field models of nuclei. Here the analysis by Friar, Madland, and Lynn(J.\ Friar, D.\ G.\ Madland, B.\ W.\ Lynn, Phys. Rev. C 53), (1996) 3085. of naturalness in a relativistic point-coupling model is extended. A more general relativistic effective lagrangian, consistent with the symmetries of quantum chromodynamics, is constructed with pion and nucleon degrees of freedom only. Fits to experimental nuclear data support naive dimensional analysis as a useful principle and imply a mean-field expansion analogous to that found for mean-field meson models.(R. J. Furnstahl, B. D. Serot, and H.-B. Tang, Nucl.\ Phys.\ A615) (1997) 441.
[CC.02] Saturation of Nuclear Matter with in-Medium Meson Exchange Interactions
R. Rapp (SUNYSB), R. Machleidt (UIM), J.W. Durso (MHCSH), G.E. Brown (SUNYSB)
We show that nuclear saturation properties can be explained in terms of a microscopic nucleon-nucleon (NN) interaction, where -- in addition to the standard Dirac-Brueckner-Hartree-Fock treatment -- medium effects in the NN meson exchange potentials are accounted for. The correlated two-pion exchange is calculated microscopically with the standard many-body effects on the in-medium pion propagation included. For the vector meson exchanges in both the NN and \pi\pi interaction we assume Brown-Rho Scaling. The empirical saturation density and binding energy can be well reproduced once chiral symmetry constraints on the \pi\pi interaction are incorporated. By contrast, one-boson exchange models with proportionally scaled meson masses fail to saturate.
[CC.03] The Skyrme Energy Functional and Naturalness.
James C. Hackworth, R.~J. Furnstahl (Ohio State University)
Recent studies show that successful relativistic mean-field models of nuclei are consistent with naive dimensional analysis (NDA) and naturalness, as expected in low-energy effective field theories of quantum chromodynamics.(R. J. Furnstahl, B. D. Serot, and H.-B. Tang, Nucl.\ Phys.\ A615) (1997) 441. The nonrelativistic Skyrme energy functional is found to have similar characteristics.(James C. Hackworth and R. J. Furnstahl, Ohio State University preprint OSU-97-232, 1997.) The NDA provides an organizational principle for Skyrme-like models that suggests that current models are truncated prematurely.
[CC.04] Proton-Nucleus Elastic Scattering with Densities from Effective Chiral Lagrangians.
L.~J. Kerr--Kurth, B.~C. Clark, R.~J. Furnstahl, John Rusnak (Ohio State University)
A new class of relativistic hadronic mean-field models, based on chiral effective lagrangians for nuclei, has recently been studied (see preceding talks). Models with both nucleon and meson degrees of freedom(R. J. Furnstahl, B. D. Serot, and H.-B. Tang, Nucl.\ Phys.\ A615) (1997) 441. and with nucleons only (``point-coupling'' model)(J. J. Rusnak and R. J. Furnstahl, Ohio State University preprint OSU--97-030, 1997.) have been developed. Parameters for these models are determined by extensive fits to bulk properties of closed-shell nuclei. In this work, the nuclear densities from these analyses are used as input to relativistic impulse approximation calculations for medium-energy proton scattering from spin-zero targets.
[CC.05] Light-Front Hamiltonian Approach to the Bound-State Problem in Quantum Electrodynamics
Billy D. Jones (TRIUMF)
Why is the study of the Lamb shift in hydrogen, which at the level of detail found in this paper was largely completed by Bethe in 1947, of any real interest today? While completing such a calculation using new techniques may be very interesting for formal and academic reasons, our primary motivation is to lay groundwork for precision bound-state calculations in QCD. The Lamb shift provides an excellent pedagogical tool for illustrating light-front Hamiltonian techniques, which are not widely known; but more importantly it presents three of the central dynamical and computational problems that we must face to make these techniques useful for solving QCD: How does a constituent picture emerge in a gauge field theory? How do bound-state energy scales emerge non-perturbatively? How does rotational symmetry emerge in a non-perturbative light-front calculation?
[CC.06] Dimensionally Regulated Nonrelativistic Field Theories
Martin Savage (University of Washington)
It is argued that in order to maintain consistent velocity power counting in dimensional regularization, NRQCD must include two distinct gluon fields, one corresponding to real gluons and one corresponding to an instantaneous potential. In this scheme power counting is manifest in any gauge, and also holds for non-gauge interactions. Cancellation of infrared divergences in the matching conditions for an external current is shown to require both gluon fields. The matching conditions for an external vector current in NRQCD are calculated to O(g^2v^2). Subtleties which arise in the matching conditions at subleading order are addressed.
[CC.07] The Nuclear Spin-Orbit Force in Chiral Effective Field Theories.
R.J. Furnstahl, John J. Rusnak (Ohio State University), Brian D. Serot (Indiana University)
The concepts and methods of effective field theory (EFT) have recently elucidated the successful nuclear phenomenology of relativistic field theories of hadrons, called quantum hadrodynamics (QHD).(R. J. Furnstahl, B. D. Serot, and H.-B. Tang, Nucl.\ Phys.\ A615) (1997) 441. One of the most compelling features of QHD mean-field phenomenology has been the reproduction of spin-orbit splittings in finite nuclei based only on a fit to equilibrium properties of infinite nuclear matter. This successful result occurs because fitting the velocity dependence of the equivalent central potential also\/ specifies the spin-orbit interaction when one works in a four-component Dirac framework. Does this connection survive in the more general EFT framework? Here we reexamine the nature of the spin-orbit force in chiral effective field theories of nuclei. A particular emphasis is the role of the tensor coupling of the isoscalar vector meson (ømega) to the nucleon (or its analog in point-coupling models(J. J. Rusnak and R. J. Furnstahl, preprint OSU--97-030, 1997.) ).
[CC.08] Mean Field Theories of Collective Motion
Ts. Dankova, G. Rosensteel (Tulane U.)
Nuclear collective models may be defined by irreducible unitary representations of Lie algebras of one-body fermion operators. The microscopic interpretation of an algebraic model is given by a decomposition of Fock space into irreducible subspaces. For example, the adiabatic rotational model is associated with the Lie algebra rot that is spanned by the angular momentum and the quadrupole operator r^2Y^(2)_\mu(Ømega); its decomposition is constructed by a change of variables to collective and intrinsic coordinates.
An alternative approach to the microscopic interpretation derives a mean field theory from the algebraic model. The benefits of this derivation are theoretical simplicity and computational tractability. The states of the mean field theory are a single orbit of the collective motion group in Fock space. The dynamics on the orbit manifold is defined by the natural Poisson structure inherited from Fock space. The mean field theories corresponding to rot(3) and other algebraic models will be discussed.
[CC.09] Nonlinear Collective Motion Theory
G. Rosensteel, J. Troupe (Tulane U.)
The geometrical collective models are based upon the general linear group GL(3,R) and its subgroups SL(3,R) and SO. A serious physical limitation imposed upon these models is that the nuclear velocity field is assumed to be linear. This strong condition is violated unambiguously in some circumstances, e.g., fissioning isotopes with a neck or exotic shapes, and possibly broken strongly for other nuclear states, even at low energy. We report the discovery of nonlinear velocity fields on Euclidean space that close under commutation and construct collective models compatible with such nonlinear velocity fields.
[CC.10] Random matrix theory of effective interactions
Calvin Johnson (Louisiana State University)
Many properties of atomic nuclei are well-described by random matrices. I propose to exploit the quasi-random nature of nuclear Hamiltonians in approximating the effective Hamiltonian for use in the nuclear shell model. Specifically, the first and second moments of the effective interaction are estimated via random matrices and then used to generate a statistical effective interaction which approximates the exact effective interaction. I demonstrate with a simple example.