Session X15: Nuclear Theory

Common signatures of Coulomb fragmentation of excited realistic nuclei and phase transitions in hypothetical confined matter

The phenomenon of binary and multiple Coulomb fragmentation of realistic nuclei is compared to the time-asymptotic fragmentation of nuclear matter confined in a hypothetical freezeout volume. It is shown within the framework of schematic microcanonical nuclear thermodynamics that both types of processes may be described by similar mathematical equations and both may exhibit signatures of second-order phase transitions at onsets of different fragmentation channels. In the present context, phase transitions are identified as changes in the most likely fragmentation channel/state as the excitation energy of the system increases. They occur as the conditional entropy functions corresponding to different fragmentation channels/states cross at characteristic excitation energies. The critical role of the diffuse surface domain of finite nuclei is discussed, along with the importance of a proper approximation of the microcanonical ensemble involved.   

Properties of Unitary Fermi Gas from the Epsilon Expansion

An analytical technique similar to the Epsilon expansion in the theory of critical phenomena has been recently proposed for dilute Fermi gas with two body interaction characterized by infinite scattering length and zero effective range called Unitary Fermi Gas (Nishida and Son, Phys.Rev.Lett.97:050403, 2006). I will describe some recent results: 1. effective Lagrangian (Landau-Ginzburg-like functional) for Unitary Fermi Gas and its applications (superfluid vortex structure, surface tension of the normal/superfluid phase interface in the polarized (imbalanced) gas); 2. low energy density-density correlation function and the dynamic structure factor.   

Quasiparticle Density Functional Theory with Dispersive Optical Model Self Energies

The quasiparticle extension of Kohn-Sham Density Functional Theory proposed by Van Neck et al.\footnote{D. Van Neck, et al., Phys. Rev. A 74, 042501 (2006)} and further applied to atoms\footnote{S. Verdonck, et al., Phys. Rev. A 74, 062503 (2006)} is promising for nuclear calculations, because overlap functions and spectroscopic factors are in principle calculable. Starting with spherical Skyrme-Hartree-Fock-Bogolyubov calculations,\footnote{K. Bennaceur, J. Dobaczewski, Comput. Phys. Comm. 168 (2005) 96-122} and self energies provided by Dispersive Optical Model calculations,\footnote{R. J. Charity, et al., Phys. Rev. C 76, 044314 (2007) and R. J. Charity, et al., Phys. Rev. Lett. 97, 162503 (2006)} new quasiparticle functionals are explored for nuclei using this method.   

Generalized Auxiliary Field Monte Carlo method:a new efficient variational method for CBF theory

A principle goal in nuclear theory is the development of computational methods to calculate hadronic systems properties. Correlated basis function theory, CBF, is believed to offer an accurate wave-function. Two approaches that have made important contributions are the diagrammatic viewpoint that try to compute in a self consistent way to all orders the dominant leading order diagrams such as the Fermi hypernetted Chain/ Single Operator Chain and Coupled Cluster theory, and, on the other hand, there are methods like Green function Monte Carlo, that aim to compute expectations of observables by stochastically evaluating the integrals via Monte Carlo method. Each of these approaches suffer important limitations that make further advances very difficult. To circumvent the principle obstacle, being that these correlations are state dependent and thus making any evaluation of such complex wave-function impractical for large systems, a new method designated as the Generalized Auxiliary Fields Variational Monte Carlo, GAFVMC method has been successively implemented for the stochastic sampling of the CBF-type wave-functions with $v_6$ type operators. Some encouraging results will be given.   

Odd-even Mass Nuclei in Nuclear Energy Density Functional theory

Energy Density Functional (EDF) theory provides a global and consistent framework to describe nuclear structure. Almost all of the current parametrizations of the EDF were obtained by starting from an effective two-body interaction, e.g. of the Skyrme type, and only experimental observables relative to even nuclei were taken into account in the fit of the parameters of the interaction. This implies that, although the EDF is constructed out of both time-even and time-odd fields, the latter have not been really probed during the fitting procedure. A consequence of this bias is that spectroscopic properties of atomic nuclei are rather poorly described in self-consistent EDF approaches. Efficient EDF solvers together with super-computing facilities allow us to change this strategy and probe the time-odd fields in a more systematic way. The talk will briefly review the formalism of the energy density functional theory and present the first results of systematic self-consistent HFB blocking calculations in the rare-earth region. Effects coming from the interaction, from the presence of tensor terms and of time-odd fields will be presented and the consequence on the fit of new generations of functionals discussed.   

Meson Spectroscopy in Light-Front Quark Model

Although a theory of the strong force, Quantum Chromodynamics (QCD), has existed for many years, it has not been possible to solve it exactly. As such, models based on the essential characteristics of the strong force, which have been gleaned from approximate solutions of QCD, have been very useful in understanding the properties of bound states of quarks. The light-front quark model (LFQM) has generally been successful in predicting the properties of two-body (quark-antiquark) bound states called mesons. While experimental data on mesons with certain quantum numbers have matched well with the model predictions, the $^3P_0$ (scalar) mesons have not. In fact, more scalar states have been observed experimentally than should exist if they were all two-body bound states. It is suspected that other ``exotic'' forms of matter, which have been predicted by QCD but have never been directly confirmed in experiments, are complicating the scalar meson spectrum. These exotic states have the same quantum numbers as the scalar mesons, and are thus allowed to mix with them. The result is that the states observed experimentally are actually quantum-mechanical superpositions of the scalar mesons and these other exotic forms of matter, thus making them difficult to clearly identify. We will discuss how the LFQM is used to predict the properties of mesons in general, as well as how it can be used to shed light on the more complicated structure of the scalar states.   

A study of No-pair two-body equation with non-central potentials.

The No-pair two-body equation was proposed by Sucher$^{1}$ some time ago but calculations have been done for central potentials only. We study the no-pair two-body equation with both central and tensor interactions and preliminary numerical results will be presented. (1) G. Hardekopf and J. Sucher, Phys. Rev. A. 30, (1984)703   

Hadron Confinement Theory

A theory is presented based on QCD and Dirac equation solutions with well-defined energy, momentum, and angular momentum for quarks and gluons. Dynamic chiral symmetry breaking occurs when massless quarks and gluons have identical velocities resulting in color electric fields being cancelled by countervailing color magnetic fields. Massless quarks are entrapped in magnetic containment bottles, while massless gluons are entrapped in quantized bundles of color magnetic flux. Each entwined massless quark-gluon combination behaves as a composite particle that acquires mass as inertial magnetic forces reduce its velocity below the speed of light. The quark-gluon composite particles are identified with the point-like quarks observed in collider experiments. Each quark flavor is associated with one of the degenerate ground states associated with the quantized color magnetic flux bundles and their associated winding numbers. The \textit{up}, \textit{charm} and \textit{top} quark masses obey a specific scaling law as do the \textit{down}, \textit{strange} and \textit{bottom} quarks. The six quark flavors obey a single scaling law for$\beta $, the speed of each flavor relative to speed of light. Calculations of the hadron mass spectra are presented. The theory provides an explanation for the proton spin crisis.   

Octet Baryon Magnetic Moments from QCD Sum Rules

We report results on the magnetic moments of octet baryons using the method of QCD sum rules. Three sum rules from three independent tensor structures are derived for each member in the octet ($p$, $n$, $\Lambda$, $\Sigma^+$, $\Sigma^-$, $\Sigma^-$, $\Xi^0$, and $\Xi^-$) using generalized interpolating fields. They are analyzed in conjunction with the corresponding mass sum rules. The convergence of each sum rule is studied, taking into account transitions in the intermediate states. Individual u, d and s quark contributions to the magnetic moment are also isolated. The results are compared to previous calculations and experiment.