Session H15: Nuclear Theory

Operator evolution for {\em ab initio} electric dipole transitions of $^4$He

A goal of nuclear theory is to make quantitative predictions of low-energy nuclear observables starting from accurate microscopicinternucleon forces. Modern effective interaction theory, applying unitary transformations to soften the nuclear Hamiltonian and hence accelerate the convergence of {\em ab initio} calculations as a function of the model space size, is a major element of such an effort. The consistent simultaneous transformation of external operators, however, has been overlooked in applications of the theory, particularly for non-scalar transitions. We study the evolution of the electric dipole operator in the framework of the similarity-renormalization group method and apply the renormalized matrix elements to the calculation of the $^4$He total photo absorption cross section and electric dipole polarizability. All observables are calculated within the {\em ab initio} no-core shell model. We find that, although seemingly small, the effects of induced operators on the photo absorption cross section are comparable in magnitude to the correction produced by including the three-nucleon force and cannot be neglected.   

Ab Initio Neutron Drops with Chiral Hamiltonians

Ab initio calculations for neutron drops are of interest for insights into neutron-rich nuclei and neutron star matter, and for examining the neutron-only sector of nucleon-nucleon and 3-nucleon interactions. I present ab initio results calculated using the no-core shell model with 2- and 3-body chiral Hamiltonians for neutron drops up to 20 neutrons confined in a 10 MeV harmonic trap. I discuss ground state energies, internal energies, radii, and evidence for pairing. In addition, excitation energies can be used to investigate the spin-orbit splittings in the $p$-shell and $sd$-shell. Prior Green's Function Monte Carlo calculations using the Argonne $v^\prime_8$ potential with added 3-nucleon forces serve as a comparison.   

Yang-Mills generalization of the geometrical collective model

The geometrical or Bohr-Mottelson model is generalized and recast as a Yang-Mills theory. The gauge symmetry determines conservation of Kelvin circulation. The circulation commutes with the Hamiltonian when it is the sum of the kinetic energy and a potential that depends only on deformation. The conventional Bohr-Mottelson model is the special case of circulation zero, and wave functions are complex-valued. In the generalization, any quantized value of the circulation is allowed, and the wave functions are vector-valued. The Yang-Mills formulation introduces a new coupling between the geometrical and intrinsic degrees of freedom. The coupling appears in the covariant derivative term of the collective kinetic energy. This kind of coupling is sometimes called ``magnetic" because of the analogy with electrodynamics.   

Spinors and Polarization Vectors Interpolated Between Instant Form and Front Form

As an effort to understand how the familiar instant form dynamics (IFD) transforms to light-front dynamics (LFD), we interpolate spinors and polarization vectors between these two forms of relativistic Hamiltonian dynamics by introducing an interpolation angle. We report our derivation of the helicity spinors for spin-1/2 fermion and the polarization vectors for photon that interpolate between IFD and LFD and the application of our results to the lowest-order QED scattering amplitudes. The spin orientation of the interpolating helicity spinors is derived and the Melosh transformation is generalized to any interpolation angle. We also find the Coulomb gauge in IFD and the light-front gauge in LFD are naturally linked by the unified general physical gauge that interpolates between these two forms of dynamics. The calculation of the lowest-order scattering processes for an arbitrary interpolation angle shows a universal J-shaped correlation independent of the specific scattering kinematics.   

Self Organizing Maps for use in Deep Inelastic Scattering

Self Organizing Maps are a type of artificial neural network that has been proven to be particularly useful in solving complex problems in neural biology, engineering, robotics and physics. We are attempting to use the Self Organizing Map to solve problems and probe phenomenological patterns in subatomic physics, specifically in Deep Inelastic Scattering (DIS). In DIS there is a cross section in electron hadron scattering that is dependent on the momentum fraction x of the partons in the hadron and the momentum transfer of the virtual photon exchanged. There is a soft cross part of this cross section that currently can only be found through experimentation; this soft part is comprised of Structure Functions which in turn are comprised of the Parton Distribution Functions (PDFs). We aim to use the Self Organizing Process, or SOP, to take theoretical models of these PDFs and fit it to the previous, known data. The SOP will also be used to probe the behavior of the PDFs in particular at large x values, in order to observe how they congregate. The ability of the SOPto take multidimensional data and convert it into two dimensional output is anticipated to be particularly useful in achieving this aim.   

Algebraic Apect of Helicities in Hadron Physics

We examined the relation of polarization vectors and spinors of $ (1,0)\oplus(0,1)$ representation of Lorentz group in Clifford algebra $ Cl_{1,3}$, their relation with standard algebra, and properties of these spinors. $ Cl_{1,3}$ consists of different grades:e.g. the first and the second grades represent $ (1/2,1/2)$ and $ (1,0)\oplus(0,1)$ representation of spin groups respectively with 4 and 6 components. However, these Clifford numbers are not the helicity eigenstates and thus we transform them into combinations of helicity eigenstates by expressing them as spherical harmonics. We relate the spin-one polarization vectors and $(1,0)\oplus(0,1) $ spinors under one simple transformation with the spin operators. We also link our work with Winnberg's work [1] of a superfield of a spinors of Clifford algebra by giving a physical meaning to Grassmann variables and discuss how Grassman algebra is linked with Clifford algebra. \\[4pt] [1] J.O.Winnberg, J. of Math Phys Vol 18, 625 (1977).   

Decoding the nuclear genome using nuclear binding and fusion energies

In several publications the author has presented the theory that protons and neutrons and other baryons are the chromo-magnetic monopoles of Yang-Mills gauge theory and used that to deduce the up and down current quark masses from the tightly-known Q$=$0 empirical electron mass and the neutron minus proton mass difference with commensurately high precision. This is then used as a springboard to closely fit a wide range of empirical nuclear binding and fusion energy data and to obtain the proton and neutron masses themselves within all experimental errors. This presentation will systematically pull all of this together and a) establishes that this way of defining current quark masses constitutes a valid measurement scheme, b) lays out the empirical support for this theory via observed nuclear binding and fusion energies as well as the proton and neutron masses themselves, c) solidifies the interface used to connect the theory to these empirical results and uncovers a mixing between the up and down current quark masses, and d) presents clearly how and why the underlying theory is very conservative, being no more and no less than a deductive mathematical synthesis of Maxwell's classical theory with both the electric and magnetic field equations merged into one, Yang-Mills gauge theory, Dirac fermion theory, the Fermi-Dirac-Pauli Exclusion Principle, and to get from classical chromodynamics to QCD, Feynman path integration.