Session L14: Few-Body Systems

Realistic NN Interactions in Momentum Space - Visual Comparisons

It is challenging to gain physical intuition for non-local operators such as realistic NN interactions. In addition, whenever one truncates a local operator, such as approximating it in a finite matrix representation, one introduces non-locality. We portray contour plots in momentum space of the realistic NN interaction, JISP16 [1], as well as the identity operator and the kinetic energy operator truncated to a finite oscillator basis space. We present results as a function of the cutoff scale and compare with similar plots of the Chiral N3LO interaction [2] processed through the Similarity Renormalization Group (SRG) [3]. We visually search for well-matched features as a function of the renormalization scale as well as through the calculated nuclear properties resulting from these interactions [4]. A selection of these comparisons will be presented. \newline \newline [1] A.M. Shirokov, J. P. Vary, A. I. Mazur and T. A. Weber, Phys. Letts. B {\bf 644}, 33 (2007). \newline [2] D. R. Entem and R. Machleidt, Phys. Rev. C {\bf 68}, 04100R (2003). \newline [3] R. Furnstahl, www.physics.ohio-state.edu/$\sim$ntg/srg/ \newline [4] S. K. Bogner, R. J. Furnstahl, P. Maris, R. J. Perry, A. Schwenk, J. P. Vary, arXiv:0708.3754, Nuc. Phys. A (to appear).   

Measurement of the Cross Section and Analyzing Powers for $\vec{\rm d}$+p Elastic Scattering at 180 MeV

We have measured cross sections and analyzing powers for various $\vec{\rm d}$+d reaction channels, including $\vec{\rm d}$+d elastic and $\vec{\rm d}$+d$\to$p+t at 130 MeV and 180~MeV, with the hope of providing a testing ground for new 4-body theoretical predictions. These data were collected at the KVI cyclotron (Groningen) using the Big Bite spectrometer and a polarized deuteron beam. In addition to the $\vec{\rm d}$+d channels, we also measured the cross section and analyzing powers ($A_y$ and $A_{yy}$) for $\vec{\rm d}$+p elastic scattering at the same energies for comparison with existing data and with 3-body calculations (with and without three nucleon forces). We report here our results for the $\vec{\rm d}$+p elastic data at 180 MeV. The analysis procedure will be reviewed and several preliminary results will be shown.   

Cluster separability and currents in the Poincar\'e invarant three-nucleon problem

We examine the quantitative implication of the requirement of cluster separability in Poincar\'e-invariant formulations of the quantum mechanical three-body problem. One can formulate the problem using two-body interactions in a representation that satisfies Poincar\'e invariance, but which violates cluster separability. An additional non-trivial unitary transformation restores cluster properties. This unitary transformation is needed for a consistent computation of matrix elements of currents that have cluster expansions in systems of three particles or more, as well as bound-state properties of four particles or more. We exhibit the nature and size of these effects in a model form factor of a three-body system consisting of a nucleon in the presence of a spectator deuteron by comparing the calculation of current matrix elements with and without these unitary transformations.   

A realistic three-nucleon interaction in the $^4$He scattering system

Using the framework of the refined resonating group (RRGM) variational technique we investigate the $J^\pi =0^+$ partial wave of the $^4$He scattering system for an adjusted version of the realistic Illinois potential model (IL) which was devised as an extension of the Urbana IX (UIX) model. We compare the results to an R-matrix analysis and an RRGM calculation for the UIX potential. The binding energy, the S-, P-, D-state probabilities, the average charge- and mass radii of the $^4$He bound state are given as well. We find all results consistent with the UIX ones and note only a difference in the t-p and $^3$He-n phase shifts in the region of the $T=0$ resonance.   

Theoretical Fully Differential Cross Sections for Four-Body Processes

Atomic collisions present a valuable opportunity to study the few body problem. Advances on the theoretical side now allow for an essentially exact numerical calculation of one of the simplest the few-body problems - the three-body problem. However, study of the four-body problem is still in its infancy, and the agreement between experiment and theory for kinematically complete experiments is far from satisfactory. The simplest four-body problem is a charged particle collision with helium in which both atomic electrons change state. Two theoretical models will be discussed for several possible outcomes of this type of collision. The first Born approximation (FBA) treats the projectile as a plane wave, and ignores the post collision Coulomb interaction between the two final state continuum electrons. The more sophisticated four-body distorted wave (4DW) model treats all continuum particles as distorted waves and explicitly includes the post collision Coulomb interaction between the two outgoing electrons. Fully differential cross sections calculated using the FBA and 4DW models will be compared to absolute experimental results, as well as other theories.   

Solving Schrodinger Equation in Mixed Representation

Solving the Schrodinger equation with relativistic kinematics is easier in momentum space since the momentum operators under the radical sign simply become numbers. But power law potentials become singular in momentum space and subtraction procedures become necessary. By using the coordinate representation for the potential part and momentum representation for the kinetic energy part, one can solve these problems, but the resulting equation has an oscillating integral with a spherical Bessel function. We expand the wave function in a complete set of basis functions which has an exact Fourier transform and study the convergence of the solution by using different integration methods.   

Physical Properties of Human Whole Salivary Mucin:A Dynamic Light Scattering Study

Human salivary mucin, a primary mucous membrane coating glycoprotein forms the first line of defense against adverse environments, attributed to the complex formation between mucin subunits and non mucin species. Aim of the study was to emphasize the effect of pH, denaturants (guanidinum hydrochloride, urea) and detergents (CHAPS, TRITON X -100, SDS on human whole salivary mucin. Hydrodynamic size distribution was measured using DLS. It was observed that aggregation was due to increase in hydrophobic interactions, believed to be accomplished by unfolding of the protein core. Whereas, the detergents which solubilize the proteins by decreasing hydrophobicity lead to disaggregation of mucin into smaller fragments. Mucin subjected to tobacco extract and upon subsequent addition of nicotine was found to have a disaggregating effect on it, suggesting nicotine may be one of the factors responsible for the disaggregating effect of tobacco on mucin, an important carcinogenetic mechanism.