Reworking the Tucson-Melbourne Three-Nucleon Potential

We introduce new values of the strength constants (i.e., $a$, $b$, $c$, and $d$ coefficients) of the Tucson-Melbourne (TM) 2$\pi$ exchange three nucleon potential. The new values come from contemporary dispersion relation analyses of meson factory $\pi$N scattering data. We make variational Monte Carlo calculations of the triton with the original and updated three-body forces to study the effects of this update. We remove a short-range -- $\pi$-range part of the potential due to the $c$ coefficient and discuss the effect on the triton binding energy.Comment: 12 pages, to appear in Few-Body System

Benchmark calculations for polarization observables in 3N scattering

High precision benchmark calculations for phase-shifts and mixing parameters as well as observables in elastic neutron-deuteron scattering below the deuteron breakup threshold are presented using a realistic nucleon-nucleon potential. Two totally different methods, one using a variational principle in configuration space and the other solving the Faddeev equations in momentum space are used and compared to each other. The agreement achieved in phase-shifts and mixing parameters as well as in the polarization observables is excellent. The extreme sensitivity of the vector analyzing power Ay to small changes of the phase shifts and mixing parameters is pointed out.Comment: 22 pages, 5 postscript figure

Momentum and Coordinate Space Three-nucleon Potentials

In this paper we give explicit formulae in momentum and coordinate space for the three-nucleon potentials due to $\rho$ and $\pi$ meson exchange, derived from off-mass-shell meson-nucleon scattering amplitudes which are constrained by the symmetries of QCD and by the experimental data. Those potentials have already been applied to nuclear matter calculations. Here we display additional terms which appear to be the most important for nuclear structure. The potentials are decomposed in a way that separates the contributions of different physical mechanisms involved in the meson-nucleon amplitudes. The same type of decomposition is presented for the $\pi - \pi$ TM force: the $\Delta$, the chiral symmetry breaking and the nucleon pair terms are isolated.Comment: LATEX, 33 pages, 3 figures (available as postscript files upon request

Modern nuclear force predictions for the neutron-deuteron scattering lengths

The nd doublet and quartet scattering lengths have been calculated based on the modern NN and 3N interactions. We also studied the effect of the electromagnetic interactions in the form introduced in AV18. Switching them off for the various nuclear force models leads to shifts of up to +0.04 fm for doublet scattering length, which is significant for present day standards. The electromagnetic effects have also a noticeable effect on quartet scattering length, which otherwise is extremely stable under the exchange of the nuclear forces. For the current nuclear force models there is a strong scatter of the 3H binding energy and the doublet scattering length values around an averaged straight line (Phillips line). This allows to use doublet scattering length and the 3H binding energy as independent low energy observables.Comment: 16 pages, 1 table, 4 ps figure

Triton calculations with π\pi and ρ\rho exchange three-nucleon forces

The Faddeev equations are solved in momentum space for the trinucleon bound state with the new Tucson-Melbourne $\pi$ and $\rho$ exchange three-nucleon potentials. The three-nucleon potentials are combined with a variety of realistic two-nucleon potentials. The dependence of the triton binding energy on the $\pi NN$ cut-off parameter in the three-nucleon potentials is studied and found to be reduced compared to the case with pure $\pi$ exchange. The $\rho$ exchange parts of the three-nucleon potential yield an overall repulsive effect. When the recommended parameters are employed, the calculated triton binding energy turns out to be very close to its experimental value. Expectation values of various components of the three-nucleon potential are given to illustrate their significance for binding.Comment: 17 pages Revtex 3.0, 4 figures. Accepted for publication in Phys. Rev.

Definition of valid proteomic biomarkers: a bayesian solution

Clinical proteomics is suffering from high hopes generated by reports on apparent biomarkers, most of which could not be later substantiated via validation. This has brought into focus the need for improved methods of finding a panel of clearly defined biomarkers. To examine this problem, urinary proteome data was collected from healthy adult males and females, and analysed to find biomarkers that differentiated between genders. We believe that models that incorporate sparsity in terms of variables are desirable for biomarker selection, as proteomics data typically contains a huge number of variables (peptides) and few samples making the selection process potentially unstable. This suggests the application of a two-level hierarchical Bayesian probit regression model for variable selection which assumes a prior that favours sparseness. The classification performance of this method is shown to improve that of the Probabilistic K-Nearest Neighbour model

Analysis of three-nucleon forces effects in the A=3A=3 system

Using modern nucleon-nucleon interactions in the description of the $A=3,4$ nuclear systems the $\chi^2$ per datum results to be much bigger than one. In particular it is not possible to reproduce the three- and four-nucleon binding energies and the $n-d$ scattering length simultaneously. This is one manifestation of the necessity of including a three-nucleon force in the nuclear Hamiltonian. In this paper we perform an analysis of some, widely used, three-nucleon force models. We analyze their capability to describe the aforementioned quantities and, to improve their description, we propose modifications in the parametrization of the models. The effects of these new parametrization are studied in some polarization observables at low energies.Comment: 10 pages, to be published in Few-Body Systems. Presented at the workshop on "Relativistic Description of Two- and Three-body Systems in Nuclear Physics" ECT* Trento, 19 - 23 October 200

A New Treatment of 2N and 3N Bound States in Three Dimensions

The direct treatment of the Faddeev equation for the three-boson system in 3 dimensions is generalized to nucleons. The one Faddeev equation for identical bosons is replaced by a strictly finite set of coupled equations for scalar functions which depend only on 3 variables. The spin-momentum dependence occurring as scalar products in 2N and 3N forces accompanied by scalar functions is supplemented by a corresponding expansion of the Faddeev amplitudes. After removing the spin degrees of freedom by suitable operations only scalar expressions depending on momenta remain. The corresponding steps are performed for the deuteron leading to two coupled equations.Comment: 19 page

Three-Nucleon Force Effects in Nucleon Induced Deuteron Breakup: Predictions of Current Models (I)

An extensive study of three-nucleon force effects in the entire phase space of the nucleon-deuteron breakup process, for energies from above the deuteron breakup threshold up to 200 MeV, has been performed. 3N Faddeev equations have been solved rigorously using the modern high precision nucleon-nucleon potentials AV18, CD Bonn, Nijm I, II and Nijm 93, and also adding 3N forces. We compare predictions for cross sections and various polarization observables when NN forces are used alone or when the two pion-exchange Tucson-Melbourne 3NF was combined with each of them. In addition AV18 was combined with the Urbana IX 3NF and CD Bonn with the TM' 3NF, which is a modified version of the TM 3NF, more consistent with chiral symmetry. Large but generally model dependent 3NF effects have been found in certain breakup configurations, especially at the higher energies, both for cross sections and spin observables. These results demonstrate the usefulness of the kinematically complete breakup reaction in testing the proper structure of 3N forces.Comment: 42 pages, 20 ps figures, 2 gif figure

Three-Nucleon Photodisintegration of 3He

The three-nucleon photodisintegration of 3He has been calculated in the whole phase space using consistent Faddeev equations for the three-nucleon bound and scattering states. Modern nucleon-nucleon and 3N forces have been applied as well as different approaches to nuclear currents. Phase space regions are localized where 3N force effects are especially large. In addition semi-exclusive cross sections for 3He(gamma,N) have been predicted which carry interesting peak structures. Finally some data for the exclusive 3N breakup process of 3He and its total breakup cross section have been compared to theory.Comment: 28 pages, 6 png figures, 11 ps figures, modified version with changed figures, conclusions unchanged, to appear in Phys.Rev.