A Spin-Isospin Dependent 3N Scattering Formalism in a 3D Faddeev Scheme

We have introduced a spin-isospin dependent three-dimensional approach for formulation of the three-nucleon scattering. Faddeev equation is expressed in terms of vector Jacobi momenta and spin-isospin quantum numbers of each nucleon. Our formalism is based on connecting the transition amplitude $T$ to momentum-helicity representations of the two-body $t$-matrix and the deuteron wave function. Finally the expressions for nucleon-deuteron elastic scattering and full breakup process amplitudes are presented.Comment: 17 page

6^6Li in a Three-Body Model with Realistic Forces: Separable vs. Non-separable Approach

{\bf Background:} Deuteron induced reactions are widely used to probe nuclear structure and astrophysical information. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques. {\bf Purpose:} Faddeev equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. However, it needs to be demonstrated that their solution based on separable interactions agrees exactly with solutions based on non-separable forces. {\bf Results:} The ground state of $^6$Li is calculated via momentum space Faddeev equations using the CD-Bonn neutron-proton force and a Woods-Saxon type neutron(proton)-$^4$He force. For the latter the Pauli-forbidden $S$-wave bound state is projected out. This result is compared to a calculation in which the interactions in the two-body subsystems are represented by separable interactions derived in the Ernst-Shakin-Thaler framework. {\bf Conclusions:} We find that calculations based on the separable representation of the interactions and the original interactions give results that agree to four significant figures for the binding energy, provided an off-shell extension of the EST representation is employed in both subsystems. The momentum distributions computed in both approaches also fully agree with each other

Modern NN Force Predictions for the Total ND Cross Section up to 300 MeV

For several modern nucleon-nucleon potentials state-of-the-art Faddeev calculations are carried out for the $nd$ total cross section between 10 and 300 MeV projectile energy and compared to new high precision measurements. The agreement between theory and data is rather good, with exception at the higher energies where a 10% discrepancy builds up. In addition the convergence of the multiple scattering series incorporated in the Faddeev scheme is studied numerically with the result, that rescattering corrections remain important. Based on this multiple scattering series the high energy limit of the total $nd$ cross section is also investigated analytically. In contrast to the naive expectation that the total $nd$ cross section is the sum of the $np$ and $nn$ total cross sections we find additional effects resulting from the rescattering processes, which have different signs and different behavior as function of the energy. A shadowing effect in the high energy limit only occurs for energies higher than 300 MeV. The expressions in the high energy limit have qualitatively a similar behavior as the exactly calculated expressions, but can be expected to be valid quantitatively only at much higher energies.Comment: 22 pages, 5 figure

The Operator form of 3H (3He) and its Spin Structure

An operator form of the 3N bound state is proposed. It consists of eight operators formed out of scalar products in relative momentum and spin vectors, which are applied on a pure 3N spin 1/2 state. Each of the operators is associated with a scalar function depending only on the magnitudes of the two relative momenta and the angle between them. The connection between the standard partial wave decomposition of the 3N bound state and the operator form is established, and the decomposition of these scalar function in terms of partial wave components and analytically known auxiliary functions is given. That newly established operator form of the 3N bound state exhibits the dominant angular and spin dependence analytically. The scalar functions are tabulated and can be downloaded. As an application the spin dependent nucleon momentum distribution in a polarized 3N bound state is calculated to illustrate the use of the new form of the 3N bound state.Comment: 21 pages, 1 table, 8 figures, revtex

Ab initio Translationally Invariant Nonlocal One-body Densities from No-core Shell-model Theory

[Background:] It is well known that effective nuclear interactions are in general nonlocal. Thus if nuclear densities obtained from {\it ab initio} no-core-shell-model (NCSM) calculations are to be used in reaction calculations, translationally invariant nonlocal densities must be available. [Purpose:] Though it is standard to extract translationally invariant one-body local densities from NCSM calculations to calculate local nuclear observables like radii and transition amplitudes, the corresponding nonlocal one-body densities have not been considered so far. A major reason for this is that the procedure for removing the center-of-mass component from NCSM wavefunctions up to now has only been developed for local densities. [Results:] A formulation for removing center-of-mass contributions from nonlocal one-body densities obtained from NCSM and symmetry-adapted NCSM (SA-NCSM) calculations is derived, and applied to the ground state densities of $^4$He, $^6$Li, $^{12}$C, and $^{16}$O. The nonlocality is studied as a function of angular momentum components in momentum as well as coordinate space [Conclusions:] We find that the nonlocality for the ground state densities of the nuclei under consideration increases as a function of the angular momentum. The relative magnitude of those contributions decreases with increasing angular momentum. In general, the nonlocal structure of the one-body density matrices we studied is given by the shell structure of the nucleus, and can not be described with simple functional forms.Comment: 13 pages, 11 Figure

Nucleon-Nucleon Scattering in a Three Dimensional Approach

The nucleon-nucleon (NN) t-matrix is calculated directly as function of two vector momenta for different realistic NN potentials. To facilitate this a formalism is developed for solving the two-nucleon Lippmann-Schwinger equation in momentum space without employing a partial wave decomposition. The total spin is treated in a helicity representation. Two different realistic NN interactions, one defined in momentum space and one in coordinate space, are presented in a form suited for this formulation. The angular and momentum dependence of the full amplitude is studied and displayed. A partial wave decomposition of the full amplitude it carried out to compare the presented results with the well known phase shifts provided by those interactions.Comment: 26 pages plus 10 jpg figure