Solving the relativistic inverse scattering problem with allowance for inelasticity effects on the basis of <Emphasis Type="Italic">N/D</Emphasis> equations and application of the resulting solution to an analysis of nucleon-nucleon interaction

A manifestly Poincaré-invariant approach to solving the inverse scattering problem is developed with allowance for inelasticity effects. The equations of the N/D method are used as dynamical equations in this approach. Two versions of the approach are considered. In the first version (method A), the required equations are constructed on the basis of the maximal-analyticity principle, which constitutes the basis of dynamical S-matrix theory. In formulating the second version of equations (method B), it is assumed that a partial-wave scattering amplitude may develop dynamical singularities that violate the requirement of maximal analyticity. The dynamics of interaction components that violate maximal analyticity is described within the model of a nonlocal separable potential. The method is used to analyze nucleon-nucleon interaction in the ¹S₀ and ³S₁ states. The results obtained by solving the inverse scattering problem for potential functions are compared with the predictions of the one-boson-exchange model.     

Relativistic optical model on the basis of the Moscow potential and lower phase shifts for nucleon-nucleon scattering at laboratory energies of up to 3 GeV

Data of a partial-wave analysis of nucleon-nucleon scattering at energies of up to E _lab = 3 GeV (lower partial waves) and the properties of the deuteron are described within the relativistic optical model based on deep attractive quasipotentials involving forbidden states (as exemplified by the Moscow potential). Partial-wave potentials are derived by the inverse-scattering-problem method based on the Marchenko equation by using present-day data from the partial-wave analysis of nucleon-nucleon scattering at energies of up to 3 GeV. Channel coupling is taken into account. The imaginary parts of the potentials are deduced from the phase equation of the variable-phase approach. The general situation around the manifestation of quark effects in nucleon-nucleon interaction is discussed.     

On The Contribution of the P and D Partial-Wave States to the Binding Energy of the Triton in the Bethe-Salpeter-Faddeev Approach

The influence of the partial-wave states with nonzero orbital moment of the nucleon pair on the binding energy of the triton T(nnp) in the relativistic case is considered. The relativistic generalization of the Faddeev equation in the Bethe-Salpeter formalism is applied. Two-nucleon t matrix is obtained from the Bethe-Salpeter equation with separable kernel of nucleon-nucleon interaction of the rank one. The kernel form factors are the relativistic type of the Yamaguchi functions. The following two-nucleon partial-wave states are considered: ¹S₀, ³S₁, ³D₁, ³P₀, ¹P₁, ³P₁. The system of the integral equations are solved by using the iteration method. The binding energy of the triton and three-nucleon amplitudes are found. The contribution of the P and D states to the binding energy of triton is given.

     

The Rank-One Separable Interaction Kernel for Nucleons with Scalar Propagator

In the paper the covariant kernel of the nucleon-nucleon interaction of particles with scalar propagators is analyzed. The Bethe–Salpeter equation for the T matrix is considered in the rank-one separable kernel. The parameters of the kernel for the specific partial-wave channels explicitly connect with the observables low energy scattering parameters and phase shifts, deuteron binding energy. Covariant separable kernels for the partial-wave channels with total angular momentum J = 0 (¹S₀, ³P₀) and J =1 (³S₁ ? ³D₁, ¹P₁, ³P₁) are constructed.     

Effect of rescattering on polarization observables of the reaction γd → ppπ in the delta-resonance region

The effect of pion-nucleon and nucleon-nucleon rescatterings on polarization observables of the reaction γd → ppπ^? are calculated in the delta-isobar region. Pion-nucleon and nucleon-nucleon rescatterings are considered on the basis of a diagrammatic approach. Lorentz invariant expressions are used for the operators of photoproduction and of pion scattering on a free nucleon. A unitarization procedure in the K-matrix approximation is used for resonance partial-wave amplitudes. It is shown that, in the delta-resonance region, rescattering has a sizable effect on polarization observables of the reaction γd → ppπ^? at high momenta of final protons.     

Three-body scattering in configuration space

The asymptotic forms of the wavefunction and Faddeev components in configuration space are shown to determine uniquely the solutions of the Schrödinger or Faddeev differential equations for 2 → (2, 3) and 3 → (2, 3) processes. An antisymmetrized form of the Faddeev differential equation for three equivalent fermions is given and its angular analysis is performed in the general case of local potentials with tensor interaction for neutron-deuteron scattering. We describe a numerical method for solving the corresponding boundary value problem and apply it to scattering and break-up at E_n^1ab = 14.4 MeV in the doublet S state for the four local potentials of Malfliet and Tjon, Reid, de Tourreil and Sprung, and de Tourreil, Rouben and Sprung. For the three realistic potentials, elastic scattering amplitudes differ by 5%, and amplitudes for break-up in the two-neutron state ¹S₀ differ by less than 4%.     

The asymptoticS-state amplitude of the deuteron wave function

Bounds on the asymptoticS-state amplitudeA _S of the deuteron wave function are calculated as a function of assumed impulse approximation values for the quadrupole moment. Alternatively, for a given value ofA _S, a bound is obtained on the minimum contribution to the experimental value ofQ _D from meson-exchange currents, relativistic effects and isobar contributions. The extraction ofA _S from low energy elastic nucleon-nucleon scattering data is discussed in detail.     

On the correlation between the deuteron quadrupole moment,the deuteron asymptotic <Emphasis Type="Italic">D/S</Emphasis> ratio,and the <Emphasis Type="Italic">S</Emphasis>-wave normalization constant

The correlation between the deuteron quadrupole moment Q, the deuteron asymptotic D/S ratio η, and the deuteron asymptotic normalization constant AS is studied. For local nucleon-nucleon potentials, it was found that the quantities Q/η and A _S ² are related by a linear equation. Owing to this, the deuteron quadrupole moment Q can be determined from known values of AS and η with an absolute precision of about 0.0003 fm². The inclusion of the correction for meson-exchange currents and the use of the experimental neutron-proton phase shifts from the GWU partial-wave analysis made it possible to estimate the deuteron quadrupole moment at Q = 0.2852 fm², which is in good agreement with experimental data.     

Pseudo resonance behavior in nucleon-nucleon scattering

In a relativistic unitary model for intermediate energy nucleon-nucleon scattering there are strong indications that the resonance-like looping behavior of the ³F₃ and ¹D₂ amplitudes is not due to a resonance pole but to the coupling with the inelastic NNπ channel. In its most simple form the looping behavior is caused by a square root branch cut.     

Effective-range function for doublet nd scattering from an analysis of modern data

The parameters of the generalized effective-range function K(k ²) having a pole are found by using the results that were obtained by calculating the S-wave phase shift δ(E) for doublet nd scattering and the triton binding energy on the basis of Faddeev equations and within the N/D method and which were presented in the literature. The convergence of the expansion of K(k ²) in powers of momentum is studied. The binding energy of the virtual triton and the residues of the partial-wave scattering amplitudes at the poles corresponding to the bound and virtual states are calculated. Correlations between the binding energies of the bound and virtual states of the triton, on one hand, and the doublet scattering length for nd interaction, on the other hand, are considered. The function K(k ²) is also calculated within a two-body model featuring various potentials.     

Dispersion-relation analysis of K+p scattering below 2 GeV/c

We have obtained K⁺p scattering amplitudes that fit a large body of data below 2 GeV/c, satisfy phenomenological partial-wave backward dispersion relations, and are consistent with forward dispersion relations for the spin-non-flip amplitude, and forward dispersion-relation sum rules for the K⁺p P-wave scattering lengths. This has been achieved by firstly making an energy-dependent phase-shift analysis of 1 660 pieces of K⁺p data below 2 GeV/c, using parameterised partial-wave dispersion relations, with the additional constraints of forward dispersion relations and P-wave scattering lengths obtained from forward dispersion-relation sum rules, and then checking the resulting solutions for consistency with backward K⁺p dispersion relations.     

Impact parameter analysis of KN and πN scattering in the intermediate energy region

We have evaluated the s-channel-helicity partial-wave amplitudes for $\text{K}\text{N and πN}$ scattering as functions of the impact parameter using partial-wave data in the energy range P_L≈1.0–2.0 GeV/c. We find that the $\text{K}\text{N}$ background and resonance amplitudes exhibit features consistent with the dual absorptive picture for pomeron and f + ω and A₂ + ? exchanges. Comparison of the πN low-energy amplitude with the partial-wave decomposition of a quantitative Regge model gives evidence for local duality between the s-channel resonance and t- and u-channel Regge exchanges.     

Tensor interaction in heavy-ion scattering: (II). Partial-wave expansions

The turning-point-model relations between components of rank-2 tensor analysing power in polarized heavy-ion scattering, which were derived semi-classically in our previous work, are re-derived quantum-mechanically without resorting to any classical concept. Using partial-wave expansions of the scattering amplitudes, the turning-point-model relation is reduced to a relation between the diagonal and off-diagonal components of the tensor scattering amplitude for each type of tensor interaction (T_R, T_P and T_L). Numerical investigations and analytical investigations using a plane-wave expansion method show that these relations arise from universal features of heavy-ion scattering: large angular momenta and the short-range nature of the tensor potentials. An interrelation between the three types of tensor interaction is also obtained for each partial wave.     

Low-energy parameters of neutron-neutron interaction in the effective-range approximation

The effect of the mass difference between the charged and neutral pions on the low-energy parameters of nucleon-nucleon interaction in the ¹ S ₀ state is studied in the effective-range approximation. On the basis of experimental values of the singlet parameters of neutron-proton scattering and the experimental value of the virtual-state energy for the neutron-neutron systemin the ¹ S ₀ state, the following values were obtained for the neutron-neutron scattering length and effective range: a _nn = ?16.59(117) fm and r _nn = 2.83(11) fm. The calculated values agree well with present-day experimental results.     

Analytical approach to constructing effective hadron-hadron and hadron-nucleus interaction operators in low-momentum space of states

The approach to constructing effective hadron-hadron and hadron-nucleus potentials in the low-momentum space of the states, based on the use of analytic properties of scattering amplitudes and solution of the inverse quantum scattering problem for determining short-range interaction components is developed. The approach is applied to constructing effective potentials in S-wave channels of NN and n³H scattering.     

A partial-wave analysis for proton compton scattering in the Δ(1232) energy region

Based on the nowadays available phenomenological multipoles for pion photoproduction, a systematic dispersion theoretic calculation of Compton partial amplitudes has been performed. By comparing with the new experimental data in the Δ(1232) region it is found that the hitherto existing discrepancies between the data and theory remain. Our results allow us to isolate the basis of this problem. It is due to the fact that the imaginary parts of the Compton amplitudes determined already by unitarity, give too large contributions to the cross section thus leaving no space for real parts required by the dispersion integrals.Therefore a simultaneous partial-wave analysis for Compton scattering and pion photoproduction was carried through employing only the unitarity connections between both. The resulting amplitudes give a good fit to the Compton cross section and all photoproduction data; moreover the photoproduction multipoles agree essentially with those of the previous analyses. On the other hand for Compton scattering, phenomenological amplitudes are obtained for the first time and a model independent test of dispersion theoretic amplitudes can be carried out. For the resonating f_MM¹⁺ amplitude which describes the M1 excitation and deexcitation to the Δ-isobar, large discrepancies have been found. Possible consequences especially for the forward scattering amplitude and the validity of the Kramers-Kronig relation are discussed.     

Variational calculations of ν8 models of nuclear matter

We report variational calculations of ν8 models of nuclear matter which contain central, spin, isospin, tensor and spin-orbit potentials. These semi-realistic models can explain the nucleon-nucleon scattering in 1S0, 3S1?3D1, 1P1 and 3P2?3F2 states up to ～ 300 MeV. The variational wave function has two-body central, spin, isospin, tensor and spin-orbit correlations. The terms in the cluster expansion of the energy expectation value, that do not contain the spin-orbit correlations are summed by chain summation techniques developed for the ν6 models. Of the terms containing spin-orbit correlations, the two-body and three-body-separable ones are calculated, and the magnitude of the rest is estimated. Results for three phase-equivalent ν8 models, which differ significantly in the strength of tensor and spin-orbit potentials, are reported. They suggest that simple ν8 models may not be able to simultaneously explain the binding energy and density of nuclear matter.