Field-theoretical three-body relativistic equations for the multichannel πN↔γN↔ππN↔γπN reactions

A new kind of the relativistic three-body equations for the coupled πN and γN scattering reactions with the ππN and γπN three particle final states are suggested. These equations are derived in the framework of the standard field-theoretical S-matrix approach in the time-ordered three-dimensional form. Therefore, corresponding relativistic covariant equations are three-dimensional from the beginning and the considered formulation is free of the ambiguities which appear due to a three dimensional reduction of the four dimensional Bethe-Salpeter equations. The solutions of the considered equations satisfy the unitarity condition and they are exactly gauge invariant even after the truncation of the multiparticle (n>3) intermediate states. Moreover, the form of these three-body equations does not depend on the choice of the model Lagrangian and it is the same for the formulations with and without quark degrees of freedom. The effective potential of the suggested equations is defined by the vertex functions with two on-mass shell particles. It is emphasized that these INPUT vertex functions can be constructed from experimental data. Special attention is given to the construction of the intermediate on shell and off shell Δ resonance states. These intermediate Δ states are obtained after separation of the Δ resonance pole contributions in the intermediate πN Green function. The resulting amplitudes for the Δ⇔Nπ; Δ⇔Nγ; Δ^′⇔Δγ transition have the same structure as the vertex functions for transitions between the on-mass shell particle states with spin 1/2 and 3/2. Therefore it is possible to introduce the real value for the magnetic momenta for the Δ^′⇔Δγ transition amplitudes in the same way as it is done for the N^′⇔Nγ vertex function.     

Phenomenological model for describing pion-pair production on a proton by virtual photons in the energy region of nucleon-resonance excitation

A phenomenological model is developed for describing the production of π ⁺ π ^? pairs on a proton by virtual photons in the energy region of nucleon-resonance excitation.The cross sections are calculated for the channels γp → π ^?Δ⁺⁺, γp → π ⁺Δ⁰, and γp → ρp, which make a dominant contribution to pion-pair production, and the results are compared with available experimental data.The contributions of nucleon resonances to the cross section for the reaction γp → π ^?Δ⁺⁺ are predicted within the developed approach.     

Single- and double-pion production in nucleon collisions on the nucleon and on nuclei—the ABC effect and its origin in a dibaryonic resonance

The ABC effect-an intriguing low-mass enhancement in the ππ invariant mass spectrum-is known from inclusive measurements of two-pion production in nuclear fusion reactions. First exclusive measurements carried out at CELSIUS-WASA for the fusion reactions leading to d or ³He reveal this effect to be a σ-channel phenomenon associated with the formation of a ΔΔ system in the intermediate state and combined with a resonance-like behavior in the total cross-section. Together with the observation that the differential distributions do not change in shape over the resonance region the features fulfill the criteria of an isoscalar s-channel resonance in pn and NNππ systems, if the two emitted nucleons are bound. It obviously is robust enough to survive in nuclei as a dibaryonic resonance configuration. In this context also the phenomenon of NΔ resonances is reexamined.     

πo photoproduction on quasi-free neutrons in the reaction γd → πo np in the Δ region

The possibility of obtaining information about the reaction γn → π^on in the Δ resonance region from the reaction γd → π^onp is analyzed. To this aim, the differential cross sections d³σ/dE_ndΩ_πdΩ_n both for unpolarized particles and in case of polarized photons and deuterons as well as the asymmetry Σ for linearly-polarized photons are calculated at photon energies from 250 to 400 MeV in the diagrammatic approach. The contributions from the pole diagrams as well as one-loop diagrams both with n-p and π-N-rescattering are taken into account. The main contribution to the differential cross sections of π^o photoproduction on the neutron in the quasi-free kinematics arises from the neutron pole diagram. The correction due to n-p rescattering decreases with increasing pion angle and becomes to be less than 8% at Θ_π ≥ 90°. The contributions of the proton pole diagram and the one of π -N rescattering were found to be negligible. Background effects are more pronounced in the case of the asymmetry Σ. However, they are also strongly suppressed in the neutron quasi-free kinematics at photon energies above 300 MeV.     

Evaluation of the photoproduction of negative pions on neutrons in the region of the first resonance

In this paper we extend our systematic investigation of pion photoproduction to the case of negative pion production on neutrons. In our approach two phenomenological parameters occur in the electric and magnetic dipole amplitudesE ₀₊ andM _1?. These constants have been determined by a least squares fit of the total cross section data of the ABBHHM collaboration. We obtain a very good fit, also the prediction of the asymmetry ratio for polarized photons agrees with experiment at energies below and at the resonance. Serious discrepancies between theory and experiment are found for theπ ^?/π ⁺ ratio, moreover the relationship between the electric dipole at threshold, the Panofsky ratio and the difference ofs-waveπN-scattering lengths is fulfilled only within 20%. These discrepancies are discussed thoroughly.     

A study of meson-baryon couplings in the constituent quark model

Within the framework of the constituent quark model we discuss the effects of different types of meson-baryon-baryon vertex operators on the form factors and the coupling strengths of the lowest-lying positive and negative parity non-strange baryons. We compare the quark pair creation model (³P₀-model) with the SU(6)-model in which mesons are treated as elementary fields that directly couple to the quarks. The latter model is employed both in the so-called static limit and in a modification motivated by Galilei invariance. It is demonstrated that the inclusion of non-static effects simulates some features of the³P₀ vertex. Especially the reaction πN→ππN is found to be very sensitive to the different assumptions on the dynamics of theq¯q pair creation process. More indirect hints for the internal structure of the mesons might be obtained from the predicted asymmetry for the two form factors ofN→Δ+π andΔ→N+π, which occurs in the³P₀-model, only.     

Two-channel separable potential model for the low-energy hyperon-nucleon interaction

A two-channel separable potential model is given such that the T-matrix is given in the form of a N/D matrix. This model is used to examine the relationships between the three different definitions for a resonance in the two-channel problem, particularly for a ³S₁ Λp resonance. In order to obtain a phenomenological hyperon-nucleon (YN) scattering T-matrix in the present model, a least-squares fit is performed to the existing available data for the $\text{I =}\text{1}\text{2}\text{YN}$ scattering cross sections and angular distributions at low energies using the s- and p-wave N/D solutions which carry sixteen independent parameters. Several solution sets of potential parameters are found, for which we can obtain good fits to the Λp → Λp, Σ^?p → Λn and ΣN → ΣN data, particularly to the cross-section data for these processes. The p-wave contributions are estimated, and particularly the possibility of p-wave YN resonances is pointed out for the solutions for which we do not assume a ³₁ Λp resonance.     

Electromagnetic moments and nuclear charge radii for neutron-deficient Tb isotopes and the deformation jump nearZ=64,N=90

Optical isotope shifts and hyperfine structures of the^{147–153,155,157,159} Tb isotopes have been measured by the resonance ionization spectroscopy method. Nuclear moments and changes in nuclear charge radiiΔ 〈r ²〉 have been deduced. The “jump” inΔ 〈r ²〉 atN=88–90 has been revealed. It is compared with the relevant data for nuclei with other proton numbers.     

Pion-nucleon scattering in the K-matrix approach

The K-matrix approach with effective Lagrangians is used to describe the S and P pion-nucleon partial-wave amplitudes in the energy range E _lab≤ 1 GeV. It is demonstrated, that treating the resonance as K-matrix a pole gives the natural way to separate the resonance and non-resonance parts of the πN amplitude. The model includes all the four-star πN resonances, the non-resonance contributions are calculated from relevant Feynman graphs without any phenomenological form factors. Different contributions to the inelastic π⁻ p→ηn amplitude are estimated. Received: 9 July 1998     

BKLT equations for the coupled NN-πNN system

It is shown that the Baer, Kouri, Levin and Tobocman (BKLT) many-body scattering formalism provides a simple and formally exact set of dynamical equations for the transition amplitudes for a phenomenological hamiltonian model of the coupled NN-πNN system. The Δ isobar can be included as a πN scattering resonance or the ΔN mode may be introduced as a third sector of Focke space. Similarly, the dibaryon resonance can be treated as a ΔN scattering resonance or it can be treated as a distinct particle requiring a fourth sector of Focke space.     

Nuclear charge asymmetry in the a = 3 nuclei

The nuclear charge asymmetry in the A = 3 system is determined by making a perturbative estimate of the direct electromagnetic (e.m.) contribution to the ³He-³H binding energy difference. All local e.m. contributions are estimated in an almost model-independent way using experimental charge form factors and the relation exploited previously by Fabre de la Ripelle and Friar only for the contribution of the static Coulomb interaction. Model-dependent wave functions are used for the contribution of the small non-local terms of the e.m. interaction and the proton-neutron mass difference. Only 81 ± 29 keV of the experimental binding-energy difference has to be attributed to nuclear charge asymmetry, an amount smaller than previous estimates. The nearly model-independent method is used to estimate the contribution of some two-body charge asymmetric potentials, both theoretical and phenomenological, to the binding-energy difference.     

The role of the imaginary form factor in the microscopic description of (p,p′) scattering from nuclei with one closed shell

The inelastic scattering of protons from the lowest 2⁺ and 3^? levels in ⁴⁰Ca, Ni, Sn and N = 50 isotopes is analyzed for different incident proton energies. The addition of a collective imaginary term to the microscopic real form factor very much improves the agreement between the calculated and experimental cross section angular distributions. The variation with energy of the relative contributions of the ΔT = 1 and gDT = 0 isospin parts of the transitions is discussed.     

Excitation of the giant dipole resonance in the scattering of isoscalar projectiles

The excitation of the giant dipole resonance in nuclei with N > Z by isoscalar projectiles α and d is discussed within a simple collective model for isoscalar dipole excitations. Calculations have been performed for ²⁰⁸Pb; they are compared to recent data on the excitation of the new giant resonance at E_x = 13.8 MeV. For α scattering the effect of dipole excitation is quite weak but significant contributions are obtained for d scattering.     

Excited baryons in the bag

We calculate the negative parityN ^* andΔ ^* states in the chiral bag model. After projecting out spurious center of mass states we reproduce the known masses reasonably well. Both the colour gluon exchange diagrams and the quark-quark spindependent forces due to the presence of Goldstone pions give important contributions to the ordering of the states. Previous calculations are examined and we conclude that the chiral bag models can sucessfully account for the negative parity states as well as the baryon ground states.     

The magnitude of annihilation and penguin contributions to charm-meson decays

A consistent treatment of color singlet and octet contributions in the spectator constituent gluon model for pseudoscalar meson decays is attempted. The result comes out one order of magnitude too small to explain the observed life-time difference of D⁰ and D⁺. Furthermore, it is found that ‘penguin’ interactions in the annihilation channel may give contributions to the asymmetry of the (D⁰ → K⁺K^?)/(D⁰ → π⁺π^?) ratio of the order of the phase-space difference or larger. Finally, it is argued that annihilation cannot explain the $\text{ΔI =}\text{1}\text{2}$ rule for kaon decays; dynamical effects including the penguin interactions seem still to be needed.     

Further phenomenological analysis of experimental data on eta-meson photoproduction on protons

The results of a phenomenological analysis of recent experimental data on the differential cross sections for eta-meson photoproduction on protons and respective asymmetry in a beam of linearly polarized bremsstrahlung are presented along with the estimates of the Breit—Wigner parameters for the S ₁₁ (1535) nucleon resonance.     

Investigation of the EPR parameters and local structures for Cu2+ in Bis(l-asparaginato) M(II) catalysts (M=Zn,Cd, Mg)

The electron paramagnetic resonance (EPR) parameters (g factors and hyperfine structure constants) for Cu²⁺ in Bis(l-asparaginato) M(II) catalysts (M=Zn, Cd, Mg) are theoretically investigated using the high order perturbation formulas of these parameters for 3d⁹ ions in orthorhombically elongated octahedra. Ligand orbital and spin–orbit coupling contributions are included from the cluster approach in view of strong covalency. The ligand octahedra (i.e., [CuO₄N₂]^12? clusters) are found to experience axial and perpendicular local bond length variations Δ (≈0.19–0.25 Å) and δ (≈0.12–0.14 Å) due to the Jahn–Teller effect and size mismatch, which are dissimilar to those of host M²⁺ sites in pure compounds. The theoretical EPR parameters based on the above local structures show good agreement with the observed values, and some improvements are achieved as compared with those in the previous work. The local structures of these centers are discussed.     

Critical behavior of the E.S.R. line widths in a quasi two-dimensional antiferromagnet MnTiO3

The critical behavior of the electron paramagnetic resonance line widths have been studied in the quasi two-dimensional antiferromagnet MnTiO₃. Line widths diverge like ΔH∝(T?T_N)^?0.49, which is in good agreement with the theoretical value predicted by Kawasaki.