Isobar configurations in nuclei

A comprehensive review of the role of nucleon resonances in nuclear structure is given with emphasis on the two-, three-, and four-nucleon systems and nuclear matter.     

Isobar configurations in closed shell nuclei

Explicit expressions for one- and two-N¹ isobar configurations in closed shell nuclei have been derived in the impulse approximation and applied to ⁴He and ¹⁶O. Conventional transition potentials with π- and ?-exchange have been used and the influence of potential regularization and short-range correlations have been studied. The dominant isobar configurations are found to be the one- and two-Δ components and originate from two-nucleon pairs in a relative S-state. The probability for finding a nucleon as a Δ-isobar is about 4.5% in ⁴He and about 3.2% in ¹⁶O. These numbers should be considered as upper limits due to uncertainties in off-shell effects of the transition potentials.     

Two quark excitations in two nucleon system

The unambiguously determined bases of the finite dimensional irreducible representation of the unitary and orthogonal groups are constructed. It is shown that the bases can be successfully applied in finding decomposition coefficients when the system of physical particles is divided into two subsystems. The general forms for some of these coefficients are presented.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

Isobar channels and nucleon resonances in π + π − electroproduction on protons

Acomprehensive set of differential cross sections for the reaction γ _ν p → π ^? π ⁺ p at the square of the photon 4-momentum in the range 0.2 < Q ² < 0.6 GeV² and the invariant mass of final-state hadrons in the range 1.3 < W < 1.6 GeV was first obtained with the CLAS detector at the Thomas Jefferson Laboratory. An analysis of these data on the basis of the phenomenological model developed by physicists from the Institute of Nuclear Physics at Moscow State University (INP MSU) and Thomas Jefferson Laboratory (INP MSU-Hall B at Jefferson Lab Collaboration) made it possible to determine, for the first time, the contributions of all isobar channels to the differential cross sections in question. The possibility of extracting the Q ² dependences of the electromagnetic form factors for the P ₁₁(1440) and D ₁₃(1520) resonances in a kinematical region that is the most sensitive to the contribution of the meson-baryon cloud to the structure of nucleon resonances is demonstrated.     

Calculations on the three-nucleon system using a separable expansion of local potentials

A separable expansion for local potentials called the unitary pole expansion (UPE) has been applied to the singlet-S soft-core Reid potential. The separable potentials obtained are used in conjunction with a separable tensor potential to calculate the triton binding energy, the nd doublet scattering length and the nd phase shifts in the state above and below break up. The convergence of the UPE is good especially for repulsive terms. The one term approximation (UPA) gives a triton energy differing by 0.04 MeV and a doublet scattering length differing by 0.14 fm from the values found for the local potential. The calculated phase shifts are in good agreement with the phase-shift analysis of Van Oers and Seagrave.     

Pockets in heavy-ion potentials and nucleon transfer

A schematic model is described for taking into account the effect of potential pockets (motivated by positron experiments at GSI) on sub-Coulomb nucleon transfer cross sections. Results for single-neutron transfer in ²³⁸U-²³⁸U collisions bear a remarkable resemblance to data for some bombarding energies.     

Some properties of bound states in the three-body problem with separable potentials

A system of three identical bosons with the pair separable S-interaction is considered. The monotonic (Yamaguchi potential) and oscillating pair potentials for the three-alpha model of¹²C have been investigated. In the case of the Yamaguchi potential many excited states (second, third, etc.) have been found.The author is thankful to Prof. V. G. Neudatchin and Prof. Yu. F. Smirnov for valuable discussions on the problems concerned.     

Equivalent neutron optical potentials in the separable energy-dependent approximation

The single-term separable energy-dependent approximation for the two-body t-matrix is extended to the case of non-hermitian potentials. The formalism is applied to construct a separable potential for neutron scattering at low energies. Comparison with the exact scattering data gives good agreement.     

Tests of resonance recognition criteria in coupled channel problems with separable potentials

Exactly soluble two-body two-channel problems are set up with separable potentials. Resonance is defined theoretically then the empirical resonance recognition criteria used in two-body data analyses are tested. Results are summarized in the last section of the paper.     

A study of the ground-state energy of He with nucleon–nucleon potentials

Ground-state properties are evaluated for the finite nucleus ⁴He starting from realistic nucleon–nucleon interactions within the framework of the Green’s function approach. For the sake of comparison, the same calculations are performed using the Brueckner–Hartree–Fock approximation. For that purpose four high-quality modern nucleon–nucleon interactions represented in momentum space are employed: the Argonne V18, CD-Bonn, Bonn A and N³LO potentials. In these potentials, the effects of charge dependence are taken into account. Additional binding energy is obtained from the inclusion of the hole–hole scattering term within the framework of the Green function approach. It has been shown that the Green function results agree well with the results obtained by accurate methods for few-nucleon systems such as the Faddeev–Yakubovsky calculation. In this study, a comparison of the calculated ground-state energies, obtained by using the Green function approach and different nucleon–nucleon potentials, with experimental values is carried out. The results show good agreement between the calculated values and the experimental ones.     

Three-nucleon results for separable potentials modelled on the Reid soft-core potential

Using a solution to the inverse scattering problem we have generated phase-equivalent separable potentials in the ${}^1\text{S}{}_0$ and ${}^3\text{S}{}_1\text{?}{}^3\text{D}{}_1$ states, which have nearly the same singlet UPA form factors and deuteron parameters (E_D, P_D, Q_D, A_S and $\text{A}{}_{\mathrm{D}}\text{A}{}_{\mathrm{S}}$) as the Reid soft-core potential. We compare our results for the binding energy of the triton and the neutron-deuteron doublet scattering length with the corresponding values for the Reid soft-core potential.     

The two nucleon interaction and the Cohen approximation

The Cohen approximation to the scalar Bethe-Salpeter equation is used to study the exchange of mesons between nucleons. Numerically, the Cohen approximation is more accurate than the Blankenbecler-Sugar approximation in all partial waves.     

Radiative reactions in two and three nucleon systems

Summary We have reviewed the theoretical and experimental situation regarding radiative processes in two and three nucleon system. There has actually been a lot of recent progress. Data sets from different experiments which agree with one another have now replaced the factor of two discrepancies of just a few years ago for several of the processes. New data on spin observables are now available for a variety of energies. New experiments are in progress for both proton proton and neutron bremsstrahlung. The theorists have not kept up. Although there has been a lot of work, there exists no theory which quantiatively describes all the data for eithern + p d + or forp + d ³He + . Thus there is still a lot to do if we are to fully understand these most basic processes.Invited talk to the symposium Measons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.Support in part from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged.     

Dyon theory with two related potentials

A self-consistent two-potential model of dyon theory is proposed. The treatment is based on the application of path-dependent exponential gauges. It is shown that a consistent definition of relations between the two potentials leads to n-independent physical results. Supplementary infrared problems do not appear in this treatment.     

Orientational transitions in a simple system with configurations anisotropy

Using the example of a linear chain with periodically distributed impurity ions, we study the basic features of orientational transitions in systems with configurational anisotropy. The possibility of orientational transitions due to a relative change in the magnitudes of the anisotropy and exchange energies with no difference in the signs of the anisotropy constants for impurity ions and ions of the matrix system is pointed out. Phase diagrams for the system in an external magnetic field are constructed.Translated form Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 84–89 April, 1985.The authors thank A. V. Deryagin for useful discussions of the results.     

Off-shell extension of the π-nucleon transition matrix and separable π-nucleon potentials

The off-shell extension of the P-wave π-nucleon transition matrix given by the Chew-Low model is compared with the one obtained from a separable potential. It is shown that the two off-shell extensions are rather different; π-deuteron scattering results are compared for the two cases.     

Parametrization of the 1S0 two nucleon transition matrix

The ¹S₀ two-nucleon transition matrix T is constructed from the symmetric part σ of its half-shell elements. The on-shell component of σ is given by the phase shift, while a wide class of parametrizations is suggested for the off-shell part. Restrictions on the off-shell part of σ arising from the short range and the proper one-pion-exchange tail of the nucleon-nucleon interaction are investigated. Using σ in the ¹S₀ and the Reid soft-core potential in the other partial waves, the binding energy per particle in nuclear matter and ¹⁶O and the ¹⁸O shell-model spectrum are computed. The sensitivity of these nuclear-structure results is tested with respect to (i) smooth off-shell changes in σ, (ii) various assumptions on the high-energy phase shift, (iii) the charge dependence of the phase shift, and (iv) experimental uncertainties in the phase shift.