Δ-isobar Excitation Research Articles

Contribution of the Δ-isobar excitation mechanism to the pp → {pp}sπ0 reaction

The differential cross section of the reaction pp → {pp} s π0, where {pp} s is the proton pair in the 1S0 state at a small excitation energy E pp < 3 MeV, is calculated using the box diagram with the excitation of the Δ-isobar. The model demonstrates a clear bump observed in the experimental data at the beam energy of ∼0.6 GeV and the zero diproton outgoing angle; however, its absolute value strongly depends on the off-shell extrapolation of the πNΔ vertex factor and underestimates the data.

Role of the Δ-isobar excitation mechanism in the reaction pp → {pp} s π0

The mechanism of Δ-isobar excitation in the intermediate state of the reaction pp → {pp}sπ0, where {pp}s is a pair of protons in state 1S0 at excitation energy E pp < 3 MeV, is used to calculate the differential cross section of this reaction in the energy range of 0.3–1 GeV. It is shown that the main contribution is made by three partial waves in the pp channel: 3 P 0, 3 P 2 and 3 F 2. The model explains the position of the peak observed at a beam energy of GeV and a zero diproton scattering angle, but cannot describe its absolute value.

Investigation of the Deuteron Breakup on Proton Target in the Forward Angular Region at 130 MeV

A set of differential cross-section data of the 1 H(d, pp)n breakup reaction at 130 MeV deuteron beam energy has been measured in the domain of very forward polar angles with the use of the Germanium Wall detector at the Forschungszentrum Julich. The data obtained for over 1000 kinematical points (112 geometries) are compared with the theoretical predictions based on various models of the three-nucleon (3N) dynamics. They comprise: the realistic nucleon-nucleon potentials alone or combined with the three-nucleon force (3NF), the coupled-channel calculations with the explicit treatment of the Δ-isobar excitation and finally, the potentials derived from chiral perturbation theory. In the part of the phase space studied, the Coulomb interaction between protons has a strong impact on the differential cross section of the breakup reaction. The strongest Coulomb effects are found in regions where the relative energy of the two protons is the smallest. In these regions the data are well reproduced exclusively by calculations which include the electromagnetic repulsion between protons. In spite of the dominance of the Coulomb force in the phase space studied, the contribution of 3NF effects is also observed.

Deuteron–deuteron scattering above four-nucleon breakup threshold

Deuteron–deuteron elastic scattering and transfer reactions in the energy regime above four-nucleon breakup threshold are described by solving exact four-particle equations for transition operators. Several realistic nuclear interaction models are used, including the one with effective many-nucleon forces generated by the explicit Δ-isobar excitation; the Coulomb force between protons is taken into account as well. Differential cross sections, deuteron analyzing powers, outgoing nucleon polarization, and deuteron-to-neutron polarization transfer coefficients are calculated at 10 MeV deuteron energy. Overall good agreement with the experimental data is found. The importance of breakup channels is demonstrated.

Chiral nuclear thermodynamics

We calculate the equation of state of nuclear matter for arbitrary isospin-asymmetry up to three loop order in the free energy density in the framework of in-medium chiral perturbation theory. In our approach 1π- and 2π-exchange dynamics with the inclusion of the Δ-isobar excitation as an explicit degree of freedom, corresponding to the long- and intermediate-range correlations, are treated explicitly. Few contact terms fixed to reproduce selected known properties of nuclear matter encode the short-distance physics. Two-body as well as three-body forces are systematically included. We find a critical temperature of about 15 MeV for symmetric nuclear matter. We investigate the dependence of the liquid–gas first-order phase transition on isospin-asymmetry. In the same chiral framework we calculate the chiral condensate of isospin-symmetric nuclear matter at finite temperatures. The contribution of the Δ-isobar excitation is essential for stabilizing the condensate. As a result, we find no indication of a chiral phase transition for densities ρ≲2ρ0 and at temperatures T≲100 MeV.

1 S 0 diproton formation in the pd → {pp} s n reaction and short-range NN interaction

Recent COSY results on the deuteron breakup reaction pd → {pp}sn with formation of the fast 1S0pp pair in forward direction at beam energies 0.6–1.9 GeV are reviewed. A contribution of the three-body forces related to the Δ-isobar excitation is found to be dominant at 0.6–1 GeV. A high sensitivity of the pd → {pp}sn cross section to the short-range NN-interaction is emphasized.

Four-nucleon system with Δ-isobar excitation

The four-nucleon bound state and scattering below three-body breakup threshold are described based on the realistic coupled-channel potential CD Bonn+Δ which allows the excitation of a single nucleon to a Δ isobar. The Coulomb repulsion between protons is included. In the four-nucleon system the two-baryon coupled-channel potential yields effective two-, three- and four-nucleon forces, mediated by the Δ isobar and consistent with each other and with the underlying two-nucleon force. The effect of the four-nucleon force on the studied observables is much smaller than the effect of the three-nucleon force. The inclusion of the Δ isobar is unable to resolve the existing discrepancies with the experimental data.

Differential cross section and analyzing power measurements forn→delastic scattering at 248 MeV

The differential cross sections and vector analyzing powers for nd elastic scattering at En=248 MeV were measured for 10°–180° in the center-of-mass (c.m.) system. To cover the wide angular range, the experiments were performed separately by using two different setups for forward and backward angles. The data are compared with theoretical results based on Faddeev calculations with realistic nucleon-nucleon (NN) forces such as AV18, CD Bonn, and Nijmegen I and II, and their combinations with the three-nucleon forces (3NFs), such as Tucson-Melbourne 99 (TM99), Urbana IX, and the coupled-channel potential with Δ-isobar excitation. Large discrepancies are found between the experimental cross sections and theory with only 2N forces for θc.m.>90°. The inclusion of 3NFs brings the theoretical cross sections closer to the data but only partially explains this discrepancy. For the analyzing power, no significant improvement is found when 3NFs are included. Relativistic corrections are shown to be small for both the cross sections and the analyzing powers at this energy. For the cross sections, these effects are mostly seen in the very backward angles. Compared with the pd cross section data, quite significant differences are observed at all scattering angles that cannot be explained only by the Coulomb interaction, which is usually significant at small angles.2 MoreReceived 13 November 2006DOI:https://doi.org/10.1103/PhysRevC.76.014004©2007 American Physical Society

Nucleon-deuteron scattering with Δ-isobar excitation: Perturbation theory

A perturbative approach for the description of elastic and inelastic nucleon-deuteron scattering is developed. Its validity is discussed. The aim of the perturbative approach is the isolation of details of different reaction mechanisms. The dynamics is based on a two-baryon potential allowing for the excitation of a nucleon to a $\ensuremath{\Delta}$ isobar. The coupled-channel potential yields an effective three-nucleon force in three-nucleon scattering. The purely nucleonic reference potential is the charge-dependent CD-Bonn potential.

Nucleon-deuteron scattering with Δ-isobar excitation: Chebyshev expansion of two-baryon transition matrix

A new technique for solving three-nucleon scattering equations is developed. It is based on the two-dimensional Chebyshev expansion of the two-baryon transition matrix. Its validity and its effectiveness are demonstrated. The dynamics of the examples is based on a two-baryon potential which allows for the excitation of a nucleon to a \ensuremath{\Delta} isobar; the coupled-channel potential yields an effective three-nucleon force in the three-nucleon system. The purely nucleonic reference potential is the charge-dependent Bonn potential.

TWO-BODY ELECTRO DISINTEGRATION OF THE TRINUCLEON BOUND STATE

The contribution describes inelastic electron scattering from 3 He with two-body final states. The description allows for single Δ-isobar excitation and includes final-state interaction and meson exchange currents.

Trinucleon Photo-Reactions with Δ-Isobar Excitation: Radiative Nucleon-Deuteron Capture and Two-Body Photo-Disintegration of the Three-Nucleon Bound State

Radiative nucleon-deuteron capture and photo disintegration of the three-nucleo n bound state with two-body final states are described. The description uses nucleon degrees of freedom extended to include the excitation of a single nucleon to a \diso. The baryonic interaction and the electromagnetic cu rrent couple nucleonic states and states with a \diso. Exact solutions of three-p article scattering equations are employed for the initial or final states of the reactions. The current has one-baryon and two-baryon contributions. The role of t he \diso in the description of the considered photo reactions is discussed and fo und to be moderate. The spin observables $A_{yy}$ and $T_{20}$ at $90^{\circ}$ la b scattering angle can be calculated model-independently from the $E1$ Siegert te rm in the long-wavelength limit.

Coherent π0 Electroproduction on the Deuteron

A general analysis of polarization phenomena for coherent pion electroproduction on deuterons is presented. The spin and isospin structures of the γ*+d→d+P0 amplitudes (where γ* is a virtual photon) are established and relationships between meson electroproduction on deuterons and on nucleons are given in the framework of the impulse approximation. The reaction e+d→e+d+π0 is investigated in detail, for a relatively large value of momentum transfer, 0.5 GeV2≤−k2≤2 GeV2, both at threshold and in the region of Δ-isobar excitation. Special attention is devoted to the sensitivity of different contributions to the exclusive cross section for d(e, eπ0)d, as the γ*πω form factor or the NN-potential. The predicted k2-dependence of the cross section agrees well with the available experimental data.

Nucleon–deuteron scattering with Δ-isobar excitation

Nucleon–deuteron scattering with Δ-isobar excitation

Description of electromagnetic processes in the three-nucleon system with Δ-isobar excitation

Description of electromagnetic processes in the three-nucleon system with Δ-isobar excitation

Three-nucleon force mediated by Δ-isobar excitation: Application to nucleon–deuteron scattering

Three-nucleon force mediated by Δ-isobar excitation: Application to nucleon–deuteron scattering

Backward elastic pd scattering at intermediate energies

The theoretical approaches to the description of backward elastic pd scattering at energies 0.5–2 GeV are reviewed. In addition to the mechanisms of neutron exchange and single pN scattering, the role of N * -isobar exchange is studied using the six-quark model for the dNN * vertex. Relativistic effects are taken into account within the Hamiltonian dynamics of systems with a fixed number of particles. The important role of Glauber rescatterings in the initial and final states in the neutron-transfer mechanism is displayed. Special attention is paid to the mechanism of Δ-isobar excitation, which, despite the large momentum transfer, is rather weakly sensitive to the high-momentum components of the deuteron wave function and dominates at incident protonenergies T p =0.5–1 GeV . The reaction pp→pnπ + is studied in the Δ-resonance region in order to determine the parameters of the amplitudes for NN↔NΔ transitions needed to calculate the Δ-isobar contribution to the process pd→dp. It is shown that the amplitude of the Δ-resonance mechanism for the process pd→dp is very sensitive to the parameters of the πNN, πNΔ, ρNN, and ρNΔ vertex form factors. The role of more exotic mechanisms is briefly discussed.

Isovector P-odd ππ exchange in the pp-system: Δ-isobar contribution

The contribution of the Δ-isobar excitation in the intermediate state to the weak two-pion exchange in the NN interaction is calculated. The structure of the nucleon is described in the potential quark model. The value of the Δ-isobar contribution to the longitudinal analyzing power A L in the low-energy pp scattering is linearly scaled by the constant f of the weak πNN coupling. For existing limits on the f-value the considered contribution proves to be small (⩽1%).

Validity of approximative treatments of Δ-isobar degrees of freedom

A perturbative approach to Δ-isobar components of the three-nucleon ground-state wave function is developed. It is based on the transition potential connecting nucleon-nucleon partial waves and partial waves with isobars. The perturbative results with single Δ-isobar excitation are compared to those of an exact coupled-channel calculation and turn out to be in satisfactory agreement for many Δ-effects. Within the perturbative method the role of the ρ-exchange in the transition potential and the importance of double Δ-excitations in the three-nucleon ground state are discussed. Effective nuclear operators such as three-nucleon forces and exchange currents, when simulating Δ-propagation in static approximation, are found to grossly overestimate Δ-effects.

Properties of the three-nucleon bound states with virtual Δ-isobar excitation

Wave function components containing a single Δ-isobar are included in the calculation of the three-nucleon bound states. Multiple Δ-effects are ignored. The two-nucleon interaction acts in all partial waves up to total angular momentum I = 2. The presence of a Δ-isobar increases the three-nucleon binding energy by about 0.3 MeV, 0.6 MeV repulsion being a dispersive two-body effect, and 0.9 MeV attraction arising from the three-nucleon force with an intermediate Δ-isobar. The effect of the Δ on the three-nucleon charge and magnetic form factors and on the weak decay is investigated.