Single Pion Photoproduction Research Articles

Tests of vector-meson dominance relations in the electric Born model for pion photoproduction

Within the framework of the electric Born model and its hadronic analog we examine the validity of various vector-meson dominance relations for single-pion photoproduction.

Phenomenological Analysis of Single-Pion Photoproduction

A phenomenological fit of the data on single-pion photoproduction is presented for laboratory photon energies up to 1.2 BeV. The analysis is made in terms of a simple model in which the photoproduction amplitude consists of three separate contributions: (1) the Born approximation with electric coupling only; (2) Breit-Wigner resonances for which the positions and widths are taken from pion-nucleon scattering data, but whose amplitudes are adjustable parameters; and (3) additional contributions in the low partial waves having $J=\frac{1}{2},\frac{3}{2},\mathrm{and} \frac{5}{2}$. A criterion for success of the model is that these added terms, which are the principal adjustable parameters, should vary smoothly with energy. Most of the resonances found in the phase-shift analysis of pion-nucleon scattering are included in the fit. In particular, there is reasonably good evidence in the photoproduction data for a broad $S$-wave resonance near 1560 MeV. The analysis is carried out in terms of the helicity-amplitude formalism, which is more convenient for this purpose than the conventional representation in terms of multipole amplitudes.

Chiral Lagrangian Model of Single-Pion Photoproduction

We have constructed a chiral-invariant Lagrangian model for single pion photoproduction. We have used this Lagrangian to calculate threshold values for the differential cross sections. These threshold results were found to be in reasonable agreement with recent current-algebra calculations. For the cases where data were available, the comparison with experiment was favorable.

Chiral Dynamics withoutA1

The nonlinear realization method of Weinberg is used to construct a chiral-invariant Lagrangian consisting of $\ensuremath{\pi}$, $N$, ${N}^{*}(1236)$, and $\ensuremath{\rho}$, but not ${A}_{1}$. Chiral invariance can be, of course, maintained without invoking the ${A}_{1}$ meson. In view of the experimental status of ${A}_{1}$, it may be worthwhile studying such a model. The tree-diagram technique is used, with an off-mass-shell ${N}^{*}$ propagator, to calculate pion-nucleon $s$-wave scattering lengths, isobar production parameters, and single-pion photoproduction differential cross sections. A comparison with the current-algebra method is made.

Backward single pion photoproduction and the symmetric quark model

We calculate the contribution of baryonic resonances to the differential cross-sections for single pion photoproduction in the backward direction using the quark model. The absence of peaks due to the D 13(1520) and the F 15(1680), and the presence of I = 3 2 peaks in photoproduction from protons is explained. Differential cross sections for photoproduction from neutrons are predicted.

Pion Photoproduction and Fixed-tDispersion Relations

We review the dispersion-theoretic models of the isobar approximation which predict single-pion photo-production in the region of the $\ensuremath{\Delta}(1236)$ resonance. The differences between the various models are explained and their consequences discussed. Considerable efforts are made to look for further improvements of the theory from the confrontation of theory and experiment. Anticipating the development of experimental techniques, we discuss finally an example for a more complete photoproduction experiment. Specifically, we study the usefulness of a ${\ensuremath{\pi}}^{0}$-photoproduction experiment with polarized $\ensuremath{\gamma}$'s and/or polarized target for the region of the $\ensuremath{\Delta}(1236)$ resonance.

Analysis of single π− and π+ photoproduction on deuterium at high energies and low momentum transfers

Using impulse approximation and accounting for the complete spin-isospin structure of the deuteron, it is shown that the photoproduction of single charged pions on the deuteron is suppressed by a factor of about 1− 1 3 S(q) ( S, q denote the deuteron form factor and the momentum transfer to the pion) with respect to the photoproduction on the free nucleon. For π + photoproduction the Glauber correction is estimated to be less than 12%.

Single pion photoproduction near threshold

The latest theoretical predictions for single pion photoproduction are compared with the Kroll-Ruderman limit and a recent extension. The role of the omega meson in π o photoproduction is elucidated, and threshold predictions for π o photoproduction from neutrons are presented.

Photoproduction of Single Charged Pions from Deuterium and Hydrogen

Differential cross sections for the photoproduction of single charged pions from deuterium and hydrogen have been measured at pion center-of-mass angles between 30\ifmmode^\circ\else\textdegree\fi{} and 90\ifmmode^\circ\else\textdegree\fi{} and at photon energies between 3.0 and 3.7 GeV. The ratio of ${\ensuremath{\pi}}^{\ensuremath{-}}$ to ${\ensuremath{\pi}}^{+}$ cross sections from deuterium is found to be appreciably smaller than 1.

Photoproduction of Pions at the Second Pion-Nucleon Resonance

The resonant amplitudes for the single pion photoproduction from the nucleon are calculated at the second pion-nucleon resonance. A simple model is used, in which the second resonance and nucleon ground states are represented by solutions of the Klein-Gordon equation with effective potentials chosen suitably. The amplitudes for the electric dipole and the magnetic quadrupole transitions, E2- and M2-, and the total cross section for the resonant photoproduction of neutral pions are computed. The main features of the resonant photoproduction process are well explained by this simple model.

Photoneutron production from the proton at high energy

The total neutron yield from the (γ, n) reaction in hydrogen has been measured as a function of the energy of the primary electron using the bremsstrahlung beam from the Orsay Linear Electron Accelerator. The yield has been interpreted as a contribution from single and double pion photoproduction in hydrogen. Close to threshold the results are consistent with the theoretical prediction of CGLN for single pion photoproduction. In the energy region (250÷450) MeV the results are consistent with the experimentally measured values of the total positivepion photoproduction cross-section. At higher energies the results indicate a higher yield than previously anticipated for double pion photoproduction in the particular channel γ+p→n+π++π0.

Application of the Current Commutation Relations to theN***Photoproduction

We derive three sum rules by taking the expectation values between proton states at rest of three commutation relations of electric quadrupole and magnetic octupole operators. If we assume that the sum rules are saturated by only one intermediate state, the $I=\frac{1}{2}$, $J={\frac{5}{2}}^{+}$ pion-nucleon resonance ${N}^{***}(1688)$, we obtain a consistency relation which appears to be satisfied by experimental numbers. We then derive the ratio of the ${E}_{3\ensuremath{-}}$ and ${M}_{3\ensuremath{-}}$ amplitudes in single-pion photoproduction and we get a result in good agreement with experiment.

Sum Rules for Magnetic Quadrupole and Electric Dipole Moments: An Application of the Algebra of Current Components

Assuming simple commutation relations between the various components of the vector current density, we derive three commutation relations between electric dipole and magnetic quadrupole operators. Taking these commutators between proton states at rest, we get three sum rules. Considering only one intermediate state, namely the $I=\frac{1}{2}$, $J={\frac{3}{2}}^{\ensuremath{-}}$ pion-nucleon resonance ${N}^{**}(1518)$, we have a consistency relation between them. The sum rules are then used for deriving the ratio between the ${E}_{2}$ and ${M}_{2}$ amplitudes in single-pion photoproduction, and one obtains a result in good agreement with experiment.

One-particle exchange theory of pion photoproduction: I. General calculation

A calculation of single pion photoproduction from single nucleons is given using the one-particle exchange model involving the exchange of one pion, one ϱ, one ω, one φ, one nucleon, one N ∗ , and one N ∗∗ . Crossed diagrams, previously neglected, have also been included in the calculation. An imaginary part of the amplitudes is included using a Breit-Wigner type formula and experimentally observed widths. The theory should be a good representation of pion photoproduction up to about 800 MeV incident laboratory photon energy. A numerical evaluation of the theory will be given in a subsequent paper.

Polarization of the Recoil Proton fromπ0Photoproduction in Hydrogen

The polarization of the recoil proton in neutral single-pion photoproduction from hydrogen, $\ensuremath{\gamma}+p\ensuremath{\rightarrow}p+{\ensuremath{\pi}}^{0}$, has been measured for pion center-of-mass angles near 90\ifmmode^\circ\else\textdegree\fi{} at 7 photon energies from 450 to 900 MeV. The polarization rises to a maximum of 0.58 near 600 MeV and is still 0.42 at 900 MeV. The sign of the polarization is negative in the sense of k\ifmmode\times\else\texttimes\fi{}q, where k is the photon momentum and q is the pion momentum. The measured values are given as functions of laboratory photon energy and c.m. pion angle as follows: 450 MeV, 109\ifmmode^\circ\else\textdegree\fi{}, -0.16\ifmmode\pm\else\textpm\fi{}0.14; 525 MeV, 84\ifmmode^\circ\else\textdegree\fi{}, -0.36\ifmmode\pm\else\textpm\fi{}0.19; 585 MeV, 86\ifmmode^\circ\else\textdegree\fi{}, -0.58\ifmmode\pm\else\textpm\fi{}0.15; 660 MeV, 77\ifmmode^\circ\else\textdegree\fi{}, -0.51\ifmmode\pm\else\textpm\fi{}0.17; 755 MeV, 76\ifmmode^\circ\else\textdegree\fi{}, -0.55\ifmmode\pm\else\textpm\fi{}0.15; 810 MeV, 89\ifmmode^\circ\else\textdegree\fi{}, -0.45\ifmmode\pm\else\textpm\fi{}0.17; 895 MeV, 90\ifmmode^\circ\else\textdegree\fi{}, -0.42\ifmmode\pm\else\textpm\fi{}0.16. The recoil protons were momentum-analyzed with a magnetic spectrometer. Nuclear emulsion was used as scatterer and detector. The emulsion technique is discussed in detail. The number of individual scatterings in emulsion used for each measurement varied between 750 and 1000.

Nucleon compton scattering I: Dispersion relations

Nucleon Compton scattering is analyzed assuming the validity of the Mandelstam representation. The six covariant amplitudes which determine the scattering amplitude for this process are chosen in such a way that no kine-matical singularities are introduced. From the analytic properties of the covariant amplitudes implied by the Mandelstam representation, subtracted dispersion relations are written for quantities which are simply related to the elements of the total angular momentum submatrices of the scattering matrix; the subtraction constants are determined from an application of the low-energy Compton scattering theorem. The one-particle intermediate state contributions to the absorptive parts are considered exactly. The two-particle intermediate state contributions to the absorptive parts in Channels I and II are approximated by using the matrix elements of the Chew, Goldberger, Low, and Nambu single pion photoproduction analysis. For the two-particle intermediate state contribution to the absorptive part in Channel III a pole-term approximation is used after the I = 0 amplitude alone is shown to contribute. No higher mass intermediate states in any channels are considered. The numerical evaluation and comparison with experimental data of the derived dispersion relations is considered in a following paper.

Small-angle photoproduction of single positive pions on hydrogen at energies around the « second resonance »

Cross-sections of single positive pions produced in hydrogen by photons of laboratory energies between 550 and 900 MeV at centre of-mass angle between 0° and 10° have been measured, using a magnetic spectrometer and an appropriate counter arrangement. The experiment is described in detail. Angular distributions at constant y-ray energy and the dependence of the differential cross-section on energy at variousconstant centre-of-mass angles are given and their significance discussed.

Photoproduction of Single Neutral Pions from Hydrogen at Energies 0.6 to 1.2 BeV

Measurements of the differential cross section for the process $\ensuremath{\gamma}+p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}+p$ have been made at three pion center-of-mass angles: 60\ifmmode^\circ\else\textdegree\fi{}, 90\ifmmode^\circ\else\textdegree\fi{}, and 120\ifmmode^\circ\else\textdegree\fi{}. Values were obtained at intervals of 0.05 BeV (incident laboratory photon energy, $k$) from approximately 0.6 to 1.2 BeV. Most of the data were obtained by detecting only the recoil protons with a large, wedge-shaped, single-focusing magnetic spectrometer and associated equipment. For ${{\ensuremath{\theta}}^{\ensuremath{'}}}_{{\ensuremath{\pi}}^{0}}=60\ifmmode^\circ\else\textdegree\fi{}$ and $k\ensuremath{\le}0.94$ BeV the ${\ensuremath{\pi}}^{0}$ decays were also required, the decay photons being detected by a lead glass total absorption counter. Although the experimental resolution was considerably narrower than that of most of the previous experiments, its averaging effect was still appreciable in certain regions. Using a six-parameter fit, the data at each angle were unfolded in an effort to eliminate the effects of resolution and to obtain the true cross sections as a function of energy. The results compare reasonably well with those of previous experiments once differences in resolutions and systematic errors are taken into account. The results did not agree with the predictions of a simple resonance model with the resonance quantum numbers suggested by Peierls. The positions and widths of the two cross-section peaks in this energy region are quite similar to those observed in ${\ensuremath{\pi}}^{\ensuremath{-}}p$ scattering.

Regge Pole Hypothesis and High Energy Behavior of the Single Pion Photoproduction

Regge Pole Hypothesis and High Energy Behavior of the Single Pion Photoproduction

Partial wave dispersion relations for photon-nucleon scattering and nucleon-antinucleon production by photons

Partial wave dispersion relations for the processes γ Open image in new window →→γ+ Open image in new window and γ+γ→ Open image in new window + Open image in new window to the ordere2 are derived with the help of the Mandelstam representation. The angular momentum decomposition for both processes is carried out and the analytic properties of the partial wave amplitudes are determined. The absorptive parts of these amplitudes along part of the physical branch cuts are calculated by means of the unitarity condition. For γ+ Open image in new window →γ+ Open image in new window the resulting expressions involve amplitudes for single pion photoproduction; for γ+γ→ Open image in new window + Open image in new window they involve theT=0s-wave pion-pion phase shift and the total cross-section for the process γ+π→π+π. The discontinuities along the unphysical branch cuts are calculated by means of crossing symmetry and of analytic continuation through Legendre polynomials. The limits of convergence of the Legendre expansions are discussed and reasons for the importance of the two-pion exchange contribution in photon-nucleon scattering are presented.