Polarization of recoil nucleons in π0-photoproduction on protons below 500 MeV. I

Using the model of pion photoproduction recently discussed byBall andSchmidt a prediction for the polarization of the recoil protons is given for unpolarized photons. The strong dependence on the assumed values ofE ₀₊ andM _1? is shown. Taking into account this result and assuming thatM ₁₊ and the higher multipoles are sufficiently known, the possibility of determining the small multipoles from measurements is discussed.     

Effects of core polarization and exchange currents on the magnetic form factors of 0f 7/2 and 0g 9/2-shell nuclei

We have studied core polarization and exchange current effects on the magnetic form factors with the highest multipolarities allowed by the shell model:M 7 for⁴⁹Ti,⁵¹V, and⁵⁹Co, andM9 for⁸⁷Sr and⁹³Nb. One-pion exchange currents partially remove discrepancies between density-dependent Hartree-Fock-Bogoliubov calculations and experiments.     

Parity violation in pion electroproduction and photoproduction with a proton target

Parity violation in pion electroproduction and photoproduction on a proton target is investigated as a possible means of elucidating the structure of the electronic and non-leptonic neutral weak currents. We calculate both parity-violating effects caused directly by Z-boson exchange, which contributes only to electron scattering, and those due to parity-violating electromagnetic and nuclear interactions. The asymmetry in electroproduction is of order 20^?5, whereas that in photoproduction is ～10^?7. The sensitivity to the parameter sin²θ_w is investigated; it is a maximum at backward electron scattering angles. In addition to the Born terms, contributions from the Δ(1232) resonance and the light vector mesons [?(776) and ω(782)] are included in the model. Fits to the observed π⁰ and π⁺ electroproduction and photoproduction cross sections indicate that the model accounts for the production data in the medium energy region.     

Charged pion photoproduction from 10B and 13C

Positive and negative pion photoproduction cross sections from ¹⁰B and ¹³C leading to the ground state of the residual nucleus have been calculated in the plane-wave and distorted-wave impulse approximations. The results are compared with experiment and with other theoretical calculations. While a large discrepancy is observed between experiment and theory in the case of negative pion photoproduction from ¹³C, fair agreement is obtained between experiment and the plane-wave calculations in all other reactions. It is found that in all reactions studied, except in the case of positive pion production from ¹³C, the inclusion of the pion-wave distortions moves the theory away from the experimental points. It is also found that the photopion differential-cross-section calculations show a sensitivity to the nuclear wave function different from that predicted by the electron scattering form-factor calculations.     

Charged pion photoproduction from light nuclei

The photoproduction of 0–150-MeV charged pions from light nuclei is studied from a distorted wave impulse approximation (DWIA) approach. The final nuclear states are restricted to a finite set of isospin analogs of excited states of the target nucleus. The final state interactions of the pion with the residual nucleus are incorporated via optical potentials. The elementary photoproduction operator used is that of Blomqvist and Laget which is derived in a general reference frame. To gain insight into the predictive power of this DWIA approach, total and differential cross sections for π^± production from ⁶Li, ⁷Li, ¹⁰B, ¹²C, and ¹⁴N are calculated and compared with available data. It is found that, with a few exceptions, reasonable agreement is obtained between theory and experiment as long as the nuclear wave functions are constrained to fit other electromagnetic and weak processes and the optical potentials are constrained to fit pion-nucleus elastic scattering data. We conclude that, at this stage, using the Blomqvist-Laget operator in a DWIA calculation adequately describes the dynamics of charged pion photoproduction from complex nuclei. We illustrate how this reaction can be used to obtain information on the short range nature of the pion wave function and on nuclear wave functions. Shortcomings of and improvements on this calculation are also suggested.     

A dispersion analysis of pion photoproduction from nucleons. II

The paper gives an account of numerical results forl=0 andl=1 multipole amplitudes of pion photoproduction. They have been obtained by solving integral equations which originate from fixed angle dispersion relations that have been deduced in an earlier paper. In this Part II presented are solutions of truncated integral equations for photoproduction amplitudes, which take into account coupling with the most important transitionsM ₁₊ ⁽³⁾ (in the isovector case) andE ₀₊ ⁽⁰⁾ (in the isoscalar case). Discussed are implications of such an approach and a comparison of results obtained by a different method is being made.     

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.     

Inclusive charged pion photoproduction on12C using tagged photons in the energy range (200–390) MeV

The photoproduction of charged pions on¹²C has been investigated using the tagged photon beam facility at the Bonn 500 MeV synchrotron. Pions were detected in a broad range magnetic spectrometer. Double differential cross sections for pion emission at fixed photon energies are presented. The integration of the measured distributions yields the total cross section for inclusive pion production. The data are compared to the predictions of a simple model that takes the quasifree production of pions and their subsequent scattering and reabsorption into account.     

Double pion photoproduction from3He at low energies

A generalization of the “Gauge-invariant OPE model” to double pion photoproduction on³He is presented. Results for the total and differential cross-sections are shown. The relevance of double pion photoproduction in the nuclear shadowing of photons is remarked.     

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.     

Measurement of coherent π0 photoproduction on3He and3H in the resonance region

Neutral pion photoproduction has been measured on³He and³H nuclei in theΔ(1232) resonance region. Resonance averaged cross-sections are presented as a function of momentum transfer and compared to theoretical calculations.     

DWIA in the momentum space for (γ, π0) reaction near threshold

The differential and total cross-sections of neutral pion photoproduction off⁴He,¹²C and⁴⁰Ca nuclei are calculated in the framework of the DWIA in the momentum space. It is shown that the inclusion of pion wave distortion gives a less than 25% increase of the total cross sections. A good agreement with experimental data is achieved by using the full elementary amplitude that includes the pion-momentum nonlinear terms and the terms depending on nucleon momenta.     

The pion mass difference in threshold pion reactions on light nuclei

We investigate the effect of the pion mass difference in scattering and photoproduction of pions on light nuclei near threshold. The effect is found to be most easily described in a nuclear K-matrix formalism where the nuclear K-matrix elements are shown to be independent of the mass difference.     

A unitary isobar model for pion photo- and electroproduction on the proton up to 1 GeV

A new operator for pion photo- and electroproduction has been developed for nuclear applications at photon equivalent energies up to 1 GeV. The model contains Born terms, vector mesons and nucleon resonances (P₃₃(1232), P₁₁(1440), D₁₃(1520), S₁₁(1535), F₁₅(1680), and D₃₃(1700)). The resonance contributions are included taking into account unitarity to provide the correct phases of the pion photoproduction multipoles. The Q² dependence of electromagnetic resonance vertices is described with appropriate form factors in the electromagnetic helicity amplitudes. Within this model we have obtained good agreement with the experimental data for pion photo- and electroproduction on the nucleon for both differential cross sections and polarization observables. The model can be used as a starting point to predict and analyze forthcoming data.     

Evaluation of multipoles for photo- and electroproduction of pions

In this paper we present the detailed results of an evaluation of the multipole amplitudes for photoproduction of pions on nucleons. We have solved the dispersion relations for the multipolesE ₀₊,M _1?,M ₁₊,E ₁₊,E _2?2 andM _2? by the Muskhelishvili-Omnès method using an appropriate ansatz for the inelastic multipole amplitudes. Four phenomenological parameters occuring in our theory have been determined by a least squares fit of theπ ⁰ experimental different cross section data. Except at pion CM-angles between 50°0 and 80°0 and at 180°0 inπ ⁰ production there is satisfactory agreement between theory and experiment for all measured differential cross sections, polarizations and asymmetries ofπ ⁰- andπ ⁺-photoproduction.     

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.     

Threshold photoproduction of charged pions on14N

Pion photoproduction processes¹⁴N_gs(γ, π ⁺)¹⁴C and¹⁴N_gs(γ, π ^?)¹⁴O have been studied in the threshold region. These processes provide an excellent tool to study the corrections to soft pion theorems and Kroll-Ruderman limit as applied to nuclear processes. The agreement with the available experimental data for these processes is better with the empirical wave functions while the shell-model wave functions predict a much higher value. Detailed experimental studies of these reactions at threshold, it is shown, are expected to lead to a better understanding of the shell-model inputs and radial distributions in the 1p state.     

Formation of two pions on nuclei in A(γ, ππN)B reactions

A model is proposed for double pion photoproduction on nuclei that is accompanied by nucleon emission. Simple models that faithfully reproduce single-particle differential cross sections are used to describe photon interactions with intranuclear nucleons. The calculated cross sections for pion photoproduction on ¹²C nuclei are compared with inclusive pion spectra measured in the second resonance region of photon energies.     

Coherent two pion photoproduction on 12C

We develop the formalism for coherent two pion photoproduction in nuclei and perform actual calculations of cross sections for π⁻π⁺ and π⁰π⁰ photoproduction on ¹²C. We find that due to the isospin symmetry the cross section for π⁰π⁰ production is very small and has a maximum when the pions propagate together. However, the kinematical region where the energies and polar angles of the two π⁰ mesons are equal and their relative azimuthal angle Ø = 180° is forbidden. Conversely in the π⁻π⁺ production the pions prefer to have a relative azimuthal angle 180° and the production of the pions propagating together is suppressed. The dominant one-body mechanism in both channels is related to the excitation of the Δ isobar. Hence the reaction can serve as a source of information about Δ's properties in nucleus. We have found that the reaction is sensitive to effects of the pion and Δ renormalization in the nuclear medium, similar to those found in the coherent (γ, π⁰) reaction, but magnified because of the presence of the two pions.     

High energy pion photoproduction amplitudes from fixed-t dispersion relations and duality

Contributions to the high energy imaginary parts of the charged and neutral pion photoproduction amplitudes from degenerate ? and A₂ exchanges and ω and B exchanges are parametrized similarly to the dual absorptive model. These contributions together with the imaginary parts of the amplitudes found at low energies from partial-wave analyses are then used to evaluate the high energy real parts of the photoproduction amplitudes from fixed-t dispersion relations. A fit is made to data on pion photoproduction at 3.4 and 16 GeV incident photon energies, for momentum transfers up to ?1(GeV/c)². It is shown that much of the data is reproduced both qualitatively and quantitatively by our model. The high energy imaginary parts of the photoproduction amplitudes given by the fit are shown to be in accord with their average low energy behaviour.