We investigate the importance of crossing symmetry in effective field models and the effects of phenomenological nucleon resonance widths on the paradigmatic case of pion photoproduction. We use reaction models containing four star resonances up to 1.8 Gev ($Δ$(1232), N(1440), N(1520), N(1535), $Δ$(1620), N(1650), $Δ$(1700), and N(1720)) with different prescriptions for crossed terms and widths, to fit the latest world database on pion photoproduction. We compare $χ^2$ results from selected multipoles and fits. The $χ^2$ is highly dependent on the fulfillment of crossing symmetry and the inclusion of $u$ channels.
We compare results for the D13(1520) photon-decay amplitudes determined in analyses of eta- and pion-photoproduction data. The ratio of helicity amplitudes (A_3/2 / A_1/2), determined from eta-photoproduction data, is quite different from that determined in previous analyses of pion-photoproduction data. We consider how strongly the existing pion-photoproduction data constrain both this ratio and the individual photon-decay amplitudes.
We have obtained the transition matrix elements for pion photoproduction by considering the number of gamma matrices involved. The approach based on the most general conditions of gauge invariance, current conservation and transversality. The approach is fairly consistent with literatures.
We consider multipole amplitudes for low-energy pion photoproduction, constructed with minimal model dependence, at single energies. Comparisons with fits to the full resonance region are made. Explanations are suggested for the discrepancies and further experiments are motivated.
We summarize results obtained in our studies of the pion-nucleon coupling constant. Several different techniques have been applied to pi-N and NN elastic scattering data, and the existing database for single-pion photoproduction. The most reliable determination comes from pi-N elastic scattering. The sensitivity in this reaction was found to be greater, by at least a factor of 3, when compared with analyses of NN elastic scattering or single-pion photoproduction.
We calculate the cross sections for inclusive one-pion, two-pion and eta photoproduction in nuclei in the photon energy range from 300 MeV to 900 MeV within the framework of a semi-classical BUU transport model. Our results are compared with existing experimental data and discussed with respect to a calculation of the total photoabsorption cross section.
We investigate the influence of new Jefferson Lab polarization-transfer data, Cx and Cz, and recoil polarization, Py, measurements in multipole fits to the single-pion photoproduction database. Results are compared to those found with the addition of a double-polarization quantity associated with the Gerasimov- Drell-Hearn sum rule.
A self-consistent analysis of pion scattering and pion photoproduction within a coupled channels dynamical model is presented. In the case of pion photoproduction, we obtain background contributions to the imaginary part of the S-wave multipole which differ considerably from the result based on the K-matrix approximation. Within the dynamical model these background contributions become large and negative in the region of the S_{11}(1535) resonance. Due to this fact much larger resonance contributions are required in order to explain the results of the recent multipole analyses. For the first S…
The scattering amplitude of the photoproduction of $π^{+}$ is calculated using the helicity formalism. The pseudovector coupling $π$-N interaction with the non-perturbative term is applied to the perturbative expansion. The parameters for the self-energy are taken from the results of the $π$-N scattering in our previous study.
Incoherent photoproduction of pions on the deuteron in the Delta(1232) resonance region is studied, where besides the impulse approximation complete two-body rescattering in the nucleon-nucleon and pion-nucleon final state subsystems is included.
The possibilities of a model-independent partial wave analysis for pion, eta or kaon photoproduction are discussed in the context of complete experiments. It is shown that the helicity amplitudes obtained from at least 8 polarization observables including beam, target and recoil polarization can not be used to analyze nucleon resonances. However, a truncated partial wave analysis, which requires only 5 observables will be possible with minimal model assumptions.
The two-body currents for s-wave pion photoproduction on the NN system are derived to O(Q^4) in chiral perturbation theory. For the interesting case of 3S1 <-> 1S0 transitions, we show that an axial isovector two-nucleon contact term connects the short-distance physics of pion photoproduction to pion production and several important electroweak reactions. We also find that the standard chiral Lagrangian gives a gamma pi pi N N vertex that have not been explicitly mentioned in previous literature. The corresponding Feynman rule is presented here and some processes where it should be important a…
We show that a recent claim of huge kaon loop corrections to the electric dipole amplitude in neutral pion photoprodcution at threshold is incorrect. The difference between the two and three flavor chiral perturbation theory calculation is marginal and thus previous claims of a good understanding of this reaction remain valid.
A partial-wave analysis of single-pion photoproduction data has been completed. This study extends from threshold to 2 GeV in the laboratory photon energy, focusing mainly on the influence of new measurements and model-dependence in the choice of parameterization employed above the two-pion threshold. Results are used to evaluate sum rules and estimate resonance photo-decay amplitudes. These are compared to values obtained in the MAID analysis.
Two approaches for analysis of pion photo- and electroproduction on nucleons in the resonance energy region are checked at $Q^2=0$ using the results of GWU(VPI) partial-wave analysis of photoproduction data. The approaches are based on dispersion relations and unitary isobar model. Within dispersion relations good description of photoproduction multipoles is obtained up to $W=1.8 GeV$. Within unitary isobar model, modified with increasing energy by incorporation of Regge poles, and with unified Breit-Wigner parametrization of resonance contributions, good description of photoproduction multipo…
We shall review here our current knowledge and new frontiers of the pion photoproduction study, from threshold through the Delta resonance region, emphasizing the hadron physics program, of interest to a 250 MeV, high duty factor electron facility, such as the upgraded MAX-lab at the Lund University, Sweden, where it would be possible to produce tagged photons of high quality, with energy below approximately 200 MeV.
The influence of final state $NN$- and pi N-rescattering in incoherent pion photoproduction on the deuteron has been investigated. For the elementary photoproduction operator an effective Lagrangian model is used which describes well the elementary reaction. The interactions in the final two-body subsystems are taken in separable form. While NN-rescattering shows quite a significant effect, particularly strong for neutral pion production, pi N-rescattering is almost negligible. Inclusion of such effects leads to an improved and quite satisfactory agreement with experiment.
Based on a prior model on double pion photoproduction on the proton, successfully tested in total cross sections and invariant mass distributions, we make a theoretical study of the angular dependence of helicity asymmetries from the interaction of circularly polarized photons with unpolarized protons. We show that this observable is sensitive to details of the internal mechanisms and, thus, represents a complementary test of the theoretical model.
A covariant, unitary and gauge invariant theory for pion photoproduction on a single nucleon is presented. To achieve gauge invariance at the operator level one needs to include both the $πN$ and $γπN$ thresholds. The final amplitude can be written in terms of a distorted wave in the final $πN$ channel provided one includes additional diagrams to the standard Born term in which the photon is coupled to the final state pion and nucleon. These additional diagrams are required in order to satisfy gauge invariance.
Using an isobar model which can reproduce the existing experimental data of kaon photoproduction on the nucleon we investigate some related phenomenological aspects, i.e. the hadronic form factors, contributions of kaon-hyperon final states to the anomalous magnetic moment of the nucleon, and missing nucleon resonances. By reggeizing the appropriate propagators we extend the model to the higher photon energy regime.
Charged pion photoproduction is proposed as a new method to study halo nuclei. In particular, it is demonstrated that the reaction 17O(gamma,pi^-)17F(1/2+, 0.495 MeV) is well-suited to investigate the well-known proton halo in 17F which is not amenable to radioactive beam experiments. The cross sections are shown to be very sensitive to the halo structure of the loosely bound proton.
Using a model for two pion photoproduction on the proton previously tested in total cross sections and invariant mass distributions, we evaluate here polarization observables on which recent experiments are providing new information. We evaluate cross sections for spin 1/2 and 3/2, which are measured at Mainz and play an important role in tests of the GHD sum rule. We also evaluate the proton polarization asymmetry $Σ$ which is currently under investigation at GRAAL in Grenoble.
Photo production of pions on the deuteron is studied in the spectator nucleon model. The Born terms of the elementary production amplitude are determined in pseudovector $π$N coupling and supplied with a form factor. The $Δ$ resonance is considered both in the $s$ and the $u$ channel. The parameters of the $Δ$ resonance and the cutoff of the form factors are fixed on the leading photoproduction multipoles. Results for total and differential cross sections are compared with experimental data. Particular attention is paid to the role of Pauli correlations of the final state nucleons in the quasi…
We explore the photoproduction mechanisms for charged and neutral pion pairs off a heavy nucleus at threshold. We calculate the production of charged pairs in the Coulomb field of the nucleus in the Born approximation using explicit expressions for the differential cross sections and their connection with the total cross-section. The production of sigma mesons at threshold and their subsequent decay into pions is an important mechanism and is investigated quantitatively in a framework that can be used for both charged and neutral pions. Sigma mesons can be produced via electromagnetic (photon …
We investigate the pion photoproduction in the Δ(1232) region in the framework of an effective Lagrangian including pions, nulceon and Δ(1232). We work to third order in a small scale expansion with both $m_π$ and $M_Δ-M_N$ treated as light scales. We note that in the $Δ$ region, straightward power counting breaks as the amplitudes become very large, to deal with this problem, we suggest that the appropriate way to compare theoretical calculations with experimental data is via weighted integrals of the amplitudes through the $Δ$ region.
Based on an effective field theory of hadrons in which quantum chromodynamics is assumed to provide the necessary bare cutoff functions, a gauge-invariant theory of pion photoproduction with fully dressed nucleons is described. The formalism provides consistent dynamical descriptions of pi-N --> pi-N scattering and Gamma-N --> pi-N production mechanisms in terms of nonlinear integral equations for fully dressed hadrons. The dressed hadron currents and the pion photoproduction current satisfy gauge invariance in a self-consistent manner. Approximations are discussed that make the nonlinear form…
A breakdown of the Impulse Approximation is studied in pion photoproduction on $^3$He at high momentum transfers. The usual DWIA formalism with Faddeev wave functions which works well for small momentum transfers deviates from experimental measurements by up to two orders of magnitude for $Q^2>6 fm^{-2}$. It is found that the explicit inclusion of two-body mechanisms, where the photon is absorbed on one nucleon and the pion is emitted from another nucleon can restore agreement with the data.
Photoproduction of two pions on nucleon and deuteron is studied for photon energies from threshold up to $E_γ= 1.5$ GeV. For the elementary operator an effective Lagrangean approach is used with resonance and Born contributions. The model parameters are fixed by resonance decay widths and multipole analyses of single pion photoproduction. A satisfactory description of total cross sections of two-pion production on the proton for various charge channels is achieved, except for $π^0π^0$ production for which a significant underestimation is found near threshold. The operator then serves for the e…
The Ward-Takahashi identities are central to the gauge invariance of the photoproduction amplitude. Here we demonstrate that unitarity and in particular the inclusion of both the $πN$ and $γπN$ thresholds on equal footing yields a photoproduction amplitude that satisfies both two-body unitarity and the generalized Ward-Takahashi identities. The final amplitude is a solution of a set of coupled channel integral equations for the reactions $πN\rightarrowπN$ and $γN\rightarrowπN$. % Figures available from the authors upon request, % e-mail: phchv@pippin.cc.flinders.edu.au % Submitted to Physical …
We give predictions for the partial wave amplitudes of pion photoproduction near threshold by means of dispersion relations at fixed t. The free parameters of this approach are determined by a fit to experimental data in the energy range 160 MeV $\le E_γ \le$ 420 MeV. The observables near threshold are found to be rather sensitive to the amplitudes in the resonance region, in particular to the $Δ$ (1232) and $N^*$ (1440). We obtain a good agreement with the existing threshold data for both charged and neutral pion production. Our predictions also agree well with the results of chiral perturbat…
We present theoretical results for $(γ, π^0 π^0)$ production on nucleons and nuclei in the kinematical region where the scalar isoscalar $ππ$ amplitude is influenced by the $σ$ pole. The final state interaction of the pions modified by the nuclear medium produces a spectacular shift of strength of the two pion invariant mass distribution induced by the moving of the $σ$ pole to lower masses and widths as the nuclear density increases.
Some open topics in the field of low energy photon-nucleon interactions are discussed--which in my opinion are of interest both for obtaining new information on nucleon structure as well as for precision tests of our theoretical understanding of chiral dynamics. In particular, I discuss p-wave multipoles in charged pion photoproduction off protons as well as the role of spin-dependent effects in (unpolarized) Compton scattering off nucleons. There the concept of dynamical spin polarizabilities is found to be essential for the understanding of differential Compton cross sections above 120 MeV c…
Within a dynamical model, rescattering effects are studied in coherent pion photoproduction on the deuteron in the $Δ$(1232) resonance region. The model consists of a system of coupled equations for the N$Δ$, NN$π$ and NN channels. Pion rescattering leads in general to a significant reduction of total and differential cross sections resulting in a better description of experimental data. Only a few polarization observables are sensitive to rescattering effects. In particular $T_{20}$ allows an analysis of the reaction mechanism for specific kinematics. The question how rescattering affects the…
Deuteron Compton scattering below pion photoproduction threshold is considered in the framework of the non-relativistic diagrammatic approach with the Bonn OBE potential. The complete gauge-invariant set of diagrams is taken into account which includes resonance diagrams without and with rescattering and diagrams with one- and two-body seagulls. The obtained results are compared with predictions of other models and with experimental data. A possibility of determining isospin-averaged electromagnetic polarizabilities of the nucleon is discussed.
We develop the formalism for coherent two pion photoproduction in nuclei and perform actual calculations of cross sections for $π^-π^+$ and $π^0π^0$ photoproduction on $^{12}C$. We find that due to the isospin symmetry the cross section for $π^0π^0$ 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 $π^0$ mesons are equal and their relative azimuthal angle $ϕ=180^0$ is forbidden. Conversely in the $π^-π^+$ production the pions prefer to have a relative azimuthal angle 180$^0$ and the produ…
Formal expressions are developed for the general five-fold differential cross section of incoherent $π$-photoproduction on the deuteron including beam and target polarization. The polarization observables of the cross section are described by various beam, target and beam-target asymmetries for polarized photons and/or polarized deuterons. They are given as bilinear hermitean forms in the reaction matrix elements divided by the unpolarized cross section. In addition, the corresponding observables for the semi-exclusive reaction $\vec d(\vec γ,π)NN$ are also given.
A relativistic and non-local model for the coherent photoproduction of pions on spin-zero nuclei is presented. The production operator is derived from an effective Lagrangian model that contains all the degrees of freedom known to contribute to the elementary process. Using the framework of DWIA, the matrix elements of this operator are evaluated using relativistic bound state wave functions. Final state interactions are accounted for via a pion-nucleus optical potential. The effects of in-medium modifications of the production operator are discussed. We give results for $^{12}C$ and $^{40}Ca$…
Incoherent pion photoproduction on the deuteron is studied for photon energies from threshold up to 1 GeV with special emphasis on polarization observables. The elementary $γN\toπN$ amplitude is taken from the MAID model. The influence of final state interactions on total and semi-exclusive cross sections $\vec d(\vecγ,π)NN$ is investigated by including complete rescattering in the final $NN$- and $πN$-subsystems. For charged pion-production the influence of $NN$-rescattering is moderate whereas $πN$-rescattering is almost negligible. Much stronger influences of $NN$-rescattering are seen in n…
The photoproduction of pion off nucleon is investigated within a dynamical coupled-channels approach based on the Juelich pi-N model, which has been quite successful in the description of pi-N to pi-N scattering for center-of-mass energies up to 1.9 GeV. The full pion photoproduction amplitude is constructed to satisfy the generalized Ward-Takahashi identity and hence, it is fully gauge invariant. The calculated differential cross sections and photon spin asymmetries up to 1.65 GeV center-of-mass energy for the reactions gamma p to pi^+ n, gamma p to pi^0 p and gamma n to pi^- p are in good ag…
Methods are set forth for determining the hadron electromagnetic structure in the sub-$N\bar{N}$-threshold timelike region of the virtual-photon ``mass'' and for investigating the nucleon weak structure in the spacelike region from experimental data on the process $πN\to e^+e^- N$ at low energies. These methods are formulated using the unified description of photoproduction, electroproduction, and inverse electroproduction of pions in the first resonance region in the framework of the dispersion-relation model and on the basis of the model-independent properties of inverse electroproduction. A…
We show theoretical results for $(γ, π^0 π^0)$ production on nucleons and nuclei in the kinematical region where the scalar isoscalar $ππ$ amplitude is influenced by the $σ$ pole. The final state interaction of the pions modified by the nuclear medium produces a spectacular shift of strength of the two pion invariant mass distribution induced by the moving of the $σ$ pole to lower masses and widths as the nuclear density increases.
Pion photoproduction reactions are investigated in a dynamical coupled-channel approach based on the Juelich pi-N model, which presently includes the hadronic pi-N and eta-N stable channels as well as the pi-Delta, sigma-N and rho-N effective channels. This model has been quite successful in the description of pi-N to pi-N scattering for center-of-mass energies up to 1.9 GeV. The full pion photoproduction amplitude is constructed to satisfy the generalized Ward-Takahashi identity and hence, it is fully gauge invariant. The calculated differential cross sections and photon spin asymmetries up t…
We present theoretical results for (gamma,pi0 pi0) and (gamma,pi+- pi0) production on nucleons and nuclei in the kinematical region where the scalar isoscalar pi pi amplitude is influenced by the sigma pole. The final state interaction of the pions modified by the nuclear medium produces a spectacular shift of strength of the pi0 pi0 invariant mass distribution induced by the moving of the sigma pole to lower masses and widths as the nuclear density increases.
We present a detailed quark-model study of pion photoproduction within the effective Lagrangian approach. Cross sections and single-polarization observables are investigated for the four charge channels, $γp\to π^+ n$, $γn\to π^- p$, $γp\to π^0 p$, and $γn\to π^0 n$. Leaving the $πNΔ$ coupling strength to be a free parameter, we obtain a reasonably consistent description of these four channels from threshold to the first resonance region. Within this effective Lagrangian approach, strongly constrainted by the quark model, we consider the issue of double-counting which may occur if additional {…
Spin observables for the three charge states of the pion for the pion photoproduction reaction on the deuteron, $γd\toπNN$, with polarized photon beam and/or oriented deuteron target are predicted. For the beam-target double-spin asymmetries, it is found that only the longitudinal asymmetries $T_{20}^{\ell}$ and $T_{2\pm 2}^{\ell}$ do not vanish, whereas all the circular and the other longitudinal asymmetries do vanish. The sensitivity of spin observables to the model deuteron wave function is investigated. It has been found that only $T_{21}$ and $T_{22}$ are sensitive to the model deuteron w…
Effects of non-resonant photoproductions arising from two different $πNN$ couplings are investigated in the $γN\toππN$ reaction. We find that the pseudoscalar (PS) $πNN$ coupling is generally preferable to the pseudovector (PV) $πNN$ coupling and particularly the total cross sections are successfully described by the model with the PS $πNN$ coupling. In order to see the difference between the two couplings, we also show the results of invariant mass spectra and helicity-dependent cross sections in various isospin channels calculated with the PS and PV couplings.
We present an ongoing project to assess the importance of D-waves and the $Δ(1232)$ resonance for descriptions of neutral pion photoproduction in Heavy Baryon Chiral Perturbation Theory. This research has been motivated by data published by the A2 and CB-TAPS collaborations at MAMI [1]. This data has reached unprecedented levels of accuracy from threshold through to the $Δ$ resonance. Accompanying the experimental work, there has also been a series of publications studying the theory that show that, to go beyond an energy of $E_γ=170$ MeV, it is necessary to include other aspects, in particula…
We present a pion photoproduction model on the free nucleon based on an Effective Lagrangian Approach (ELA) which includes the nucleon resonances ($Δ(1232)$, N(1440), N(1520), N(1535), $Δ(1620)$, N(1650), and $Δ(1700)$), in addition to Born and vector meson exchange terms. The model incorporates a new theoretical treatment of spin-3/2 resonances, first introduced by Pascalutsa, avoiding pathologies present in previous models. Other main features of the model are chiral symmetry, gauge invariance, and crossing symmetry. We use the model combined with modern optimization techniques to assess the…
The inclusive A(gamma,pi+ pi-)X reaction is studied theoretically. A sizeable enhancement of the cross section is found, in comparison with the scaling of the deuteron cross section (sigma_deuteron * A/2). This enhancement is due to the modifications in the nuclear medium of the gamma N ----> pi pi N amplitude and the pion dispersion relation. The enhancement is found to be bigger than the one already observed in the (pi,pi pi) reaction in nuclei.
The contribution of the two-step process gamma + d -> p + n -> pi0 + d to the imaginary part of the amplitude for coherent pion production on the deuteron is calculated exploiting unitarity constraints. The result shows that this absorptive process is not negligible and has to be considered in an extraction of the elementary neutron production amplitude from the gamma + d -> pi0 + d cross section at threshold. In addition, it is argued that a consistent calculation of gamma + d -> pi0 + d in baryon chiral perturbation theory beyond next-to-leading order requires the inclusion of this absorptiv…
We examine cross sections for the processes $γN\to NK\bar{K}$ in the framework of a phenomenological Lagrangian. We include contributions from $Λ$ and $Σ$ resonances up to spin 3/2, as well as those from an exotic $Θ^+$. We allow the $Θ^+$ to have spin 1/2 or 3/2, with either positive or negative parity in each case. We also allow the state to be either isovector or isoscalar. We find that the scenario that most closely matches observations at Jefferson Laboratory requires a moderately large coupling of the $Θ^+$ to $NK^*$.
Deuteron Compton scattering below pion photoproduction threshold is considered in the framework of the nonrelativistic diagrammatic approach with the Bonn OBE potential. A complete gauge-invariant set of diagrams is taken into account which includes resonance diagrams without and with NN-rescattering and diagrams with one- and two-body seagulls. The seagull operators are analyzed in detail, and their relations with free- and bound-nucleon polarizabilities is discussed. It is found that both dipole and higher-order polarizabilities of the nucleon are needed for a quantitative description of rec…
A Regge model with absorptive corrections is employed in a global analysis of the world data on positive and negative pion photoproduction for photon energies from 3 to 8 GeV. In this region resonance contributions are expected to be negligible so that the available experimental information on differential cross sections and single polarization observables at -t \leq 2 GeV^2 allows us to determine the non-resonant part of the reaction amplitude reliably. The model amplitude is then used to predict observables for photon energies below 3 GeV. Differences between our predictions and data in this…
We calculate the quasifree photoproduction of pions and eta mesons on nuclei from 12C to 208Pb. Assuming that for the quasifree process the cross sections for pi/eta - photoproduction on a nucleon in medium are -- besides a lowering due to Pauli blocking -- identical to those on a free nucleon, we use these as an input. The produced mesons or resonances then propagate through the nucleus where they can undergo several scattering and absorption processes. This final state interaction, which leads to a lowering of the initial meson yield up to 70%, we simulate in a coupled channel Boltzmann-Uehl…
In the present paper we investigate a method to describe low-energy scattering events of pions and nuclei within a Boltzmann-Uehling-Uhlenbeck (BUU) transport model. Implementing different scenarios of medium modifications, we studied the mean free path of pions in nuclear matter at low momenta and compared pion absorption simulations to data. Pursuing these studies we have shown, that also in a regime of a long pionic wave length the semi-classical BUU model still generates reasonable results. We present results on pi-induced events in the regime of 10 MeV < Tkin < 130 MeV and photo-induced p…
We present an extraction of the E2/M1 ratio of the $Δ$(1232) from experimental data applying an effective Lagrangian model. We compare the result obtained with different nucleonic models and we reconcile the experimental results with the Lattice QCD calculations.
Model dependence of multipole analysis has been explored through energy-dependent and single-energy fits to pion photoproduction data. The MAID energy-dependent solution has been used as input for an event generator producing realistic pseudo data. These were fitted using the SAID parametrization approach to determine single-energy and energy-dependent solutions over a range of lab photon energies from 200 to 1200 MeV. The resulting solutions were found to be consistent with the input amplitudes from MAID. Fits with a $χ$-squared per datum of unity or less were generally achieved. We discuss e…
Incoherent pion photoproduction on the deuteron is studied in the first resonance region. The unpolarized cross section, the beam asymmetry, and the vector and tensor target asymmetries are calculated in the framework of a diagrammatic approach. Pole diagrams and one-loop diagrams with $NN$ scattering in the final state are taken into account. An elementary operator for pion photoproduction on the nucleon is taken in various on-shell forms and calculated using the SAID and MAID multipole analyses. Model dependence of the obtained results is discussed in some detail. A comparison with predictio…
Several methods for the treatment of pion photoproduction in the region of the Delta(1232) resonance are discussed, in particular the effective Lagrangian approach and the speed plot analysis are compared to a dynamical treatment. As a main topic, we discuss the extraction of the genuine resonance parts of the magnetic dipole and electric quadrupole multipoles of the electromagnetic excitation of the resonance. To this end, we try to relate the various values for the ratio R_{EM} of the E2 to M1 multipole excitation strengths for the Delta(1232) resonance as extracted by the different methods …
A model for the pion photoproduction on nuclei in the $A\left({γ,\, πNN} \right)B$ reaction is presented. This is an extension of our recent model for the $A\left({γ,\, πN} \right)B$ reaction. In this approach we have moved beyond the standard shell-model considering $Δ$\textit{N} correlations in the nuclear wave functions, which are caused by the virtual transitions $NN \to ΔN \to NN$ in the ground state of the nucleus. The main ingredients of the model are the two- and three-particle density matrices and the transition operators $γΔ\to Nπ$ and $γN \to Nπ$. The direct and exchange reaction me…
