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Register a new userA three-body calculation of incoherent $pi^0$ photoproduction on a deuteron
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Incoherent $pi^0$ photoproduction on a deuteron in the $Delta(1232)$ region is treated in a three-body scattering approach using separable two-body interactions. Results are presented for total and differential cross sections. It turns out that the role of higher order terms beyond the first order in the multiple scattering series is insignificant, and their inclusion cannot explain the existing discrepancy between theory and experiment.
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We discuss the possibility of extracting the neutron-neutron scattering length $a_{nn}$ and effective range $r_{nn}$ from cross section data ($d^2sigma/dM_{nn}/dOmega_pi$), as a function of the $nn$ invariant mass $M_{nn}$, for $pi^+$ photoproduction on the deuteron ($gamma dto pi^+nn$). The analysis is based on a $gamma dto pi^+nn$ reaction model in which realistic elementary amplitudes for $gamma pto pi^+n$, $NNto NN$, and $pi Nto pi N$ are built in. We show that $M_{nn}$ dependence (lineshape) of a ratio $R_{rm th}$, $d^2sigma/dM_{nn}/dOmega_pi$ normalized by $dsigma/dOmega_pi$ for $gamma ptopi^+ n$ and the nucleon momentum distribution inside the deuteron, at the kinematics with $theta_pi=0^circ$ and $E_gammasim 250$ MeV is particularly useful for extracting $a_{nn}$ and $r_{nn}$ from the corresponding data $R_{rm exp}$. It is found that $R_{rm exp}$ with 2% error, resolved into the $M_{nn}$ bin width of 0.04 MeV (corresponding to the $p_pi$ bin width of 0.05 MeV$/c$), can determine $a_{nn}$ and $r_{nn}$ with uncertainties of $pm 0.21$ fm and $pm 0.06$ fm, respectively, for the case of $a_{nn}=-18.9$ fm and $r_{nn}=2.75$ fm. The requirement of such narrow bin widths indicates that the momenta of the incident photon and the emitted $pi^+$ have to be measured with high resolutions. This can be achieved by utilizing virtual photons of very small $Q^2$ from electron scattering at Mainz MAMI facility. The proposed method for determining $a_{nn}$ and $r_{nn}$ from $gamma dto pi^+ nn$ has a great experimental advantage over the previous one utilizing $pi^- dtogamma nn$ for being free from the formidable task of controlling the neutron detection efficiency and its uncertainty.
The first experimental investigation of the near-threshold cross section for incoherent $pi^-$ photoproduction on the deuteron $gamma$ d -> $pi^-$ pp is presented. The experimental technique involved detection of the ~131 MeV gamma ray resulting from the radiative capture of photoproduced $pi^-$ in the target. The total cross section has been measured using an unpolarized tagged-photon beam, a liquid-deuterium target, and three very large NaI(Tl) spectrometers. The data are compared to theoretical models that give insight into the elementary reaction $gamma$ n -> $pi^-$ p and pion-nucleon and nucleon-nucleon final-state interactions.
Neutral kaon photoproduction on the deuteron has been investigated by including the final state effects and compared with the experimental data. Comparison shows that the models used in this calculation can reproduce the data in the $Sigma$ channel regions fairly well but still give over predictions in the $Lambda$ channel. It seems that the tensor target asymmetries are more suitable for studying the final state effects. The extractions of the elementary photoproduction amplitude are also demonstrated.
In this paper, we study the relativistic effects in a three-body bound state. For this purpose, the relativistic form of the Faddeev equations is solved in momentum space as a function of the Jacobi momentum vectors without using a partial wave decomposition. The inputs for the three-dimensional Faddeev integral equation are the off-shell boost two-body $t-$matrices, which are calculated directly from the boost two-body interactions by solving the Lippmann-Schwinger equation. The matrix elements of the boost interactions are obtained from the nonrelativistic interactions by solving a nonlinear integral equation using an iterative scheme. The relativistic effects on three-body binding energy are calculated for the Malfliet-Tjon potential. Our calculations show that the relativistic effects lead to a roughly 2% reduction in the three-body binding energy. The contribution of different Faddeev components in the normalization of the relativistic three-body wave function is studied in detail. The accuracy of our numerical solutions is tested by calculation of the expectation value of the three-body mass operator, which shows an excellent agreement with the relativistic energy eigenvalue.
Recent data from the PIONS$@$MAX-lab Collaboration, measuring the total cross section of the pion incoherent photoproduction $gamma dtopi^-pp$ near threshold, have been used to extract the E$_{0+}$ multipole and total cross section of the reaction $gamma n!to!pi^-p$, also near threshold. These are the first measurements of the reaction $gamma dtopi^-pp$ in the threshold region. The value of E$_{0+}$ is extracted through a fit to the deuteron data in a photoproduction model accounting for final-state interactions. The model takes an $S$-wave approximation for the elementary reaction $gamma n!to!pi^-p$ with E$_{0+}! = $ const in the threshold region. The obtained value E$_{0+} = -31.86pm 0.8$ (in $10^{-3}/m_{pi^+}$ units) is in agreement with other existing results. Model predictions for the total cross section $sigma(gamma n!to!pi^-p)$ are also given.
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