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Register a new userPion Absorption Cross Section for ^2H and ^3He in the Delta-Isobar Region: A Phenomenological Connection
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H. Kamada
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The absorption of pi^+ on ^3He in the $Delta$-region is evaluated with exact inclusion of the final state interaction among the three emerging protons. The absorption is described by a $pi N to Delta$ vertex and a $NDelta - NN$ transition t-matrix which are calculated from a phenomenological model for NN and pi d reactions. In a calculation where the initial pion scattering effects are neglected, the predicted peaks of the pion absorption cross sections for ^2H and ^3He lie too high in energy in relation to the data. The effect of the final state three-nucleon interaction turns out to be too small for changing the magnitude and shifting the peak position of the total absorption cross section for ^3He. We demonstrate that the adjustment of the peak position for the deuteron cross section by small modifications of the $Delta$-parameters, automatically leads to the correct peak position in ^3He.
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In a kinematically complete experiment at the Mainz microtron MAMI, pion angular distributions of the $^3$He(e,e$pi^+)^3$H reaction have been measured in the excitation region of the $Delta$ resonance to determine the longitudinal ($L$), transverse ($T$), and the $LT$ interference part of the differential cross section. The data are described only after introducing self-energy modifications of the pion and $Delta$-isobar propagators. Using Chiral Perturbation Theory (ChPT) to extrapolate the pion self energy as inferred from the measurement on the mass shell, we deduce a reduction of the $pi^+$ mass of $Delta m_{pi^+} = (-1.7^{+ 1.7}_{- 2.1})$ MeV/c$^2$ in the neutron-rich nuclear medium at a density of $rho = (0.057^{+ 0.085}_{- 0.057})$ fm$^{-3}$. Our data are consistent with the $Delta$ self energy determined from measurements of $pi^0$ photoproduction from $^4$He and heavier nuclei.
The 3He transverse electron scattering response function R_T(q,omega) is calculated in the quasi-elastic peak region and beyond for momentum transfers q = 500, 600 and 700 MeV/c. Distinct from our previous work for these kinematics where we included meson exchange currents and relativistic corrections we now additionally include Delta isobar currents (Delta-IC). The Delta-IC contribution increases the quasi-elastic peak height by about 5% and leads to an excellent agreement with experimental data in the whole peak region. In addition it is shown that effects due to the three-nucleon force largely cancel those due to the Delta-IC in the peak region. Finally, we have found that Delta-IC are important for three-body break-up reactions in the so-called dip region. This could explain why in a previous study of such a reaction, where Delta degrees of freedom were not included, no agreement between experimental and theoretical results could be obtained.
The recently derived long-range two-pion exchange (TPE) contributions to the nuclear current operator which appear at next-to-leading order (NLO) of the chiral expansion are used to describe electromagnetic processes. We study their role in the photodisintegration of 2H and 3He and compare our predictions with experimental data. The bound and scattering states are calculated using five different parametrizations of the chiral next-to-next-to-leading order (N2LO) nucleon-nucleon (NN) potential which allows us to estimate the theoretical uncertainty at a given order in the chiral expansion. For some observables the results are very close to the predictions based on the AV18 NN potential and the current operator (partly) consistent with this force. In the most cases, the addition of long-range TPE currents improved the description of the experimental data.
Mechanisms of the charge exchange reaction $dpto {pp}_{!s} Npi$, where ${pp}_{!s}$ is a two-proton system at low excitation energy, are studied at beam energies 1 -- 2 GeV and for invariant masses $M_X$ of the final $Npi $ system that correspond to the formation of the $Delta(1232)$ isobar. The direct mechanism, where the initial proton is excited into the $Delta(1232)$, dominates and explains the existing data on the unpolarized differential cross section and spherical tensor analyzing power $T_{22}$ for $M_X> 1.2$ GeV/$c^2$. However, this model fails to describe $T_{20}.
The neutrino-nucleon --> lepton pion QE reaction on the A-target is used as a signal event or/and to reconstruct the neutrino energy, using two-body kinematics. Competition of another processes could lead to misidentification of the arriving neutrinos, being important the fake events coming from the CC1-pion background. A precise knowledge of cross sections is a prerequisite in order to make simulations in event generators to substract the fake ones from the QE countings, and in this contribution we analyze the different nuclear effects on the CC1-pion channel. Our calculations also can be extended for the NC case.
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