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Register a new userDispersive Analysis of Low Energy $gamma Ntopi N$ Process and Studies on the $N^*(890)$ Resonance
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Yao Ma
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We present a dispersive representation of the $gamma Nrightarrow pi N$ partial-wave amplitude based on unitarity and analyticity. In this representation, the right-hand-cut contribution responsible for $pi N$ final-state-interaction effect are taken into account via an Omnes formalism with elastic $pi N$ phase shifts as inputs, while the left-hand-cut contribution is estimated by invoking chiral perturbation theory. Numerical fits are performed in order to pin down the involved subtraction constants. It is found that good fit quality can be achieved with only one free parameter and the experimental data of the multipole amplitude $E_{0}^+$ in the energy region below the $Delta(1232)$ are well described. Furthermore, we extend the $gamma Nrightarrow pi N$ partial-wave amplitude to the second Riemann sheet so as to extract the couplings of the $N^ast(890)$. The modulus of the residue of the multipole amplitude $E_{0}^+$ ($S_{11pE}$) is $2.41rm{mfmcdot GeV^2}$ and the partial width of $N^*(890)togamma N$ at the pole is about $0.369 {rm MeV}$, which is almost the same as the one of $N^*(1535)$, indicating that $N^ast(890)$ strongly couples to $pi N$ system.
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We use a dispersion representation based on unitarity and analyticity to study the low energy $gamma^* Nrightarrow pi N$ process in the $S_{11}$ channel. Final state interactions among the $pi N$ system are critical to this analysis. The left-hand part of the partial wave amplitude is imported from $mathcal{O}(p^2)$ chiral perturbation theory result. On the right-hand part, the final state interaction is calculated through Omn`es formula in $S$ wave. It is found that a good numerical fit can be achieved with only one subtraction parameter, and the eletroproduction experimental data of multipole amplitudes $E_{0+}, S_{0+}$ in the energy region below $Delta(1232)$ are well described when the photon virtuality $Q^2 leq 0.1 mathrm{GeV}^2$.
Low-energy partial-wave $pi N$ scattering data is reexamined with the help of the production representation of partial-wave $S$ matrix, where branch cuts and poles are thoroughly under consideration. The left-hand cut contribution to the phase shift is determined, with controlled systematic error estimates, by using the results of $mathcal{O}(p^3)$ chiral perturbative amplitudes obtained in the extended-on-mass-shell scheme. In $S_{11}$ and $P_{11}$ channels, severe discrepancies are observed between the phase shift data and the sum of all known contributions. Statistically satisfactory fits to the data can only be achieved by adding extra poles in the two channels. We find that a $S_{11}$ resonance pole locates at $sqrt{z_{r}}=(0.895pm0.081)-(0.164pm0.023)i$ GeV, on the complex $s$-plane. On the other hand, a $P_{11}$ virtual pole, as an accompanying partner of the nucleon bound-state pole, locates at $sqrt{z_{v}}=(0.966pm0.018)$ GeV, slightly above the nucleon pole on the real axis below threshold. Physical origin of the two newly established poles is explored to the best of our knowledge. It is emphasized that the $mathcal{O}(p^3)$ calculation greatly improves the fit quality comparing with the previous $mathcal{O}(p^2)$ one.
The production of eta mesons in photon- and hadron-induced reactions has been revisited in view of the recent additions of high-precision data to the world data base. Based on an effective Lagrangian approach, we have performed a combined analysis of the free and quasi-free gamma N -> eta N, N N -> N N eta, and pi N -> eta N reactions. Considering spin-1/2 and -3/2 resonances, we found that a set of above-threshold resonances {S_{11}, P_{11}, P_{13}}, with fitted mass values of about M_R=1925, 2130, and 2050 MeV, respectively, and the four-star sub-threshold P_{13}(1720) resonance reproduce best all existing data for the eta production processes in the resonance-energy region considered in this work. All three above-threshold resonances found in the present analysis are essential and indispensable for the good quality of the present fits.
The experimental data on pi N scattering in the elastic energy region T_pi < 250 MeV are analyzed within the multichannel K-matrix approach with effective Lagrangians. Isospin invariance is not assumed in this analysis and the physical values for masses of the involved particles are used. The corrections due to pi^+- pi^0 and p-n mass differences are calculated and found to be in a reasonable agreement with the NORDITA results. Analysis shows the good description of the all experimental observables. From the data, new values for mass and width of the Delta^0 and Delta^{++} resonances were obtained. The isospin symmetric version gives phase shifts values close to the new solution for the pi-N elastic scattering amplitude FA02 by the GW group based on the latest experimental data. Our analysis leads to a considerably smaller < 1% isospin violation in the energy interval T_pi ~ 30-70 MeV as compared to 7% in some older analyses, however, it does confirm recent calculations based on chiral perturbation theory.
The $(n,gamma f)$ process is reviewed in light of modern nuclear reaction calculations in both slow and fast neutron-induced fission reactions on $^{235}$U and $^{239}$Pu. Observed fluctuations of the average prompt fission neutron multiplicity and average total $gamma$-ray energy below 100 eV incident neutron energy are interpreted in this framework. The surprisingly large contribution of the M1 transitions to the pre-fission $gamma$-ray spectrum of $^{239}$Pu is explained by the dominant fission probabilities of 0$^+$ and $2^+$ transition states, which can only be accessed from compound nucleus states formed by the interaction of $s$-wave neutrons with the target nucleus in its ground state, and decaying through M1 transitions. The impact of an additional low-lying M1 scissors mode in the photon strength function is analyzed. We review experimental evidence for fission fragment mass and kinetic energy fluctuations in the resonance region and their importance in the interpretation of experimental data on prompt neutron data in this region. Finally, calculations are extended to the fast energy range where $(n,gamma f)$ corrections can account for up to 3% of the total fission cross section and about 20% of the capture cross section.
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