The submitted manuscript has been created by the University of Chicago as Operator of Argonne N%tional Laboratory ( zargonne ) under ConIract No. W-31-109-ENG-38 with MJ4PR i@ -I OJ2 73 the U.S. Department of Energy. The US. Governmen! retains for itself, and others acting on its behalf, a paid-up, nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government. ust/ Dynamical study of A excitation with N(e, e n) reaction T.-S. H. Leea and T. Satob * aphysics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA bdepartment of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan The dynamical model of Ref. [1]has been extended to investigate pion electroproduction. The model can describe most of the recent data of p(e, e z ) reaction from Jlab and MIT- Bates. The extracted ikfl, E2 and C2 form factors for the TN + A transition are presented. 1. INTRODUCTION We report on the results from our investigation of pion electroproduction based on the dynamical model developed in Ref. [l](sl Model). The essential point of SL model is to have a consistent description of the TN scattering and yn ~ TN transition. This is important in extracting the TN + A form factors since it was found in Ref. [1] that the nonresonantmechanisms and the final TN interaction can account for about 40 Yoof the Ml strength at Q2 = O. The details have been discussed in Ref. [1] and the talk given by T. Sato in this conference. Here we only present our results for the TN ~ A form factors. 2. Results To compare with the results of Kamalov and Yang[5], we follow them to the TN ~ A form factors as parametrize G(Q2) = G~(Q2)(l + ~Q2)exp( @Q2). (1) where G~(Q2) = (1/(l+Q2/0.71 (GeV/c)2))2 is the usual proton form factor. We fmd that by choosing & = 0.154 (GeV/c)-2 and /3 = 0.166 (GeV/c)-2 the Jlab data[2] of p(e, e ~ ) at Q2 = 2.8 and 4 (GeV/c)2 can be described very well. The resulting model also give a good description of the data from MIT-Bates[3] and more recent Jlab data[4]. In Fig.1, we show one case from our fairly extensive calculations. From the predicted multipole amplitude kf~~ of TN ~ nn, we can calculate the Ml form factor for the yn a A. To compare with the result of Ref.[5], we use their definition and evaluate the following at the A resonance energy mn 8~Ak= G>= ~Im(Mf~) (2) % T *This work was supported by U.S. DOE Nuclear Physics Division Contract No. W-31-109-ENG-38 and JSPS Grant-in-Aid for Scientific Research (C) 12640273.
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o 60 120 180 0 60 120 (3X 6. Figure 1. The predicted differential cross sections at W = 1.235GeV, Q2 = and off-plane angles @ = 165,15 are compared with the recent Jlab data[2] 180 2.8( GeV)2 1 0.5 - --...... Dressed Bare w--- 0 0 1 2 34 Q2(GeV\c)2 Figure2. Thedressed(solid curve) and bare(dotted curve) Ml form factors are compared.
REM -5 0 ~...=...e... $ -lo -15-5 -20 0 1 2 34 Q2(GeV\c)2 o I 01 34 &(G:V /c)* I Figure3. Theratios R~~and RE~the~N+A form factors. Here experimental width TA = l151fev is used. The result(solid curve) is shown in Fig.2. We see that it deviates significantly from the dipole form GD for the proton form factor. In the same figure, we also show that the corresponding bare Ml form factor accounts only about 60!70 of the dressed form factor at Q2 = O, but approaches to the dressed one at high Q2. The strengths of E2 and C2 components of the TN + A transition can be seen from their ratios REM and RsM with the Ml strength. Our results are shown in F ig.3. Again we see that the results for the dressed form factors (solid curves) are significantly different from those for the bare form factors(dotted curves). Our complete results will be published in Ref.[6] REFERENCES 1. 2. 3. 4. 5. 6. T. Sato and T.-S. H. Lee, Phys. Rev. C54 (1996) 2660. V. V. Frolov et al., Phys. Rev. Lett. 82 (1999) 45; P. Stoler, private communication. C. E. Vellidis et al., Proc. of the second workshop on Electronuclear Physics and the BLAST Detector, ed. R. Alarcon and R. Milner, World Scientific (1999). T. Botto, talk in this conference. V. Burkert, talk in this conference; L. Elouadrhiri, talk in this conference. S. S. Kamalov and S. N. Yang, Phys. Rev. Lett. 83 (1999) 4494; S. Kamalov, talk in this conference. T. Sato and T. -S. H. Lee, in preparation.