INPC 2007 Tokyo 6 June 2007 Interpretation of

INPC 2007, Tokyo, 6 June, 2007 Interpretation of recent JLab results on quasi elastic (e, e’p) reactions off few-nucleon systems H. Morita, Sapporo Gakuin Univ. , Sapporo, JAPAN C. Ciofi degli Atti, Univ. of Perugia, ITALY L. P. Kaptari, BLTP JINP, Dubna, RUSSIA

1. Motivations To clarify …. 1. Validity of Standard Model of nuclei. 2. Nucleon propagation in the medium. 3. Nucleon properties in the medium. (form factors, NN correlations, etc. ) (e, e’p) reaction from few-nucleon system is one of the most effective tool. < Subject of my talk > Theoretical analysis of 3 He(e, e’p)2 H(pn) and 4 He(e, e’p)3 H data recently produced at JLAB.

2. Framework of the Calculation for the A(e, e’p)B Reaction < Cross Section of A(e, e’p)B > ＊We use Factorization Ansatz. We release it at Section 5 e-N cross section nuclear distorted spectral function If “B”(recoil system) is bound state distorted by FSI nucleon distorted momentum distribution

Nuclear Distorted Spectral Function in 3 He(e, e’p)2 H(pn) process C. Ciofi degli Atti, L. P. Kaptari, Phys. Rev. C 71, 024005 (2005) 3 He(e, e’p)2 H SG: Glauber Operator ：Pisa Group’s w. f. with AV 18 pot. 3 He(e, e’p)pn A. Kievsky et al. , Nucl. Phys. A 551(1993) 241 P ρ P t=(Pp-Pn)/2 ｒ n

Generalized Eikonal Approximation（GEA） L. L. Frankfurt et al. , Phys. Rev. C 56, 1124(1997) and M. M. Sargsian et al. , Phys. Rev. C 71 044614(2005) C. Ciofi degli Atti, L. P. Kaptari, Phys. Rev. C 71, 024005 (2005) Conventional Glauber Approximation q, ω P P Frozen Approximation n Generalized Eikonal Approximation q, ω P P n Consider the Fermi motion

Diagramatic representation of the process 3 He(e, e’p)2 H(pn) L. L. Frankfurt et al. , Phys. Rev. C 56, 1124(1997) and M. M. Sargsian et al. f. NN + PWIA ：IA + Single resc. ：Single Resc. Double resc. ：Double Resc. Calculating each graphs, we get SGEA(i) No free parameters !

3. Results of 3 He(e, e’p) 2 H(pn) Reaction C. Ciofi degli Atti, L. P. Kaptari, Phys. Rev. Lett. 95, 052502 (2005) Data: JLab E 89044 Q 2～ 1. 55(Ge. V/c)2, x=1 M. M. Rvachev et al. , Phys. Rev. Lett. 94(2005) 192302 GEA Calculation reproduces the data almost perfectly. 2 bbu channel

Results of 3 He(e, e’p) pn 3 bbu channel C. Ciofi degli Atti, L. P. Kaptari, Phys. Rev. Lett. 95, 052502 (2005) Data: JLab E 89044 Q 2～ 1. 55(Ge. V/c)2, x=1 F. Benmokhtav et al. , Phys. Rev. Lett. 94(2005) 082325 GEA Calculation reproduces the data quite well. <Saclay Kinematics> At Parallel Kinem. FSI small NN correlation can be studied.

4. Results of 4 He(e, e’p)3 H Reaction - JLab E 97 -111: B. Reitz et al. , Eur. Phys. J. A S 19(2004) 165 C. Ciofi degli Atti, L. P. Kaptari and H. Morita, Nucl. Phys. A 782(2007) 191 Perpendicular Kinem. Same Calc. for 4 He ATMS w. f. Q 2=1. 78(Ge. V/c) ω=0. 525(Ge. V) agreement is quite good.

5. Non factorized cross section: Results of 3 He(e, e’p)2 H C. Ciofi degli Atti and L. P. Kaptari, nucl-th/0705. 3951 Data: JLab E 89044 Current Operator: cc 1 First Calc. Full Calc. in momentum space (no p/q expansion) Breaking down of the Fact. App. at large negative pm > 300(Mev/c)

Left-Right Asymmetry ATL Data can not be reproduced completely. Detailed study is going on. Calc. for 4 He is now in progress C. Ciofi degli Atti, L. P. Kaptari and H. Morita, to appear

6. Summary-1 Without any free parameters, the data of 3 He(e, e’p)2 H(pn) and 4 He(e, e’p)3 H were well reproduced by the GEA calculation. 1. 2. 3. Validity of standard model of nuclei. OK, for JLAB energies. Nucleon propagation in the medium. Can be described by the generalized Glauber type operator. Nucleon properties in the medium. No apparent changes of nucleon properties at JLAB energies. At proper (parallel) kinematics we can study NN correlations.

Summary-2 • We performed a non Factorization calculation (in momentum space) for 3 He(e, e’p)2 H process and found that the violation of Factorization approximation is appreciable at negative pm> 300(Me. V/c). Extension to 4 He(e, e’p)3 H process is now in progress.