Interpretation of recent JLab results on quasi elastic (e,e ’ p) reactions off few- nucleon systems INPC2007, Tokyo, 6 June, 2007 H. Morita, Sapporo Gakuin Univ., Sapporo, JAPAN C. Ciofi degli Atti, Univ. of Perugia, ITALY L.P. Kaptari, BLTP JINP, Dubna, RUSSIA

1.Motivations 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. To clarify …. 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 nuclear distorted spectral functione-N cross section If “B”(recoil system) is bound state ＊ We use Factorization Ansatz. nucleon distorted momentum distribution distorted by FSI We release it at Section 5

Nuclear Distorted Spectral Function in 3 He(e,e’p) 2 H(pn) process 3 He(e,e’p) 2 H 3 He(e,e’p)pn S G : Glauber Operator P P n ｒ ρ t=(P p -P n )/2 ： Pisa Group’s w.f. with AV18 pot. A. Kievsky et al., Nucl. Phys. A551(1993) 241 C. Ciofi degli Atti, L.P. Kaptari, Phys. Rev. C71, (2005)

Generalized Eikonal Approximation （ GEA ） L.L.Frankfurt et al., Phys. Rev. C56, 1124(1997) and M.M. Sargsian et al., Phys. Rev. C (2005) C. Ciofi degli Atti, L.P. Kaptari, Phys. Rev. C71, (2005) Conventional Glauber Approximation Generalized Eikonal Approximation P P n q,ω P P n Frozen Approximation Consider the Fermi motion

Diagramatic representation of the process 3 He(e,e’p) 2 H(pn) f NN PWIA ++ ： Single Resc. ： Double Resc. ： IA Calculating each graphs, we get S GEA (i) No free parameters ! L.L.Frankfurt et al., Phys. Rev. C56, 1124(1997) and M.M. Sargsian et al. Double resc.Single resc.

3.Results of 3 He(e,e’p) 2 H(pn) Reaction C. Ciofi degli Atti, L.P. Kaptari, Phys. Rev. Lett. 95, (2005) Q 2 ～ 1.55(GeV/c) 2, x=1 Data: JLab E89044 M.M. Rvachev et al., Phys. Rev. Lett. 94(2005) GEA Calculation reproduces the data almost perfectly. 2bbu channel

Results of 3 He(e,e’p) pn 3bbu channel C. Ciofi degli Atti, L.P. Kaptari, Phys. Rev. Lett. 95, (2005) Q 2 ～ 1.55(GeV/c) 2, x=1 Data: JLab E89044 F. Benmokhtav et al., Phys. Rev. Lett. 94(2005) GEA Calculation reproduces the data quite well. At Parallel Kinem. FSI small NN correlation can be studied.

4. Results of 4 He(e,e’p) 3 H Reaction - JLab E97-111: B. Reitz et al., Eur. Phys. J. A S19(2004) C. Ciofi degli Atti, L.P. Kaptari and H. Morita, Nucl.Phys. A782(2007) 191 Perpendicular Kinem. Q 2 =1.78(GeV/c) ω=0.525(GeV ) agreement is quite good. ATMS w.f. Same Calc. for 4 He

5. Non factorized cross section: Results of 3 He(e,e’p) 2 H C. Ciofi degli Atti and L.P. Kaptari, nucl-th/ Current Operator: cc1 (no p/q expansion) Full Calc.in momentum space Breaking down of the Fact. App. at large negative p m > 300(Mev/c) Data: JLab E89044 First Calc.

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

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.Validity of standard model of nuclei. 2.Nucleon propagation in the medium. 3.Nucleon properties in the medium. OK, for JLAB energies. Can be described by the generalized Glauber type operator. 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 p m > 300(MeV/c). Extension to 4 He(e,e’p) 3 H process is now in progress.