Interpretation of recent JLab results on Interpretation of recent JLab results on quasi elastic (e,e’p) reactions off few-nquasi elastic (e,e’p) reactions off few-nucleon systems ucleon systems

Interpretation of recent JLab results on Interpretation of recent JLab results on quasi elastic (e,e’p) reactions off few-nquasi elastic (e,e’p) reactions off few-nucleon systems ucleon 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 3He(e,e’p)2H(pn) and 4He(e,e’p)3H data recently produced at JLAB.

< Subject of my talk >

2.Framework of the Calculation for the A(e,e’p)B Reaction

)E,( 6

mmDeppe

SKdpddd

dp

nuclear distorted spectral functione-N cross section

25

)( σ

mDeppe

Kddd

dp

If “B”(recoil system) is bound state

＊ We use Factorization Ansatz.

nucleon distorted momentum distribution

distorted by FSI

< Cross Section of A(e,e’p)B >

We release it at Section 5

)(

),(),()(),(

3

33

2

2

HeDm

f

M

HeGMD

immD

EEE

ddSeES m

rρρrρrrp ρp

Nuclear Distorted Spectral Function in 3He(e,e’p)2H(pn) process

3He(e,e’p)2H

)(

),(),()()2(

),(

3

33

121

2

2

3

3

HeN

m

f

M

HeGnpsi

mmD

EM

E

ddSed

ES m

t

rρρrρrrt

p tρp

3He(e,e’p)pn

SG: Glauber Operator

P

P

nｒ

ρt=(Pp-Pn)/2

33

M

He ： 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, 024005 (2005)

Generalized Eikonal Approximation （ GEA ） L.L.Frankfurt et al., Phys. Rev. C56, 1124(1997) and M.M. Sargsian et al., Phys. Rev. C71 044614(2005)C. Ciofi degli Atti, L.P. Kaptari, Phys. Rev. C71, 024005 (2005)

Conventional Glauber Approximation

Generalized Eikonal Approximation

P

P

n

q,ω

P

P

n

q,ω Frozen Approximation

Consider the Fermi motion

Diagramatic representation of the process 3He(e,e’p)2H(pn)

fNNfNN

PWIA

+ +

)1(GEAS ： Single Resc.

)2(GEAS ： Double Resc. )0(S ： IA

)(

),()(),(

3

33

23

2)2()1()0(

23

He

fm

f

M

HeGEAGEAf

mmD

EEE

ddSSSES

rρρrrp

Calculating each graphs, we get SGEA(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 3He(e,e’p) 2H(pn) ReactionC. Ciofi degli Atti, L.P. Kaptari, Phys. Rev. Lett. 95, 052502 (2005)

Q2～ 1.55(GeV/c)2, x=1

Data: JLab E89044

M.M. Rvachev et al., Phys. Rev. Lett. 94(2005) 192302

GEA Calculation reproduces the data almost perfectly.

2bbu channel

Results of 3He(e,e’p) pn 3bbu channel

C. Ciofi degli Atti, L.P. Kaptari, Phys. Rev. Lett. 95, 052502 (2005)

Q2～ 1.55(GeV/c)2, x=1

Data: JLab E89044

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 4He(e,e’p)3H Reaction - JLab E97-111: B. Reitz et al., Eur. Phys. J. A S19(2004) 165 -

C. Ciofi degli Atti, L.P. Kaptari and H. Morita, Nucl.Phys. A782(2007) 191

Perpendicular Kinem.

Q2=1.78(GeV/c) ω=0.525(GeV)

agreement is quite good.

)1(σ

)(n 5

D ccKddd

dp ep

pem

HeH 43 , ATMS w.f.

Same Calc. for 4He

5. Non factorized cross section: Results of 3He(e,e’p)2H

C. Ciofi degli Atti and L.P. Kaptari, nucl-th/0705.3951

Current Operator: cc1

(no p/q expansion)Full Calc.in momentum space

Breaking down of the Fact. App. at large negative pm > 300(Mev/c)

i

mmAiiMott

m

EQWVddEd

d),,,(

''2

3

6

pp

0

Data: JLab E89044

First Calc.

Left-Right Asymmetry ATL

)180()0(

)180()0(

TLA

Calc. for 4He 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-1Without any free parameters, the data of 3He(e,e’p)2H(pn) and 4He(e,e’p)3H 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 3He(e,e’p)2H process and found that the violation of Factorization approximation is appreciable at negative pm> 300(MeV/c).

Extension to 4He(e,e’p)3H process is now in progress.