Nuclear spectral function based on the two-nucleon correlation model

1. KEK theory center workshop on Short-range correlations and tensor structure at J-PARC September 25,2009 KEK, Tsukuba Nuclear spectral function based on the two-nucleon correlation model H. Morita, Sapporo Gakuin Univ., Sapporo, JAPAN C. Ciofi degli Atti, Univ. of Perugia, ITALY

2. 1. Introduction • Nuclear Spectral Function • Two-Nucleon Correlation (TNC) Model • Spectral Function by TNC Model • Outline of my talk (Subject of our research)

3. Nuclear Spectral Function < Cross Section of A(e,e’p)B > P(Pm,Em) plays a key role for NN correlation study. e-N cross section nuclear spectral function For heavier nuclei, full calculation is almost impossible! We need some model.

4. k→large 2 1 A A-2 TNC Model L. Frankfurt and M.I. Strikman, Phys. Rept. 76,215(1981) C. Ciofi, S. Simula, L.L. Frankfurt and M.I. Strikman, Phys. Rev.C44, R1(1991) < claims > High momentum components of nA(k) are created by a correlated NN pair. Recently such features are confirmed experimentally. A. Tang, et al., Phys. Rev.Lett. 90, 042301(2003) R. Shneor et al., Phys. Rev.Lett. 99, 072501(2007) R. Subedi et al., Science320, 1476(2008)

5. MA-2 Spectral Function by TNC Model Excitation energy of (A-1)

6. MA-2 Improved Two Nucleon Correlation Model C. Ciofi, S. Simula, L.L. Frankfurt and M.I. Strikman, Phys. Rev.C44, R1(1991) C. Ciofi and S. Simula, Phys.Rev C53, 1689(1996) Strong Weak to what extent can this model describe the (e,e’p) data?

7. in order to compare the results with (e,e’p) data…. We must take into account FSI. If we include it, the cross section of A(e,e’p)B reaction will be given by Distorted Spectral Function distorted by FSI In this talk I will show • our formulation of the distorted spectral function • results of its application to 3He(e,e’p)pn and 12C(e,e’p)X reaction

8. Outline of my talk • Introduction • Distorted Spectral Function by TNC Model • Application to 3He(e,e’p)pn reaction • Application to 12C(e,e’p)X reaction • Summary

9. r 2 1 R A-2 2. Distorted Spectral Function by TNC Model Ref) C. Ciofi and S. Simula, Phys.Rev C53, 1689(1996) • In order to take into account the FSI, we must improve (extend) the (TNC model) spectral Function… • In order to do so, let us check once again its basic idea… φ(1,2) at high k region Factorization Deuteron scaling

10. x y Check of the “Factorization” 1 :Wave function is factorized!

11. x y Check of the “Factorization” 2 :Wave function is not factorized!

12. Deuteron vs Complex Nuclei at high momentum region C. Ciofi and S. Simula, Phys.Rev C53, 1689(1996) Momentum Distributions n(k) Ratio to the Deuteron 3He,4He,16O, 56Fe and N.M. 2H n(k) at high Momentum regions are similar to it of the Deuteron Almost Flat!

13. r 2 1 R A-2 Distorted Spectral Function

14. r 2 1 R A-2 r:small Here we will take Since R is Large. R:Large suggested by “deuteron scaling” at high Pm region

15. C. Ciofi and S. Simula, Phys.Rev C53, 1689(1996)

16. Check of 3He Spectral Function - Undistorted case - We can compare the results with full realistic calculations. Peak behavior is well reproduced! Normalization

17. 3. Application to 3He(e,e’p)pn reaction - Data - Q2=1.55(GeV/c)2 ω=0.84(GeV) ref) F. Benmokhtar, et al., Phys.Rev.Lett. 94, 082305(2005)

18. 3. Application to 3He(e,e’p)pn reaction - PWIA - G(12)=1 FSI is strong!

19. 3. Application to 3He(e,e’p)pn reaction - FSI - Data is reproduced reasonably well! PD(Pm,Em) works well!

20. 4. Application to 12C(e,e’p)X reaction • Data : P. Monaghan, Ph.D. thesis, MIT 2008 • They provide Em distributions at three kinematics. e’ e p

21. PEXP(Pm,Em) at Pm=550(MeV/c) Preliminary data Distorted Spectral Function is not very meaningful!! S. Gilad, ICTP08, Trieste Large Difference!

22. Kinematic II ( Pm=550 (MeV/c) ) Preliminary data Data is reproduced reasonably well.

23. Kinematic III ( Pm=550(MeV/c) ) a little bit underestimate the data. Preliminary data Effect of FSI is larger than Kinem. II

24. Pm=550(MeV/c) Preliminary data FSI explains the feature of the data at least Qualitatively.

25. Kinematic III Pm=600(MeV/c) Preliminary data Data is well reproduced!

26. Kinematic III Pm=650 (MeV/c) Preliminary data Data is well reproduced as the same level as 3He!

27. Summary • We extend TNC-model Spectral Function to take into account FSI. • Distorted Spectral Function reproduces the 3He(e,e’p)pn data rather well. • Also 12C(e,e’p)X reaction data are explained reasonably well. But before getting a definite conclusion we need more study. • Distorted Spectral Function gives us an information of the strength of FSI. It will give an information where is the good kinematics for NN correlation study.

28. A 2H A-2 Hiko TNC(SRC and/or Tensor) Advantage of Nuclear Spectral Function Mom. Dist. : Ratio to the Deuteron nA(k) scales to CAnD(k) TNC are magnified in nucleus A !

29. n P ～ ～ ＜Choice of Z-axis＞ i p1 // z |b1-bi| p1 ejected proton’s Momentum 1 z zi-z1 Glauber Operator G(ij) 1st nucleonStruck proton Usual Parameterization σtot ←Particle Data Group (http://pdg.lbl.gov/) α　←　Partial-Wave Analysis Facility (http://lux2.phys.va.gwu.edu/) not q !!

30. Distorted Momentum Distributions Ref) N.Nikolaev, S. Jeschonnek et al. The distorted momentum distributions are also scaled to the deuteron’s one at high Pm region.