Studying Short range Correlation in Nuclei at the

Studying Short range Correlation in Nuclei at the Repulsive Core Limit via the triple Coincidence (e, e’ p N) Reaction Hall A / TJNAF Proposal 07 -006 (Next Generation of E 01 -015) e’ e p p or n PAC 31 / TJNAF Jan. 2007

2 N-Short Range Correlations (2 N-SRC) 2 N-SRC 5 o ~1 fm 1. f 1. 7 fm 1. 7 f o = 0. 17 Ge. V/fm 3 Nucleons

Why should we care about 2 N-SRC ? Study of cold dense nuclear matter complementary to study of hot dense nuclear matter Dynamics of neutron star formation and structure Coulomb sum rule SRC in nuclei Quark vs. hadronic degrees of freedom in nuclei NN interaction: short range repulsive core and the role played by the tensor force

What do we want to know about 2 N-SRC ? • What fraction of the momentum distribution is due to 2 N-SRC ? • What is the relative momentum between the nucleons in the pair? ·What is the pair CM momentum distribution ? • What is the ratio of pp to pn pairs? • Are these nucleons different from free nucleons (e. g size, shape, mass, etc. )?

Triple – coincidence measurements of large momentum transfer high energy reactions: <1 fm “Redefine” the problem in momentum space K 1 K 2 K 1 @ K 2 A pair with “large” relative K 1 > KF , momentum between the K 2 > KF nucleons and small CM momentum.

Triple – coincidence measurements: p EVA / BNL p E 01 -015 / Jlab e e n p e e p p

Triple coincidence (p, p pn) measurements at EVA / BNLn p γ Directional correlation np-SRC pairs have been observed. Removal of a proton with momentum above the Fermi sea level from 12 C is 92± 818 % accompanied by the emission of a neutron with momentum equal and opposite to the missing momentum. * 2 N-SRC dominance (74 -100% are partners in 2 N-SRC). * np-SRC dominance: Did not observe pp-SRC. Upper limit of 13% for pp-SRC contribution to protons with momentum above 275 Mev/c in 12 C. A. Tang Phys. Rev. Lett. 90 , 042301 (2003) Piasetzky, Sargsian, Frankfurt, Strikman, Watson PRL 162504(2006).

What did we want to achieve in E 01 -015 / Jlab ? Identify pp-SRC pairs in nuclei. (e, e’ p p) Determined the abundance of pp-SRC pairs. (e, e’ p p) / (e, e’ p) Verify the abundance of np-SRC pairs as deteremind by the EVA / BNL experiment. (e, e’ p n) / (e, e’ p) Determined the pp-SRC / np-SRC ratio. (e, e’ p p) / (e, e’ p n) It is important to identify pp-SRC pairs and to determined the pp. SRC/np-SRC ratio since they can tell us about the isospin dependence of the strong interaction at short distance scale. E 01 -015 Simultaneously measurements of the (e, e’ p) , (e, e’ p p) (e, e’ p n) reactions.

E 01 -105: An Custom Experiment to study 2 N-SRC Q 2 = 2 Ge. V/c , x. B ~ 1. 2 , Pm=250 -650 Me. V/c, E 2 m<140 Me. V Luminosity ~ 1037 -38 cm-2 s-1 Kinematics optimized to minimize the competing processes High energy, Large Q 2 The large Q 2 is required to probe the small size SRC configuration. MEC are reduced as 1/Q 2. Large Q 2 is required to probe high Pmiss with x. B>1. FSI can treated in Glauber approximation. x. B>1 Reduced contribution from isobar currents. Large pmiss, and Emiss~p 2 miss/2 M Large Pmiss_z

Kinematics optimized to minimize the competing processes FSI with the A-2 system: Small (10 -20%). Kinematics with a large component of pmiss in the virtual photon direction. Pauli blocking for the recoil particle. Geometry, (e, e’p) select periphery. Can treated in Glauber approximation. Canceled in some of the measured ratios. FSI in the SRC pair: These are not necessary small BUT: Conserve the isospin structure of the pair. Conserve the CM momentum of the pair.

00 ”M e. V /c , ” 5 The selected kinematics for the measurement ”, ” 40 0” p “ 3 00 Ee’ = 3. 724 Ge. V Pm = e’ Ee = 4. 627 Ge. V 19. 50 e 40. 1, 35. 8, 32. 00 00 M e. V/c 50. 40 P=3 00 -6 p= n or p 99 ± 50 Q 2=2 (Ge. V/c)2 qv=1. 65 Ge. V/c X=1. 245 1. 4 5, 1. 42 , 1. 36 p Ge V/c

Experimental setup HRS EXP 01 -015 / Jlab n array p p e n e Big Bite Lead wall

Big. Bite Spectrometer EXP 01 -015 Jlab / Hall A Neutron Detector Dec. 2004 – Apr. 2005

12 C(e, e’p) “ 300 Me. V/c” “ 400 Me. V/c” x. B>1 “ 500 Me. V/c” 12 C(e, e’p)11 B “ 500 Me. V/c” “ 300 Me. V/c” (e, e’p) (e, e’∆) “ 400 Me. V/c”

(e, e’pp) Pmis=“ 300” Me. V/c (Signal : BG= 1. 5: 1) (e, e’pp) Pmis=“ 400” Me. V/c (Signal : BG= 2. 3: 1) (e, e’pp) Pmis=“ 500” Me. V/c (Signal : BG= 4: 1) (e, e’pn) Pmis=“ 500” Me. V/c (Signal : BG= 1: 7) TOF [ns]

Directional correlation 12 C(e, e’pp) MCEEP Simulation with pair CM motion σCM=136 Me. V/c BG (off peak) p p γ

Directional correlation 12 C(e, e’pn) n γ MCEEP Simulation with pair CM motion σCM=136 Me. V/c BG (off peak) p

CM motion of the pair: Pc. mverical , “ 500 Me. V/c “ setup MCEEP with pair CM motion: σCM=50 Me. V/c σCM=100 Me. V/c σCM=136 Me. V/c 2 components of and 3 kinematical setups This experiment : σCM=0. 136± 0. 015 Ge. V/c (p, 2 pn) experiment at BNL : σCM=0. 143± 0. 017 Ge. V/c Theoretical prediction (Ciofi and Simula) : σCM=0. 139 Ge. V/c

ry a n i lim Pre 9. 5 ± 2 % 107 ± 23 % R. Subedi et al. , To prepared R. Shneor et al. , To be submitted

Assuming in 12 C nn-SRC = pp-SRC 1 -2 x x x and 2 N-SRC=100% A virtual photon with x. B >1 “sees” all the pp pairs but only 50% of the np pairs.

For 275 -600 Me. V/c protons in 12 C: Assuming for 12 C nn-SRC = pp-SRC pn - SRC 74 – 93 % 4. 75 ± 1 % 2 N –SRC dominance np-SRC dominance Notice: 100% is the sum of all the nucleons in this momentum range

Thus, the deduced 12 C structure is: 80 ± 4. 5 % - single particle moving in an average potential. 60 -70 % - independent particle in a shell model potential. 10 -20 % - shell model long range correlations (e, e’) 18. 4 ± 4. 5 % - SRC np pairs. 20 ± 4. 5 % - 2 N SRC. (e, e’p) (p, 2 pn) 0. 95± 0. 2% - SRC pp pairs. or 0. 95± 0. 2 % - SRC nn pairs. (e, e’pp) Small ~1% - SRC of “more than 2 nucleons”. ? ~1% -non nucleonic degrees of freedom (e, e’)

The (e, e’pn) / (e, e’pp) ratio 179 ± 39 Corrected for detection efficiency: Corrected for SCX (using Glauber): TOF for the neutrons [ns] 116± 17 In Carbon:

The ratio of pp-SRC / pn-SRC pairs in 12 C From the EVA / BNL 12 C(p, ppn) data : Piasetzky, Sargsian, Frankfurt, Strikman, Watson PRL 162504(2006). From the combined EVA /BNL 12 C(p, ppn) and the E 01 -015 12 C(e, e’pp) data: From the E 01 -015 12 C(e, e’pp) / 12 C(e, e’pn) data: There are 18 ± 2 times more np-SRC than pp-SRC pairs in 12 C. Why ?

At 300 -500 Me. V/c there is an excess strength in the np momentum distribution due to the strong correlations induced by underline tensor NN potential. np pn 3 He pp np pp V 18 pp 3 He Bonn pp/np Schiavilla, Wiringa, Piere, Carson, nucl-th /0611037 (2006). 3 He Sargsian, Abrahamyan, Strikman, Frankfurt PR C 71 044615 (2005).

Proposal 07 -006 Measurement of the 4 He(e, e’pp) 4 He(e, e’pn) reactions over the 4 He(e, e’p) missing momentum range from 400 to 875 Me. V/c. 3 He “d” E 01 -105 12 C (scaled to 4 He) This proposal - 4 He 3 He Density distribution Sargsian et al. Schiavilla et al. (e, e’p. N) calculations scaled to 4 He +FSI PWIA Sargsian +FSI PWIA Laget

The neutron-array Veto counters 4 layers of neutron detectors Shield wall 2” lead+1” iron D(e, e’pn) D(e, e’n)

56 Scintillators: 350 x 25 x 2. 5 mm 3 E 01 -015 24 24 3 mm ∆E counters 30 mm E counters 56 counters 12 New for PR 07 -006 Auxilary plan 350 x 2. 5 mm 3 Fibers with 2 PMs 56 350 x 25 x 2. 5 mm 3 scintillaor bars with one PM

The Proposed Measurements: Pmiss [Mev/c] days (e, e’pp) events (e, e’pn) events 400 5 110 200 625 5 235 160 750 5 280 150 875 5 320 140 Setup, calibrations, checks: 4 days Total number of triple coincidence events ~ 2000 ( E 01 -015 : Total number of triple coincidence events ~ 600 ) Total requested beam time: 29 days.

Summary E 01 -015 Simultaneous measurement of the (e, e’pp), (e, e’pn), and (e, e’p) reactions on 12 C over the (e, e’p) missing momentum range 300 -500 Me. V/c. pp-SRC and np-SRC pairs were identified and their abundances were determined. Data show sensitivity to the short-range NN tensor force. l PR 07 -006 Simultaneous measurement of these reactions on 4 He over (e, e’p) missing momentum range of 400 -875 Me. V/c. The data is expected to be sensitive to the NN tensor force and the NN short range repulsive force. The proposed experiment uses the Hall A cryotarget, the two HRSs, Big. Bite, and an array of neutron counters. The experiment can be ready to run in 6 month from approval. Total beam time request: 29 days

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Theory: Frankfurt, Sargsian, and Strikman New CLAS A(e, e') Result: K. Sh. Egiyan et al. PRC 68, 014313. K. Sh. Egiyan et al. PRL. 96, 082501 (2006) The observed “scaling” means that the electrons probe the high -momentum nucleons in the 2/3 nucleon phase, and the scaling factors determine the pernucleon probability of the 2/3 NSRC phase in nuclei with A>3 relative to 3 He. The probabilities for 3 -nucleon SRC are smaller by one order of magnitude relative to the 2 N SRC. For 12 C: 2 N-SRC(np, pp, nn) = 0. 20 ± 0. 045% 3 N-SRC Less than 1% of total

Why FSI are predicted to be small in the chosen kinematics? The FSI with the A-2 system The FSI of the recoil proton with the rest of the nucleus Suppressed due to Pauli blocking and the geometry of the (e, e’p) reaction. Pandharipande and Pierper PR C 45, 791 (1992). The FSI of the fast proton with the rest of the nucleus 2. 4 fm p The large anti-parallel component of pmiss (>k. F) reduce the FSI. Frankfurt, Sargsian, Strikman PR C 56, 1124 (1997). The absorptive (imaginary) part of the FSI amplitude does not modify the (e, e’pp)/(e, e’p) ratio. The small reduction in the (e, e’pp)/(e, e’p) ratio due to the transparency of the low energy proton is partially compensated by a small increase in the ratio by single charge exchange that can turn pn-SRC pairs into (e, e’pp) events.

Simple estimates of the FSI effects, based on a Glauber approximation show that these are small compared to the large errors of the data. Mardor, Piasetzky, Alster, and Sargsian PR C 761 (1992) The transparency of the low momentum protons is about 0. 8. i. e the measured (e, e’pp)/(e, e’p) ratio should be increased by 20% The same ratio should be decreased by 8 -16% due to SCX. These two, within the errors, compensate each other.

Simple estimates of the FSI effects, based on a Glauber approximation show that these are small compared to the large errors of the data. Mardor, Piasetzky, Alster, and Sargsian PR C 761 (1992) The data itself indicate that FSI are small. The extracted pair c. m distribution is a combination of c. m motion and FSI. The fact that we get : a narrow width (σcm=136 Me. V/c), similar in the transverse and longitudinal directions, Same as in previous measurements of the (p, 2 pn) reaction, Same as theoretical predications, indicates that FSI contribution are not dominant. The node in the pp / np ratio resulted from the NN-SRC Is not filled by FSI.

we adjust the effective cross section to obtain the measured Transparency: We used the measured effective cross section at 180 Me. V/c and the energy dependent of the mean free path as calculated by Pandharipande and Pieper (Phys. Rev C 45(1992)791. ).

The transparency of the recoil particle in the triple coincidence experiment is higher than that calculated for (e, e’p) since the (e, e’p) already selected an interaction point in the nucleus where the transparency of the (e, e’p) proton is high and therefore the transparency of the recoil proton is also high. We calculated the conditioned transparency as: Single Charge Exchange (SCX) Assuming the (e, e’pn) is 5 -10 times the magnitude of the (e, e’pp), the contamination of (e, e’pp) events with contribution from the np correlated pairs is 8 -16%. Since the SCX is very forward peaked at these energies we assumed that each proton produced in a SCX process will be considered a correlated partner.

The FSI between the two nucleons in the SRC pair Calculations by M. Sargsian 3 He (unpublished) Notice: that the FSI in the SRC pair conserve the CM momentum of the pair and the isospin structure of the pair. PWIA+FSI (only in the pair) PWIA

A B At the deep: For pp A~0 For np Since AB is negative FSI contribute more to pp M. Sargsian (private communication )

Calculations by J. M. Laget (unpublished)

Calculations by J. M. Laget (unpublished)

Calculations by J. M. Laget (unpublished)