Momentum Distribution in A = 3 Asymmetric Nuclei Jefferson Lab - PowerPoint PPT Presentation

Momentum Distribution in A = 3 Asymmetric Nuclei Jefferson Lab Hall-A Experiment E12-14-011 Florian Hauenstein, Old Dominion University SRC/EMC Workshop, MIT, 03.12.16

Kinetic Energy Sharing Pauli-Principle: SRC np pairs <T>(Majority) > <T>(Majority) < <T> (Minority) <T> (Minority)

VMC Prediction for <T> <T>(Majority) < <T> (Minority) R. Wiringa et al. (Phys. Rev. C 89 , 024305 (2014))

3 He SRC and Nucleon Counting P n p R >2 Simple Nucleon Counting R =1 rRegion 4

The A = 3 System 3 H • 3 He and 3 H are mirror nuclei • Neutron in 3 He = Proton in 3 H P n • Two-ways to study the proton-to-neutron momentum n distribution ratio in 3 He: 3 He • Measure the 3 He(e,e’p) / 3 He(e,e’n) ratio (Low accuracy due to the neutron measurement) P n p • Measure the 3 He(e,e’p) / 3 H(e,e’p) ratio. (Tritium Target necessary, available at JLab Hall-A (MARATHON)) 5

Extraction of Momentum Distribution from A(e,e‘)p ( ) σ PWIA = k ⋅ σ ep ⋅ S p E miss , p miss E miss = ω − T p − T A − 1 → → → → = q − p ' = − p init p miss Complications: • Rescattering of the outgoing proton. • Off-shell proton cross-section. • Meson Exchange Currents (MEC). • Delta production (i.e. IC). 6

Previous Hall-A 3 He (e,e’p)X measurements 3 He( e,e’p ) d 3 He( e,e’p ) np Full • Dominated by FSI at large momentum PWIA • Well described by PWIA theory p m [MeV/c] Data: Rvachev et al ., PRL94 192302 (2005); Benmokhtar et al ., PRL94 082305 (2005) Theory: Ciofi degli Atti and Kaptari, PRL95 052502 (2005) ; Alvioli et al ., PRC81 021001 (2010) 7

Minimizing FSI Effects in d(e,e‘)p FSI effects • θ nq = 45 o θ nq = 35 o decrease for smaller values θ nq = 75 o of θ nq Assume similar • suppression for A = 3 nuclei Boeglin et al. (Hall-A Collaboration), PRL 107 (2011) 262501

Access Momentum Distribution w/o FSI R = σ Full / σ PWIA ( ) 3 He e , e ' p • Rescattering minimized at small angles (verified for deuterium). 500 MeV/c • Small angles => x B >1 => suppress 400 MeV/c MEC and IC effects. 3 He ( ) 200 MeV/c Q 2 = 2 GeV 2 3 H e , e ' p θ nq = 30º PWIA Calculation Rescattering effects cancel in the Full Calculation 3 He/ 3 H ratio

JLab-Hall A Measurement E12-14-011 < p m > x E e θ e p p θ p Time 3 H+ 3 He (MeV/c) (GeV) (days) 100 1.15 3.47 20.9 o 1.61 48.7 o 1 300 1.41 3.64 20.4 o 1.35 58.6 o 10 Kinematics: Setup: • E b = 4.4 GeV • MARATHON Target • I beam = 20 μA • HRS spectrometer in Hall-A at Jefferson • Q 2 = 2 GeV 2 Lab • Low luminosity L ( 3 H) = 8×10 36 nucleons • x = Q 2 /2mω> 1 (quasi-elastic) cm -2 s -1 • θ nq < 40º 10

140 [degree] 2 10 No cut on Q 2 120 Simulation Results for 3 H rq 100 θ 80 10 60 40 20 similar for 3 He, 0 1 0 50 100 150 200 250 300 350 400 450 500 no full acceptance cuts! |P | [MeV/c] miss preliminary preliminary Q 2 > 2 GeV 2 Θ rq < 40 o

Expected Results 3 He and 3 H reduced cross- sections; Compared to calculations. Proton/neutron momentum ratio Kinetic Energy Sharing; Mapping of Inversion

Summary and Outlook • Measurement of momentum distribution in A = 3 mirror nuclei • Approved experiment scheduled for december 2017 at JLab Hall-A • Improved kinematic setting to reduce FSI, MEC and IC effects • Since E b = 4.2 GeV next year kinematic setting will change slightly • Other theoretical calculation i.e 𝜓 PT?

Backup Slides

Simulation 3 H Results (2) 2.4 ] 2.4 2 2 ] 10 90 2 /c /c 2 2.3 2 2.3 [GeV [GeV 80 2.2 2.2 70 2 2 Q Q 2.1 2.1 60 10 2 2 50 1.9 1.9 40 1.8 1.8 30 1.7 1 1.7 20 1.6 1.6 10 1.5 1.5 1.4 0 1.4 0 100 200 300 400 500 600 0 20 40 60 80 100 120 140 θ |P | [MeV/c] [degree] rq miss

Simulation 3 H Results: P miss & E miss Cut Q 2 > 2 GeV 2 and θ nq < 40º , no cross section scaling 600 600 | [MeV/c] | [MeV/c] 100 <p miss > = 100 MeV/c 300 500 500 miss miss 250 80 |P |P 400 400 200 60 300 300 150 40 200 200 100 <p miss > = 300 MeV/c 20 100 100 50 0 0 0 0 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 E [MeV/c] E [MeV/c] miss miss

3 He Spectral Function 2-body breakup channel E 2BB = m p + m d –m 3He min E 3BB = 2m p + m n –m 3He 3-body breakup channel from Rey

Previous 3 H(e,e’p) measurements A. Johansson, PR136, 1030B (1964) 18

Hall A H Experimental Setup – Hall A A Reynier Cruz Torres 19

Marathon Target Entrance window • Open cell design allows a wide range of scattering angles • Wall thickness 0.018” Al (120 mg/cm 2 ) • Entrance and exit windows: 0.010” Al (65 mg/cm 2 ) • The proton HRS will not see the cell windows 20 Adopted From David Meekins

P miss distributions (slow kinematics configuration, scaled to 4 days) ß before R-cut after R-cut à 3 He 3 He 4337 3135 events events 3708 2681 events events 3 H 3 H 2217 1592 events events 1961 1407 events events from Rey