Semi-Inclusive Reactions: N, Z, Nucleon momenta, and Pairing - PowerPoint PPT Presentation

Semi-Inclusive Reactions: N, Z, Nucleon momenta, and Pairing Lawrence Weinstein Old Dominion University

N, Z and high momentum nucleons: “54-40 or Fight” aka “The CaFe Experiment” • Goal: understand pairing mechanisms in symmetric and asymmetric nuclei – Neutron skins – Connection to EMC effect • Method: Measure A (e,e’p) at low and hi missing momentum at kinematics sensitive to n ( k ) • Targets: D, 12 C, 40 Ca, 48 Ca, 54 Fe – Add p , n symmetrically from D to 12 C to 40 Ca – Add 8 neutrons from 40 Ca to 48 Ca – Add 6 protons from 48 Ca to 54 Fe 2 L. Weinstein, EMC SRC MIT 2016

N, Z and high momentum nucleons: “54-40 or Fight” aka “The CaFe Experiment” • Goal: understand pairing mechanisms in symmetric and asymmetric nuclei – Neutron skins 54 Fe + 6 Protons – Connection to EMC effect • Method: Measure A (e,e’p) at low and hi missing momentum at kinematics sensitive to n ( k ) • Targets: D, 12 C, 40 Ca, 48 Ca, 54 Fe – Add p , n symmetrically from D to 12 C to 40 Ca 48 Ca – Add 8 neutrons from 40 Ca to 48 Ca 40 Ca – Add 6 protons from 48 Ca to 54 Fe - 8 Neutrons 3 L. Weinstein, EMC SRC MIT 2016

Adding neutrons to 40Ca Two models: • More neutrons, similar volume � larger p n • More neutrons, more np pairs � larger p p With Correlations +8% 40 Ca 48 Ca No Correlations -12% L. Weinstein, EMC SRC MIT 2016 4 M. Vanhalst, et al., J. Phys. G 42 , 055104 (2015)

Adding neutrons to 40Ca Two models: • More neutrons, similar volume � larger p n • More neutrons, more np pairs � larger p p Integrated momentum density 1.20E+00 1.00E+00 protons N2LO 8.00E-01 Larger p n saturation 6.00E-01 neutrons 4.00E-01 2.00E-01 0.00E+00 0.00E+00 2.00E-01 4.00E-01 6.00E-01 8.00E-01 1.00E+00 1.20E+00 1.40E+00 1.60E+00 1.80E+00 2.00E+00 0.5 1.5 2.0 0.0 1.0 sum p sum n 5 L. Weinstein, EMC SRC MIT 2016 Hagen et al, Nature Phys 12 , p186 (2015)

Focusing on 48 Ca Momentum space: Coordinate space: [CREX] [CaFe] 0.15 – 0.3 fm No SRC + nn-SRC Proton + np-SRC Neutron Adding correlations: • Reduce the radius. • Inverts the momentum skin? Proton Neutron Proton Neutron M. Vanhalst, et al., J. Phys. G 42 , 055104 (2015) L. Weinstein, EMC SRC MIT 2016 6

Focusing on 48 Ca Momentum space: Coordinate space: [CREX] [CaFe] 0.15 – 0.3 fm No SRC Depends on pairing mechanisms in asymmetric + nn-SRC Proton + np-SRC nuclei! Neutron Adding correlations: • Reduce the radius. • Inverts the momentum skin? Proton Neutron Proton Neutron 7 M. Vanhalst, et al., J. Phys. G 42 , 055104 (2015) 16

The CaFe Triplet: A Lab for Asymmetric Nuclei 54 Fe 48 Ca has a 40 Ca 48 Ca 40% neutron excess!! L. Weinstein, EMC SRC MIT 2016 8

The CaFe Triplet: A Lab for Asymmetric Nuclei Nucleus Z N 20 20 Symmetric double magic 40 Ca 20 28 + Full neutron shell (1f 7/2 ) 48 Ca 26 28 Almost symmetric double 54 Fe magic How do the neutrons from the outer 1f 7/2 shell correlate with the 40 Ca core? 9 24 L. Weinstein, EMC SRC MIT 2016

What do we already know? (e,e’) cross-section ratios at x B >1 are sensitive to the TOTAL NUMBER OF SRC PAIRS: 1.44 1.2 ~5% norm 0.96 uncertainty not shown => 48 Ca: + 20% nucleons, +20% SRC pairs! 10 Z. Ye Ph.D. Thesis, UVA. arXiv: 1408.5861 Z. Ye, JLab Users Group Meeting Talk (2016)

What do we already know? (e,e’) cross-section ratios at x B >1 are sensitive to the TOTAL NUMBER OF SRC PAIRS: 1.44 1.2 Due to the extra 8 neutrons 0.96 The neutrons in the outer 1f 7/2 shell (i.e. in the skin) are 11 equally correlated as the nucleons in the 40 Ca core! Z. Ye Ph.D. Thesis, UVA. arXiv: 1408.5861 Z. Ye, JLab Users Group Meeting Talk (2016) 26

What do we already know? (e,e’) cross-section ratios at x B >1 are sensitive to the TOTAL NUMBER OF SRC PAIRS: 1.4 The crust neutrons form MANY SRC pairs! 1.2 Due to the extra 8 neutrons [What types? What’s their impact?] 1.0 The neutrons in the outer 1f 7/2 shell (i.e. in the skin) are 12 equally correlated as the nucleons in the 40 Ca core! Z. Ye Ph.D. Thesis, UVA. arXiv: 1408.5861 Z. Ye, JLab Users Group Meeting Talk (2016) 27

detect the proton (e,e’p) Cross section factorizes (in PWIA): d σ p miss , E miss ) d σ free = KS ( ! dE e d Ω e dT p d Ω p d Ω Complications: E miss = ν − T p − T A − 1 • Rescattering of the outgoing proton. p miss = ! ! q − ! p p = − ! • Off-shell proton cross-section. p initial • Meson Exchange Currents (MEC). • Delta production (i.e. IC). => Spectral function is not an observable! d σ / K d σ free S D ( ! p miss , E miss ) = dE e d Ω e dT p d Ω p d Ω Compare cross sections for high (SRC) and low (MF) missing momentum protons in various nuclei 13 L. Weinstein, EMC SRC MIT 2016

R = σ Full / σ PWIA Minimizing FSI ( ) 3 He e , e ' p 500 MeV/c Full = PWIA + FSI Sargsian Θ rq = angle between q 400 MeV/c and recoil d ( e , e ’ p ) 200 MeV/c 20 40 60 80 100 120 θ nq = 35 o θ rq θ nq = 75 o Avoid rescaaering Full peak at θ rq ≈ 70 o PWIA 0.1 0.5 0.5 0.1 14 P miss (GeV/c) Boeglin et al., PRL 107 (2011) 262501 L. Weinstein, EMC SRC MIT 2016

Optimizing (e,e’p) kinematics • E beam = 11 GeV @ 40 uA to maximize rates. • 1 H, 2 H, 12 C, 40 Ca, 48 Ca, and 54 Fe targets. • Q 2 ≈ 3.5 GeV 2 – Reduces non-nucleonic currents (MEC, IC). – Proton energies high enough for Glauber FSI calculahons. • x B = Q 2 /2mω > 1.2 to minimize non-nucleonic currents. • θ rq < 50 o to minimize FSI. • Two Kinemahcs: – 350 < p miss < 600 MeV/c (“SRC”) – p miss < 250 MeV/c (“Mean-Field”) L. Weinstein, EMC SRC MIT 2016 15

“Observables” • Distorted spectral funchons ( i.e. , reduced σ) – Need theory support to interpret • Double rahos of σ ( SRC ) / σ ( MF ) A 1 σ ( SRC ) / σ ( MF ) A 2 – � extra SRC p from A 1 to A 2 • e.g.: from 40 to 48Ca � np pairs created by 8 more n – Reduced transparency (FSI) correchons – Compare symmetric and asymmetric nuclei • 40 and 48Ca; 6 and 7Li • d, C, Ca, Fe 16 L. Weinstein, EMC SRC MIT 2016