Kinetic energy of protons and neutrons in asymmetric nuclei

16 8 08 Pb neutron p n proton Kinetic energy of protons and neutrons in asymmetric nuclei A data-mining project using JLab CLAS data Meytal Duer Tel-Aviv University July 3, 017 International Workshop on (e,e'p) Processes, Bled 1

np-dominance in N-SRC SRC Pair Fraction [%] np Hall-A & BNL 11 CC N-SRC n-p pp n-n Missing Momentum [GeV/c] Subedi et al., Science 30 (008). p-p np Hall-B pp A Hen et al., Science 346 (014)

np-dominance in asymmetric nuclei N>Z Pauli principle T n > T p? T p > T n SRC n(k) k T p ( n) = n p( n ) d 3 k m nd (k) ~KF K Possible inversion of the momentum sharing 3 Sargsian Phys. Rev. C89 (014) Hen et al., Science 346, 614 (014)

Theoretical prediction Light nuclei (A<1) T n / T p N>Z Variational Monte-Carlo calculations by the Argonne group Neutron Excess [(N-Z)/Z] Z>N: 3 He (N-Z)/Z = -1 T n / T p = 1.31.R. B. Wiringa, R. Sehiavilla. S.C. Pieper, J. Carlson Phys. Rev. C89, 04305 (014) 4

Theoretical prediction - T n / T p Heavy nuclei (A>1) N>Z Low-order Correlation operator Approximation (LCA) Neutron Excess [(N-Z)/Z] Ryckebusch, J.Phys G4 (015). 5

Analysis I Simple np-dominance model n p (k) k0 : n M.F. η n = M.F. p ( k) k< k 0 A a ( A / d ) nd ( k) Z k> k 0 * 300 MeV/c * kf ( k): 1A-1 A * Wood-Saxon * Serot- Walecka * Ciofi & Simula 80% ~80% ~80% n d ( k) : AV18 NN potential ~0% ~k 0 ~K a ( A/ d): Scaling factor η determined by: (for neutrons: Z N) 0 n p A- 0% n p(n)( k) d k=1 3 6 Sargsian Phys. Rev. C89 (014) Hen et al., Science 346 (014)

Analysis I T n / T p Simple np-dominance model N>Z Neutron Excess [(N-Z)/Z] k 3 T p ( n) = n p ( n) d k m 7

Calculation Measurement Simple estimate based on np-dominance 08 protons k>k Pb : Z =8 0 R P= =0.3 protons k<k 8 0 F Rn = F SRC fractions SRC=0% N =16 neutronsk> k F neutronsk< k F 0 =0.19 16 0 ns o t o r p Neutron Excess [(N-Z)/Z] 8

The goal: A(e,e' N) high/ low Extracting 1 C ( e,e ' N ) high/ low ratios ( N=n/ p) The steps: * Identify (e,e'n) mean-field events (low missing momentum) * Identify (e,e'n) N-SRC events (high missing momentum) * Extract ratios and their uncertainties 9

Analysis I Analysis II Future plans Simple prediction based on the np-dominance model A(e,e' n) high/ low SRC fractions 1 C ( e,e ' n) high/ low A(e,e' p) high/ low 1 C ( e,e ' p) high/ low ns o t o r p # A(e,e' N ) neu tron s Neutron Excess [(N-Z)/Z] n (k)k dk SRC n (k)k dk M.F. k< k 0 k> k 0 10

Data-Mining EG Experiment Run at 004 in Hall-B 5.014 GeV electron beam Data set for: Deuterium + Solid target ( 1C / 7 Al / 56 Fe / 08 Pb ) Electron Vertex [cm] 11

Hard knocked-out reactions (e,e'n) & (e,e'p) Incident electron Scattered electron γ* Not detected Recoil partner proton / neutron Knocked-out neutron / proton 1

Particle Identification p p = p n 1.5 GeV / c Δ p/ p: p n 1% 10% El Fassi, Phys. Lett B 71, (01) Hen, Phys. Rev. C 85, 01 Hen, Science 346, 614 (014) Detecting neutrons in CLAS EC (M. Braverman TAU thesis, 014) 13

Detecting neutrons in CLAS o 8 θ 45 o * Hit inside the EC fiducial cut Neutral particle Y [cm] * No signals from Drift-Chambers & Time-Of-Flight Counters X [cm] * n/γ separation: β<0.95 Neutron β 14

Neutron resolution & detection efficiency σ ϵ P n [ GeV / c] P n [ GeV / c] d ( e, e ' p π+π-n) ϵ= d ( e, e ' p π+π)- n + - Using an exclusive reaction d (e, e ' p π π n) 15

Motivation Analysis I Future plans Analysis of QE events: I. Identifying A(e,e'N) mean-field events II. Identifying A(e,e'N) high-momentum events N=n/p 16

Motivation Analysis II Selecting M.F. QE events Emiss [GeV ] protons neutrons 0.5 0.5 0.4 0.4 0.3 0.3 0. 0. 0.1 0.1 0.1 0. 0.3 0.4 0.5 0.1 0. 0.3 0.4 0.5 Pmiss [GeV /c] Problem: QE peak: Pmiss<0.5 GeV/c Emiss<0.08 GeV p miss = p N q Poor resolution in the EC - Δ P 0.1GeV / c Emiss =ω T N T B 17 ONeill et al., Phys. Lett. B 87 (1995), Abbott et al. Phys. Rev. Lett. 80 (1998), Garrow et al. Phys. Rev. C. 66 (00)

Motivation Solution I Using electron & nucleon angular cuts Protons QE cuts:pmiss<0.5 GeV/c Emiss<0.08 GeV Before the QE cuts y θ pq [deg.] After the QE cuts ω [GeV ] y [( M A 0.05< y< 0.5 0.95< ω<1.7gev W = ( M + ω ) q + ω) λ M W q λ ]/ W A 1 A Q [GeV /c ] θ pq < 8o λ =( M A 1 M N + ω ) / 18

Motivation Solution II Using smeared protons to: * Define and test the cuts * Study bin migration σ P n [ GeV / c] P p P smeared = Gauss(P p,σ ) P p Psmeared [GeV /c] 19

neutrons 0.5 0.5 0.4 0.4 Emiss [GeV ] Emiss [GeV ] smeared protons Analysis II 0.3 0. 0.1 0.3 0. 0.1 0.1 0. 0.3 0.4 0.5 Pmiss [GeV /c ] With cuts: 0.05 < y < 0.5 0.1 0. 0.3 0.4 0.5 Pmiss [GeV /c ] 0.95< ω<1.7gev θ pq < 8 o Problem: How to determine the Pmiss and Emiss cuts? 0

False Positive & Negative probabilities bad event good event (un-smeared p) 1

False Positive & Negative probabilities bad event smeared p good event (un-smeared p)

False Positive & Negative probabilities bad event smeared p False positive good event (un-smeared p) False negative 3

False Positive & Negative probabilities bad event smeared p False positive good event (un-smeared p) False negative Goal: Find cuts that minimize false positive & negative 4

Analysis II False Negative [%] False Positive [%] False Positive & Negative probabilities smeared p/n cuts: 'impurity' Emiss <[GeV ] P miss <0.3GeV /c, Emiss <0.19 GeV un-smeared p cuts: 'inefficiency' P miss <0.5GeV /c, Emiss <0.08 GeV False Positive False Negative 10 % Pmiss cut[gev /c] 5

Analysis I The selected cuts: smeared protons P miss <0.3GeV /c Emiss <0.19 GeV un-smeared protons P miss <0.5GeV /c Emiss <0.08 GeV 0.05< y< 0.5 0.95< ω<1.7gev o θ pq < 8 False Positive False Negative 10 % 6

Motivation Analysis I Future plans Analysis of QE events: Identifying A(e,e'N) mean-field events Identifying A(e,e'N) high-momentum events N=n/p 7

Motivation st 1 step: (e,e'p): Identify high momentum events following analysis by O. Hen (Phys. Rev. C 85, 01) nd step: (e,e'n): Modifying the cuts * Low statistics * Identifying the leading nucleon x B >1.1 P N 0.6 q 1.1 θ pq 5 * Poor resolution o smeared protons 8

Analysis I False Negative [%] False Positive [%] False Positive & Negative probabilities smeared p/n cuts: M miss < [GeV /c ] 'impurity' 0.4<P miss <1GeV /c, M miss <1.175GeV /c un-smeared p cuts: 'inefficiency' Pmiss lower cut [GeV /c] 0.3<P miss<1gev /c, M miss <1.1GeV /c False Positive False Negative 15 % 9

Analysis I The selected cuts: smeared protons un-smeared protons x B >1.1 0.6< p / q <1.1 x B >1. 0.6< p / q <0.96 0.4<P miss <1GeV / c M miss <1.175GeV / c 0.3<P miss<1gev /c M miss <1.1GeV /c θ pq < 5o θ pq < 5o False Positive False Negative 15 % 30

Analysis I Future plans Compare smeared & un-smeared protons A (e, e ' p) C (e,e ' p) smeared protons un-smeared protons SRC Mean-Field A Next step: Blind analysis for neutrons 31

Results 3

A(e,e'n)/A(e,e'p) ratios SRC σ A (e,e' p)/ σ ep σ A (e,e' n)/ σ en Mean-Field Neutron Excess ( N Z)/ Z 33

A(e,e'n)/A(e,e'p) ratios SRC σ A (e,e' p)/ σ ep σ A (e,e' n)/ σ en Mean-Field Neutron Excess ( N Z)/ Z 34

A(e,e'n)/A(e,e'p) ratios SRC σ A (e,e' p)/ σ ep σ A (e,e' n)/ σ en Mean-Field Neutron Excess ( N Z)/ Z 35

A(e,e'n)/A(e,e'p) ratios SRC σ A (e,e' p)/ σ ep σ A (e,e' n)/ σ en Mean-Field Neutron Excess ( N Z)/ Z 36

SRC Pair Fraction [%] np-dominance in N-SRC A np fractions extracted from (e,e'p) & (e,e'pp) events: #np = #p - #pp 37 O. Hen et al., Science 346, 614 (014)

Protons and neutrons super ratios A( e,e ' N )high / A(e,e' N)low 1 C ( e,e ' N )high / C (e,e' N )low SRC fractions 1 Neutron Excess [(N-Z)/Z] Correlated p go n go 38

Protons and neutrons super ratios A( e,e ' N )high / A(e,e' N)low 1 C ( e,e ' N )high / C (e,e' N )low SRC fractions 1 Neutron Excess [(N-Z)/Z] Our simple model works 39

Protons and neutrons super ratios A( e,e ' N )high / A(e,e' N)low 1 C ( e,e ' N )high / C (e,e' N )low T n / T p SRC fractions 1 Neutron Excess [(N-Z)/Z] Protons move faster than neutrons in N>Z nuclei > 40

What happens in N>>Z? protons neutrons T p / T n n-star?? Neutron Excess [(N-Z)/Z] 41

A (e, e' n) C (e,e ' n) To be continued by: Neutrons transparency ratios Detecting neutrons in CLAS LAC 3N- SRC )e,e'npp( 4

Acknowledgment Data-Mining collaboration CLAS collaboration I would like to thank the organizers for the invitation 43

Backup Slides 44

Counting high-momentum nucleons Incident electron Scattered electron γ* High-momentum nucleons can be selected by restricting only the e kinematics.

Detecting neutrons in CLAS o 8 θ 45 o * Hit inside the EC fiducial cut Y [cm] * No signals from Drift-Chambers & Time-Of-Flight Counters Neutral particle X [cm] * n/γ separation: β<0.95 (β<0.936) Neutron β 46

+ Neutron resolution & detection efficiency σ ϵ P n [ GeV / c] P n [ GeV / c] d ( e, e ' p π+π-n) ϵ= d ( e, e ' p π+π)- n + - Using an exclusive reaction d (e, e ' p π π n) 47

Motivation Solution I Using electron & nucleon angular cuts Protons QE cuts:pmiss<0.5 GeV/c Emiss<0.08 GeV Before the QE cuts y θ pq [deg.] After the QE cuts ω [GeV ] y [( M A 0.05< y< 0.5 0.95< ω<1.7gev W = ( M + ω ) q + ω) λ M W q λ ]/ W A 1 A Q [GeV /c ] θ pq < 8o λ =( M A 1 M N + ω ) / 48

Motivation Solution II Using smeared protons to: * Define and test the cuts * Study bin migration σ P n [ GeV / c] P p P smeared = Gauss(P p,σ ) P p Psmeared [GeV /c] 49

Analysis II Future plans Sanity Check: Mean-Field ratios R σ ep (n) = ϵτ G E +G M A(e,e ' p)/z A(e,e' n)/n Q τ=, 4 M N 1 σ ep /σ en [1] Data 1 C 7 Al θ ϵ=[1+(1+τ )tan ( e )] 56 Fe 08 Pb Taken into account: Acceptance correction & detection efficiency (different for p/n), transparency 50 [1] W. P. Ford, S. Jeschonnek & J. W. Van Orden, arxiv:1411.3306v1 [nucl-th] (014)

Blind analysis Ratios for neutrons: A(e,e'n)/C(e,e'n) σ A /σ C A A Opportunity for a 1st measurement of neutron nuclear transparency! 51

Comparing un-smeared protons Emiss <0.08GeV QE cuts: P miss <0.5GeV / c y All un-smeared protons θ p [ deg. ] y EC un-smeared protons 5

Comparing un-smeared protons xb y QE events Q [GeV /c ] EC un-smeared protons Q [GeV /c ] All un-smeared protons x b 1 53 ω [GeV ] ω [GeV ]

Checking the event selection Energy momentum conservation: ' (Ebeam,(0,0, Ebeam))+(M N, 0)=(E, P e' )+(E N, P N ) neutrons Pn [GeV /c] P p [GeV /c] smeared protons P N = ( E+ M N P e ' ) M N Pe ' [GeV / c] Pe ' [GeV / c] 54

Checking the event selection From energy momentum conservation: ϕ N ϕ e ' =180 smeared protons ϕ p ϕe ' [deg.] o neutrons ϕ n ϕe ' [deg.] 55

Comparing the smeared protons and neutrons smeared protons Pe [GeV /c] ω[gev ] neutrons θe [deg.] y Q [GeV /c ] xb 56

Comparing the smeared protons and neutrons smeared protons neutrons P p/n [GeV /c] θ p/n [deg.] θ pq/nq [deg.] ϕ p/n ϕ e [deg.] 57

Applying corrections protons neutrons * Coulomb correction * Detection efficiency * Detection efficiency * Acceptance correction * Acceptance correction 58

Protons simulation * 10,000 electrons from the data. * Proton momentum & scattering angle uniformly distributed. * 100xphi angle uniformly distributed. * Running through CLAS MC simulation. * Dividing event by event by the ratio of reconstructed/generated. 59

Protons simulation - results Sector #1 Sector # Sector #3 Sector #4 Sector #5 Sector #6 60

Uncertainties of the event selection Cut Cuts sensitivity Range C -0.05<y<0.5 ±0.05 0.95<ω<1.7 GeV Fe Pb 0.84% 0.83% 0.58% 0.81% ±0.05 GeV.1% 1.9% 1.9% 1.7% ±1º.0% 1.8% 1.5% 1.4% 1.3<Q < 3.5 GeV / c ±0. GeV²/c² 0.61% 0.39% 0.68% 0.35% Pmiss < 0.3 GeV / c ±0.05 GeV/c 0.8% 0.49% 0.56% 0.38% Emiss <0.4 GeV ±0.0 GeV 1.9%.%.1%.1% EC fiducial cut: 10 cm 30 cm 0.1% 0.11% 0.10% 0.09% θ pq < 8 o Al 61

Contributions to the uncertainty Nuclei A(e,e'p)/A(e,e'n) Statistics C.37±0.3 Al Neutron Effic. Simulation Event selection ±0.15 (59%) ±0.07 (7%) ±0.031 (11%) ±0.19 (74%).36±0.6 ±0.19 (73%) ±0.08 (9%) ±0.030 (11%) ±0.17 (6%) Fe.48±0.4 ±0.15 (6%) ±0.07 (9%) ±0.03 (1%) ±0.18 (75%) Pb.1±0.4 ±0.18 (75%) ±0.09 (37%) ±0.034 (1%) ±0.13 (54%) 6

Protons and neutrons M.F ratios np-dominance model: protons M.F. ratios neutrons Data: protons neutrons A Corrected for transparency and normalized by Z (N). 63

Motivation Analysis I Future plans Identifying the Leading Nucleon smeared protons neutrons P p / q P n / q θ pq [deg.] un-smeared protons P p / q We adopted the cuts (O. Hen 01): 0.6 P N q 0.96 θ pq 5 o 64

Analysis I Missing Mass cut M miss=(q+m N P lead ) un-smeared protons neutrons M miss [GeV /c ] M miss mean+mπ =1.1GeV /c smeared protons M miss [GeV /c ] M miss <? 65

Future plans The selected events: This analysis Proton analysis (smeared protons & neutrons) (O. Hen et al.) x B >1.1 x B > 1. 0.6< p/q<0.96 0.6< p/q<0.96 θ pq<5o θ pq<5o M miss <1.GeV /c 0.4<Pmiss <1GeV /c M miss <1.1GeV /c 0.3<P miss <1GeV /c 66

Comparing smeared protons & neutrons distributions: Pe [GeV /c] Q [GeV /c ] θe [deg.] ω[gev ] xb 67

Comparing smeared protons & neutrons distributions: P p/n [GeV /c] θ p/n [deg.] Pmiss [GeV /c] θ pq/nq [deg.] 68

Analysis I Missing energy distribution Emiss [GeV ] Emiss [GeV ] 69 Emiss [GeV ]

A(e,e'p)/C(e,e'p) ratios (for smeared protons) Corrections: 1. Normalization: target density & beam charge (FC) C Al Fe Pb Beam charge 3581.8 719.4 563.3 5079.6 Thickness [g/cm²] 0.3 0.156 0.315 0.159. Radiative correction 3. False positive & negative probabilities C Al Fe Pb False positive [%] 15.1 14.5 15.0 14. False negative [%] 14.9 14.7 14.8 14.6 70

Radiative Correction Done using Misak code (CLAS NOTE 90-007) for inclusive (e,e') processes Input file: 71

θe [deg.] Output file: E [GeV ] σ σ R σ R /σ ' xb For each target 34 files: 13.5<θe <30[deg.] Final correction: Nuclei C Al Fe Pb Correction factor 0.776 0.785 0.79 0.74 7

Contributions for the uncertainty Al/C Fe/C Pb/C.0±0.1 3.±0.3 7.6±0.8 Event selection ±0.13 (9%) ±0.5 (80%) ±0.75 (93%) False positive & negative ±0.0 (14%) ±0.03 (10%) ±0.08 (10%) Statistics ±0.08 (57%) ±0.06 (0%) ±0.15 (19%) σ A /σ C 73

Protons and neutrons high momentum ratios High momentum ratios np-dominance model: protons * * neutrons Data: protons neutrons A Corrected for transparency and normalized by Z (N) 74

Motivation Analysis II Future plans A(e,e'p)/A(e,e'n) SRC ratios Not normalized by Z/N! (e,e' p) (e,e' n) σ ep /σ en [1] Data 1 C 7 Al 56 Fe 08 Pb Corrections: Acceptance correction & detection efficiency (different for p/n), transparency 75 [1] W. P. Ford, S. Jeschonnek & J. W. Van Orden, arxiv:1411.3306v1 [nucl-th] (014)

Spectroscopic factors for (e, e p) reactions show only 60 70% of the expected single particle strength. L. Lapikas, Nucl. Phys. A553, 97c (1993) MISSING : Correlations Between Nucleons SRC ~RN LRC ~RA Benhar et al., Phys. Lett. B 177 (1986) 135.

Future Experiments 78

Momentum distribution in A=3 asymmetric nuclei p n p Nucleon counting Measure ³He(e,e'p)/³He(e,e'n) ratio Low accuracy due to the neutron measurement 79

Approved experiment at Jlab Hall-A (E1-14-011) Mirror nulcei p n n p n n p in ³H = n in ³He p Measure ³He(e,e'p)/³H(e,e'p) ratio MARATHON target HRS Spectromter Hall-A 80

CaFe Experiment Proposed for JLab Hall-C protons neutrons 0 0 6 8 0 8 81

What do we already know? (e,e ) cross-section ratios at xb>1 are sensitive to the total number of SRC pairs E08-014 Hall-A Data 48 Ca: + 0% nucleons, +0% SRC pairs! Z. Ye Ph.D. Thesis, UVA. ArXiv: 1408.5861 (014) The (e,e ) reaction can not distinguish protons and neutrons need (e,e p) 8 Ryckebusch, Vanhalst & Cosyn, arxiv:1405.3814v3 [nucl-th] (015). Neutron Excess [(N-Z)/Z]

The observable (e,e p) cross-section Ratios for: A1 ( e,e' p) SRC/ Mean Field A ( e,e ' p) SRC / Mean Field 40 48 54 A= Ca, Ca, Fe will tell us about pairing of external nucleons 40 with the Ca core. Kinematics: 83

Analysis I N - Short Range Correlations (SRC) k A pair with: * Large relative momentum (k rel >k F ) * Small C.M. momentum (k CM < k F ) k 1 k1 > kf Single nucleons k > k F k 1 k N -SRC 84

Momentum distribution 1 C (Ciofi, PRC 96) Can be explained by correlations. n(k) [fm³] High-momentum tail: Cor rela ti HO ons P [GeV/c] Can be explained by N-SRC dominance n(k) [fm³] Similar shape for all nuclei: SCALING. Fe C n A (k )=C A nhe3 D (k ) D Adapted from Ciofi degli Atti K [fm] P [GeV/c] na(k) = CA nd(k) 85

Counting high-momentum nucleons Incident electron Scattered electron σa / A σ D / γ* Observed scaling for xb>1.5 & Q²>1.5 GeV²/c² na(k>kf) = a(a) nd(k) Q xb = Mω Hall-C: Fomin et al., PRL 108, 0950 (01) More data: Hall-B: Egiyan et al. PRL. 96, 08501 (006) Hall-B: Egiyan et al. PRC 68, 014313 (003) SLAC: Day et al. PRL 59,47(1987)

Structure of high-momentum nucleons na(k>k0) = a(a) nd(k>k0) K0~1.1kF ~4-5 ~4% = ~0% 1 A- A- ~0% n p ~80% ~KF 87