axel schmidt - weizmann institute of science · axel schmidt march 28, 2017 lns laboratory for...

Short-range correlations in nuclei:

an overview of experimental developments

Axel Schmidt

March 28, 2017

LNSLaboratory for Nuclear Science

1

20% of nucleons in a nucleus belong to

short-range correlated pairs.

kF 2kF 3kF

Probability

Nucleon momentum

Fermi gas in a box

kF 2kF 3kF

2

20% of nucleons in a nucleus belong to

short-range correlated pairs.

kF 2kF 3kF

High-momentum tail

Probability

Nucleon momentum

Fermi gas in a boxTypical nucleus

kF 2kF 3kF

Characteristics:

60–70% of kinetic energy

Correlated partner

High relative momentum

(> kF )

Low c.o.m momentum

(< kF )

≈ 90% np pairs for nucleons

between 300–600 MeV

3

We can probe SRC pairs with hard knock-outs.

Probe: e–, p, γ...

Recoil nucleon Leading nucleon

4

We can probe SRC pairs with hard knock-outs.


5

Example: high-resolution spectrometers

Jefferson Lab Hall A

25 m

6

Example: high-resolution spectrometers

Jefferson Lab Hall A

e–

Leadingproton

Recoilnucleon

e– beam

7

Example: large acceptance spectrometers

CLAS (Hall B)

Leadingproton

Scattered e–Recoil proton

Toroid MagnetIncoming e–

8

An experimental overview of SRC pairs

1 The Past

Previous experiments that tell us what we know

2 The Present

Exciting recent developments

3 The Future

What questions do we want to answer?

9


1 The Past


2 The Present


3 The Future


10

Early signs of short-range correlations

came from inclusive eA scattering.


Measure:

1 Scattering angle

2 Momentum

Kinematical variables:

1 Q2 = −(pe − p′e)2 : resolution scale

2 xB = Q2/2m(E − E ′) : dynamic scale

11

High-momentum nuclei can be selected

by restricting only the e− kinematics.

1 kF

2 kF

3 kF

0.5 1 1.5 2

InterestingStrucknucleon

momentum

more energy transfer ←− xB −→ more momentum transfer

1 kF

2 kF

3 kF

0.5 1 1.5 2

Inelastic

ForbiddenForbidden

12

High-xB cross sections scale!

1

2

3

1

2

3

2

4

1 1.25 1.5 1.75 2

4He/3He

12C/3He

56Fe/3He

xB

3·σA

A·σ3He

K.S. Egiyan et al. PRL 96, 082501(2006)

1 kF

2 kF

3 kF

0.8 1 1.2 1.4 1.6 1.8 2

Interesting

Nuc

leon

mom

entu

m

xB −→ more momentum transfer

1 kF

2 kF

3 kF

0.8 1 1.2 1.4 1.6 1.8 2

Forbidden

Scaling constant a2:

σA = a2 ×A

2σd

13

Tagging a recoil ensures high momentum.


14

Tagging a recoil ensures high momentum.


15

Without tagging, scaling starts at xB ≈ 1.5.

2

4

6

8

1 1.2 1.4 1.6 1.8

σHe2σd

xB

N. Fomin et al., PRL 108 092502 (2012)

16

Recoil tagging can extend the scaling region!

2

4

6

8

1 1.2 1.4 1.6 1.8

PRELIMINARY

σHe2σd

xB

N. Fomin et al., PRL 108 092502 (2012)Analysis by N. Muangma (Hall A)

17

Conclusions from inclusive scattering:

2

4

6

8

1 1.2 1.4 1.6 1.8

PRELIMINARY

σHe2σd

xB

N. Fomin et al., PRL 108 092502 (2012)Analysis by N. Muangma (Hall A)

1 kF

2 kF

3 kF

0.8 1 1.2 1.4 1.6 1.8 2

Nuc

leon

mom

entu

m

xB −→ more momentum transfer

1 kF

2 kF

3 kF

0.8 1 1.2 1.4 1.6 1.8 2

Forbidden

Universal shape to

high-momentum tail

Independent of size/density

Approximately 20% of nucleons

Hints of correlated pairs.

18

Exclusive measurements show correlated pairs.


19

Correlated pairs are back-to-back.

-1

-0 .8

-0 .6

-0 .4

-0 .2

0

0 .2

0 .4

0 .6

0 .8

1

0.05 0.1 0 .15 0.2 0 .25 0.3 0 .35 0.4 0 .45 0.5 0 .55-1

-0 .8

-0 .6

-0 .4

-0 .2

0

0 .2

0 .4

0 .6

0 .8

1

0.05 0.1 0 .15 0.2 0 .25 0.3 0 .35 0.4 0 .45 0.5 0 .55-1

-0 .8

-0 .6

-0 .4

-0 .2

0

0 .2

0 .4

0 .6

0 .8

1

0.05 0.1 0 .15 0.2 0 .25 0.3 0 .35 0.4 0 .45 0.5 0 .55-1

-0 .8

-0 .6

-0 .4

-0 .2

0

0 .2

0 .4

0 .6

0 .8

1

0.05 0.1 0 .15 0.2 0 .25 0.3 0 .35 0.4 0 .45 0.5 0 .55

pn(GeV /c)

cos

γ

5.9 GeV/c, 988.0 GeV/c, 989.0 GeV/c, 98

5.9 GeV/c, 947.5 GeV/c, 94

Recoil neutron momentum [GeV]

Leading

Recoil

γ

Parallel

Anti-parallel

J.L.S. Aclander et al., Phys. Lett. B 453, 211 (1999)

A. Tang et al., Phys. Rev. Lett. 90, 042301 (2003)

E. Piasetzky et al., PRL 97 162504 (2006)

p scattering from Carbon:

Always a correlated partner

Anti-parallel momenta

20

From k ≈ 300–600 MeV/c, np pairs dominate.

These kinematic settings covered (e,e'p) missingmomenta, which is the momentum of theundetected particles, in the range from 300 to600 MeV/c, with overlap between the differentsettings. For highly correlated pairs, the missingmomentum of the (e,e'p) reaction is balancedalmost entirely by a single recoiling nucleon,whereas for a typical uncorrelated (e,e'p) event,themissingmomentum is balanced by the sum ofmany recoiling nucleons. In a partonic picture, xBis the fraction of the nucleon momentum carriedby the struck quark. Hence, when xB > 1, thestruck quark has more momentum than the entirenucleon, which points to nucleon correlation. Todetect correlated recoiling protons, a largeacceptance spectrometer (“BigBite”) was placedat an angle of 99° to the beam direction and 1.1m from the target. To detect correlated recoilingneutrons, a neutron array was placed directlybehind the BigBite spectrometer at a distance of 6m from the target. Details of these custom protonand neutron detectors can be found in thesupporting online material (16).

The electronics for the experiment were setup so that for every 12C(e,e'p) event in the HRSspectrometers, we read out the BigBite andneutron-detector electronics; thus, we could deter-mine the 12C(e,e'pp)/12C(e,e'p) and the 12C(e,e'pn)/12C(e,e'p) ratios. For the 12C(e,e'pp)/12C(e,e'p)ratio, we found that 9.5 ± 2% of the (e,e'p) eventshad an associated recoiling proton, as reported in(12). Taking into account the finite acceptance ofthe neutron detector [using the same procedureas with the proton detector (12)] and the neutrondetection efficency, we found that 96 ± 22% ofthe (e,e'p) events with a missing momentum above300 MeV/c had a recoiling neutron. This resultagrees with a hadron beam measurement of(p,2pn)/(p,2p), in which 92 ± 18% of the (p,2p)events with a missing momentum above the Fermi

momentum of 275 MeV/c were found to have asingle recoilingneutroncarrying themomentum(11).

Because we collected the recoiling proton12C(e,e'pp) and neutron 12C(e,e'pn) data simulta-neously with detection systems covering nearlyidentical solid angles, we could also directlydetermine the ratio of 12C(e,e'pn)/12C(e,e'pp). Inthis scheme, many of the systematic factorsneeded to compare the rates of the 12C(e,e'pn)and 12C(e,e'pp) reactions canceled out. Correct-ing only for detector efficiencies, we determinedthat this ratio was 8.1 ± 2.2. To estimate the effectof final-state interactions (that is, reactions thathappen after the initial scattering), we assumedthat the attenuations of the recoiling protons andneutrons were almost equal. In this case, the onlycorrection related to final-state interactions of themeasured 12C(e,e'pn)/12C(e,e'pp) ratio is due to asingle-charge exchange. Because the measured(e,e'pn) rate is about an order of magnitude largerthan the (e,e'pp) rate, (e,e'pn) reactions followedby a single-charge exchange [and hence detectedas (e,e'pp)] dominated and reduced the measured12C(e,e'pn)/12C(e,e'pp) ratio. Using the Glauberapproximation (17), we estimated that this effectwas 11%. Taking this into account, the correctedexperimental ratio for 12C(e,e'pn)/12C(e,e'pp) was9.0 ± 2.5.

To deduce the ratio of p-n to p-p SRC pairs inthe ground state of 12C, we used the measured12C(e,e'pn)/12C(e,e'pp) ratio. Because we used(e,e'p) events to search for SRC nucleon pairs, theprobability of detecting p-p pairs was twice thatof p-n pairs; thus, we conclude that the ratio ofp-n/p-p pairs in the 12C ground state is 18 ± 5(Fig. 2). To get a comprehensive picture of thestructure of 12C, we combined the pair factionresults with the inclusive 12C(e,e') measurements(4, 5, 14) and found that approximately 20% ofthe nucleons in 12C form SRC pairs, consistent

with the depletion seen in the spectroscopy ex-periments (1, 2). As shown in Fig. 3, the com-bined results indicate that 80% of the nucleons inthe 12C nucleus acted independently or as de-scribed within the shell model, whereas for the20% of correlated pairs, 90 ± 10% were in theform of p-n SRC pairs; 5 ± 1.5%were in the formof p-p SRC pairs; and, by isospin symmetry, weinferred that 5 ± 1.5% were in the form of SRCn-n pairs. The dominance of the p-n over p-pSRC pairs is a clear consequence of the nucleon-nucleon tensor force. Calculations of this effect(18,19) indicate that it is robust anddoes not dependon the exact parameterization of the nucleon-nucleon force, the type of the nucleus, or theexact ground-state wave function used to de-scribe the nucleons.

If neutron stars consisted only of neutrons, therelatively weak n-n short-range interaction wouldmean that they could be reasonably well approxi-mated as an ideal Fermi gas, with only perturba-tive corrections. However, theoretical analysis ofneutrino cooling data indicates that neutron starscontain about 5 to 10% protons and electrons inthe first central layers (20–22). The strong p-nshort-range interaction reported here suggeststhat momentum distribution for the protons andneutrons in neutron stars will be substantiallydifferent from that characteristic of an ideal Fermigas. A theoretical calculation that takes intoaccount the p-n correlation effect at relevantneutron star densities and realistic proton concen-tration shows the correlation effect on the mo-mentum distribution of the protons and theneutrons (23). We therefore speculate that thesmall concentration of protons inside neutronstars might have a disproportionately large effectthat needs to be addressed in realistic descriptionsof neutron stars.

References and Notes1. L. Lapikas, Nucl. Phys. A. 553, 297 (1993).2. J. Kelly, Adv. Nucl. Phys. 23, 75 (1996).3. W. H. Dickhoff, C. Barbieri, Prog. Part. Nucl. Phys. 52,

377 (2004).4. K. S. Egiyan et al., Phys. Rev. C Nucl. Phys. 68, 014313

(2003).

Missing Momentum [GeV/c]

0.3 0.4 0.5 0.6

SR

C P

air

Frac

tion

(%)

10

210

C(e,e’p) ] /212C(e,e’pp) /12pp/2N from [

C(e,e’p)12C(e,e’pn) /12np/2N from

C(p,2p)12C(p,2pn) /12np/2N from

C(e,e’pn) ] /212C(e,e’pp) /12pp/np from [

Fig. 2. The fractions of correlated pair combinations in carbon as obtained from the (e,e'pp) and (e,e'pn)reactions, as well as from previous (p,2pn) data. The results and references are listed in table S1.

Fig. 3. The average fraction of nucleons in thevarious initial-state configurations of 12C.

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E. Piasetzky et al., PRL 97 162504 (2006)

R. Shneor et al., Phys. Rev. Lett. 99, 072501 (2007)

R. Subedi et al., Science 320, 1476 (2008)

21

This has been verified over many nuclei.

nuclei. This backward peak is a strong signatureof SRC pairs, indicating that the two emittedprotons were largely back-to-back in the initialstate, having a large relative momentum and asmall center-of-mass momentum (8, 9). This is adirect observation of proton-proton (pp) SRCpairs in a nucleus heavier than 12C.Electron scattering fromhigh–missing-momentum

protons is dominated by scattering from protonsin SRC pairs (9). The measured single-protonknockout (e,e′p) cross section (where e denotesthe incoming electron, e′ the measured scatteredelectron, and p the measured knocked-out pro-ton) is sensitive to the number of pp and np SRCpairs in the nucleus, whereas the two-protonknockout (e,e′pp) cross section is only sensitive tothe number of pp-SRC pairs. Very few of thesingle-proton knockout events also contained asecond proton; therefore, there are very fewpp pairs, and the knocked-out protons predom-inantly originated from np pairs.To quantify this, we extracted the [A(e,e′pp)/

A(e,e′p)]/[12C(e,e′pp)/12C(e,e′p)] cross-section dou-ble ratio for nucleus A relative to 12C. The doubleratio is sensitive to the ratio of np-to-pp SRCpairs in the two nuclei (16). Previous measure-ments have shown that in 12C nearly every high-momentum proton (k > 300 MeV/c > kF) has acorrelated partner nucleon, with np pairs out-numbering pp pairs by a factor of ~20 (8, 9).To estimate the effects of final-state interac-

tions (reinteraction of the outgoing nucleons inthe nucleus), we calculated attenuation factorsfor the outgoing protons and the probability ofthe electron scattering from a neutron in an nppair, followed by a neutron-proton single-chargeexchange (SCX) reaction leading to two outgoingprotons. These correction factors are calculatedas in (9) using the Glauber approximation (22)with effective cross sections that reproduce pre-viously measured proton transparencies (23), andusing themeasured SCX cross section of (24).Weextracted the cross-section ratios and deduced therelative pair fractions from the measured yieldsfollowing (21); see (16) for details.Figure 3 shows the extracted fractions of np

and pp SRC pairs from the sum of pp and nppairs in nuclei, including all statistical, systematic,and model uncertainties. Our measurements arenot sensitive to neutron-neutron SRC pairs. How-ever, by a simple combinatoric argument, even in208Pb these would be only (N/Z)2 ~ 2 times thenumber of pp pairs. Thus, np-SRC pairs domi-nate in all measured nuclei, including neutron-rich imbalanced ones.

The observed dominance of np-over-pp pairsimplies that even in heavy nuclei, SRC pairs aredominantly in a spin-triplet state (spin 1, isospin0), a consequence of the tensor part of the nucleon-nucleon interaction (17, 18). It also implies thatthere are as many high-momentum protons asneutrons (Fig. 1) so that the fraction of protonsabove the Fermi momentum is greater than thatof neutrons in neutron-rich nuclei (25).In light imbalanced nuclei (A≤ 12), variational

Monte Carlo calculations (26) show that this re-sults in a greater average momentum for theminority component (see table S1). The minoritycomponent can also have a greater average mo-mentum in heavy nuclei if the Fermimomenta ofprotons and neutrons are not too dissimilar. Forheavy nuclei, an np-dominance toy model thatquantitatively describes the features of the mo-mentum distribution shown in Fig. 1 shows thatin imbalanced nuclei, the average proton kineticenergy is greater than that of the neutron, up to~20% in 208Pb (16).The observed np-dominance of SRC pairs in

heavy imbalanced nuclei may have wide-rangingimplications. Neutrino scattering from two nu-cleon currents and SRC pairs is important for theanalysis of neutrino-nucleus reactions, which areused to study the nature of the electro-weak in-teraction (27–29). In particle physics, the distribu-tion of quarks in these high-momentum nucleonsin SRC pairs might be modified from that of freenucleons (30, 31). Because each proton has agreater probability to be in a SRC pair than aneutron and the proton has two u quarks foreach d quark, the u-quark distribution modifica-tion could be greater than that of the d quarks(19, 30). This could explain the difference be-tween the weak mixing angle measured on aniron target by the NuTeV experiment and that ofthe Standard Model of particle physics (32–34).In astrophysics, the nuclear symmetry energy

is important for various systems, including neu-tron stars, the neutronization of matter in core-collapse supernovae, and r-process nucleosynthesis(35). The decomposition of the symmetry energyat saturation density (r0 ≈ 0.17 fm−3, the max-imum density of normal nuclei) into its kineticand potential parts and its value at supranucleardensities (r > r0) are notwell constrained, largelybecause of the uncertainties in the tensor com-ponent of the nucleon-nucleon interaction (36–39).Although at supranuclear densities other effectsare relevant, the inclusion of high-momentumtails, dominated by tensor-force–induced np-SRCpairs, can notably soften the nuclear symmetry

energy (36–39). Our measurements of np-SRCpair dominance in heavy imbalanced nuclei canhelp constrain the nuclear aspects of these cal-culations at saturation density.Based on our results in the nuclear system, we

suggest extending the previous measurements ofTan’s contact in balanced ultracold atomic gasesto imbalanced systems in which the number ofatoms in the two spin states is different. Thelarge experimental flexibility of these systems willallow observing dependence of the momentum-sharing inversion on the asymmetry, density,and strength of the short-range interaction.

REFERENCES AND NOTES

1. S. Tan, Ann. Phys. 323, 2952–2970 (2008).2. S. Tan, Ann. Phys. 323, 2971–2986 (2008).3. S. Tan, Ann. Phys. 323, 2987–2990 (2008).4. E. Braaten, in Lecture Notes in Physics (Springer, Berlin, 2012),

vol. 836, p. 193.5. L. Lapikás, Nucl. Phys. A. 553, 297–308 (1993).6. K. I. Blomqvist et al., Phys. Lett. B 421, 71–78 (1998).7. R. Starink et al., Phys. Lett. B 474, 33–40 (2000).8. E. Piasetzky, M. Sargsian, L. Frankfurt, M. Strikman, J. W. Watson,

Phys. Rev. Lett. 97, 162504 (2006).9. R. Subedi et al., Science 320, 1476–1478 (2008).10. K. Sh. Egiyan et al., Phys. Rev. Lett. 96, 082501 (2006).11. N. Fomin et al., Phys. Rev. Lett. 108, 092502 (2012).12. V. R. Pandharipande, I. Sick, P. K. A. deWitt Huberts,

Rev. Mod. Phys. 69, 981–991 (1997).13. J. Arrington, D. W. Higinbotham, G. Rosner, M. Sargsian,

Prog. Part. Nucl. Phys. 67, 898–938 (2012).14. J. T. Stewart, J. P. Gaebler, T. E. Drake, D. S. Jin, Phys. Rev. Lett.

104, 235301 (2010).15. E. D. Kuhnle et al., Phys. Rev. Lett. 105, 070402 (2010).16. Materials and methods are available as supplementary

materials on Science Online.17. R. Schiavilla, R. B. Wiringa, S. C. Pieper, J. Carlson, Phys. Rev. Lett.

98, 132501 (2007).18. M. M. Sargsian, T. V. Abrahamyan, M. I. Strikman, L. L. Frankfurt,

Phys. Rev. C 71, 044615 (2005).19. L. Frankfurt, M. Strikman, Phys. Rep. 160, 235–427 (1988).20. B. A. Mecking et al., Nucl. Inst. Meth. A 503, 513–553

(2003).21. O. Hen et al., Phys. Lett. B 722, 63–68 (2013).22. I. Mardor, Y. Mardor, E. Piasetsky, J. Alster, M. M. Sargsyan,

Phys. Rev. C 46, 761–767 (1992).23. D. Dutta, K. Hafidi, M. Strikman, Prog. Part. Nucl. Phys. 69, 1–27

(2013).24. J. L. Friedes, H. Palevsky, R. Stearns, R. Sutter, Phys. Rev. Lett.

15, 38–41 (1965).25. M. M. Sargsian, Phys. Rev. C 89, 034305 (2014).26. R. B. Wiringa, R. Schiavilla, S. C. Pieper, J. Carlson, Phys. Rev. C

89, 024305 (2014).27. L. Fields et al., Phys. Rev. Lett. 111, 022501 (2013).28. G. A. Fiorentini et al., Phys. Rev. Lett. 111, 022502 (2013).29. Neutrino-Nucleus Interactions for Current and Next Generation

Neutrino Oscillation Experiments, Institute for NuclearTheory (INT) workshop INT-13-54W, University of Washington,Seattle, WA, 3 to 13 December 2013.

30. O. Hen, D. W. Higinbotham, G. A. Miller, E. Piasetzky,L. B. Weinstein, Int. J. Mod. Phys. E 22, 133017 (2013).

31. L. B. Weinstein et al., Phys. Rev. Lett. 106, 052301 (2011).32. G. P. Zeller et al., Phys. Rev. Lett. 88, 091802 (2002).33. G. P. Zeller et al., Phys. Rev. Lett. 90, 239902 (2003).34. I. C. Cloët, W. Bentz, A. W. Thomas, Phys. Rev. Lett. 102,

252301 (2009).35. J. M. Lattimer, Y. Lim, Astrophys. J. 771, 51 (2013).36. A. Carbone, A. Polls, A. Rios, Europhys. Lett. 97, 22001 (2012).37. I. Vidana, A. Polls, C. Providencia, Phys. Rev. C 84, 062801(R)

(2011).38. C. Xu, A. Li, B. A. Li, J. Phys. Conf. Ser. 420, 012090 (2013).39. B.-A. Li, L.-W. Chen, C. M. Ko, Phys. Rep. 464, 113–281

(2008).

ACKNOWLEDGMENTS

This work was supported by the U.S. Department of Energy (DOE)and the National Science Foundation, the Israel ScienceFoundation, the Chilean Comisión Nacional de InvestigaciónCientífica y Tecnológica, the French Centre National de la

616 31 OCTOBER 2014 • VOL 346 ISSUE 6209 sciencemag.org SCIENCE

Fig. 3. The extractedfractions of np (top)and pp (bottom) SRCpairs from the sum ofpp and np pairs innuclei.The green andyellow bands reflect68 and 95% confidencelevels (CLs), respec-tively (9). np-SRC pairs dominate over pp-SRC pairs in all measured nuclei.

SR

C P

air

fract

ion

(%)

100

50

010 50 100 A

C Al Fe Pb

68% C.L.

95% C.L.

np fraction

pp fraction

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O. Hen et al, Science 346, 614 (2014)

22

A quick recap

kF 2kF 3kF

High-momentum tail

Pro

babi

lity

Nucleon momentumkF 2kF 3kF

≈ 20% of nucleons have k > kF .

Mom. distributions scale for large k .

High-momentum nuclei have correlated

partner.

The two momenta are back-to-back.

90% of pairs are neutron-proton.

23


1 The Past


2 The Present


3 The Future


24

Three highlights from CLAS data mining

1 Center-of-mass momentum distributions of short-range pairs

See talk by Erez Cohen!

2 The evolution of np dominance with momentum

3 Kinetic energy in asymmetric nuclei

See talk by Meytal Duer!

25

Only previous data are on 12C and 4He.

See talk by Erez Cohen.

26

The C.M. width saturates for large A.

See talk by Erez Cohen.

27

The C.M. width saturates for large A.

Also see talks by R. Weiss, R. Cruz Torres, C. Ciofi degli Atti

28

np dominance comes from tensor interaction.

Potential

Distance

Scalar part of the NN interaction

29


Tensor interaction dominatesPotential

Distance


30


Tensor interaction dominates

Scalar term takes over

Potential

Distance


We expect that the pp fraction should rise with nucleon momentum.

31

The fraction of pp pairs increases with k .

Analysis by E. Cohen, O. Hen et al.

32

Which species has more kinetic energy

in an asymmetric nucleus?

kF 2kF 3kF

〈Tm〉< 〈TM〉Probability

Nucleon momentum

MajorityMinority

kF 2kF 3kF

33

Which species has more kinetic energy

in an asymmetric nucleus?

kF 2kF 3kF

〈Tm〉> 〈TM〉Probability

Nucleon momentum

MajorityMinority

kF 2kF 3kF

34

There are two competing forces.

kF 2kF 3kF

〈Tm〉< 〈TM〉Probability

Nucleon momentum

MajorityMinority

kF 2kF 3kF kF 2kF 3kF

〈Tm〉> 〈TM〉Probability

Nucleon momentum

MajorityMinority

kF 2kF 3kF

Which is stronger?

35

The np dominance model makes a prediction.

Neutron Excess [(N-Z)/Z]0 0.1 0.2 0.3 0.4 0.5 0.6

pσ(e

,e'p

)/Aσ

nσ(e

,e'n

)/Aσ

0.8

1

1.2

1.4

1.6

1.8

C12 Al27 Fe56 Pb208

M.F.

N/Z

SRC

Pro

babi

lity

Nucleon momentum

MajorityMinority

PRELIMINARY

Analysis by Meytal Duer

36

This suggests that the minority has more energy.


⟩ pT⟨/⟩ n

T⟨

0.8

0.85

0.9

0.95

1

C12 Al27

Fe56

Pb208PRELIMINARY

See talks by Meytal Duer, Misak Sargsian, Jan Ryckebusch.

37


1 The Past


2 The Present


3 The Future


38

Some remaining questions:

How do short-range pairs evolve with A and (N − Z )?What role do SRCs play in the EMC effect?

What happens to the remnant nucleus after hard knockout?

Are there three-N correlations?

39

Two proposals to look at asymmetric nuclei

Tritium (e, e ′p)

Approved for JLab Hall A

(E12-14-011)

Isospin symmetry: 3H ↔ 3He

See F. Hauenstein, R. Cruz Torres

CaFe Experiment

Proposed for JLab Hall C

Look at dependence on mass

and neutron excess40Ca → 48Ca → 54Fe

53

ProtonsDynamicsinNeutronRichNuclei

FocusedStudyofSRCdynamicsin48CabycomparingtotheCaFetriplet.

40Ca

54Fe

48Ca-8Neutrons

+6Proton

s

48Ca

Crust

G.Hagenetal.,NaturePhysics12,186(2016)

40

EMC Effect: nuclear medium changes quark

distributions. 24

8

0 0.2 0.4 0.6 0.8x

0.7

0.8

0.9

1

1.1

R

Lead

0 0.2 0.4 0.6 0.8x

0.7

0.8

0.9

1

1.1

R

NuclearMatter

0 0.2 0.4 0.6 0.8x

0.7

0.8

0.9

1

1.1

R

Oxygen

0 0.2 0.4 0.6 0.8x

0.7

0.8

0.9

1

1.1

R

Calcium

FIG. 5: Ratio functions for 16O, 40Ca and 208Pb showing data for Carbon, Calcium and Gold, respectively, from SLAC-E139[30]. The nuclear matter calculation shows extrapolated data [32].

mesons carry a small amount of plus momentum [21] that vanishes as A ! �. The closer to y = 1 the peak is inFig. 2, the less pronounced the minimum in Fig. 5, all else remaining constant. The second e↵ect is due to M , whichreaches a minimum at 56Fe corresponding to a more pronounced minimum of the ratio function than for A < 56 orA > 56, keeping the scalar meson contribution constant.

Using a Gaussian parameterization of the plus momentum distribution and the experimental binding energy pernucleon via the semi-empirical mass formula, we have modeled the dependence of the minimum of the ratio function,R(x ' 0.72), on the number of nucleons in the nucleus in Fig. 6. The motivation for the use of Gaussian plusmomentum distributions is based on the expansion [5]

F2A(xA) = F2N (xA) + ✏xAF 02N (xA)

+�[2xAF 02N (xA) + x2

AF 002N (xA)] (5.5)

where ✏ ⌘ 1 �Z

dyyfN(y) (5.6)

� ⌘Z

dy(y � 1)2fN (y) (5.7)

The Gaussian parameterization uses the peak location and width, hyi and (hy2i � hyi2)1/2 respectively, from therelativistic Hartree calculations in Fig. 2, and is normalized to unity. This allows us to obtain a plus momentumdistribution for any A with minimal e↵ort. We show the combined e↵ect of scalar mesons and binding energy pernucleon on the ratio function along with the e↵ect of scalar mesons alone using a constant binding energy per nucleonof �8.5 MeV independent of A. It can be seen that a changing M with A has the most e↵ect for nuclei much largerthan Iron, but does not change the general trend that the minimum of the ratio function becomes less pronounced as Aincreases due to the vanishing scalar meson contribution and the peak of the plus momentum distribution approachingunity. This dependence of the binding e↵ect on A is quite di↵erent, both in magnitude and shape, than the trendin experimental data summarized in Ref. [32] which satisfies R(x ' 0.72) ⇠ A�1/3, so that the minimum becomesmore pronounced as A increases. This fully demonstrates the inadequacy of conventional nucleon-meson dynamics to

FIG. 25: The measured EMC e↵ect in gold (Gomezet al., 1994) compared to a nucleons-only calculation of

the EMC e↵ect in lead (Smith and Miller, 2002).

Frankfurt and Strikman (Frankfurt and Strikman, 1987)also included an important relativistic correction knownas the ’flux factor’, which significantly reduces the e↵ectsof nuclear binding.

Going beyond the zero width approximation onlymakes this problem worse (Miller and Machleidt, 1999a).The inclusion of the e↵ects of short-ranged correlationsbroadens the function fN (y) leading to a value of theratio that exceeds unity for small values of x, an e↵ectfound earlier in (Dieperink and Miller, 1991). A viola-tion of the sum rule by a few percent is actually a hugeviolation, because the EMC e↵ect itself is only a 10-15%e↵ect. Thus nucleon-only models are logically inconsis-tent and therefore wrong, even if they can be arrangedto describe the data.

One might argue that sum rules can not be applieddirectly to the data because of the need to incorporateinitial and final state interactions. Nevertheless, in usingthe convolution formalism in the nucleon-only approxi-mation one must use a light-front wave function of thenucleus consistent with the conservation of baryon num-ber and momentum, as discussed above. There is no wayto avoid the constraints imposed by the sum rules.

Indeed, the application of sum rules and simple rea-soning shows that Eq. (21) leads to the result that thenucleon-only hypothesis can not explain the EMC ef-fect. Under the Hugenholz van Hove theorem (Hugen-holtz and van Hove, 1958; Miller and Smith, 2002; Smithand Miller, 2002) nuclear stability (pressure balance) im-plies (in the rest frame) that P+ = P� = MA. But to anexcellent approximation P+ = A(MN � 8 MeV). Thusan average nucleon has p+ = MN � 8 MeV. As carica-tured in Eq. (24), the function fN (y) is narrowly peakedbecause the Fermi momentum is much smaller than thenucleon mass. This means that the value of y in the in-tegral of Eq. (21) is constrained to be very near unity.Thus F2A/A is well approximated by F2N and one getsno substantial EMC e↵ect this way (Miller and Smith,2002; Smith and Miller, 2002). This is shown as the solid

curve in Fig. 25.

FIG. 26: The Drell-Yan process. A quark withmomentum fraction x1 from the incident proton

annihilates with an anti-quark from the nuclear targetwith momentum fraction x2 to form a time-like virtualphoton which decays to a µ+µ� pair. Figure adapted

with slight modifications from (Bickersta↵ et al., 1986).

2. Nucleons plus pions

Nucleons-only models fail, but it was natural to con-sider the idea that the missing momentum ✏ of Eq. (28)is carried by non-nucleonic degrees of freedom, e.g., pions(Ericson and Thomas, 1983; Llewellyn Smith, 1983). Inthis case,

P+ = P+N + P+

⇡ = MA. (29)

Many authors, see the reviews (Arneodo, 1994; Frankfurtand Strikman, 1988b; Geesaman et al., 1995; Piller andWeise, 2000) found that using P+

⇡ /MA = 0.04 is su�-cient to account for the EMC e↵ect. However, if nuclearpions carry 4% of the nuclear momentum (in the restframe the plus component of momentum is the nuclearmass) then there should be more nuclear sea quarks (i.e.,both quarks and anti-quarks). This enhancement shouldbe observable in a nuclear Drell-Yan experiment (Bicker-sta↵ et al., 1984, 1986; Ericson and Thomas, 1984). Theidea, see Fig. 26, is that a quark from an incident proton(defined by a large value of x1) annihilates an anti-quarkfrom the target nucleus (defined by a smaller value ofx2). A significant enhancement of pions would enhancethe anti-quarks and enhance the nuclear Drell-Yan re-action. But no such enhancement was observed (Aldeet al., 1990) as shown in Fig. 27. This caused Bertsch etal. (Bertsch et al., 1993) to announce “a crisis in nucleartheory” because conventional theory does not work. Thisstatement is the verification of the title of this subsection.

The reader might ask at this stage, if the two-pionexchange e↵ects discussed in the Appendix and Sects. I& II lead to a significant pion content and an enhancedsea in the nucleus. Explicit calculations show that thepionic content associated with the tensor potential is verysmall (Miller, 2014).

J. Gomez et al., Phys. Rev. D 49 4348 (1994)

J.R. Smith, G.R. Miller, Phys. Rev. C 65 055206 (2002)

41

There is a curious SRC/EMC correlation.

−0.1

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5 6

2H

3He

4He

9Be

12C

56Fe

197Au

EM

CSl

ope

(−dR/dx B

)

SRC-pair density (a2)

42

We will run two new experiments to investigate

the SRC-EMC connection.

DIS on deuterium, tagging a recoil nucleon.

Large-Angle Detector

(LAD)

Approved for JLab Hall C

e ′ detected in Hall C

spectrometers

Backward-Angle Neutron Detector

(BAND)

Approved for JLab Hall B

e ′ detected in CLAS-12

spectrometer

For more on medium modifications, see talks by Gerry Miller

Larry Weinstein.

43

We want to investigate SRCs with new probes.

Proposals:

1 Inverse kinematics at Dubna

−→ detect remnant nucleus

For related physics: see talk by Thomas Aumann

2 Protons at GSI

3 Photons at GlueX

44

1

CHtarget

TOF

TOF

LAND

P1

P2

12CBeam A-2,Recoil

A new proton scattering experiment at GSI will be

a high-statistics data set of SRC pairs.

Proton scattering enhances

SRC cross section

Use existing HADES,

NeuLAND detectors

Chance to look at 3-nucleon

correlations

See my colleague, George Laskaris

NeuLAND

proton beam

HADES

46

Glue-X: study SRC pairs with real photons.

Glue-X detector at JLab Hall D

Study neutrons with chargedfinal states:

γn −→ π−p

Tests of vector meson

dominance and transparency

See my colleague, Maria Patsyuk

47

To recap:

kF 2kF 3kF

High-momentum tail

Pro

babi

lity

Nucleon momentumkF 2kF 3kF

High momentum tail populated

by short-range correlated pairs

Directly measured with

coincidence experiments

Highlights from CLAS data

mining

Remaining questions

48

To recap:







mining

Remaining questions

49

To recap:






mining

Remaining questions

50

To recap:






mining

Remaining questions

51

To recap:


pσ(e

,e'p

)/Aσ

nσ(e

,e'n

)/Aσ

0.8

1

1.2

1.4

1.6

1.8

C12 Al27 Fe56 Pb208

M.F.

N/Z

SRC






mining

Remaining questions

52

To recap:

−0.1

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5 6

2H

3He

4He

9Be

12C

56Fe

197Au

EM

CSl

ope

(−dR/dx B

)

SRC-pair density (a2)






mining

Remaining questions

53

Conclusions

Our consistent picture of short-range correlations has come from

many different probes and techniques.

A diverse experimental program going forward is important for

making progress on tough remaining problems.

54

axel schmidt - weizmann institute of science · axel schmidt march 28, 2017 lns laboratory for...

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