Novel observation of isospin structure of short-range correlations in calcium isotopes
D. Nguyen, Z. Ye, P. Aguilera, Z. Ahmed, H. Albataineh, K. Allada, B. Anderson, D. Anez, K. Aniol, J. Annand, J. Arrington, T. Averett, H. Baghdasaryan, X. Bai, A. Beck, S. Beck, V. Bellini, F. Benmokhtar, A. Camsonne, C. Chen, J.-P. Chen, K. Chirapatpimol, E. Cisbani, M. M. Dalton, A. Daniel, D. Day, W. Deconinck, M. Defurne, D. Flay, N. Fomin, M. Friend, S. Frullani, E. Fuchey, F. Garibaldi, D. Gaskell, S. Gilad, R. Gilman, S. Glamazdin, C. Gu, P. Guèye, C. Hanretty, J.-O. Hansen, M. Hashemi Shabestari, D. W. Higinbotham, M. Huang, S. Iqbal, G. Jin, N. Kalantarians, H. Kang, A. Kelle her, I. Korover, J. LeRose, J. Leckey, S. Li, R. Lindgren, E. Long, J. Mammei, D. J. Margaziotis, P. Markowitz, D. Meekins, Z.-E. Meziani, R. Michaels, M. Mihovilovi\v, N. Muangma, C. Munoz Camacho, B. E. Norum, Nuruzzaman, K. Pan, S. Phillips, E. Piasetzky, I. Pomerantz, M. Posik, V. Punjabi, X. Qian, Y. Qiang, X. Qiu, P. E. Reimer, A. Rakhman, S. Riordan, G. Ron, O. Rondon-Aramayo, A. Saha, L. Selvy, A. Shahinyan, R. Shneor, S. \v, K. Slifer, P. Solvignon, N. Sparveris, R. Subedi, V. Sulkosky, D. Wang, J. W. Watson, L. B. Weinstein, B. Wojtsekhowski, S. A. Wood, I. Yaron, X. Zhan, J. Zhang, Y. W. Zhang, et al. (4 additional authors not shown)
NNovel observation of isospin structure of short-range correlations in calcium isotopes
D. Nguyen,
1, 2, ∗ Z. Ye, † P. Aguilera, Z. Ahmed, H. Albataineh, K. Allada, B. Anderson, D. Anez, K. Aniol, J. Annand, J. Arrington, T. Averett, H. Baghdasaryan, X. Bai, A. Beck, S. Beck, V. Bellini, F. Benmokhtar, A. Camsonne, C. Chen, J.-P. Chen, K. Chirapatpimol, E. Cisbani, M. M. Dalton,
1, 6
A. Daniel, D. Day, W. Deconinck, M. Defurne, D. Flay, N. Fomin, M. Friend, S. Frullani, E. Fuchey, F. Garibaldi, D. Gaskell, S. Gilad, R. Gilman, S. Glamazdin, C. Gu, P. Gu`eye, C. Hanretty, J.-O. Hansen, M. Hashemi Shabestari, D. W. Higinbotham, M. Huang, S. Iqbal, G. Jin, N. Kalantarians, H. Kang, A. Kelleher, I. Korover, J. LeRose, J. Leckey, S. Li, R. Lindgren, E. Long, J. Mammei, D. J. Margaziotis, P. Markowitz, D. Meekins, Z.-E. Meziani, ‡ R. Michaels, M. Mihoviloviˇc, N. Muangma, C. Munoz Camacho, B. E. Norum, Nuruzzaman, K. Pan, S. Phillips, E. Piasetzky, I. Pomerantz,
28, 36
M. Posik, V. Punjabi, X. Qian, Y. Qiang, X. Qiu, P. E. Reimer, A. Rakhman, S. Riordan,
1, 39
G. Ron, O. Rondon-Aramayo, A. Saha, § L. Selvy, A. Shahinyan, R. Shneor, S. ˇSirca,
42, 33
K. Slifer, P. Solvignon,
30, 6, § N. Sparveris, R. Subedi, V. Sulkosky, D. Wang, J. W. Watson, L. B. Weinstein, B. Wojtsekhowski, S. A. Wood, I. Yaron, X. Zhan, J. Zhang, Y. W. Zhang, B. Zhao, X. Zheng, P. Zhu, and R. Zielinski (The Jefferson Lab Hall A Collaboration) University of Virginia, Charlottesville, Virginia 22904 Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Institut de Physique Nucl´eaire (UMR 8608), CNRS/IN2P3 - Universit´e Paris-Sud, F-91406 Orsay Cedex, France Syracuse University, Syracuse, New York 13244 Old Dominion University, Norfolk, Virginia 23529 Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606 Kent State University, Kent, Ohio 44242 Saint Mary’s University, Halifax, Nova Scotia, Canada California State University, Los Angeles, Los Angeles, California 90032 University of Glasgow, Glasgow G12 8QQ, Scotland, United Kingdom Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 College of William and Mary, Williamsburg, Virginia 23187 China Institute of Atomic Energy, Beijing, China Nuclear Research Center Negev, Beer-Sheva, Israel Universita di Catania, Catania, Italy Duquesne University, Pittsburgh, Pennsylvania 15282 Hampton University, Hampton, Virginia 23668 INFN, Sezione Sanit`a and Istituto Superiore di Sanit`a, 00161 Rome, Italy Ohio University, Athens, Ohio 45701 CEA Saclay, F-91191 Gif-sur-Yvette, France Temple University, Philadelphia, Pennsylvania 19122 University of Tennessee, Knoxville, Tennessee 37996 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 Rutgers, The State University of New Jersey, Piscataway, New Jersey 08855 Kharkov Institute of Physics and Technology, Kharkov 61108, Ukraine Duke University, Durham, North Carolina 27708 Seoul National University, Seoul, Korea Tel Aviv University, Tel Aviv 69978, Israel Indiana University, Bloomington, Indiana 47405 University of New Hampshire, Durham, New Hampshire 03824 Virginia Polytechnic Inst. and State Univ., Blacksburg, Virginia 24061 Florida International University, Miami, Floria 33199 Jozef Stefan Institute, Ljubljana, Slovenia Universit´e Blaise Pascal/IN2P3, F-63177 Aubi`ere, France Mississippi State University, Starkville, Mississippi 39762 The University of Texas at Austin, Austin, Texas 78712 Norfolk State University, Norfolk, Virginia 23504 Lanzhou University, Lanzhou, China University of Massachusetts, Amherst, Massachusetts 01006 Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem, Israel Yerevan Physics Institute, Yerevan 375036, Armenia Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia a r X i v : . [ nu c l - e x ] A p r University of Science and Technology, Hefei, China (Dated: April 27, 2020)Short Range Correlations (SRCs) have been identified as being responsible for the high momentumtail of the nucleon momentum distribution, n(k). Hard, short-range interactions of nucleon pairsgenerate the high momentum tail and imprint a universal character on n(k) for all nuclei at largemomentum. Triple coincidence experiments have shown a strong dominance of np pairs, but thesemeasurements involve large final state interactions. This paper presents the results from JeffersonLab experiment E08014 which measured inclusive electron scattering cross-section from Ca isotopes.By comparing the inclusive cross section from Ca to Ca in a kinematic region dominated bySRCs we provide a new way to study the isospin structure of SRCs.
PACS numbers: 13.60.Hb, 25.10.+s, 25.30.Fj
The na¨ıve nuclear shell model has guided our under-standing of nuclear properties for 60 years and it is stillappealing as a predictive and illustrative nuclear model.This model, with nucleons moving in an average (mean-field) generated by the other nucleons in the nucleus, pro-vides a quantitative account of a large body of nuclearproperties. These include shell closures (“magic num-bers”), the foundation of which is the appearance of gapsin the spectrum of single-particle energies [1].The shell model is not without certain deficits whicharise from what are generally called correlations - ef-fects that are beyond mean field theories such as long-range correlations associated with collective phenomena:giant resonances, vibrations and rotations. In addi-tion, electron-nucleus and nucleon-nucleus scattering ex-periments have unambiguously shown large deviationsfrom the shell model predictions, arising from the occur-rence of strong short-range nucleon-nucleon correlations.These two-nucleon SRCs (2N-SRC) move particles fromthe shell model states to large excitation energies andgenerate a high-momentum tail in the single particle mo-mentum distribution. Consequently, over large range ofA the number of protons found in the valence shells or-bitals is significantly less than expected, typically 60%–70% of the predicted shell model occupancy [2, 3].Inclusive experiments are able to isolate the 2N-SRCthrough selective kinematics: working at large momen-tum transfer ( Q ≥ . ) and small energy transfer( ν ≤ Q m ), corresponding to x = Q mν >
1, where m is the mass of the proton. In this region, it is kinemati-cally impossible for mean field nucleons to contribute andwhere competing inelastic processes are minimized [4–6]. It was through inclusive experiments [7–9] that 2N-SRCs were first revealed by the appearance of predictedplateaus [4] in the A/ H per-nucleon cross section ra-tio of nuclei to the deuteron. The height of the plateauis related to probability of finding a 2N-SRC in nucleusA, relative to the deuteron, indicating that ∼
20% ofthe protons and neutrons in medium-to-heavy mass nu-clei have momenta greater than the Fermi momentum k F (cid:39)
250 MeV [8]. The bulk of these nucleons do notarise in a shell model description as they are the resultof brief short-range interaction among pairs of nucleons giving rise to large relative momenta and modest center-of-mass motion, k CM < k F [4].The isospin dependence of 2N-SRCs has been deter-mined via A( p, p (cid:48) pN ) [10, 11] and A( e, e (cid:48) pN ) [12–14]reactions in which the scattered particle (either a pro-ton or an electron) is measured in coincidence witha high-momentum proton. The struck proton’s initialmomentum, reconstructed assuming plane wave scatter-ing, is approximately opposite that of the second high-momentum nucleon.These measurements exhibit a dominance of np pairsover pp pairs for initial nucleon momenta of 300-600 MeVwhich has been traced to the tensor part of the NN inter-action [15–18]. These triple-coincidence experiments aresensitive to the isospin structure of the SRC through di-rect measurement of the final state nucleons. Because thesignature of large back-to-back momenta is also consis-tent with striking a low-momentum nucleon which rescat-ters, there are large contributions from final state inter-actions (including charge exchange) that need to be ac-counted for in comparing pp and np pairs [12–14]. Isospindependence has never been established in inclusive scat-tering, A( e, e (cid:48) ) until now.We present here new A( e, e (cid:48) ) measurements performedas part of Jefferson Lab experiment E08-014 [19]. Initialresults on the search for three-nucleon SRCs in heliumisotopes were published in Ref. [20]. This work focusedon a measurement of the isospin dependence of 2N-SRCsin the cross section ratio of scattering from Ca and Ca. The excess neutrons in Ca change the relativeratio of potential pp , np , and nn pairs, yielding a dif-ferent isospin distribution of high-momentum pairs dif-ferently for isospin-independent SRCs and np-dominatedSRCs. This can be seen in a simple estimate for thetwo cases. As a starting point, we take the fraction ofnucleons in SRCs to be identical for these two targets,based on the observation of an A-independent value of a , the A/ H cross section ratio for 1 . < x <
2, forheavy nuclei [7, 9]. In the case of isospin-independentSRCs, protons and neutrons will have the same proba-bility of appearing at momenta above k F , giving a crosssection ratio of σ Ca / σ Ca / = (20 σ ep +28 σ en ) / σ ep +20 σ en ) / ≈ .
93 tak-ing σ ep /σ en ≈ .
5, corresponding to the kinematics ofthis experiment. If SRCs are dominated by np pairs, thecross section ratio would be unity for isoscalar nuclei andslightly lower for non-isoscalar nuclei [21–24].Jefferson Lab experiment E08-014 [19] ran during theSpring of 2011. A 3.356 GeV continuous wave electronbeam was directed onto a variety of targets, including H, He, He, C and targets of natural calcium (mainly Ca) and an enriched target of 90.04% Ca (referred toas the Ca and Ca targets, respectively). The scat-tered electrons were detected at angles of θ =21 ◦ , 23 ◦ ,25 ◦ , and 28 ◦ , though no Calcium data was taken at28 ◦ . The data presented here cover a kinematic region of1 . < Q < . and 1 < x < x and applied to the measured yield for eachbin. Pions were rejected (with negligible remaining pioncontamination) by applying additional cuts on both theCerenkov counter and the lead glass calorimeter with effi-ciencies of 99.5% and 99.6% respectively, with a trackingefficiency of 98.5%. Detailed descriptions of the experi-mental setup and data analysis can be found in [28, 29].The angle and momentum of the scattered electronwere reconstructed from the detected track at the VDCsusing a set of optics matrices. The optics from anotherexperiment [30], having the identical magnetic tune asthis experiment, was used for the LHRS. The tune for theRHRS had to be modified because the third quadrupolecouldn’t run at the required field, and lack of a com-plete set of optics data led to a reduced resolution in theRHRS. The reduced resolution impacts the extraction ofthe cross section at large x values where the cross sectionfalls extremely rapidly, requiring larger correction. Be-cause the RHRS was typically taking data in the samekinematics as the LHRS, we use only the data from theLHRS except for the 21 ◦ data, where the largest x val-ues were measured only in the RHRS. For this setting weinclude the ratios from the RHRS, as the smearing has anegligible impact on the cross section ratios in the regionwhere the ratio is flat.The yield for the experiment is simulated using a de- tailed model of the HRS optics and acceptance, withevents generated uniformly and weighted by a radia-tive cross section model [29, 31]. The model uses a y -scaling fit [32, 33] for quasi-elastic cross section (initiallybased on previous data, and iteratively updated to matchthe extracted cross sections from this experiment) and aglobal fit [34] for the inelastic contribution. The Borncross section is extracted by taking the model cross sec-tion and correcting it by the ratio of measured to sim-ulated yield. Comparing the results extracted with thefinal model and the model before being adjusted to matchour data indicates a model uncertainty of 0.5% in boththe absolute cross sections and the target ratios.The cross section ratio obtained from the enrichedand natural Calcium targets are then corrected to yield Ca/ Ca ratio, based on the isotopic analysis of the tar-gets. No correction was applied to the natural Calcium,while the enriched Calcium target had a 9.96% contri-bution of Ca and 90.04% Ca (by number of atoms).Thus, the cross section for Ca was obtained by correct-ing the enriched Ca target data using the measured Cacross sections; the correction is typically 2%. x - - -
10 1 [ nb / s r / M e V ] W / d E ' / d s d (cid:176) = 25 q (cid:176) = 23 q (cid:176) = 21 q Ca Models (cid:176) = 25 q (cid:176) = 23 q (cid:176) = 21 q Ca Models FIG. 1. Ca and Ca cross sections for three different anglesettings, along with the cross section model used in the analy-sis. Uncertainties shown include statistical and point-to-pointsystematic uncertainties; an additional normalization uncer-tainty of 2.7% for Ca and 3.0% for Ca is not shown.
The measured cross sections are presented in Figure 1.For the cross sections, the point-to-point systematic un-certainty is estimated to be 1.9%, with dominant con-tributions coming from the acceptance (1.5%), radiativecorrections (1%), and the model dependence of the crosssection extraction (0.5%). In addition, there is an overallnormalization uncertainty of 2.7%, coming mainly fromthe acceptance (2%), radiative correction (1%), and tar-get thickness (1%). These are the uncertainties for the Ca target, while the dilution correction used to extractthe Ca cross section increases these, giving 2.1% point-to-point and 3.0% normalization uncertainties. x / ) C a s / ) / ( C a s ( (cid:176) = 25 q (cid:176) = 23 q (cid:176) = 21 q FIG. 2. Ratio of the cross section per nucleon for Ca and Ca for three scattering angles. Uncertainties shown includestatistical and point-to-point systematic uncertainties; an ad-ditional normalization uncertainty of 1% is not shown.
The per nucleon cross-section ratio of Ca to Cais presented in Figure 2 for each of the three scatteringangles and in Figure 3 after combining of the data sets.Because the cross section and experimental conditionsare very similar for the two targets, many of the uncer-tainties in the cross sections cancel or are reduced in theratio. The systematic uncertainty on the ratios is 0.9%,dominated by the model dependence in the extraction(0.5%), measurement of the beam charge (0.5%) and theradiative correction (0.5%). An additional 1% normaliza-tion uncertainty, associated with the uncertainty in therelative target thicknesses, is not shown. When combin-ing the angles for Fig. 3, we combine the statistics of theindividual sets and then apply the 0.9% point-to-pointuncertainty (and 1% normalization uncertainty) to thecombined result.Note that the rise from x = 1 to x = 1 . H ratios.This is expected as the shape in the A/ H ratios isdriven by the deuterium cross section, which is nar-rowly peaked at and roughly symmetric about x=1. Theline in Fig. 3 indicates the value of R SRC, the aver-age in the plateau region: 1 . < x <
2. The fit gives R = 0 . . R SRC, and the normal-ization uncertainty of the ratios. The cut dependence istaken to be the RMS scatter of R SRC values fit sepa-rately to the three scattering angles for three differentminimum x values, x min = 1 . , . R SRC = 0 . R SRC = 0 .
93 for these kinematics). So while inclusivescattering cannot isolate contributions from protons and x / ) C a s / ) / ( C a s ( FIG. 3. Ratio of the cross section per nucleon for Ca and Ca combining all three data sets. A 1% normalization un-certainty is not shown. The line indicates the fit for the crosssection ratio in the SRC region neutrons, comparing Calcium isosoptes with different issensitive enough to provide evidence for an enhancementof np pairs over pp and np pairs.To interpret this ratio in terms of relative np , pp , and nn SRC contributions, and to compare these results toobservables from previous measurements, we use a sim-ple model to estimate the inclusive, exclusive, and two-nucleon knockout ratios in terms of a few parameters. Wetake the number of 2N-SRCs to be a product of the num-ber of total pairs, the probability for any two nucleons tobe close enough together to interact via the short-rangeNN interaction ( f sr ), and the probability that the NN in-teraction generates a high-momentum pair ( p NN ). Thetotal number of np , pp , and nn pairs are N Z , Z ( Z − / N ( N − /
2, respectively. The fraction of nucle-ons at short distance, f sr , depends on the nucleus andis assumed to be identical for nn , np , and pp pairs. Theprobability that these nucleons generate high momentumpairs, p np and p pp = p nn , depends on the momentumrange of the initial nucleons, ∆ P i , defined by the experi-ment for coincidence measurements or by the kinematicsin inclusive scattering. Given this, we can express thenumber of np and pp SRCs as: N np = N Z · f sr ( A ) · p np (∆ P i ) (1) N pp = Z ( Z − / · f sr ( A ) · p pp (∆ P i ) (2)While p np and p pp may depend strongly on ∆ P i , weassume that their ratio has a much weaker dependence,as observed in Ref. [14], and so their ratio extracted fromdifferent measurements should be qualitatively compara-ble. This leaves only f sr ( A ) as an unknown. In compar-ing different observables on the same nucleus, e.g. takingthe ratio of A(e,e’pp) to A(e,e’pn), f sr ( A ) cancels out. Inthe limit of large nuclei, any given nucleon will be sen-sitive to short-range interactions with nucleons in somefixed volume, while the number of nucleons grows with A , suggesting that f sr ( A ) should scale as 1 /A . With thisassumption, our model produces a constant value of a for heavy isoscalar nuclei, consistent with the observationof approximate saturation [35].Using this simple approach, we can calculate the num-ber of pp , np , and nn pairs in the Calcium targets, andthen weigh this by the cross section for elastic scatteringfrom the two nucleons in each pair to obtain the inclusivecross section in the SRC region for both targets. In crosssection ratio, only the A dependence of f sr ( A ) remains,and the cross section ratio can then be written in termsof the A dependence of f sr ( A ), the ratio of p np to p pp ,the enhancement factor of np pairs to high momentumrelative to pp and nn pairs. The average value of σ ep /σ en is 2.55-2.60 for these kinematics, this model predicts thecross section ratio to be 0.93 for isospin independence,and 0.972 for np dominance. The np-dominance pre-diction is slightly below unity; the model predicts thatfor an isoscalar nucleus, the fraction of np-SRCs, andthus the cross section per nucleon, would be identical forheavy nuclei. Because Ca has 20 ·
28 potential NP pairs,rather than 24 ·
24 for an isoscalar A=48 nucleus, the ra-tio is suppressed by a factor of (20 · / (24 ·
24) = 0 . . np dominance. Taking intoaccount its uncertainty, we find that p np /p pp > . p np /p pp > . np dominance using theisospin structure of the target, rather than the detectednucleons, to study the isospin structure.Note that the ratio p np /p pp is not directly compara-ble to the enhancement factor of ∼
10 obtained in triplecoincidence experiments [13, 14], as it removes the contri-bution from simple pair counting. For example, He hasfour np pairs and only one pp pair, and thus one wouldexpect np pairs to dominate, even if the generation ofhigh-momentum pairs had no isospin dependence. Us-ing our simple model we can extract p np /p pp from othermeasurements, A(e,e’pp)/A(e,e’pn) or A(e,e’p)/A(e,e’n),allowing for a more direct comparison. As noted before, p np and p pp depend on the momentum of the struck nu-cleon in the initial-state SRC, while for the inclusive case,they correspond to an average over the range probed inthe scattering which depends on Q and the x range ofthe data. Because of this, the extracted enhancementfactor for inclusive scattering corresponds to a range ofmomenta that should be similar, but not identical, tothe momentum range selected in the coincidence knock-out reactions.Writing out the ratio of A(e,e’pp)/A(e,e’pn) in termsof p np /p pp allows us to take the observed ratios and ex-tract the np enhancement factor. For He [14], the pp/npfraction is (5.5 ± .
10. For C, the pp/np fraction is (5.6 ± . < p np /p pp <
11. The full expressions are provided in the supplementarymaterial. These correspond to the lowest P m bins forthe triple-coincidence measurements, P m from roughly400-600 MeV/c, to more closely match the main contri-butions to the inclusive measurement. As noted above,these values are not exactly equivalent to the values ex-tracted from the inclusive scattering, but they paint aconsistent picture of significant np dominance in SRCsover a range of light and heavy nuclei. In conclusion,the per nucleon cross section ratio of Ca/ Ca is con-sistent with significant np dominance in the creation ofSRCs. It shows an enhancement of np pairs over pp pairsat more than the three sigma level.This data provides the first evidence of np domi-nance from inclusive scattering, making use of the isospinstructure of the target rather than the final N N pair.This approach avoids the significant corrections requiredto interpret triple-coincidence measurements, but doesnot provide a quantitative measure of the enhancementfactor because of the small difference between isospin-independent and np-dominance assumptions. A recentexperiment measured the inclusive ratio for scatteringfrom H and He, which is significantly more sensi-tive [36]. The H/ He cross section ratio is approximately0.75 for isospin independence and 1 for np dominance,giving almost an order of magnitude more sensitivitythan the Ca/ Ca ratio, without having to make anyassumption about the A dependence of f sr ( A ) in compar-ing the two nuclei. A measurement of this inclusive crosssection ratio with comparable uncertainties may providethe best quantitative measurement of the enhancementof np pairs at high momentum.We acknowledge the outstanding support from the HallA technical staff and the JLab target group. This workwas supported in part by the Department of Energy’sOffice of Science, Office of Nuclear Physics, under con-tracts DE-AC02-06CH11357 and DE-FG02-96ER40950,and the National Science Foundation, and under DOEcontract DE-AC05-06OR23177, under which JSA, LLCoperates JLab. The Ca isotope used in this researchwas supplied by the Isotope Program within the Officeof Nuclear Physics in the Department of Energys Officeof Science. Experiment E08-014 was developed by Pa-tricia Solvignon whose passing is still mourned by ourcommunity. ∗ contact email: [email protected] † contact email: [email protected] ‡ present address: Argonne National Laboratory § deceased[1] E. Caurier, G. Martinez-Pinedo, F. Nowacki, A. Poves,and A. P. Zuker, Rev. Mod. Phys. , 427 (2005).[2] J. Kelly, Adv. Nucl. Phys. , 75 (1996).[3] L. Lapikas, Nucl. Phys. A , 297 (1993). [4] L. Frankfurt and M. Strikman, Physics Reports , 215(1981).[5] M. M. Sargsian et al. , J. Phys. G29 , R1 (2003).[6] J. Arrington, D. Higinbotham, G. Rosner, andM. Sargsian, Prog. Part. Nucl. Phys. , 898 (2012).[7] L. L. Frankfurt, M. I. Strikman, D. B. Day, andM. Sargsyan, Phys. Rev. C , 2451 (1993).[8] K. S. Egiyan et al. , Phys. Rev. C 68 , 014313 (2003).[9] N. Fomin et al. , Phys. Rev. Lett. , 092502 (2012).[10] A. Tang et al. , Phys. Rev. Lett. , 042301 (2003).[11] E. Piasetzky, M. Sargsian, L. Frankfurt, M. Strikman,and J. W. Watson, Phys. Rev. Lett. , 162504 (2006).[12] R. Shneor et al. , Phys. Rev. Lett. , 072501 (2007).[13] R. Subedi et al. , Science , 1476 (2008).[14] I. Korover et al. , Phys. Rev. Lett. , 022501 (2014).[15] R. Schiavilla, R. B. Wiringa, S. C. Pieper, and J. Carlson,Phys. Rev. Lett. , 132501 (2007).[16] M. Alvioli, C. Ciofi degli Atti, and H. Morita, Phys. Rev.Lett. , 162503 (2008).[17] R. B. Wiringa, R. Schiavilla, S. C. Pieper, and J. Carlson,Phys. Rev. C 78 , 021001 (2008).[18] R. Wiringa, R. Schiavilla, S. C. Pieper, and J. Carlson,Phys. Rev.
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