Article Revealing the short-range structure of the mirror nuclei3H and3He

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Article

Revealing the short-range structure of the

”mirror nuclei” 3H and 3He

S. Li1,2, R. Cruz-Torres3,2, N. Santiesteban1,3, Z. H. Ye4,5D. Abrams6, S. Alsalmi7,41 ,

D. Androic8, K. Aniol9, J. Arrington2,5,∗, T. Averett10 , C. Ayerbe Gayoso10 , J. Bane11 ,

S. Barcus10, J. Barrow11, A. Beck3, V. Bellini12, H. Bhatt13 , D. Bhetuwal13, D. Biswas14,

D. Bulumulla15, A. Camsonne16 , J. Castellanos17, J. Chen10, J-P. Chen16 , D. Chrisman18 ,

M. E. Christy14,16, C. Clarke19 , S. Covrig16, K. Craycraft11, D. Day6, D. Dutta13 , E. Fuchey20,

C. Gal6, F. Garibaldi21, T. N. Gautam14, T. Gogami22 , J. Gomez16, P. Gu `

eye14,18,

A. Habarakada14, T. J. Hague7, J. O. Hansen16, F. Hauenstein15 , W. Henry23 ,

D. W. Higinbotham16 , R. J. Holt5, C. Hyde15, T. Itabashi22, M. Kaneta22 , A. Karki13 ,

A. T. Katramatou7, C. E. Keppel16, M. Khachatryan15, V. Khachatryan19, P. M. King24 ,

I. Korover25 , L. Kurbany1, T. Kutz19 , N. Lashley-Colthirst14 , W. B. Li10, H. Liu26 , N. Liyanage6,

E. Long1, J. Mammei27, P. Markowitz17, R. E. McClellan16, F. Meddi21, D. Meekins16,

S. Mey-Tal Beck3, R. Michaels16, M. Mihoviloviˇ

c28,29,30, A. Moyer31, S. Nagao22, V. Nelyubin6,

D. Nguyen6, M. Nycz7, M. Olson32 , L. Ou3, V. Owen10, C. Palatchi6, B. Pandey14 ,

A. Papadopoulou3, S. Park19, S. Paul10, T. Petkovic8, R. Pomatsalyuk33, S. Premathilake6,

V. Punjabi34 , R. D. Ransome35 , P. E. Reimer5, J. Reinhold17, S. Riordan5, J. Roche24,

V. M. Rodriguez36 , A. Schmidt3, B. Schmookler3, E. P. Segarra3, A. Shahinyan37, K. Slifer1,

P. Solvignon1, S. ˇ

Sirca29,28, T. Su7, R. Suleiman16, H. Szumila-Vance16 , L. Tang16 , Y. Tian38,

W. Tireman39, F. Tortorici12 , Y. Toyama22, K. Uehara22, G. M. Urciuoli21, D. Votaw18 ,

J. Williamson40, B. Wojtsekhowski16 , S. Wood16 , J. Zhang6, X. Zheng6

When protons and neutrons (nucleons) are bound into atomic nuclei, they are close

enough together to feel signiﬁcant attraction, or repulsion, from the strong,

short-distance part of the nucleon-nucleon interaction. These strong interactions lead

to hard collisions between nucleons, generating pairs of highly-energetic nucleons

referred to as short-range correlations (SRCs). SRCs are an important but relatively

poorly understood part of nuclear structure1–3 and mapping out the strength and

isospin structure (neutron-proton vs proton-proton pairs) of these virtual excitations is

thus critical input for modeling a range of nuclear, particle, and astrophysics

measurements 3–5. Hitherto measurements used two-nucleon knockout or

“triple-coincidence” reactions to measure the relative contribution of np- and pp-SRCs

by knocking out a proton from the SRC and detecting its partner nucleon (proton or

neutron). These measurements6–8 show that SRCs are almost exclusively np pairs, but

had limited statistics and required large model-dependent ﬁnal-state interaction (FSI)

corrections. We report on the ﬁrst measurement using inclusive scattering from the

mirror nuclei 3H and 3He to extract the np/pp ratio of SRCs in the A=3 system. We

obtain a measure of the np/pp SRC ratio that is an order of magnitude more precise

than previous experiments, and ﬁnd a dramatic deviation from the near-total np

dominance observed in heavy nuclei. This result implies an unexpected structure in

the high-momentum wavefunction for 3He and 3H. Understanding these results will

improve our understanding of the short-range part of the N-N interaction.

1University of New Hampshire, Durham, New Hampshire 03824, USA 2Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 3Massachusetts Institute of

Technology, Cambridge, Massachusetts 02139, USA 4Tsinghua University, Beijing, China 5Physics Division, Argonne National Laboratory, Lemont, Illinois 60439, USA

6University of Virginia, Charlottesville, Virginia 22904, USA 7Kent State University, Kent, Ohio 44240, USA 8University of Zagreb, Zagreb, Croatia 9California State University,

Los Angeles, California 90032, USA 10 The College of William and Mary, Williamsburg, Virginia 23185, USA 11 University of Tennessee, Knoxville, Tennessee 37966, USA

12 INFN Sezione di Catania, Italy 13 Mississippi State University, Mississippi State, Mississippi 39762, USA 14 Hampton University, Hampton, Virginia 23669, USA 15 Old

Dominion University, Norfolk, Virginia 23529, USA 16 Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA 17 Florida International University,

Miami, Florida 33199, USA 18 Michigan State University, East Lansing, Michigan 48824, USA 19 Stony Brook, State University of New York, New York 11794, USA 20 University

of Connecticut, Storrs, Connecticut 06269, USA 21 INFN, Rome, Italy 22 Tohoku University, Sendai, Japan 23 Temple University, Philadelphia, Pennsylvania 19122, USA 24 Ohio

University, Athens, Ohio 45701, USA 25 Nuclear Research Center -Negev, Beer-Sheva, Israel 26 Columbia University, New York, New York 10027, USA 27 University of

Manitoba, Winnipeg, MB R3T 2N2, Canada 28 Joˇ

zef Stefan Institute, 1000 Ljubljana, Slovenia 29 Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana,

Slovenia 30 Institut f ¨

ur Kernphysik, Johannes Gutenberg-Universit¨

at Mainz, DE-55128 Mainz, Germany 31 Christopher Newport University, Newport News, Virginia 23606, USA

32 Saint Norbert College, De Pere, Wisconsin 54115, USA 33 Institute of Physics and Technology, Kharkov, Ukraine 34 Norfolk State University, Norfolk, Virginia 23529, USA

35 Rutgers University, New Brunswick, New Jersey 08854, USA 36 Divisi´

on de Ciencias y Tecnolog´

ıa, Universidad Ana G. M´

endez, Recinto de Cupey, San Juan 00926, Puerto

Rico 37 Yerevan Physics Institute, Yerevan, Armenia 38 Syracuse University, Syracuse, New York 13244, USA 39 Northern Michigan University, Marquette, Michigan 49855,

USA 40 University of Glasgow, Glasgow, G12 8QQ Scotland, UK 41 King Saud University, Riyadh 11451, Kingdom of Saudi Arabia * email:JArrington@lbl.gov

arXiv:2210.04189v1 [nucl-ex] 9 Oct 2022

Article

Nuclei are bound by the attractive components of the nucleon-nucleon (NN) interaction and the low-momentum

part of their wavefunction is accurately described by mean-ﬁeld or shell-model calculations9. These calculations show

that the characteristic nucleon momenta in nuclei grow with target mass number A in light nuclei, becoming roughly

constant in heavy nuclei. The strong, short-distance components of the NN interaction - the tensor attraction and

short-range repulsive core - give rise to hard interactions between pairs of nucleons that are not well captured in mean-

ﬁeld calculations. These hard interactions create high-momentum nucleon pairs - two-nucleon short-range correlations

(2N-SRCs) - which embody the universal two-body interaction at short distances and have a common structure in all

nuclei1, 10.

SRCs are challenging to isolate in conventional low-energy measurements, but can be cleanly identiﬁed in inclusive

electron scattering experiments for carefully chosen kinematics. Elastic electron-proton (e-p) scattering from a station-

ary nucleon corresponds to x=Q2/(2Mν) = 1, where Q2is the four-momentum transfer squared, νis the energy

transfer, and Mis the mass of the proton. Scattering at ﬁxed Q2but larger energy transfer (x < 1) corresponds to

inelastic scattering, where the proton is excited or broken apart. Scattering at lower energy transfer (x > 1) is kinemat-

ically forbidden for a stationary proton, but larger xvalues are accessible as the initial nucleon momentum increases,

providing a way to isolate scattering from moving nucleons and thus study high-momentum nucleons in SRCs2, 10.

Inclusive A(e,e0) measurements at SLAC10 and Jefferson Lab (JLab)11, 12 compared electron scattering from heavy

nuclei to the deuteron for x > 1.4at Q2>1.4GeV2, isolating scattering from nucleons above the Fermi momentum.

They found identical cross sections up to a normalization factor, yielding a plateau in the A/2H ratio for x > 1.4, con-

ﬁrming the picture that high-momentum nucleons are generated within SRCs and exhibit identical two-body behavior

in all nuclei. Using this technique, experiments have mapped out the contribution of SRCs for a range of light and

heavy nuclei10–13.

Figure 1 |Ratio of np-SRC to pp-SRCs in nuclei. The ratio of np- to pp-SRC number from two-nucleon knockout measurements: solid

circles8, solid triangle7, and hollow circle6. Error bars indicate the 1σuncertainties, and the shaded band indicates the average ratio and 68%

conﬁdence level region (excluding Ref.6for which the FSI corrections applied are estimated to be ∼70% too small8).

Because inclusive A(e,e0) scattering sums over proton and neutron knockout, it does not usually provide informa-

tion on the isospin structure (np, pp, or nn) of these SRCs. The isospin structure has been studied using A(e,e0pNs)

triple-coincidence measurements in which scattering from a high momentum proton is detected along with a spectator

nucleon, Ns(either proton or neutron), from the SRC pair with a momentum nearly equal but opposite to the initial

proton. By detecting both np and pp ﬁnal states, these measurements extract the ratio of np- to pp-SRCs and ﬁnd that

np-SRCs dominate6–8 while pp-SRCs have an almost negligible contribution, as seen in Fig. 1. Note that the observed

np to pp ratio for SRCs depends somewhat on the range of nucleon momenta probed. This allows for measurements

of the momentum dependence of the ratio7, but also means that direct comparisons of these ratios have to account for

the momentum acceptance of each experiment. While these measurements provide unique sensitivity to the isospin

structure, they have limited precision, typically 30–50%, and require large ﬁnal-state interaction (FSI) corrections.

Charge-exchange FSIs, where an outgoing neutron rescatters from one of the remaining protons in the nucleus, can

produce a high-momentum proton in the ﬁnal state that came from an initial state neutron (or vice versa). Because

Article

there are far more np-SRCs than pp-SRCs, even a small fraction of np pairs misidentiﬁed as pp will signiﬁcantly mod-

ify the observed ratio3. Modern calculations14 suggest that this nearly doubles the number of pp-SRCs detected in the

ﬁnal state8, while earlier analyses estimated a much smaller (∼15%) enhancement6. Because of this, we exclude the

data of Ref.6in further discussion. Combining the remaining measurements in Fig. 1, we ﬁnd that the average pp-SRCs

is only (2.9±0.5)% that of np-SRCs. This implies that the high-momentum tails of the nuclear momentum distribution

is almost exclusively generated by np-SRCs and thus have nearly identical proton and neutron contributions, even for

the most neutron rich nuclei.

This observed np dominance was shown to be a consequence of the short-distance tensor attraction15–17, which yields

a signiﬁcant enhancement of high-momentum isospin-0 np pairs. The isospin structure of 2N-SRCs determines the

relative proton and neutron contributions at large momentum, impacting scattering measurements (including neutrino

oscillation measurements), nuclear collisions, and sub-threshold particle production, making a clear understanding of

the underlying physics critical in interpreting a range of key measurements3–5, 18, 19 . In addition, the observation of an

unexpected correlation between the nuclear quark distribution functions20 and SRCs11 in light nuclei suggested the

possibility that they are driven by the same underlying physics. If so, the isospin structure of SRCs could translate into

a quark ﬂavor dependence in the nuclei. While this possibility has been examined in comparisons of EMC and SRC

measurements3, 12, 21–23, existing data are unable to determine if such a ﬂavor dependence exists.

A new possibility for studying the isospin structure of SRCs was demonstrated recently when, for the ﬁrst time, an

inclusive measurement24 observed np-SRC enhancement by comparing the isospin distinct nuclei 48Ca and 40Ca. The

measurement conﬁrmed np-dominance, but only extracted a 68% (95%) conﬁdence level upper limit on the pp/np ratio

of 3.2% (11.7%). We report here the results of a signiﬁcantly more precise extraction of the isospin structure of SRCs

in the A = 3 system making use of the inclusive scattering from the mirror nuclei 3H and 3He. This avoids the large

corrections associated with ﬁnal-state interactions of the detected nucleons in two-nucleon knockout measurements,

does not require a correction for the difference in mass between the two nuclei, and provides a dramatic increase in

sensitivity compared to the measurements on calcium or previous two-nucleon knockout data.

Data for experiment E12-11-112 were taken in Hall A at JLab in 2018, covering the quasielastic (QE) scattering

at x>

∼1. Electrons were detected using two High Resolution Spectrometers (HRSs), described in detail in Ref.25,

each consists of three focusing quadrupoles and one 45-degree dipole with a solid angle of ∼5 msr. The primary data

were taken in the second run period (fall 2018) with a 4.332 GeV beam energy and the Left HRS at 17 degrees. This

corresponds to Q2≥1.4GeV2in the SRC plateau region, which has been demonstrated to be sufﬁcient to isolate

scattering from 2N-SRCs at large x3, 10, 13, 26. We also include data from experiment E12-14-011, taken during spring

2018 run period27 at 20.88◦scattering angle, corresponding to Q2≈1.9GeV2in the SRC plateau region. A new target

system was developed for these experiments; details of the target system, including the ﬁrst high-luminosity tritium

target to be used in an electron scattering measurement in the last thirty years, are presented in the Methods section.

The electron trigger required signals from two scintillator planes and the CO2gas-Cherenkov chamber. Electron

tracks were identiﬁed using the Cherenkov and two layers of lead-glass calorimeters, and reconstructed using two

vertical drift chambers and optics matrices25 were used to determine the angle, momentum, and position along the

target for the scattered electrons. Acceptance cuts on the reconstructed scattering angle (±30 mrad in-plane, ±60 mrad

out-of-plane), momentum (<4% from the central momentum), and target position (central 16 cm of the target). The

ﬁnal cut suppresses endcap contributions and the residual contamination was subtracted using measurements on an

empty cell, as illustrated in Extended Data Fig. 1. The spectrometer acceptance was checked against Monte Carlo

simulations and found to be essentially identical for all targets, so the cross section ratio is extracted from the yield

ratio after after we apply a correction for the slight difference in the acceptance and radiative corrections. Additional

details on the analysis and uncertainties is provided in the Methods section.

Meson-exchange currents (MEC) and isobar contributions are expected to be negligible2, 28 for large energy transfers

(ν>

∼0.5GeV), Q2>1GeV2, and x > 1. To isolate SRCs, we take data with x≥1.4and Q2>1.4GeV2, which

yields ν > 0.4GeV with an average value of 0.6 GeV. Final-state interactions at these kinematics are expected to be

negligible2, 28 except between the two nucleons in the SRC, and these are assumed cancel in the target ratios1–3. At x > 1,

the minimum initial momentum of the struck nucleon increases2with xand Q2, and previous measurements have shown

that for Q2≥1.4GeV2,x > 1.4–1.5 is sufﬁcient to virtually eliminate mean-ﬁeld contributions and isolate 2N-SRCs.

For the light nuclei considered here, scaling should be even more reliable: the reduced Fermi momentum leads to a

faster falloff of the mean-ﬁeld contributions, providing earlier isolation of the SRCs, and any small residual MEC or

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ArticleRevealingtheshort-rangestructureofthemirrornuclei3Hand3HeS.Li1;2,R.Cruz-Torres3;2,N.Santiesteban1;3,Z.H.Ye4;5D.Abrams6,S.Alsalmi7;41,D.Androic8,K.Aniol9,J.Arrington2;5;,T.Averett10,C.AyerbeGayoso10,J.Bane11,S.Barcus10,J.Barrow11,A.Beck3,V.Bellini12,H.Bhatt13,D.Bhetuwal13,D.Biswas14,D.Bulum...

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