Can long-range nuclear properties Be influenced by short range interactions? A chiral dynamics estimate

Can long-range nuclear properties Be influenced by

short range interactions? A chiral dynamics estimate

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Citation

Miller, G. A. et al. "Can long-range nuclear properties Be influenced

by short range interactions? A chiral dynamics estimate." Physics

Letters B 793 (June 2019): 360-364 © 2019 The Author(s)

As Published

http://dx.doi.org/10.1016/j.physletb.2019.05.010

Publisher

Elsevier BV

Version

Final published version

Citable link

https://hdl.handle.net/1721.1/126445

Terms of Use

Creative Commons Attribution 4.0 International license

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Can

long-range

nuclear

properties

Be

influenced

by

short

range

interactions?

A

chiral

dynamics

estimate

G.A. Miller

a

,

∗

, A. Beck

b

,

1

,

S. May-Tal Beck

b

,

1

, L.B. Weinstein

c

, E. Piasetzky

d

,

O. Hen

b a_{DepartmentofPhysics,UniversityofWashington,Seattle,WA98195,UnitedStatesofAmerica}

b_{MassachusettsInstituteofTechnology,Cambridge,MA02139,UnitedStatesofAmerica} c_{OldDominionUniversity,Norfolk,VA 23529,UnitedStatesofAmerica}

d_{TelAvivUniversity,TelAviv69978,Israel}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received 9 November 2018

Received in revised form 25 February 2019 Accepted 6 May 2019

Available online 8 May 2019 Editor: W. Haxton

Recent experiments and many-body calculations indicate that approximately 20% of the nucleons in medium and heavynuclei ( A_≥12) are part ofshort-rangecorrelated (SRC) primarily neutron-proton (np)pairs.Wefindthatusingchiraldynamicstoaccountfortheformationofnp pairsduetotheeffects ofiteratedandirreducibletwo-pionexchangeleadstovaluesconsistentwiththe20%level.Wefurther applychiraldynamicstostudy howthesecorrelationsinfluencethecalculationsofnuclearchargeradii, thattraditionallytruncatetheireffect,tofindthattheyarecapableofintroducingnon-negligibleeffects.

©2019TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Electriccharge distributionsarea fundamentalmeasureofthe arrangementofprotonsinnuclei [1].Thevariation ofcharge dis-tributionsofelementsalongisotopicchainsisofparticularinterest duetoitssensitivitytobothsingleparticleshellclosureand bind-ingeffects,aswellaspropertiesofthenucleon-nucleon(N N) in-teraction.Inaddition,differencesbetweentheneutronandproton matter radii in neutron rich nuclei are extensively used to con-strain the nuclearsymmetry energy andits slope around satura-tiondensity,andthushavesignificantimplicationsforcalculations ofvariousneutronstarproperties,includingtheirequationofstate [2–4].

Modernchargeradiuscalculationsgofarbeyondthesingle par-ticleapproximation.Abinitiomany-bodycalculationscanbedone usingvarioustechniques [5–7],butaregenerallyvery calculation-allydemanding, especiallyfor medium andheavy nuclei. The re-centdevelopmentofchiraleffectivefieldtheory(EFT)inspiredsoft interactionsthatoffersystematicevaluationoftheaccuracyofthe calculation, and methods using similarity renormalization group (SRG)evolutiontechniquestoreduce thesize ofthe modelspace are especially usefulas they significantly simplify calculations of energylevels.Whilegenerallysuccessful,thesecalculationsobtain

*

Corresponding author.

E-mailaddress:miller@uw.edu(G.A. Miller).

1 _{On sabbatical leave from Nuclear Research Centre Negev, Beer-Sheva, Israel.}

a systematicunderestimateofnuclearcharge radiiandtheir vari-ation along isotopic chains [8–10]. This is a known, butnot yet explainedfeaturethesecalculations.

However, both procedures mentioned above are often imple-mented in a manner that truncateshigh momentum can reduce the high-momentum components of the nuclear wave function that could be important in computing matrix elements of ob-servablequantities.Herewe discusstheimpactofneutron-proton Short-RangeCorrelations(np-SRC) [11–13] onnuclearchargeradii. Overthelastdecadeconsiderableevidencehasaccumulated re-garding the attractive nature ofthe short-ranged neutron-proton interaction inthespin tripletchannel.Measurementsofrelatively high-momentumtransferinclusiveelectron-scatteringeactions in-dicatethatabout20%ofthenucleonsinmediumandheavynuclei ( A

≥

12) have momentum greater than the nuclear Fermi mo-mentum (kF

≈

275 MeV/c) [14–18]. In the momentum range of

300–600 MeV/c, these high-momentum nucleons were observed to be predominantly members of np-SRC pairs, defined by hav-ing largerelative andsmallercenter-of-massmomentarelative to

kF [11,12,19–24]. Thisis an operationalmomentum-space

defini-tionoftheterm‘short-range’.

Calculationsindicatethattheoriginofthesecorrelatednp-SRC

pairs lies in the action of a strong short-ranged tensor interac-tion [25–27]. Theseexperiments andinterpretivecalculations are based onthe idea that athigh-momentumtransfers the reaction factorizes, allowing cancellationof reaction mechanism effectsin cross-section ratios of different nuclei and the use of the im-https://doi.org/10.1016/j.physletb.2019.05.010

0370-2693/©2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3_.

pulse approximation (with suitable modest corrections) in other cases [11,28]. In effective field theory language, this corresponds tousing a high-resolution scale in the similarityrenormalization groupSRGtransformations [29].

Inthecaseofneutron-richnuclei,recentmeasurements[30] in-dicatethat,fromAltoPb,thefractionofcorrelatedneutrons(i.e., theprobability fora neutron tobelong to an np-SRCpair)is ap-proximatelyconstantwhilethatoftheprotonsgrowswithnuclear asymmetryapproximatelyas N

/

Z (where N and Z arethe num-bersofneutronsandprotonsrespectively).Thisisafirstindication ofapossiblesignificant impactofnp-SRContheproton distribu-tionsinneutronrichnuclei.

The effects of tensor-induced np-SRC pairs in nuclei were shownto have significant impact on issues such asthe internal structureofboundnucleons(the EMCeffect)[11,31–33], neutron-starstructure andthenuclear symmetry energyat supra-nuclear densities[28,34–36],theisospindependenceofnuclearcorrelation functions[37].However,itisnaturaltoexpectthatduetothe ten-sorinteraction’sshort-rangednature,itsimpactonlongrange(i.e., low-energy)observablescanbeneglected.

Thisexpectation is examined here by focusing on the partic-ularproblem highlighted in Ref. [8]:the computed difference in chargeradiibetween52_Caand48_{Caissmallerthanthemeasured} value. The ab initio calculations in that work are based on sev-eral interactions that include NNLOsat, which is fit to scattering data up to 35 MeV and to certain nuclear data from nuclei up to A

=

24 [38],andtheinteractions SRG1andSRG2.Thelatteris derived fromthe nucleon-nucleoninteractionofRef. [39] by per-formingan evolutionto lower resolutionscales via thesimilarity renormalizationgroup(SRG) [29].Ref. [8] speculatesthatthe rea-sonforthediscrepancybetweentheoryandexperimentisalackin thedescription ofdeformedintruderstatesassociated with com-plexconfigurations.TheNNLOsat interactiondoesgivethecorrect 40_{Ca radiusandincludesshort-rangecorrelationsforlikenucleon} pairsimplicitlythroughitsoptimizationprocedure.

Herewestudyanotherpossiblereasonforthediscrepancythat stems from the use of soft interactions. We view all of the in-teractions employed in Ref. [8] as soft interactions that reduce theinfluenceofshort-rangecorrelations. Wearguethatincluding omittedeffectsofnp-SRCpairs betweenprotonsandneutrons in theouter shellsofneutron-richnucleimaychangethecomputed valueoftheprotonMSchargeradiusforsomeneutron-richnuclei. Notethattheuseofsoftinteractions,causedbyusingformfactors that reduce the probability for high-momentum transfer should beaccompaniedbyincludingmodifiedelectromagneticcurrentsas demanded by currentconservation.If insteadthe SRG isused, it shouldbe accompaniedby correspondingunitary transformations on the operators. If these modifications to currentoperators are donecompletelyaccuratecalculationsmaybepossible.

Webeginbyusingthesimplestpossibleillustrationofthe pos-sibleimpact of SRCson computed charge radii. Thisis based on atwo-statesystemandisintendedonlytoexplain thebasicidea. Wethenusechiraldynamicstoestimatetheprobability of short-rangecorrelations, andfurtherstudyhow thesecorrelationsmay influencecalculationsofnuclearchargeradii.

2. Schematicmodel

Consider the evaluation of an operator

O

in a framework in whichSRCeffectscanbetruncated.Weexaminetheeffectofthis truncationonthecomputationofrelevantmatrixelements.

Theconsistentapplication [40,41] ofSRGevolutionina many-body calculation requires that the Hamiltonian, H , aswell as all other operators, be transformed according to

O →

U

O

U†. Here

U isa unitary operator, chosen to simplifythe evaluationof

en-ergies by reducing the matrix elements of H between low- and high- momentumsubspaces.Theaimistoobtainablock-diagonal Hamiltonian.Such transformationshavenoimpactonobservables andincludetheeffectsofshort-rangephysics.However,inthecase ofprotonMScharge radiuscalculations,severalworks [8] further simplifythecalculationbyevaluatingtheexpectationvalueofthe

un-transformed mean square charge radius operator onthe trans-formed wavefunctions.

Tounderstandthegeneraleffectofusingsuchun-transformed operators we consider a simple two-state model with two com-ponents,

|

P



and

|

Q



, respectively representing low-lying shell model states andhigh-lying states within the model space. The

Q -space is intended to represent the states that enter into the many-bodywavefunctionduetotheshort-rangecorrelations.Thus the Q -space dominates the high-momentum part of the ground stateone-bodydensity [42].

Since we are concerned with nuclear charge radii, the sim-ple model must be further defined by the matrix elements of the charge radius squared operator, R2_{. This operator is of long} rangeandisnotexpectedtoallowmuchconnectionbetweenthe

P and Q spaces. Therefore, thismodel is definedby the simple statement:



P

|

R2

_|

_Q

_

₌

_{0.Themotivationforthisstatementcomes} from thesingle-particle harmonicoscillator model: the action of the square ofthe radius changes the principal quantum number by at most one unit. One may arrange model spaces satisfying thisconditionbyusingsuperpositionsofharmonicoscillatorwave functions.Aconsequenceofthisisthat



Q

|

R2

_|

_Q

_

_{− }

_P

_|

_R2

_|

_P

_

_>

_0.

TheHamiltonianforatwo-statesystemisgivenby H

=



−



V V





(1)

where 2



is theenergy splitting between

|

P



and

|

Q



and V is

theshort-distancecouplingbetweenthem.Theexactgroundstate

|

G S



can be computed andthe occupation probability of the Q

spaceisgivenby

P

Q

≡

V2

/

[(



+ )

2

+

V2

]

,with



≡

√



2

₊

_V2_.

P

Q inthismodelcorrespondstotheprobabilitythataproton

be-longs to a short range correlated pair. The mean-square charge radiusisthengivenby:



G S

|

R2

|

G S

 = 

P

|

R2

|

P

 + (

Q

|

R2

|

Q

 − 

P

|

R2

|

P

)

P

Q (2)

withthesecond termrepresentingtheinfluenceofthehigh-lying states.

WeinterprettheresultEq. (2) intermsoftheSRG.Fora two-state system the complete SRG transformation simply amounts to diagonalizing the Hamiltonian. The resulting renormalization-groupimprovedHamiltonianH is

˜

adiagonalmatrixwithelements givenby

±

.Theunitarytransformationsetsthematrixelements of H between

˜

the low andhigh momentum sub-spaces to zero. Applyingthesameunitarytransformationtotheoperator R2,one wouldobtain the sameresultasEq. (2). However, the procedure ofRef. [8],andothers,forexample, [9,10],corresponds to simply using



G S

|

U R2U†

|

G S

 ≈ 

G S

|

R2

|

G S

 = 

P

|

R2

|

P

,

(3)

which contrastswiththe complete calculationof Eq. (2).For the givenmodel,

(



Q

|

R2

|

Q



− 

P

|

R2

|

P

)

>

0, sothat theomissionof theunitarytransformationontheR2 _{operatorleadstoareduction} in the matrix element. Inrealistic situations the correction term

(



Q

|

R2

_|

_Q

_

_{− }

_P

_|

_R2

_|

_P

_)

_P

Q would be thedifference betweentwo

largenumbers,soitcouldbepositiveornegative.

Thetwo-componentmodelpresentedaboveshowsthepossible qualitative effect on the computed mean-square radius of trun-cating SRCs. However, it cannot be used to make a quantitative prediction.

3. Chiraldynamicsestimate

We now turnto a more complete calculation to estimate the magnitudeofthe effectforthe specificcaseof addinganeutron tothe1 f5/2

−

2p3/2 shellarounda48Cacore.Theadditional neu-tronismainlylocatedintheouteredgeofthenucleus.Inthepure shellmodel, thisneutronwould notaffect theproton MS charge radius. However, it is natural to wonder if the attractive, short-rangeneutron-protontensorinteraction thatcreatesnp-SRCpairs will causethe protons to move closer to the additional neutron, therebyincreasingthechargeradius.

Thecalculationstartswitha48Cawave functionthathasbeen obtainedusinganinteractionthatexplicitlyincludestheeffectsof high-momentumcomponents,andconsiderstheeffectofa miss-ing short-ranged potential V on an np product wave function

|

n

,

α

)

,wheren and

α

representtheneutronandprotonorbitals re-spectively.Fornumericalwork,inthisexploratoryeffort,weignore the spin orbit force and use harmonic oscillator single-nucleon wave functions, with frequency,



=

10

.

3 MeV, that yields the measuredcharge radiusof3.48fm,andthecorresponding length parameter,b2

₌

₁

_/(

_M

_)

₌

₄

_.

_{02 fm}2_{.TheinteractionV ismeantto} representtheeffectsincludingtheshort-rangestrengthmaskedby theSRG procedure, andalsocorrectionsto the effectsof usinga verysoftnucleon-nucleoninteraction.TheeffectofV onthewave functionisgivenby

|

n,

α

 =

C−1/2



|

n,

α

)

+

1

E

Q G

|

n,

α

)



,

(4)

whereG istheBrucknerG-matrixthatsumstheinteractions V on

thepairandincludestheeffectsofshort-range correlations.Note that

|

represents the full wave function while

|)

representsthe productstate. Theenergydenominator



E

≡

En

+

Eα

−

H0,with

H0theHamiltonianintheabsenceofV ,Q theprojectionoperator thatplacestheneutronandprotonabovetheFermiseaandCnα is

thenormalizationconstant:

Cnα

=

1

+

Inα

,

(5)

withInα

≡



m,β>EF

(n,α|G|mβ)(m,β|G|n,α) (En+Eα−Em−Eβ)2 .

DefiningtheprotonMS radius asthe expectationvalueofthe operatorR2

p,wewanttoknowthequantity



n,

α

|

R2_p

|

n,

α

 =

C_n−_α1

[(

n,

α

|

R2_p

|

n,

α

)

+ (

n,

α

|

G Q 1

E

R 2 p 1

E

Q G

|

n,

α

)

],

(6) obtainedbyusingthefactthattheone-bodyoperatorR2

pdoesnot

connectthestates

|

n

α

)

and

|

m

β)

thatdifferbytwoorbitals.Using thedefinitions: R2_nα

≡

1 Inα

(n,

α

|

G Q 1



ER 2 p 1

E

Q G

|

n,

α

)

(7) and R2_α

≡ (

α

|

R2_p

|

α

),

(8) onefinds



n,

α

|

R2_p

|

n,

α

 =

R2_α

+

P

_nS RC_α

(R

_n2_α

−

R2_α

),

(9) with

P

S RC

nα

=

1+InIαnα

≈

0

.

2 isthemeasuredSRCprobability [14–17]. Probabilitiesofthissize havebeenobtainedby both ancientand modern computations [6,43–48]. The effect of SRCs is embodied in the second term of Eq. (9), as in Eq. (2). Note the similar-itybetweenthe two equations.Giventhat

P

S RC

nα cannot be zero,

the effectofSRCsmust eitherincreaseordecreasethecomputed mean-square charge radius. Insome cases,there could be a can-cellation betweenthe two parts of the correction term, butthis shouldnotbeexpectedtooccurforallconfigurations.

Wenextshowthatthe

∼

20%valueof

P

_nS RC_α isconsistentwith the chiral dynamics treatment of Refs. [49,50]. In that work the chiral dynamics interaction, dominated by the iterated effects of theone pionexchangepotential (OPEP)isshownto bethecause ofnuclear binding.Furthermore,the reductionofthiseffectwith increasing nucleardensitythrough theeffectsofthePauli princi-ple on the intermediate nucleon-nucleon state is responsible for nuclearsaturation.TheideasofRefs. [49,50] accountforthe qual-itativefeaturesofnuclearphysicswithstartlingsimplicity.

The keypoint forusisthatthe dominantsourceofattraction comesfromashortdistanceeffect,well-representedbyzero-range deltafunctioninteraction(denoted hereas V00)proportional toa cut-off parameter



, that is consistent withthe requirements of chiralsymmetry.Thisinteractionaccountsforanattraction“inthe hundredMeVrange(pernucleon)forphysicallyreasonablevalues of the cut-off, 0

.

5

<



<

1

.

0 GeV.”These authors also note that thetwopionexchangeinteractioncontainsafactorthatfavorsthe isospin 0 two-nucleon state by a factor of 9 over the isospin 1 state.Thenp dominancediscussedaboveisanaturalconsequence ofthechiraldynamicsinteraction.

The calculation of the iterated OPEP was repeated in Ap-pendix AofRef. [11].Inagreementwith[49,50],thatworkshows that theiterationofthe spin-tripletone-pion exchange(OPE) po-tential(includingthetransitions3S

→

3D

→

3S)resultsinastrong attractiveeffectiveshort-rangeinteractionthatactsintherelative

S state(seealso[51,52]).Thestrengthisofthecorrectmagnitude toroughlyaccountforthedeuteron D-stateprobability,and there-fore maybe expectedtoroughly account forthe probability that annp pairisinashortrangecorrelation.

Refs. [49,50] explainsthat V00 shouldnot beiterated with it-self or with 1

π

exchange. Therefore the iterated OPE term V00 approximatelycorrespondstotheG

−

matrixofEq. (4).That refer-encegives V00

(

r

)

= −

8

π

2M( gA 4

π

fπ

)

4

(

1

−

(

3g 2 A

+

1

)(g

2A

−

1

)

10g4_A

)

× (

1

−

2

.

18kF M

)(

3

−

2

τ

1

·

τ

2

)δ(

r

)

≡

V0

(

3

−

2

τ

1

·

τ

2

)δ(

r

),

(10) where M is the nucleonmass, gA theaxial vector coupling

con-stant, andthe piondecayconstant fπ

=

92.4MeV. The effectof thePauliprincipleisencodedinthetermproportionaltokF.This

expressionincludesthesmallerrepulsiveeffectsoftheirreducible two-pionexchangegraphs.

Theinteractioncausesachangeinthewavefunction:

|δ

n,α

)

≡

Q

E

V00|n,

α

),

(11)

which accounts for the second term of Eq. (4). To proceed, we need the operator _Q_E.We useits value in nuclearmatter under the referencespectrumapproximation [53],whichis qualitatively valid for use along with short-ranged interactions [54]. Then in thecoordinate-spacerepresentation(r1,2

=

R

±

r

/

2)thisis approx-imatedbytheexpression:



R

,

r

|

Q

E

|

R 

_,

_r

_{ = −}



d3K

(

2

π

)

3 d3k

(

2

π

)

3

×

eiK·(R−R ₎ eik·(r−r) 2 A2

+

W

+

K 2 4M∗

+

k2 M∗

,

(12)

whereM∗

=

0

.

6M

,

A2

≈

100 MeV,andW isastartingenergy [53]. ThequantitykF istheeffectiveFermimomentumforagiven

nu-cleus, here taken as 1.36 fm−1_{. The short-ranged nature of the} interactionisexpectedto excitethatpartofthephasespacethat involves regions of relative low K and relatively high k. Thus, theintegral is simplified by replacing K2 by its averagevalue of

(

6

/

5

)

k2_F

/

M,wherekF istheeffectiveFermimomentumforagiven

nucleus.Thendefining

γ

2

_≡

_M∗

₍

_{2 A}

2

+

W

+ (

3

/

10

)

k2_F,wefindthat



R

,

r

|

Q

E

|

R 

_,

_r

_{ ≈ δ(}

_R

₋

_R

₎

_f

₍

_|

_r

₋

_r

_|),

₍₁₃₎ with f

(

r

)

=

₄M_π∗_re−γr_.Then



R

,

r

|δ

n,α

)

≈

f

(r)V

0

(

3

−

2

τ

1

·

τ

2

)φ

n

(

R

)φ

α

(

R

).

(14) Then 



α Inα

≈





α



d3R

|φ

n

(

R

)φ

α

(

R

)

|

241

(M

∗V0

)

2 8

π γ

(15)

where



_{α denotes}an averageover theboundproton levels.The factor41arisesfromthe averageof thecontributions of92

=

81 (fromthe T

=

0 componentofannp pair)and1(romthe T

=

1 component). Given the change in wave function of Eq. (11) one findstheresultthat

R2_nα

≈



d3R R2

|φ

n

(R

)φ

α

(R

)

|

2



d3_R

_|φ

n

(R)φ

α

(

R)

|

2

.

(16)

ThisamountstousingtheknownZero-RangeApproximation, pre-viouslyshowntosuccessfullyreproduceSRCeffects [52].

Wenextapplythisideatothespecificcaseofaddingneutrons to 48_{Ca, withthe added neutron in either the n}

₌

_{0 f}

5/2 or n

=

1p3/2 state.We willusethe averageoverthe Lz substates. Given

parametersmentionedabove,wefindthat

P

S RC

nα

≈

0

.

2

±

0

.

02 (17)

for all of the orbitals considered. The dependence on the start-ingenergyW isweakbecauseitismuchsmallerthan2 A2

=

200 MeV. Then the effects of short-range correlations on the mean-squarechargeradiusofanorbitaln aregivenby:

R

2

(n)

≡





α

P

S RC nα

(R

n2α

−

R2α

)

(18)

Numericalevaluationleadsto

R

2

(

0 f5/2

)

=

0

.

17

±

0

.

12 fm2

,

R

2

(

1p3/2

)

= −

0

.

8 fm2

.

(19) The variation seen for



R2

₍

_{0 f}

5/2

)

results from increasing the

b-parameter by an amount up to 10%. Thisis done becausethis stateisweakly (ifatall)bound. Thevalue of



R2

(

1p3/2

)

is rela-tivelyinsensitive to suchchanges. Its negative naturearises from thenode in 1p3/2 state wave function which appears inthe nu-clear surface. This calculation may appear somewhat crude, but isreasonablywell-constrainedby using

P

S RC

nα

≈

0

.

2 andthe

mea-suredcharge radiusof the48Ca corestate.The effectunder con-sideration is not obviously zero,and the specific values we find arelarge enough tobe takenseriously.Thus we suggestthat the effectofshortrangecorrelationsoncomputedchargeradiishould beconsideredinmoredetailedcalculationsthatincludemany con-figurationsandaimathighprecision.

Wenote that theabinitio triton calculationof [55] findsthat ignoring the effect of the unitary transformation on the charge radiussquared operatorleads to an overestimate ofthe value by about0.04fm, notdissimilarinpercentagetoourresults.

4. Discussion

Ref. [8] explains various possible reasons (in addition to the effects of deformed intruder states) for the differences between theexperimental andcomputedvaluesofcharge radii.The calcu-lations arebasedon thesingle-reference coupled-clustermethod, whichisideallysuitedfornucleiwithatmostoneortwonucleons outside a closed (sub-) shell. Many calculations in the literature considerably underestimate the large charge radius of 52Ca. Dy-namicalquadrupoleandoctupoleeffectscouldberesponsible,but seemtobetoosmall.Theseauthorsmentioncorebreakingeffects. Theirabiniitio calculationsdoshow“a weak,butgradual erosion oftheprotoncoreasneutronsare added.”Thus ourstatement is that including theeffects of shortrange correlationscould make theerosionoftheprotoncorestrongerandinfluencetheresulting computedchargeradii.Doingthenecessaryabinitio calculationis beyondthe scope of thispaper,but we dosuggest that such ef-fectsshouldbe consideredinmoredetailedcalculationsofcharge radiithataimathighprecision.

Wenext discussthemotivationforpursuingsuchcalculations. Theexperimentaldataaccumulatedinthelastdecade,in conjunc-tionwithun-truncated abinitio andeffectivecalculations, allows quantifying the abundance andproperties of SRC pairs in nuclei with unprecedented detail. Recent measurements of asymmetric nucleiindicate that SRCpairsare dominatedby np pairseven in very neutron rich nuclei [30]. This implies that the protons are morecorrelatedthanneutronsinneutronrichnuclei.

Moderncalculationsrelatethethicknessoftheneutronskinof 208_{Pbto thenuclear equation ofstate andhence toneutron star} properties [2–4]. A high priority experiment at Jefferson Lab is planned to measure the neutronskin thicknessusing parity vio-latingelectronscattering[56]. However,hithertoneglected short-range effectswhich reduce the neutronskin thicknessshould be includedtoaccuratelyrelatetheneutronskinthicknesstothe nu-clearEOS.

The indicated larger probability of protons to be part of SRC pairsinneutronrichnuclei,incombinationwiththelargeraverage neutronradius,indicatesthatshort-rangecorrelationscanhavean impact on long-range nuclear propertiessuch asthe nuclear MS charge radius. The presentwork shows that the 20% probability foran np pair to stronglycorrelated is a naturalconsequence of the chiral dynamics of Refs. [49,50]. Thiseffect is dominated by thetensorforcewhichislargeinthestatewithdeuteronquantum numbers.Moreover, wefind thatincludingtheeffects ofnp-SRCs

seems to be necessaryto achieve a calculation ofhighprecision. This is somewhat surprising because it is a long-range effect of ashort-range, typicallytruncated, partofthe N N interaction.We hope thatthe ideapresentedherecanbe confirmedorruledout bymoreadvancedcomputations.

Acknowledgements

G.A. Millerwouldliketo thanktheLab forNuclear Scienceat MIT for support that enabled this work. We thank A. Schwenk, R. Stroberg and U. van Kolck for useful discussions. This work was supported by the U. S. Department of Energy Office of Science, Office of Nuclear Physics under Award Numbers DE-FG02-97ER-41014,DE-FG02-94ER40818andDE-FG02-96ER-40960, thePAZYFoundation,andbytheIsraelScienceFoundation(Israel) underGrantsNos.136/12and1334/16.

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