Competition of Deformation and Pairing Correlations in N = Z (Stable or Unstable) Nucleintse.khb.ru/files/uploads/2018/presentations/Cheoun.pdf · 2018. 11. 14. · 1 Competition

1

CompetitionofDeformation andPairingCorrelations

inN=Z(StableorUnstable)Nuclei

Myung-KiCheoun1incollaborationwith

EunjaHa1 ,T.Kajino2,HiroyukiSagawa3 ,A.Faessler4,F.Simkovic51) DepartmentofPhysicsandOriginofMatterandEvolutionofGalaxy(OMEG)

Institute,SoongsilUniversity,Seoul156-743,Korea2) NationalObservatoryofJapanandBeihangUniv.,China

3) RIKENandUniversityofAizu,Aizu-Wakamatsu,Fukushima965-8560,Japan4) TuebingenUniversity,Germany

5) BratislavaUniv,SlovakiaandDUBNA,Moscow,Russia

International Conference “Nuclear Theory in the Supercomputing Era”29 Oct.-2 Nov., 2018, Daejeon, Korea

1. Motivation

2.Spinsingletandspintripletpairingcorrelationsonshapeevolutioninsd- andpf-shellN=Znuclei.

3.EffectsoftheCoulombandthespin-orbitinteractioninadeformedmeanfieldontheresidualpairingcorrelations forN=Znuclei.

4.Competitionofdeformationandneutron-protonpairinginGamow-Tellertransitionsfor56,58Niand62,64Ni.

5.Summary

2

Contents

Motivations Results SummaryFormalism

NTSE 2018, Daejeon, Korea

3


• like-pairing(pp andnn pairing):IV• unlike-pairing(np pairing):IV&IS

v Pairingcorrelation

v T=1,S=0(Isovector(IV),spin- singlet) v T=0,S=1(Isoscalar(IS),spin- triplet)

Ø Aretheresomedeuteron-likestructuresinnuclei?Ø ForN=Znuclei,isthenp pairingmoredominant thanthelike-pairing?

Inthesenuclei,protonsandneutronsoccupythesameorbitalandhavethemaximalspatialoverlap,whichmakesespeciallyT=0pairingimportant.

Ø TherehavebeenmanydiscussionsaboutthecoexistenceofISandIVandtheircompetitions.Isitplausibleorfeasible?

Ø ThenuclearstructureofN≠Znuclei,60<N<70and57<Z<64,mayalsobeaffectedbynpcorrelations.Thenp pairingevenforN≠Z??PRL106,252502(2011)

p n


4


Ø M1spintransitiondatashowtheIVquenchingfortheN=Zsd-shellnuclei.;T=0pairingbythetensorforcewell-knownindeuteronstructuremaybecomemoresignificanteveninsidenuclei.PRL115,102501(2015)

Ø Inourearlypapers,thenp pairingwasdiscussedforGTanddouble-betadecayusingsphericalQRPA,whichdidnotincludethedeformationexplicitlyandtheISnp pairingwastakenintoaccountbyrenormalizingtheIVnppairing.SimilarapproachhasbeendoingbyvariousDFTforpairinginteractions!M.K.Cheoun etal.NPA561(1993),NPA564(1993)…

Ø Butinourrecentworks,theeffectsofdeformationandISnp pairingaretakenintoaccountexplicitlyintheHFBapproachandDQRPAapproach.

Ø Alsosomepossibilitiesofisospincondensationinnucleiarediscussed.


5NTSE 2018, Daejeon, Korea

6


Ø M1spintransitiondatashowtheIVquenchingfortheN=Zsd-shellnuclei.;T=0pairingbythetensorforcewell-knownindeuteronstructuremaybecomemoresignificanteveninsidenuclei.PRL115,102501(2015)

Ø Inourearlypapers,thenp pairingwasdiscussedforGTanddouble-betadecayusingsphericalQRPA,whichdidnotincludethedeformationexplicitlyandtheISnp pairingwastakenintoaccountbyrenormalizingtheIVnppairing.SimilarapproachhasbeendoingbyvariousDFTforpairinginteractions!M.K.Cheoun etal.NPA561(1993),NPA564(1993)…

Ø Butinourrecentworks,theeffectsofdeformationandISnp pairingaretakenintoaccountexplicitlyintheHFBapproachandDQRPAapproach.

Ø Alsosomepossibilitiesofisospincondensationinnucleiarediscussed.


1. Motivation2.Spinsingletandspintripletpairingcorrelationsonshapeevolution

insd- andpf-shellN=Znuclei.3.EffectsoftheCoulombandthespin-orbitinteractioninadeformedmeanfieldontheresidualpairingcorrelationsforN=Znuclei.

4.Competitionofdeformationandneutron-protonpairinginGamow-Tellertransitionsfor56,58Ni.

5.Summary

7

Contents



v SingleparticlestateE(SPSE)byDWSof24Mg

Motivations SummaryFormalism Results

Ø Inasimpleshell-fillingmodel,weassumethat- nosmearing,whichmeansthattheoccupationprovabilityofnucleon,v2,is1or0.- Fermienergyislocatedontheeachoutermostshell(blackdottedline).

v Asimpleshell-fillingmodelHaetal.PRC97,024320(2018)

:EHF:Egs

8

Strutinsky correction is in progress !

Close Open


v HFenergyandcorrectedgroundstateenergy

åå

å

å å

==

=

=

+e=-e+=

+=

+=

A

1iii

A

1iiii

A

1iWSi

A

1i

A

j,iigs

)t(2

1))t(

2

1t(

)iVi2

1t(

ijVij2

1tE

åå

å å

==

= =

e=+=

+=

A

1ii

A

1iWSi

A

1i

A

1jiHF

)iVit(

)ijVijt(E

å=

e¹\A

1iigsE

( )iiws tiVi -e=!

:SingleparticleE


(a)withoutnp-pairing(b)withnp-pairing(c)withenhancedT=0(d)withenhancedT=0+selfE


Ø T=0contributionmakestheboundingmorestrongerduetoitsattractiveproperty.

Ø EnhancedISnp pairingcorrelationsmaybeanindispensableingredienttounderstandtheprolatedeformation.

selfpair'MFtot

coulSOcDWS0

int0

EEEE

)VVV(VTH

HHH

++=

+++=

+=

10

v Shellevolutionof24Mgtotalenergy


11

v Why we consider the EnhancedT=0pairingcorrelationforN=Znuclei

T=0, S=1 (Isoscalar(IS), spin- triplet)

Ø M1spintransitiondatashowstheIVquenchingfortheN=Znucleiinsd-shell;T=0pairingbecomesmoresignificant.enhancedT0 =(T=0)ⅹ1.5(IVquenching)ⅹ2(↑↑+↓↓)

enhancedT0 =3ⅹ(T=0)

p n

Sagawaetal.




v Evolutionofpairingstrengthof24Mg


enhancedT=0

Ø Allresultsarefittedtoreproduceempiricalnp-pairinggaps.Nodifferenceofgreenandblueresults!!

Ø gnp*becomessmallerin,thatis,thesmallerg_np^*wehave,but,thelargerpairingenergyisobtained.

Ø ItindicatesthattherecanbeT=0pairing(Isoscalar)condensationinlargedeformation.Ø ThereisthecoexistenceofT=0andT=1pairingin

.3.02 >b

.3.02 >b 13NTSE 2018, Daejeon, Korea

PHYSICAL REVIEW C 97, 024320 (2018)


v Shellevolutionof32S

Ø 32Scanbeprolate deformedbythestrongT=0pairingcorrelations.

14

How about 28Si which is known as oblate ????


15

5/2+1 state



vInpf-shellN=Znuclei

Haetal.PRC97,064322(2018)


17

v Pairinggaps&FermiEevolutioninsd- &pf-shellN=Znuclei


Ø Empiricalpairinggapbyfivemassformula.Ø Theoreticalpairinggapsareadjustedtoreproducetheempiricalpairinggaps.

Specifically,np-pairinggapsarealmostsaturatedinpf-shellN=Znuclei.Ø ThegapbetweenprotonandneutronFermiEincreasesasthenumberofmass

increases. NTSE 2018, Daejeon, Korea


v Shellevolutionof44Ti

TheenhancedT=0forcemakestheboundingmorestronger.



v Shellevolutionof48Cr



v Shellevolutionof52Fe



v Shellevolutionof64Ge



v Shellevolutionof68Se



v Shellevolutionof72Kr

23

Even the oblate deformation can be explained by the unlike-pairing correlations !



Ø ThereisalsothecoexistenceofT=0andT=1pairingatlargedeformationsimilarlytosd-shellN=Znuclei.

enhanced T=0

v Evolutionofpairingstrengthof72Kr



insd- andpf-shellN=Znuclei.3.EffectsoftheCoulombandthespin-orbitinteractioninadeformedmeanfieldontheresidualpairingcorrelationsforN=Znuclei.

4.Competitionofdeformationandneutron-protonpairinginGamow-Tellertransitionsfor56,58Ni.

5.Summary

25

Contents


The Wigner SU(4) spin-isospin symmetry on the pairing gaps!


v Pairinggapsofpp,nn,andnpforsd-shellN=Z24Mg Haetal.submittedtoPRC


Ø Thechargeindependencesymmetryisapproximatelyconservedfor24Mg.

Ø ThesmearingoftheFermisurfacedecreasesbytheSOforce,whichdecreasesthepairinggap.

§ ConstantPME(pairingmatrixelement):thepairingundertheWignerspin-isospinSU(4)symmetry.§ BruecknerG-MatrixPME:statedependent,therealisticdescriptionofgroundstate.


v Shellevolutionwith(without)spin-orbit(SO)forcein36Ar


Ø TherearemanydegeneratestatesbytheSOforce.Ex)0d3/2+0d5/2 à 0dØ ThesmearingoftheFermisurfaceincreases(decreases)bytheSOforce,which

increases(decreases)thepairinggap.Ø ThesmearingdependsonwheretheFermilevellies. 27NTSE 2018, Daejeon, Korea

v inpf-shellN=Znuclei48CrMotivations SummaryFormalism Results

Ø TheSOforceincreasesthesmearingattheFermisurface,whichincreasesthepairinggap.

Ø Thechargeindependencesymmetryisapproximatelyconservedfor48Cr.


v insdgh-shellN=Znuclei128GdMotivations SummaryFormalism Results

Ø TheCoulombeffectsappearexplicitlybyincreasingthepairinggapwithG-MatPME.

Ø TheSU(4)symmetryismoreorlessviolatedbytheSOandtheColoumb forceonthepairinggaps.Butitisstillagoodsymmetryevenonthepairing(seegreentriangles).


v ReorderingofSPSEin128GdbytheCoulombforceMotivations SummaryFormalism Results

30

§ With Coulomb force § Without Coulomb force

Ø Theoccupationprobability:0h11/2 +1d5/2 (withCF)>0h11/2 +2s1/2 (w/oCF)Ø ThelargesmearingbytheCFmakesalargepairinggap.


v Ratioofisovector andisoscalar np-pairingMotivations SummaryFormalism Results

Ø IScondensationbytheenhancedT=0np pairingmayhappenindeformed24Mgand48Cr.Ø ThereisarapidphasetransitionfromIVtoIScomponentinthenp pairing.Butitmay

happenslowerinheavynuclei,whichmaymeanthecoexistenceinsomedeformationregion.

Ø Forheavynucleisuchas108XethephasetransitionmayhappenmoreeasilyevenwiththenormalT=0.

a)∼c):enhancedT=0,d)normalT=0



insd- andpf-shellN=Znuclei.3. EffectsoftheCoulombandthespin-orbitinteractioninadeformedmeanfieldontheresidualpairingcorrelationsforN=Znuclei.

4.Competitionofdeformationandneutron-protonpairinginGamow-Tellertransitionsfor 56,58Niand62,64Ni.

5.Summary

32

Contents




Ø Inparticular,56Niisthoughttobealmostsphericalbecauseofitsdoublemagicnumbers.Ø Ifwetakeα-clustermodelfor56Ni,thegroundstatemaybeslightly deformed.PRC84,

024302(2011)Ø ThenppairingeffectsturnouttobeabletoproperlyexplaintheGTstrengthalthoughthe

deformationisalsoanotherimportantproperty.Thehigh-lyingGTpeakinthetwopeaksstemsfromtherepulsivenp pairingthroughthereductionofFermienergiesofprotonsandneutrons.

v Gamow-Tellerstrengthfor56Ni Haetal.acceptedtoPRC



Ø TheshiftoftheGTstrengthdistributionsbytheenhancedT=0nppairingismainlyattributedtotheIScouplingcondensation.Evenwiththesmalldeformation,thesecondpeakappearsbytheT=0pairing.

v ISnp pairingeffectsonB(GT)



Ø ThenppairingmakestheIAR(isobaricanalogueresonance)concentratedaround12MeV,whichisconsistentwiththeresultsinPRC69(2004)atβ2= 0.2.

Ø ThedeformationeffectturnedouttobemoreimportantratherthanthenppairingcorrelationssincethenppairingeffectsbecomethesmallerwiththeincreaseofN- Znumber.SomespuriousstatespeculiartoQRPAleadtosmalldistributionofIARstate.

v Gamow-TellerstrengthandIAR for58Ni(N=Z+2)


v protonandneutronFermiEMotivations SummaryFormalism Results

p n

Without np-pairing

∆Ɛ=ʎp-ʎn

ʎn

ʎp

p n

With np-pairing

ʎn

ʎp

36

The np pairing makes the Fermi energy difference small, which can induce the GT transitionmore effectively and give rise toThe high-lying GT states !!!


37

Motivations ResultsFormalism Summary

1. Wefindacoexistenceoftwotypesofsuperconductivities(T=0andT=1)atthe|β2|>0.3regionin24Mg.

3. TheIScondensationbytheenhancedT=0pairingmayhappennotonlyinsd-shell,butalsoinpf-shellnuclei.

4. TheIScondensationpartplaysavitalroletoexplaintheGTstrengthdistributionof56,58,62,64Ni nucleus,withthedeformationandtheunlike-pairingcorrelations.

5. TheCoulombforceandtheSOforceareshowntochangethesmearingbychangeoforderingofSPS. Remember the splitting by the SO as well

as the deformation.6. Thestate-dependentBrueckner G-PMEtakesintoaccountshellstructureeffectsontheresidualinteractionandenablesustodorealisticdescriptionofgroundstatesoftheN=Znuclei.

7.ForheavyN=Znuclei,thetransitionmayhappenmoreeasilyevenwiththenormalT=0pairingwithaphasetransition.

Summary


38


1. Spinsingletandspintripletpairingcorrelationsonshapeevolutioninsd-shellN=Znuclei.Ha,MKCetal.PRC97,024320(2018)

2.Neutron-protonpairingcorrelationsanddeformationforN=Znucleiinpf-shellbythedeformedBCSandHFBapproach.Ha,MKCetal.PRC97,064322(2018)

3.Competitionofdeformationandneutron-protonpairinginGamow-Tellertransitionsfor56,58Ni.Ha,MKCetal.acceptedtoPRC

4.EffectsoftheCoulombandthespin-orbitinteractioninadeformedmeanfieldontheresidualpairingcorrelationsforN=Znuclei.Ha,MKCetal.submittedtoPRC.

5.IsoscalarcondensationinN=Znuclei.Ha,MKCetal.tobepublishedActaPhysicaPolonicaB(2018).

6.…

v Referencesofour recentpapers


Thanks for your attention !!


Back-up files


41

v How to include the deformation?Motivations Summary

Deformed Woods-Saxon(WS) potential(cylindrical WS, Damgaard et al 1969)

( )Cv,Cuz,)v,u(S/)v,u(CS),;v,u(

)p)((Vgrad)mc2/(V,a/exp1

V)(V

v,u42

2so

0

==Ñ=

´-=+

-=

rbb

sl

!

""!#

!!

distance function surface function

ResultsFormalism

Deformed SPS Sph. HO w. f.

Ø To exploit G-matrix elements, which is calculated on the spherical basis, deformed bases are expanded in terms of the spherical bases.

β2 : quadrupole deformation parameterβ4 : hexadecapole deformation parameter

Ø We can determine these two parameters by taking values giving the minimum ground state energy.


42


for 2+, Q2+ = -2/7 Q0

Q2+ : experimental quadrupole moment

Q0 : intrinsic quadrupole moment

Ø 28Si is not heavy. Where does it come from ?

v In sd-shell N=Z nuclei , Qexp of 28Si is different from 24Mg and 32S

)2.1()2(

3

4 3/10

2/1

220

2 ARe

EB

ZR=ú

û

ùêë

é =

pb


v Pairing correlation

43


J=0T=1 j m j -m

Ω -Ω(J=0,1, 2, 3 ∙∙∙)T=0 J=1, 3, 5, ∙∙∙T=1 J=0, 2, 4, ∙∙∙

BCS deformed BCS

Ω= ½j ≥ Ω

!21

2721

2521

2321

21j W

K=0

K

JLaboratory frame

Intrinsic frame

Ø Since the deformed SPS are expanded in terms of the spherical SP bases the different total angular momenta of the SP basis states would be mixed.

L+S=W

(Coupled system)


v Pairing correlation

44


K=0Ω

Ω -Ω

deformed HFB deformed BCS

K=0

-Ω

BCS

HFB


v Self energy in BCS

( )[ ]

0:bbV0;aavu

J:abVJ:abJv

.eqBCS

vuv2H

aaab

2

J,a

2a2

1b

bbb

A

bbbb2

1b2

1b

2b0

å

å

å

-=D

-=µ

µ-l-eºh

D-µ+h=

Motivations SummaryResultsFormalism

: self energy

: pairing gap

Ø The self energy term was usually neglected in BCS eq. because it results from particle-hole correlations beyond the BCS and affects a renormalization of the single particle energy.

Emean Eself Epair


v Shell evolution & the simplest shell model of 28Si



v Shell evolution & the simplest shell model of 32S



48



49

v Parameter set of Deformed Woods-Saxon

backup file


v In gd-shell N=Z nuclei


v Used parameters in this work.

( )( )

strength.int)holeparticle(particleparticle)15.1(99.0)g(g*

formulamasstermfive:gappairing*

.paramuniversal:parametersinputWS*

basisdeformed5N*

basisspherical10N*

phpp

max

max

--=-

=

=



v ground state E of 104Te




v ground state E of 116Ce



v ground state E of 128Gd


Realistic two body interaction inside nuclei was taken by Brueckner g-matrix, which is a solutionof the Bethe-Salpeter Eq., derived from the Bonn-CD potential for nucleon-nucleon interaction infree space.

v Two-body interaction

56


cd,ab0

pcd,abcd,abcd,ab )(g

HQ

VV)(g ww

w-

+=

a,b,c,d : single particle states from the Woods-Saxon potential.Vab,cd : phenomenological nucleon-nucleon potential in free space.


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Competition of Deformation and Pairing Correlations in N = Z (Stable or Unstable) Nucleintse.khb.ru/files/uploads/2018/presentations/Cheoun.pdf · 2018. 11. 14. · 1 Competition