Isoscalarspin-tripletpairingandtensorcorrela1onsonSpin-Isospinresponse-------------　Osaka,Japan,November16-19,2015-----------------

HiroyukiSagawaRIKEN/UniversityofAizu

・Skyrmetensorinterac1onsShellevolu1oninmedium-massnucleiSpin-isospinexcita1onsandsumrules・Pairingcorrela1onsT=1,S=0andT=0,S=1pairsEnergyspectraofN=Zodd-oddnuclei.Gamow-Tellerexcita1onsinN=Z+2pf-shellnucleiinterplaybetweenT=0pairingandtensorcorrela1ons

Tensorinterac1oninmean-fieldanddensityfunc1onaltheoryapproachestonuclearstructureProgressinPar1cleandNuclearPhysicsVolume76,May2014,pp.76-115(2014)H.SagawaandG.Colo

Spin-tripletandspin-singletpairingcorrela1onsInSpin-Isospinexcita1onsBohr-Mo_elsonNovelPrize40thanniversarymemorialissusePhysicsScripta(2015)H.Sagawa,C.L.BaiandG.Colo

T.H.R.Skyrme,Nucl.Phys.9,615(1959).F.L.Stancu,D.M.BrinkandH.Flocard,PLB68,108(1977).

Skyrme-typetensorinterac1ons

T.Lesinski, M. Bender, K. Bennaceur, T. Duguet, J. Meyer, Phys. Rev.C76, 014312(2007). G.Colo, H. Sagawa, S. Fracasso, P.F. Bortignon, Phys. Lett. B 646 (2007) 227. B.A.Brown, T. Duguet,T. Otsuka, D. Abe and T. Suzuki, Phys. Rev. C74(2006) 061303(R)

:Triplet-even

:Triplet-odd

　　　　　　　　 TwoAdvantages1. Asimpleformulaforspin-orbitsplidng2. Analy1cformulasformul1poleexpansionforspin-dependentexcita1ons

(L = S = 0)J = 0,T =1 ⇒ ( j = j ' )J = 0,T =1

(L = 0,S =1)J =1,T = 0 ⇒

a (l = l ' j = j ' )J =1,T = 0 + b ((l = l ' ) j, j ' = j ±1)J =1,T = 0

T=1,S=0pair

T=0,S=1pair

Ifthereisstrongspin-orbitsplidng,itisdifficulttomake(T=0,S=1)pair.But,T=0J=1+statecouldbeGamow-TellerstatesinnucleiwithN~ZèstrongGTstatesinN=Z+2nuclei

Twopar1clesystems

p(n)　 p(n)

p n

SU(4)supermul1pletinspin-isospinspace

Well-knowninlightp-shellnuclei(LScouplingdominance)

0.8 1 1.2 1.4 1.6 1.8f=GT=0/GT=1

−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

Pairi

ng C

orre

latio

n E

nerg

y (M

eV)

l=1 with T=0l=3 with T=0l=1 with T=1l=3 with T=1

HS,Y.TanimuraandK.Hagino,PRC87,034310(2013)

G.F.BertschandY.Luo,PRC81,064320(2010)

Evenwithlargespin-orbitsplidngforf-orbits,thespin-tripletcorrela1onswillbelargerthanthespin-singletoneforf>1.5

Pairingcorrela1onenergyof(J,T)=(0,1)and(1,0)statesinpfshell

DiagonalisetheHamiltonianV(T=1,S=0)+V(T=0,S=1)+V(spin-orbit)

HFB+QRPAwithT=1andT=0pairingT=1pairinginHFBT=0pairinginQRPAHowlargeisthespin-tripletT=0pairingcorela1on?

O(GT ) =στ ±

Coopera1onofT=0andT=1pairinginGamow-TellerstatesinN=Znuclei

C.L.Bai,H.S.,M.Sasano,T.Uesaka,K.Hagino,H.Q.Zhang,X.Z.Zhang,F.R.Xu

Asapossiblemanifesta1onofT=0S=1pairingcorrela1onsinnucleiN=Z.

Phys.Le_.B719,pp.116-121(2013)

B = (Xuπvν −Yuνvπ ) π O(GT ) ν

C = X 2 −Y 2

EXP:Sasanoetal.,PRL107(2011)

Supermul1plet:WignerSU(4)symmetry(E.Wigner1937,F.Hund1937)(T=1,S=0)à(T=0,S=1)GTtransi1onisallowedandenhanced.

HFB+QRPAwithT=1andT=0pairingT=1pairinginHFBT=0pairinginQRPA

O(GT ) =στ ±

Gamow-TellerTransi1onsinnucleiwithN=Z+2C.L.Bai,HS,G.Colo,Y.Fujitaetal.,

σ , τ and στ are generators of SU(4)

PRC90,054335(2014)

np n

(T=0,S=1) (T=1,S=0)

B(GT)=6

σ ⋅τ

Supermul1plet:WignerSU(4)symmetry(T=1,S=0)à(T=0,S=1)GTtransi1onisallowedandenhanced.

Spacialsymmetryisthesamebetweentheini1alandfinalstates

n

Whathappensinpfshellnucleiwithstrongspin-tripletpairinginterac1ons?

protonsneutrons

1d3/2

1f7/2

2p3/22p1/21f5/2

Fermienergy

p-ptypeexcita1on

T=0S=1

BCSvacuum

v2 v2

Gamow-Tellertransi1onsinBCSvacuum

p-htypeexcita1on

ApairofSU(4)supermul1plet

T=1S=0

Gamow-Tellertransi1onsinN=Z+2pfnuclei

42Ca

O(GT ) =στ ±

HFB+QRPAwithT=1andT=0pairingT=0pairingstrengthinQRPAischangedbyafactorf=spin-triplet/spin-singlet

p-hspin-isospininterac1onisstronglyrepulsiveèhigherenergycollec1veGamow-Tellerstates.Spin-tripletT=0paringisa_rac1veandshipdownGTstrengthnearIASàSU(4)symmetryrestora1on

IAS

f=IS/IVpairingY.Fujitaetal.,PRL112,112502(2014)

Effectoftensorcorrela1onsissmallin42Ca.

Tensoreffectisseenin50Cr!

Tensoreffect

Summary

1.  Corpera1veeffctofT=0andT=1pairingcorrela1onsenhancethelow-energyGTstrengthinN=ZandN=Z+2nuclei.èRestora1onofsupermul1pletsymmetryin(T=1,J=0)and(T=0,J=1)statesinpfshellnuclei2.Acoopera1veeffectofT=0pairingandtensorinterac1onsarefoundinnucleiatthemiddleofpfshell.3.TheT=0pairingstrengthisdeterminedtobealmostthesamestrengthastheT=1pairingfromtheobservedrela1veenergiesofIASandthelow-energyGTstates;f=strength(T=0)/(T=1)~1.0irrespec1veoftheadoptedinterac1ons.

a.  FurtherstudyofPar1cle-vibra1oncoupling:YifeiNiu,GianlucaColob.  Finefidngsofenergydensityfunc1onsforRPAandQRPA(whichwasdonealreadyforShellmodelinterac1ons:ToshioSuzuki,MichioHonma

Theory