Isoscalarspin-tripletpairingandtensorcorrela1onsonSpin-Isospinresponse--KyotoCANHP2015Workshop5thweek“Energydensityfunc1onals”---Oct.19,2015

HiroyukiSagawaRIKEN/UniversityofAizu

・Skyrmetensorinterac1onsSpin-isospinexcita1onsandsumrules・Pairingcorrela1onsT=1,S=0andT=0,S=1pairsEnergyspectraofN=Zodd-oddnuclei.Gamow-Tellerexcita1onsinN=Z+2pf-shellnucleiinterplaybetweenT=0pairingandtensorcorrela1ons

Tensor correlations on Nuclear Structure

Shell evolution by tensor correlations　（spin-orbit splitting)

Binding energies Deformations EOS

Spin-Isospinexcita1onsa)  Gamow-Tellerexcita1onsb)  Spin-Dipole(SD)excita1onsQuenchingofsumrules　withinRPAmodelMul1poledependenceofSDexcita1ons

A self-consistent framework to describe nuclei in the whole mass region

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-orbitsplicng2. Analy1cformulasformul1poleexpansionforspin-dependentexcita1ons

Mean field ----Spin-orbit splitting----

1) 0, ( == pnq qq −=1'

5T

5

52211

5221121

100MeV.fmU)(T245

MeV.fm170125

MeV.fm9.48)(81

MeV.fm7.80)(81)(

81

=+=

−==

−=+−=

=+−−=

β

U

xtxt

xtxttt

T

C

C

α

β

α

smaller positive larger negative ,

splittingorbit -spin sign βα

5T

5

MeV.fm)2(60

MeV.fm)2(60family

−=+=

−=+=

IβJ

TIJ

C

TC

ββ

ααα

Exp. = AME2012 FRDM (1992)

σth = 0.6478 MeV

0 20 40 60 80 100 120 140 160 Neutron Number N

− 5 − 4 − 3 − 2 − 1

0 1 2 3 4

Mas

s D

iffer

ence

Mex

p − M

th (M

eV)

Exp. = AME2012 FRDM (2012)

σth = 0.5728 MeV

− 4 − 3 − 2 − 1

0 1 2 3 4 5

ADNDT(2015)inpress.

-

Z N

21

−= lj

21

+= lj21

+= lj

Effect of tensor interaction on spin-orbit splitting

21

−= lj

α:n-n or p-p larger with j> β：n-p smaller　with j>

G.Colo, H. Sagawa, S. Fracasso, P.F. Bortignon, Phys. Lett. B 646 (2007) 227.

TαTβ

2/91g

2/71g

2/111h

2/91h

2/111h

protons

neutrons

Z=50

N=70

Exp. Data : J.P.Schiffer et al., P.R.L.92, 162501(2004)

Notonlytensor,butalsopairingandpar1cle-vibra1oncouplingeffectsmayplayequallyimportantroles.Itismarginaljusttolookats.p.statestofindoutthetensorcorrela1ons!

1.Experiments:Spectroscopicfactors2.Theory:ConsistentSkyrmespin-orbitinterac1onparametersincludingtensorinterac1ons

Spin-isospin physics: Gamow-Teller responses

Progress in Last century

●　1963 GT giant resonance predicted, GT(Ikeda) sum rule 3(N-Z) collectivity? l  ∼1980 GT giant resonances established l  Strength quenched/missing: 50-60% of 3(N-Z) due to Δ-h or 2p-2h ? l  1997 ∼90% of 3(N-Z) found (2p-2h dominance) l  Charge-exchange reactions on stable target nuclei l  CHEX reactions: (p,n)/(n,p) and (3He,t)/(t,3He) reactions at intermediate energy

l  C. Garrde, NPA396(1982)127c.

l Wakasa et al., PR　C 55, 2909 (1997)

GT strength quenching problem

C. Gaarde NP A396, 127c(1983)

l Wakasa et al., PR　C55, 2909 (1997)

CourtesyofH.Sakai

●●

●Yakoetal.,

Giant Resonance

Ex

Strength

Low energy state

2

0ˆ)( λOiEkmi

ik∑=

[ ][ ]0 ˆ,,ˆ021)1( λλ OHOm =

Energy-weighted(EW)andNEWsumrules

Gamow-TellerIkedasumrule

11

Model-independent sum rule : GT(Ikeda) sum rule

cf: Fermi transition

=30for90Zr

=132for208Pb

Thetensorforceandcharge-exchangeexcita2ons

The main peak ismoved downward bythe tensor force butthecentroidismovedupwards!

Z N

21

−= lj

−tσ

21

+= lj

Gamow-Teller

C.L.Bai, HS, H.Q.Zhang, X.Z.Zhang, G.Colo and F.R.Xu, P.L.B675,28 (2009). C.L.Bai, H.Q. Zhang, X.Z.Zhang, F,R,Xu, HS and G.Colo, PRC79, 041301(R) (2009).

21

+= ljS3T

+=1πλ

Tensorcorrela1onsonSpin-Isospinmode

S3+Tensor

O− =σ t−O+ =σ t+

=3(N-Z)

About10%ofstrengthismovedbythetensorcorrela1onstotheenergyregionabove30MeV.RelevancefortheGTquenchingproblem.

1p-1htensor 1p-1htensor

Energy-weightedsumrules2

0ˆ)( λOiEkmi

ik∑=

[ ][ ]0 ˆ,,ˆ021)1( λλ OHOm =

m−(0)−m+(0) = 3(N − Z ) = 30 for 90Zr132 for 208Pb

Mul1poleExpansionofTensorInterac1ons

21

212

*121

)()ˆ()ˆ()(rrrrrYrYrr lmlm

lm

−=− ∑

δδ

!!

VT ∝T(λ,κ ){[σ1 ×[∇1 ×Yl=1(r1)](λ )}(κ )[σ 2 ×[∇2 ×Yl=1(

r2 )](λ ' )}(κ )}(0)δ(r1 − r2 )

1+ T(λ=λ '=2,κ=1)

⇒ repulsive

1+ T(λ=2,λ '=0,κ=1)

⇒ strong mixing between Gamow-Teller and

spin-quadrupole excitations!

WhydoesTensorinterac1ondecreaseGTstrengthinpeakregion?

+++

+

=×

⋅

3,2,1 ]Y[ excitation Quadrupole-Spin excitationTeller -Gamow : 1

)(2

2 λσ

τσλr

About10%ofstrengthismovedbythetensorcorrela1onstotheenergyregionabove30MeV.RelevancefortheGTquenchingproblem.

1p-1htensor 1p-1htensor

Energy-weightedsumrules2

0ˆ)( λOiEkmi

ik∑=

[ ][ ]0 ˆ,,ˆ021)1( λλ OHOm =

m−(0)−m+(0) = 3(N − Z ) = 30 for 90Zr132 for 208Pb

•  Totalstrength–  Asymmetricsinglebump

  Extendupto～50MeV  Sameas90Zr(p,n)results

–  SIIIprovidesbeperdescrip1on•  0-strength

–  Quenched  Seemstobefragmented

•  1-strength–  Soqenedcomparedwiththeory

  PeakshiqtolowerEx•  2-strength

–  Hardenedcomparedwiththeory  PeakshiqtohigherEx

PuzzleinSDStrengthDistribu1ons（Wakasa,SIR2010,18-21Feb.,2010)

  No Skyrme int. which reproduces both total and separated strengths   ΔJπ-dependent correlation ? → Require further investigations

H. Sagawa et al., PRC 76, 024301 (2007).

Asystema1cstudyoftensorinterac1onsonSpin-Isospinexcita1ons

(T , U) SG2+Te1 (500,-350) Te2 (600, 0) Te3 (650, 200) Sly5+Tw (888,-408)

BAI, SAGAWA, COLO, ZHANG, AND ZHANG PHYSICAL REVIEW C 84, 044329 (2011)

FIG. 3. (Color online) The charge-exchange SD strength distributions of 208Bi, calculated with the T43 interaction. The dashed, dotted, anddashed-dotted curves show the results without tensor interaction, with the only triplet-even and only triplet-odd tensor interactions, respectively,while the solid curve shows the results with the full tensor interaction. The discrete RPA results have been smoothed by using Lorentzianfunctions having a width of 2 MeV. See the text for more details.

Let us examine further the effects of the triplet-even andtriplet-odd tensor interactions in 16O in comparison with 208Pb.In Figs. 2 and 3, we show how the T and U tensor termschange the peaks of the SD strength distributions in 16F and208Bi, respectively. In the left and right panels the results ofSGII+Te3 and T43 are shown, respectively. We will firstexamine 16F SD strength in Fig. 2. For 0− excitations, therole of T and U are opposite in the case of SGII+Te3, whileboth terms act repulsively in the case of T43. The T term ofSGII+Te3 gives a repulsive effect and the U term induces anattractive effect, while both terms are repulsive in the case ofT43. This can be understood from Eq. (2) and the signs of Tand U in Table I. For 1−, the correlations become oppositethose for 0−, namely the T and U terms of SGII+Te3 givean attractive and a repulsive effect, respectively, while bothterms are attractive in the case of T43. The energy differencebetween the main peaks of 0− and 1− is 0.9 and 0.7 MeV forSGII+Te3 and T43 without the tensor terms, while it becomes2.5 and 3.9 MeV for SGII+Te3 and T43 with the tensor terms.Thus the energy difference between the two main peaks in16F reflects the sign of U term effectively since the negative(positive) sign enhances (quenches) the difference. The 2−

strength distributions are not much affected by the tensorcorrelations, while the sum rule values are slightly enhanced.

The roles of the T and U terms are demonstrated in Fig. 3 forthe case of 208Bi. For the 0− and 1− multipoles, the qualitative

features are the same as in 16F, i.e., the T and U terms pushthe main peak in opposite directions in the case of SGII+Te3,while they both push up the main peak in the case of T43.In the 2− case, one can see appreciable tensor effects on thestrength distributions which are spread in a wide energy regionin 208Bi.

We will study next the peak energy difference δEp between0− and 1− in both 16F and 208Bi in Table IV. The energydifference is rather small without the tensor interactions,namely it is about 1 MeV in both nuclei. The triplet-evenT term gives clear separations of the peak energies, that is,3–4 MeV in 16F and 11–12 MeV in 208Bi. The triplet-odd

TABLE IV. Energy differences between the main 0− and 1−

peaks, δEp ≡ E(0−) − E(1−), in 16F and 208Bi. The four RPAresults correspond to the case without tensor interactions, with thetriplet-even T term, with the triplet-odd U term and with both T andU terms, respectively.

W/o tensor With T With U With T and U

16F T43 0.7 3.1 1.5 3.9SGII+Te3 0.9 4.0 −0.6 2.5

208Bi T43 1.2 11.0 4.9 13.6SGII+Te3 1.9 12.0 −2.9 8.2

044329-4

BAI, SAGAWA, COLO, ZHANG, AND ZHANG PHYSICAL REVIEW C 84, 044329 (2011)

FIG. 3. (Color online) The charge-exchange SD strength distributions of 208Bi, calculated with the T43 interaction. The dashed, dotted, anddashed-dotted curves show the results without tensor interaction, with the only triplet-even and only triplet-odd tensor interactions, respectively,while the solid curve shows the results with the full tensor interaction. The discrete RPA results have been smoothed by using Lorentzianfunctions having a width of 2 MeV. See the text for more details.

Let us examine further the effects of the triplet-even andtriplet-odd tensor interactions in 16O in comparison with 208Pb.In Figs. 2 and 3, we show how the T and U tensor termschange the peaks of the SD strength distributions in 16F and208Bi, respectively. In the left and right panels the results ofSGII+Te3 and T43 are shown, respectively. We will firstexamine 16F SD strength in Fig. 2. For 0− excitations, therole of T and U are opposite in the case of SGII+Te3, whileboth terms act repulsively in the case of T43. The T term ofSGII+Te3 gives a repulsive effect and the U term induces anattractive effect, while both terms are repulsive in the case ofT43. This can be understood from Eq. (2) and the signs of Tand U in Table I. For 1−, the correlations become oppositethose for 0−, namely the T and U terms of SGII+Te3 givean attractive and a repulsive effect, respectively, while bothterms are attractive in the case of T43. The energy differencebetween the main peaks of 0− and 1− is 0.9 and 0.7 MeV forSGII+Te3 and T43 without the tensor terms, while it becomes2.5 and 3.9 MeV for SGII+Te3 and T43 with the tensor terms.Thus the energy difference between the two main peaks in16F reflects the sign of U term effectively since the negative(positive) sign enhances (quenches) the difference. The 2−

strength distributions are not much affected by the tensorcorrelations, while the sum rule values are slightly enhanced.

The roles of the T and U terms are demonstrated in Fig. 3 forthe case of 208Bi. For the 0− and 1− multipoles, the qualitative

features are the same as in 16F, i.e., the T and U terms pushthe main peak in opposite directions in the case of SGII+Te3,while they both push up the main peak in the case of T43.In the 2− case, one can see appreciable tensor effects on thestrength distributions which are spread in a wide energy regionin 208Bi.

We will study next the peak energy difference δEp between0− and 1− in both 16F and 208Bi in Table IV. The energydifference is rather small without the tensor interactions,namely it is about 1 MeV in both nuclei. The triplet-evenT term gives clear separations of the peak energies, that is,3–4 MeV in 16F and 11–12 MeV in 208Bi. The triplet-odd

TABLE IV. Energy differences between the main 0− and 1−

peaks, δEp ≡ E(0−) − E(1−), in 16F and 208Bi. The four RPAresults correspond to the case without tensor interactions, with thetriplet-even T term, with the triplet-odd U term and with both T andU terms, respectively.

W/o tensor With T With U With T and U

16F T43 0.7 3.1 1.5 3.9SGII+Te3 0.9 4.0 −0.6 2.5

208Bi T43 1.2 11.0 4.9 13.6SGII+Te3 1.9 12.0 −2.9 8.2

044329-4

C.L.Baietal.,PRL105,072501(2010)

SLy5+Tw

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

=⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

−−

=−

−

−

210

for 50/1

6/11

125V

2

,1TE)( λλ

λ hOpT

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

=⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

−=−

−

−

210

for 50/1

6/11

125V

2

,1TO)( λλ

λ hOpU

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

=⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

−

−

−

210

for repulsiveattractiverepulsive

λ

ττλλλ .

21

21V matrix icantisymmtr AST,

)(⎥⎦

⎤⎢⎣

⎡ +−= UbTa

2ー

１ー

０ー

σ

l

l

l

σ

σ

=aT

=bU

T(triplet-eventensor)iswellconstrainedbyspin-isopinexcita1onsirrespec1veofcentralpartofSkyrmeforces.T=500+/-100MeVfm^(5)

U(triplet-odd)isnotwellconstrainedbyexis1ngsetsofexperimentaldata.

Asystema1cstudyoftensorinterac1onsonSpin-Isospinexcita1onsbyHF+RPA

(L = 0,S =1)J =1,T = 0 ⇒

T=1,S=0pair

T=0,S=1pair

p(n)　 p(n)

p n

T=1S=0pairingandT=0S=1pairinginterac1ons

Howwecandisentangleinquantummany-bodysystems.ètwokindsofsuperfluidity?

(L = S = 0)J = 0,T =1 ⇒

T=1S=0pairingpairinginterac1ons

T=1pairing(n-n,p-ppairingcorrela1ons)èisovectorspin-singletsuperfluidity●mass(odd-evenstaggering) ●energyspectra(gapbetweenthefirstexcitedstateandthegroundstateineven-evennuclei)●momentofiner1a●n-norp-pPairtransferreac1ons●fissionbarrier(largeamplitudecollec1vemo1on)

Ø binding energy

Sn (N)= B(N) – B(N-1)

pairing gap parameter

Bohr-Mopelson,NuclearStructureI(1969)

Δ(pairinggap)

Quasi-par1cleexcita1on

Snisotopes:2+states

rigidji ji

xInglis I

jJiI =

−= ∑

> εε

2

2 ∑ +

−=

ji ji

jijixpairing EE

uvvujJiI

,

22)(

2

rigid rotor vs. superfluid rotor

　　　　Moment of Inertia

Rota1onofdeformednucleus

Bohr-Mopelson,NuclearStructureII(1975)

T=1S=0pairingandT=0S=1pairinginterac1ons

T=1pairing(n-n,p-ppairingcorrela1ons)èspinsingletsuperfluid●mass(odd-evenstaggering) ●energyspectra(gapbetweenthefirstexcitedstateandthegroundstateineven-evennuclei●momentofiner1a●n-norp-pPairtransferreac1ons●fissionbarrier(largeamplitudecollec1vemo1on)

T=0pairing(p-npairingwithS=1)èspintripletsuperfluid?●N=ZWignerenergy(s1llcontroversial)●EnergyspectrainnucleiwithN=Z(T=0andJ=Jmax)●n-ppairtransferreac1on●low-energysuper-allowedGamow-Tellertransi1oninN=ZandN=Z+2betweenSU(4)supermul1ples(C.L.Baietal.)

(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-orbitsplicng,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-orbitsplicngforf-orbits,thespin-tripletcorrela1onswillbelargerthanthespin-singletoneforf>1.5

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

Measured1+1and0+1levelsofodd-oddN=Znuclei

147N7

189F9 30

15P15 3417Cl17 42

21Sc21g.s.(1+,0)

(Jπ,T)=(0+,1)2.31MeV

1.04MeV0.68MeV

-0.46MeV -0.61MeV

5829Cu29

0.20MeV

•  n-pPaircorrela1onsstudiedby3-bodymodelü  T=0,1twochannelsü  T=0,S=1isaprac1vestrongerthanT=1,S=0pair　cf.dueteron,matrixelementsinshellmodelsü  InfinitenucleiN>Z,thestrongspin-orbitcouplingmayquenchorevenkillT=0pairing

　　 whenlislarger,thespin-orbitislargerandT=0paircorrela1onsdecrease

Y.Tanimura,HS,K.Hagino,PTEP053D02(2014)

Determina1onofparametersv0,vls:neutronsepara1onenergyvs,vt:pnscaperinglengthwithEcut(=20MeV)vs/vt=1.7(spin-tripletpairingismuchstrongerthanspin-singlet)xS,xt,α:1+,3+,0+in18Fenergiesarefiped

n

p

Core

3体模型

2粒子配位でHを対角化

Three-bodyModel

Diagonaliza1oninalargemodelspace

pnpairinginterac1on

vt/v

s

Ecut=kcut2/2m

g.s.(1+,0)

(Jπ,T)=(0+,1)2.31MeV

1.04MeV0.68MeV

-0.46MeV -0.61MeV 0.20MeVB(M1)=0.047 19.71 1.32 0.08 6.16

(a)実験 (NNDC,hBp://www.nndc.bnl.gov/)

(b)計算結果

0.05MeV

1.04MeV

0.02MeV

-0.69MeV -0.61MeV0.68MeV

6.80 0.580.1518.19

147N7

189F9 30

15P15 3417Cl17 42

21Sc21 5829Cu29

(0.24)(0.68)

1.E0+-E1+andB(M1)ü 　Inversionof1+and0+

ü 18F,42Scn LargeB(M1)n AccurateE0+-E1+(42Sc)

Experiment

Three-bodymodel

Theinversionof1+and0+showsaclearmanifesta1onofthecompe11onbetweenspin-orbitandthespin-tripletpairing.

Y.Tanimura,HS,K.Hagino,PTEP053D02(2014)

Results

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LargeB(M1)in18Fand42Sc18F：

1+and0+canbeconsideredasthestatesinthesameSU(4)mul1plets(LST)=(0,1,0),(0,0,1)Thesameas42Scin1f-orbits

18F

18O 18Ne

...

...

...(Jπ,T)=(0+,1) (0+,1)

(1+,0)

(0+,1)

SU(4)6重項

Large (small)SU(4)generator

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1+àP(S=1)=90.1%,(1d)20+àP(S=0)=82.2%,(1d)2

mul1plet

results

14N 18F 30P 34Cl 42Sc 58Cu

Valenceorbital p1/2 d5/2 s1/2 d3/2 f7/2 p3/2

orbital 1.09 1.28 0.21 2.28 2.91 0.09

-2.78 7.44 -1.21 -3.65 6.34 1.47

5x10-5 3x10-3 3x10-5 -1x10-4 2x10-3 -2x10-3

B(M1)↓(μN2)Exp. 0.047 19.71 1.32 0.08 6.16 ---

Calc. 0.68 18.19 0.24 0.15 6.80 0.58

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SeparateContribu1onto<f||O(M1)||i>(μN)

18Fand42Sc:largeB(M1)

ü (j=l-1/2)2spinandorbitalarecancelled(Lisetskiyetal.,PRC60,064310(’99))ü (j=l+1/2)2　spinandorbitalcoherent　　　　　　　　　(Lisetskiyetal.,PRC60,064310(’99))ü goodSU(4)symmetry

ü evenj=l+1/2notgoodSU(4)symmetry

14N,34ClB(M1)small

18F,42Sc　B(M1)large

58Cuは(M1)small

2.Gamow-TellerB(GT)

(Z,A) (Z+1,A)

0+

1+

1+

0+

A=18,42:strongtransi1onto1+1àgoodSU(4)symmetry

A=58:aweakB(GT)to1+1ànoSU(4)symmetry

D.R.Tilleyetal,NPA595,1(’95)T.Kurtukianetal,PRC80,035502(’09)Y.Fujitaetal,EPJA13,411(’02)Y.Fujita,privatecommunica1ons

※HalseandBarrep,Ann.Phys.(N.Y.)192,204(’89).Consistentresults

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

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.Lep.B719,pp.116-121(2013)

protonsneutrons

1d3/2

1f7/2

2p3/22p1/21f5/2

Fermienergy

BCSvacuum

v2 v2

Gamow-Tellertransi1onsfromBCSvacuuminN=Znuclei

T=1pair

protonsneutrons

1d3/2

1f7/2

2p3/22p1/21f5/2

Fermienergy

p-htypeexcita1on

BCSvacuum

v2 v2

Gamow-Tellertransi1onsinBCSvacuum

protonsneutrons

1d3/2

1f7/2

2p3/22p1/21f5/2

Fermienergy

p-ptypeexcita1onT=0S=1

BCSvacuum

v2 v2

Gamow-Tellertransi1onsinBCSvacuum

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

B = (Xuπvν −Yuνvπ ) π O(GT ) ν

C = X 2 −Y 2

Beyondmeanfieldeffect:Niuetal.,PRC85,034314(2012)

Sasanoetal.,PRC86,034324(2012) With(0.74)2quenchingfactor,s1ll30%missingstrength

Fineadjustmentofshellmodelint.

NostrongGTtransi1onsin6232Geè6231Gaβdecaywhichisconsistentwithourpictureofcollec1vityandnp-pairing.

GSIRISINGexperiment,E.Grodneretal.,PRL113,092501(2014)

SumofB(GT)=0.52

62Geè62Gaβdecay

Summary:N=Znucleus

1.Inversionof1+and0+statesintheenergyspectraandstrongM1transi1onsinodd-oddN=ZnucleiisinducedbyastrongT=0pairingcorrela1onscompe1ngwithT=1pairingandspin-orbitforce.

2.Coopera1veroleofT=0andT=1pairingsisstudiedinGamow-Tellertransi1onsofN=Znuclei3.ItispointedoutthatthelowenergypeakappearduetothestrongT=0pairingcorrela1onsinthefinalstates.Supermul1pletsofT=1,S=0andT=0andS=1pair4.  Energydifferenceoftwopeaksin56Nièsmallerspin-orbitsplicng5.  Futureperspec1ve(experiment):NewexperimentsinN=Znuclei,48Cr,wasapprovedbyPACinRIKEN.Furtherexperimentin64Ge.

a.  FurtherstudyofPar1cle-vibra1oncoupling:YifeiNiu,GianlucaColob.  Fineficngsofenergydensityfunc1onsforRPAandQRPA(whichwasdonealreadyforShellmodelinterac1ons:ToshioSuzuki,MichioHonma

Theory