Yoshitaka Fujita

Gamow-Teller strengthsin p-, sd- and pf-shell nucleias a test case of shell-model calculations-Comparison of B(GT): Exp. & SM-Y. Fujita, Osaka Univ.at SM workshop, Tokyo, 2006. Jan.26-28NS Workshop 2006

Vibration Modes in Nuclei (Operators)NS Workshop 2006

B(GT) derivation★b decay :fundamental, but Ex range :limited "Q-windowlimitation"★(p, n) reaction at intermediate energies (E = 100-500 MeV)"proportionality" : B(GT) and s(0 o )s(0 o ) = KNst | Jst(0 o ) | 2 B(GT)⇒Breakthrough against "Q-window limitation"but resolution : rather poor (DE = 200-400 keV)★( 3 He, t) reaction at intermediate energies (E = 130-150 MeV/u)"high resolution" (DE < 50 keV)☆magnetic spectromerter, matching techniques"proportionality" : good (B(GT) > 0.03)⇒Breakthrough against "Energy resolution limitation"⇒Reliable B(GT) values for individual transitionsNS Workshop 2006

Direct Reactions with Light Projectilesinteraction(operator)Projectile3Heby Berta RubioTarget|i> |f>Pick-upCoulomb ExcitationElastic ScatteringInelastic ScatteringStrippingCharge-exchangeNS Workshop 2006Similarity with b decay!Ejectile t

B(GT) derivation★b decay :fundamental, but Ex range :limited "Q-windowlimitation"★(p, n) reaction at intermediate energies (E = 100-500 MeV)"proportionality" : B(GT) and s(0 o )s(0 o ) = KNst | Jst(0 o ) | 2 B(GT)⇒Breakthrough against "Q-window limitation"but resolution : rather poor (DE = 200-400 keV)★( 3 He, t) reaction at intermediate energies (E = 130-150 MeV/u)"high resolution" (DE < 50 keV)☆magnetic spectromerter, matching techniques"proportionality" : good (B(GT) > 0.03)⇒Breakthrough against "Energy resolution limitation"⇒Reliable B(GT) values for individual transitionsNS Workshop 2006

Nucleon-Nucleon Int. : E in dependenceat q =0central-type interactionsSimple one-step reaction mechanismat intermediate energies!V 0V stV tV sNS Workshop 2006

stN.-N. Int. : st & Tensor-t q-dependencelargest at q=0 !larger than others !TtNS Workshop 2006Love & Franey PRC 24 (’81) 1073

28Si: CEReactions(I)E p =135 MeVB.D.Anderson et al.,P.R.C 43 (‘91) 5028Si( 3 He,t)E t =67 MeV/uJ.Janecke et al.,N.P.A 526 (‘91) 1NS Workshop 2006

28Si: CEReactions(II)E p =135 MeVB.D.Anderson et al.,P.R.C 43 (‘91) 50Y.Fujita et al.,P.R.C 55 (’97) 1137NS Workshop 2006

(p, n) spectra for Fe and Ni IsotopesNS Workshop 2006

(p, n) spectra for A>90 NucleiGT-GRNS Workshop 2006

B(GT) derivation★b decay :fundamental, but Ex range :limited "Q-windowlimitation"★(p, n) reaction at intermediate energies (E = 100-500 MeV)"proportionality" : B(GT) and s(0 o )s(0 o ) = KNst | Jst(0 o ) | 2 B(GT)⇒Breakthrough against "Q-window limitation"but resolution : rather poor (DE = 200-400 keV)★( 3 He, t) reaction at intermediate energies (E = 130-150 MeV/u)"high resolution" (DE < 50 keV)☆magnetic spectromerter, matching techniques"proportionality" : good (B(GT) > 0.03)⇒Breakthrough against "Energy resolution limitation"⇒Reliable B(GT) values for individual transitionsNS Workshop 2006

26Mg(p, n) 26 Al & 26 Mg( 3 He,t) 26 Al spectraR. Madey et al.,PRC 35 (‘87) 2001Y. Fujita et al.,PRC 67 (‘03) 064312NS Workshop 2006

T=1 system1+0+Real Energy SpaceCoulomb Energy: importantA=26 system(p,n)-typeNS Workshop 200626MgT z=+11 + 1+1+1+0+ , IAS1+(stable)26AlT z=01+0+b + -decay26SiT z=-1

T=1 symmetry : Structures & Transitions1+T z=+1 T z=0 T z=-1(in isospin symmetry space*)1 +(p,n)-typeV st1+1+1+0+ 0+ , IASV tt 0+1+T z=+1 T z=0T z=-126MgV stNS Workshop 2006Z=12, N=1426AlZ=13, N=131+b + -decaystst26SiZ=14, N=12

B(GT) values from SymmetryTransitions (A=26)from ( 3 He,t)B(GT)0.106(4)1 +3.724from b-decayB(GT)0.117(4) 1+ 2.740 0.113(5)0.112(4) 1+1 +2.072 0.091(4)0.527(15)1.851 0.537(14)1.081(29) 1 + 1.058 1.098(22)0 + 0 + IAS0.22805++26 Mg 26 26 Al SiT z =+1 T z =0 T z =-1NS Workshop 2006

54Fe(p,n) & 54 Fe( 3 He,t)B(GT)0.74(5)B(GT)0.50(6):preliminary!54Fe(p, n) 54 CoEp = 135 MeVB.D. Anderson et al.,PRC 41 (’90) 1474NS Workshop 2006

54Fe(p,n) & 54 Fe( 3 He,t)+widthat N=28: Good agreement!NS Workshop 2006

56Fe target: ( 3 He,t ) vs. (p, n)( 3 He,t) with 600 keV width1.7 MeV GT stateenhanced!NS Workshop 200612 N g.s.140 MeV/nucleonat N=30, exceptional enhancement of lowest GT state!(p, n)Ep=160 MeV

56Fe( 3 He,t) : low-lying GT states2p 3/2 2p 3/2NS Workshop 2006Z=26 N=30

Wave function (radial direction)1d1f2p: with “node”!56Fe → 56 Co lowest 2p 3/2→ 2p 3/2GT transition low-lying 2p 3/2→ 2p 1/2higher Ex 1f 7/2→ 1f 5/2Due to “surface nature” of ( 3 He,t), reactionstrength may be affected by the presence of the node.NS Workshop 2006

?? Proportionality ??*proportionality has been most well studied in ( 3 He,t)Universal proportionality X for all mass ASpecific proportionality O for each A(of the order of a few - 10%)Larger uncertainties of the proportionality:1) for the j < j < transitions (weak!)(ex. p 1/2 p 1/2 , d 3/2 d 3/2 )2) when a w.f. has a node(ex. 2s 1/2 2s 1/2 , 2p 3/2 2p 3/2 )at N=18 at N=30NS Workshop 2006

***at the sd -shell region***NS Workshop 2006

**A=23 T=1/2 1/2 transitionsNS Workshop 2006

A=23 B(GT) : Comp. Exp. & SMIAS23Na( 3 He,t) 23 Mgdifferent vertical scales !quenching factor (0.7*) 2 is needed!NS Workshop 2006

**A=26 T=1 0 transitionsNS Workshop 2006

26Mg( 3 He,t) spectrum and SM cal. B(GT)NS Workshop 2006by H. Nakada, USD int.

B(GT) distributions (low-lying): Exp. & SMquenching included!NS Workshop 2006

**A=28 T=0 1 transitionsNS Workshop 2006

Isospin StructureofT=0 Nucleus 28 SiNS Workshop 200628P28Si28Al

28Si Comp:( 3 He,t) & (e, e’)NS Workshop 2006

A=28 B(GT) : Comp. Exp. & SMNS Workshop 2006

A=28 B(M1) : Comp. Exp. & SMB(M1)NS Workshop 2006

***at the Ni region offp –shell***NS Workshop 2006

(p,n) exp.SM cal.SM-cal: GT- from Ni isotopesNS Workshop 2006E. Caurier et al., NPA653 (‘99) 439KB3G int.

Comparison of B(GT): Exp. & TheoryY. Fujita et al.,Eur. Phys. J 13 (’02) 411KB3GNS Workshop 2006

InteractionDependencebyM. HonmaNS Workshop 2006

64Ni( 3 He,t) 64 Cu spectrumby L-A. PopescuNS Workshop 2006

B(GT) Running Sum0 2 4 6 Exp 3/2 p 3/2 p 3/2 p 1/2f 5/2 f 5/2 f 7/2 f 5/2NS Workshop 2006

60,62,64Ni( 3 He,t)60,62,64CuSpectraIASs are alignedNS Workshop 2006

GT transitions from Ni isotopesIsospinsymmetryenergy&Ratio ofisospin CGcoefficientsNS Workshop 2006

Ni isotopesT 0 -1T0 T 0 +1NS Workshop 2006IASs are aligned

(p, n) spectra for Fe and Ni IsotopesNS Workshop 2006

***at the lower part offp -shell region***NS Workshop 2006

**Critical case: A=41,T z =3/21/2 transitionsNS Workshop 2006

T=3/2 system: structures & transitions(p,n)-typeg.s.(stable)b+-decayTz=+3/2(Z,N+3)IASIASb+-decayg.s.g.s.T=1/2Tz=+1/2 Tz=-1/2 Tz=-3/2(Z+1,N+2) (Z+2,N+1) (Z+3,N)NS Workshop 2006g.s.19 41 K 22 2041Ca 21 2141Sc 20 2241Ti 19T=3/2T=3/2

Comparison of two b-decay resultsNucl. Phys. A621 (1997) 689Phys. Rev. C 58 (1998) 2677NS Workshop 2006

Comparison:41K( 3 He,t) 41 Ca&41Ti b-decayY. Fujita et al.,PRC 70 (’04) 054311NS Workshop 2006

Comparison:41K( 3 He,t) 41 Ca&Shell ModelY. Fujita et al.,PRC 70 (’04) 054311B.A. BrownNS Workshop 2006

( 3 He,t) B(GT) : J = 1/2, 3/2, 5/2NS Workshop 2006

Exp. & SM B(GT) : J = 1/2, 3/2, 5/2Exp.SM cal.NS Workshop 2006

**A=46, T=0, 1 systemNS Workshop 2006

46Ti( 3 He,t)T. Adachi et al.PRC in pressNS Workshop 2006

B(GT)ExperimentvsCalculationsNS Workshop 2006

B(GT) : Exp. vs. SMM. Honma, T. Otsuka et.al.deformation mixing of sd -shell configurationsNS Workshop 2006

**”Width” represents a lot !NS Workshop 2006

26Mg( 3 He,t) spectraNS Workshop 2006

Importance of Isospin : p-decay of 26 Alp25 Mg + protonn+ProtondecayTz : 1/2 + (-1/2) = 026 AlT : 1/2 + 1/2 = 0 or 13/2 + 1/2 = 1 or 2#Sp (p-sep. energy) in 26Al : 6.31 MeV#T=3/2 state in 25Mg : Ex > 7.79 MeVeffective S p in 26Alfor T = 0, 1 states : Ex = 6.31 MeVfor T = 2 states : Ex = 14.1 MeVNS Workshop 2006pn

Comparison: 26 Mg( 3 He,t) 26 Al and 26 Mg(d, 2 He) 26 NaT. Niizeki et al.,NS Workshop 2006N.P. A577 (1994) 37c

26Mg( 3 He,t) spectrum and SM cal. B(GT)NS Workshop 2006by H. Nakada, USD int.

9Be( 3 He,t) 9 B spectrum (at various scales)NS Workshop 2006

9Be( 3 He,t) 9 B spectrum (II)Isospin selection rule prohibitsproton decay of T=3/2 state!NS Workshop 2006

**Limitation of the SpaceNS Workshop 2006

(p,n) and ( 3 He,t) Spectra on 11 B11B(p, n) 11 CE p =200 MeVT.N. Taddeucci et al.,PRC 42 (1990) 935Y. Fujita et al., PRC 70(2004) 011206(R)NS Workshop 2006

Comparison:11B( 3 He,t) 11 C&Shell Modelsnon-core SMcal:By Navratil & OrmandPhys. Rev. C 68 (’03)034305NS Workshop 2006Y. Fujita et al., PRC 70(2004) 011206(R)

Summary*Observed strengths are well reproduced(by including the recommended“quenching factor”)*Fragmentation of strengths:A=23, 26 very good !A=28 not so wellA=41 sd & f should be includedA=46 deformed: fp and sd are neededA=58 GXPF1 reproduced well !*Widths of states: more sophisticated !?NS Workshop 2006