Nuclear Physics Revealed by the study of Gamow-Teller excitations ガモフ・テラー遷移の研究から見える原子核物理 Yoshitaka FUJITA Yoshitaka FUJITA RCNP & Dept. Phys., Osaka Univ. RCNP & Dept. Phys., Osaka Univ. つくば不安定核セミナー January 21, 2016 Department of Physics, Jyvaskyla, August, 2014 GT : Important weak response, simple operator Neptune = Neptune driving Waves weak interaction Powerful Waves = strong interaction) 1
Vibration Modes in Nuclei (Schematic) Gamow- Teller mode ( ) Isovector & Spin excitation Gamow-Teller transition ｓ Mediated by operator S = -1, 0, +1 and T = -1, 0, +1 ( L = 0, no change in radial w.f. ) no change in spatial w.f. Accordingly, transitions among j > and j < configurations j > j > , j < j < , j > j < example f 7/2 f 7/2 , f 5/2 f 5/2 , f 7/2 f 5/2 Note that Spin and Isospin are unique quantum numbers in atomic nuclei ! GT transitions are sensitive to Nuclear Structure ! GT transitions in each nucleus are UNIQUE ! 2
**Basic common understanding of -decay and Charge-Exchange reaction decays : Absolute B (GT) values, but usually the study is limited to low-lying states (p,n), ( 3 He,t) reaction at 0 o : Relative B (GT) values, but Highly Excited States ** Both are important for the study of GT transitions! -decay & CE Nuclear Reaction 2 1 -decay GT tra. rate = ( GT ) f B t K 1 / 2 B (GT) : reduced GT transition strength (matrix element) 2 = |<f| |i>| 2 *Nuclear (CE) reaction rate (cross-section) = reaction mechanism x operator =(matrix element) 2 x structure 3
-decay & Nuclear Reaction 2 1 -decay GT tra. rate = ( GT ) f B t K 1 / 2 B (GT) : reduced GT transition strength (matrix element) 2 = |<f| |i>| 2 *Nuclear (CE) reaction rate (cross-section) = reaction mechanism x operator =(matrix element) 2 x structure *At intermediate energies (100 < E in < 500 MeV) d /d ( q =0) : proportional to B (GT) Nucleon-Nucleon Int. : E in dependence at q =0 Strength central-type interactions Simple one-step reaction mechanism at intermediate energies ! V V V V Energy/nucleon Love & Franey PRC 24 (’81) 1073 4
N.-N. Int. : & Tensor- q -dependence T largest at q =0 ! larger than others ! Love & Franey PRC 24 (’81) 1073 -decay & Nuclear Reaction 2 1 -decay GT tra. rate = ( GT ) f B t K 1 / 2 B (GT) : reduced GT transition strength (matrix element) 2 = |<f| |i>| 2 *Nuclear (CE) reaction rate (cross-section) = reaction mechanism x operator =(matrix element) 2 x structure *At intermediate energies (100 < E in < 500 MeV) d /d ( q =0) : proportional to B (GT) 5
Simulation of -decay spectrum f-factor (normalied) 5000 1.2 Counts + 50 Cr( 3 He,t) 50 Mn g.s.(IAS),0 + 1 0.651,1 4000 E=140 MeV/nucleon o 0.8 θ =0 3000 + + 2.441,1 3.392,1 Q EC =8.152 MeV 0.6 2000 0.4 1000 0.2 0 0 0 1 2 3 4 5 6 5 0 Mn (MeV) E x in 5000 β intensity (relative) + β -decay: 50 Fe --> 50 Mn g.s.(IAS),0 + 0.651,1 4000 *expected spectrum assuming isospin symmetry 3000 + + 2.441,1 3.392,1 Q EC =8.152 MeV 2000 1000 0 0 1 2 3 4 5 6 5 0 Mn (MeV) x in E Y.F, B.R, W.G, PPNP, 66 (2011) 549 ( p , n ) spectra for Fe and Ni Isotopes T=1 Fermi GTR GTR Fermi GTR GTR Fermi GTR GTR Rapaport & Sugerbaker 6
Comparison of (p, n) and ( 3 He,t) ０ o spectra 58 Ni( p , n ) 58 Cu Counts E p = 160 MeV IAS J. Rapaport et al. 58 Ni( 3 He, t ) 58 Cu NPA (‘83) E = 140 MeV/u GTR Y. Fujita et al., GT EPJ A 13 (’02) 411. H. Fujita et al., PRC 75 (’07) 034310 0 2 4 6 8 10 12 14 Excitation Energy (MeV) Comparison of (p, n) and ( 3 He,t) ０ o spectra 58 Ni( p , n ) 58 Cu E p = 160 MeV Counts J. Rapaport et al. 58 Ni( 3 He, t ) 58 Cu NPA (‘83) E = 140 MeV/u GTR Y. Fujita et al., EPJ A 13 (’02) 411. H. Fujita et al., PRC 75 (’07) 034310 High selectivity for GT excitations. Proportionality: d /d B(GT) 0 2 4 6 8 10 12 14 Excitation Energy (MeV) 7
-decay & Nuclear Reaction 2 1 -decay GT tra. rate = ( GT ) f B t K 1 / 2 B (GT) : reduced GT transition strength Study of Weak Response of Nuclei (matrix element) 2 by means of *Nuclear (CE) reaction rate (cross-section) Strong Interaction ! = reaction mechanism using -decay as a reference x operator =(matrix element) 2 x structure A simple reaction mechanism should be achieved ! we have to go to high incoming energy **GT transitions in each nucleus are UNIQUE and INFORMATIVE ! *( 3 He,t): high resolution and sensitivity ! 8
**GT transitions in each nucleus are UNIQUE and INFORMATIVE ! - sd -shell nuclei - Spectra of p -shell Tz=1/2 Nuclei A=7 A=9 A=11 9
T=1/2 Isospin Symmetry Koelner Dom in Germany (157m high) Analogous Structures and Transitions in T=1/2 System Real Energy Space Isospin Symmetry Space (p,n)-type (p,n)-type -decay -decay g.s. -decay -decay g.s. g.s. -decay Q EC -decay Tz=+1/2 Tz=-1/2 (Z,N+1) (Z+1,N) g.s. (stable) Tz=+1/2 Tz=-1/2 (Z,N+1) (Z+1,N) (stable) 10
9 Be( 3 He,t) 9 B spectrum (at various scales) Relationship: Decay and Width Heisenberg’s Uncertainty Priciple x p t E Width E *if: Decay is Fast, then: Width of a State is Wider ! *if t =10 -20 sec E ~100 keV (particle decay) t =10 -15 sec E ~ 1 eV (fast decay) 11
9 Be( 3 He,t) 9 B spectrum (II) Isospin selection rule prohibits proton decay of T=3/2 state! C. Scholl et al, PRC 84, 014308 (2011) Isospin Selection Rule : in p -decay of 9 B p + 8 Be* 9 B* 1p-1h + p n p n T z : -1/2 + 0 = -1/2 T : 1/2 + 0 (low lying) = 1/2 T : 1/2 + 1 (higher Ex) = 1/2 & 3/2 *T=1 state in 8 Be is only above E x =16.6 MeV Therefore, p -decay of T=3/2 states is forbidden! 12
9 Be( 3 He,t) 9 B spectrum (III) 14.7 MeV T=3/2 state is very weak! Strength ratio of g.s. & 14.7 MeV 3/2 - states: 140:1 Shell Structure and Cluster Structure Excited state: Shell Model-like T=3/2 9 Li 9 C -decay T z =3/2 T z =-3/2 neutron: p 3/2 closed g.s.: Cluster-like proton: p 3/2 closed α α n p α α suggestion by 9 Be 9 B Y. Kanada-En’yo T z =1/2 T z =-1/2 13
-decay and ( 3 He,t) results C. Scholl et al, PRC 84, 014308 (2011) L.Buchmann et al., PRC 63 (2001) 034303. U.C.Bergmann et al., Nucl. Phys. A 692 (2001) 427. 9 Be( 3 He,t) 9 B spectrum (III) Information on: •Excitation Energy •Transition Strength •Decay Width 14.7 MeV T=3/2 state is very weak! Strength ratio of g.s. & 14.7 MeV 3/2 - states: 140:1 14
7 Li( 3 He,t) 7 Be spectrum 7 Li and 7 Be are Mirror Nuclei ! x 50 If 3 He+ a Compact structure Shell Structure and Cluster Structure Compact (Shell model-like) T=3/2 7 He 7 B T z =3/2 T z =-3/2 proton: s 1/2 closed g.s.: Cluster-like neutron: s 1/2 closed t T=1/2 α α 7 Li 7 Be T z =1/2 T z =-1/2 15
Spectra of p -shell Mirror Nuclei A=7 A=9 A=11 (p,n) and ( 3 He,t) Spectra on 11 B 11 B(p, n) 11 C E p =200 MeV T.N. Taddeucci et al., PRC 42 (1990) 935 Y. Fujita et al., PRC 70 (2004) 011206(R) 16
GT transitions to J =3/2 - states: J allowed Why 3/2 - 3 so weak! Y. Fujita et al., PRC 70 E ~300 keV (2004) 011206(R) Comparison: 11 B( 3 He,t) 11 C 8.105 & 3/2 - Shell Models No-core SM-cal: by Navratil & Ormand Phys. Rev. C 68 (’03)034305 8.105, 3/2 - state is not reproduced ! “quenching” included 17
11B → 11C: GT transition strengths 11 B(3He,t) 11 C Y. Fujita, et al. PRC 70, 011306(R)(2004). no-core shell-model small B(GT) : missing of 3/2 - 3 in NCSM calculation Shell-model-like and Cluster structures in 12 C E x (MeV) 8 [ Be( 2 ) l 2 ] ,... 0 J 12 C linear-chain like equilateral-triangular 0 + 3 3 clusters develop 3 - 1 3 threshold & 0 + 2 various structures 7.4 MeV appear dilute cluster gas Hoyle state shell model like shell model like ～ 0 + 0 MeV 1 E. Uegaki, et al. Prog. Theor. Phys. 57 , 1262 (1977) M. Kamimura, et al. J. Phys. Soc. Jpn. 44 (1978), 225. A. Tohsaki, et al. Phys. Rev. Lett. 87 , 192501 (2001) by Suhara & En’yo ‘08 Y. Kanada-En’yo, Prog. Theor. Phys. 117 , 655 (2007) etc 18
Coexistence of shell-model and cluster states by Y. Kanada-En’yo PRC 75 (’07) 024302 12 C 11 C ( 11 B) Excited 3 7 Li+ 2 + 3 He p 3/2 p 3/2 low-lying sub-shell shell- closure model-like 11 B → 11 C* GT-transition strength by Y. Kanada-En’yo PRC 75 (’07) 024302 Y. Fujita, et al. PRC 70, 011306(R)(2004). no-core shell-model 11 C AMD B(GT) 0.45 0.48 0.71 0.68 0.02 0.57 0.8 exp 0.7 AMD 0.6 Small B(GT) of 3/2 - 3 : well reproduced SM 0.5 0.4 0.3 0.2 0.1 0 2 + 3 He 3/2 - 5/2 - 3 2 19
**Connection between GT and E0 transitions** T=1/2 Isospin Symmetry Koelner Dom in Germany (157m high) 20
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