Neptune = Neptune driving Waves weak interaction Powerful Waves = - PowerPoint PPT Presentation

Roles of pairing interactions in the formation of low- and high-energy Gamow-Teller excitations Yoshitaka FUJITA Yoshitaka FUJITA RCNP & Dept. Phys., Osaka Univ. RCNP & Dept. Phys., Osaka Univ. COMEX5, Sep. 14-18, 2015 Department of Physics, Jyvaskyla, August, 2014 GT : Important weak response, simple  operator

Neptune = Neptune driving Waves weak interaction Powerful Waves = strong interaction)

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 !

IS & IV pairing and “Residual Interactions” However, J  values of even-even nuclei are J  =0 + . We notice the importance of the spin-spin coupling. (pairing interaction) = 4 He =  1s 1/2 ex. J  =0 + proton neutron In general, interactions that are not included in a model are called “residual interactions” ex. “deuteron model” Isovector T=1 J  =0 + unbound J  =1 + Isoscalar T=0 bound=deuteron

**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 & 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)

Simulation of  -decay spectrum f-factor (normalied) 1.2 5000 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) x in E 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

Rapaport & Sugerbaker ( p , n ) spectra for Fe and Ni Isotopes GTR GTR GTR GTR GTR GTR Fermi Fermi Fermi T=1

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)

Large Angl Spectromet Grand Raiden Spectrometer ( 3 He, t) reaction 3 He beam 140 MeV/u

RCNP, Osaka Univ.  E=30 keV Dispersion Matching Techniques were applied!  E=150 keV

T=1 Isospin Symmetry GT GT 42 22 Ti 20 42 42 20 Ca 22 21 Sc 21 T z = +1 T z = 0 T z = -1

T=1 symmetry : Structures & Transitions

 -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 ! - pf -shell nuclei -

58 Ni N 54 Fe 50 Cr 46 Ti 42 Ca rp -process path N=Z line Z

42 Ca( 3 He,t) 42 Sc in 2 scales B(GT) = 2.2 (from mirror  decay) B(F)=2 80% of the total B(GT) strength is concentrated in the excitation of the 0.611 MeV state.

GT strengths in A=42-58 GT-GR

GT states B(F)=N-Z in A=42-54 Peak heights are T z =0 nuclei proportional to B(GT) values Y. Fujita et al. PRL 2014 PRC 2015 T. Adachi et al. PRC 2006 Y. Fujita et al. PRL 2005 T. Adachi et al. PRC 2012

GT-strength: Cumulative Sum GXPF1 M. Homma et al.

SM Configurations of GT transitions 28 20   Target nuclei: N = Z + 2 ( T z = +1) Final nuclei : N = Z ( T z = 0)

rp -process Path 58 Zn (T=1 system) Z 54 Ni f -shell nuclei !  transition among f 7/2 & f 5/2 shells ! 58 Ni **  E (f 5/2 – f 7/2 ) ~ 5 - 6 MeV 50 Fe 54 Fe N=Z line 46 Cr 50 Co 42 Ti 46 Ti 42 Ca N

Role of Residual Int. (repulsive) Single particle-hole 1p-1h strength strength strength distribution Graphical solution of the Ex RPA dispersive eigen-equation positive = repulsive Ex p-h configuration + IV excitation collective = repulsive strength (GR) Collective excitation strength formed by the repulsive residual interaction Ex

Role of Residual Int. (repulsive) 1p-1h strength strength Collective excitation formed by the repulsive residual interaction Ex Ex collective strength (GR) strength Ex

42 Ca( 3 He,t) 42 Sc in 2 scales B(GT) = 2.2 (from mirror  decay)

QRPA calculations using Skyrme int. (with IV pairing corr.) Calculation by P. Sarrigren, 8 0 4 12 CSIC, Madrid E x (MeV)

SM Configurations of GT transitions 28 20   particle-hole configuration + IV-type int. = REPULSIVE

SM Configurations of GT transitions 28 20    -p -  -p configurations particle-hole configurations sensitive to IS pairing int. + IV-type excitation (  )  attractive  repulsive (spin-triplet, IS int. is stronger than spin-singlet, IV int.) by Engel, Bertsch, Macchiavelli

SM Configurations of GT transitions 28 20   particle-particle int. (attractive) particle-hole int. (repulsive) (IS p-n int. is attractive) Isoscalar interaction Overwhelming the repulsive nature of  int. ! can play Important roles !

GT strength Calculations: HFB+QRPA + pairing int. Bai, Sagawa, Colo et al., PL B 719 (2013) 116 IV IS Results (using Skyrme int. SGII) at f =0: there is little strength in the lower energy part, at f =1.0~1.7: coherent low-energy strength develops!

QRPA-cal. GT-strength (with IS-int.) by Bai Sagawa Colo 42 Ca 42 Ca  42 Sc (Q-value)

Role of Residual Int. (attractive) strength Single particle-hole strength distribution Ex Graphical solution of the RPA dispersive eigen-equation Ex negative=attractive collective Collective excitation formed strength by the attractive IS strength (GR) residual interaction Ex

Role of Residual Int. (attractive) Collective excitation formed strength by the attractive IS residual interaction Ex 42 Ca( 3 He,t) 42 Sc Ex collective strength strength (GR) Ex

Configurations are in phase! C.L. Bai, H. Sagawa, G. Colo QRPA cal. including IS int.

42Ca  42Sc: Shell Model Cal.: Transition Matrix Elements SM cal: M. Honma 1 + 1 Matrix Elements are in-phase !

42 Ca( 3 He,t) 42 Sc in 2 scales GT IAS Low-energy collective GT excitation ! B(GT) = 2.2 (collectivity is from IS p-n int. !) Low Energy Super GT state Y. Fujita, et al., PRL 112, 112502 (2014). PRC 91, 064316 (2015).

Super-allowed GT transitions in  decay (smaller log ft  larger B(GT)) GT Fermi 5 0 10 log ft 6 He, 0 +  6 Li, 1 + log ft = 2.9 Super-allowed 18 Ne, 0 +  18 F, 1 + log ft = 3.1 GT transitions 42 Ti, 0 +  42 Sc, 1 + log ft = 3.2

Super-Multiplet State *proposed by Wigner (1937) In the limit of null L ・ S force, SU(4) symmetry exists. We expect: a) GT excitation strength is concentrated in a low-energy GT state. b) excitation energies of both the IAS and the GT state are identical.  Super-Multiplet State In 54 Co, we see a broken SU(4) symmetry. In 42 Sc, we see a good SU(4) symmetry.  attractive IS residual int. restores the symmetry !  0.611 MeV state in 42 Sc has a character close to Super-Multiplet State ! We call this state the Low-energy Super GT state !

SM Configurations of GT transitions particle-particle int. (attractive) particle-hole int. (repulsive) (T=0, IS p-n int. is attractive) Isoscalar interaction Overwhelming the repulsive  N=Z LS-closed Core nature of  int. ! can play Important roles ! + 2 nucleon system !

GT transitions forming Low-Energy Super GT state J  = O +  1 +  (Sum rule) = 3 x |N-Z| = 6 2 H (d) 2n B(GT) = 6.0 ? Large ! g.s. 6 Li 6 He B(GT) = 4.73 g.s. 18 O 18 F B(GT) = 3.09 g.s. 42 Ca 42 Sc B(GT) = 2.17 Smaller ! 1 st E x state ( IAS is the g.s .)

Low-energy collective GT excitation: B(GT)=3.1 18 O( 3 He,t) 18 F at 0 o Low Energy Super GT state

6 He   -decay & 6 Li(p,n) 6 Be  2p +   =92 keV 6 Be  -decay log ft = 2.9 [B(GT) = 4.7] 0 10 20 MeV 0 Low Energy Super GT state Ex