High-resolution study of Gamow- Teller transitions in pf-shell nuclei Tatsuya ADACHI
Type II supernova Electron Capture (EC) & β decay Neutrino induced reaction A Z-1X N+1 daughter EC β A ZX N parent (A,Z) + e - (A,Z) + e + (A,Z-1) +ν e (A,Z+1) +ν e Fermi (τ) B(F) = N-Z Gamow-Teller (στ) 1 B(GT) = 2Ji +1 1 2 2 C GT 2T f +1 J f T f A 2 Σ j=1 (σ j τ j ) J i T i
GT transitions from T z =+1 to T z =0 by ( 3 He,t) reactions (n,p) (p,p ) g.s. 0 + ( 3 He,t) g.s. T=0 βdecay 0 + g.s. 0 + T=1 T=1 IAS T z =+2 T z =+1 T z = 0 T z =-1 T z =-2 T=2 V Mn Cr Fe Mn Co Fe Ni Co Cu
B(GT) Measurement in Charge Exchange Reactions Cross Section for L=0 Max At 0 deg. στ Dominant An incident beam energy E i >100MeV/u One-Step Reaction Dominant σ(0 ) = K GT N GT J στ 2 B(GT) ^ σ GT : Unit Cross Section T.N. Taddeucci et. al., NPA469 (1987) 125. Cross section Relative B(GT) values are obtained. In order to obtain absolute B(GT) values ^ σ GT standard B(GT) value from β decay (a) 1 (b) + (c) 1/2,3/2,5/2 1/2,3/2,5/2 σ^ g.s. GT 0 + g.s. Tz ^σ GT Tz -1 3/2 3/2 T z =+1/2 T z =-1/2 σ GT 0 + g.s. 0 + IAS 0 + g.s. σ F B(F) B(GT) T z = +1 T z =0 T z =-1
WS Beam Line Grand-Raiden Spectrometer at θ lab = 0 T. Wakasa et al., NIM A482 (2002) 79. High-Dispersive WS beam line Ring Cyclotron E 3He = 140MeV/u
Dispersion Matching Techniques Achromatic Beam Transportation focal plane Y. Fujita et. al., NIM B126 (1997) 274. H. Fujita et. al., NIM A484 (2002) 17. Dispersive Beam Transportation Magnetic Spectrometer target ΔE ~ 200 kev for 3 He 420 MeV ΔE ~ 35 kev Hori. Angle Resolution θ ~ 5mrad
High-resolution ( 3 He,t) spectra 10 1000 0 42 Ca( 3 He,t) 42 Sc ΔE=60 kev 3000 2000 1000 6000 4000 Counts 2000 46 Ti( 3 He,t) 46 V ΔE=33 kev Cr( 3 He,t) Mn ΔE=29 kev g.s(ias) g.s.(ias) g.s (IAS) 3000 2000 1000 Fe( 3 He,t) Co g.s.(ias) ΔE=21 kev 3.377 3.895 4.5 4.828 5.921 0.937 0.652 2.411 2.694 3.6 4.332 5.728 3.392 0.994 1.433 2.461 2.699 3.870 2.978 3.689 0.611 16 F g.s. 0.193 0.424 12 N g.s. 12 N 0.960. T. Adachi et. al., PRC 73, 024311 (2006) Y. Fujita et. al., PRL 95 2121 (2005) 0 0 2 4 6 8 10 12 E x in daughter nuclei (MeV)
β decay from T z = -1 to T z =0 nuclei T=2 g.s. 0 + ( 3 He,t) σ GT T=0 βdecay B(GT) g.s. 0 + g.s. 0 + T=1 T=1 IAS T z =+2 T z =+1 T z = 0 T z =-1 T z =-2 V Cr Mn Fe Co V.T. Koalowsky et. al., NPA624 (1997) 293. Mn Fe Co Ni Cu I. Reusen et. al., PRC59 (1999) 2416.
Ratio of the GT and Fermi Unit Cross Section Proportionality for GT and Fermi σ GT (0 ) = K GT N GT J στ 2 σ F (0 ) = K F N τ J τ 2 B(GT) =σ ^ GT B(GT) B(F) =σ^ F B(F) T.N. Taddeucci et. al., NPA 469 (1987) 125. (p,n) experiment Definition of R 2 value R 2 = σ ^ GT σ^ F Fermi Unit Cross Section σ ^ F = σ F B(F) All Fermi Strengths Concentrate to IAS B(F) = N-Z If mass systematics of R 2 values is studied, σ ^ GT = R 2 σ^ F
Derivations of R 2 values for various nuclei 1/2,3/2,5/2 1/2,3/2,5/2 0 + g.s. 0 + IAS g.s. T z Tz -1 62 Ni 64 Ni 68 Zn 78 Se 118 Sn 120 Sn 140 Ce 178 Hf σ^ F ^σ GT 62 Cu 64 Cu 68 Ga 78 Br 118 Sb 120 Sb 140 Pr 178 Ta 3/2 3/2 T z =+1/2 σ F +σ GT T z =-1/2 7 Li 23 Na 27 Al ^ σ GT 7 Be 23 Mg 27 Si 0 + g.s. 0 + IAS 0 + g.s. B(F) T z = +1 T z =0 T z =-1 18 O 26 Mg 34 S σ GT σ F 18 F 26 Al 34 Cl B(GT) 18 Ne 26 Si 34 Ar
Nuclear Mass Dependence of R 2 14 12 10 8 23 Na 64 Ni 68 Zn 78 Se 118 Sn 120 Sn 140 Ce 178 Hf R 2 ^ ^ = σ GT /σ F 6 7 Li 18 O 34 S 4 26 Mg 0 20 40 60 80 100 120 140 160 180 Nuclear Mass
B(GT) Derivation in Mn & 42 Sc Y. Fujita et. al., PRL 95 2121 (2005). β decay Fe Mn 42 Ti 42 Sc T 1/2 (msec) 155(12) 199(6) 1 = T 1/2 tf Σ 1 i=gt t i K K B(F) = (g ff t v /g A ) 2 B(GT) = F fi t i R 2 = σ ^ GT σ^ F B(GT) = σ GT B(GT) = σf B(F) σ GT 1 σ F B(F) R 2 1 = Σ T 1/2 B(F) (g v /g A ) [ff σ F + 2 f R 2 i σ i ] K σ F i=gt K : 6145(6) g v /g A : -1.266(4) B(F) : N-Z =2
Y. Fujita et. al., PRL 95 2121 (2005) 0 + 0 + 0 + 0 1 2 3 4 Ex (MeV) T z = +1 T z = 0 T z = -1 4000 2000 0 4000 2000 0 1.2 0.8 0.4 0.0 0 1 2 3 4 Ex (MeV) Estimation of f F σ F & f GT σ GT F-factor normalized Cr( 3 He,t) Mn Fe Mn Expected βdecay spectrum Assuming isospin symmetry 0.652 (IAS) Cr Mn Fe 42 Ca 42 Sc 42 Ti f GT σ GT f F σ F (IAS) counts counts
Nuclear Mass Dependence of R 2 values 14 12 10 8.1(9) 8 7.8(9) 6 7 Li 23 Na 18 O 26 Mg 34 S 58 Ni 62 Ni 64 Ni 68 Zn Cr 42 Ca 118 Sn 78 Se 7.6±1.1 5.5±0.3 120 Sn 140 Ce 178 Hf R 2 ^ ^ = σ GT /σ F 4 0 20 40 60 46 80 100 120 140 160 180 Nuclear Mass
Comparison between B(GT) s in Mn Exp. and Shell Model counts 10 1000 0 S p = 4.6 MeV Cr( 3 He,t) Mn 0 0.6 0.4 Cr( 3 He,t) Mn B(GT) distribution 0.2 B(GT) 0.0 0.6 0.4 Shell Model By M. Honma and T. Otsuka 0.2 Σ B(GT) 6.0 4.0 2.0 0.0 Cumulative Sum Red :Exp Blue: SM Green: Continuous Region Included 0 2 4 6 8 10 12 E x in Mn (MeV)
counts Comparison between B(GT) s in Co Exp. and Shell Model 900 600 300 Sp = 4.4 MeV Fe( 3 He,t) Co B(GT) 0 0.6 0.4 0.2 0.0 0.6 0.4 Fe( 3 He,t) Co Shell Model Preliminary B(GT) distribution By M. Honma and T. Otsuka 0.2 Σ B(GT) 0.0 6.0 4.0 2.0 0.0 Cumulative Sum Red :Exp Blue: SM Green: Continuous Region Included 0 2 4 6 8 10 12 E x in Co (MeV)
Isospin symmetry structure in A= nuclei and analogous transitions (n,p) (p,p ) ( 3 He,t) B(GT + ) B(GT - ) g.s. 0 + g.s. T z =+2 T z =+1 T z = 0 25 Mn 29 26 Fe 28 27 Co 27 0 + T=2 T=1 T=0 T=1 (IAS) (p,p ) experiment Scattering angle at 0 incident beam energies (more than 100 MeV/u) IE IE σ(0 ) = K N στ J στ 2 B(σ)
Identification of the isospin values 1 B(GT) = 2Ji +1 J f T f 1 B(σ) = 2Ji +1 1 2 Analogous transitions Σ A 2 (σ j τ j ) J i T i j=1 j=1 2 C GT 2 2T f +1 C M1 2 B(σ) C M1 <f στ i> 2 = 2 B(GT) C GT <f στ i> 2 2 C M1 1/2 1/2 T z =+1 T z = 0 26Fe 28 3 : 1 1 : 1 2 C GT 1/6 1/2 27Co 27 T=2 T=1 1 2 2T f +1 ( 3 1/3 J f T f Σ A 2 (p,p ) He,t) T=0 (σ j τ j ) J i T i g.s. g.s. T=1 (IAS)
Fe( 3 He,t) Co & Fe(p,p ) Fe spectra counts 800 400 T = 2 Fe( 3 He,t) Co T = 0 counts 0 12 7 2 Instrumental Background Fe(p,p ) Fe E p = 160 MeV at 0 at IUCF T = 2 C. Djalali et. al., PRC 35, 1201 (1987). 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 E x (MeV)
Identification of Isospin values B(GT) 0.3 0.2 0.1 T = 0 T = 1 T = 2 Fe( 3 He,t) Co B(σ) 0.3 0.2 0.1 T = 1 T = 2 Fe(p,p ) Fe B(GT) B(σ) 4.0 3.0 2.0 1.0 0.0 T = 1 T = 2 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 E x (MeV)
Summary 1. GT transitions from T z =+1 ( 42 Ca, 46 Ti, Cr, Fe) to T z =0 ( 42 Sc, 46 V, Mn, Co) pf-shell nuclei were measured by high-resolution ( 3 He,t) experiments. 2. B(GT) values were derived from the β decay data. Nuclear mass dependence of R 2 values were systematically studied. 3. Experimental distributions were compared with those of Shell Model calculation. 4. Fe( 3 He,t) Co and Fe(p,p ) Fe spectra were compared. Isospin values T= 0, 1 and 2 of GT and M1 states were identified.