g -Factor measurements of high-spin isomers and condensed matter - PowerPoint PPT Presentation

g -Factor measurements of high-spin isomers and condensed matter studies using spin-aligned isomeric beams Hiroshi Watanabe Applied Nuclear Physics Laboratory, The Institute of Physical and Chemical Research Outline • Introduction • g -Factor measurements of the high-spin isomers in N = 83 isotones • Condensed matter studies with spin-aligned isomeric beams

Overview of nuclear isomers 5 f electrons Overview of nuclear isomers presented over the chart of nuclei presented over the chart of nuclei Octupole Pb (Fission isomers) 4 f electrons Oblate + 126 Octupole Prolate 4 d electrons (K-isomers) Sn 3 d electrons Oblate 82 Spherical A large number of isomeric states Protons Ni with various lifetimes and spins Ca 50 have been discovered so far ! O 20 28 He 2 8 Neutrons Nuclear isomerism Spin Spin selection orientation rules

Spin-oriented isomers as probes for studies of nuclear moments and solid-state physics B ext ω L Oscillation curve 0.6 exp (- t / τ N ) 0.4 0.2 R ( t ) 0 -0.2 m a e B 1 / ω L -0.4 -0.6 0 500 1000 1500 2000 2500 3000 t [ns] Larmor frequency Nuclear structure β known • Configuration of the isomer µ β Isomeric g -factor g B ( T ) ω = N N ext • Effect of shell-closure L h Local susceptibility g known Material science + µ g ( J 1 ) B ( 0 ) χ = β − = • Local moment J B ( T ) 1 loc 3 k T B Nuclear relaxation time 4 f electron spin fluctuation • Exchange + µ h π 2 ( J 1 ){ g B ( 0 ) } 2 4 τ = τ N N τ = ε − 1 interaction − { D ( ) J ( T )} 2 k T 1 N J J c F cf B J h

g -Factor measurements of the high-spin isomers in N = 83 isotones Systematics of the high-spin isomers in N = 83 isotones 49/2+ 35ns 49/2+ 0.95us 9 (27+) 10ns (27+) 1.1us (27+) >2us 49/2+ 0.51us 49/2+ 28ns 8 7 Excitation Energy [MeV] 6 5 4 27/2- 27ns 3 21/2+ 4ns 27/2- 510ms 2 11- 4.5ns 13/2+ 6.8ns 13/2+ 12ns 13/2+ 12.5ns 13/2+ 22ns 1 9+ 0.71us 9+ 235us 9+ 2m 349d 7/2- 340d 4.59d 38h 4m 7/2- 5- 4- 7/2- 7/2- 0 143 Nd 144 Pm 145 Sm 146 Eu 147 Gd 143 Tb 149 Dy

Properties of the high-spin isomer in 147 Gd O.Häusser et.al., Nucl. Phys. A379 (1982) 287. i 13/2 h 9/2 d 3/2 f 7/2 Experimental g -factor h 11/2 64 82 Isomeric configuration [ π（ h 11/2 2 ）ν（ f 7/2 h 9/2 i 13/2 ） ] 49/2 + d 5/2 d 3/2 g 7/2 s 1/2 0 DIPM calc. Experimental Q -moment -0.02 exp. -0.04 -0.06 Sphere Deformation -0.08 -0.1 β = -0.19 β -0.12 -0.14 -0.16 -0.18 ※ These properties are well reproduced Oblate -0.2 by the DIPM calculation. -0.22 0 5 10 15 20 25 30 35 40 Spin [ ħ ] Does the other N = 83 high-spin isomers have the same properties as the 147 m Gd ?

Configuration predicted by the DIPM calc. 149 Dy Level Structure 47 49 = = h h I I 2 2 E ex (MeV) N =82 core excitation Z =64 core excitation 14 834* 613* 1137* 915* 13 335.1 303.1 197.7 543.7 602.8 861.0 802.0 848.2 12 1354.3 1008.6 704.2 750.4 Oblate shape Spherical shape 11 962.1* β = -0.041 β = -0.166 10 456.5 829.3 667.5 294.2 9 595.4 E ex = 8.52MeV, T 1/2 = 28ns High-Spin Isomer (49/2+) 249* 475* 8 861* 1232.5 635* 43/2+ 253.3 491.1 7 350.3 168.1 41/2+ 213.0 479.2 1064.1 742.1 1408.9 1143.5 39/2+ 930.5 6 580.8 430.3 700.3 269.8 37/2+ 525.4 Z =64 core excitation 254.9 5 35/2+ 1393.5 1138.2 1337.7 199.6 4 33/2+ 239.8 31/2+ 29/2+ 984.9 3 510 ms 110.9 27/2- 21/2+ proton 299.0 2 proton 2 17/2+ 1178.8 146 Gd (11/2-) + proton hole 12.5 ns 1 13/2+ 1 neutron 1584.0 1073.0 neutron 4.23 min 0 7/2-

143 Nd Level Structure Angular distribution Linear polarization E ex = 8.98MeV, T 1/2 = 35ns, I π = 49/2 + Configuration predicted by the DIPM calc. 49 = h I 2 Z = 64, N =82 core excitation Oblate shape β = -0.176

Experimental details RIKEN Accelerator Research Facility (RARF) Injector : RIKEN Heavy-ion Linac (RILAC) Main accelerator : K540 RIKEN Ring Cyclotron (RRC) Production of the high-spin isomer in 149 Dy � Projectile : 132 Xe 7.0 MeV/u, T = 1 μ s � Target : natural Mg of 6.0 mg/cm 2 thickness Production of the high-spin isomer in 143 Nd � Projectile : 136 Xe 7.6 MeV/u → 6.5 MeV/u, T = 1 μ s � Target : 12 C of 1.7 mg/cm 2 thickness

Experimental setup for the measurement of g -factors Ge detector ε γ = 0.04% for 1MeV Target Vacuum Ar gas cell Ar Gas Beam 90° Pb Stopper Dipole Magnet Pb Shield ① Inverse reaction & Recoil shadow method Only γ rays emitted through isomeric states can be detected ② Spin relaxation control ( Ⅰ ) Recoil into Gas Suppress the nuclear spin relaxation during the flight ( Ⅱ ) Stopper heating system Make the relaxation time long after stopping

Experimental Technique γ -ray Time-Differential Perturbed Angular Distribution (TDPAD) technique ) ( ln 2 γ θ = − ⋅ θ Intensity of ray : N ( t , , B ) N exp t W ( t , , B ) γ γ eff 0 eff T 1 / 2 ∑ θ = γ θ − ω ⋅ Angular distributi on : W ( t , , B ) B ( I ) A ( ) P [cos( t )] γ γ eff k k k L k , even θ − θ + π N ( t , , B ) N ( t , / 2 , B ) θ = γ γ eff eff R ( t , , B ) B γ eff θ + θ + π N ( t , , B ) N ( t , / 2 , B ) γ γ eff eff 3 A ≅ θ − ω ⋅ ≤ 22 cos[ 2 ( t )] for k 2 γ + L 4 A 22 ω : Larmor frequency L ω h ＝ L g factor : g µ B N eff = + = β B B B ( T ) B eff ext int int β + µ ( T ) : Paramagnet ic g ( J 1 ) B ( 0 ) β = + J B ( T ) 1 3 k T Correction Factor B

Calibration of the paramagnetic field 4.5 152 Dy I = 21 isomer (present work ) 4 3.5 For Dy 3+ ion : J = 15/2, g J = 4/3 3 ｇ·β(T) 2.5 2 1.5 calibrated with the known g -factor 1 of the isomeric state in 152 Dy 152 Dy I = 21 isomer (g = 0.55±0.06) 0.5 (produced concurrently with the 149 m Dy) β (T) : calculation (5% uncertainty) 0 0 0.001 0.002 0.003 0.004 1/T [K -1 ] For Nd 3+ ion : J = 9/2, g J = 8/11 calibrated with B (0) = 3.51(10) MG for Nd 3+ ion given by D.Riegel et al.

Result for the high-spin isomer in 149 Dy 0.2 T = 328 K 0.15 0.1 ω L 0.05 T g exp β R(t) [K] [rad/ns] 0 -0.05 328 0.19(2) 6.4(9) 0.41(7) -0.1 -0.15 533 0.11(2) 3.6(5) 0.41(9) -0.2 0 10 20 30 40 50 60 g exp = 0.41(6) t [ns] 0.2 T = 533 K 0.15 0.1 Configuration (DIPM) g cal 0.05 I π R(t) 0 47/2 - π (h 11/2 3 g 7/2 -1 ) ν (i 13/2 ) 0.82 -0.05 -0.1 49/2 + π (h 11/2 2 ) ν (f 7/2 h 9/2 i 13/2 ) 0.46 -0.15 -0.2 0 10 20 30 40 50 60 ＊ g ℓ ( π ) = 1.1, g ℓ ( ν ) = -0.03, g s = 0.6g s (free) t [ns]

Result for the high-spin isomer in 143 Nd 0.4 Measured at T = 302 K 0.3 0.2 0.1 R(t) 0 -0.1 -0.2 -0.3 -0.4 0 10 20 30 40 50 60 70 80 90 100 t [ns] ω L = 0.082 ± 0.006 rad/ns g exp = 0.56 ± 0.04

Experimental g -factors of the high-spin isomers in N = 83 isotones 0.65 0.6 0.55 g -factor 0.5 0.45 π (h 11/2 2 ) ν (f 7/2 h 9/2 i 13/2 ) 0.4 0.35 0.3 143 Nd 144 Pm 145 Sm 146 Eu 147 Gd 148 Tb 149 Dy Z = 64 shell-gap energies which reproduce the experimental excitation energies of the high-spin isomers in N = 83 isotones Z = 64 shell-gap energy [MeV] 2.4 2.35 2.3 2.25 2.2 2.15 2.1 2.05 2 1.95 1.9 143 Nd 144 Pm 145 Sm 146 Eu 147 Gd 148 Tb 149 Dy

Condensed matter studies with spin-aligned isomeric beams 4 d atomic-shell 4 f atomic-shell Ex Ex Nucleus T1/2 I μ[nm] Q[b] Nucleus T1/2 I μ[nm] Q[b] [keV] [keV] 85Y 266 170 ns 5/2- 1.33 134Ce 3209 308 ns 10+ -1.87 1.32 88Zr 2889 1.32μs 8+ -1.81 0.51 136Ce 3096 2.2 μs 10+ -1.8 90Zr 3589 134 ns 8+ 10.84 -0.51 138Ce 3538 82 ns 10+ -1.7 91Zr 3167 3.6μs 21/2+ 9.82 -0.86 139Ce 2632 70 ns 19/2- 3.99 97Zr 1264 102 ns 7/2+ 1.37 136Pr 548 90 ns 4+ 2.3 90Nb 1881 477 ns 11- 8.78 138Nd 3172 330 ns 10+ -1.74 91Nb 2037 3.4 μs 17/2- 10.82 148Nd 3621 330 ns 10+ -1.75 92Nb 2203 167 ns 11- 9.7 142Sm 2372 170 ns 7- 0.42 1.1 90Mo 2875 1.1 μs 8+ -1.391 0.58 151Sm 92 77 ns 9/2+ -0.95 92Mo 2760 190 ns 8+ 11.3 -0.34 145Eu 716 0.49 μs 11/2- 7.46 94Mo 2956 98 ns 8+ 10.46 0.47 147Eu 635 765 ns 11/2- 7.05 93Tc 2186 10.1 μs 17/2- 10.46 148Eu 720 235 ns 9+ 6.12 93Ru 2082 2.4 μs 21/2+ 8.97 0.04 144Gd 3433 130 ns 10+ 12.76 -1.46 100Rh 75 215 ns 2+ 4.324 147Gd 8587 510 ns 49/2+ 10.9 -3.24 112+x 140 ns 7+ 4.69 158Dy 99 1.66 μs 2+ 0.72 104Rh 215.5+x 47 ns 6- 2 168Er 1094 112.5 ns 4- 0.96 96Pd 2532 2.22 μs 8+ 10.97 169Tm 316 660 ns 7/2+ 0.156 157Yb 494+x 45 ns 13/2+ -0.75

Why Ce beam ? Properties of Ce-based systems Many physical phenomena, such as ferro- 4 f electrons and anti-ferromagnetism, Kondo effect, superconductivity, and heavy-fermion ε F >> E f ε F << E f behavior can take place in Ce-based compounds and alloys. The RKKY interaction Demagnetization is gives rise to various kinds caused by the of magnetic ordering. Kondo effect. T k T RKKY T k B T RKKY ~ J 2 cf D c ( ε F ) k B T K ~ exp[-1/ J cf D c ( ε F )] T N critical point Quantum ε F ≈ E f localize around itinerate in Heavy-fermion Compete the atom the crystal A.F. (Fermi liquid) J cf D c ( ε F ) CeIn 3 CeCu 2 Si 2 CeCu 6 CeRu 2 Si 2 CeNi CeAl 2 CeAl 3 CeSn 3 Heavy fermion system CeB 6