1. Determining the limits to K isomerism Phil Walker

2. Determining the limits to K isomerism Phil Walker K-isomer perspectives ends of isomer chains with short half-lives reduced-hindrance dependence on N p N n multi-quasiparticle states in 178 W

3. K-forbidden γ-ray transitions I=K=8 I=R=8 λ=1 transition is 7-fold forbidden (ν = 7) degree of forbiddenness, ν = ΔK – λ symmetry axis angular momentum has both magnitude and direction! collective non-collective

4. K-mixing mechanisms ￭ chance near-degeneragies – hard to predict! ￭ Coriolis mixing (rotational – orientation change) ￭ γ tunnelling (vibrational – shape change) ￭ level density (thermal – statistical) K R

5. Segre chart with isomers adapted from Walker and Dracoulis, Nature 399 (1999) 35 K isomers in deformed nuclei

6. Hf-178 new level scheme [Smith et al., Phys. Rev. C68 (2003) 031302(R)] 2-quasiparticle isomer at 1.1 MeV 4-quasiparticle isomer at 2.4 MeV ~2Δ 106 72

7. half-lives vs A multi-quasiparticle K isomers > 5ns 2-, 3-qp 4-, 5-qp 6-, 7-qp 8-, 9-qp excludes 2-qp isomers in odd-odd nuclei 178 Hf Walker, AIP-CP819 (2006) 16 178 Hf

8. K π = 6 + isomers (Z = 72) Kondev et al., ADNDT in press

9. K π = 6 + isomers (Z = 72) Kondev et al., ADNDT in press

10. Cullen et al., Phys. Rev. C60 (1999) 057303

11. transition-rate hindrance factors contains the physics Weisskopf hindrance reduced hindrance (hindrance per degree of K forbiddenness) degree of K forbiddenness

12. Swan et al., Phys. Rev. C83 (2011) 034322 170 Hf: NpNn = 10x16 = 160 f ν < 23 180 Hf: NpNn = 10x18 = 180 f ν = 7.3 180 Hf: Kondev et al., ADNDT in press ↓ ↓ K-forbidden E2 transitions from 2-qp isomers in even-even nuclei 170 Hf

13. Swan et al., Phys. Rev. C83 (2011) 034322 170 Hf: NpNn = 10x16 = 160 f ν < 23 180 Hf: NpNn = 10x18 = 180 f ν = 7.3 180 Hf: Kondev et al., ADNDT in press ↓ ↓ K-forbidden E2 transitions from 2-qp isomers in even-even nuclei 170 Hf 178 W

14. partial scheme Purry et al., PRL75 (1995) 406 8-qp 6-qp 4-qp

16. Summary K isomer limits f ν dependence: N p N n (E2 transitions, 2-qp isomers) Coriolis effects γ tunnelling level-density chance near-degeneracy Half-lives needed for short-lived K isomers

17. “But you’ve no idea what a difference it makes, mixing it with other things” Lewis Carroll, Through the Looking Glass (Macmillan and Co., London, 1872)

18. Hf-178 hindrances E1 M2 E3 M4 E5 178 H f K=8 K=16 ↑ ↑

19. Löbner systematics 1 10 2 10 4 10 6 10 8 10 10 Löbner, Phys. Lett. B26 (1968) 369

20. Single-particle energies 178 Hf has N=106, Z=72, β 2 ~0.25 Woods-Saxon potential 106 72 [F.R. Xu et al., Phys. Lett. B435 (1998) 257]

21. f(nu) vs E(K)-E(R)/0.85 179Ta (49/2) [Kondev] 175Hf (57/2) [Kondev] 4-,5-,7-,9-qp isomers (+Δ= 0.9 for odd-mass) 174Yb (14) [Dracoulis] Walker et al., Phys. Lett. B408 (1997) 42; Acta Phys. Pol. 36 (2005) 1055 A~180 region level-density dependence E2 and E3 transitions increasing level density

22. 2-qp E2 reduced hindrances even-even nuclides, K π = 6 +, 10 + isomers increasing deformation fig. updated from Walker, J. Phys. G16 (1990) L233 134 Ce 244 Cm

23. 170 Dy: doubly mid-shell P.H. Regan et al., Phys. Rev. C65 (2002) 037302 A.K. Rath et al., Phys. Rev. C68 (2003) 044315 172 Er ? 170 Dy ? E2 transitions K π = 6 + isomers 174 Yb predictions