The excitation and decay of nuclear isomers 2. Isomer decay rates Phil Walker CERN and University of Surrey, UK ● issues from yesterday ● isomer types ● isomers and the shell model ● K isomers ● K-isomer decay rates

Issues from yesterday 1. Parity mixing in γ decay: 180mHf 8- isomer J.R. Stone et al., Phys. Rev. C76 (2007) 025502 at CERN-ISOLDE 2. Isomer de-excitation by Coulex: 68mCu beam (722 keV, 4 min. isomer) interacting with 120Sn I. Stefanescu et al., Phys. Rev. Lett. 98 (2007) 122701 at CERN-ISOLDE 3. Isomer discovery by laser spectroscopy 80mGa and 80gGa seen with laser spectroscopy (with no decay required) B. Cheal et al., Phys. Rev. C82 (2010) 051302(R) at CERN-ISOLDE 4. Isomer discovery in a Penning trap 65mFe and 65gFe seen in a Penning trap (with no decay required) M. Block et al., Phys. Rev. Lett. 100 (2008) 132501 at NSCL 5. Longest-lived and shortest-lived ground states M2 + E2

shortest: 19Mg 4 ps, 2p decay [PRL99(2007)182501] Issues from yesterday 1. Parity mixing in γ decay: 180mHf 8- isomer J.R. Stone et al., Phys. Rev. C76 (2007) 025502 at CERN-ISOLDE 2. Isomer de-excitation by Coulex: 68mCu beam (722 keV, 4 min. isomer) interacting with 120Sn I. Stefanescu et al., Phys. Rev. Lett. 98 (2007) 122701 at CERN-ISOLDE 3. Isomer discovery by laser spectroscopy 80mGa and 80gGa seen with laser spectroscopy (with no decay required) B. Cheal et al., Phys. Rev. C82 (2010) 051302(R) at CERN-ISOLDE 4. Isomer discovery in a Penning trap 65mFe and 65gFe seen in a Penning trap (with no decay required) M. Block et al., Phys. Rev. Lett. 100 (2008) 132501 at NSCL 5. Longest-lived and shortest-lived ground states M2 + E2 longest: 128Te 7.2x1024 y, 2β- decay shortest: 19Mg 4 ps, 2p decay [PRL99(2007)182501]

Extreme isomers decay rates vary over at least 32 orders of magnitude long half-life: 180Ta, 9–, 75 keV, >1016 y high spin/energy*: 212Rn, 38+, 13 MeV, 12 ns low energy: 229Th, 3/2+, 8 eV, ~10 h? p rich: 94Ag, 21+, 5.8 MeV, 300 ms n rich: 130Cd, 8+, 2.1 MeV, 220 ns high mass: 270Ds, 10–, 1 MeV, 6 ms PRC 2006 PLB 2008 PRL 2007 Nature 2006 EPJA 2001 decay rates vary over at least 32 orders of magnitude * unbound to both p and n emission

isomer types energy K traps K β yrast line shape traps yrast traps I lowest energy for a given spin I spin I(I+1) [Walker and Dracoulis, Physics World (Feb 1994) 39]

high-spin isomer types seniority isomer K isomer E4 decay E3 decay 7h 31y 93Mo 178Hf yrast traps => long lived

high-spin isomer types seniority isomer K isomer E4 decay E3 decay 7h 31y 93Mo 178Hf seniority isomer K isomer 190ns E1 decay 4s E2 decay 178Hf 92Mo

Isomers and the shell model Low-lying isomers => single-particle spin differences => test of shell model (other non-isomeric single-particle states are in principle just as useful for testing the shell model, but only if they can be identified in the first place) This is just as true now, in regions of shell changes, as it was historically.

neutron h11/2 isomers (β decays) Z = 48 isotopes figure from: Huck et al., Phys. Rev. C40 (1989) 1384

neutron h11/2 isomers Z = 48 isotopes Nilsson diagram 1.8 s 3.4 h figure from: Huck et al., Phys. Rev. C40 (1989) 1384

neutron (h11/2)-2 10+ isomers (γ decays) N = 80 isotones Valiente-Dobon et al., Phys. Rev. C69 (2004) 024316

proton and neutron (g9/2)-2 8+ isomers 590 ns 480 ns 220 ns Jungclaus et al., PRL99 (2007) 132501

212Rn 212Rn126 Highest spin isomer I = (38), 12 ns states above 86 triple neutron core excitations 212Rn 12.5 MeV I = (38), 12 ns 212Rn126 states above 5.4 MeV 204Hg(13C, 5n) 86 CAESAR at ANU 5.4 MeV

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

178W bands K isomers and rotational bands in a deformed nucleus 1999 K isomers and rotational bands in a deformed nucleus 178W bands 8.8 MeV 6.6 MeV data from GAMMASPHERE at Berkeley: 170Er(13C, 5n) 5.3 MeV 3.7 MeV Note: 175Hf holds the record for the highest spin/energy K isomer (see previous lecture)

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

Single-particle energies 178Hf has N=106, Z=72, β2~0.25 Single-particle energies 106 72 [F.R. Xu et al., Phys. Lett. B435 (1998) 257] Woods-Saxon potential

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

K isomers - structure deformed shell model - energies - transition rates?

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

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

Weisskopf transition rates

partial γ-ray half-life: T1/2 level isomer other branches 100-x-y % γ-ray branch x % electron branch y % γ T1/2 = T1/2 . 100/x level

178Hf Hf-178 new level scheme 72 4-quasiparticle isomer M4 E3 E5 E1 0.005% M4 E3 E5 495-keV gate E1 2-quasiparticle isomer 178Hf M2 72 data from the 8π spectrometer at TRIUMF [Smith et al., Phys. Rev. C68 (2003) 031302(R)]

↑ Hf-178 hindrances 178Hf K=8 K=16 E1 M2 E3 M4 E5 ↑

Löbner systematics Löbner, Phys. Lett. B26 (1968) 369 1 102 104 106 108 1010 1 102 104 106 108 1010 Löbner, Phys. Lett. B26 (1968) 369

Löbner systematics from the gradients: for each additional degree of K forbiddenness, the hindrance increases by a factor of ~100 1 102 104 106 108 1010 1 102 104 106 108 1010 Löbner, Phys. Lett. B26 (1968) 369

2- and 3-qp E2 reduced hindrances lower fν => more K mixing (Coriolis and/or γ deformation) Walker, J. Phys. G16 (1990) L233 Dracoulis et al., Phys. Rev. C71 (2005) 044326

2- and 3-qp E2 reduced hindrances increasing deformation lower fν => more K mixing (Coriolis and/or γ deformation) NpNn: product of valence nucleon numbers, e.g. 174Yb (+) has Z=70, Np=12; N=104, Nn=22 => NpNn=264 Walker, J. Phys. G16 (1990) L233

2- and 3-qp E2 reduced hindrances 171Tm Walker et al. Phys. Rev. C79 (2009) 044321 increasing deformation NpNn: product of valence nucleon numbers, e.g. 174Yb (+) has Z=70, Np=12; N=104, Nn=22 => NpNn=264

171Tm 1.7 μs 171Tm isomer ΔE = 11 keV (V=12 eV) Walker et al. Phys. Rev. C79 (2009) 044321

171Tm 1.7 μs 171Tm isomer chance near-degeneracy of two 19/2+ levels ΔE = 11 keV (V=12 eV) 171Tm isomer chance near-degeneracy of two 19/2+ levels Walker et al. Phys. Rev. C79 (2009) 044321

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

K-mixing mechanisms ￭ chance near-degeneragies – hard to predict! ￭ Coriolis mixing (rotational – orientation change) ￭ γ tunnelling (vibrational – shape change) ￭ level density (thermal – statistical) larger deformation (NpNn) => less Coriolis mixing K R

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

Where next?

Where next? - need for quantitative theory - compare with other mass regions - make and test predictions for exotic nuclei

2-qp E2 reduced hindrances even-even nuclides, Kπ = 6+, 8+, 10+ isomers 244Cm 162Dy: Swan et al., Phys. Rev. C83 (2011) 034322 190W: Lane et al., Phys. Rev C82 (2010) 051304(R) ● ● 134Ce increasing deformation fig. updated from Walker, Nucl. Phys. A834 (2010) 22c

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

K-forbidden γ-ray transitions Summary K-forbidden γ-ray transitions fν dependence: NpNn (E2 transitions, 2-qp) Coriolis effects γ tunnelling level-density (multi-qp) chance near-degeneracy theory needed, but predictions possible n-rich predictions – long-lived isomers

K-forbidden γ-ray transitions Summary K-forbidden γ-ray transitions fν dependence: NpNn (E2 transitions, 2-qp) Coriolis effects γ tunnelling level-density (multi-qp) chance near-degeneracy theory needed, but predictions possible n-rich predictions – long-lived isomers Other decay modes (p, n, α, fission): tomorrow’s lecture/seminar

“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)

γ tunnelling γ = 0o γ = -60o γ = -120o potential energy surface prolate γ = -60o oblate Narimatsu et al., Nucl. Phys. A601 (1996) 69 γ = -120o

tunnelling 174Yb (K=6) E2 γ-tunnelling description of K-isomer decay A~180 region 174Yb (K=6) see Dracoulis et al. Phys. Rev. C71 (2005) 044326 isomer→gsb E2 transitions Chowdhury et al., Nucl. Phys. A485 (1988) 136