K-isomer decay rates. Phil Walker. - introduction - exploring the different degrees of freedom - exotic nuclei

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1 K-isomer decay rates Phil Walker - introduction - exploring the different degrees of freedom - exotic nuclei

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

3 4-quasiparticle isomer at 2.4 MeV Hf-178 new level scheme ~2 ~2 2-quasiparticle isomer at 1.1 MeV [Smith et al., Phys. Rev. C68 (2003) (R)]

4 178 Hf has N=106, Z=72, 2 ~0.25 Single-particle energies Woods-Saxon potential [F.R. Xu et al., Phys. Lett. B435 (1998) 257]

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

6 K-isomer energy/spin limit 9-qp > 10 ns 175 Hf 9-qp isomer 7455 kev 9-qp isomer in 175 Hf Gjørup et al. Z. Phys. A337 (1990) Te( 48 Ca,3n) reaction 7-qp 5-qp 3015 kev

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

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

9 Weisskopf transition rates

10 partial -ray half-life: T 1/2 other branches 100-x-y % electron branch y % level T 1/2 isomer -ray branch x % level T 1/2 = T 1/2. 100/x

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

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

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

14 Löbner systematics Löbner, Phys. Lett. B26 (1968) 369

15 2- and 3-qp E2 reduced hindrances Dracoulis et al., Phys. Rev. C71 (2005) Walker, J. Phys. G16 (1990) L233

16 2- and 3-qp E2 reduced hindrances increasing deformation N p N n : product of valence nucleon numbers, e.g. 174 Yb (+) has Z=70, N p =12; N=104, N n =22 => N p N n =264 Walker, J. Phys. G16 (1990) L233

17 2- and 3-qp E2 reduced hindrances increasing deformation 171 Tm Walker et al. Phys. Rev. C79 (2009) N p N n : product of valence nucleon numbers, e.g. 174 Yb (+) has Z=70, N p =12; N=104, N n =22 => N p N n =264

18 171 Tm 1.7 s 171 Tm isomer E = 11 kev (V=12 ev) chance near-degeneracy of two 19/2 + levels Walker et al. Phys. Rev. C79 (2009)

19 K-mixing mechanisms chance near-degeneragies hard to predict! Coriolis mixing (rotational orientation change) larger deformation (N p N n ) => less Coriolis mixing tunnelling (vibrational shape change) level density (thermal statistical) K R

20 γ γ γ tunnelling = 0 o Narimatsu et al., Nucl. Phys. A601 (1996) 69 = -120 o = -60 o

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

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

23 back to 2- and 3-qp isomers

24 back to 2- and 3-qp isomers 185 Ta: Lane et al., Phys. Rev. C80 (2009) qp 3-qp (3, 3 ) 3-qp (other) Walker et al., Phys. Rev. C81 (2010) (R)

25 back to 2- and 3-qp isomers 185 Ta: Lane et al., Phys. Rev. C80 (2009) qp (3, 3 ) 3-qp (other) Walker et al., Phys. Rev. C81 (2010) (R)

26 Where next?

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

28 252 No Sulignano et al. EPJA33 (2007) 327 K = 8 isomers, E1 decays ( = 7) N=106 and allowance for Coriolis mixing: Dracoulis et al., PRC79 (2009) (R) increasing Coriolis mixing (dynamic/kinematic) extends analysis of Walker et al., Phys. Rev. C49 (1994) 1718

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

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

31 hafnium (Z=72) 4-qp isomers 178 Hf 188 Hf expt. calc. predictions Walker and Dracoulis, Hyp. Int. 135 (2001) 83

32 Nilsson+BCS blocked BCS calculations calculation see Matt Reed's talk stable isomers may be longer lived than the ground state [Walker and Dracoulis, Hyp. Int. 135 (2001) 83]

33 Summary K isomers & K mixing f νdependence: NpNn (E2 transitions, 2-qp) Coriolis effects tunnelling level-density (mqp) chance near-degeneracy theory needed, but predictions possible n-rich predictions long-lived isomers

Nuclear isomers: stepping stones to the unknown

Nuclear isomers: stepping stones to the unknown P.M. Walker Department of Physics, University of Surrey, Guildford GU2 7XH, UK Abstract. The utility of isomers for exploring the nuclear landscape is discussed,