Chong Qi Dept. of Physics, KTH, Stockholm

1. Swedish Nuclear Physics meeting 16-17 November, 2010, Uppsala Deviations of alpha decay half-lives from the Geiger-Nuttall lawas a manifestation of nuclear structure effects Chong Qi Dept. of Physics, KTH, Stockholm Collaborators: R.J. Liotta, R. Wyss (KTH, Stockholm) A.N. Andreyev, M. Huyse, P. Van Duppen (KU Leuven, Belgium)

2. Experimental status and the Geiger-Nuttall law of alpha decays • Microscopic two-step description of alpha decay and generalization of the GN law;Clustering (formation) + Penetration • Abrupt change in alpha decay half-lives and alpha formation amplitudes; • Explanation in term of pairing collectivity; • Possible manifestation in other observables.

3. 1) Progress in experiments • α radioactivity ~ 400 eventsobserved in A > 150 nuclei; Decay of N~Z nuclei Fine structure Alpha decay as a spectroscopic probe S.N.Liddick et al., Phys.Rev.Lett. 97, 082501 (2006) D.Seweryniak et al., Phys.Rev. C 73, 061301 (2006) A.N. Andreyev et al., Nature 405 430 (2000)

4. Theoretical understanding The Geiger-Nuttall law of alpha decays H. Geiger and J. M. Nuttall, Philos. Mag. 22, 613 (1911). • Schematically: quantum tunneling interpretation • by Gamow in 1928 • The Gamow theory does not carry structure information

5. 2) Microscopic description of alpha decay R is the distance between the center of mass of the cluster and daughter nucleus which divides the decay process into an internal region and complementary external region. Shell Model H.J. Mang, PR 119,1069 (1960); I. Tonozuka, A. Arima, NPA 323, 45 (1979). BCS approach HJ Mang and JO Rasmussen, Mat. Fys. Medd. Dan. Vid. Selsk. (1962) DS Delion, A. Insolia and RJ Liotta, PRC46, 884(1992).

6. Alpha formation amplitude R should be large enough that the nuclear interaction is negligible, i.e., at the nuclear surface. CQ et al, Phys.Rev.C80,044326 (2009); 81,064319 (2010).

7. On the logarithm scale the differences in the formation probabilities are usually small fluctuations along the straight lines predicted by the Geiger-Nuttall law; • The smooth trend is a consequence of the smooth transition in the nuclear structure that is often found when going from a nucleus to its neighboring nuclei ->BCS. Generalization of the Geiger-Nuttall law: Universal decay law of alpha and cluster decays C.Qi, F.R.Xu,R.J.Liotta,R.Wyss, PRL103, 072501 (2009), PRC80,044326 (2009)

8. a division occurs between decays corresponding to N <126 and N >126; • Sudden change at N = 126; • The case that shows the most significant hindrance • corresponds to the α decay of the nucleus 210Po, one order of magnitude smaller than that of 212Po. • Discrepancy between experimental decay half-lives and UDL calculations->; • Around the N=126 shell closure, UDL underestimate the half-lives by large factors.  210Po

9. 3) Theoretical explanation 210Po vs 212Po (The later is the textbook example of alpha emitter ) If we neglect the proton-neutron interaction Two-body clustering

10. Two-body clustering Configuration mixing from higher lying orbits is important for clustering at the surface r1=9fm 210Pb 206Pb

11. Two-body clustering R=r1=r2 • The two-body wave functions are indeed strongly enhanced at the nuclear surface; • The enhancement is much weaker in 206Pb(gs) than that in 210Pb(gs) • Relatively small number of configurations in the hole-hole case; • p1/2 dominance in 206Pb(gs); • Radial wave functions of hole states less extended.

12. Alpha formation amplitude • Alpha particle is formed on the nuclear surface; • The clustering induced by the pairing mode is inhibited if the configuration space does not allow a proper manifestation of the pairing collectivity.

13. Odd-even staggering of binding energies and pairing correlation energies Larger pairing energy => Enhanced two-particle clustering at the nuclear surface

14. Previous explanations Reduced widths [similar to F(R)] of Po isotopes as a function of A • Calculations underestimated the formation probability by several orders of magnitude due to the limited model space employed. • Sn(206Po)>Sn(208Po)>Sn(210Po).

15. The role played by proton-neutron correlation on alpha decays of N>>Z nuclei is marginal

17. 4) Possible manifestation in other observables cross sections of (p,t) reactions on Pb isotopes M. Takahashi, PRC27,1454(1983)

18. 5) Next-step Suppression of alpha formation probabilities in neutron-deficient Po isotopes and limitation of the GN law C. Qi et al., to be published Alpha decay of neutron-deficient nuclei and Z=82 shell closure A.N. Andreyev et al., to be published.

19. 5) Summary Alpha decay as a probe of nuclear structure. • Microscopic studies of the alpha decay process and generalization of the GN law • An abrupt change in alpha formation amplitudes is noted around the N=126 shell closure; • Interpretation in term of pairing collectivity. • Alpha decay as a probe of nuclear structure Thank you!

20. Delta-function approximation The clustering induced by the pairing mode is inhibited if the configuration space does not allow a proper manifestation of the pairing collectivity.