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Recent advances in the theory of nuclear alpha decay: 100 years after its introduction

ISOLDE, CERN, 20 July, 2011. Recent advances in the theory of nuclear alpha decay: 100 years after its introduction. Chong Qi Dept. of Physics, Royal Institute of Technology, Stockholm. Outline. The Geiger-Nuttall law and experimental status of alpha decay studies

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Recent advances in the theory of nuclear alpha decay: 100 years after its introduction

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  1. ISOLDE, CERN, 20 July, 2011 Recent advances in the theory of nuclear alpha decay: 100 years after its introduction Chong Qi Dept. of Physics, Royal Institute of Technology, Stockholm

  2. Outline • The Geiger-Nuttall law and experimental status of alpha decay studies • Historic development of alpha decay theory • Microscopic two-step description of alpha decay and generalization of the GN law;Clustering (formation) + Penetration Proton decay and heavier cluster decays • Important role played by the pairing correlation • Influence of the neutron-proton correlation • Summary

  3. Reminder: What was going on 100 years ago E. Rutherford. May 1911, Philos. Mag, 21:669-688 J.P. Schiffer, Nucl. Phys. A 805, 98c (2008)

  4. The gold foil experiment in 1909 The interaction of alpha particle with the atom (nucleus) plays a fundamental role in the development of nuclear physics Alpha-nucleus scattering experiment by Geiger and Marsden A. Wright, Nature Phys. 5, 380 (2009)

  5. Geiger published three papers in one issue The Geiger-Nuttall law H. Geiger and J. M. Nuttall, Philos. Mag. 22, 613 (1911). http://www.tandfonline.com/toc/tphm17/22/130

  6. Experimental Progress • α radioactivity ~ 400 eventsobserved in A > 150 nuclei;α decay of N≈Z nuclei (2000s) • Heavy-cluster decays 11 events observed in trans-lead nuclei • 223Ra(14C), Rose and Jones, Nature 307, 245 (1984); • Proton decay more than 40 events observed in the rare-earth region. • New decay modes • Di-proton decay • Neutron decay • 12C cluster decay

  7. SHE probe Decays of N~Z nuclei Fine structure S.N.Liddick et al., Phys.Rev.Lett. 97, 082501 (2006) D.Seweryniak et al., Phys.Rev. C 73, 061301 (2006) I. Darby et al., Phys. Rev. Lett. 105, 162502 (2010). A.N. Andreyev et al., Nature 405 430 (2000) Yu. Ts. Oganessian et al., PhysRevLett.104.142502 (2010)

  8. Theoretical understanding “Standard” picture of the alpha decay process • Quantum tunneling interpretation • G. Gamow, Z. Phys. 51, 204 (1928). • R. W. Gurney and E. U. Condon, Nature 122, 439 (1928). Heavy particle radioactivity D. N. Poenaru et al., arXiv:1106.3271

  9. Viola-Seaborg formula V. E. Viola and G. T. Seaborg, J. Inorg. Nucl. Chem. 28, 741 (1966). The coefficients of the GN law depends on the charge number of the emitter. h takes into account the odd-even staggering Shelleffect B. Buck, A. C. Merchant, and S. M. Perez, Phys. Rev. Lett. 65, 2975 (1990). Alpha emitters below and above N=126 follow different systematics

  10. Alpha clustering in heavy nuclei Enhanced E1 transition • Astier et al., Phys. Rev. Lett. 104, 042701 (2010); Eur. Phys. J. A 46, 165–185 (2010). • D. S. Delion et al., to be published. • M.P. Carpenter, Physics 3, 8 (2010)

  11. The alpha particle is not a basic constitute of the atomic nucleus Alpha particle model of atomic nucleus before the neutron was discovered • Light nuclei may exhibit profound alpha clustering structure • The Gamow theory does not carry structure information Clustering structure in 12C F. Hoyle, Astrophys. J. Suppl. Ser. 1, 121 (1954). M. Chernykh et al., Phys. Rev. Lett. 98, 032501 (2007) E. Epelbaum et al., Phys. Rev. Lett. 106, 192501 (2011).

  12. Alpha (and cluster) decay as a fission-like processD.N. Poenaru et al., J . Phys. G : Nucl. Phys., 5, L169 (1979); Phys. Rev. C 73, 014608 (2006)

  13. Many-body approach of alpha clustering F(R) describes the formation property of the alpha particle inside the nucleus Yes, it depend on the radius. 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).

  14. The formation as a “factor” CQ, A. N. Andreyev, M. Huyse, R. J. Liotta, P. Van Duppen, and R. A. Wyss, PRC 81,064319 (2010). Even for the simple case of proton decay, it may not be that simple arXiv:1102.3721

  15. A two-step description 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. The Coulomb function is relatively well understood.

  16. 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).

  17. 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.

  18. Generalization of the Geiger-Nuttall law Universal decay law of alpha and cluster decays CQ, F.R.Xu,R.J.Liotta,R.Wyss, PRL103, 072501 (2009), PRC80,044326 (2009)

  19. A two parameter fit

  20. 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

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

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

  23. Effect of the pairing correlation ______________________________________________________ _________ _________ Separable Force

  24. 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.

  25. 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.

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

  27. Earlier works 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).

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

  29. Q value?

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

  31. Work on-going Suppression of alpha formation probabilities in neutron-deficient Po isotopes and limitation of the GN law Alpha decay of neutron-deficient nuclei and Z=82 shell closure A.N. Andreyev et al., to be published.

  32. Decay to excited states

  33. Alpha formation properites in N~Z nuclei

  34. Spin-aligned neutron-proton pair coupling in N=Z nuclei B. Cederwall et. al., Nature 469, 68 (2011). CQ et al., PRC (R) (in press)

  35. 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; • Effect of pairing collectivity; • Influence of the neutron-proton correlation on alpha formation • Alpha decay as a probe of nuclear structure

  36. Collaborators: A.N. Andreyev (Univ. of the West of Scotland, UK) M. Huyse, P. Van Duppen (KU Leuven, Belgium) D.S. Delion (IFIN-HH, Romania) R.J. Liotta, R. Wyss (KTH, Sweden) Thank you!

  37. 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.

  38. θ Evaluation of deformation effects 1. Effective approach: 2. Froman approach: The transimission matrix Ka=c

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