Chong QiDept. of Physics, KTH, Stockholm

Deviations of alpha decay half-lives from the Geiger-Nuttall law

as a manifestation of nuclear structure effects

Swedish Nuclear Physics meeting16-17 November, 2010, Uppsala

Collaborators:R.J. Liotta, R. Wyss (KTH, Stockholm)A.N. Andreyev, M. Huyse, P. Van Duppen (KU Leuven, Belgium)

Experimental status and the Geiger-Nuttall law of alpha decaysMicroscopic 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.

1) Progress in experiments1) Progress in experiments

α radioactivity ~ 400 events observed in A > 150 nuclei;

A.N. Andreyev et al., Nature 405 430 (2000)

S.N.Liddick et al., Phys.Rev.Lett. 97, 082501 (2006)D.Seweryniak et al., Phys.Rev. C 73, 061301 (2006)

Decay of N~Z nuclei Fine structure

Alpha decay as a spectroscopic probe

Theoretical understandingTheoretical 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

2) Microscopic description of alpha decay2) Microscopic description of alpha decay

Shell ModelH.J. Mang, PR 119,1069 (1960); I. Tonozuka, A. Arima, NPA 323, 45 (1979).BCS approachHJ Mang and JO Rasmussen, Mat. Fys. Medd. Dan. Vid. Selsk. (1962)DS Delion, A. Insolia and RJ Liotta, PRC46, 884(1992).

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m→d +α

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.

Alpha formation amplitudeAlpha formation amplitude

CQ et al, Phys.Rev.C80,044326 (2009); 81,064319 (2010).

R should be large enough that the nuclear interaction is negligible, i.e., at the nuclear surface.

C.Qi, F.R.Xu,R.J.Liotta,R.Wyss, PRL103, 072501 (2009), PRC80,044326 (2009)

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

a division occurs between decays corresponding to N <126 and N >126;Sudden change at N = 126;The case that shows the most significant hindrancecorresponds to the α decay of the nucleus 210Po, one order of magnitude smaller than that of 212Po.

210Po

Discrepancy between experimental decay half-lives and UDL calculations->;Around the N=126 shell closure, UDL underestimate the half-lives by large factors.

3) Theoretical explanation210Po vs 212Po (The later is the textbook example of alpha emitter )

3) Theoretical explanation210Po vs 212Po (The later is the textbook example of alpha emitter )

If we neglect the proton-neutron interaction

Two-body clustering

210Pb

206Pb

Two-body clusteringTwo-body clusteringConfiguration mixing from higher lying orbits is important for clustering at the surface

r1=9fm

R=r1=r2

Two-body clusteringTwo-body clustering

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.

Alpha formation amplitudeAlpha 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.

Odd-even staggering of binding energies and pairing correlation energies

Larger pairing energy => Enhanced two-particle clustering at the nuclear surface

Previous explanations

Calculations underestimated the formation probability by several orders of magnitude due to the limited model space employed.Sn(206Po)>Sn(208Po)>Sn(210Po).

Reduced widths [similar to F(R)] of Po isotopes as a function of A

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

4) Possible manifestation in other observables

cross sections of (p,t) reactions on Pb isotopes

4) Possible manifestation in other observables

cross sections of (p,t) reactions on Pb isotopes

M. Takahashi, PRC27,1454(1983)

5) Next-step5) Next-step

Alpha decay of neutron-deficient nuclei and Z=82 shell closureA.N. Andreyev et al., to be published.

Suppression of alpha formation probabilities in neutron-deficient Po isotopes and limitation of the GN lawC. Qi et al., to be published

5) Summary Alpha decay as a probe of nuclear structure.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!

Delta-function approximationDelta-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.