Transcript Skyrme Mean-field description of exotic nuclear structures

Swedish Nuclear Physics meeting
16-17 November, 2010, Uppsala
Deviations of alpha decay half-lives from the
Geiger-Nuttall law
as 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)
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.
1) Progress in experiments
α radioactivity
~ 400 events observed in A > 150 nuclei;
Alpha decay as a spectroscopic probe
Decay of N~Z nuclei
S.N.Liddick et al., Phys.Rev.Lett. 97, 082501 (2006)
D.Seweryniak et al., Phys.Rev. C 73, 061301 (2006)
Fine structure
A.N. Andreyev et al., Nature 405 430 (2000)
Theoretical understanding
Schematically: quantum tunneling interpretation
by Gamow in 1928
The Geiger-Nuttall law of alpha decays
H. Geiger and J. M. Nuttall, Philos. Mag. 22, 613 (1911).
The Gamow theory does not carry structure
information
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.
m d  
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).
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).
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)
Discrepancy between experimental
decay half-lives and UDL calculations->;
Around the N=126 shell closure, UDL
underestimate the half-lives by large
factors.
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.

210Po
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
Two-body clustering
Configuration mixing from higher lying orbits is important
for clustering at the surface
r1=9fm
210Pb
206Pb
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.
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.
Odd-even staggering of binding energies and pairing correlation energies
Larger pairing energy => Enhanced two-particle clustering at the nuclear
surface
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).
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
M. Takahashi, PRC27,1454(1983)
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.
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 approximation
The clustering induced by the pairing mode is inhibited if the configuration space does not
allow a proper manifestation of the pairing collectivity.