shell-model approaches to two-proton decay · cluster-decay model (brink, arima etc) (45/43) is a...
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Shell-Model Approaches to Two-Proton Decay
BABFred Barker (ANU)
General commentsApplication to 2p decay of 45Fe and 48NiApplication to 2p decay widths of light nucleiPredictions for 2p lifetimes of heavier nuclei
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45Fe: Two-Proton Radioactivity Observed
GSI GANIL
Q(exp) = 1.14 (5) MeV, T(exp) = 3-10 ms
“…should lead to lifetimes longer than 10-12 sec, a possible lower limit for the process to be called radioactivity.”
“…should lead to lifetimes longer than 10-12 sec, a possible lower limit for the process to be called radioactivity.”
Joseph Cerny and J. C. Hardy, Annu. Rev. Nucl. Part. Sci. 27 (1977) 333
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Conditions for Two-Proton Radioactivity
Special cases where two-proton decay is allowed, but one-proton decay is “forbidden”.
Large Coulomb barrier in heavy nuclei makes the states narrow (eV or less), in particular the phase-space “tails” for one-proton decay are much reduced.
Q value for the two-proton decay is just right so that the lifetime is competitive with beta decay, but not too short for experimental observation - about 0.1 to 10 ms.
Very few cases.
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Quiz about New York Times article
What is the year?
Who was the group?
What was the decay?
What are the first four?
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Definitions
Di-Proton Decay Sequential Decay
12O
11N+p
10C+p+p
12O
10C+2p
10C+p+p
12O 10C+2p11N+p 12O 10C+2p11N+p
Simultaneous Decay
12O
10C+p+p
12O 10C+2p11N+p
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Three-Body Models (Grigorenko et al.)L. V. Grigorenko et al., Phys. Rev. Lett. 85 (2000) 22
I will assume the middle picture with the two-protons correlatedin their L=0 (T=1) resonance state.
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Two problems for the decay width
• Can we calculate the Q value? – Yes, but not better than to within about 100 keV
• If the experimental Q value is known to a better accuracy we should constrain the calculation to give this value in order to discuss the structure (overlap) questions.
• Can we calculate the overlap?
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Basic R-Matrix Formulation
Decay widthP(a) = penetration factor
Reduced widthS = spectroscopic factor
Dimensionless single-particlereduced widthu = cluster wave function from V(r).
Channel radius
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Basic R-Matrix Formulation
In many cases the same potential V can be used to calculate the scattering cross section as a function of energy from the phase shift. The widths of resonances obtained this way are the same as the R-matrix model typically within about 20%.
But the R-matrix formalism is useful when the resonance is very narrow and we need to include intermediate states.
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Two-Proton Resonance
is replaced by
Where c1 comes from norm
Effective-range resonance parameters; c, A and B.
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Many-Body Physics (e.g. for 45Fe)
Cluster-decay model (Brink, Arima etc)(45/43) is a center of mass correctionLambda = 2N+L = 6 (two protons in pf shell)L = 0N = 3 = number of nodes in the cluster wfG = projection of di-proton cluster onto the pf shellA = projection of di-proton cluster onto the specific
two-particle overlap <45Fe|a+a+|43Cr>
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Cluster wave function u(r)
Potential depth used to obtainThe experimental Q value.
Potential shape taken fromdeuteron scattering analysis.
N=3 for number of nodes (twoparticles in the pf shell).
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45Fe: Di-Proton or Sequential?G. Audi and A.H. Wapstra, Nucl. Phys. A595 (1995) 409
But coulomb energysystematics indicate that the one-proton decay is forbidden and the state should be very narrow.
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Q-value results for 45Fe
Q(exp) = 1.14 (5) MeV
Q(th) = 1.15 (9) Brown 1991
1.28 (18) Ormand 1996
1.22 (5) Cole 19
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Structure results for 45Fe
• The 45Fe wf has the form [ (proton pf)6 (neutron sd)-1 ]
• But the neutron hole is a spectator and the spectroscopic results essentially comes from the proton (pf)6 -> (pf)4 part.
• From the pf wave functions S=0.195.
• Although the wf are 90% f7/2, the f7/2 part alone would give S=0.06. The small admixtures of the p 3/2 has a large effect.
• In two-neutron transfer the p3/2 was called a “hot” orbit.
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Structure results for 45Fe
• Q(exp) = 1.14 (5) MeV, T(exp) = 3-10 ms.
• With S=0.195.
• From the R-matrix (T_o is without the pp interaction)
Q (MeV) T_d (ms) T_o (ms)
1.09 300 0.0601.14 45 0.0131.19 15 0.004
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Structure results for 45Fe
• T(exp) = 3-10 ms
• Theoretical rate need may need to be increased by a factor of 2-4. This would imply S=0.6.
• Similar situation to the pf-shell (p,t) reaction cross sections in the 1970’s.
• One requires an “enhancement factor” which is understood in terms of an enhanced pairing from small mixing with orbits outside the pf shell.
Q (MeV) T_d (ms)
1.09 300 1.14 45 1.19 15
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Results for 48Ni
• Q (predicted) = 1.36 (13) MeV (Brown 1991)
• S=0.14
Q (MeV) T_d (ms) T_d (ms) (with enhancement)
1.23 260 651.36 8 21.49 0.4 0.1
48Ni belongs to a class of “new magic nuclei” (ask at the end)
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Two-Proton Decay of 6Be
g.s.
1.67
0.59
-1.374He+2p
5Li+p6Be
(0+)(3/2-)
(2+)
D.F. Geesaman et al., Phys. Rev. C15, 1835 (1977).
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Structure results for 6Be (Barker paper)
• Q(exp) = 1.37 MeV, Gamma(exp) = 92(6) keV.
• S=1.25 from the p-shell wf.
• Di-proton (th) = 85 keV (2 MeV without pp correlations)
• Inclusion of sequential would give 64-80 keV (a reduction!)
• Perhaps another sign of enhanced pairing correlations.
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Two-Proton Decay of 12O
Old
New
??2.0 MeV1.8 MeV
1.8 MeV ~1.5 MeV
Di-Proton
Sequential
R.A. Kryger et al., Phys. Rev. Lett. 74, 860 (1995)
12O 11N+p 10C+2p
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Structure results for 12O (Barker paper)
• Q(exp) = 1.77 MeV, Gamma(exp) = 400(250) keV.
• S=1.0 estimate from the p-sd shell wf (dominated by large sd-shell admixture)
• Di-proton (th) = 5 keV
• Inclusion of sequential (dominated by s-wave) would give about 100 keV.
• Dominated by sequential.
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Structure results for 16Ne
• Q(exp) = 1.41 MeV, Gamma(exp) = 122 keV.
• S=1.0 (estimate)
• Di-proton (th) = 0.1 keV
• Dominated by s-wave sequential.
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Two-Proton Decay of 18Ne?J. Gomez del Campo et al., Phys. Rev. Lett. 86 (2001) 43
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• One-proton decay width (keV)
§ Sequential two-proton decay though the ½+ ghost (eV)
§ Di-proton decay width (eV)6 3 10
§18Ne total two-proton decay width (eV)
16 23 19
Exp
50(5)
20-60
• Two-proton decay width (eV)
10 20 9
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Watch out for the ghosts!
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N=Z line
Predicted separation energiesfor proton-rich nuclei used for the rp-processA=53-76
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Results for Heavier Nuclei
Nucleus Q (MeV) T_d (ms)
54Zn 1.33 50763Se 1.51 600067Kr 1.76 26271Sr 2.06 12
Assume S=1
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Two-Proton Decay - A New Type of Radioactivity
• The new mode of two-proton radioactivity has recently been observed for 45Fe [1-2].
• The Q value is in excellent agreement with a prediction [3].
[1] J. Giovinazzo, et. al., Phys. Rev. Lett. 89, 102501 (2002).[2] M. Pfutzner, et. al., Eur. Phys. J. A 14, 279 (2002).[3] B. A. Brown, Phys. Rev. C43, 1513 (1991).[4] B. A. Brown and F. C. Barker, submitted to Phys. Rev. C.
• We have applied a new R-matrix model which includes the two-proton resonance as an intermediate state to calculated the di-proton decay lifetime [4].
• The spectroscopic factor is calculated microscopically from the full pf-shell wave functions and is sensitive to the pairing correlations.
• The results are near the upper limit of the experiment with agreement being obtained with an enhanced pairing. 48Ni is another good candidate.
45Fe
43Cr
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Answers to Quiz
1983
Cerny et al.
Beta delayed 2p (22Al)
Alpha, beta, fissionone-proton
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New Magic Nuclei
• New data for 22O, 24O and N=34 taken together with previous observations, one finds a new “rule” for the observed magic numbers:
• If there is an oscillator magic number (2, 8, 20 or 40) for one kind of nucleon, then the other kind of nucleon has a magic number for the filling of every possible (n,l,j) value.
• This rule accounts for 16 doubly-magic nuclei shown by the circles.
• There are no exceptions to the rule.• New magic nuclei are predicted
(open circles).• These results were predicted but are
not yet fully understood.