Alpha-Decay Hindrance Factors. Program ALPHAD. Edgardo Browne Decay Data Evaluation Project Workshop May 12

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Alpha-Decay Hindrance Factors.Program
ALPHAD.Edgardo BrowneDecay Data Evaluation
Project WorkshopMay 12 14, 2008Bucharest,
Romania
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• The probability of a decay depends on the
• Energy of the a particle
• Parent and daughter nuclear structure
  configurations
• A useful definition of hindrance factor is
• HF T1/2(a) exp./T1/2(a) theor.
• Notice that T1/2(a) T1/2/ a branching.
• HF depends only on the nuclear structure
  configurations. The energy dependence has been
  removed.
• T1/2(a) theor. is from The Theory of Alpha
  Radioactivity, M.A. Preston, Phys. Rev. 71, 865
  (1947!!)

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HF(0 to 0, even-even nucleus) 1by
definition. All other hindrance factors are
relative to this value.Hindrance factors for
odd-A and odd-odd nuclei are relative to HF
values for the 0 to 0 a transitions in the
neighboring even-even nuclei
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The Radius Parameter r0

• This parameter is roughly equivalent to the
  nuclear radius, and it may be determine for each
  nucleus from the 0 to 0 a transition in
  even-even nuclei, and assuming HF1.
• See Review of Alpha-Decay Data from Doubly-Even
  Nuclei, Y.A. Akovali, Nucl. Data Sheets 84, 1
  (1998).

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Favored alpha-particle transition in odd-A nuclei

• If HF lt 4 then initial and final levels have the
  same spin (J) and parity (p).

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The radius parameter r0(Y. Akovali, Oak Ridge)

• Odd-N nucleus (Z, A)
• r0(Z, N) r0(Z, N-1) r0(Z, N1)/2
• Odd-Z nucleus (Z, A)
• r0(Z, N) r0(Z-1, N) r0(Z1, N)/2
• Odd-Odd nucleus (Z, A)
• r0(Z, N) r0(Z, N-1) r0(Z, N1)/2
• r0(Z-1, N1)r0(Z-1, N-1)r0(Z1, N1) r0(Z1,
  N-1)/4

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Example
219Rn ?215Po (Odd-N) r0 (Z84, N131)
r0(84, 130) r0(84, 132) /2 From
1998Ak04 r0(84,214) 1.559 8 r0(84,216)
1.5555 2, therefore
r0 (Z84, N131) 1.557 Use Table 1
Calculated r0 for even-even nuclei (1998Ak04).
Insert R0 in comment record
CA HF R0 Run program ALPHAD to
calculate hindrance factors. HF(401 keV) 3.4
(Favored a decay).
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Estimating an a-decay branching
0
9 ms
210Th
a
90
?
2
474
0
0
100 HF1
206Ra
88
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HF Systematic for Even-even Thorium Nuclei

• Parent nucleus Jp Daughter nucleus Jp
  HF
• 210Th 0 206Ra
  2 ?
• 228Th 0 224Ra
  2 0.92
• 230Th 0 226Ra
  2 1.1
• 232Th 0 228Ra
  2 1.0
• We expect HF(210Th) 1

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Computer Program ALPHAD

Z A
90. 210.
Q ALPHA E TOTAL ALPHA HALF
LIFE RADIUS RZERO TOTAL HALF LIFE
ALPHA BRANCH 8.0530 8.0881 1.042E-07
D 9.0867E-13 1.5386 9.000E-03 S
1.000E00
ENERGY LEVEL
ABUNDANCE CALC. HALF LIFE HINDRANCE FACTOR
0.00 1.00E00 1.04E-07
1.00E00 474.00 1.00E-01 3.35E-06
3.11E-01 474.00 5.00E-02
3.35E-06 6.22E-01 474.00 3.00E-02
3.35E-06 1.04E00 474.00
1.00E-02 3.35E-06 3.11E00 474.00
5.00E-03 3.35E-06 6.22E00
474.00 3.00E-03 3.35E-06
1.04E01 474.00 1.00E-03 3.35E-06
3.11E01 474.00 1.00E-04
3.35E-06 3.11E02
So a(474) 3