Alpha-Decay Hindrance Factors.
Program ALPHAD.
Edgardo Browne
Decay Data Evaluation Project
Workshop
May 12 – 14, 2008
Bucharest, Romania
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!!)
HF(0+ to 0+, even-even nucleus) = 1
by 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
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 HF=1.
See “Review of Alpha-Decay Data from
Doubly-Even Nuclei,” Y.A. Akovali, Nucl.
Data Sheets 84, 1 (1998).
Favored alpha-particle transition in
odd-A nuclei
If HF < 4 then initial and final levels have the same
spin (J) and parity (p).
The radius parameter r0
(Y. Akovali, Oak Ridge)
•
Odd-N nucleus (Z, A)
r0(Z, N) = [r0(Z, N-1) + r0(Z, N+1)]/2
• Odd-Z nucleus (Z, A)
r0(Z, N) = [r0(Z-1, N) + r0(Z+1, N)]/2
• Odd-Odd nucleus (Z, A)
r0(Z, N) = [r0(Z, N-1) + r0(Z, N+1)]/2 =
[r0(Z-1, N+1)+r0(Z-1, N-1)+r0(Z+1, N+1) +r0(Z+1, N-1)]/4
Example
215Po (Odd-N)
r0 (Z=84, N=131) = [r0(84, 130) + r0(84, 132)] /2
From 1998Ak04:
r0(84,214) = 1.559 8
r0(84,216) = 1.5555 2, therefore
219Rn
r0 (Z=84, N=131) = 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).
Estimating an a-decay branching
9 ms
0+
210Th
a
2+
474
0+
0
206Ra
88
90
?
~100%
HF=1
HF Systematic for Even-even Thorium Nuclei
Parent nucleus
210Th
228Th
230Th
232Th
Jp
0+
0+
0+
0+
Daughter nucleus Jp
206Ra
2+
224Ra
2+
226Ra
2+
228Ra
2+
We expect HF(210Th) ~ 1
HF
?
0.92
1.1
1.0
Computer Program ALPHAD
Q ALPHA
8.0530
E TOTAL
8.0881
ENERGY LEVEL
0.00
474.00
474.00
474.00
474.00
474.00
474.00
474.00
474.00
Z
90.
ALPHA HALF LIFE
1.042E-07 D
ABUNDANCE
1.00E+00
1.00E-01
5.00E-02
3.00E-02
1.00E-02
5.00E-03
3.00E-03
1.00E-03
1.00E-04
CALC. HALF LIFE
1.04E-07
3.35E-06
3.35E-06
3.35E-06
3.35E-06
3.35E-06
3.35E-06
3.35E-06
3.35E-06
A
210.
RADIUS
9.0867E-13
RZERO
1.5386
HINDRANCE FACTOR
1.00E+00
3.11E-01
6.22E-01
1.04E+00
3.11E+00
6.22E+00
1.04E+01
3.11E+01
3.11E+02
So a(474)~ 3%
TOTAL HALF LIFE
9.000E-03 S
ALPHA BRANCH
1.000E+00