1. Alpha-Decay Hindrance Factors. Program ALPHAD. Edgardo Browne Decay Data Evaluation Project Workshop May 12 – 14, 2008 Bucharest, Romania

2. The probability of  decay depends on the: Energy of the  particle Parent and daughter nuclear structure configurations A useful definition of hindrance factor is: HF = T 1/2 (  ) exp./T 1/2 (  ) theor. Notice that T 1/2 (  ) = T 1/2 /  branching. HF depends only on the nuclear structure configurations. The energy dependence has been removed. T 1/2 (  ) theor. is from “The Theory of Alpha Radioactivity,” M.A. Preston, Phys. Rev. 71, 865 (1947!!)

4. 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+  transitions in the neighboring even-even nuclei

5. The Radius Parameter r 0 This parameter is roughly equivalent to the nuclear radius, and it may be determine for each nucleus from the 0+ to 0+  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).

7. Favored alpha-particle transition in odd-A nuclei If HF < 4 then initial and final levels have the same spin (J) and parity (  ).

8. The radius parameter r 0 (Y. Akovali, Oak Ridge) Odd-N nucleus (Z, A) r 0 (Z, N) = [r 0 (Z, N-1) + r 0 (Z, N+1)]/2 Odd-Z nucleus (Z, A) r 0 (Z, N) = [r 0 (Z-1, N) + r 0 (Z+1, N)]/2 Odd-Odd nucleus (Z, A) r 0 (Z, N) = [r 0 (Z, N-1) + r 0 (Z, N+1)]/2 = [r 0 (Z-1, N+1)+r 0 (Z-1, N-1)+r 0 (Z+1, N+1) +r 0 (Z+1, N-1)]/4

9. Example 219 Rn  215 Po (Odd-N) r 0 (Z=84, N=131) = [r 0 (84, 130) + r 0 (84, 132)] /2 From 1998Ak04: r 0 (84,214) = 1.559 8 r 0 (84,216) = 1.5555 2, therefore r 0 (Z=84, N=131) = 1.557 Use Table 1 – “Calculated r 0 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  decay).

10. Estimating an  -decay branching ~100% HF=1 ? 0+ 2+ 0 474 206 Ra 210 Th 0+9 ms  88 90

11. HF Systematic for Even-even Thorium Nuclei Parent nucleus J  Daughter nucleus J  HF 210 Th 0+ 206 Ra 2+ ? 228 Th 0+ 224 Ra 2+ 0.92 230 Th 0+ 226 Ra 2+ 1.1 232 Th 0+ 228 Ra 2+ 1.0 We expect HF( 210 Th) ~ 1

12. 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 1.000E+00 ENERGY LEVEL ABUNDANCE CALC. HALF LIFE HINDRANCE FACTOR 0.00 1.00E+00 1.04E-07 1.00E+00 474.00 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 1.04E+00 474.00 1.00E-02 3.35E-06 3.11E+00 474.00 5.00E-03 3.35E-06 6.22E+00 474.00 3.00E-03 3.35E-06 1.04E+01 474.00 1.00E-03 3.35E-06 3.11E+01 474.00 1.00E-04 3.35E-06 3.11E+02 So  (474)~ 3% Computer Program ALPHAD