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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