Alpha-Decay Hindrance Factors.Program ALPHAD.Edgardo Browne

Decay Data Evaluation Project Workshop

May 12 – 14, 2008Bucharest, Romania

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 = T1/2() exp./T1/2() theor.

Notice that T1/2() = T1/2/ branching.

HF depends only on the nuclear structure configurations. The energy dependence has been removed.

T1/2() 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+ 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+ 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 ().

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

Example219Rn 215Po (Odd-N) r0 (Z=84, N=131) = [r0(84, 130) + r0(84, 132)] /2From 1998Ak04:r0(84,214) = 1.559 8r0(84,216) = 1.5555 2, therefore 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 decay).

Estimating an -decay branching

~100% HF=1

?

0+

2+

0

474

206Ra

210Th

0+9 ms

88

90

HF Systematic for Even-even Thorium Nuclei

Parent nucleus J Daughter nucleus J HF210Th 0+ 206Ra 2+ ?228Th 0+ 224Ra 2+ 0.92230Th 0+ 226Ra 2+ 1.1232Th 0+ 228Ra 2+ 1.0

We expect HF(210Th) ~ 1

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