Decay times for 'b' mode production are underestimated

[pkienzle]

The 'b' mode production comes during decay chains where the daughter product of the neutron activation decays into a grand daughter that emits beta radiation. During exposure the buildup of the grand daughter is recorded, but after exposure the further build up from the active daughter is not calculated. This means the decay time will be underestimated.

For example, 48Ca(n,γ)49Ca(β)49Sc(β)49Ti. In this case a mass of 1 g at fluence 1e8 n / cm²/s reaches a steady state at about 37 μCi each of 49Ca (T½=8.7 min) and 49Sc (T½=57.3 min). During decay the 49Ca will turn into 49Sc (about 145 min), which will extend the 49Sc decay time by a couple of hours (18 hr rather than 16 hr).

Assuming we don't fix it, the docs need to warn that reaction 'b' decay is incorrect. The web interface can flag those lines in the activation table and include a warning in the output.

The following code shows b-mode isotopes:

import periodictable as pt
for el in pt.elements:
    for isonum in el.isotopes:
        iso = el[isonum]
        acts = getattr(iso, 'neutron_activation', [])
        for k, ak in enumerate(acts):
            if ak.reaction == 'b':
                print(f"{ak.isotope} => {acts[k-1].daughter} (T½={acts[k-1].Thalf_str}) => {ak.daughter} (T½={ak.Thalf_str})")

Output:

Ca-48 => Ca-49t (T½=8.72 m) => Sc-49 (T½=57.3 m)
Se-82 => Se-83t (T½=22.4 m) => Br-83 (T½=2.39 h)
Nb-93 => Nb-92mt (T½=10.13 d) => Nb-92 (T½=37 My)
Mo-92 => Nb-92mt (T½=10.13 d) => Nb-92 (T½=37 My)
Mo-98 => Mo-99st (T½=66 h) => Tc-99 (T½=0.21 My)
Ru-96 => Ru-97t (T½=2.9 d) => Tc-97 (T½=2.6 My)
Ru-104 => Ru-105t (T½=4.44 h) => Rh-105 (T½=35.4 h)
Pd-110 => Pd-111t (T½=22 m) => Ag-111 (T½=7.47 d)
Sn-124 => Sn-125m (T½=9.5 m) => Sb-125 (T½=2.76 y)
Te-128 => Te-129t (T½=69.6 m) => I-129 (T½=16 My)
Te-130 => Te-131t (T½=25 m) => I-131 (T½=8.04 d)
Xe-124 => Xe-125t (T½=16.8 h) => I-125 (T½=59.9 d)
Xe-136 => Xe-137t (T½=3.9 m) => Cs-137s (T½=30.17 y)
Ce-136 => Ce-137t (T½=9 h) => La-137 (T½=60 ky)
Ce-142 => Ce-143t (T½=33 h) => Pr-143 (T½=13.58 d)
Nd-146 => Nd-147t (T½=11.06 d) => Pm-147 (T½=2.6234 y)
Nd-148 => Nd-149t (T½=1.8 h) => Pm-149 (T½=53.1 h)
Nd-150 => Nd-151t (T½=12 m) => Pm-151 (T½=28.4 h)
Nd-150 => Pm-151 (T½=28.4 h) => Sm-151 (T½=90 y)
Sm-144 => Sm-145t (T½=340 d) => Pm-145 (T½=17.7 y)
Eu-151 => Eu-152m1 (T½=9.3 h) => Gd-152 (T½=110 Ty)
Eu-151 => Eu-152t (T½=12.7 y) => Gd-152 (T½=110 Ty)
Gd-160 => Gd-161t (T½=3.7 m) => Tb-161 (T½=6.91 d)
Dy-156 => Dy-157t (T½=8.1 h) => Tb-157 (T½=150 y)
Er-162 => Er-163t (T½=75.1 m) => Ho-163 (T½=4570 y)
Er-170 => Er-171t (T½=7.52 h) => Tm-171 (T½=1.92 y)
Yb-176 => Yb-177t (T½=1.9 h) => Lu-177 (T½=6.74 d)
Pt-198 => Pt-199t (T½=31 m) => Au-199 (T½=3.14 d)
Bi-209 => Bi-210t (T½=5.01 d) => Po-210 (T½=138.38 d)

The 't' in the first daughter indicates transient equilibrium via beta decay. It is missing from some of the entries above:

124Sn => 125mSn
150Nd => 151Nd => 151Pm => 151Sm
151Eu => 152m1Eu

Note that 150Nd has two 'b' mode reactions in a row, with the 151Sm reaction using the 151Nd halflife rather than 151Pm halflife. I don't know if this is correct.

[pkienzle]

Added warning in the web calculator for all b mode rows and t daughter products.