UKDMC Home Page |
## UK DM project: radioactivity test results |
UKDMC Intranet |

- A concentration
*C*(g/g) of an element with activity^{1}*B*_{g}Bq g^{-1}in a 4p shield results in a g flux at the centre of that shield of:

F (cm ^{-2}s^{-1}) =*CB*_{g}l_{g}(1 - e^{-x/lg});(1) reducing to:

F » *CB*_{g}*x*(1a) for thin shields, where

*x*is shield thickness in g cm^{-2}(*i.e*. the activity is reduced by a factor*x*/l_{g}compared with a thick slab). The attenuation length l_{g}is of order 20-25 g cm^{-2}for a typical equilibrium photon cascade. - Some data are presented as total a-counts (usually in counts
per hour per cm
^{2}); though these cannot be unambiguously related to source activities (because a ranges are energy-dependent and very short), they can be used to place approximate upper limits on U or Th concentration or on^{210}Pb activity. Numerical integration over a spectra and approximate ranges result in:

1cph cm ^{-2}® < 500 ppb U; or ® < 2000 ppb Th; or ® < 60 Bq kg ^{-1}~ 3500 dpm kg^{-1}~ 5 Mtru^{210}Pb(cph = counts per hour; ppb = parts per billion = parts in 10

^{9}; dpm = disintegrations per minute; tru^{2}= disintegrations per day per kg). - For an isotope of mass
*A*AMU and half-life_{i}*t*_{½}years, the number of atoms required to give one disintegration per day is:

*N*= 527_{i}*t*_{½};(2) and the mass concentration to give one disintegration per day per kg is:

*C*= 8.75 ´ 10^{-25}*A*_{i}*t*_{½}.(3) If the isotope is present in the natural element (mean atomic mass

*A*) with an atomic fraction*f*, then these become:_{i}*N*= 527*t*_{½}*f*_{i}(2a) *C*= 8.75 ´ 10^{-25}*A*_{i}*t*_{½}*/f*;_{i}(3a) for a chain of

*n*decays (from Th or U), these must be divided by*n*. For Th,*n*= 10; for U, there is the added complication that 95.6% of primary decays are^{238}U (*n*= 14), and 4.4%^{235}U (*n*= 11), giving*n*= 13.87.For materials external to the target, the short-range a, b particles have low probability of producing `events' - though bremsstrahlung from higher energy bs must be considered. Consequently, we are generally only concerned with the g activity, for which we have (X-rays

**not**included):-*n*_{g}= 0.107(K), 2.65(Th), 2.20(U).In the target itself, b activity is also relevant (a decays, being contained within the target apart from those within a few mm of the target surface, should be rejected by their ~ MeV energies), and we have:-

*n*_{b}= 0.893(K), 4(Th), 5.91(U).Hence:

1 ppm K ® 0.0309 Bq kg ^{-1}= 1.86 dpm kg ^{-1}= 2.67 ktru; ® 0.00331 Bq kg ^{-1}= 0.199 dpm kg ^{-1}= 0.286 ktru in g (ppm = parts per million);

alternatively,

1 Bq kg

^{-1}of 40 K ® 32.3 ppm K; 1 Bq kg^{-1}in g ® 302 ppm K.For disintegrations of the

**parent**^{232}Th (or any daughter on a 100% branch), we have:1 ppb Th ® 0.00406 Bq kg

^{-1}® 0.243 dpm kg^{-1}® 351 tru;and, in particular,

1 Bq kg

^{-1}of^{228}Ac ® 246 ppb Th; 1 Bq kg^{-1}of^{208}Tl ® 685 ppb Th (36% branch).If the decay chain (

^{232}Th ®^{208}Pb + 6a + 4b+ 2.65g) is in equilibrium, we also have, from the**full chain**,1 ppb Th ® 0.0406 Bq kg ^{-1}= 2.43 dpm kg ^{-1}= 3.51 ktru (a + b) ® 0.0108 Bq kg ^{-1}= 0.645 dpm kg ^{-1}= 0.929 ktru (g) ® 0.0162 Bq kg ^{-1}= 0.974 dpm kg ^{-1}= 1.40 ktru (b). For `natural' (non-depleted) U, parent decays are:

1 ppb U ® 0.0123 Bq kg ^{-1}® 0.738 dpm kg ^{-1}® 1.06 ktru from ^{238}U+

5.7 ´ 10 ^{-4}Bq kg^{-1}® 0.034 dpm kg ^{-1}® 49 tru from ^{235}U,® 0.0129 Bq kg ^{-1}® 0.772 dpm kg ^{-1}® 1.11 ktru in all; and

1 Bq kg

^{-1}of^{226}Ra or^{214}Bi ® 81.3 ppb U; 1Bq kg^{-1}of^{235}U ® 1.76 ppm U.For decay chains in equilibrium (

^{238}U ®^{206}Pb + 8a + 6b+ 2.18g;^{235}U ®^{207}Pb + 7a + 4b+ 2.53g), we have, from the**full chain**,1 ppb U ® 0.179 Bq kg ^{-1}= 10.8 dpm kg ^{-1}= 15.5 ktru (a + b) ® 0.0284 Bq kg ^{-1}= 1.70 dpm kg ^{-1}= 2.46 ktru (g) ® 0.0752 Bq kg ^{-1}= 4.51 dpm kg ^{-1}= 6.50 ktru (b).

- Strictly, the becquerel (Bq) and other disintegration units refer to the totality of decays and not, as here, to the decays in a particular branch. However, this (ab)usage is very convenient, and careful use should cause no ambiguity.
- The introduction of a `total rate unit' (tru) arises from the decision
to adopt a standard `differential rate unit' (dru) of 1 event per keV per day per kg for
background spectra. Integration then gives 1 tru = 1 per day per kg (1 Mtru = 10
^{6}per day per kg).