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UK DM project: radioactivity test results

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Useful numbers and relationships

  1. A concentration C (g/g) of an element with activity1 Bg Bq g-1 in a 4p shield results in a g flux at the centre of that shield of:
    F (cm-2 s-1) = CBglg(1 - e-x/lg); (1)

    reducing to:

    F » CBgx (1a)

    for thin shields, where x is shield thickness in g cm-2 ( i.e. the activity is reduced by a factor x/lg compared with a thick slab). The attenuation length lg is of order 20-25 g cm-2 for a typical equilibrium photon cascade.

  2. Some data are presented as total a-counts (usually in counts per hour per cm2); 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 210Pb 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 210Pb

    (cph = counts per hour; ppb = parts per billion = parts in 109 ; dpm = disintegrations per minute; tru2 = disintegrations per day per kg).

  3. For an isotope of mass Ai AMU and half-life t½ years, the number of atoms required to give one disintegration per day is:
    Ni = 527 t½; (2)

    and the mass concentration to give one disintegration per day per kg is:

    C = 8.75 ´ 10-25 Ai t½. (3)

    If the isotope is present in the natural element (mean atomic mass A) with an atomic fraction fi, then these become:

    N = 527  t½fi (2a)
    C = 8.75 ´ 10-25 Ai t½/fi; (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 238U (n = 14), and 4.4% 235U (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):-

    ng = 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:-

    nb = 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 232Th (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 228Ac ® 246 ppb Th; 1 Bq kg-1 of 208Tl ® 685 ppb Th (36% branch).

    If the decay chain (232Th ® 208Pb + 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 238U

    +

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

    and

    1 Bq kg-1 of 226Ra or 214Bi ® 81.3 ppb U; 1Bq kg-1 of 235U ® 1.76 ppm U.

    For decay chains in equilibrium (238U ® 206Pb + 8a + 6b+ 2.18g; 235U ® 207Pb + 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).

  1. 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.
  2. 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 = 106 per day per kg).