3. Automated Processes
In Sec. 2, a number of techniques used in batch processes were discussed. These techniques have been used to study short-lived nuclides with half-lives of several seconds. In order to obtain statistically significant data for low-intensity gamma transitions and for coincidence data, the separation had to be repeated a large number of times. Further, the handling of large numbers of samples manually resulted in exposure to large radiation doses. When the half-life is very short (for example, very close to 1 s) it is extremely difficult, if not impossible, to carry out a multistep batch separation manually in a time comparable with the half-life. The nuclear chemistry group at the University of Mainz developed and used the first completely automated system for rapid radiochemical separation [Sch69, Tra72]. The entire sequence of irradiation, transport, various steps in chemical separation, and counting was controlled by electronic timers. Autobatch systems, which were developed from the principles learned in these systems, have been used in a large number of short-lived nuclide studies. Single-batch separations numbering over 10,000 have been performed to accumulate data using autobatch techniques [Hen81].
Because there is a certain limit to the half-life of isotopes that can be efficiently isolated by the batch technique, continuous-separation techniques have been developed. The continuous procedures use recoiling nuclear-reaction products from a thin target. Gas-phase chemistry techniques can be considered as leading to the use of chemistry within the ion source of an on-line isotope separator in order to provide both A (mass) and Z separation. Continuous processes allow data collection in a shorter time relative to batch processes. The data collection efficiency of autobatch systems has been compared with a continuous system by Stevenson and the Fast Chemistry Group at the Lawrence Livermore National Laboratory (LLNL) [Ste78, Mey80, Lie81]. They concluded that the efficiency of autobatch systems is acceptable even for nuclides with a half-life of 1 s under certain conditions. The details are discussed in the following section.
3.1 Comparison of Efficiencies of Autobatch and Continuous Processes
Here, as first given by Stevenson [Ste78], we review the analysis of the efficiencies of batchwise versus continuous operations. The calculation of the efficiency ratio can be given using the following assumptions:
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The detector used is operated at a count rate which does not exceed A0.
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The continuous separation system gives a constant count rate of A0.
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The sample delivered by the autobatch separation system gives a count rate of A0 initially and decreases exponentially with the half-life of the separated nuclide.
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The detector used in the autobatch system collects data for a duration of k1 half-lives. The system remains off for k2 half-lives, during which time the current sample is discarded and a new sample is brought to the counting station.
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The abundance of the activity of interest is optimized.
For the continuous system, it is assumed that the data is accumulated during the entire period of (k1 + k2) half-lives. The number of events Nc accumulated is given by
Nc = (k1+ k2)t1/2A0 .
(10)
In the case of the batch system, the count rate starts at the maximum count rate A0 and decreases exponentially for the duration of k1 half-lives. The total number of events accumulated by the batch system is given by
= (A0 / λ) [1− exp(−λk1t1/2)]
= (A0t1/2 / ln 2) [1 − exp(−k1 ln 2)] .
(11)
The relative efficiency η is given by
η = Nb / Nc = A0t1/2{1 − exp[−k1(ln 2)]} / (ln 2)[A0t1/2(k1 + k2)]
= {1 − exp[−k1(ln 2)]} / [(ln 2)(k1 + k2)] .
(12)
The variable k2 is the time required for discarding the current sample and positioning the new one; hence, k2 will depend on the chemical separation being used, the transport time of the separated sample to the detector position, and other physical restrictions of the autobatch system. It is convenient to maximize η for a given k2.
dη/dk1 = 0
= ((ln 2){exp[−k1(ln 2)]} / (ln 2)(k1 + k2)) − {1 − exp[−k1(ln 2)]} / [(ln 2)(k1 + k2)2] .
(13)
The above equation can be solved for k2, or
k2 = {exp [(k1)opt(ln 2)] − 1 } / ln 2 − (k1)opt .
(14)
From the k2 equation, the optimum counting time k1 can be deduced. Figure 11 shows a plot of k1 as a function of k2. For any value of k2, the optimum counting time k1 can be obtained from the graph. For example, if the sample changing time k2 is 1 (one half-life), then the optimum counting time k1 is 1.35 half-lives; if k2 is 2, the value for k1 is 1.9. The optimum counting time k1 increases as k2 increases.
For a given value of k2 and the corresponding optimum k1 value, the maximum efficiency ηmax can be calculated:
