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coupled to one or more photomultiplier tubes. An anticoinci- dence circuit uses the signal from the mantle to exclude events in which the detector and the mantle simultaneously produce a count, since an event in both detectors would indicate the detection of a particle from outside the source region. The anticoincidence ring may effect a reduction in the background of a beta-ray counter of about 50. The overall reduction in background over a bare detector by the apparatus of Fig. 51(a) is often between 100 and 150. It is difficult to reduce the background of a large Nal(Tl) gamma-ray detector by using an anticoincidence mantle. In the energy region of 0-3 Mev, the background of such a gamma-ray detector may be reduced by a factor of only 2 to 5 through the use of a liquid or a plastic scintillator anticoincidence mantle. For the high-energy range above 3 Mev, in which the background 97 is chiefly due to mesons, the background is reduced by a factor of 103 to 10s. B. Small-Volume Counters. When the counter can be made very small, the experimental arrangement is much simpler. For instance, because the sensitive volume of a liquid scintillation counter can be so small, the shielding is often accomplished by a mercury shield so thick that an anticoincidence mantle is not required. An end-window beta proportional counter of small dimensions will have a low background simply because its sensi- tive volume is small. If this small counter is placed inside a larger detector [Fig. 51(b)] and the two are placed in anti- coincidence, a reduction in the background of at least a factor of 10 may be obtained. This entire assembly may be inserted into a massive shield for a further background reduction. The "Omni/Guard" detector manufactured by Tracerlab, Inc., is designed in this way and has a background of < 0.5 c/m. VIII. DETERMINATION OF THE DISINTEGRATION RATE In this Part we will discuss the special techniques for determination of the disintegration rate, often called absolute counting to distinguish it from relative counting procedures. Absolute counting may be performed directly as in 47T/3 counting; more often, absolute counting involves equipment normally employed for relative counting which has been calibrated by use 114
of a standard source. For details of the techniques to be described, the reader may consult the excellent review by 9 8 Steinberg, ' and proceedings of several conferences on this subject.99'100 1. Absolute Alpha Counting A. General Considerations. Alpha particles have a short range in matter, so a good alpha source must be very thin. By the same token, counter windows or other material through which the alpha particles must pass also should be thin; it is common to use windowless counters for such purposes. Scattering in the sample itself is not a serious problem with alpha particles, since the particles scatter only slightly in thin sources. Scattering from the source mount is appreci- able at small angles to the source plane but is negligible at angles normal to the source plane. The amount of backscattering increases with the atomic number of the scatterer and with decreasing energy of the particles. A variety of geometries are used. The usual one for moderate precision is the internal sample counter (a pro- portional counter or ionization chamber) with ZTT geometry. Here, the backscattered particles are also counted, so the effective geometry for sources on polished platinum plates is found to be in the range of 51 to 52%, depending on the energy. Work of the highest precision with sources on metal plates requires collimation to eliminate the backscattered particles; both low- and medium-geometry counters have been used very successfully. If the source to be standardized can be mounted on a thin, essentially weightless, film, then a 47T proportional counter may be used for accurate assay. ' Many alpha sources must be counted in the presence of intense beta activities; therefore, it is essential that the detector and electronic system have a short resolving time, lest beta-induced pulses pile up and be counted as though they were alpha pulses. Fast detectors suitable for precision alpha counting are scintillation counters, semiconductor detectors, and proportional counters. B. Low-Geometry Counters. When very accurate assays are required, or when the source intensity is very high, a low- geometry alpha counter is used. The general technique has been 115
discussed by Curtis, et al., and Robinson. A design by Robinson is shown in Fig. 52. The chamber has a factor of about 1/2600 of 4-n geometry. The chamber must be evacuated to a pressure of about 200 microns or less. Because the wall diameter is so near the collimator diameter, the eight baffles are required to prevent scattering particles off the walls and into the detector; without baffles, scattering amounts to about 1% of the total count. The high degree of collimation effectively eliminates backscattered particles from the source. Many low-geometry chambers use a proportional counter as a detector, which requires a gas-tight window between it and the evacuated chamber. Some proportional counters also may require efficiency corrections because of the anode wire supports. The scintillation counter sketched in Fig. 52 is free of these problems. If all important dimensions are known to 1 part in 10,000, then the accuracy is mainly limited by counting statistics. The plateaus can be held flat to 0.05% with proper attention to the electronic equipment, and the influence of sample size on the geometry is not great because of the large distance between source and detector. As an example of the accuracy of the method, assays of the same sample by workers at the AERE (Harwell, England), and LRL (Berkeley, California) agreed within 104 0.1%, using low-geometry chambers of different design. C. Precision, High-Geometry Counters. When the amount of activity to be assayed is small, it is necessary to use some sort of high-geometry configuration to obtain good counting statistics in a reasonable time. Although the 4ji counter is a very attractive arrangement, the required source must be mounted on a nearly weightless backing. Most alpha sources are mounted on backing plates, for which the 47T method is not suitable. For relative counting it is quite convenient to use an internal sample counter with 2it geometry, for which the overall efficiency, or counting yield, may be calibrated with standards if desired. When counting at high geometry, it is advisable to elimi- nate the backscattered alpha particles by reducing the geometry to about one TI steradian, which leads to an acceptance angle of 120 . When this is done, the geometry factor becomes very sensitive to the size and position of the source. This sensitivity to sample position is greatly improved by 116
masking the detector of a high-geometry counter with a stop of the proper shape. Figure 53 shows the design by Robinson. The chamber has a calculated geometry of 0.19748. A 2 mm diameter source on platinum gave an essentially constant counting rate for displacements up to several mm from the center of the source holder. That this device is indeed a highly precise counter was established by a cross comparison with a low-geometry counterâthe two agreed to within - 0.03%. FILLED WITH MINERAL OIL SILVER TYGON REFLECTOR COLLIMATOR PHOTOTUBE AND PREAMPLIFIER PAINTED WHITE GLASS PLATE WITH SCINTILLATOR ZnS(Ag) 8 BAFFLES 1/16x31/16-in. SOURCE Fig. 52. Low-geometry alpha counter for high-precision absolute alpha counting (Robinson36). 2. Absolute Beta Counting A. Introduction to Beta Counting Techniques. If an experimenter is so unfortunate as to be faced with the problem of determining the disintegration rate of a beta emitter, his 117
PHOTOMULTIPLIER TUBE AND PREAMPLIFIER PAINTED WHITE 452-mm-DIA. COLLIMATOR ZnS(Ag) SCINTILLATOR Fig. 53. Precision high-geometry alpha counter which uses a stop to reduce the effect of sample position on geometry (Robinson, in reference 100). problem is much more complicated than the alpha assay problem already discussed. The complications arise from the effects of scattering and absorption of electrons in matter, combined with the distribution in energy of the beta particles. It is usual to combine all experimental quantities which affect the counting rate into a counting yield e, which relates the observed counting rate N and the disintegration rate ND: e - £- ⢠(21) 118
Although ⬠is usually determined experimentally, it can, 9 8 in principle, be separated into the following factors: the geometry; the intrinsic efficiency of the detector; an absorption factor for the air between source and detector, in addition to the detector window; a correction for air scatter- ing; a factor for the backscattering by the source support; a factor to correct for scattering by environment; and a correction for the self-absorption and self-scattering by the finite mass Q Q of the source. The review article by Steinberg discusses the magnitudes and dependences of the various factors on the experi- mental situation. It is usually possible to determine a beta disintegration rate with an end-window counter to better than 5%. The counting yield of an essentially weightless source on a thin backing can be standardized to this accuracy either by use of an absolute standard, or by use of experimentally determined values of geo- metry, absorption, and scattering effects. Calibration standards must be used for the assay of thick beta sources to an accuracy of better than - 10%. A carrier- free sample of the desired activity is prepared and its disinte- gration rate determined. Aliquots of the sample are then processed, taking care that the amounts of carrier, mounting procedures, and other details are the same as for the unknown. In this way, the counting yield is measured directly for the particular experiment. B. End-Window Counters. By far the most common detector in use at present is the end-window counter. Much of the early information on beta counting was obtained with end-window Geiger tubes, although they have now been largely supplanted by end-window proportional counters (Section V.2.B.). The pro- portional counters are more stable and reliable, and because they usually are filled to one atmosphere pressure, their windows can be made very thin (0.2 to 1 mg/cm2) for good sensi- tivity to low-energy beta particles. The mechanical dimensions of end-window Geiger and proportional counters are similar, as are the dimensions of their source holders; therefore, some of the published data for Geiger counters can still be used in modern counting applications. C. Z7T Counters. For counting either low-intensity samples, where a high geometry is needed, or low-energy beta particles, where it is desirable to eliminate the detector 119
window, a 2v counter is very convenient. An additional advantage of this arrangement is that anisotropic scattering effects are less important here than in the end-window case. The general procedure for calibration of the counting yield is similar to that described above for end-window counters. A carrier-free sample on a nearly weightless backing does not eliminate scattering in a 27T geometry, because some structural material is almost certain to be nearby; for this reason, it is advisable to standardize the counting yield for sources mounted on a backing which gives saturation backscattering. D. 47T Counting. The most generally used techniques for primary standardization is the 4ir geometry beta counter, or 47T/3 counter. This instrument was described briefly in Section V.2.B. Coincident gamma rays or internal conversion electrons, when detected, are always counted simultaneously with the associated beta particle, and thus result only in a single count. Any discharges caused by scattering of the primary particle or by secondary radiation will also fall within the resolving time and will not affect the measured rate. A well-designed 47T/3 proportional counter will have a geo- metrical efficiency in excess of 99.5% and a plateau whose slope is less than 0.1%; therefore, the accuracy with which the disintegration rate may be determined depends mainly on absorption in the source and in the mounting film. Absorption will in all likelihood remain the factor limiting the accuracy of 47T/3 counting. Self-absorption was studied for specific source materials by Pate and Yaffe,105 and by Yaffe and Fishman,100 who showed how their correction method could be applied to other 47T counter sources. The source-film absorption correction has been determined in three ways: (1) the "sandwich" procedure of Hawkings, et al., in which the counting rate of a source on a known thickness of backing is measured, followed by a determination with an identical film covering the sample; (2) a calculated correction, proposed by Seliger and co-workers, was based on measurements of Zit and 47T single-film and "sandwiched" counting rates; (3) a determination of the counting rate as a 108 function of actual source film thickness was made by Smith, 109 and has been studied exhaustively by Pate and Yaffe. Any of these methods is useful above a few hundred kev, but (3), the 120
absorption curve technique, appears to be the most accurate, even at energies below 100 kev. Films to be used as source mounts should be rendered electrically conducting, preferably by vacuum evaporation of a metallic coating at least 2 |ag/cm2 thick. This coating will guard against distortion of the electric field by electrostatic charging of the source film or by a penetration of the field of one counter into the other. A systematic study of the general technique of 47T/3 counting has been published by Pate and Yaffe.102'105,109,110 Measurements at the National Bureau of Standards and the results of inter- comparisons of sources by various laboratories were discussed by Seliger and co-workers.107'111' The proceedings of a symposium on the metrology of nuclides contains a series of useful papers on the latest techniques of 47T/3 counting. Some work has also been performed using as 47 T detectors liquid scintillation counters and counters with radioactive-gas filling. These techniques, which are as yet rather specialized and of limited application, are described in papers included in references 99 and 100. E. Coincidence Counting. When two radiations are emitted in sequence during the decay of a radionuclide, coincidence counting is a convenient and accurate method for determining the disintegration rate. Consider the simple case of a single beta group followed by a single gamma ray. The counting rate of the beta counter NO is given by N,3 ' ND â¬0 ' (22) where N- is the disintegration rate and â¬â the counting yield. Similarly, the gamma-ray counting rate N is Ny = ND â¬y ' (23> Here, e is the counting yield of the gamma detector. The coincidence rate N is Nc " ND â¬0 â¬y ' (24) A recent report of the theory and practice of this technique was made by Campion.113 121
which reduces to Note that the determination of the disintegration rate by this technique does not require that the counting yields be known. The counting rates in the beta, gamma, and coincidence channels must be corrected for background rates and dead-time losses. Because each detector must only be sensitive to a single type of radiation, the background correction in the beta channel must also include the contribution arising from the gamma sensitivity. An additional correction to the coincidence rate is the random coincidence rate, N = 2r Ng N ; the rates in the beta and gamma channels should be total rates before background subtraction. As previously, 2r is the coincidence resolving time. Another coincidence "background" arises from the detection of gamma-gamma cascades in the two detectors, if the decay scheme is complex. Nuclides with several beta groups may be assayed by the beta-gamma coincidence technique, if the sensitivity of either the beta or gamma detector is the same for all branches of the 114 decay scheme. Because of its high, uniform efficiency, the 47T/3 counter makes a very useful beta detector for coincidence counting. When counting nuclides with complex decay schemes by the 47T/3-y coincidence method, the corrections arising from the decay scheme usually turn out to be rather small. Since the beta-gamma coincidence technique is insensitive to counting losses from absorption in the source and its backing, it offers another way of calibrating the counting yield for thick sources in a 47T/3 counter.113'115 With quantitative infor- mation about the decay scheme of a particular nuclide, it should be possible to standardize sources by 47T/3-y coincidence counting to a few tenths of a per cent. 3. Absolute Gamma Counting Gamma-ray counting by the scintillation method was dis- cussed above in Section II. 3. Spectrometry at a defined solid angle will yield an accuracy of about - 5%âmore accurate data 112.
require calibration with sources of known disintegration rates. Integral counters, such as well-type scintillation detectors, must be standardized. The most precise instrument for secondary standardization of gamma emitters is the high-pressure ionization chamber (Section III.5.). A precision of about - 0.05% can be obtained when intercomparing sources. The coincidence method of absolute counting is not limited to beta-gamma counting but may be extended to any coincident pair of radiations, such as beta- electron coincidences, X ray-gamma coincidences, and especially gamma-gamma coincidences. The National Bureau of Standards has used the gamma-gamma coincidence counting technique for assay ' of Co60. In this situation, where two cascade gamma rays are of equal intensities, disintegration rates can be obtained to as good an accuracy as by other methods. IX. SOURCE MOUNTING 1. Introduction By now it is probably obvious that the choice of a chemical separation procedure, the choice of a radiation detector, and the choice of source mount are not independent. Factors such as the nature of the radiation to be counted often will determine the type of source to be employed; the source, in turn, will usually place restrictions on the choice of chemical procedure and counting equipment. There is so much variety in these interrelated factors which must be considered that this section will not attempt to set down firm rules for choosing the best source-preparation method. Instead, some of the common ones will be discussed in a general way so that the experimenter will be given sufficient information about methods in use to make a choice for his own problem. For a more extensive discussion it is suggested that the reader consult the summaries of the source-preparation problem by Overman and Clark and SIHtis. These authors quote extensive references for further reading. 2. Desiccated Sources A. Evaporation from Solution. It is often desirable to 123
prepare a source which is very thin. The most straightforward approach is evaporation of an aliquot of a carrier-free solution on a suitable backing. To produce a thin source this way is very difficult, because it is essential that the solution contain no chemical compounds which will contribute appreciable mass to the final deposit. A technique which avoids concentrating impurities in the final product is the use of a very small bed of ion-exchange resin to which the carrier-free activity is adsorbed; after washing, the activity is eluted in the smallest possible volume of reagent. An unavoidable feature of evaporation from solution is that solids will not form a uniform deposit. In some experi- ments, such as 47T/3 counting of low-energy beta particles, self-absorption of aggregates may be excessive, and another method of depositing the source may be required. Metal Backing Plates. Alpha particles exhibit a short range in matter, and sources of these particles must be quite thin. As was seen in Section VIII.1., alpha backscattering is small and is easily determined, so a metal plate makes a convenient source backing. If the volume of solution to be evaporated on a metal plate is very large, it may be helpful to confine the solution to the desired region by a border of Zapon lacquer. After drying, the lacquer and any volatile impurities can be removed by ignition in an induction heater or an open flame, provided that the sample proper is nonvolatile. Further information on the use of metal foils as source backings will be found in reviews by Dodson, etal., and by Hufford and Scott. 118 A very useful spreading technique for preparation of uniform foils of heavy elements calls for mixing the nitrate of the desired element, dissolved in an organic solvent, with a dilute solution of Zapon lacquer. This mixture is painted on a metal plate, and, after drying, the plate is heated to destroy the organic residue and to convert the nitrate to the oxide. After each ignition the deposit is rubbed with tissue to insure that successive layers will adhere. Quite uniform deposits with smooth vitreous surfaces can be prepared by application of many successive coats, each very thin. This procedure is generally useful for any case where the element deposited has a nonvolatile compound which can be dissolved in an organic solvent; the foil must have a melting point high enough to with- 124
stand ignition. Another technique which makes use of an organic solution of a nitrate has been described by Carswell and Milstead. In their method the solution is sprayed from a capillary tube by the influence of a strong electric field. The space from the capillary tip to the metal plate is adjusted so that only fine, dry particles are collected. Thin, uniform sources may be prepared, even on extremely thin gold-coated plastic films.121 Very Thin Backings. In many beta counting applications, it is necessary to mount carrier-free sources on as thin a backing as possible. The usual technique is to transfer an aliquot of the appropriate solution onto the thin film by means of a micro pipette. The liquid is carefully evaporated by gently heating with an infrared lamp; the process is accelerated by flowing a stream of air over the source during evaporation. Methods for preparing thin films are to be reviewed in a monograph of this series by Yaffe. The article on source and window technique by Slatis remains a very useful reference on thin films and other aspects of the source problem. Gamma-Ray Sources. Although any of the methods already described can be used to prepare gamma-ray sources, the rela- tively low absorption of gamma rays by matter makes possible a rather simple and rapid procedure for mounting an aliquot of solution for gamma-ray assay. This method uses a small disc of blotting paper or "filter accelerator" taped onto a card. An aliquot of the solution to be determined is merely allowed to soak into the paper. After the sample has been dried by using an infrared heat lamp, the source should be covered by cello- phane or Mylar tape. B. Use of Slurries. Frequently, it is convenient to transfer small amounts of precipitate to a source mount and evaporate the solvent. The precipitate may, for example, lie collected in the tip of a centrifuge tube at the last step of a chemical separation procedure. A suitable organic liquid (e.g., alcohol or acetone) is added, and the resulting slurry is drawn into a transfer pipette; when discharging the contents of the pipette into a planchet, care must be exercised to insure that the spreading of the precipitate is uniform. After drawing off excess liquid, the sample is dried on the planchet am then covered with a thin plastic film to prevent spillage. 125
There are occasions in which it may be convenient to perform the final centrifugation in a demountable centrifuge tube whose bottom is a source planchet. This method has the advantage that the final deposits obtained are more uniform than those formed by pipetting slurries. C. Filtration of Precipitates. When large numbers of samples must be prepared, the most convenient method is fil- tration, using a filter paper disk as a combination source mount and filter. Rather large masses of precipitate can be accommodated, and with proper technique, the area and thickness can be controlled sufficiently to insure good reliability. Several designs for filtration devices have been published and a few are on the market. In all of these a disk of fine- grade filter paper (e.g., Whatman No. 42) lies on a flat support, which may be either a sintered glass filter disk or perforated stainless steel plate, attached to the end of a tube. A hollow cylinder of glass or stainless steel, into which the slurry is introduced, is clamped firmly over the top of the filter paper disk. Once the precipitate is caught on the filter paper it may be washed and dried before removing it from the apparatus. If there is a tendency for the cake of precipitate to break up, a dilute solution of organic binder such as collodion may be passed through the filter before the final drying. When the weight of final precipitate is needed to deter- mine a chemical yield, a tare weight should be determined by using several filter paper disks identical to those employed for the unknown. Naturally, the tare papers should be subjected to the same wash solutions, binder, and drying procedure as the unknown. 3. Sublimation Some of the most uniform sources are prepared by subli- mation in vacuum. This method is applicable when the radio- nuclide of interest can be prepared in a chemical compound whose vapor pressure is at least 0.1 mm at a temperature below that for rapid decomposition. Examples of this technique will be found in references 118, 119, and 123. The apparatus consists of a demountable vacuum chamber, in which are situated either a crucible or a ribbon filament, with 126
the collector plate a fraction of an inch away. Usually it is desirable to evaporate the source solution onto a shallow trough or depression in the filament, so when the filament is heated the sublimed material is collimated onto the collecting plate. A crucible, heated with electrical resistance wire or by electron bombardment, has similar collimating properties. For the preparation of thin sources, it is helpful to be able to swing the collector away during the initial heating of the sample. It is then possible to "cook off" various impuri- ties (such as organic residues) at low temperature, without subliming them onto the source mount. Most of the procedures for vacuum sublimation are time consuming and have yields of less than 50%. Pate and Yaffe have designed a system for subliming from a crucible onto a thin film with nearly 100% yield. Their results suggest that it should be possible to prepare sources which are not only uniform and thin, but also contain a known aliquot of a stock solution. The possibilities of such a technique in the fields of 41T/3 and alpha-particle counting are very promising. 4. Electrodepos it ion Perhaps the most convenient source mounting technique, except for simple evaporation of a solution, is electro- deposition. Although it is not, in principle, as generally applicable as vacuum evaporation, it has enjoyed widespread use, especially for samples of the heavy-element alpha-particle emitters. Very uniform films can be obtained by this method, ranging from trace amounts to a few mg/cm2. Because the method is so well suited to the preparation of alpha-particle sources, extensive literature has been published on the electrodeposition of the heavy elements. Procedures for polonium, thorium, uranium, neptunium, and plutonium have been reported in the published records of the Manhattan Project,118' 119, 124 and an article by Ko125 gives electro- deposition procedures for all the actinide elements through curium. Where no procedures are available for carrier-free electrodeposition of a particular element, information in the standard analytical and electrochemical texts may be used as a guide; however, as is well known, the carrier-free element may not behave in the same way as do weighable amounts. In such a
situation, it may be helpful to add a small amount of carrier to avoid these difficulties. The apparatus for electrodepositing on radionuclides counting plates has been described in the literature; for example, in references 115, 118, 119, and 124. Several devices are available commercially. 5. Sources Containing Gases Samples of certain nuclides, notably the rare gases, are most conveniently assayed as gases. The experimenter may elect to introduce the gas into an ionization chamber, proportional counter, or Geiger counter as a component of the detector gas; or, he may choose to contain the gas in some way and mount it externally to the counter. The highly specialized and well-developed techniques for internal gas counting have been adequately described in the current literature, as the list of references given by Overman and Clark attests. Application of the method to the use of nuclides such as C1 * (as CO2) has been treated by Tolbert and Siri.15 A gas simply may be pumped into a container having a thin window for the exit of the particles to be counted. In spite of its convenience, this technique is not often used for abso- lute counting because the counting geometry of such a diffuse source is not well defined. If gamma-ray counting is to be performed, a gas sample may be contained by adsorption on a bed of activated charcoal or on one of the clathrates. The trap requires such thick construction material that beta counting is to be preferred. A method for preparing thin, permanent samples of rare gases on metals has been described by Momyer and Hyde. In their method the rare gas is introduced, along with nitrogen or air as carrier gas, into a glass chamber containing two electrodes, which may be either two parallel platinum plates, or a helical anode surrounding a central wire collector (cathode) of platinum. A glow discharge is struck between the two electrodes at a pressure of 100-1000 microns, taking care to limit the current to only 2-3 ma. In 5 minutes it is possible to obtain yields of a few per cent. No detectable loss of gas occurs from these sources at room temperature, and they appear to be quite thin. 128
6. Liquid Sources For the beta counting of liquid samples, the liquid scintillation method (Section II.2.) is ideal. The current literature may be consulted for the latest recipes for samples compatible with the most common solution scintillators. General information on the subject may be found in references 10, 15, and 115. Gamma-ray emitters may be contained very conveniently in small, biological-type test tubes for counting in a well-type Nal(Tl) scintillation counter (Section II.3.C.). Larger ali- quots of solution may be contained in centrifuge tubes of up to 50-ml capacity; these may be assayed in high-pressure, gamma- sensitive ionization chambers, such as were described in Section III.5. 129
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