A versatile and comprehensive analysis code for automated reduction of gamma-ray spectral data

A VERSATILE AND COMPREHENSIVE ANALYSIS FOR AUTOMATED REDUCTION OF GAMMA-RAY SPECTRAL DATA

Department

CODE

J. P. MANEY, J. L. FASCHING* and P. K. HoPKEt of Chemistry, University of Rhode Island, Kingston, RI 02881, U.S.A. (Received 18 October 1976)

Abstract-PIDAQ. a Fortran IV program, quantifies and qualifies a 4096-channel Ge(Li) spectrum for neutronactivation analysis. PIDAQ employs code based on Fourier-transform and cross-correlation functions for peak analysis. Isotope identification of peaks involves a search through a disc stored library of 6590gamma-rays by using a polynomial fit for time-saving direct-access. Comparative method and/or the double ratio technique can be utilized to quantify spectra. The standard comparative method ratios the activities of known peaks to the activities of corresponding unknown peaks, corrects for decay and dead-time and calculates the concentration of elements with their related error in the unknown sample. The double ratio method eliminates matrix problems by employing a double ratio in which the concentration of a component of the unknown must be predetermined. PIDAQ, as written, can analyze up to 50 spectra. If core size allows, changes could be made to increase this Iimit. Quantification can be performed on any combination of these spectra. The program is running on an IBM 370155 computer under Batch OS and with output on remote terminals.

INTRODUCTION

Neutron

activation analysis, (NAA), employing the NaI(Tl) detector has long been known for its sensitivity in simple matrices and with the advent of the less efficient but greater resolving Ge(Li) detector, analysis of more complicated samples has become possible. Previously, trace level analysis required the sensitivity of NAA. However, in recent years competition from other less-expensive techniques has increased considerably with advances in such methods as mass spectrometry, emission atomic absorption and spectroscopy especially spectroscopy. Simultaneous analysis in some cases of over 30 elements and also its non-destructive properties (instrumental neutron activation analysis, INAA) secures a permanent place for NAA in the foreseeable future of instrumental analysis. However, application of NAA should not be limited to the above cases for with automated data handling N AA can be competitive in situations where other techniques may be initially favored. The union of computers and NAA was unavoidable since overlapping peaks of complex spectra when using a NaI(Tl) detector required sophisticated mathematical techniques for peak extraction. Computer manipulation of data eventually evolved to automated qualification and quantification of NaI(Tl) spectra (Tunnicliff d al.. 1970). The greater resolution of the Ge(Li) detector allowed the analysis of more complicated samples, due to a tremendous decrease in peak overlap. The resulting simplified spectra did not, however, result in the use of less complicated programming. The exacting peak identification and peak integration methods which followed the arrival of the Ge(Li) detector involved sophisticated computer code (Iouye et nl., 1%9; Baedecker, 1971). Some of the earlier investigators exploited the simpler Ce(Li) spectra by using simplified peak extraction computer techniques for the qualification and the quantification of data. One *To whom inquiries should be directed. ttnstitute

for Environmental

Studies,

Urbana-Champaign, It 6LEXl1,U.S.A.

University of Illinois,

author (Anders, 1969) identified isotopes by a half-life determination from two consecutive spectra and a library containing information on isotopes expected to be present. The peak area is extrapolated back to the time the irradiation ended, the amount of self-shielding is estimated and the concentration is determined by the absolute method. The absolute method can introduce error by uncertainties in cross-sections, length of irradiation, counting efficiencies and/or geometry factors. Dams et al. (1970) employed a standard comparative method for long irradiations while analyzing short irradiations with the absolute method. Peaks are searched for by examining the expected area of appearance (as indicated by a gamma ray library), in a calibrated spectrum. Unless the matrices of samples are strictly monitored the partial examination of a spectrum may allow an interfering element to be overlooked, leading to erroneous results. Biloen et al. (1973) identified peaks by examining the least-squares smoothed second derivative for consecutive negative values. The Cove11 method (Covell, 1959) was employed to calculate the peak area which was used in an absolute method to determine the concentration of the element. for Peak PIDAQ, whose name is an acronym Identification And Quantification is a very comprehensive processor of Ge(Li) spectra. PIDAQ employs a revised form of Gamanal (Iouye et a[., t%9) for peak analysis. The peak data supplied by Gamanal is the qualified and/or quantified. Qualification requires referal to a library, containing 6590 gamma rays, by means of a time-saving non-linear regression direct-access process. Quantification is done by the standard comparative method when sample and standard are assumed to have similar matrices, the ratio method is employed when a difference is expected. The concentration of the element and its error is determined and listed in the output. Upper-limits are calculated for undetected elements. PIDAQ has been in use since the beginning of 1973 and in the last two years has been used extensively by the research laboratories at Rhode Island and Illinois foT such diverse analyses as geological samples (Luedtke et 257

258

J. P.

MANEY, .I.

L.

FASCHINGand

a[., l976), atmospheric aerosols (Duce ei ul., 1976), blood samples (Zdankeiwicz et a[., 1975) and analytical techniques (Piotrowicz et al., 1975). leaching (Karin et al., 1975) and chelation studies (Buono et al., 1975). PRINCIPLES Peak analysis The first step in the processing of Ge(Li) spectra is to find and analyze the peaks. A modification of the program Gamanal has been developed for this purpose. Gamanal was originally written by the Nuclear Engineering group at MIT. for the analysis of (n, y) data (Iouye et al., 1%9). The major feature of this program was smoothing of the raw data by performing a Fourier transform followed by an inverse transform after weighting the transformed data with a filter function. The basic concept is that statistical fluctuations can be considered as high frequency noise imposed on the low frequency peaks. Thus, by applying a high frequency filter, the peaks should remain above a smoothed background. The data are then searched for minima, and a background spectrum is linearly interpolated and subtracted from the data so that only the peaks remain. The original version then searched for peaks by examining the first derivative of the background subtracted, smoothed data. We found this method unsatisfactory for finding all of the real peaks. Investigating peak-extraction techniques, the cross-correlation function approach (Black, 1969) proved very successful. The cross-correlation function of the raw data with a standard Gaussian curve is generated and searched for peaks by ,examination of its first and second derivatives. The location of possible peaks are stored for subsequent analysis. The peaks are then analyzed for their centroid and net area. Starting from the location of possible peaks found by the auto-correlation routine, the program searches for zero values in background-subtracted data as the start and stop points of a peak. The centroid is then calculated by the weighted average method. The area is determined by summing the raw data and the background spectrum over the peal channels. The net area is calculated by subtracting the background from the gross area. The counting error is calculated as the square root of the sum of the gross area and the background. The centroids are later used to identify the peak for elemental analysis and the calculated area used for the quantification of the element. The possible peaks ace examined to see if it is large enough, well-separated, and meets full-width at half-maximum (FWHM) criterion. From these peaks, an equation of FWHM squared as a quadratic function of channel number is determined by a least-square fit. Peak centroid, area, error in the area, measured full-width at half maximum calculated FWHM from the fitted function, and the width of the peak base are calculated for all peaks. Multiple peaks are treated as sums of two or three gaussian peaks with half-widths calculated from the fitted function. Extensive comparisons between results of the program and calculations by hand indicate that the program yields results within statistical uncertainty of the hand calculations. Each spectrum can have a maximum of 150 peaks analyzed for peak areas and peak errors. This data is stored in a large common array for easy access by other subroutines. Calibration PIDAQ cannot

employ

the

above

peak

data

for

P. K. HOPKE

qualification and quantification until energy is calibrated to channel number. An exacting calibration is required since qualitative analysis is determined solely by the energy of the emitted gamma ray and most often more than one gamma ray falls within a 1 keV range. Quantitative analysis also relies upon energy calibration to correctly match peaks in the known spectra with the gamma energies of standard isotopes stored in a library. Calibration requires individual counting of two separate multiple-isotope energy standards. The first calibration standard contains Co-60 and Cs-137. This standard and the background must be such that the three major peaks in the spectrum correspond to the energies listed in Table 1, under Standard 1. The presence of other smaller peaks can be ignored by setting peak location and peak error criteria. PIDAQ ignores these peaks by using an optional parameter which determines the highest area error which a peak may have and still be considered as a standard peak, (default value = 3%). The channel number at which search for the three major peaks initiates, can also be determined by input (default value = 150). Subroutine LIR after extracting the correct peaks performs a linear regression of channel number as a function of energy. This least-squares fit serves a two-fold purpose. It informs the program of the amplifier gain setting of the analyser. Secondly the slope and intercept are used to determine what portion of the second standard spectrum subroutine CALIB will inspect for a particular peak. Calibration standard II contains Mn-54, Co-60, Y-88, Cs-137 and Ta-182. The present activity of our sources require counting for ten minutes with an eleven percent Ge(Li) detector. These isotopes emit gamma-rays (Table 1) with various energies up to 1836 MeV. Examination of a different region of the gamma ray spectrum (e.g. O4MeV or 2-4MeV) only requires the use of different Table

1

STANDARD I cs-137

1332.5 KeV 1173.2 661.6

Mn-54 Co-60

1332.5

Co-60

STANDARD

II

Y-88 0-137 Ta-182

834.8KeV 1173.2 1836.I 898.0 661.6 1289.1 1213.7 1257.3 1230.9 1221.3 1189.0

1121.7 1001.7 264.1 229.3 222.1 198.4 179.4 156.4 152.4 100.1 67.8

An analysis code for automated reduction of gamma-ray spectral data isotopes which emit in the area of interest and the addition of these peak energies to the calibration library. Subroutine CALIB examines the spectrum of calibration standard II for peaks and matches them with energies stored in the calibration standard library. This search is done in a twelve channel region specified by the slope and intercept (determined with standard I) and the library energy. Only peaks with possible error in area less than or equal to 18% are considered for matching. The library energies which have been matched with peaks and the peak centroids (units of channel numbers) are stored in two separate working arrays. Subroutine POLFIT, a slightly revised form of a published program (Bevington, 1969) performs a non-linear regression using the above mentioned working arrays, producing a polynomial fit to the fifth degree of energy to channel number. The fifth degree polynomial was employed because its reduced chi-square value indicated a slightly better fit than the third or fourth degree polynomial. Table 2 contains results of the polynomial fit for a typical run. The second column lists the channel numbers corresponding to the peaks which were matched with the library energies listed in the first column. The third column lists the energies calculated using the coefficients determined in the non-linear regression.

Library energies

Channel No. of cent&d

Calculated energies

67.8 100.1 152.4 156.4 179.4 198.4 222.1 229.3 264.1 661.6 834.8 898.0

135.449 200.692 306.476 314.687 360.276 401.287 446.081 460.580 530.348 1327.266 1674.007 1800.444 2008.1Sl 2247.419 2351.471 2383.079 2447.813 2467.002 2520.052 255 I X78 2582.792 2670.127 3676.352

67.6 100.215 152.261 156.354 179.080 199.527 221.863 229.093 263.888 661.651 834.830 897.988 1001.751 1121.299 1173.294 1189.090 1221.441 1231.031 1257.544 1273.451 1288903 1332.559 1836.099

1121.7 1173.2 1189.0 1221.3 1230.9 1257.3 1273.7 1289.1 1332.5 1836.1

calibration standard. Matching of this calculated energy is attempted by searching through a library which contains 6590 gamma-rays (Lis et a[., 197Sa, b). This compilation is intended for use in thermal neutron, fast (14 MeV) neutron and photon activation analysis. It contains the accurately known data of those radionuclides which can be produced by (n, y), (n, 2n), (n, p). (n, a). (n, n’) or (n, d) reaction with any of the stable nuclides from z = 1 to z = 83. Only radionuclides with halflives greater than or equal to one second are included. Considering the size of the compilation, a matching process which involved a successive comparison of each library energy until a match was found, would be too time-consuming. To overcome this problem a directaccess method was employed. This method operates by storing each gamma-ray on disc in order of increasing energy. Each gamma-ray is assigned a record address in the disc data block. A non-linear regression of these gamma-ray energies and their record addresses produced a polynomial of the fourth degree which allows a computer directed search to go immediately to that portion of the library where matching is the most likely to occur. RECORD ADDRESS = - 2.39533 + 5.3365* -O.l1213*E+ -0.00158*E3 + 0.00005*E4

Table 2

1GQl .I

259

If a given analyser is stable the standard counted once. If drifting or gain changes the standard can be recounted to recalibrate It has proven advisable to count standards when counting for extended periods (more

need only be are suspected the analyser. at least twice than 4 hr).

Establishment of the correlation between energy and channel number allows qualification and quantification to proceed. Subroutine QUAL uses the centroid data supplied by the peak analysis performed in the first portion of the program. The centroid is converted to a corresponding energy using the polynomial acquired from the second

What constitutes a match is determined by the user who sets the limit on the difference of the calculated energy and that found in the library. The nuclide which falls into the selected limits are printed along with its relative intensity, its half-life, other associated gamma-rays and the means of producing the radionuclide. If no match is found this is so indicated in the print-out. The limits which constitute a match are variable, however the desired limit is the smallest value that the stability of the analyser and the peak area (which determines accuracy of centroid) allows. A limit of kO.4 KeV of the calculated energy is usually suitable. Quite frequently more than one nuclide falls within the limits of a match, all of these will be included in the print-out. The correct nuclide is chosen by checking for the closest match and examining the means of production and the presence of associated gamma-rays. Table 3 contains typical output produced by PIDAQ when it is employed to qualify the spectrum of a tellurium standard. Quantification Quantification uses the centroid and peak areas, which are calculated in the first portion of the program and then stored in a large common array. The centroids are used to locate peaks in the known and unknown spectra. The peak areas are used to determine the amount of unknown by comparison of its area with that of a standard. PIDAQ wiI1 quantitate any two spectra. The spectra to be quantified do not have to be stored on tape or disc in sequential order. The comparative method was chosen over the absolute method of quantification. The absolute method determines elemental abundance by calculating the amount of the element required to yield the activity recorded by an analyser. These calculations involve exact knowledge of the length of irradiation, cross-sections, flux, decay time, counting geometry and counting efficiency. This method can introduce significant error due to uncertainties in time, cross-section data, counting geometry and efficiency. Flux variation are usually accounted for by

260

J. P. MANEY,J. L. FASCHINGand P. K. HOPKE

An analysis code for automated reduction of gamma-ray spectral data use of a flux-monitor. However unless a proven flux monitor is employed uncertainties in the results of an absolute determination can be compounded. The compounded uncertainty arises from the initial use of the absolute method to determine the flux from the activity of the flux-monitor. The comparative methods (standard and double ratio) eliminate most of the above uncertainties by irradiating a standard with the unknown in the same flux for the identical time period. The standard and unknown are counted on the same detector. The elemental abundance is determined by a ratio of the activity of the unknown to that of the standard. The ratio cancels the uncertainties in cross-section, length of irradiation, geometry and counting efficiency. Flux-monitors can be employed if the unknown and standard are exposed to different fluxes. A ratio of the unknown and the standard flux activities is used to cancel the flux uncertainties which are innate to the absolute method. The double ratio comparative method is employed when physical properties of the standard and the unknown differ enough that analysis may be affected. Regardless of which method of quantification is chosen, they both call upon the quantitative standard gamma ray library. This library has storage capacity for four different standards or a total of 2000 gamma ray energies (KeV) with their half-lives, concentration and an alphaneumeric label of the users choice. It is advisable to list more than one gamma ray per element of interest, if possible. During a run, if the standard comparative method is chosen, subroutine QUANT matches peaks in the standard spectrum with those stored in the quantitative standard library. Matching is accomplished by first converting the centroid value, given in units of channel numbers, to its corresponding energy. This conversion uses the same polynomial produced during calibration and employs this polynomial as discussed under the section on qualification. This energy is then compared to the library energy. What constitutes a match is determined by the user. A value of f 0.2 KeV of the library energy is usually more than ample. These matched peaks are stored until the next standard is required. This eliminates the repetitive analysis of the same standard spectrum when it is compared to more than one unknown spectrum. The peaks of the standard spectrum which have been successfully matched with library energies are now compared with their corresponding peaks in the unknown spectrum. A match between standard and unknown peaks occurs when the previous described criteria for a match are fulfilled. A limit detection process is employed, when a matching unknown peak is not found in the spectra data produced by peak analysis. Subroutine LIMDTZ refers to that part of the original unknown 40% channel spectrum where the peak should have occurred. The background is summed over a region in channel numbers equal to twice the full width at half-maximum of the standard peak. Twice the squareroot of the summed background is assumed to be the maximum area of an undetected peak. Quantification continues in a normal fashion by treating the theoretical maximum peak area as a real peak area. The output includes a notation that describes such peaks as an upper-limit. All time manipulations are done in subroutine TIME. Subroutine TIME determines the decav time in seconds by considering the end of time of irradiation, and time of count. The time of count is adjusted to account for the

261

decreasing count rate of short half-life samples (Gordus, 1%7). Dead time is also detected by examining the area of the pulser peak (60 Hz pulser) which is located in the high energy end of the spectrum. These time determinations allow for dead time and decay time corrections of peak area. PIDAQ also calculates flux corrections if the standard and unknown experience different flux. This correction requires that the weight of the flux-monitor and its activity be submitted along with the input. The mass of the unknown is now determined by ratioing of the decay and dead time corrected areas of the unknown peak (A,) to that of the standard peak (A,). The product of this ratio and the mass of the standard (M,) yields the mass of the unknown (M,), M.=+M,, 5

that can be converted into various concentrations or mass units. A number of isotopes have nearly identical gamma rays which cause interference during quantification (Salbu et al., 1975). To counter this problem PIDAQ does not print an average mass of the unknown. Average masses are calculated by averaging the results of two or more gamma rays from the same element. PIDAQ prints the unknown masses as calculated for each individual gamma-ray of an element. This comprehensive listing decreases the possibility of interference going unnoticed. If interference is discovered, the mass calculated with the area of an unhindered peak is used. The mass (or concentration) of the unknown is listed in the output with its possible error. The possible error is calculated by the appropriate methods used to determine error propagatidn in the various mathematical processes employed in quantification. The double ratio method is employed to eliminate the problem of counting geometry caused by the physical differences between the standard and the unknown, This method can also be used when counting samples with high dead times or samples which have experienced fluxes different from that of the standard. This method has been tested extensively, (Hoffman et al., 1974). The double ratio method is programmed in much the same way as the standard comparative method. However this method requires that the concentration of a component of the unknown be predetermined by a secondary method. Subroutine QUANT recognizes that the double ratio method has been chosen and searches for the peak of the predetermined element in the standard and the unknown spectra. The decay corrected area of these peaks (A,, A,) are then ratioed with their respective concentrations (M,,M.). The concentration of the standard is known and stored in the standard library. The concentration of the unknown component was determined by a secondary method and entered with the input. A second ratio of these two ratios yields a normalization factor (k), which can account for the sample differences.

M

-2 k,

=$’ L.

The concentration

is determined

by multiplying a ratio

262

J. P.

MANEY, J. L. FASCHINGand

of the decay corrected activities of the standard (A,) and the unknown (A.) times the concentration of the undetermined elements.

Table 4 consists of typical output produced by PIDAQ when employed for quantification.

PIDAQ was written to take advantage of the facilities of the Rhode Island Nuclear Science Center, which is located in Narragansett, R.I. The center has a swimming pool type reactor which is presently operating at 2 MW with a thermal neutron flux of 4 x 10’2n/cmz/s. The gamma ray counting equipment includes three Ortec lithium drifted germanium detectors with associated electronics. The program was used extensively with two of these systems. The first of these analysers is a Nuclear Data-2200 4096 multi-channel anaiyser with an optional clock accurate to a hundreth of a minute, a unit to sequentially tagword spectra and a pulser. These three features were exploited by PIDAQ. The clock was used to print the time of count along with the assigned tagword and the length of count at the beginning of each spectra. The puiser creates a peak which is used along with the length of the count to determine dead-time. This analyser is on-line with an AMPEX TM-7 computer compatible tape deck. The second analyser is a Digital Equipment Corporation, Pulse Height Analyser system (PHA-11). The PHA-II system includes a PDP-III40 computer with 24 K of memory, a disc-drive, computer compatible magnetic tape deck and two complete 4096 multi-channel analysers. The available Ge(Li) detectors are: a 380.~ with resolution of the Co-60 1332 peak yielding a FWHM of 2.1 KeV, a 6Occ with a FWHM of 2.5 KeV and a 18Occ with FWHM of 2.2 KeV. The output tapes obtained from the above described analysers are available for computer analysis. PIDAQ is presently running on an IBM-370-155 computer and requires 256 K of core. This core requirement can be decreased by overlaying techniques. PIDAQ is stored in a program library in a compiled form. The program can be submitted by Batch or CALL-OS by submitting the data tape, job control language and data cards. Depending upon the complexity of the spectra and the type of analysis central processing unit time per spectra can range from 15 to 60s. PIDAQ can be run reading the data directly from the tape, however it has proven beneficial to transfer data from tape to disc. Access of data on disc is much faster and also decreases the chance of a tape reading error which could result in the termination of an expensive analysis run. This transfer of data from tape to disc is performed by a separate program named READTP. Figure 1 is a simplified flow chart of the algorithm employed in PIDAQ. The program initiates with a reading of data cards and spectra data. The first four data cards which the user must submit contain the parameters chosen for peak analysis. The first card determines if and what type of output is produced during peak analysis and whether a plotting routine will be employed to display spectra. The second and third card contain the criteria for peak and background calculations. The fourth card is a blank card which terminates peak analysis. The following determine how the peak-analyzed spectra are to be

P. K.

HOPKE

An analysis code for automated

reduction

of gamma-ray

spectral data

263

264

J. P. MANEY, J. L. FASCHINGand P. K. HOPKE

further treated. The fifth and sixth card allow labels to be appropriately printed in the output, controls other aspects of output, contains the matching limits for qualification and quantification and additional control information. Each spectrum to be analyzed has its own data card. This card contains the spectrum’s @word and its associated spectrum data necessary for the chosen analysis. If qualification is desired a zero follbws the tagword. Quantification requires that the number of the quantitative standard used, the time of day and day of irradiation, and the day of counting of the standard and the unknown follow the tagword of the standard and unknown. If the spectrum is that of the second calibration standard a minus number follows the tagword. This negative number will indicate which calibration standard will be used (different standards are required for different portions of the gamma spectrum). The remaining data cards following the spectrum cards list the gamma ray energies, half-life and concentration of the elements which constitute the quantitative standards. Peak analysis foIlows the reading of input. Peak analysis proceeds as previously described, analyzing all of the submitted spectra and stores the peak data in an array for future reference. Subroutine FIND is called upon by following sections of the program to search this array and locate the peak data of a particular spectra being analyzed. Calibration, qualification and quantification follow peak analysis. The first spectrum card encountered is that of the first calibration standard (Co-60 and Cs-137) and is used to calculate the linear fit of energy to channel number. This linear fit is used with the second calibration to yield a more refined fit of energy to channel number. The calibration of the first standard as well as the other major sections of the program produce output. For the sake of organization, this copious output is stored in an output buffer zone. This allows selected printing and consolidation of output according to spectrum regardless of which subroutine or in which chronological order the output was produced. This method creates a more readable and logical output. As previously mentioned the value and sign of the associated spectrum data determines in which way the following spectra will be analyzed. PIDAQ ceases analysis when a spectrum card with a tagword of zero is encountered. Print-out is then produced according to criteria determined by the user. Output can be restricted to only listing the results of qualification and quantification. Output, if chosen, can also include the unaltered 4096 channel spectrum and the results of peak analysis. The more comprehensive output keeps the human element involved. All times and data are readily available in the output for a check by hand calculations. RESULTS

PIDAQ has proven to be a dependable program, analyzing thousands of spectra over the last three years.

Many of these analyses were for previously mentioned publications, however many more unpublished and routine analyses have been completed. This program has saved hundreds of man hours which would have been necessary to qualify and quantify spectra by hand. In addition PIDAQ’s comprehensive listing eliminates the blind-faith which some programs demand when they merely print the desired answer. The listing allows one not only to see that the program has functioned properly but with a cursory glance one usually can determine if the analyser was operating correctly. PIDAQ after the initial de-bugging stage has always agreed with the many hand-calculated checks performed. A computer code such as PIDAQ is an asset to any analytical program which relies upon N.A.A. or I.N.A.A. Acknowledgement-This research was supported by the National Science Foundation, Office for the International Decade of Ocean Exploration, under NSF-IDOE Grant GX-33777. The authors wish to express their appreciation to the staff of the University of Rhode Island Computer Center for their assistance. REFERENCES

Anders, 0. U. (1%9), Anal. Chem. 41, 428.

Baedecker, P. A. (1971), Anal. Chem. 43,405. Bevington, P. R. (1969), in Data Reduction and Error Analysis for the Physical Sciences, p. 134. McGraw-Hill. Biloen, P., Dorrepaal, J. & van der Heijde, H. B. (1973), Anal. Chem. 45.288. Black, W. w. (1969), Nucl. Instr. Methods, 71, 125. Buono. J. A.. Karin, R. W. & Fasching, J. L. (1975), Anal. Chem. Acta. 80. 327. Covell, D. h. (1959), Anal. Chem. 31, 1785. Dams, R., Robbins, J. A., Rahn, K. A. & Winchester, J. W. (l%), Anal. Chem. 42, 861. Duce, R. A., Hoffman, G. L., Ray, B. J., Flecher, I. S., Wallace, G. T., Fasching, J. L., Piotrowicz, S. R., Walsh, P. R., Hoffman, E. J., Miller, J. M. & Heffter, J. L. (1976), in Marine Pollutant Transfer, Windom, H. and Dnce, R A., Eds., Heath, Lexington, MA; Gordns, A. A. (1%7), Anal. Chem. 39, 1672. Hoffman, G. L., Walsh, P. R. & Doyle, M. P. (1974)Anal. Chem. 46,492. IouYe, T., Harper, T. & Rasmussen, N. C. (1969), Nucl. In&r. Methods, 61, 125. Karin, R. W., Buono, J. B. & Fasching, J. L. (1975), Awl. Chem. 41.22%. Lis, S. A., Hopke, P. K. & Fasching, J. L. (197Sa), L Radionnnl. Chem. 24, 125. Lis, S. A., Hopke, P. K. & Fasching, J. L. (197Sb), J. Radioanal, Chem. 25,303. Luedtke, N., Hammock, J. P. $ Fasching, J. L. (1976). Private Communication. Luedtke, N., Hammock, J. P. & Fasching, J. L. (1976), Private Piotrowicz, S. R., Fasching, 1. L., Zdankiewicz, R. W. (1975), Anal. Chem. 41, 2326. Salbu, B., Steinnes, E. & Pappas, A. C. (1975), 1011. Tunnicliff, D. D., Bowers, R. C. & Wyld, C. E. Chem. 42, 1048. Zdankeiwicz, D. D. & Fasching, J. L. (1976), 1361.

D. D. & Karin, Annl Chem. 4’7, A. (1970), Anal. Clin. Chem. 22,