A LAPLACE TRANSFORM PAIR MODEL TO DETERMINE BREMSSTRAHLUNG SPECTRA FROM ATTENUATION DATA (RADIATION, X-RAY, SPECTRAL MODELING)

Every x-ray attenuation curve inherently contains all the information necessary to extract the complete energy spectrum of a beam. To date, attempts to obtain accurate spectral information from attenuation data have been inadequate.^ This investigation presents a mathematical pair model, grounded in physical reality by the Laplace Transformation, to describe the attenuation of a photon beam and the corresponding bremsstrahlung spectral distribution. In addition the Laplace model has been mathematically extended to include characteristic radiation in a physically meaningful way. A method to determine the fraction of characteristic radiation in any diagnostic x-ray beam was introduced for use with the extended model.^ This work has examined the reconstructive capability of the Laplace pair model for a photon beam range of from 50 kVp to 25 MV, using both theoretical and experimental methods.^ In the diagnostic region, excellent agreement between a wide variety of experimental spectra and those reconstructed with the Laplace model was obtained when the atomic composition of the attenuators was accurately known. The model successfully reproduced a 2 MV spectrum but demonstrated difficulty in accurately reconstructing orthovoltage and 6 MV spectra. The 25 MV spectrum was successfully reconstructed although poor agreement with the spectrum obtained by Levy was found.^ The analysis of errors, performed with diagnostic energy data, demonstrated the relative insensitivity of the model to typical experimental errors and confirmed that the model can be successfully used to theoretically derive accurate spectral information from experimental attenuation data. ^

Measurement of isotopic uranium in water for compliance monitoring by liquid scintillation counting with alpha/beta discrimination

A simple and inexpensive method is described for analysis of uranium (U) activity and mass in water by liquid scintillation counting using $\alpha$/$\beta$ discrimination. This method appears to offer a solution to the need for an inexpensive protocol for monitoring U activity and mass simultaneously and an alternative to the potential inaccuracy involved when depending on the mass-to-activity conversion factor or activity screen.^ U is extracted virtually quantitatively into 20 ml extractive scintillator from a 1-$\ell$ aliquot of water acidified to less than pH 2. After phase separation, the sample is counted for a 20-minute screening count with a minimum detection level of 0.27 pCi $\ell\sp{-1}$. $\alpha$-particle emissions from the extracted U are counted with close to 100% efficiency with a Beckman LS6000 LL liquid scintillation counter equipped with pulse-shape discrimination electronics. Samples with activities higher than 10 pCi $\ell\sp-1$ are recounted for 500-1000 minutes for isotopic analysis. Isotopic analysis uses events that are automatically stored in spectral files and transferred to a computer during assay. The data can be transferred to a commercially available spreadsheet and retrieved for examination or data manipulation. Values for three readily observable spectral features can be rapidly identified by data examination and substituted into a simple formula to obtain $\sp{234}$U/$\sp{238}$U ratio for most samples. U mass is calculated by substituting the isotopic ratio value into a simple equation.^ The utility of this method for the proposed compliance monitoring of U in public drinking water supplies was field tested with a survey of drinking water from Texas supplies that had previously been known to contain elevated levels of gross $\alpha$ activity. U concentrations in 32 samples from 27 drinking water supplies ranged from 0.26 to 65.5 pCi $\ell\sp{-1}$, with seven samples exceeding the proposed Maximum Contaminant Level of 20 $\mu$g $\ell\sp{-1}$. Four exceeded the proposed activity screening level of 30 pCi $\ell\sp{-1}$. Isotopic ratios ranged from 0.87 to 41.8, while one sample contained $\sp{234}$U activity of 34.6 pCi $\ell\sp{-1}$ in the complete absence of its parent, $\sp{238}$U. U mass in the samples with elevated activity ranged from 0.0 to 103 $\mu$g $\ell\sp{-1}$. A limited test of screening surface and groundwaters for contamination by U from waste sites and natural processes was also successful. ^