Answer to Question #1540 Submitted to "Ask the Experts"

Q

Are there any reliable algorithms for calculating (or approximating) shielding requirements from large amounts (5+ Ci) of high-energy beta-emitting sources—in particular one that takes into account beta dose rates and bremsstrahlung dose rates? A reference in the literature would also be very useful.

A

Your question concerns the availability of algorithms for evaluating dose rates from curie quantities of shielded, high-energy beta emitters, and you express interest in both the beta dose rates and bremsstrahlung dose rates. Since you are apparently employed by a company that produces radioactive sources, and considering the technical nature of your question, I am assuming that you have a technical background. While there are limited approaches to estimating the beta and bremsstrahlung dose rates of interest using convenient and reasonably simple algorithms, there are some approaches that are applicable and acceptable, but often with restrictions. I will exclude probabilistic computer codes, Monte Carlo codes in particular, from most of this discussion. While such codes are powerful and desirable for doing the kinds of estimations that you may be interested in, they are not easy to use without experience and require a considerable investment of time and, in some instances, money to achieve success with them. Having said that, however, they do provide the best solutions to the kinds of problems you describe, and if you are into computer techniques you might want to pursue these. (Among the more popular codes for these kinds of problems are the EGS4 code and the MCNP code, modified to handle electrons and bremsstrahlung. These are available through RSICC, noted below.) There is a deterministic code called VARSKIN Mod 2, commonly used by health physicists for routine beta skin-dose calculations for skin contamination, that is easy to use for some limited cases. It is restricted to source geometries that may be approximated as point sources, circular discs, or cylinders. There is also a rectangular slab source geometry option, but it is not reliable for many calculations. The code calculates beta dose (rates) to live skin and allows the user to input the source characteristics and thickness and density of any attenuating material and an air gap if such exist. For the disc and cylindrical sources, doses are calculated below the circular face of the source. The code package, called Varskin 2, includes VARSKIN Mod 2 and SADDE Mod 2. The latter code allows the user to input pertinent information for beta-emitting radionuclides that are not in the VARSKIN library. The code does not calculate bremsstrahlung dose (rates). The code was written by J.S. Durham at Pacific Northwest Laboratories. It is highly likely that a health physicist at your own company has a copy of the code. It can also be obtained from the Radiation Safety Information Computation Center (RSICC). Since the code was written for different applications from what you likely have in mind, it may not be sufficiently flexible for your purposes, although you may find it useful for some estimations. The few mathematical expressions that have been generated to estimate dose rates from beta sources in attenuating media are point source dose distribution functions. One of these is a semiempirical expression developed some time ago by R. Loevinger ("The Dosimetry of Beta Sources in Tissue. The point source function"; Radiology, Vol. 66, p.55, 1956). This function is intended for estimating beta doses from sources surrounded by soft-tissue type material or by air. Another point source function is that described by G. Chabot, et al. ("When Hot Particles are not on the Skin," Radiation Protection Management, Vol. 5, No. 6, 1988). The latter paper describes a technique for converting different attenuating material thicknesses to water-equivalent thicknesses to estimate doses from point isotropic sources as beta particles are transmitted through different media. The point source functions can be extended to other regular source geometries through appropriate integration over the source volume. This has been described in another paper by Chabot, et al. ("A Technique to Correct for Self Absorption in Beta Radiation Sources and for Attenuation in Other Media," Radiation Protection Management, 9(4), pp. 50-62, 1992). I am not including the actual point source functions here, since a reasonable explanation of what the various parameters represent and how they are evaluated would be too time consuming. The bremsstrahlung situation is worse yet. To my knowledge, there are no single equations that are available to estimate bremsstrahlung dose rates from attenuated beta sources, although there is a lot of literature related to bremsstrahlung radiation and its production. The problem is made complex by the facts that any beta-emitting nuclide emits a whole spectrum of beta particles with energies ranging from zero to the maximum beta energy, and each beta particle is capable of generating bremsstrahlung radiations that range in energy from zero to the individual beta particle energy. Some useful discussion and mathematical descriptions of bremsstrahlung production from beta sources can be obtained from some fairly common reference text books (for example, R.D. Evans, The Atomic Nucleus, pp. 617-621, Krieger Publishing Co., 1955, Malabar, Florida, reprinted 1982; J.K. Shultis and R.E. Faw, Radiation Shielding, pp.108-111, Prentice Hall PTR, 1996, Upper Saddle River, NJ). At the 45th annual meeting of the Health Physics Society, G. Chabot presented a paper by Chabot and Roldan in which he described a method to determine the bremsstrahlung energy distribution when beta radiation was stopped in a thick attenuator ("Algebraic Expressions for the Bremsstrahlung Energy Distributions from Beta Radiation Incident on Thick Targets"). The method folded together a polynomial representation of the beta energy distribution and a mathematical expression for the bremsstrahlung energy distribution from monoenergetic electrons and, through appropriate integrations, algebraic solutions were obtained for the differential bremsstrahlung energy distribution and for the bremsstrahlung energy emitted in a finite energy interval. The formulations obtained are for allowed beta transitions, although they are acceptable for first forbidden, nonunique transitions and probably reasonable estimators for unique first forbidden transitions (although nonconservative). The results are useful for dose and shielding calculations; by defining reasonably narrow energy intervals and defining the effective energy for each interval as the midpoint energy, one can apply conventional photon shielding calculations to evaluate doses through fixed thicknesses of attenuators. Calculations can be done by hand or using a deterministic code, such as Microshield (Grove Engineering, 3416 Olandwood Court, Suite 211, Olney, MD 20832; phone: 301-929-3028). Again, the formulations described by Chabot and Roldan are rather lengthy and would require more space and time than would be appropriate here. I am sorry that I do not have a simpler and more direct answer to your question. I hope some of the references I have noted will be helpful to you. Please contact the HPS Web site Editor if you wish to contact me for additional materials. George Chabot, PhD, CHP