Shielding Equations and Buildup Factors Explained

Transcription

1 Sheldng Equatons and uldup Factors Explaned Gamma Exposure Fluence Rate Equatons For an explanaton of the fluence rate equatons used n the unshelded and shelded calculatons, vst ths US Health Physcs Socety webpage: t s a very good whte paper by George Chabot, CHP, PHD that takes you from electrc charge produced n the ar by the photons to a usable equaton and also explans where the smplfed rule of thumb R/hr = 6CEN equaton comes from. Lnear ttenuaton Sheldng Formula: = * e μx Where: = the shelded dose rate = the ntal dose rate μ = the lnear attenuaton coeffcent n cm x = the sheld thckness n cm The lnear attenuaton coeffcent can be consdered as the fracton of photons that nteract wth the sheldng medum per centmeter of sheldng. Ths coeffcent assumes that all photons that nteract are removed and gnores Compton scatter and par producton photons (underestmates the shelded dose rate and the sheldng requred). t s also known as narrow beam condtons because the source and detector are assumed to be collmated and the measurement made at a short dstance. No photons are scattered. The only way to make ths happen s to sde and back sheld the source and the detector (collmate). Ths only apples at close dstances though. Further away, the ar scatters the photons n real lfe. Ths s dealstc and wthout the collmaton or at a longer dstance, the dose-rate s underestmated Source n shelded pg. End sheld plug removed (collmated source) Sheld Narrow eam Condtons Detector wth sde sheld collar Detector end only exposed (collmated detector) Lnear Energy bsorpton Sheldng Formula: = * e μenx

2 Where: = the shelded dose rate = the ntal dose rate μ en = the lnear energy absorpton attenuaton coeffcent n cm x = the sheld thckness n cm The lnear energy absorpton attenuaton coeffcent can be consdered the fracton of energy removed from the photons by the sheldng medum per centmeter of sheldng or the fracton of energy absorbed. Ths coeffcent takes nto account Compton scatter and par producton photons but t assumes that all scattered photons reach the detector (overestmates the shelded dose rate and the sheldng requred). t s also known as broad beam condtons because the source and detector are assumed to be uncollmated. Scattered electromagnetc energy ncluded (but all scattered photons are assumed to reach the detector) Ths s unrealstc and overestmates the shelded dose-rate. Unshelded source Unshelded detector Sheld road eam Condtons

3 FQ: What s a uldup Factor? Scattered electromagnetc energy ncluded (but only some of the scattered photons reach the detector) Unshelded source Unshelded detector Sheld Usng uldup (closer to real lfe) Many of the people who use my software are not radaton protecton or health physcs professonals. Some are students and some are engneers of other dscplnes who fnd themselves n a poston to occasonally perform sheldng equatons,.e. desgners of thckness gauges and other test equpment that utlze radoactve sources. was gettng ths queston so often, t prompted me to wrte ths paper. Snce usng the attenuaton coeffcent (method 1) underestmates the dose-rate on the other sde of the sheld and usng the energy absorpton coeffcent (method 2) overestmates t, a method of gettng closer to the real-world dose-rate was needed. buldup factor s a correcton factor to multply the number obtaned from usng the attenuaton coeffcent by that hopefully gves us the correct answer, a number n between method 1 and method 2 results. Some may call t a fudge factor. Through the years, teams of professonals worked together to come up wth tables of buldup factors for sheldng calculatons. Tables of many buldup factors are requred because the factor vares wth gamma energy, sheld materal and wth sheld thckness. The most recently accepted tables come from the mercan Nuclear Socety (NS) and the mercan Natonal Standards nsttute (NS), publshed n New work has been done on buldup factors snce then. n 1991, the numbers ndcate that at low energes the buldup factor s 1 or close to t. New studes and new calculatons ndcate that t s not so. paper publshed n 2001, Low and Hgh energy factors for selected materals updated wth Monte Carlo code factors : Chban, Omar, "New Photon Exposure uldup Factors", Nuclear Scence and Engneerng, Volume 137, 2001 has supplemental numbers to the NS/NS tables at low and hgh energes and explans the physcs and reasons behnd the new numbers. Work on new buldup factors has slowed n recent years, probably due to the release of new Monte Carlo based codes whch seem to be gvng a hgher level of accuracy than buldup factors. These codes are expensve and have a steep learnng curve so the 1991 tables, along wth the Omar Chban numbers are stll useful, especally when a hgh degree of accuracy s not requred. f one s desgnng a nuclear reactor dome, havng a hghly accurate number could

4 save hundreds of yards of concrete and tme to pour t. Monte Carlo code s a must then. f one has a small source to shp and needs to calculate a pg thckness, the dfference between 5 or 6 centmeters of lead may not matter. Lnear ttenuaton Sheldng Formula Wth uldup: = * b * e μx Where: = the shelded dose rate = the ntal dose rate b = the buldup factor for one energy at the sheld thckness x μ = the lnear attenuaton coeffcent n cm x = the sheld thckness n cm Ths formula attempts to estmate the correct number of scattered photons that reach the detector (closest estmate) by usng a correcton factor to add n the Compton scatter and par producton photons that are gnored by the lnear attenuaton coeffcent formula. Lnear ttenuaton Sheldng Formula Wth uldup for Multple Photon Energes: = μ1x μ2x μ3 *( b * f * e + b * f * e + b * f * e x... + b * f * e μ x ) Where: = the shelded dose rate = the ntal dose rate b = the buldup factor for each energy (up to the th energy) at the sheld thckness x μ = the lnear attenuaton coeffcent for each energy (up to the th energy) n cm e * n f = the fracton of that comes from each photon energy (e n MeV) = e * n n = the yeld or probablty of emsson factor for each atomc decay for each energy x = the sheld thckness n cm Ths formula attempts to estmate the correct number of scattered photons that reach the detector (closest estmate) for each energy by usng correcton factors to add n the Compton scatter and par producton photons that are gnored by the lnear attenuaton coeffcent formula. ttenuaton and energy absorpton coeffcents can be found on lne at: and

5 The numbers n the table are mass attenuaton coeffcents and the mass energy absorpton coeffcents or μ/ρ n cm 2 /g. These represent the fracton of photons removed and the energy removed respectvely per unt densty of materal. You have to multply the table factors by densty n g/cm 3 to get the lnear factor equvalents n cm. uldup factors are obtaned from tables avalable for a cost from the mercan Nuclear Socety. They are not avalable onlne anywhere that we could fnd. You have to calculate the number of relaxaton lengths, R or mean free paths (mfp) to use the table. μx = 1 relaxaton length or 1 mean free path (MFP) = ln( / ) Where μ s the lnear attenuaton coeffcent and x s the sheld thckness Your energy wll end up n between two numbers as wll your number of relaxaton lengths. You wll have to do a 4 way nterpolaton between the four values that you obtan from that table. For Co-60, you have two energes, so you wll have to do the four way nterpolaton twce, once for each energy. Each energy wll have ts own MFP value because each has ts own μ value. Wth sotopes that have multple energes (Ra-226 wth daughters has well over 26 energes) t gets complcated and the math by hand or even wth a spreadsheet would be ntense. That s why we developed computer code to do all of that work for you. On the last page s a typcal buldup factor table for tungsten. Ray McGnns, MT Rad Pro Calculator Software Development

6 Energy MeV R(mfp) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+46 1E E+47 2E+47 3E E E E E E E E+50 2E+47 2E+47 4E+47 4E+47 1E E E E E E+49 5E E E E E E E E E+54

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