( ) thick ( ) Input: Pb or Concrete Shielding with Build-up factor B: 4 ) Distance (cm) and photon flux. 1 4 π d 2.

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Lee Gardner
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1 Dose calculator for photons Uses μ/ρ abs, Include Pb or Concrete shielding with Buid-up. Setup for gammas Data from NIST, for water, bone and Pb. Shielding is also set up for upto gammas. This is special for 6 Co Ebone= EH ) (μ/ρ) a for Water, Bone, and (μ/ρ) for Pb. bone water EPb PbS Data From NIST to interpolate MeV cm /g cm /g cm /g cm /g μu := Econc μconc μconc := ( μconc ) = cm /g ) Source strength in Ci Ci := 3.7 Input decays per second A := Dps := A Ci Dps = ) Number of photons per decay Input N g := energies (MeV) fractions ev.677 ergs/ev e g :=.. n <= Could expand to more gammas g := with their fractions..

2 ) Distance (cm) and photon flux Solid angle Input cm d := 5 dω := π d dω = ) Input: Pb or Concrete Shielding with Build-up factor B: Shielding cm abs cm := 5 abs := <= abs = for Pb, abs= for concrete, abs > for Pb with no buildup B= if abs ( abs cm.) otherwise thick := abs cm.35 thick = cm /g Bx := 3. if x 7.7 <= The build-up factor is from 6 Co data from Evans (old numbers) +.77 x otherwise Not Used in this template. B( abs cm ) =.3635 μ ρ ( x) linterp μu 3 μu := if abs ( μconc ) otherwise linterp μconc The following build-up factors are interpolated from the tables in the book by Bevelacqua. μx := thick thick thick thick μ ρ e g μ ρ e g μ ρ e g μ ρ e g3 μ ρ =.97 Bxx( x, y) := if abs > cm /g Bxx e g, μx (.66 ) Bpb( x, y) if abs = B con ( xy, ) otherwise =.93 = Bxx e g, μx

3 Intensity reduction from shielding n γ := n g Bxx e g, μx e μx n g Bxx e g, μx e μx n g Bxx e g, μx e μx n g3 Bxx e g3, μx 3 e μx 3 Bxx(.66, xx) Bxx(.33, xx) Bxx(., xx) xx Mean free paths <= Build-upFactors for different E γ. n γ = γ ps :=.6.8 n g R := R n γ Gammas/sec after shielding n γ Dps γ ps = = n γ R := R n = g Gamma flux after shielding ( #/cm s ) γflux := γ ps dω γflux = ) Dose for Water: Use NIST (μ/ρ) a values. Mass energy absoption coefs μρ water ( x) linterp μu μu :=

4 μρ water e ( g =.38 μρ ) water e ( g =.9 ) Energy in ev Absorbed by g/cm of water per hour N g de ev := ii = 6) rads/hr and rems/hr QF := de erg := de ev ( ev) μρ water e g e = μρ water e gii e g γflux ii e ii de erg = 36.6 de erg de erg rads hr := rems hr := QF de ev =.87 3 d = 5 abs cm = 5 abs = rads hr = 3.66 rems hr = 3.66 For Water ) Dose for Bone, use NIST (μ/ρ) a values. μρ bone ( x) linterp μu μu := μρ bone e g =.785 N g DE ev 36 6 μρ bone e gii := e g γflux ii e DE ii ev =. 3 ii = DE erg := DE ev ( ev) DE erg = ev =.6 DE erg DE erg rad hr := rem hr := QF rad hr = rem hr = For Bone ==============================================================================

5 Input: Data from NIST (g/cm ) (μ/ρ) a for HO, Bone, but (μ/ρ) for Concrete, Pb μu μu μu μconc 3 Absorption for Water Absorption for Bone Total Scattering for Lead Total Scattering for Concrete μu, μu, μu 3, μconc MeV

6 .56 linterp μu μu linterp μu μu linterp μu μu x :=. = linterp μu μu =.886 =.585 = 5.59 linterp μu 3 μu =.738 linterp μconc μconc ) INTERPOLATE THE Buid-up Factors for Pb for Energies ( - 6. MeV) and Mean Free paths (-) Egam.5... μx μx μx μx μx μx μx.8 5 μx

7 B ( k) linterp Egam, μx, k B ( k) linterp Egam, μx, k B 5 ( k) linterp Egam, μx 5, k B ( k) linterp Egam, μx, k B 7 ( k) linterp Egam, μx 7, k B ( k) linterp Egam, μx, k B ( k) linterp Egam, μx, k B ( k) linterp Egam, μx, k μxx 7 5 B x ( k) B ( k) B ( k) B ( k) B ( k) B 7 ( k) B ( k) B 5 ( k) B ( k) Bpb( k, xx) linterp μxx, B x ( k), xx e g =.73 Bpb(, ) = 5.3 = Bpb e g, B ( k) B 5 ( k) B ( k) B 7 ( k) B ( k) B ( k) B ( k) Bpb( k, 7) k MeV

8 9) SHIELDING and BUILD-UP for CONCRETE, the function calls are: μ c (E γ ) = Tot. scattering mass attenuation, and the buid-up:b con (E γ,μx). E conc x c b ( l) linterp E conc, x c, l b 7 ( l) linterp E conc, x c7, l x c b = b 7 =.7 x c Ex E conc x c x c b ( k) linterp E conc, x c, k b = 8.7 b 5 ( k) linterp Ex, x c5, k b ( kk) linterp Ex, x c, kk b 5 = 33. b = 5.6 μx c 7 5 b x ( lk) b ( lk) b 7 ( lk) b ( lk) b 5 ( lk) b ( lk)

9 B con ( kk, z) linterp μx c, b x ( kk), z μ c ( x) linterp μconc μconc := μ c =.78 B con (.5, xx) B con (., xx) B con (.5, xx) B con (, xx) xx Mean free paths

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