[ RadSafe ] Gamma shielding puzzle (UNCLASSIFIED)

[Falo, Gerald A Dr CIV USA MEDCOM CHPPM]

Classification:  UNCLASSIFIED 
Caveats: NONE

Joel,

It's been a while since I've done something like this, but I'll try.

With some assumptions and with some good data, an iterative process
might work.

For a given material, transmission factor (Tg), and thickness:

(1) Guess a reasonable energy.
(2) Look up the attenuation coefficient. (Mass or linear depending on
your preference. You might need to use an absorption coefficient
depending on how the buildup factors are calculated.)
(3) Calculate (mu*t)
(4) Look up the appropriate buildup factor. (This depends on energy,
quantity under consideration (e.g., dose versus intensity), source
geometry, shield material, and detector geometry)
(5) Calculate a transmission factor (Tc).
(6) Compare Tc to Tg.
(7) Based on 6, return to step 1 and repeat until Tc is acceptably close
to Tg.

It's a bit tedious, and it can be hard to find good data.  Creating a
table with energy, mu, mu*t, B(mu*t), e^-(mu*t), and Tc as column
headings and then working the calculations across rows seems to be a
good way to do hand calculations.  Someone out there in RADSAFE smarter
than I could probably work this with a spreadsheet, MathCAD,
Mathematica, or the like.

Also, the value of the attenuation coefficients as function of energy
might not always be unique so some care must be used.  It seems to me
from a quick skim of mass attenuation coefficients that if you stay away
from very low (less than about 10 keV) and very high energies (greater
than about 10 MeV) depending on the quality of your data, this approach
could work.

If I've really messed up somewhere, let me know.

Good luck,
Jerry Falo

-----Original Message-----
From: radsafe-bounces at health.phys.iit.edu
[mailto:radsafe-bounces at health.phys.iit.edu] On Behalf Of Joel C.
Sent: Monday, March 15, 2010 4:57 PM
To: radsafe at health.phys.iit.edu
Subject: [ RadSafe ] Gamma shielding puzzle


Here's a puzzle;  impute the gamma ray energy if you know the
transmission factor thru (thick) concrete.  T = B exp(-mu x t) is the
simple equation, but B is a function of energy, so you cant just solve
for mu and go the mu vs. E curve.  Anybody confronted this one?
(Distance-- r squared --effects can be ignored.)

Joel I. Cehn, CHP 
joelc at alum.wpi.edu 
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Classification:  UNCLASSIFIED 
Caveats: NONE