The regions of incident electron energy
E0 and absorber atomic
number Z to which EMID is applicable are given below for each parameter. The
formulas and the algorithm of
EMID can also be used outside the energy regions given, possibly down to a half
of the lower limit and up to
twice the upper limit, if a moderate errors are tolerated.
- Dcp: charge deposition by primary electrons
- E0 = 0.5-24 MeV, Z = 4-92; accuracy not evaluated numerically
(Ref. 1; Ref. 8 for the extrapolated range).
- De: energy deposition
- E0 = 0.1-20 MeV, Z = 4-92; rms deviation = 0.7-2.5% (Ref. 10).
- Deb: Energy deposition via bremsstrahlung
- E0 = 0.1-100 MeV, Z = 4-92; rms deviation relative to the total
energy deposition < or = 2.0%
- Dec: energy deposition via collision
- E0 = 0.1-20 MeV, Z = 4-92; rms deviation is about 0.7-2.5% (Ref.
- hE: energy-reflection ratio of electrons
- E0 = 0.005-100 MeV, Z = 4-92; accuracy not evaluated numerically,
but agreement with ITS Monte Carlo results are satisfying when hpE
is larger than 0.005 (the formula for the number-reflection ratio in Ref. 4
multiplied by the formula for the fractional energy of reflected electrons
in Ref. 13).
- hpE: energy-reflection ratio of photons
- E0 = 0.1-100 MeV, Z = 4-92; rms deviation = 7.2% (Ref. 5).
- hN: number-reflection ratio of electrons
- E0 = 0.001-22 MeV, Z = 4-92; rms deviation = 5.6% (Ref. 4).
- k: number-transmission ratio
- - For normal incidence, E0 = 0.008-30 MeV, Z = 4-82; the average
of rms deviation = 3.4% with respect to experimental data published
(Ref. 2, the formula is also in Ref. 9).
- For non-normal incidence, E0 = 0.5-10 MeV, Z=13, angle of
incidence up to 75 deg; rms absolute deviation is about 0.03
(Ref. 3, the formula is also given in Ref. 12).
- r0: continuous slowing-down approximation range
- E0 = 0.1-100 MeV, Z = 4-92; rms deviation = 0.7%, maximum
deviation = 1.5% with respect to EPSTAR database (Ref. 8);
can be used down to 0.01 MeV with moderate accuracy.
- Rav: average reach
- E0 = 0.008-30 MeV, Z = 4-82; accuracy not evaluated numerically
- Rex: extrapolated range
- E0 = 0.1-100 MeV, Z = 4-92; rms deviation = 0.9%, maximum
deviation = 2.0% with respect to ITS Monte Carlo results (Ref. 8); can be used
down to 0.01 MeV with moderate accuracy.
- zav: average penetration depth
- E0 = 1-50 MeV, Z = 4-92; maximum deviation < or = 2.1% (Ref. 11
with the formula for r0in Ref. 8); for phantom materials used in
medical dosimetry, another formula with higher accuracy is also proposed
in Ref. 11.