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Nuclear structure

A = mass number, #nucleons

Z = #protons

A-Z = #neutrons

Characteristic photon energy (higher j shell to lower i shell)

Eij = Ej - Ei

Ejected Auger electon energy

Eijk = (Ei - Ej) - Ek

(Ejected electron from higher k shell as a result of a transition from the higher j shell to the lower i shell)

Half life

t1/2 = ln2/λ = 0.693/λ

A(t) = A0e-λt

A(t) = A0e-((0.693 x given time)/half-life)

 A0 = A(t)e((0.693 x given time)/half-life)

Effective half-life

Effective half-life denotes the halving of radioactive material in a living organism by means of radioactive decay and biological excretion.

{\lambda_e} \, = {\lambda_p} \, + {\lambda_b} \,

 t_{1/2} = \frac{\ln (2)}{\lambda_e}

 t_{e} = \frac{t_{p}\times t_{b}} {t_{p} + t_{b}}.

Mean/average life

tavg = 1.44t1/2

Total dose = (initial dose rate)(time)(1.44)

Specific activity


NA= avogadro's number

AW= atomic weight

λ = disintegration rate

Time required to reach a certain activity


Brachy exposure rate calc


Γ= gamma constant (R·cm2/mg·hr)

A= radionuclide activity

d= distance from source

mgRaEq --> mCi

mgRaEq = (Γradionuclide/ Γradium)(# mCi of radionuclide)

 # mCi of radionuclide = (Γradium/ Γradionuclide)(mgRaEq)

Brachy PDD

PDD = Dose at distance d from surface of cylinder/dose a surface of cylinder.

Inverse square

I2/I1 = (r1/r2)2

Inverse square factor

ISF = [(SSDcal+dmax)/(SSDtreat+dmax)]2

Mayneord F-factor

Standard table of PDD are usually generated at the calibration SSD.  It is sometimes necessary to increase the SSD in order to treat a large field.  Since PDD is dependent on SSD, thistable of PDD will not be correct for the new SSD.  The Mayneord F-factor five the PDD at the new SSD.


Mayneords F overestimates PDD at large SSD's.

PDD at different SSD's



Equivalent square




TMR (Tissue maximum ratio)



Electron cutout thickness to reduce dose to 5%

For lead = electron energy/2mm

For cerrobend=1.2(lead thickness)

Gap Calc (S)

S=S1+S2=(d/2)(L1/SSD1 + L2/SSD2)


d= depth of junction

L= field length

If technique is SAD, this can be substituted for SSD.

CSI collimator angle

Θcoll = arctan(L1/2·SSD)

L1= legnth of posterior spine field

SSD is for the posterior spine field

CSI couch kick angle

Θcouch = arctan(L2/2·SAD)

L2= legnth of lateral cranial field

SAD is for the cranial field.

Hinge Angle

Wedge Angle



 WA = (180 - HA)/2

Half-value layer


 μ: linear attenuation coefficient

Tenth value layer


Electron range, 90%, and 80% isodose




TBI distance calc

(desired field size/standard field size)SAD=treatment distance to obtain desired field size

Factors for TMR MU calc


CAL: Calibration factor

TMR: Tissue maximum ratio (dose at depth d/dose at d max)

TSF: Tissue scatter factor

OAF: Off axis factor

WF: wedge factor

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