Linear Energy Transfer units and conversions

In engineering often times we are confronted with quantities measured in units far removed from the safety of the SI.

Linear Energy Transfer (LET) as defined by ECSS is the rate of energy deposited through ionisation from a slowing energetic particle with distance travelled in matter, the energy being imparted to the material.

What would that be in SI ?

Energy deposited in the track per unit pathlength:

$$ \frac{J}{m} = \frac{kg \cdot m^2 \cdot s^{−2}}{m} = kg \cdot m \cdot s^{−2} $$

That looks familiar, turns out it is simply Newtons.

In nuclear physics this quantity is referred to as the linear stopping power.

In dosimetry and radiation engineering LET is usually expressed in the units \(MeVcm^2/mg\). Why ?

Using MeV as an energy unit is natural, as the energies of ionising particles in the environment of space are expressed in MeV (more convenient than pico Joules for example). What about the other terms ?

Looking closely at the ECSS, section 8.2.2 of E-HB-10-12A shows the relationship between the linear stopping power and LET:

$$ LET(x) \approx \frac{1}{\rho} \frac{dE}{dx}(x) $$

That is to say that the LET as defined in ECSS is really the mass stopping power, which is the stopping power independent of material density. The actual energy deposited by an energetic particle depends on the material density, as higher density means more particle interactions. By dividing by the material density, we can obtain a quantity that is independent of the material of interest.

When performing simulations to prepare for a radiation test with tools like SRIM-2013, energy loss is frequently expressed in \(eV/ \mathring{A}\). By converting the linear stopping power to mass stopping power we can derive the LET, and the absorbed Total Ionising Dose for a given particle fluence.