Mass dependent multiple scattering

[A.R.]

What is the dependence between multiple scattering (Moliére formula) and the mass of incident particles?
I'm reading on my book:

"the effect of multiple scattering is generally small for heavy charged particles"

but I really can't find a correlation with mass in the Molière formula, while the Rutherford cross section for single scattering seems to INCREASE with mass, for particles with same momentum:

so it's proportional to (m/p²)².

I haven't found neather a plot of Moliére probability distribution for different particles.
Can you explain me why the text says so? In formulae and/or by logic.

Thank you.

EDIT: (m/p²)² instead of (m/p)².

 

[mfb]

Same momentum but more mass means a slower particle. Slower particles get scattered more, both for single scattering events and for multiple scattering.

 

[A.R.]

Which is exactly the opposite of what the book says and the same thing I was pointing out. This doesn't answer my question.
The effect of scattering may be smaller for heavier particles with the same VELOCITY of lighter ones, but velocty isn't usually a term for comparison. The context from which the quote has been taken comprehend the simple definition of particle range, that ignores the effects of multiple scattering along the path. Thus, real range is actually smaller than that extrapolated from the simple definition, although "the effect of multiple scattering is generally small for heavy charged particles". How do you explain this sentence in its context?

 

[mfb]

Can you quote the context of that statement?
Heavy particles at the same speed get scattered less. What is wrong with using speed (or gamma factor)?

 

[A.R.]

The context, as I said, defines the concept of particle range. Quote:
"Experimentally, the range can be determined by passing a beam of particles at the desired energy through different thicknesses of the material in question and measuring the ratio of transmitted to incident particles.".
The typical curve Transmission vs Adsorber thickness follows, along with the definitions of Mean and Extrapolated range and Straggling. It continues:
"From a theoretical point of view, we might be tempted to calculate the mean range of a particle of a given energy, T₀ , by integrating the dE/dx formula,
$S(T_0)=\int_0^{T_0}(\frac{dE}{dx})^{-1}dE$
This yelds the approximate pathlength travelled. The equation above ignores the effect of multiple Coulomb scattering, however, which causes the particle to follow a zigzag path through the absorber. Thus, the range, defined as the straight-line thickness, will generally be smaller than the total zigzag pathlength.
As it turns out, however, the effect of multiple scattering is generally small for heavy charged particles, so that the total path length is, in fact, a relatively good approximation to the straight-line range.".
Bold by me. The text seems to compare heavy particles with light particles with same ENERGY, not SPEED.

 

[mfb]

Hmm... I guess that is a general statement for hadrons.

It is different for electrons because those make showers at higher energies or have significant scattering at lower energies. Either way, you cannot neglect those effects for electrons.

 

[A.R.]

How being a lepton/meson/hadron influence the effect of Moliére multiple scattering? It doesn't include strong interactions. As I pointed out, single scattering cross section goes with (m/p²)², so it just depends on mass (for particles "of a given energy")...but in the opposite way in respect to what the text says.

 

[mfb]

Bremsstrahlung for example is not part of the multiple scattering you consider here, but it is relevant for electrons.

but in the opposite way in respect to what the text says.

I don't think the text was supposed to mean what you are interpreting here.

 

[A.R.]

I don't get what the text supposes to mean then. Where it states "generally", i see "with the same speed", which isn't so general. Is there something basic I'm missing?

 

[mfb]

"generally" = "unless you have very unusual conditions"
And it is "the effect of multiple scattering is generally small for [heavy charged particles]", not "the effect of multiple scattering is generally small for heavy charged particles".