The backscattering of electrons obviously happens with the core of the atoms or ions. If it is related to the mass I would expect an impact of protons and neutrons. If it is an impact of the charge (quite unlikely since plus and minus should attract each other) it should be proportional to the the protons only (i.e. Z, the atomic or periodic number). Nevertheless, it is not a single event since we have a practically unlimited number of interactions which should be related to the number of atoms (cores). This would bring the packing or mass density (or in first approximation the materials density) into the business. This from my present point of view very logical conclusion is in strict contradiction to experimental observations: comparing lead (density around 10g/cm³) and gold (density around 20g/cm³ ), lead has a higher backscatter coefficient. Does anybody have an idea, why the backscatter coefficient scales with Z and not with the density...or something else like a proton-density since the mass density also considers the neutrons?
If we talk about the tabulated backscattering coefficient of the element, it cannot contain contribution from the packing, otherwise we would have to have a special coefficient for each compound that contains this element. For example, density of the gold-containing compounds can range from 3 to 20 g/cm3. It is much more convenient to separate the contributions from the element and packing, providing the former in the database and calculating the latter every time from the known structure.
As for the driving force, it is Z. But the electron does not have to hit the nucleus directly. The classical analogy is movement of the long-period or non-periodic comets in the Solar system: the purely attractive gravitational interaction forces them to turn around the Sun and leave the inner part of the system with high 'scattering angle'.
Every event of back scattering occurs when an electron meets an atomic nucleus.That and only that is important. Probability of scattering from a nucleus is a function of atomic number. Dense material may have more nuclei per per square inch/mm/light year but every back scatter event occurs only for one electron and one nucleus. Density is not important.
@Vladimir: How do you explain the numerous deviations of materials which do not really match the prediction using Z? Or do you think the results come from incorrect measurements? How do you explain that there are (at least from my point of view) only non-physical decriptions available using polynoms or some logarithmic functions with "strange" parameters... What is the driving force? The mass of the core (Isn't Z_1/Z_2 proportional to m_1/m_2?)? Or only Z? How much I can "dilute" a material (increase the distance between adjacent atoms and why then other atoms in between make a different)? What is the difference to a solid solution keeping the packing density, e.g. add a bit Sn in Pb compared to the former example of Au? The probability to "hit" a core is quite small if we consider dimension of it in comparison to the distance between adjacent atoms...
I knew of course your above argumentation but I do not understand it... Therefore my question...
If we talk about the tabulated backscattering coefficient of the element, it cannot contain contribution from the packing, otherwise we would have to have a special coefficient for each compound that contains this element. For example, density of the gold-containing compounds can range from 3 to 20 g/cm3. It is much more convenient to separate the contributions from the element and packing, providing the former in the database and calculating the latter every time from the known structure.
As for the driving force, it is Z. But the electron does not have to hit the nucleus directly. The classical analogy is movement of the long-period or non-periodic comets in the Solar system: the purely attractive gravitational interaction forces them to turn around the Sun and leave the inner part of the system with high 'scattering angle'.
Hi Alexander, exactly...therefore my assumption that it considers both, neutrons AND protons. Regarding the packing...it is clear that you need to consider the mean Z which takes all other chemical constituents into account. I never checked graphite and diamond whether graphite really shows the same amunt of BSE like diamond.
see e.g.
http://www.minsocam.org/ammin/AM66/AM66_362.pdf
or slide 14 in
https://indico.cta-observatory.org/event/487/contributions/7849/attachments/6746/7622/PDE_of_PMTs-c_Lorenz.pdf
Single event of back scattering is a very simple physical phenomena, depends only on nucleus charge (i.e. Z), sophomore students can be given an assignment to calculate it. Concurring events, that are not Z dependent, are somewhat more complicated, but I was physicist-sophomore too many years ago to remember anything about their computations. But as I remember these things only "smear" backscatter coefficient and do not change the main tendency.
Makes me wonder if some analytical technique could be possible to analyze compounds by comparing their real backscatter coefficients with theoretical ones, like peak widening analysis in XRD.
Its a nice observation that, why Z? and why not density?
I would say that in the planet-asteroid analogy if any asteroid passes close to planet, due to gravity field of planet, asteroid can have some change in the travelling path. Similar thing happens at the atomic level (but due to opposite charge and not by gravity).
higher is the atomic no. bigger and stronger is the field around the nucleus (for Pb it suits well). For Au higher density suggest that more no. of nucleus (with slightly weaker field) are available in a given volume compared to Pb. But in contrast to planetary system where lots of free space (almost zero gravity) is present. In atomic structure, there are no space exist where the electron not feel the opposite charge of attraction from nucleus, thus increasing the no. density of the nucleus is not affecting the BSE to that extent that it can beat at. no. effect.
But I feel that (although not checked the literature) the higher no. of nucleus in Au would definitely affect something to some extent. May be the profiles (backscatter coefficient vs. tilt angle) for Au and Pb can have some difference because of density.
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