monte carlo bse coefficient

[Probeman]

It's interesting that nuclear screening has come up with regards to BSE coefficient.

I wonder whether it would be possible to see atomic screening 'artifacts', such as the poor screening by 4f electrons (cause of the 'lanthanide contraction') or the 'd-block' contraction, and if this difference would be discernible with our BSE detectors. Could be an interesting experiment!

Hi Jon,
I think you might be on to something here!

I ran your idea by a couple of physicists at UofO as to whether one might be able to detect subtle variations in the effective nuclear screening for transition series elements in the electron backscatter signal, and they said that it was "plausible".  In fact this might be the solution to the famous (infamous?) "Heinrich kink" dilemma, from his 1968 paper, which we know from physical considerations cannot be due to mass effects.  Here is a plot of Heinrich's measurements and my own measurements:



So at the time (late 1990s) I knew that his measurements from the 60s were good, but I could not explain them. I was guessing something along the lines of subtle differences in electron backscatter diffraction (channeling) between these elements, but I wasn't very convinced by it.

Since I could reproduce Heinrich's measurements 30 years later using my SX100 at UC Berkeley, I know that his measurements were good, but just couldn't convincingly explain them.  But I think you just might have!

I am running some high precision Monte Carlo calculations now and will post these in about a week or so when they are finished. In the meantime please see the attached pdf from an old document I wrote up in the 90s which has more details about this.

This could very well deserve a short paper by us together!
john

[JonF]

'Plausible' from physicists is high praise indeed!

That kind of effect from the raw data is more what I was expecting - I was puzzled as to whether the effect would be noticeable having seen the monte carlo simulations showing up a smooth curve (although you mention this in your paper!)

This may well be opening Pandora's box, but I've been wondering if the shielding of the nucleus in pure elements can be observed, whether the effects of bonding would also be discernible in compounds...

[Probeman]

'Plausible' from physicists is high praise indeed!

That kind of effect from the raw data is more what I was expecting - I was puzzled as to whether the effect would be noticeable having seen the monte carlo simulations showing up a smooth curve (although you mention this in your paper!)

This may well be opening Pandora's box, but I've been wondering if the shielding of the nucleus in pure elements can be observed, whether the effects of bonding would also be discernible in compounds...

Maybe?  But only very high precision measurements can say.

The Heinrich "kink" measurements that was able to reproduce are in the one or two percent level, so these are difficult measurements.  I can't wait to see the Penepma Monte Carlo simulations.

The funny thing was that the 1975 NIST Monte Carlo code seemed to correlate with the A/Z curve as Heinrich tried to demonstrate, but I noticed that they used a "multiscattering" electron model where they did lots of averaging to obtain faster results (computers were sloooow in those days).  And guess what?  When I asked Bob Myklebust about it, he confirmed that they utilized mass fraction to calculate the effects.  Ha!

Of course the 1998 MQ NIST Monte Carlo *single* scattering model did not show any such mass effect.

The question now is: how accurately does Penepma model these nuclear screening effects for elastic scattering of electrons? I really should ask Xavier, but I'll let the calculations finish first.

I'm running 100,000 sec per element so I hope that's enough precision. I did remember to optimize for BSE production. It's only on the 3rd element as seen here:



I might plot up what I have on Monday though...

[Philippe Pinard]

Thank you John for the detailed explanation.

Would you still have the raw data (i.e. backscatter coefficients for different compounds) you used in the paper back in 2003? I wonder what Figure 2c would look like if the tabulated Mott or PENELOPE elastic cross sections were used instead Rutherford.

Philippe

[Probeman]

Thank you John for the detailed explanation.

Would you still have the raw data (i.e. backscatter coefficients for different compounds) you used in the paper back in 2003? I wonder what Figure 2c would look like if the tabulated Mott or PENELOPE elastic cross sections were used instead Rutherford.

Philippe

Hi Philippe,
I'm sure I have the data somewhere but I would have to search.

However Ben Buse plotted up some Penepma calculated BSEs here:

https://probesoftware.com/smf/index.php?topic=1111.msg7478#msg7478

The plot is a little confusing because he included some "original Z" values, so just ignore the violet colored symbols and you'll see that the remaining Z^0.8 symbols plot nicely on a line.

I should probably re-run all the compounds and pure elements I did back in 2003 again with Penepma just for fun.
john

[Probeman]

Many moons ago we published a paper (Donovan, Pingitore and Westphal, 2003) on electron backscattering and the effects on that by atomic mass vs. atomic number. 

The bottom line is that mass has essentially zero effect on backscatter loss, while the BSE effect is essentially solely related to the effective nuclear charge of the nucleus, therefore the effect is almost entirely due to electrostatics. This claim is something that physical scientists generally accept after a few minutes of thought, but some, at least at the time, seemed surprised by our results. 

After the paper was published, we had a response from Stephen Reed who suggested our "proposal should be treated with caution, pending more rigorous testing".  Of course we are all for caution and more rigorous testing, but we still stand by the claim today, and more recently we have repeated these measurements and calculations, and found them to be reproducible both empirically, and theoretically, based new measurements and on the latest Monte Carlo models, as seen above in this topic.

For those interested in the gory details, the full paper and the response by Reed and our response to Reed's response are attached to this post:

https://probesoftware.com/smf/index.php?topic=1111.msg7448#msg7448

However I had noticed soon after we had published our response to Reed back in 2003, that there is a small typo in our response that we should have caught at the time. The error is highlighted in yellow:



Can you see the math error?

Well, since the largest mass effect of an electron interacting with a hydrogen nucleus, in the case of a perfectly elastic collision (180 degrees backscatter) with a single proton, the energy loss is roughly 1/2000. And for higher mass atoms, the effect is much smaller!  OK, so you spotted the math error?  Yes, 1/2000 is not 0.2% as stated in our response, it is only 0.05%.  Doh!     

So, yes, the mass effect on electron backcattering is even smaller that we claimed!   

There will be more to say on this subject, but please feel free to make your own measurements and calculations and share them with us.

[Probeman]

Just to follow up on this BSE "brain teaser" which Ben Buse posted about a while ago, attached below is an abstract accepted for M&M 2019 showing some Penepma BSE simulations for pure elements and compounds and also some rough absorbed current measurements which we hope to do more of before M&M, but in the meantime it's worth a look I think.
john

[Probeman]

This is an interesting read:

https://en.wikipedia.org/wiki/Slater%27s_rules

It makes me wonder if using a Z fraction^0.7 weighted average atomic number, to compensate for nuclear screening by inner orbital electrons, could be further improved by considering whether the atoms in our beam incident materials are truly neutral atoms or not.

I mean we're knocking electrons off of them constantly, right?  Probably a 10-4 effect (for inner orbitals anyway), but maybe someone would be willing to do some calculations...

[Probeman]

Here is a pdf of my presentation given this week at M&M 2019, in case anyone who missed the talk is interested (please login to see attachments).