[Wien] why we need to divide plasma frequency by root(2)?

[Dr. K. C. Bhamu]

Thank you Prof. Gerhard for taking concern over the issue!

I really do not know whats happening inside the code about the concept of
sqrt(2).





But I tried all possible combinations. With sqrt(2), without sqrt(2). With
TETRA 101 or 0.000.

The w_pl is same for up and dn spin.

In one test I saw in case.outputjointup/dn

   !!! WARNING: w_pl = sqrt( w_pl^2(up-spin) + w_pl^2(dn-spin) )!!!


Regards

Bhamu





The optics programm tells about the SP Plasma frequencies:
> w_pl = sqrt( w_pl^2(up-spin) + w_pl^2(dn-spin) )
>




>
> where does this come from
> remember the classical approach where the plasma frequency is proportional
> to root(n) with n being the density of free electrons (number of electrons
> per Volume)
>





> now what do you have in the SP case ? Shouldn't that be root/n_up+n_dn) ?
> The programm however delivers  w_up proportional to root(n_up) and w_dn
> prop to root(n_dn) and you see where the above equation is comming from
>
> Finally show what happens when the two densities are equal  n_up=n_dn and
> you see where the root(2) is coming from and when to use it
>
> (Note that the root(2) is here not because of surface plasmons)
>
> Ciao
> Gerhard
>
> DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
> "I think the problem, to be quite honest with you,
> is that you have never actually known what the question is."
>
> ====================================
> Dr. Gerhard H. Fecher
> Institut of Inorganic and Analytical Chemistry
> Johannes Gutenberg - University
> 55099 Mainz
> and
> Max Planck Institute for Chemical Physics of Solids
> 01187 Dresden
> ________________________________________
> Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von Gavin
> Abo [gsabo at crimson.ua.edu]
> Gesendet: Sonntag, 22. Oktober 2017 00:42
> An: wien at zeus.theochem.tuwien.ac.at
> Betreff: Re: [Wien] why we need to divide plasma frequency by root(2)?
>
> I could be wrong, but I think you just need to take the sqrt(2) of each
> plasma frequency:
>
> 2.074/sqrt(2) 2.074/sqrt(2) 1.264/sqrt(2)
>
> then put them in case.inkram (not case.injoint).
>
> You should be able to use multiple plasma frequencies in case.inkram but
> don't forget to add a Gamma for drude value for each of the plasma
> frequencies [ https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.
> at/msg14495.html ].
>
> On 10/21/2017 4:29 PM, Dr. K. C. Bhamu wrote:
>
> ---------------------case.injoint
> xx
> xx
> 1                                              >> correction
> 2.0740      2.0740      1.2640
> xx
> -----------------------------------
>
> were xx means no change in lines of case.inkram.
>
>
>
> At page numer  164 under section "8.11 KRAM (Kramers-Kronig
> transformation) in UG"
>
>
> "For a metal, the Plasma-frequencies (intraband transitions) for up and dn
> should be added, but then divided by√2, before using x kram."
>
> Does it mean that we need to add all three components and then divide by
> root(2) and put a single number [(2.074+2.074+1.264)/root(2)=3.88]
> instead of all three in case.injoint?
>
>
> kind regards
>
> Bhamu
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