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

[Fecher, Gerhard]

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