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To calculate the susceptibility

Susceptibility is defined as:

Xq ' ' (w)=S(q,w)/(exp(hw/KBT)-1)-1

and Xq it is expected to factorize as: Xq(w)=hq*X(w) (see PRE 61 3 2730 (2000), Wuttke et al.), confer to Making a master curve

_sgto convert input y(x,z) to another representation
10option to calculate the susceptibility
msaTo group detectors to have less spectra with better statistics
zto group by z values, i.e. by detector angle in this case
10the tolerance: will group detectors every 10 degrees in 2*theta
yproceed using channel numbers. this is done because the points in different spectra are not at the same energy. this may cause problems. alternative: put the data on a common grid beforehand using mgr. however, be also aware of mgr, it sometimes does strange things.
??you must write the number of the file where you have the susceptibilty files
tuconvert axes. We use it to “translate” from meV to frequency
1more energy = higher frquency
Hznew unit of x (frida knows it)
Hz-1new unit of y

Now we will substract the empty can

oyto act on the y axis
“N1”to act in file number N#. (from now on N wiull be the number of file we are acting on)
-Funtion - to substract
y2An y axis from another file
N2To substract the y axis from file number 2 (we are doing, therefore Yn1-Yn2). A lot of numbers will then appear. This is the same issue as above with the channel numbers. if it does, be aware and check the result carefully before submitting to phys rev lett.
dfyou can se what you have done (hopefully!)
To calculate the Density of States (alias DOS)


In a liquid the density of states is defined as:


We will therefore, first calculate the s(q,w) in a large range of q (where the elastic line in fact dissapears). Then we will seight spectra by 1/q2, then add the spectra, and then calculate the density of states in the one phonon approximation.

fl *we load the corrected data s(2theta,w)
_coqfirst let's calculate s(q,w), but fur all q values, i.e. also for long energy transfer regions (for more details see calcuate s(q,w)
0initial energy
0.1step in energy
100max energy (or any other number)
1interp in q
0.1step in q
10max q
0.05hlaf the q step
1min num of channels

At this point you should have in 2 s(q,w) (or we will suppose it is in file 2)

2 let's work in file 2, where s(q,w) is saved
oy we operate on y (intensity)
/we want to divide (by q)
zwe ant to divide by z, i.e. by q. You will generate a file 2.
oyagain the same because we want to divide by q2
zneeds further explanations?. In file 4 we have now s(q,w)/q2 (hopefully!)
mgi We put all data inthe same grid, otherwise we will run into problems when we add all spectra, because channels are not equal for each spectra!
0firs energy
0.1steop of energy
100last energy. If you had a look, the programs proposes the same numbers as when you calculated s(q,w) (isn't it intelligent the program?)
1linear interpolation. And in file 5 you should now have all the data niceñly in the same grid
msawe add the spectra
zlet's group by z value
100a hughe number, because we want to add ALL spectra in one single spectra
1You must add over full area. In file 6 you should now have your nice s(q,w). Let's now calcualte g_1(w)
_sgspetial options
3to calculate g_1(w)
nwhy not?
0why not?
0why not?. And we get g_1(w). Now we are going to normalize it. We therefore calculat the integtral
oito make the integral
4option to integrate
0 40the range to integrate (you should have had a look at your data first ;-)
1save result as a file, and i nfile 8 you will have the integral result (one point)
7 finally we will divide by the integral value, so let's go to 7, where g_1 is calculated
oytu divide by the integral
ifwe will divide by the value in file 8, the integtral
8from file 8
9 here is somethng like the density of states

The procedure is not fully tested and may have errors!