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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: X`q(w)=hq*X`(w) (see PRE 61 3 2730 (2000), Wuttke et al.), confer to Making a master curve

 _sg to convert input y(x,z) to another representation 10 option to calculate the susceptibility msa To group detectors to have less spectra with better statistics z to group by z values, i.e. by detector angle in this case 10 the tolerance: will group detectors every 10 degrees in 2*theta y proceed 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 tu convert axes. We use it to “translate” from meV to frequency 1 more energy = higher frquency Hz new unit of x (frida knows it) Hz-1 new unit of y

Now we will substract the empty can

 oy to 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 y2 An y axis from another file N2 To 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. df you can se what you have done (hopefully!)
##### To calculate the Density of States (alias DOS)

SECTION UNDER CONSTRUCTION DO NOT TRUST TOO MUCH WHAT IS WRITTEN!

In a liquid the density of states is defined as:

p(w)=2Mhbw2*lim|k|→0Sinc(q,w)/q2

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) _coq first 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) 1 linear 0 initial energy 0.1 step in energy 100 max energy (or any other number) 1 interp in q 0 q(1) 0.1 step in q 10 max q 30 slices 0.05 hlaf the q step 1 min 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) z we ant to divide by z, i.e. by q. You will generate a file 2. oy again the same because we want to divide by q2 / aserejé z needs 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! 1 linear 0 firs energy 0.1 steop of energy 100 last 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?) 1 linear interpolation. And in file 5 you should now have all the data niceñly in the same grid msa we add the spectra z let's group by z value 100 a hughe number, because we want to add ALL spectra in one single spectra 1 You must add over full area. In file 6 you should now have your nice s(q,w). Let's now calcualte g_1(w) _sg spetial options 3 to calculate g_1(w) n why not? 0 why not? 0 why not?. And we get g_1(w). Now we are going to normalize it. We therefore calculat the integtral oi to make the integral 4 option to integrate 0 40 the range to integrate (you should have had a look at your data first 1 save 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 oy tu divide by the integral / divide if we will divide by the value in file 8, the integtral 8 from file 8 9 here is somethng like the density of states

The procedure is not fully tested and may have errors! 