The term ``spin independent'', as such,  is empty of content and depends on the context.  Given a model for dark matter, that specifies its particle content and how it interacts with ordinary matter, it's possible to compute the cross section for elastic scattering off a nucleon or a nucleus, as the case may be and use the appropriate projectors on the states of definite spin, just like in any similar calculation. Naturally, since nucleons and nuclei are composite objects, they are described by some effective theory. This is what's done in http://arxiv.org/pdf/hep-ph/0307185, where the term ``spin-independent'' refers to the contribution of a  specific term.  The paper is quite explicit, cf. eq.(23) and following, that gives, precisely, the expression asked for. The approximations involved are explained before; but, above all, what's assumed is basic knowledge of how any cross section is computed, given a Lagrangian. 

I think Stam Nicolis already answered you question. However, I would like to add one comment why one finds cross sections per nucleon and nuclei. Obviously, direct dark matter search experiments do not have single nucleons but nuclei as scattering targets. So to calculate the expected signal seen in a specific target one has to take into account the effects of the nucleus (e.g. the form factors). However, if direct searches presented their results on a per-nucleus basis a comparison between experiments using different target materials would be impossible (at least complicated). Thus, cross sections are normalized to one nucleon (see e.g. DOI:10.1016/S0927-6505(98)00025-5). I would also recommend the following review article: arXiv:hep-ph/0404175

http://arxiv.org/abs/hep-ph/0404175

http://dx.doi.org/10.1016/S0927-6505(98)00025-5

Dark matter was first suspected by Zwicky based on the velocity of galaxies within clusters. The motion of stars within galaxies gives the same indication but there is also gravitational lensing evidence and the most convincing is the growth of structure in the early universe. Galaxies formed early because dark matter could coalesce during the period when normal matter structure growth stalled due to radiation pressure prior to recombination. Any attempt to remove the need for dark matter needs to address structure formation as the top priority.

Thierry, I'm talking about structure formation during the first 400,000 years, in the range from z=103 to 105.The first stars probably didn't appear until around z=25. See the graph beside the section entitled "Linear structure" in the link which shows the growth of structure for the two components. Radiation pressure completely dominates all gravitational effects so stops growth in the normal matter component completely but has no effect on dark matter. The impact of this is clearly visible in the angular power spectrum of the CMB and in the existence of baryon acoustic oscillations.

On page 27 of your paper, you give the formula for the bending of light brazing the Sun. The first term dominates due to the factors of c and c2 in the denominator of the others so it is just the Newtonian formula. That predicts a bending angle that is half the measured value while the GR prediction gives the correct answer. Note that any contribution from the Sun's rotation would increase the angle on one side but decrease it on the other so cannot resolve that failure. Gravitomagnetism is fine as an approximation to GR (a subset of it) under limited conditions but is not sufficient in general.

https://en.wikipedia.org/wiki/Structure_formation#Linear_structure

TDM: Then you write: "so it is just the Newtonian formula". No it isn't. You forgot to take into account the factor of 2 in the first term of the equation. This factor 2 is obtained by strictly applying Gravitomagnetism.

Oops, yes I missed the factor of 2 as I was concentrating on the other terms. Of course that would also apply to the planets so to keep them in their orbits, your value of G would need to be halved, you can't have it both ways.

TDM: But I see that you don't have any other remarks about my paper on Gravitomagnetism. Consequently you approve all the other findings!

ROFL, no. Nice joke. A single failure falsifies a theory and that point was so obviously wrong, I didn't bother with the rest.

TDM: Gravitomagnetism is absolutely no subset of GR and there are no limited conditions, ... From where does these false ideas come?

See the summary on the linked Wikipedia page. Of course frame dragging in GR has been confirmed by Gravity Probe B and using the LAGEOS satellites.

TMD: If you interpret the CMB diagrams literally, the Earth becomes the centre of the Universe.

Sadly quite a few people make that mistake (and the same regarding the Hubble Law), it is complete nonsense.

TMD: The CMB laboratory and its data are restricted to very few people only, ...

Not true, the COBE data for example is available on request. It is old so held on magnetic tapes but I requested some of the data last year during a conversation regarding Robitaille's work. It took a few days to get the tapes loaded for FTP access but I now have the data. Understanding the binary coding is much harder unless you have access to the FORTRAN structures used!

TMD: When you read Prof. Robitaille on the CMB (see annexed papers), you will see that there is a big chance that the CMB is just the re-emission of waves by the oceans on Earth.

I've done a fairly comprehensive analysis of his criticism of the COBE data and what he says is complete rubbish. In the frequency band of interest, water emission is quite low, especially towards the lower frequency end, and the emissions would be dominated by a narrow oxygen molecule band. The resulting spectrum would be nothing like the Planck curve. He has also completely ignored the verification measurements done using the DMR which specifically looked for terrestrial contamination and showed that it was below the detection threshold as predicted by the design modelling. The FIRAS horn has an additional 80dB attenuation (that figure from memory, E&OE) in the direction of the limb of the shielding. His criticisms are farcical, sorry.

https://en.wikipedia.org/wiki/Gravitoelectromagnetism

You say just before equation 2.1, "Since the rest mass of light rays is zero we

must not consider the gravitation force of Newton!" but that is not the case. The acceleration due to Newton is -GMr-2 which is independent of m so it should still apply. If you want to eliminate it due to the zero mass than that's OK but you should do so consistently. Between 2.1 and 2.2 you give a formula (without derivation) for the "mass per length unit" based on the density, but if you are using zero mass for light then the mass density must also be zero. You also include a term a2 in that formula but why would the mass of a unit length of light be dependent on how far it was from the Sun? It looks as though you just picked an equation to suit the result you want.

TDM: Now this has been clarified, I am convinced that you will agree with the rest of my paper on the successes of Gravitomagnetism.

No, the more I see, the more it appears you are just picking favourable results and not applying any self-criticism.

On the CMB, the COBE results are available and I was told that the original authors would like to hear of any additional analysis done on their data. If you request it, you can get it. However, a lot of work is involved in doing real science. The choice is yours.

Regarding Robitaille, the errors in his work are so obvious that any undergraduate could see them. If you look critically yourself, I have no doubt that you will also see them. I have no interest in spending my time telling someone something they probably know already but will not admit.

However, I am aware that we have "hijacked" this thread, our conversation has nothing to do with the original question so I won't continue here. By all means contact me by private message if you like. My apologies to Basabendu Barman for disrupting the question.

TDM: George: rest mass = zero => Newton force = zero. No attraction. See all the textbooks.

The textbooks also usually continue like this:

f = GMm/r2

f = ma

Hence

a = GM/r2

so the acceleration is independent of the mass of the test particle. This of course was the subject of Galileo's apocryphal test from the tower at Pisa. That means the Newtonian acceleration should be included.

TDM: Equation (2.1)  to (2.2) : the deduction is written between (2.1) and (2.2).

Yes, I had misread a as the radius (actually r).

TDM: Mass at a velocity c is mass that will respond to the magnetic part of gravity, which is velocity-sensible. So, mass is not zero here.

That's the key question though, why do you treat the mass as not being zero when you previously said (correctly) that it was zero.

TDM: Since all the above is elementary, and your remarks were presumptuous, I think that your remarks on Robitaille can be neglected as well...

How very unscientific, by that measure since you didn't know Newtonian acceleration was independent of mass, anything else you ever say could also be neglected.

You can easily check what I said for its correctness, the CMB frequency range tested by COBE contains a resonance band from oxygen which is stronger than the continuum spectrum of water and could therefore not reproduce the black body spectrum. Everything I said about the performance of the equipment is in the COBE published papers.

@ George: if you don't understand that, maybe this will help: if m = 0 for Newton => f = GMm/r2 =GM 0 /r2 = 0 and f = ma = 0a = 0

That is incorrect, since the force is 0 and the mass is zero, the acceleration is 0/0 which is indeterminate. However, since m is common to numerator and denominator, it can cancel before we do any calculation so the acceleration is as given by Newton.

TDM: Light has a inertial moment p. Since the speed is c, the mass at speed c is p/c=m.

OK, if that is your justification (and it is not unreasonable) then you should also use that in the Newtonian formula. However, you could also say that light has energy E=pc and Newtonian energy is mv2/2 hence with v=c you have m=2p/c. Either way, you have a force proportional to mass so in finding the resulting value of acceleration, the mass cancels out. You can get an acceleration from your extra term but it should add to the Newtonian value (assuming they act in the same direction, they are vectors of course) and the total would then be 3 times the simple Newtonian gravity value, not twice. I am not saying your derivation of that part is incorrect, only that you must be consistent. You cannot assume zero mass in one place and non-zero for the same beam in another.

TDM: So, as you see, I can not be confident in your knowledge about Newton.

Nor I yours, your did not see that the mass cancels out giving an acceleration regardless of mass. However, scientific correctness is not based on trust.

TDM: How could I be confident concerning your knowledge about the CMB?

You shouldn't, nor should you trust Robitaille's. What I suggest you do is look up the information your self and decide whether my criticism is correct or not. Remember the frequency of the peak of the black body curve is strongly dependent on temperature and he is claiming that a signal generated from a body at between 250K and 300K (roughly) has the peak at exactly the frequency of a body at 2.725K and the rest of the curve matching it very tightly. Don't you find that suspicious?

TDM: Besides, the GR theory should be abandoned to the benefit of gravitomagnetism, which proves (unlike GR) that "dark matter" and "dark energy" are not needed in order to solve the alleged issues.

You still haven't explained how it can explain structure growth in a period long before the existence of the first gravitationally bound objects. That is a key piece of evidence for dark matter.

TDM: So, you say that totally massless stuff is accelerated by Newtonian gravity. How really funny reasoning you have about Newton's laws... I give up... That's what you get with nowaday's education...

Strange that Eddington in 1919 was suffering from the same "nowaday's education" when he measured the deflection of starlight during the eclipse, it was well known at the time that Newtonian theory predicted a deflection of 0.875 arc seconds. That value had also previously been calculated by Cavendish in 1784 and Soldner in 1801 so your attempt at personal abuse has only illustrated your lack of familiarity with the history of this part of science.

TDM: Concerning the alleged black body curve and the heat theory of Kirchoff: see Robitaille's comments annexed. Disillusioning!

Indeed, do you think he fails to realise that Kirchoff's Law follows from the third law of thermodynamics or does he really believe we can make "perpetual motion machines"  by violating it?

TDM: That's a pure invention without any ground, only obtained by a multitude of very indirect assumptions and poor reasoning. Nothing to do with any observation.

You should research the origin of baryon acoustic oscillations. Of course the later structure growth is well observed in a variety of large scale surveys.

TDM: Instead, the missing windings of disk galaxies prove that structure growth did not happen very long time ago ...

Missing windings? You are thinking of galaxy evolution, not structure growth.

TDM: And clusters can't get structured before the individual galaxies got.

That is correct, growth was "bottom up", but that implies cold dark matter rather than hot (e.g. neutrinos) which would produce "top down" structure growth with clusters forming first and fragmenting into galaxies.

Thierry, you seem to have a problem reading my last reply. In Newtonian gravity, all bodies accelerate regardless of their mass. You suggested this was "nowaday's education" but it is not new so Cavendish, Soldner, Einstein and Eddington all knew this as well.

TDM: And you now dismiss SR and QM, who say that the rest mass of light is zero.

Not at all, as far as I am concerned, both GR and QM are correct (up to the problems we have integrating them) and Newtonian gravity with Galilean invariance is wrong. However, you are using Newtonian gravity so it would be unfair of me to say you are wrong just because you don't use GR.

The bottom line here is that it is entirely possible that you can develop an alternative to GR which produces the same predictions for areas that are well proven but might have some testable differences that could lead to new experiments. However, you need to use Newtonian gravity consistently if you are going to use it at all.

Regarding Robitaille's paper on Kirchoff's Law, the point is that it shows that he doesn't understand the basic physics involved, I assumed that was why you cited the paper.

On the rest, you need to look up the concepts of "top down" and "bottom up" structure formation as they are used in cosmology, they have very specific meanings ("jargon") which you may not have encountered before. Which type of structure growth occurs depends on the nature of dark matter, specifically whether the typical velocity is relativistic or not, i.e. hot or cold.

I agree Thierry, if you have nothing to contribute but ad hominem attacks, there is no point continuing. Bye.