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Positive charge atomic form-factor

Have you ever heard/learned of a positive charge atomic formfactor before?  

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  1. 1. Have you ever heard/learned of a positive charge atomic formfactor before?

    • Yes, I have.
    • No, I have not.
    • I do not know what an atomic form-factor is.

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I would like to learn if you've ever heard of the positive charge atomic form-factors before my asking this question. The positive charge atomic form-factor fnn'(q) stands at the nucleus charge Z and describes the positive charge cloud in atoms for the elastic (n→n) scattering channel at large angles. It also describes the inelastic scattering channels - "hitting" nucleus by a projectile excites an atom (n→n'):


n→n'(q)/dΩ ~ |Z⋅fnn'(q) - Fnn'(q)|2


The elastic and inelastic positive charge atomic form-factors are entirely determined with the atomic wave functions ψn(r) and they have nothing in common with the Hofstadter form-factor describing the proper nucleus size.


The positive "cloud" size may be very big if the initial and the final atomic states ψn(r) are excited and metastable, like in Rydberg atoms. This is just an effect of the nucleus motion around the atomic center of inertia. Physically it is of the same nature as the negative (electron) charge atomic form-factor Fnn'(q). The numerical difference is just in the "could" sizes - the negative one is larger (~an), the positive is smaller (~(me/Mp)an for Hydrogen, for example). The scattering angles where these form-factors "work" differ essentially - at small and large angles correspondingly.


The positive charge cloud is simply an atomic nucleus (not nuclear) shell. For Hydrogen atoms it resembles the usual atomic orbitals but at smaller distances (I provide the atomic orbitals in a figure attached). As you can see in the figures, the positive charge is not concentrated at a point but smeared quantum mechanically. Each "separate" sub-cloud carries a "fractional" positive charge, just like a negative sub-cloud. Such pictures resemble sometimes the electric charge distributions in nucleons that normally used as an evidence of quark/parton nucleon structure.


The details can be found in my article "Atom as a "dressed" nucleus" in arXiv (http://arxiv.org/abs/0806.2635). The journal version of "Atom..." is available at the Central European Journal of Physics site: http://www.springerlink.com/content/...5b899036dπ=0


Final remark concerning observation of these atomic nucleus shells (it is explained in detail in "Atom..."). Observation is possible in the elastic scattering processes when the initial and the final states of the target atom is the same: ψn(r)→ψn(r). We have to deal with fast charged projectiles whose de Broglie wave-length is smaller than the positive cloud size and we have to scatter them to large angles. In these conditions a fast charged projectile transfers a big momentum q to the nucleus so the atom can get easily excited (inelastic processes dominate: ψn(r)→ψn'(r)).


In reality it is difficult, without special experimental facility, to distinguish the elastic from inelastic processes. When one observes only the scattered projectiles, all cross section (of elastic and inelastic events) are added up experimentally. It is called the inclusive cross section. It is easy to show that the inclusive cross section dσinclusive=∑dσn→n' is reduced quite accurately to the Rutherford cross section, as if the target nucleus were "free" and situated at the atomic center of inertia. This fact explains why the notion of point-like particle finds the "experimental" support. In specially designed experiments one can distinguish the elastic dσn→n from inelastic cross sections and obtain the figures presented below.


You can also leave your opinion on whether the effect of the positive charge smearing in atoms seems to you as realistic as the negative charge smearing or not. Of course, if you have not studied this subject (scattering from atoms, atomic form-factors), leave the third answer.


Do not hesitate to participate and thanks for your answers.


Vladimir Kalitvianski.


Edited by Bob_for_short
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