# Confinement and fractional charges in atoms

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In (quasi) stable atoms the positive and negative charges form "charged" clouds, which can be represented as fractionally charged sub-clouds. In order to observe them as such, we have to have the same atomic state in the in- and out-states, i.e., we have to deal with elastic scattering in the first Born approximation. Then no atomic "polarization" effects are present. Let us consider for simplicity a large-angle scattering, i.e., scattering from the positive-charge sub-clouds (see formula (3) in this paper and here):

$$\text{scattering amplitude}\propto\int{|\psi_{nlm}(\vec{r}_a)|^2\text{e}^{\text{i}\frac{m_e}{M_A}\vec{q}\sum \vec{r}_a}d\tau}$$

This integral is just a sum of integrations over different sub-clouds. If one manages to prepare the target atoms in a certain polarized state $|n,l,m\rangle$ (in order not to average over different $l_z$ projections), the resulting cross section will be an elastic cross section of scattering from fractionally charged atomic sub-clouds. However, and let us not forget it, this will be an inclusive (or deep inelastic) scattering with respect to the soft photon emissions, which carry away a tiny portion of the total transferred energy/momentum $|\vec{q}|$.

Such fractionally charged sub-clouds are confined in atoms and are never observed independently of atoms, just like quarks. I wonder whether this analogy between quarks and the "usual" sub-clouds is deep or superficial, to your opinion.

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