Talk:Rutherford model
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The final irony of the Physics is that the pudding model is always more correct than the (classical) notion of a pointlike nucleus. Indeed, the nuclei bound in a solid move around their equilibrium positions, and their positive charges are smeared over a rather wide region. Even in an isolated atom the nucleus, bound only with light electrons, turns around of atomic center of inertia, and that smears its positive charge.
The positive “cloud” in an atom is described with the second atomic form-factor fnn(q) [1] which strongly depends on the atomic state |n,l,m>. This form-factor stands at the Rutherford elastic cross section, so the purely elastic “backward” scattering is suppressed by |fnn(q)|2. The higher is the initial (and the final for elastic processes) target atom state n, the stronger is suppression of the deflected “backward” projectiles. For example, in the excited Hydrogen atom with n=43 (Rydberg state), the positive cloud is of the Bohr radius. In the ground Hydrogen state the charge is smeared within 30•10-13 cm, that is certainly larger than the “proper” proton radius.
In a “condensed matter” the positive cloud localization is of the atomic size. So the condensed matter structure resembles the pudding model.
Apart from elastic, there are inelastic second form-factors fnn’(q). They give the amplitudes of atom exciting due to transmitting the big momentum q to the nucleus at the “backward” scattering.
Ernest Rutherford, his colleagues, and the followers did not resolve the alfa-particle energies with the accuracy of 10-100 eV, so they all measured inclusive cross sections (elastic plus all energetically admitted inelastic) rather than the elastic one.
The inclusive cross section, according to the quantum mechanics, coincides with the Rutherford formula [1]. This means that in calculations of the number of scattered backward projectiles one can safely use the notion of the pointlike (“free”) nucleus, but one should never think that the target atoms (or more generally – the target energy levels) do not get excited.
All this is quite natural. As soon as we agree that the Rutherford formula is the inclusive result, we have to recognize that there is no ground for the pointlike nucleus notion. Piling up different events does not create an objective notion, but the crude classical one.
In other words, the classical “image of pointlike free” nucleus is always the sum of quantum mechanical images of different “pale photographs” of the bound system undergoing all possible transitions in course of “observations” (scattering). Thus, the inclusive picture is literally a cinematographic illusion obtained with superposing all particular images of quite different elastic and inelastic events (frames of dσnn'(q)).
By the way, this result is completely opposite to the theories of hidden variables where the “randomness” of quantum mechanics is explained with averaging a deterministic theory trajectories over some hidden parameters.
In practice there is no possibility to distinguish the fast scattered projectiles with precision of about 10 – 20 or 100 eV. It is even not possible to prepare the incident beam with that energy accuracy. That is why dealing only with scattered projectiles gives inevitably the inclusive cross section.
Another matter is observing recoil atoms. The excited atoms radiate. The atoms excited due to hitting electrons (described with the usual atomic form-factor Fnn'(q) under small angle scattering) radiate standard spectral lines. The target atoms excited due to hitting the nucleus (determined with fnn’(q) under large angle scattering) receive big momenta; therefore their spectral lines will be essentially shifted (Doppler effect). Registering simultaneously the scattered “backward” projectile and the shifted spectral lines permits distinguishing different inelastic processes. Thus, it is possible in principle to measure the elastic and inelastic cross sections separately. The target atoms should obviously be in a gas state of small density in order not to damp the excitations by the interatomic collisions.
Vladimir Kalitvianski.
1. Attenuation of the Rutherford scattering and atom exciting by fast charged particles for large-angle scattering. Ukrainian Journal of Physics, V. 38, N 6, 1993, pp. 851-854, and Preprint of Sukhumi Institute of Physics and Technology 90-8, 1990, V. Kalitvianski, (in Russian).
[edit] Duplicate article
Rutherford's model of atom is on the same topic as this article. If there is anything salvageable at that article (personally, I find it utterly illegible) it should be merged here before that article is deleted. EdC 17:04, 7 September 2006 (UTC)
