The Compton effect

There are also some questions to the Compton effect theory and, in particular, to the interpretation of two key facts of the experimental curve: 1) the dissipation on free electrons being at rest; 2) the declaration of the presence of highly (?) bound electrons with the energy greater than 1 Mev (?!). For the first fact one should make the following comment. First, at real temperatures the possibility for an electron (even free) to have zero velocity is zero, and it is necessary to consider the arbitrary motion of electrons (the real distribution). In particular, the peak should be related to the most probable, rather to zero, velocity (and for an atom - to the velocity of fixed electrons in the atom, which is rather great). Second, it would be interesting to confirm the effect on electron beams in all three quantities independently (the full balance): in angles, energies and in a number of particles. For the second fact we note that with declared high energies it would be strange not to draw out any (even internal) electron. Probably, the Compton effect (as well as Mossbauer's effect) should be considered for a body (or atom) as whole from some resonance conditions (with regard to concrete mechanisms of absorbtion and radiation in the atom). However, even in this case still remain the questions on the influence of motion of electrons in atoms and on the temperature effect on all three quantities measured in a single (!) experiment.

It would seem that for electromagnetic interactions there should be the least number of reasons to doubt in the relativistic equation of motion: ${d{\bf P}\over dt}=e{\bf E}+{e\over c}[{\bf v}\times {\bf B}]$, and, as a consequence, in relativistic conservation laws for the process of collision. Nevertheless, we shall make some remarks on the issue of validity of relativistic description of the Compton effect. Above we have already considered some uncertainties for collision of balls - an analog of the "billiard"-type Compton model. We shall analyze the experiments described in the standard tutorials, for example, in [27,30,40]. Note that if the time of coincidence of instants of recording $\gamma$-quanta and electrons $\Delta t > 10^{-20}$ sec, then the experiments not only do not prove the simultaneity of emitting of particles, but also do not allow to attribute unambiguously the particles to any act of scattering. Such an accuracy is outside the limits of even modern possibilities (that is, this is still a matter of "faith", and no statistics will help here).

It is methodically incorrect to call the electrons, participating in scattering, as free ones, because in such a case their number should be constant in the experiment. However, one has to consider this number to be different depending on a scattering angle, and if this angle is rather small, all electrons "turn out" to be bound. In fact, however, all electrons participate in the momentum transfer (owing to their motion in an atom) and capture from a $\gamma$-quantum a part of energy (because they are bound in the atomic coordinate system).

Some points in the Compton effect theory are not obvious. For example, what is the role of scattering on larger particles, than electrons, - on nuclei (whether the interference and its influence from radiation, scattered on nuclei, are possible?)? Why the non-shifted line is absent in the experiment with lithium (Compton, Wu)? On the contrary, it should always be present, for example, from scattering on a nucleon. Why for all substances there exist two peaks, situated almost symmetrically with respect to the initial line, rather than one shifted peak?

Besides, all tracks are not visualized (as in the ideal theory), but are only restored with the help of auxiliary means (and interpretations). That is, in verifying the conservation laws we are dealing with statistical hypotheses. In the experiments there are no estimates of the probability of double scattering from a specimen (but it can have a noticeable value), and the role of multiply scattered "background" from all parts of an experimental setup is evaluated nowhere. The accuracy of experiments, even on determination of a scattering cross-section, is low about $10\%$ (and this is the statistical accuracy!). In so doing, the most presentable (favorable to the theory) events are chosen. For example, in the experiment by Crane, Gaerttner and Turin only 300 cases from 10000 photos nave been chosen (whether this is not too little?), and the coincidence of the scattering cross-section data with the Klein-Nishina-Tamm formula is declared. In the case of large thickness of specimens (Kohlrausch, Compton, Chao) the double scattering must obviously be taken into account. Similarly, it is obvious from the scheme of the experiment, that in Szepesi and Bay's experiment the number of double scattering events is of the same order, as that of single scattering ones. If this fact is not taken into account, the declared accuracy of $17\%$ is rather doubtful. The declarative corrections (adjustments), made by Hofstadter in his experiment due to influence of various factors, cause bewilderment. In this case after all corrections (adjustments up to $30\%$!) the accuracy of $15\%$ is declared.

In reality, in all experiments not the dispersion directions are detected, but the hitting into the given site of space is recorded. Therefore, the experimental confirmation of a SRT interpretation occurs to be rather doubtful. For example, in the experiment by Cross and Ramsey almost a half of points, with regard to declared limits of tolerances, lie outside the theoretical curve. Of interest is the fact, that after removing a recording device from the plane of scattering the number of coincidences in scattering acts remains to be considerable: it more than three times exceeds the background value. Also rather strange is to compare Skobeltsyn's experiments with the theory with using the ratio of a number of particles scattered to various angles $N_{0^{\circ}}^{10^{\circ}}/N_{10^{\circ}}^{20^{\circ}}$. You see, each of these quantities (both numerator and denominator separately) represents some averaged (effective) quantity. And how is it possible, in the general form, to compare the ratio of average quantities (two experiments) with the ratio of true quantities (a theory) without using the fluctuation theory?

For more complete theoretical substantiation of the Compton effect not one collimator is required (for incident particles), but three collimators for separating, in addition, each type of scattered particles over narrow directions. The absorbers are also necessary for eliminating the background. Then there will remain "only" the problem of filtering all particles over energies. Thus, even such an, apparently, purely relativistic phenomenon, as the Compton effect, is not experimentally verified to a complete measure.