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Background and actual interpretation

According to theory of electromagnetic interaction with charged particle, developed by Thompson, an incident radiation of frequency f0 should accelerate an electron in the direction of propagation of the incident radiation, and the electron should undergo forced oscillations and re-radiation at frequency f, where f < f0. The frequency of the scattered radiation should depend upon the length of time of electron exposure to the incident radiation as well as the intensity of the incident radiation.
Compton experiment demonstrates contrary, more precisely, wavelength shift of x-rays scattered at a given angle is independent of both the intensity of the incident radiation and the length of exposure to the incident radiation, and depends only upon the scattering angle.
In original experiment, Compton bounced x-rays into a graphite target using three different scattering angles; 45º, 90ºand 135º. The interpretation of Compton experiment is based in actual quantum mechanic on the corpuscular aspect of electromagnetic radiation.
According to this photons are massles particle with following energy and momentum:
Compton01; Compton02 (1.22)
If we allow a beam of x-rays to strike a target, some of the photons in the beam will interact, according to quantum mechanics, with free electrons in the material. When the incoming photon gives part of its energy to the electron, then the scattered photon is measured to have a lower energy than the original photon. Those photons which, after scattering, come out at an angle θ relative to the incident beam direction “add up” to form the scattered beam of x-rays observed at that angle.
Without presenting the entire mathematical demonstration, available in any book about quantum mechanic, the wavelength of scattered beam is given by :

In Compton scattering the incoming photon scatters off an electron that is initially at rest. The electron gains energy and the scattered photon has a frequency less than that of the incoming photon
Compton scattering occurs in all materials and predominantly with photons of medium energy, i.e. about 0.5 to 3.5 MeV.

Why the actual explanation is a absurd….

It is necessary to make a comparison between photoelectric effect and Compton effect. In the original photoelectric effect, the energy of the photon is of the same order as the energy binding an electron to a nucleus, a few eV. Thus, when the photon strikes the electron it imparts only enough energy to eject that electron. In seems that in this case it is not important the ,,momentum of incident photon” and an eventually ,,momentum of electron”.
If someone takes into consideration the momentum conservation for photoelectric effect a paradox appear for actual physics, because the incident photon has not enough momentum to deviate the electron from its trajectory; it is à la mode to suppose the electron at rest (another classical stupidity!) in material, but even in this case, the incident photon momentum is not high enough to set the electron into motion.
If the Compton relation of scattered photons is analyzed another ,,weird” situations are generated for actual quantum theory.
The wavelength of scattered beam is given by:


And as is observed the scattered photon energy is dependent on the angle of collision. 
With this formula, any ,,common sense mind” will suppose that light has a ,,corpuscular” nature but in the same time this formula rule out the quantum idea .
The energy lost by photon is not related to a smallest chunk, but is related to an angle. In principle, this angle can take any values between 0 and 180 degree so … bye bye quantization.
Of course here is a lot of place for philosophy….. and actual theoreticians are masters in this field…
Does someone ask how is possible for a photon to know the angle of impact, and to change the exact quantity of energy in order to have a linear dependency of λ=f(θ)? Besides an already invented ,,special sense” of photon to know the shortest path between a multitude of possible paths, now ,,another sense” of photon must be invented in order to be able to appreciate an angle and to change a ,,specific amount of energy". 
Let’s leave aside these problems of actual quantum mechanics, and let’s pass to more realistic contradictions of actual explanation for Compton effect.
It is assumed that Compton scattering occurs predominantly with photons of medium energy, i.e. about 0.5 to 3.5 MeV. A 137Cs radioactive source is usually used to provide photons for Compton scattering. The radioactive source generates a beam of photons with energy 0,662 MeV this means 1,06x10exp(-13) J, the beam being mainly monoenergetic.
With this photon energy, it is not difficult to calculate the mass of such γ photons according to actual quantum theory:

By comparison with electron mass there is:


So, in case of a Compton effect with this photon energy, we are in particular case of elastic collision where both masses are equal and one object (electron) is considered at rest. If we reduce the experiment to have a two-ball setup, the swinging ball should come to rest as it bumps into the lone ball. And that lone ball will be accelerating to the velocity the other ball had when it struck. Therefore, in this ,,hypothetical” one-dimensional Compton effect, the photon remain at rest, and electron gain entire energy of incident photon.
It is very strange how is possible for a Compton effect to have a ,,elastic collision” and the incident photon remains with more then 93% from its initial energy, and the electron gain maximum 7% from photon energy.
In practice, there are few cases when the collision is one dimensional; more close to reality is a bi dimensional collision and scattering; in this case the situation is a little bit more complicated but manageable.
Let’s consider the case when the ball 1 collides elastically the ball 2. The set up of experiment is to have ball 2 of mass m2 at rest before collision and the ball 1 of mass m1 is moving with velocity v. The velocity v1 of ball 1 and velocity v2 of ball 2 after collision will depend upon the "aiming" distance δ, which is equal to the distance between the center of the ball 2 and the line of the motion of the ball 1 before collision.


The collision will happen if δ < r1 + r2.

The force applied to ball 2 during collision from the side of the ball 1 is directed along the line joining the centers of the balls. So, after collision the ball 2 will move at angle θ as shown in the figure.
(r1 + r2) sin θ = δ 
During the collision the energy and momentum of the motion is constant:


From these equations we can find:


Considering m1=m2, the bi dimensional collision does not fit again with observed distribution of energy before and after collision.
If there is a ,,really” elastic collision, and photon mass equal with electron mass, a larger distribution of recoil electron energy and recoil photon should be counted. It should be observed cases when incident photon loose 50% of its initial energy even 75 % percent or even more.
This is not the end of nightmare for actual theoreticians.
The up presented discussion was made for a 0,66MeV photon.
In case of a 3,5MeV photon, the mass of this photon is:

By comparison with electron mass there is:


In this case the mass of photon is significantly greater then electron mass considered at rest.
Again from classical mechanics when a greater object collides with a smaller object at rest, it is impossible for the greater object to have recoil at 135 degree. So, in case of Compton effect as the incident photon energy increases, the signal for recoil photon at an angle greater then 90 degree should vanish. Does this happen in experiments? Maybe is the time for actual theoreticians to repeat some experiments before making comments.
Long time ago, but published in 2007, and also in a internet article, an alternative explanation for Compton effect was proposed. The explanation was based on a collision between a mass photon and a electron ,,at rest” in order to have a comparison with quantum mechanics. 
At the moment, in absence of another possibility to estimate the mass of a photon, it is very difficult to draw a clear conclusion for Compton effect. 

If the mass of a γ-ray photon is comparable with electron mass, the Compton effect is caused by collision of γ-ray photon with atomic nucleus.
If the mass of γ-ray photon is much smaller then electron mass, the Compton effect can be caused by both type of collisions: γ-ray photon with electrons and γ-ray photon with atomic nucleus.
In both cases the mathematical demonstration made in Atomic structure book and in the up presented link remains valid as principle. It is necessary to establish the ,,obstacle” which deviate the photon.
Both these possibilities blow up the actual explanation and quantum theory.
It is foreseen a further revision of Compton effect in physical-chemistry book.


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