1.5 COMPTON EFFECT
1.5.1 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.
In
original experiment,
According
to this photons are massles particle with following
energy and momentum:
; 
(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 :
(1.23)
1.5.2 Proposed interpretation
In book about Corpuscular nature of
light we will show that photons are mass particle, which obey to classical
mechanic low, and consequently we have the classical energy and momentum
formula:
(1.24)
(1.25)
We describe the Compton effect in terms of collisions between individual electrons
and individual photons. General rules of kinematics apply to such collisions,
and can be used to determine the properties of the scattered photons. The
Compton effect shows that, in these collisions,
photons act precisely like particles.
We simply consider a photon as a particle
with mass τ
momentum p, and energy ε, and proceed to work out the kinematics of the
collision between such a particle and an electron.
The incoming photon is incident on the
electron considered at rest and after collision the outgoing photon is
scattered under the angle q, relative to
the initial direction of the incident photon, and the electron is scattered
under the angle j. The electron is considered initially at
rest, so its initial momentum and energy are zero.
Initial energy of photons is: 
(1.26) respectively after
scattering: 
(1.27) where τ
is the mass of photon. The moment of electron after scattering is mv.
Figure 1.9 Photon scattering in Compton effect
The equation for conservation of momentum
in the collision:
(1.28)
on axes:
(1.29)
(1.30)
Making some tricks:
(1.31)
(1.32)
With following simplifications:
(1.33)
(1.34)
(1.35)
Writing the equation for conservation of
energy in the collision:
(1.36)
(1.37)
(1.38) where 
(1.39)
(1.40)
(1.41)
(1.42)
(1.43)
The analysis of equation 1.43 and
1.23 indicate the same dependency of photon energy related to the angle
and mass of electron.
They differ regarding to a constant: mass
of photon in proposed explanation and Planck constant in case of quantum
mechanics.
According to quantum theory, the
effect should be the same in case of photon from IR,
The proposed relation is photon mass
dependent, and this fact is observed in experiments. In the same conditions the
difference of energy is smaller for a photon from visible domain comparatively
with an X-ray or g-ray photon. With these formula is it possible, like in actual interpretation to determine the
mass of electron, but also it is possible to estimate the mass of photon.
1.5.3 Inverse Compton effect
In astrophysics inverse
Figure
1.10 Inverse
The
study of inverse