Compton Shifting with Scattering Angle and Masses of Order 10-31kg To 1-0-27kg

The objective of this work is to study and observed the Compton shift of elementary particles masses lies in between within the angle between 0 radians to 3 radians. The observation shows Compton shifting ranges from . This nature of shifting is the same for all the considered masses for the same angle of scattering. Therefore this scattering is suitable for other elementary particles that lie in between considered masses. Hence the validity of Compton shifting can be used for other elementary particles scattering as elementary particles masses in between having similar nature or original Compton scattering of electron-photon interaction.

The standard model described the interaction of elementary particles with all existence forces like electromagnetic force, strong force, weak force, and gravitational force. For example, among the elementary particle gauge bosons (W and Z ) are mediated by the weak force, gluons mediate the strong nuclear force while photon mediates the electromagnetic force.
Fermions are the particle that follows Fermi-Dirac Statistics, which are half-odd integer spin like 1/2, 3/2, 5/2, etc., and obeys Pauli Exclusion Principle. There are 12 fundamental fermions without their constituent particle and divided into two categories, Quarks and Lepton.
No two fermions have the same quantum numbers. The repulsion for fermions or compelling attraction for bosons, or exchange force generally [1].

Standard Model (SM) categories boson's elementary particles based on integer spin
(including zero spins), unlike fermions. In SM, all mesons are considered bosons and are responsible for the electroweak force. Interaction between bosons are massive W + , W − and Z 0, and the charge-changing are weak interaction in between (W + and W − bosons); also, the neural particle is weak interactions in between (Z 0 boson) [2].
Bosons have an integer spin, including zero spin and don't Pauli's Exclusion Principle and occupy the same quantum state. Boson follows Bose-Einstein's statistics with intermediate vector bosons like photons, gluons, weak bosons (particles W and Z), and mesons [3].
In the quantum mechanical case, bosonic particles are indistinguishable, and particles are labeled with integer spin: 0, 1, 2, etc., while for fermion particles are distinguishable and particle is not marked with integer spin 1/2, 3/2, etc. The distribution of the fermion and boson Where is the energy of ith-state, = 1 Μ is the chemical potential. According to SM, all elementary particles are either bosons or fermions, and spin identifies them [4] Among different experiments and theories, the photoelectric effect is one theory with an experiment that shows energy quantized and absorption of energy from photon and emission of energy during transmission from material shows photon nature. Moreover, the Compton effect support this theory and develop a relation shown in equation (1), which also indicates that intensity and scattered wavelength are independent while scattering angle and incidence wavelength are dependent on each other as Where 0 is the rest mass of the electron, Compton Effect is defined as a scattering of incidence photon by bounded or unbounded charge particle, and in this scattering, some photon energy is transformed to charge particle with which photon goes interaction. This theory derived from classical theory and used for special relativity and quantum mechanics. This scattering help to understand the interactions of high energy physics theory in general, electromagnetic photon radiation with materials, like gamma rays interaction and X-ray production and Bremsstrahlung [5]. Compton length of the electron played a central part in several areas of physics and used to find the rest mass of an electron as described by Prasannakumar et al. [6], indirectly employed in the relativistic wave equation of Klein and Gordon, in the Dirac equation [7] as well as in the non-relativistic Schrodinger equation [8].
Compton scattering energy photon ranges up to a few MeV; therefore, it is one of the best studies for firmly bound atomic K-shell electrons, and some experimental data range between 0.279 to 1.0002 more detail in [9]. The interaction of matter and energy of X-rays (less than 1MeV) has different types of scattering like coherent (Rayleigh) scattering, incoherent (Compton) scattering, and photoelectric absorption [10]. In Rayleigh scattering, low-energy photons are considered; therefore, neither atom ionized nor electron goes to an excited state. On the other hand, in Compton scattering, the energy of a photon is high; therefore, atomic free-electron interact with incidence photons [11]. Thus, Compton scattering is observed in insufficient atomic numbers, while Rayleigh scattering is observed in higher atomic numbers [12].
Different experimental observations and theoretical development for non-relativistic kinematics show that physical parameters of Compton scattering are not appropriate. The change in wavelength in Compton scattering can be expressed as Δ = ′ − = 2ℎ = 0.048 52 ˚. For X-rays, the incidence for interaction and result shows that change in wavelength is about 4.852% when X-rays photon incidence with the energy of 12.41 keV. The experimental result shows that if the photon's energy is less than the rest energy (511KeV) of the photon, we can apply the Compton Effect for non-relativistic rather than relativistic cases [13]. The contribution of Bose in quantum statistical physics also shows that light is accepted as particles, and the generalization of concept by Einstein leads the concept of bosonic particles and obeys Bose-Einstein statistics. The nature of photon (particle and wave) was compounded in 1924 by Broglie and forward as both nature in a single particle but not at an instant and develop the relation as = ℎ/ to study the wave-like properties, where wavelength and p is momentum, and later names as packet energy called quanta. In 1927 after discovering electron properties as wave-like nature by Davisson and Germer experimentally, the dual nature of photon (wave and particle) was accepted in the scientific world until a contradiction is going on [14].
2. Mathematical formulation to study the Compton shifting for the different mass of the elementary particle Compton scattering and the Compton wave derivation: Considering Compton scattering as shown in figure 1, the conservation of energy in Compton scattering is given by Here = ℎ and ′ = ℎ ′, before and after scattering and rest mass-energy of the electron is = 2 . From relativistic energy-momentum, the energy of ′ = √( ′ ) 2 + ( 2 ) 2 .
On substituting these values on equation (2), we obtained an expression of energy as, Now the representation of equation (3) and conservation of momentum ′ = − ′ one can derive a relation, For, = = ℎ and = the arrangement of equation (4) becomes It is similar to equation (1), on assuming Δ = ′ − and = ℎ = 0.00249 = 2.43 is Compton wavelength as This equation (6) shows that shifting wavelength depends upon the scattering angle with the mass of the electron. For long wavelengths λ >>λc (i.e., hf<<mec 2 ), the scattering is closely elastic. In term of energy, one can be derived and extend relation (6) as Here is the energy of incident gamma rays and ′ is scattered gamma rays at an angle for considered that = and ′ = equation (7) is modified as The energy difference − denotes how much energy has been deposited to the electrons in the crystal by scattering [15]. The Compton wavelength of photons or gluons is described in the standard model (SM) of the elementary particle [16].

Result and Discussion
To study Compton shifting nature of elementary particles masses in between 10 × −27 to 10 −31 , for this, we develop code from MATLAB. We consider the two variables here to study Compton shifting the nature one is masses, and the other is the angle.
To study the Compton shifting for emitted particle electron for mass 3.11 × 10 −31 , with incidence photon energy which is higher than the threshold, are visualized below with different angle,

Conclusion
The observation shows that Compton shifting depends on both elementary particles masses and scattering angle. The Compton shifting is decreased with increasing masses and increases with scattering angle. As we consider for the masses of the elementary particles of the order 10 −31 10 −27 the nature of shifting is the same for all and ranges in between maximum to minimum10 −11 10 −18 . The shifting is maximum for electrons range mass and minimum for proton and neutrons ranges masses, shifting the order of 10 −11 for electrons mass and 10 −18 for proton and neutron masses. Hence, it concluded that Compton shifting is valid for masses from 10 −31 10 −27 that is electron mass to proton and neutron.

Declaration statement
Availability of data and materials: Data are not taken from any sources. The data was generated using MATLAB software for this work based on the equation derived above; the plot above is drawn using MATLAB code

Funding: No fund
Authors Contribution: Equally contribute