Compton wavelength

Although Dirac s equation does not directly admit of a completely self-consistent single-particle interpretation, such an interpretation is physically acceptable and of practical use, provided the potential varies little over distances of the order of the Compton wavelength (h/mc) of the particle in question. It allows, for instance, first-order relativistic corrections to the spectrum of the hydrogen atom and to the core-level densities of many-electron atoms. The latter aspect is of special chemical importance. The required calculations are invariably numerical in nature and this eliminates the need to investigate central-field solutions in the same detail as for Schrodinger s equation. A brief outline suffices. 

Classical electron radius Compton wavelength of the electron Proton mass Neutron mass... 

Dividing by pxp2 and using p = h/X, Compton s result, eqn (29), is recovered with Ac = h/mc. The term Ac is thus a constant as found experimentally, taking the value of 0.024 A, the so-called Compton wavelength. 

Here, r is distance from the center of the observed mass, A,., is the Compton wavelength of the electron, ro is the Bohr radius for the hydrogen atom, and Q is an integer larger than n, where n 5 is the quantum number of the last electron shell. 

According to the second assumption of the SLRT [5], the vacuum properties of the spacetime determined by the boundaries ce and Xcp, influence the properties of the nucleus, and consequently influence on the nuclear reactions as well, where ce is electron Compton wavelength and Lrp is proton Compton wavelength [5]. 

Electron Compton wavelength. Distance between nucleons in deuteron. Proton Compton wavelength. 

Anomalous electron moment correction Atomic mass unit Avogadro constant Bohr magneton Bohr radius Boltzmann constant Charge-to-mass ratio for electron Compton wavelength of electron... 

Compton wavelength of neutron Compton wavelength of proton Diamagnetic shielding factor, spherical H20 molecule Electron g factor Electron magnetic moment Electron radius (classical) Electron rest mass... 

The group velocity of de Broglie matter waves are seen to be identical with particle velocity. In this instance it is the wave model that seems not to need the particle concept. However, this result has been considered of academic interest only because of the dispersion of wave packets. Still, it cannot be accidental that wave packets have so many properties in common with quantum-mechanical particles and maybe the concept was abandoned prematurely. What it lacks is a mechanism to account for the appearance of mass, charge and spin, but this may not be an insurmountable problem. It is tempting to associate the rapidly oscillating component with the Compton wavelength and relativistic motion within the electronic wave packet. 

Because quantum theory is supposed only to deal with observables it may be, and is, argued as meaningless to enquire into the internal structure of an electron, until it has been observed directly. To treat an electron as a point particle is therefore considered mathematically sufficient. However, an electron has experimentally observed properties such as the Compton wavelength and spin, which can hardly be ascribed to a point particle. The only reasonable account of such properties has, to date, been provided by wave models of the electron. 

The constant Ac = 2.425 pm is called the Compton wavelength of the electron. The wavelength shift given by Eq. (1.10) can be easily reproduced theoretically if the interaction between the radiation and the electron is considered as a collision between two particles in which the energy and the linear momentum are conserved (conservation of momentum in the incident direction and in the direction perpendicular to it). These particles are a photon of energy hv and linear momentum p = hvlc=hlX and a stationary electron of mass m which acquires velocity v (Fig. 1.2). It is then found... 

Figure 2.8 shows the total probability density for the lowest-energy functions calculated for the case a=10Ac where Xc = Hlmc is the Compton wavelength for the particle, divided by 2ir (for the electron, it is Ac = 0.4 pm). 

Compton wavelength when the particle is moving relativistically, the de Broglie wavelength may be written... 

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