Compton radius

If one identifies r with the measured Compton radius, rc = h/2moc (Sect. 2.2 and Eq. 2.34), this formula yields v = c ... 

Following considerations developed by Bohr, Darwin, and Pauli, de Broglie [6] showed that it is not possible to separate the electron spin momentum from its orbital momentum because, in any direct measurement, the uncertainties on the components of the orbital momentum would be larger than the spin momenrnm. This is due to the electron having a finite size, defined by the Compton radius. 

Only the constant part is observed in a practical measurement, which gives the average velocity through a time interval much larger than v whereas the oscillatory part explains why the instantaneous velocity has eigenvalues c [5, 6], Further integration yields the time dependence of the electron coordinate Xk, and it is seen that the amplitude of the oscillatory motion is of the order of fi/2moc, the Compton radius of the relativistic electron (Sect. 2.2 and Eq. 2.34). 

This yields a harmonic relation similar to Eq. (2.35) which, when rg is the Compton radius rc, relates to a gravitational invariant S similar to Hat flne-structure constant a (Table 2.1) ... 

If Cq is the Compton radius rc, then/fe = 5.512 x 10 m 0.58 x 10 light years. The outside curvature Rp equals the frontier radius rg only if rg = rg, which is far below the Compton radius. 

From Eqs. (2.37) and (2.39), it is clear that the confinement of a charged entity oscillating at light velocity within a Compton radius defined by Eq. (2.34) cannot be related directly to the gravitational space-time curving. 

The essential idea in this chapter is that the rest mass of the electron stems from the rotational motion at light velocity, in a confined region defined by the Compton radius, of a massless charged entity. That a mass may stem from motion is nothing new since an inertial mass mo gains extra value with increasing speed v, according to... 

Table 2.2 For all known particles of the electron ftunily and for a few other common particles, measured rest mass (in MeV) and computed Compton radius (in nm)...

Particle Rest mass/MeV Charge/e Spin/ Compton radius /nm lifetime/s Discovery... 

This is about 3.28xl0 light years with the numerical values given in Tables 2.1 and 2.2. Comparing the above formula with that for the neutrino Compton radius , rc = h/2v c, yields the ratio... 

If the electron is seen as the ground state of a subsystem analogous to the Bohr atom, then the parent mu and tau leptons could be seen as its excited states , with a Compton radius decreasing as the rest mass increases. 

Calibration to absolute intensity means that the scattered intensity is normalized with respect to both the photon flux in the primary beam and the irradiated volume V. Thereafter the scattering intensity is either expressed in terms of electron density or in terms of a scattering length density. Both definitions are related to each other by Compton s classical electron radius. 

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

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. 

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... 

PROBLEM 2.11.2. Evaluate the speed of the orbital motion of an electron that has orbital angular momentum m,vr0 = h, if the mass is concentrated at the electron radius r0 estimated above either from electron-electron scattering (1(P16 m) or from its "classical radius" (2.892 x 10-15 m) or from the Compton wav elength Ac (2.426 x 10 12m). 

RRydberg constant me and trip are respectively the electron and proton masses Rp is the proton charge radius, and kQ the Compton wavelength of the electron, a is the fine structure constant e f 2 Qhc), where e is the electron charge, eg the electric constant, c the speed of light, and h the Planck constant. The Rydberg constant can be expressed in terms of other constants as a mect 2h)... 

---