Gamow equation

An equation exists which gives the probability, with many simplifying assumptions, for the penetration of this barrier. This is called the Gamow equation. ... 

This equation has occasionally been applied to electrode kinetics, but its applicability is rather difficult in the numerical sense and the Gamow equation is often still used to make approximate calculations. 

Theory of a-radioactivity by quantum tunnelling (Gamow et al). Cecilia Payne (later Payne-Gaposchkin) applies Saha s equation to the stellar spectral sequence, finding vast predominance of hydrogen and helium, but does not believe her results. 

Typically, the Gamow factor is large (2G 60-120), which makes the transmission coefficient T extremely small ( 10 - 55-10 - 27). Combining the various equations, we have... 

Considering the reaction constant k and writing the equation in terms of the relative energy E of the nuclei and the Gamow energy (a measure of the magnitude of the Coulomb barrier)... 

At the poles of the resolvent, when z = z), Eq. (5) reduces to the Gamow-Siegert equation... 

Equation (31) shows a characteristic feature of the resonance wavefunc-tions, namely that the integral over radial space (not over the spherical harmonics), involves the square of the function itself and not of its absolute value. However, due to the asymptotic behavior (25a), the integral (31) (as well as the one of Eq. (30)), is infinite, since the integrant goes like where a is the imaginary part of the complex momentum of the free Gamow orbital. 

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