Gamow factor

The matrix elements in angle brackets contain nuclear factors and (in the case of charged particles) the Coulomb barrier penetration probabilities or Gamow factors, originally calculated in the theory of a-decay, which can be roughly estimated as follows (Fig. 2.7). 

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... 

Gamow factor, which increases with increasing energy. The product of these two terms produces a peak in the overlap region of these two functions called the Gamow peak (Fig. 12.9). This peak occurs at an energy E0 = (bkT/2)2 3. 

The thermally averaged reaction rate per pair is, utilizing the astrophysical S-factor and the energy dependence of the Gamow-factor ... 

Note that the present Gamow factor gives only the order of the transmission probability and is as good as the barrier is higher and shrink, i.e.. 

It is difficult theoretically to calculate a tunnelling barrier of Gamow type (not the same as activation barrier) from first principles. This paper summarizes methods that employ molecular orbital (MO) approaches to calculate the "electronic factor" which accounts for the transmittance in the forbidden region. The electronic factor will be structure dependent and there is no reason why it should be isotropic in space. 

S. Towner, "A Mass Dependence in Hindrance Factors for Favoured Gamow-Teller Transitions", to be published. 

This so-called orthodoxy was formulated with the express purpose of discouraging wave-mechanical interpretations of quantum phenomena, which started to appear (Gamow Iwanenko, 1926) within the same year as Schrodinger s papers. As an alternative to the particle theory quantum objects are defined here as made up of waves, with internal structure described by a parameter of the form 0 = exp 2Trip/h), where p is the phase (gauge) factor, first identified by Schrodinger (1922), and which links the wave structure of an electron... 

Gamow(1928) and independently Condon and Gurney(1928,1929) have shown that such a penetration of an a particle through the potential harrier is possible in quantum mechanics. The mechanism is called tunneling. One can define a penetration factor (penetrability) P, which is the ratio of emergent and incident intensities. A detailed quantum-mechanical approximate theory gives the following expression for the penetration factor ... 

If the barrier is robust, as it is for HI fusion, Wentzel-Kramers-Brillouin (WKB) logic can be used to generate the transmission coefficient (Gamow penetration factor) as a function of the energy of relative motion s (as it is for spontaneous alpha-decay). 

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