Gamow formula

A theoretical model of the low-temperature decay of etr in MTHF discovered in ref. 30 was suggested in ref. 31. According to this model, the disappearance of et in y-irradiated MTHF at 77 K is due to electron tunneling from a trap to a hole centre. The form of the potential barrier for electron tunneling used in ref. 31 to analyze the curves of the decay of etr is represented schematically in Fig. 9(a). To evaluate the probability of tunneling per unit of time, the Gamow formula... 

Gamma rays cf. capture, neutron capture, etc., Gammastrahlen, s. auch Einfang, Neutroneneinfang, usw. 32, 97-Gamow formula, GAMOWsche Formel 16, 70, 74, 117, 118. 

This form of the cross section is the extrapolation of the original Gamow formula,... 

Based on Gamow s investigations and the results of cross-section measurements done in the early 1940s mainly for the four most important reactions, D(d, n) He, D(d, p)T, D(t, n) He and He(d, p) He, two approximate representations of the fusion cross sections have been proposed and widely used ever since. One of these representations, which is also listed in the NRL Plasma formulary (Huba 2009), was derived by Duane (1972) and the other by Peres (1979). Duane s cross sections pose particular difficulties if they are extrapolated to energies below about 20 keV because of the unphysical parameterization of the penetrabilities that was used. In general, both approximations as well as the corresponding parameterizations for the Maxwellian reactivity (cry) (where g is the cross section and v is the speed) calculated by Hively (1977, 1983) (on the basis of Duane s cross-section formula) and by Peres (1979) need to be improved (Bosch and Halle 1992) mainly for two reasons ... 

The theoretical Gamow-Condon-Gurney formula (O Eq. (2.65), Ghap. 2) describes the alpha decay constant as a function of the alpha-energy (or rather the Q-value of the alpha decay), as well as the nuclear radius and the atomic number of the daughter. 

The Gamow-Condon-Gurney formula only applies when the alpha particle is emitted with zero angular momentum. The probability for alpha decay taking away angular momentum is considerably smaller (see Eq. (2.68) and Table 2.8 in Ghap. 2). 

The description of a sub-barrier transition with the help of Gamow s formula is not rigorous for the process under consideration. We have used this formula only to estimate the orders of magnitude and to analyze the problem qualitatively (the results of this analysis coincide with conclusions obtained by a more rigorous method). A more strict treatment of the problem requires the knowledge of wave functions and Vg for an electron in the initial and the final states and the ape of potential of the interaction between an electron situated near A and the ion B (V ). This interaction in the long run results in the transition or the electron from A to B. The transition probability is proportional to the resonance integral... 

Earlier, on the basis of estimates obtained with the help of Gamow s formula, we have concluded that the probability of electron transfer for typical parameters is close to unity in many redox reactions provided, of course, that the Franck-Condon conditions are satisfied. The same result was also obtained by a more rigorous analysis of several specific reactions for which the wave functions and the interaction potentials were calculated quite reliably. 

In this case the exponent in Gamow s formula vanishes and the transition probability acquires the maximum value equal to unity. Of course, the main contribution is made by particles having nearly equal energies E > E lying in the interval of the order of kT. 

---