Gamow wave function

Random Phase Approximation Calculations of Gamow-Teller /3-Strength Functions in the A = 80-100 Region with Woods-Saxon Wave Functions... 

The final state nucleus (deuterium in its ground state) in the reaction p + p —> d + e+ + z/e, has JJ = 1 +, with a predominant relative orbital angular momentum If = 0 and Sf = 1 (triplet S-state). For a maximally probable super-allowed transition, there is no change in the orbital angular momentum between the initial and final states of the nuclei. Hence for such transitions, the initial state two protons in the p + p reaction must have /j = 0. Since the protons are identical particles, Pauli principle requires S) = 0, so that the total wave-function will be antisymmetric in space and spin coordinates. Thus, we have a process Si = 0, Z = 0 >—>, S y- 1,/y- 0 >. This is a pure Gamow-... 

The understanding, interpretation and practical tools to approach the problem of resonances states in quantum chemistry and molecular physics are basically very well studied. Generally one has either (i) concentrated on the properties of the stationary time-independent scattering solution (ii) attempted to extract the Gamow wave by analytic continuation and/or (iii) considered the time-dependent problem via a suitably prepared reference function or wave-packet. In each case the analysis prompts different explanations, numerical techniques and understanding, see e.g. Ref. [15] for a review and more details. 

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. 

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