Limited Applicability of the Theory of Nucleon Tunneling

Details Limited Applicability of the Theory of Nucleon Tunneling Limited Applicability of the Theory of Nucleon Tunneling

Sep 1964

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1964phrv..135.1323b&link_type=abstract

Physical Review, vol. 135, Issue 6B, pp. 1323-1337

Astronomy and Astrophysics

Astrophysics

14

Scientific paper

The assumptions made in the theory of the tunneling process of single-nucleon transfer are reviewed and their shortcomings discussed. A schematic form of a black-box treatment is systematized and assumptions made are pointed out. The reason for the agreement between results obtainable from this form and the earlier way of ascertaining quantum-mechanical corrections is discussed. Among the assumptions made is the legitimacy of neglecting terms that vanish when the ratio of the nucleon mass to the reduced mass is set equal to zero. The character of effects arising from these terms is illustrated by means of a one-dimensional model, and the associated inadequacy of dealing only with the relative motion of the heavy aggregates without including effects of motion with respect to the inertial system is pointed out. Further discussion concerns itself with the effects of the angular momentum of the transferred nucleon in the emitting nucleus and in the receiving one on the space dependence of the transfer function; the symmetrized forms of the transfer cross section; the effect of the relative velocity of the emitter and receiver nuclei on the matching of the angular momentum of the nucleon; the transition from the isotropic-transfer quantum treatment to the corresponding semiclassical one, including the double-limit situation involved in making the scattering angle and the space-decay parameter approach zero; the questions involved in the consideration of the exterior region, including the possible effect of deuteron, triton, alpha particle and other types of tentacles in configuration space; and the distinction between the nucleon configuration and wave-function assignments of shell-structure theory and the nucleon configurations and wave functions that matter more directly for the treatment of the exterior region and of single-nucleon transfer. The bearing of virtual Coulomb-excitation processes on applications of usual potential-barrier penetrability estimates for reaction-yield estimates made in astrophysics is mentioned, and it is pointed out that as the kinetic energy is decreased, the nuclear radii in ordinary estimates must be increased.

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