Self-Consistent Determination of the Effective Radii of Heavy Nuclei for Alpha-Particle Emission

Abstract

In attempts to use the absolute rate of natural alphaparticle decay to determine the density of- alpha particles on the nuclear surface'' the penetrability of the effective barrier surrounding the nucleus plays a dominating role. An approach to the barrier problem is proposed based on the hypothesis that for transitions of definite type---to ground states of spherical even-even nuclei beyond the double-closed shells at Pb/sup 208/---the intrinsic emisslon probability measured in single particle units, whatever its absolute magnitude, about which no assumption is made, might be expected to be proportional only to the surface area of the nucleus. The dispersion in the reduced widths inferred from the emission rates depends on the cut-off radius R = r/sup 0/A/sup 1/2/ that is chosen, so a self-consistent potential can be defined whose radius constant r/ sub 0/ minimizes this dispersion. The spherical'' nuclei show a well-defined minimum to the dispersion at r/sub 0/ = 1.57 plus or minus 0.06 fermis. The deformed nuclei have a different behavior, as is expected. This self-consistent potential is very close to that derived from an optical model analysis of alpha- particle scattering; the more » penetrabili:ies for the natural alpha-particle emitters calculated with the two potentials agree to within a factor of about 2. it is shown that if the hypothesis is modified to allow a smooth dependence of the intrinsic emission proba bility on A of the form 1 + epsilon A then the resuiting mlnimum dispersions computed as a function of epsilon themselves show a minimum with epsilon very close to zero, thereby justifying the hypothesis in its simple form. (auth) « less