SelfConsistent Determination of the Effective Radii of Heavy Nuclei for AlphaParticle 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. A new approach to the barrier problem is proposed based on the hypothesis that for transitions of definite typeto ground states of spherical eveneven nuclei beyond the double closed shells at Pb^{208}we might expect the intrinsic emission probability measured in single particle units, whatever its absolute magnitude, about which no assumption is made, to be proportional to the surface area of the nucleus only. The dispersion in the reduced widths inferred from the emission rates depends on the cutoff radius R=r_{0}A^{13} that is chosen and so we can define a selfconsistent potential whose radius constant r_{0} minimizes this dispersion. The "spherical" nuclei show a welldefined minimum to the dispersion at r_{0}=1.57+/0.06 fermis. The deformed nuclei have a different behavior as is expected. This selfconsistent potential is very close to that derived by Igo from an optical model analysis of alphaparticle scattering; the penetrabilities for the natural alphaparticle 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 probability on A of the form 1+∊A then the resulting minimum dispersions computed as a function of ∊ themselves show a minimum with ∊ very close to zero, thereby justifying the hypothesis in its simple form.
 Publication:

Physical Review
 Pub Date:
 April 1962
 DOI:
 10.1103/PhysRev.126.648
 Bibcode:
 1962PhRv..126..648W