Angular Momentum Distributions in the Atomic Nuclei

The problem of how many protons (neutrons) of a given orbital angular mo-mentum
Itr are to be found in a nucleus of a given proton number Z (neutron
number N) is reinvestigated by means of the improved Thomas-Fermi method.
Three kinds of nuclear models are calculated: The types of potentials chosen arc
(i) square well potential, (ii)-the Green™s potential, and (iii) the Green™s potential
plus 45 times the Thomas-Frenkel spin orbit term. The parameters involved in the
potentials are adopted from the paper of Hwang and Yang, which may exactly re-produce
the nuclear radii, trends of binding energies, and location of 3s and 4s
maxima in the neutron scattering cross section. The eigenvalues calculated by Green
are used to simplify the procedure of calculation. The results are then compared
with the empirical data compiled by Klinkenbeig. For the last type of potential,
the calculation is almost perfectly exact. The first appearance of particles of the
next higher angular momentum is almost exact for each model. The puzzle in the
Yang™s treatment of the first appearance problem is then solved. The crigin of the
appearance of magic numbers in the Yang s calculation is explained in the light of
the present theory.