Angular Momentum Distributions in the Atomic Nuclei

黃振麟(Jenn-Lin Hwang) ； 洪吉成(Jyi-Cherng Horng)

《Chinese Journal of Physics》 2卷2期 (1964/10) Pp. 80-83

並列摘要

The problem of how many protons (neutrons) of a given orbital angular momentum ln 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 reproduce 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.