Angular Momentum Distributions in the Thomas-Fermi Model

黃振麟(Jenn-Lin Hwang)

《Chinese Journal of Physics》 1卷2期 (1963/10) Pp. 74-80

並列摘要

We reinvestigate the problem of how many electrons (protons and neutrons) of a given orbital angular momentum ιh are to be found in an atom (a neuclens) of a given atomic number Z (proton number Z or neutron number A-Z). We point out the sources of errors inherent to this problem including the arbitrariness in selecting the manner of angnlar momentum assignment, and further show that the problem is essentially equivalent to the evaluation of WKB integral if we want the exact result. The maximum energy (Eι) max of a given angular momentum state ι should be determined as an eigenvalue. In this sense the present freatment strictly considers the quantized nature of angular momentum.Two hypothetical 'models of nuclei with an average potential of the harmonic oscillator and of the square well obeying the previously reported rules of nuclear radii are treated both by an improved method and the original Fermi's method. The results are compared with the exact values to show the superiority of the new method.