Question

(c) Discuss the phenomenological occurrence of peaks in the Binding energy per nucleon diagram (B/A vs A) showing the existing of Shell like nucleon configuration in a nucleus. (5 Marks) (d) The lowest energy levels in the Shell Model, in order of increasing energy, are 1s, 1P3/2 , 1P1/2, 1d52, 281/2, 1d 3/2, 1fj. (1) What are the possible values of j for the 1f levels? (ii) What is the value of j for the lowest 1f level? Justify your answer.

Answer 1

(c) the peaks in the binding Energy diagram occurs for locally more stable nucleus i.e., two nucleus on either side of the peak are less stable.This suggest a structure of nucleus which is shell-like ,since some configuration of nucleon is giving a stable nucleus but adding one more nucleon is making the nucleus.This behavior is really of a shell-structure.For example odd-A nuclei are unstable while even-A nuclei are stable.

(d)(i)for 1f level ,l=3 and the value of j ranges from j=l+1/2 to l-1/2,so possible value of j is 7/2 and 5/2

(ii)value of j for lowest level is 7/2 .The reason for this is that The spin-orbit interaction energy is negative.