Question

a) Look up the literature and tabulate the microscopic thermal neutron absorption (n,g) cross-sections for: Pb-208, Pb-206, Ca-40, Ca-48, Si-28, He-3, H-1, Eu-151 and B-10.

(b) Which ones of these are doubly magic nuclei and how do their cross-sections compare with those that are not?

Answer 1

a) The thermal neutron absorption cross sections for different elements are tabulated below.

The data is taken from NIST

Nuclei	absorption cross section (barn)
Pb - 208	0.00048
Pb - 206	0.03
Ca - 40	0.41
Ca - 48	1.09
Si - 28	0.177
He - 3	5333
H - 1	0.3326
Eu 151	9100
B - 10	3835

Out of these, the magic nuclei are : - Pb - 208, Ca -40, Ca - 48 and  Si - 28.

These molecules have very small values of absorption cross section. When a neutron is absorbed by a nucleus, the nucleus becomes highly energetic and undergoes some nuclear process. Since doubly magic nuclei are very stable, they are less probable to absorb a neutron and undergo a nuclear reaction.