Question

Compute the expected shell-model quadrupole moment of 209Bi () and compare with the experimental value, - 0.37 b

Answer 1

0.22 b

Step-by-step explanation:

Quadrupole moment of the nucleon is,

`Q=-(2j-1)/(2(j+1))(3)/(5)R^(2)`

And also,

`R^(2)=R^(2) _(0)A^{(2)/(3) }`

And,
`R _(0)=1.2* 10^(-15)m`

Now,

`Q=-(2j-1)/(2(j+1))(3)/(5)R^(2) _(0)A^{(2)/(3) }`

For Bismuth
`j=(9)/(2)` and A is 209.

`Q=-(2(9)/(2) -1)/(2((9)/(2) +1))(3)/(5)(1.2* 10^(-15)) ^(2)(209)^{(2)/(3) }\\Q=0.628* 35.28* 10^(-30) \\Q=22.15* 10^(-30) m^(2) \\Q=0.2215* 10^(-28) m^(2) \\Q=0.22 barn`

Therefore, the expected value of quadrupole is 0.22 b which is quite related with experimental value which is 0.37 b