Answer to Question #108337 in Quantum Mechanics for Shivi

Question

Write an expression for semi-empirical formula for binding energy of nuclei given
by Weizsacker and discuss its each term. Using this formula, calculate the binding
energy per nucleon for
235 U.

Answer 1

The semi-empirical formula for binding energy of nuclei given by Weizsacker is written below:

$$B_E=a_vA-a_sA^{2/3}-a_c\frac{Z(Z-1)}{A^{1/3}}-a_a\frac{(N-Z)^2}{A}+a_p\frac{1}{A^{1/2}},$$

where

$a_v=15.8\text{ MeV}\\ a_s=18.3\text{ MeV}\\ a_c=0.71\text{ MeV}\\ a_a=23.2\text{ MeV}\\ a_p=\pm11.2\text{ MeV}\\$

are best-fit parameters.,

$A$ - nucleon number, $N$ - neutron number, $Z -$ proton number.

The first term with subscript v is volume term.

The second term with subscript s is surface term.

The third term with subscript c is coulomb term.

The fourth term with subscript a is asymmetry term.

The fifth term with subscript p is pairing term - defines the effect of spin-coupling. It's positive with Z, N, A even, zero with A odd, negative with Z, N odd and A even.

Therefore, for ²³⁵U this will give

$$B_E=1796.1\text{ MeV}.$$