Chapter 8, Problem 92GP

The nuclear force between two neutrons in a nucleus is described roughly by the Yukawa potential

$U(r)=-U_0\frac{r_0}{r}{e}^{-r/t_0}$,

where r is the distance between the neutrons and U₀ and r₀ (≈ 10⁻¹⁵ m) are constants. (a) Determine the force F(r). (b) What is the ratio F(3r₀)/F(r₀)? (c) Calculate this same ratio for the force between two electrically charged particles where U(r) = −C/r, with C a constant. Why is the Yukawa force referred to as a “short-range” force?