​The elastic scattering process π^-p → π^-p may be treated as a hard sphere scattering. The mass of π^-, m_π ≃ 1/6 m_p. where m_p ≃ 938 MeV/c²is the mass of the proton. The total scattering cross-section is closest to​

Correct option is C

Solution:
​The masses of π- and p are approximately mₚ/6 and mₚ, respectively. If we estimate the system as a hard sphere, its diameter might be roughly approximated by the sum of the radii of π- and p,

which can be approximated as inversely proportional to the cubic root of their masses.

Let's say that : 

​where m₀ and r₀ are the mass and radius of a proton. Then the 'hard sphere' radius would be: 

Taking r₀≃1fm, R≃1.5fm, and the diameter d is therefore ≃ 3 fm. Then the total cross-section would be:

σ≃πd²≃π(3fm)²≃28fm² = 0.28 barns

The nearest matching option is 0.1 barns.