Example 3.15: Ratio of statistical weights Consider a single -particle trapped within a sphere of radius a

Example 3.15: Ratio of statistical weights Consider a single α-particle trapped within a sphere of radius a representing a nucleus. In the Coulomb region r > a the potential barrier falls off as V = +2Ze2/r; inside the sphere V = 0.

The α-particle penetrates the barrier from r = a to r =

b, b >

a, with energy E. What is the ratio of the statistical weight at r = b to that at r = a? (Answer: b2/a2)