Solving Quantum Mechanical Potential Barrier Problem

[Pilean]

Hi!
I'm struggeling with a quantum mechanical problem.

Homework Statement

An alpha-particle is "trapped" inside a uraniumcore, and the potential is simplified to
0 for R₂ < r
V₀ for R₁<= r <= R₂
0 for 0<= r < R₁

I have calculated the transmission coefficient T = 1/(1+V₀²/(4E(V₀-E))*sin²(sqrt(2m(V₀-E)/hbar*(R₁-R₂)

I am now supposed to show that for k*dR >> 1, we have
T ~ K(E)*exp(-2k*dR)
Where dR = R₂-R₁
and k = sqrt(2m(V₀-E)/hbar
And tell what K(E) is...

I have tried to use that sinx = (exp(ix)-exp(-ix))/2i, but it won't turn into the right expression..

A small additional question: For a infinite potential, is there any possibility for tunneling into this area? After what I understand from the infinite square well the probability for the particle to be in such a potential is zero?

Hope for some guidence on where to start :)

 

[sgd37]

tell me is V₀ > E if so then it should be sinh not sin

 

[Pilean]

You are totally correct! Thanks!