Barrier penetration in spontaneous symmetry breaking

Question

In spontaneous symmetry breaking discussion in Weinberg Chapter 19 section 19.1, he says that the off-diagonal elements between two vacua ($|VAC, +> \pm |VAC->$) is suppressed by the factor of $\exp({-C\mathcal{V}})$. For a scalar field ($-\frac{1}{2}(\partial \phi)^2 - V(\phi)$) theory by analogy to wave mechanical problem of barrier penetration we have $C = \int_{-\bar{\phi}}^{\bar{\phi}} \sqrt{2V(\phi)} d\phi$. I am trying to understand how to get this. Please let me know if you know how to obtain this mathematically.