quantum mechanics - Doubt in a certain equation of a research paper

In the given paper, I am stuck at equation (7). The equation that I am trying to solve for particle outside the well is : (1/g)(g'') + (1/(rg))*g' - (k_o)^2 = 0 where g = Radial wave function. r = Distance from origin.

The solution I arrived at is : AJ_0(ik_or) + BY_0(ik_or) where J ,Y are Bessel functions of first kind of order zero & second kind of order zero respectively.

My queries are : 1.) How can I reduce the solution in the form of equation (7) , i.e. , Psi = Ae^(-k_or) / (r^0.5) ?

2.) Am I solving the correct differential equation?

Link to research paper: abstract pdf

Relevant equations from this paper: