 Solution

Use the relative coordinate and reduced massTake $V=-V_0$ inside, $V=0$ outside, and $E=-B$. For $V_0>B>0$, define inverse lengthsThe radial equation becomes $u^{\prime \prime }+k^{2}u=0$ inside and $u^{\prime \prime }-{\kappa }^{2}u=0$ outside. Finiteness of the full wavefunction at the origin imposes $u(0)=0$; normalizability excludes the growing exterior exponential. HenceContinuity of $u$ was built in. Continuity of its derivative at the finite step givesFor the nodeless ground state, $\pi /2<kb<\pi$ selects the first branch. Higher roots would correspond to different wells with more bound states. Normalization is

For the requested weak-binding estimate, $B/V_0\to 0$ makes $\kappa /k\to 0$. On the first branch $kb\to \pi /2$, and $k^2\simeq 2\mu c^2{V}_0/(\hslash c{)}^2$. The leading threshold estimate isThis is the zero-binding threshold of a spherical square well, so nonzero positive binding needs a depth above it. Corrections start at order $\sqrt{B}$, not just at order $B$: setting $kb=\pi /2+ϵ$ gives $ϵ\simeq \kappa b/(\pi /2)$ and

The actual numbers permit an accuracy check: $\kappa =0.231608{\mathrm{fm}}^{-1}$ and $\kappa b=0.486377$ are not extremely small. Retaining the exterior decay, solveThis gives $x=kb=1.830503$, and the full square-well result isNeglecting $B$ only in the interior kinetic relation while retaining the measured exterior decay instead estimates $V_0\simeq 31.50\mathrm{MeV}$. These approximations should be identified: 23.2 MeV is the leading $B\to 0$ threshold, whereas matching the supplied nonzero binding requires a boundary phase shift and a deeper well.