distance, with a zero at $r_0\sim b/2$. This zero is nearly equivalent to the effect of a hard core of radius $r_0$. Hence, if $u(r)$ denotes the reduced radial wave function, the upper part of the spectrum evolves from the boundary condition $u(0)=0$ to $u(r_0)=0$, a very small change if $r_0\ll B$. As pointed out, e.g., in Refs. [@kolomeisky:022721; @PhysRevC.26.2381], the $\delta E_n\propto n^{-3}$ behaviour is equivalent to a constant “quantum defect”. For instance, the spectrum of peripheral S-waves excitations of Rydberg atoms is usually written as $$\label{Rydberg}
E_n=-{\hbar^2\over 2 \mu B^2}\,{1\over (n-\nu)^2}~,$$ where $B$ is the Bohr radius, $\mu$ the reduced mass, and $\nu$ defines the quantum defect. A constant $\nu$ is equivalent to $\delta E_n\propto n^{-3}$, as for the Trueman formula (\[eq:Trueman\]). Indeed, if the excitation of the inner electron core is neglected, the dynamics is dominated by the Coulomb potential $-1/r$ felt by the last electron, which becomes stronger than $-1/r$ when this electron penetrates the core. Within this model, one can vary the strength of this additional attraction from zero to its actual value, or even higher, and it has been claimed that the Zel’dovich effect can be observed in this way, especially at high $n$ 