the Trueman formula (\[eq:Trueman\]) can be recovered form Eq. (\[eq:basiceq\]), as shown in [@alb]. The behaviour of the first $n$S levels is displayed in Fig. \[Fig2\], for $a$ increasing from this limit: a sharp changes is clearly seen near $1/a =0$, beautifully illustrating the Zel’dovich effect.

A comprehensive analytic treatment of the Zel’dovich effect has been given by Kok et al. [@PhysRevC.26.2381] using a delta-shell interaction $v(r)\propto -\delta(r-R)$, both for S-waves and higher waves ($\ell>0$).

Rearrangement with square wells {#se:simplemod}
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Model
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The patterns of energy shifts experienced by exotic atoms when the strength of nuclear potential increases can be studied in a simplified model where the three-dimensional Coulomb interaction is replaced by a one-dimensional square well supplemented by a narrow square well in the middle: the odd-state sector has the same type of rearrangement as the exotic atoms, while the even sector shows a new type of rearrangement. The effect of symmetry breaking can be studied by moving the attractive spike aside from the middle.

The potential, shown in Fig. \[DW1D\], reads $$\label{double-well}
V(x)=-V_1 \theta(R_1^2-x^2) -V_2\, \theta(R_2^2-x^2)~,$$ with value $-V_1-V_2$ for $0<|x|<R_1$, and $-V_2$ for $R_1<|x|<R_2$ and 0 for $|x|>R_2$, see Fig. \[DW1D\]. Slightly simpler would be the 