Charged spin-1 (vector) particles behave very differently from electrons or scalars in a Coulomb field. For an infinitely heavy “pointlike” nucleus, their bound-state wave functions “fall to the center,” and embedding the system in a renormalizable electroweak-type theory does not remedy this short-distance pathology. We therefore solve the pure Coulomb problem for a finite nuclear radius $R$ and recover the point-nucleus limit by letting $R\to 0$. This approach allows us to include the crucial $\mathrm{\Upsilon }$-term in the wave equations, which for the pointlike nucleus is proportional to $\delta (r)$ and was ignored in the previous calculations of the energy spectrum. Several unusual effects emerge: (i) The $\mathrm{\Upsilon }$-term supports a tower of states located mainly inside the nucleus. As $R\to 0$ their number diverges, most lying in the negative-energy continuum (energy $\epsilon <-m{c}^2$). They trigger vacuum breakdown—particle-antiparticle pair creation that ultimately screens the nuclear charge. (ii) Ordinary Sommerfeld-like states (with binding energy smaller $m{c}^2$) persist, but a finite fraction of each wave function leaks into the nucleus, even as $R\to 0$. (iii) Charge density of a negatively charged vector particle changes sign in a vicinity of the nucleus and becomes positive charge density, whereas the $\mathrm{\Upsilon }$-term ensures its density inside the nucleus remains negative. (iv) For weak coupling, $Z\alpha \ll 1$, yet with $mR<Z\alpha$, the “nonrelativistic” solution differs qualitatively from Schrödinger theory despite binding energies that are well below $m{c}^2$; agreement is recovered only when $Z\alpha \ll mR$. These phenomena highlight the distinctive and subtle behavior of spin-1 particles in the Coulomb field.

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• Electroweak interaction
• Particle interactions
• W & Z bosons