Collapse of Coulomb Bound States of Vector Bosons

Fuente: arXiv
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Autori principali: Flambaum, V. V., Tan, H. B. Tran
Natura: Preprint
Pubblicazione: 2025
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author Flambaum, V. V.
Tan, H. B. Tran
author_facet Flambaum, V. V.
Tan, H. B. Tran
contents Charged spin 1 (vector) particles behave very differently from electrons or scalars in a Coulomb field. For an infinitely heavy point-like nucleus their bound state wave functions fall to the centre, and embedding the system in a renormalisable 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 Upsilon term in the wave equations, which for the point-like nucleus is proportional to delta(r) and was ignored in the previous calculations of the energy spectrum. Several unusual effects emerge: (i) The Upsilon term supports a tower of states located mainly inside the nucleus. As R -> 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 -> 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 Upsilon term ensures its density inside the nucleus remains negative. (iv) For weak coupling, Z alpha << 1, yet with mR <Z alpha, the non-relativistic solution differs qualitatively from Schrodinger theory despite binding energies are well below m c^2; agreement is recovered only when Z alpha << mR. These phenomena highlight the distinctive and subtle behaviour of spin-1 particles in the Coulomb field.
format Preprint
id arxiv_https___arxiv_org_abs_2512_18691
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Collapse of Coulomb Bound States of Vector Bosons
Flambaum, V. V.
Tan, H. B. Tran
High Energy Physics - Phenomenology
Nuclear Theory
Atomic Physics
Charged spin 1 (vector) particles behave very differently from electrons or scalars in a Coulomb field. For an infinitely heavy point-like nucleus their bound state wave functions fall to the centre, and embedding the system in a renormalisable 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 Upsilon term in the wave equations, which for the point-like nucleus is proportional to delta(r) and was ignored in the previous calculations of the energy spectrum. Several unusual effects emerge: (i) The Upsilon term supports a tower of states located mainly inside the nucleus. As R -> 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 -> 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 Upsilon term ensures its density inside the nucleus remains negative. (iv) For weak coupling, Z alpha << 1, yet with mR <Z alpha, the non-relativistic solution differs qualitatively from Schrodinger theory despite binding energies are well below m c^2; agreement is recovered only when Z alpha << mR. These phenomena highlight the distinctive and subtle behaviour of spin-1 particles in the Coulomb field.
title Collapse of Coulomb Bound States of Vector Bosons
topic High Energy Physics - Phenomenology
Nuclear Theory
Atomic Physics
url https://arxiv.org/abs/2512.18691