Response of the near-threshold resonances of the dtμ molecular ion to an effective atomic 2s--2p splitting

Abstract

For the nonrelativistic three-body Coulomb Hamiltonian, near-threshold resonances of the deuterium--tritium muonic molecular ion (dtμ) are supported by the long-range dipole coupling between degenerate atomic 2s and 2p states. We study the effect of atomic 2s--2p splitting on their positions and decay widths. Three-body complex-absorbing-potential calculations resolve additional members of the L^π=0⁺ and 1^- series. Their geometric spacing agrees with that expected from the 1/R² dipole attraction, where R is the atom--nucleus separation. To assess the effect of splitting, we scan a prescribed 2s--2p interval using an effective potential in a spin-independent, nonrelativistic Hamiltonian. This models the atomic splitting without an explicit Lamb-shift calculation. Within this model, the studied resonances lie closer to the dμ(2s)+t threshold and have smaller Coulomb decay widths than in the degenerate case. At an effective interval of 0.2eV, the seventh 1^- member lies within 2meV of this threshold with a full width of about 4meV, compared with $48$ and 15.6meV at degeneracy. These values characterize the response within the tested numerical representations. Its width decreases, but its separation from the threshold decreases more strongly. The long-range analysis attributes these shifts and width reductions to modified dipole mixing. It further suggests that atomic 2s--2p splitting may truncate the infinite accumulation of resonances predicted for degenerate atomic 2s and 2p levels.

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BibTeX RIS

BibTeX

@misc{zhang2026response,
  title = {{Response of the near-threshold resonances of the $\bmdtμ$ molecular ion to an effective atomic $2s$--$2p$ splitting}},
  author = {Yi Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11499},
  eprint = {2610.11499},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11499},
}

RIS

TY  - UNPB
TI  - Response of the near-threshold resonances of the dtμ molecular ion to an effective atomic 2s--2p splitting
AU  - Yi Zhang
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11499
UR  - https://arxiv.org/abs/2610.11499
AB  - For the nonrelativistic three-body Coulomb Hamiltonian, near-threshold resonances of the deuterium--tritium muonic molecular ion (dtμ) are supported by the long-range dipole coupling between degenerate atomic 2s and 2p states. We study the effect of atomic 2s--2p splitting on their positions and decay widths. Three-body complex-absorbing-potential calculations resolve additional members of the L^π=0^+ and 1^- series. Their geometric spacing agrees with that expected from the 1/R^2 dipole attraction, where R is the atom--nucleus separation. To assess the effect of splitting, we scan a prescribed 2s--2p interval using an effective potential in a spin-independent, nonrelativistic Hamiltonian. This models the atomic splitting without an explicit Lamb-shift calculation. Within this model, the studied resonances lie closer to the dμ(2s)+t threshold and have smaller Coulomb decay widths than in the degenerate case. At an effective interval of 0.2eV, the seventh 1^- member lies within 2meV of this threshold with a full width of about 4meV, compared with $48$ and 15.6meV at degeneracy. These values characterize the response within the tested numerical representations. Its width decreases, but its separation from the threshold decreases more strongly. The long-range analysis attributes these shifts and width reductions to modified dipole mixing. It further suggests that atomic 2s--2p splitting may truncate the infinite accumulation of resonances predicted for degenerate atomic 2s and 2p levels.
ER  -

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