26th Australian Institute of Physics Congress and the Australian and New Zealand Conference on Optics and Photonics

Algebraic origin and multichannel breakdown of singlet-triplet ordering in carbon Rydberg series.

Not scheduled

20m

Belinda Hutchinson Building (The University of Sydney )

Contributed Oral AIP | Atomic and Molecular Physics (ATMOP)

Description

Hund's first rule succeeds in ordering atomic excited term multiplets only about half the time; the alternating rule repairs this limitation by tying the singlet–triplet sign to the relation between coupled and uncoupled orbital angular momenta. This alternation can be traced to a phase in the electron-coupling algebra. Using the second-quantised factorisation of the interelectronic potential into a spin-independent direct operator and a spin-permutation-weighted exchange operator, we isolate this phase directly from the symmetry property of the Clebsch–Gordan coefficients and connect the resulting singlet–triplet gap to the Heisenberg exchange operator through a trace identity, thereby formulating a compact, contraction-level baseline against which real spectra can be tested channel by channel.
We then use this exchange-phase baseline as a diagnostic against experiment. A survey of 894 term pairs across 14 neutral atoms (NIST ASD) shows that violations of the alternating rule are systematic. We isolate neutral carbon's ’s 2s² 2p nd  ¹P/³P branch as a robust, full-series sign violator with anomalous quantum defects and non-exchange energy scaling. We implement a computational hierarchy from single-configuration atomic structure theory through multiconfiguration Hartree–Fock and close-coupling R-matrix calculations, treating carbon as a C⁺ target plus a Rydberg electron. We show that compact neutral-atom correlations and static orbital relaxation are insufficient to invert the sign; balanced target-channel polarisation and short-range dynamic correlations in the close-coupling treatment are what is needed to recover the observed inversion.
The result is a mechanism-resolved decomposition that separates the exchange-phase baseline fixed by angular-momentum coupling from the dynamic correlation and channel coupling acting on top of it. This framework may act as a template for diagnosing anomalous singlet-triplet orderings, including inverted-gap phenomena of active interest in molecular emitter design.