The angle-resolved Wigner time delay for Ar $3s$ photoionization has been investigated in the vicinity of the inner-shell $2p$ thresholds (approximately 250 eV) using the relativistic random-phase approximation with and without core relaxation (RRPA-R and RRPA, respectively). The calculations include quadrupole transitions, which become significant at emission angles near ${90}^{\circ },$ where dipole contributions are small. We observe distinct qualitative and quantitative features in the Ar $3s$ time delay across the $2p$ ionization thresholds, owing to interchannel coupling between the $3s$ and $2p$ photoionization channels. While the RRPA and RRPA-R results agree well below the $2p_{3/2}$ threshold and well above the $2p_{1/2}$ threshold, they diverge significantly immediately above the $2p_{1/2}$ threshold and remain different for approximately 20 eV over a range of emission angles. Specifically, at $\theta =0^{\circ }, {45}^{\circ }$, and ${60}^{\circ }$, RRPA-R predicts a positive time delay that is absent in the RRPA result. These differences demonstrate that core relaxation can qualitatively alter the Ar $3s$ time delay in the threshold region, where the weak $3s$ channel is strongly coupled to the newly opened $2p$ continua, thereby identifying energy and angular regions in which relaxation effects are expected to be most pronounced. At $\theta ={90}^{\circ }$, the delay pattern reverses within each method following the opening of the $2p_{1/2}$ channel because the dominant no-spin-flip dipole contribution vanishes due to angular-momentum geometry. The two calculations converge to nearly identical results approximately 20–30 eV beyond the threshold region. This convergence indicates that the effect of ionic-core relaxation diminishes as the interchannel-coupling contribution weakens. This study extends previous work on the Ar $3s$ Cooper-minimum region to the distinct $2p$-threshold regime, where ionic-core relaxation modifies the $2p-3s$ interchannel-coupling contribution and nondipole terms produce pronounced angular structure in the Wigner delay.

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• Light-matter interaction
• Photoemission
• Ultrafast phenomena