Wigner time delay in photodetachment of Tm\$^{\mathrm{\mathbf{-}}}$and in photoionization of Yb: A comparative study.*

Preliminary studies of Wigner time delay [1] in photodetachment spectra of negative ions have been reported [2]. Photodetachment time delay for some dipole channels of Tm$^{\mathrm{-}}$ and of Cl$^{\mathrm{-}}$ were calculated using relativistic random phase approximation (RRPA) [3,4]. Comparisons between photodetachment time delay of Cl$^{\mathrm{-}}$ and photoionization time delay of Ar were made. We investigate the photodetachment time delay for all three relativistically split nd$\to \varepsilon $f channels of Tm$^{\mathrm{-\thinspace }}$and for nd$\to \varepsilon $f channels of Yb (isoelectronic to Tm$^{\mathrm{-}})$ using RRPA. We study the effect of the shape resonance, brought about by the centrifugal barrier potential [5], on photodetachment time delay. A negative ion is a good laboratory for studying the effects of shape resonances on time delay since the phase is unaffected by the Coulomb component. [1] E. P. Wigner, \textit{Phys. Rev.} \textbf{98,} 145 (1955) [2] S. Saha, \textit{et al}, \textit{BAPS }\textbf{61}(8), 53 (2016) \quad [3] W. R. Johnson, C. D. Lin, \textit{Phys. Rev. A} \textbf{20,} 964 (1979) [4] W. R. Johnson, \textit{et al}, \textit{Phys. Rev. A} \textbf{25,} 337 (1982) [5] A. R. P. Rau and U. Fano, \textit{Phys. Rev.} \textbf{167,} 7 (1968).