1. V. Dolmatov1, A. S. Kheifets2, S. T. Manson3, P. C. Deshmukh4
Giant Autoionization Resonance Enhancement and Term-Dependence of Photoionization Time-Delay: the Mn atom
V. Dolmatov1, A. S. Kheifets2, S. T. Manson3, P. C. Deshmukh4
1University of North Alabama, Florence, AL
2The Australian National University, Canberra, Australia
3Georgia State University, Atlanta, GA
4Indian Institute of Technology, Madras, India
DAMOP-2015, Columbus, OH

2. Time-delay is a temporal delay in releasing of a photoelectron by the atom caused by elastic scattering of the photoelectron off the atomic potential barrier. In essence, it is the “scattering time-delay” defined in the Wigner-Smith scattering theory, τws. A nice tutorial on time-delay studies, both experimental and theoretical: A. Maquet, Jérémie Caillat, and Richard Taïeb: Attosecond delays in photoionization: time and quantum mechanics – J. Phys. B 47, , 2015.

3. For niℓi-photoionization, τws is defined as the energy-derivative of the phase φ(E) of a complex photoionization amplitude Tniℓi(E):
The theoretical problem, thus, reduces basically to the calculation of the photoionization amplitude - its real and imaginary parts and phase shift.

4. Tniℓi(E) = aℓi+1 Tℓi +1 (E) + aℓi -1 Tℓi -1 (E)
The dipole photoionization amplitude Tniℓi(E) of a niℓi-subshell is the weighted sum of the corresponding reduced partial amplitudes Tℓi +1 and Tℓi -1 (refer to Appendix for more details).
Tniℓi(E) = aℓi+1 Tℓi +1 (E) + aℓi -1 Tℓi -1 (E)
It is assumed that the photoelectron momentum k is parallel to the z-axis (θk = ϕk = 0) to exclude dealing with the angular dependence of the photoionization amplitude.

5. The Amplitude of Photoionization in the Random Phase Approximation with Exchange (RPAE):

6. 3p-3d Giant Autoionization Resonance in the Photoionization of Mn(3p63d54s2, 6S)
(4s1, 7S) ≈7.4 eV
4s2
(4s1, 5S) ≈ 8.6 eV
3d5
(3d4, 5D) ≈ 14.3 eV
3p → 3d ≈ 50 eV
3p6
3p6
Resonance energy ≈ 50 eV, resonance width γ ≈ 2 eV!
Suggested Review: B. Sonntag and P. Zimmermann, RPP, 55, 911, 1992

7. The 3d-photoionization cross section σ3d and photoelectron angular asymmetry parameter β3d.

8. This is a single-channel calculation accounting for only dominant 3d-f transition
Increase of the 3d-time-delay to 0.6 fs = 600 as!

9. 3d-time-delay jumps to 1300 as!
A crucial importance of accounting for a generally weaker 3d-p transition in addition to a generally dominant 3d-f transition!
3d-time-delay jumps to 1300 as!

10. e +Mn(4s1, 5S)
e +Mn(4s1,7S)
Mn(4s2, 6S)

11. CONCLUSION Financial supported from NSF and DoE is acknowledged.
The dramatic impact of the 3p → 3d resonance in Mn on the 3d- and 4s-time delay is demonstrated (τws ~ 100 – 1000 as).
Strong term-dependence of the 4s-time delay [Mn → Mn+(4s1, 5S) vs. Mn → Mn+(4s1, 7S] is unraveled.
The crucial importance of accounting for both the generally dominant 3d → f and the generally smaller 3d → p transitions in the calculation of the 3d-photoinization time delay is established.
Similar features are expected to emerge in photoionization time delays of other atoms with half-filled subshells.
Financial supported from NSF and DoE is acknowledged.

12. Appendix