# Photoelectron Angular Distributions of Nonresonant Two-Photon Atomic Ionization Near Nonlinear Cooper Minima

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## Abstract

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## 1. Introduction

## 2. Theoretical Background

## 3. Results and Discussions

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of possible electric dipole ionization pathways for two-photon ionization of a $1s$ (

**left**) and $2{p}_{1/2}$ (

**right**) electrons of neutral magnesium. The possible electric dipole ionization pathways in the single-active-electron picture are represented by red arrows. At the nonlinear Cooper minimum, the ionization pathways with highest angular momentum (right-most pathways) have zero contribution to the process. This has a significant impact upon all physical observables associated with the process.

**Figure 2.**Two-photon ionization of $1s$ (

**left**) and $2{p}_{1/2}$ (

**right**) electrons of neutral magnesium. Local minima in the total ionization cross section (first row) can be clearly seen. These so called nonlinear Cooper minima arise due to a zero contribution from the otherwise dominant ionization channel. The minima are even more strongly imprinted in the photoelectron angular distributions both for ionization of magnesium by linearly (second row) as well as circularly (last row) polarized light.

**Figure 3.**Photoelectron angular distributions of two-photon ionization of $1s$ (

**left**) and $2{p}_{1/2}$ (

**right**) electrons of neutral magnesium atoms by linearly polarized light. The distributions were normalized to the total cross section. For ionization of each shell, distributions corresponding to three different photon energies are presented. Incident photon energy matching either the nonlinear Cooper minimum in solid black (1.288 keV and 55.88 eV for ionization of $1s$ and $2{p}_{1/2}$ electrons, respectively), an intermediate level resonance ($2{p}_{1/2}$ and $3d$ for ionization of $1s$ and $2{p}_{1/2}$ electrons, respectively) in long-dashed green (1.256 keV and 55.835 eV) or an energy, which does not match either extrema in short-dashed orange (1.260 keV and 54.50 eV). From the plot, it can be clearly seen that the photoelectron angular distributions at the nonlinear Cooper minima are always distinct.

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**MDPI and ACS Style**

Hofbrucker, J.; Eiri, L.; Volotka, A.V.; Fritzsche, S.
Photoelectron Angular Distributions of Nonresonant Two-Photon Atomic Ionization Near Nonlinear Cooper Minima. *Atoms* **2020**, *8*, 54.
https://doi.org/10.3390/atoms8030054

**AMA Style**

Hofbrucker J, Eiri L, Volotka AV, Fritzsche S.
Photoelectron Angular Distributions of Nonresonant Two-Photon Atomic Ionization Near Nonlinear Cooper Minima. *Atoms*. 2020; 8(3):54.
https://doi.org/10.3390/atoms8030054

**Chicago/Turabian Style**

Hofbrucker, Jiri, Latifeh Eiri, Andrey V. Volotka, and Stephan Fritzsche.
2020. "Photoelectron Angular Distributions of Nonresonant Two-Photon Atomic Ionization Near Nonlinear Cooper Minima" *Atoms* 8, no. 3: 54.
https://doi.org/10.3390/atoms8030054