# Spin-Polarized Photoelectron Fluxes from Fullerene Anions

## Abstract

**:**

## 1. Introduction

## 2. Review of Theory

#### 2.1. Cherepkov’S Theory of Spin-Polarized Photoelectron Fluxes from Atoms

#### 2.2. Modeling Fullerene Anion Photodetachment

## 3. Results and Discussion

## 4. Conclusions

## Funding

## Conflicts of Interest

## Appendix A. Comparison of Calculated Data Obtained with the Use of U_{0} = 0.302 and 0.347 a.u.

**Figure A1.**Calculated data for a C${}_{60}^{-}\left(2p\right)$ anion obtained with the use of the depths ${U}_{0}=0.302$ a.u. (dashed lines) and $0.347$ (solid lines) a.u. for the ${U}_{\mathrm{C}}\left(r\right)$ pseudo-potential, Equation (9), as marked in the figure. (

**a**) The ${P}_{2p}\left(r\right)$ radial part of the wavefunction of the attached $2p$ electron. (

**b**–

**e**) Calculated, without account for polarizability of C${}_{60}$, ${\sigma}_{2p\to s}$ and ${\sigma}_{2p\to d}$ photodetachment cross sections, ${\beta}_{2p}$ photoelectron angular-asymmetry parameter, ${\gamma}_{1}$ spin-polarization parameter and the ${P}_{j=\frac{1}{2}}$ angle-integrated degree of photoelectron spin polarization. (

**f**–

**i**) The same as (

**b**–

**e**) but with account for polarizability of C${}_{60}$.

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**Figure 1.**Calculated ${P}_{1s}^{\mathrm{H}}\left(r\right)$ and ${P}_{1s}^{\mathrm{He}}\left(r\right)$ radial functions of the encapsulated H and He atoms, as well as the ${P}_{2p}\left(r\right)$ radial function of the attached $2p$-electron in the C${}_{60}^{-}\left(2p\right)$, H@C${}_{60}^{-}\left(2p\right)$ and He@C${}_{60}^{-}\left(2p\right)$ fullerene anions, as marked. Note: The ${P}_{2p}\left(r\right)$ functions in these anions are practically indistinguishable from one another. Vertical dotted lines mark the boundaries of the C${}_{60}$ shell.

**Figure 2.**Partial ${\sigma}_{2p\to s}$ and ${\sigma}_{2p\to d}$ photodetachment cross sections of (

**a**) C${}_{60}^{-}\left(2p\right)$, (

**b**) H@C${}_{60}^{-}\left(2p\right)$ and (

**c**) He@C${}_{60}^{-}\left(2p\right)$ calculated without account ($\alpha =0$) and with account ($\alpha \ne 0$) for polarization of the fullerene anions by the outgoing photoelectron, as marked. Inserts: ${\sigma}_{2p\to s}$ and ${\sigma}_{2p\to d}$ plotted on an extended k-scale, as marked.

**Figure 3.**The angle-integrated degree of photoelectron spin polarization, ${P}_{j=\frac{1}{2}}$, upon photodetachment of the fullerene anions calculated without account ($\alpha =0$) and with account ($\alpha \ne 0$) for polarization of the C${}_{60}$ cage by the outgoing photoelectron, as marked. (

**a**) ${P}_{j=\frac{1}{2}}$ for C${}_{60}^{-}\left(2p\right)$. (

**b**) ${P}_{j=\frac{1}{2}}$ for H@C${}_{60}^{-}\left(2p\right)$. (

**c**) ${P}_{j=\frac{1}{2}}$ for He@C${}_{60}^{-}\left(2p\right)$. (

**d**) Calculated ${P}_{j=\frac{1}{2}}$s for C${}_{60}^{-}\left(2p\right)$, H@C${}_{60}^{-}\left(2p\right)$ and He@C${}_{60}^{-}\left(2p\right)$ graphed on the same plot to ease the comparison between them.

**Figure 4.**Calculated ${\gamma}_{1}$ and $\beta $ photoelectron angular-asymmetry parameters upon $2p$-photodetachment of (

**a**) C${}_{60}^{-}\left(2p\right)$, (

**b**) H@C${}_{60}^{-}\left(2p\right)$ and (

**c**) He@C${}_{60}^{-}\left(2p\right)$, as marked. Labels: ${\gamma}_{1}$/${\gamma}_{1}^{*}$ and $\beta $/${\beta}^{*}$ are calculated data without/with account for polarizability of C${}_{60}$, respectively. (

**d**) Calculated ${\gamma}_{1}^{*}$ for C${}_{60}^{-}\left(2p\right)$, H@C${}_{60}^{-}\left(2p\right)$ and He@C${}_{60}^{-}\left(2p\right)$ graphed on the same plot to ease the comparison between them.

**Figure 5.**The angle-dependent degree of spin-polarization of photoelectron fluxes, ${P}_{j=\frac{1}{2}}\left(\theta \right)$, upon photodetachment of (

**a**) C${}_{60}^{-}\left(2p\right)$, (

**b**) H@C${}_{60}^{-}\left(2p\right)$ and (

**c**) He@C${}_{60}^{-}\left(2p\right)$ calculated at $k=0.485$ a.u. without account ($\alpha =0$) and with account ($\alpha \ne 0$) for polarization of the fullerene cage by the outgoing photoelectron, as marked.

**Figure 6.**The angle-dependent degree of spin-polarization of the photoelectron fluxes, ${P}_{j=\frac{1}{2}}\left(\theta \right)$, upon photodetachment of (

**a**) C${}_{60}^{-}\left(2p\right)$, (

**b**) H@C${}_{60}^{-}\left(2p\right)$ and (

**c**) He@C${}_{60}^{-}\left(2p\right)$ calculated at $k=0.3$ a.u. without account ($\alpha =0$) and with account ($\alpha \ne 0$) for polarization of the fullerene cage by the outgoing photoelectron, as marked.

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Dolmatov, V.K.
Spin-Polarized Photoelectron Fluxes from Fullerene Anions. *Atoms* **2020**, *8*, 65.
https://doi.org/10.3390/atoms8040065

**AMA Style**

Dolmatov VK.
Spin-Polarized Photoelectron Fluxes from Fullerene Anions. *Atoms*. 2020; 8(4):65.
https://doi.org/10.3390/atoms8040065

**Chicago/Turabian Style**

Dolmatov, Valeriy K.
2020. "Spin-Polarized Photoelectron Fluxes from Fullerene Anions" *Atoms* 8, no. 4: 65.
https://doi.org/10.3390/atoms8040065