# Polarization Transfer Rates by Isotropic Collisions between Astrophysical SiO Molecule and Electrons

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Definitions and Numerical Calculations

- –
- E being the collision energy;
- –
- ${S}_{m}$ is the SiO spin;
- –
- N is the rotational momentum of the SiO;
- –
- $j={S}_{m}+N$,
- –
- ${K}_{j}$ quantifies the angular momentum exchange between the molecular states at the time of the collision;
- –
- ${e}_{i}$ is the SiO lower electronic state and ${e}_{f}$ is the upper electronic state. In this work, ${e}_{i}$ = X ${}^{1}{\mathrm{\Sigma}}^{+}$ and ${e}_{f}$ represents the ${}^{3}\mathrm{\Pi}$, ${}^{3}\Delta $, ${}^{3}{\mathrm{\Sigma}}^{-}$ and ${}^{3}{\mathrm{\Sigma}}^{+}$ states, respectively.

## 3. Rotational Rates

## 4. Astrophysical Implications

## 5. Conclusions and Perspectives

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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## Note

1 | Derouich (2006) [7] found that collisions of the SiO in the X ${}^{1}{\mathrm{\Sigma}}^{+}$ state with the hydrogen atom in its ground state ${}^{2}S$ arise with a transfer of polarization rate of ∼ 10${}^{-10}$ cm${}^{-3}$ s${}^{-1}$ for j ≤ 8 and for the vibrational level v = 0. |

**Figure 1.**Inelastic rates ${C}^{k}$ due to isotropic collisions with electrons for 1000 K $\le T\le $ 10,000 K.

**Figure 2.**Plot, on a logarithmic scale, of the rotational elastic rates ${D}^{k}$ due to isotropic collisions of the X ${}^{1}{\mathrm{\Sigma}}^{+}$ SiO with electrons for 5 K $\le T\le $ 5000 K. All rates are similar except the case of the rate with k = 2, $j=1$ and ${j}^{\prime}$ = 2. Let us notice that for the state X ${}^{1}{\mathrm{\Sigma}}^{+}$, one has $N=j$ since ${S}_{m}=0$.

k | ${\mathit{a}}^{0}$ | ${\mathit{a}}^{1}$ | ${\mathit{a}}^{2}$ | ${\mathit{a}}^{3}$ | ${\mathit{a}}^{4}$ | |
---|---|---|---|---|---|---|

X ${}^{1}{\mathrm{\Sigma}}^{+}$ | ||||||

→${}^{3}\Pi $ | ||||||

0 | −1.5428 $\times {10}^{-11}$ | 1.7377 $\times {10}^{-14}$ | −4.1598 $\times {10}^{-18}$ | −2.5952 $\times {10}^{-22}$ | 1.0604 $\times {10}^{-25}$ | |

1 | −1.1882 $\times {10}^{-11}$ | 1.3382 $\times {10}^{-14}$ | −3.2035 $\times {10}^{-18}$ | −1.9986 $\times {10}^{-22}$ | 0.8166 $\times {10}^{-25}$ | |

2 | −0.9006 $\times {10}^{-11}$ | 1.0144 $\times {10}^{-14}$ | −2.4282 $\times {10}^{-18}$ | −1.5149 $\times {10}^{-22}$ | 0.619 $\times {10}^{-25}$ | |

X ${}^{1}{\mathrm{\Sigma}}^{+}$ | ||||||

→${}^{3}{\mathrm{\Sigma}}^{+}$ | ||||||

0 | 7.1625 $\times {10}^{-13}$ | −1.202 $\times {10}^{-15}$ | 6.5227 $\times {10}^{-19}$ | −1.4116 $\times {10}^{-22}$ | 1.0631 $\times {10}^{-26}$ | |

1 | 5.5158 $\times {10}^{-13}$ | −0.9257 $\times {10}^{-15}$ | 5.0231 $\times {10}^{-19}$ | −1.0871 $\times {10}^{-22}$ | 0.8187 $\times {10}^{-26}$ | |

2 | 4.1809 $\times {10}^{-13}$ | −0.7017 $\times {10}^{-15}$ | 3.8075 $\times {10}^{-19}$ | −0.8240 $\times {10}^{-22}$ | 0.62055 $\times {10}^{-26}$ | |

X ${}^{1}{\mathrm{\Sigma}}^{+}$ | ||||||

→${}^{3}\Delta $ | ||||||

0 | 9.8049 $\times {10}^{-13}$ | −1.7041 $\times {10}^{-15}$ | 9.5997 $\times {10}^{-19}$ | −2.1515 $\times {10}^{-22}$ | 1.6715 $\times {10}^{-26}$ | |

1 | 7.5508 $\times {10}^{-13}$ | −1.3124 $\times {10}^{-15}$ | 7.3928 $\times {10}^{-19}$ | −1.6569 $\times {10}^{-22}$ | 1.2873 $\times {10}^{-26}$ | |

2 | 5.7234 $\times {10}^{-13}$ | −0.9947 $\times {10}^{-15}$ | 5.6036 $\times {10}^{-19}$ | −1.2559 $\times {10}^{-22}$ | 0.9757 $\times {10}^{-26}$ | |

X ${}^{1}{\mathrm{\Sigma}}^{+}$ | ||||||

→${}^{3}{\mathrm{\Sigma}}^{-}$ | ||||||

0 | 2.8107 $\times {10}^{-13}$ | −4.5924 $\times {10}^{-16}$ | 2.416 $\times {10}^{-19}$ | −5.0649 $\times {10}^{-23}$ | 3.6956 $\times {10}^{-27}$ | |

1 | 2.1646 $\times {10}^{-13}$ | −3.5367 $\times {10}^{-16}$ | 1.8606 $\times {10}^{-19}$ | −3.9005 $\times {10}^{-23}$ | 2.846 $\times {10}^{-27}$ | |

2 | 1.6407 $\times {10}^{-13}$ | −2.6807 $\times {10}^{-16}$ | 1.4103 $\times {10}^{-19}$ | −2.9565 $\times {10}^{-23}$ | 2.1572 $\times {10}^{-27}$ |

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**MDPI and ACS Style**

Derouich, M.; Zaheer Ahmad, B.; Alruhaili, A.; Qutub, S.
Polarization Transfer Rates by Isotropic Collisions between Astrophysical SiO Molecule and Electrons. *Universe* **2022**, *8*, 140.
https://doi.org/10.3390/universe8030140

**AMA Style**

Derouich M, Zaheer Ahmad B, Alruhaili A, Qutub S.
Polarization Transfer Rates by Isotropic Collisions between Astrophysical SiO Molecule and Electrons. *Universe*. 2022; 8(3):140.
https://doi.org/10.3390/universe8030140

**Chicago/Turabian Style**

Derouich, Moncef, Badruddin Zaheer Ahmad, Aied Alruhaili, and Saleh Qutub.
2022. "Polarization Transfer Rates by Isotropic Collisions between Astrophysical SiO Molecule and Electrons" *Universe* 8, no. 3: 140.
https://doi.org/10.3390/universe8030140