# Low-Energy Elastic Electron Scattering from Helium Atoms

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Methods

#### 2.1. Relativistic Polarized Orbital Approach

#### 2.2. Nonrelativistic B-Spline R-Matrix with Pseudostates

## 3. Results and Discussion

#### 3.1. Scattering Phase

#### 3.2. Scattering Length

`FARM`, but start to deviate from the latter and the almost straight line when k is smaller than about 0.07. This issue could likely be addressed by changing the default numerical parameters, but our goal is to illustrate that care is required when using these general codes in such relatively extreme situations.

#### 3.3. Cross Sections

**Figure 2.**Angle-integrated elastic and momentum-transfer (momtrans) cross section for e-He scattering. The lines show the present results obtained with RPO and the STGF asymptotic code for the BSR-498 model. The symbols show the same results for the FARM asymptotic package and the CCC results of Fursa and Bray [10] taken from the LXCat database [31].

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

RPO | Relativistic Polarized Orbital |

BSR | B-Spline R-matrix |

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**Figure 1.**Extraction of the scattering length. Due to the limitations of the asymptotic FARM and STGF codes (see text for details), the smallest k-value in the BSR-498 calculation is 0.01, while the RPO code allows the calculation at zero collision energy.

k | Nesbet [9] | RMPS [11] | Wan et al. [1] | Present RPO | Present BSR-498 |
---|---|---|---|---|---|

0.1 | −0.1282 | −0.1260 | −0.1281 | −0.1262 | −0.1286 |

0.2 | −0.2655 | −0.2607 | −0.2650 | −0.2614 | −0.2560 |

0.3 | −0.4021 | −0.3979 | −0.4030 | −0.3978 | −0.4043 |

0.4 | −0.5388 | −0.5380 | −0.5319 | −0.5398 | |

0.5 | −0.6684 | −0.6617 | −0.6678 | −0.6609 | −0.6699 |

0.6 | −0.7930 | −0.7848 | −0.7907 | −0.7835 | −0.7932 |

0.7 | −0.9067 | −0.9062 | −0.8990 | −0.9088 | |

0.8 | −1.0155 | −1.0085 | −1.103 | −1.0069 | −1.0162 |

0.9 | −1.1163 | −1.1077 | −1.112 | −1.1071 | −1.1151 |

1.0 | −1.2056 | −1.202 | −1.1998 | −1.2055 | |

1.1 | −1.2848 | −1.2789 | −1.291 | −1.2854 | −1.2863 |

k | Nesbet [9] | RMPS [11] | Wan et al. [1] | Present RPO | Present BSR-498 |
---|---|---|---|---|---|

0.1 | 0.00308 | 0.0026 | 0.003029 | 0.00304 | 0.00305 |

0.2 | 0.01311 | 0.0129 | 0.01269 | 0.01264 | 0.01261 |

0.3 | 0.03063 | 0.0306 | 0.02964 | 0.02944 | 0.02945 |

0.4 | 0.05519 | 0.05390 | 0.05348 | 0.05352 | |

0.5 | 0.08605 | 0.0880 | 0.08449 | 0.08380 | 0.08386 |

0.6 | 0.1209 | 0.1244 | 0.1209 | 0.11856 | 0.11865 |

0.7 | 0.1588 | 0.1588 | 0.15535 | 0.15556 | |

0.8 | 0.1960 | 0.2000 | 0.1960 | 0.19175 | 0.19211 |

0.9 | 0.2305 | 0.2349 | 0.2305 | 0.22576 | 0.22657 |

1.0 | 0.2626 | 0.2626 | 0.25608 | 0.25772 | |

1.1 | 0.2932 | 0.2934 | 0.2932 | 0.28211 | 0.28524 |

k | Nesbet [9] | Wan et al. [1] | Present RPO | Present BSR-498 |
---|---|---|---|---|

0.1 | 0.0004 | 0.0004693 | 0.00042 | 0.00079 |

0.2 | 0.0017 | 0.001658 | 0.00165 | 0.00178 |

0.3 | 0.0037 | 0.003658 | 0.00367 | 0.00366 |

0.4 | 0.0066 | 0.006497 | 0.00650 | 0.00651 |

0.5 | 0.0104 | 0.01006 | 0.01017 | 0.01014 |

0.6 | 0.0149 | 0.01448 | 0.01471 | 0.01462 |

0.7 | 0.0203 | 0.01970 | 0.02010 | 0.02002 |

0.8 | 0.0265 | 0.02567 | 0.02630 | 0.02629 |

0.9 | 0.0335 | 0.0323 | 0.03318 | 0.03326 |

1.0 | 0.0414 | 0.0396 | 0.04060 | 0.04112 |

1.1 | 0.0501 | 0.0450 | 0.04837 | 0.04969 |

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McEachran, R.P.; Hamilton, K.R.; Bartschat, K. Low-Energy Elastic Electron Scattering from Helium Atoms. *Atoms* **2021**, *9*, 82.
https://doi.org/10.3390/atoms9040082

**AMA Style**

McEachran RP, Hamilton KR, Bartschat K. Low-Energy Elastic Electron Scattering from Helium Atoms. *Atoms*. 2021; 9(4):82.
https://doi.org/10.3390/atoms9040082

**Chicago/Turabian Style**

McEachran, Robert P., Kathryn R. Hamilton, and Klaus Bartschat. 2021. "Low-Energy Elastic Electron Scattering from Helium Atoms" *Atoms* 9, no. 4: 82.
https://doi.org/10.3390/atoms9040082