Interference Phenomenon in Electron-Molecule Collisions
This article discusses how the pattern of elastic scattering of an electron on a pair of identical atomic centers is modified if we abandon the assumption, standard in molecular physics, that outside of some molecular sphere surrounding the centers, the wave function of the molecular continuum is at...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-10-01
|
| Series: | Atoms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2218-2004/10/4/105 |
| _version_ | 1797461498798276608 |
|---|---|
| author | Arkadiy S. Baltenkov Igor Woiciechowski |
| author_facet | Arkadiy S. Baltenkov Igor Woiciechowski |
| author_sort | Arkadiy S. Baltenkov |
| collection | DOAJ |
| description | This article discusses how the pattern of elastic scattering of an electron on a pair of identical atomic centers is modified if we abandon the assumption, standard in molecular physics, that outside of some molecular sphere surrounding the centers, the wave function of the molecular continuum is atomic-like, being a linear combination of the regular and irregular solutions of the wave equation. For this purpose, the elastic scattering of slow particles by a pair of non- overlapping short-range potentials has been studied. The continuum wave function of the particle is represented as a combination of a plane wave and two spherical s-waves propagating freely throughout space. The asymptotic behavior of this function determines the amplitude of elastic particle scattering in closed form. It is demonstrated that this amplitude can be represented as a partial expansion in a set of the orthonormal functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>Z</mi><mi>λ</mi></msub><mrow><mo>(</mo><mi mathvariant="bold">r</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> other than spherical harmonics <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>Y</mi><mrow><mi>l</mi><mi>m</mi></mrow></msub><mrow><mo>(</mo><mi mathvariant="bold">r</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. General formulas for these functions are obtained. The coefficients of the scattering amplitude expansion into a series of functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>Z</mi><mi>λ</mi></msub><mrow><mo>(</mo><mi mathvariant="bold">r</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and determine the scattering phases <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>η</mi><mi>λ</mi></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> for the considered two- atomic target. The special features of the S-matrix method for the case of arbitrary non-spherical potentials are discussed. |
| first_indexed | 2024-03-09T17:20:16Z |
| format | Article |
| id | doaj.art-8c6f840669454abe9a8d8899914602b8 |
| institution | Directory Open Access Journal |
| issn | 2218-2004 |
| language | English |
| last_indexed | 2024-03-09T17:20:16Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Atoms |
| spelling | doaj.art-8c6f840669454abe9a8d8899914602b82023-11-24T13:13:41ZengMDPI AGAtoms2218-20042022-10-0110410510.3390/atoms10040105Interference Phenomenon in Electron-Molecule CollisionsArkadiy S. Baltenkov0Igor Woiciechowski1Arifov Institute of Ion-Plasma and Laser Technologies, Tashkent 100125, UzbekistanMathematics Department, Alderson Broaddus University, 101 College Hill Drive, Philippi, WV 26416, USAThis article discusses how the pattern of elastic scattering of an electron on a pair of identical atomic centers is modified if we abandon the assumption, standard in molecular physics, that outside of some molecular sphere surrounding the centers, the wave function of the molecular continuum is atomic-like, being a linear combination of the regular and irregular solutions of the wave equation. For this purpose, the elastic scattering of slow particles by a pair of non- overlapping short-range potentials has been studied. The continuum wave function of the particle is represented as a combination of a plane wave and two spherical s-waves propagating freely throughout space. The asymptotic behavior of this function determines the amplitude of elastic particle scattering in closed form. It is demonstrated that this amplitude can be represented as a partial expansion in a set of the orthonormal functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>Z</mi><mi>λ</mi></msub><mrow><mo>(</mo><mi mathvariant="bold">r</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> other than spherical harmonics <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>Y</mi><mrow><mi>l</mi><mi>m</mi></mrow></msub><mrow><mo>(</mo><mi mathvariant="bold">r</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. General formulas for these functions are obtained. The coefficients of the scattering amplitude expansion into a series of functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>Z</mi><mi>λ</mi></msub><mrow><mo>(</mo><mi mathvariant="bold">r</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and determine the scattering phases <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>η</mi><mi>λ</mi></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> for the considered two- atomic target. The special features of the S-matrix method for the case of arbitrary non-spherical potentials are discussed.https://www.mdpi.com/2218-2004/10/4/105electron elastic scatteringnonspherical potentialS-matrix method |
| spellingShingle | Arkadiy S. Baltenkov Igor Woiciechowski Interference Phenomenon in Electron-Molecule Collisions Atoms electron elastic scattering nonspherical potential S-matrix method |
| title | Interference Phenomenon in Electron-Molecule Collisions |
| title_full | Interference Phenomenon in Electron-Molecule Collisions |
| title_fullStr | Interference Phenomenon in Electron-Molecule Collisions |
| title_full_unstemmed | Interference Phenomenon in Electron-Molecule Collisions |
| title_short | Interference Phenomenon in Electron-Molecule Collisions |
| title_sort | interference phenomenon in electron molecule collisions |
| topic | electron elastic scattering nonspherical potential S-matrix method |
| url | https://www.mdpi.com/2218-2004/10/4/105 |
| work_keys_str_mv | AT arkadiysbaltenkov interferencephenomenoninelectronmoleculecollisions AT igorwoiciechowski interferencephenomenoninelectronmoleculecollisions |