dorsal/arxiv
View SchemaThe "0.4 eV" Shape Resonance of Electron Scattering from Mercury in a Franck-Hertz Tube
| Authors | Peter Nicoletopoulos |
|---|---|
| Categories | |
| ArXiv ID | physics/0402012 |
| URL | https://arxiv.org/abs/physics/0402012 |
| DOI | 10.1088/0143-0807/25/3/005 |
| Journal | European Journal of Physics, vol. 25, iss. 3, pp. 373-383, (2004) |
Abstract
The alternative version of the Franck-Hertz experiment with mercury, in which a two-grid tube is used as a combination of electron gun, equipotential collision space, and detection cell, was analyzed recently in considerable detail. In particular, it was inferred that, at optimal pressure, the formation of peaks in the anode current at inelastic thresholds is mediated inside the detection cell by the large variation, a maximum at 0.4 eV, in the cross section for elastic scattering. This variation is due to a shape resonance in the electron-mercury system and is observable persuasively at the onset of anode current as a sharp peak followed by a clear minimum. In the present paper, the passage of electrons through the second grid to anode region is analyzed in terms of kinetic theory. The discussion is based on a simplified expression for the electron current derivable from an approximate form of the Boltzmann transport equation that maintains the spatial density gradient but omits elastic energy losses. The estimated range of pressure underlying this kind of idealization is in good agreement with experiment. An explicit solution is obtained by constructing an analytic expression for the momentum transfer cross section of mercury using a recent theory of generalized Fano profiles for overlapping resonances. This solution is used in order to model successfully the formation of peaks at the threshold of anode current and at excitation potentials, and to explain the dependence of the observed profiles on the pressure and on the sign and magnitude of the potential across the detection cell.
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"abstract": "The alternative version of the Franck-Hertz experiment with mercury, in which\na two-grid tube is used as a combination of electron gun, equipotential\ncollision space, and detection cell, was analyzed recently in considerable\ndetail. In particular, it was inferred that, at optimal pressure, the formation\nof peaks in the anode current at inelastic thresholds is mediated inside the\ndetection cell by the large variation, a maximum at 0.4 eV, in the cross\nsection for elastic scattering. This variation is due to a shape resonance in\nthe electron-mercury system and is observable persuasively at the onset of\nanode current as a sharp peak followed by a clear minimum. In the present\npaper, the passage of electrons through the second grid to anode region is\nanalyzed in terms of kinetic theory. The discussion is based on a simplified\nexpression for the electron current derivable from an approximate form of the\nBoltzmann transport equation that maintains the spatial density gradient but\nomits elastic energy losses. The estimated range of pressure underlying this\nkind of idealization is in good agreement with experiment. An explicit solution\nis obtained by constructing an analytic expression for the momentum transfer\ncross section of mercury using a recent theory of generalized Fano profiles for\noverlapping resonances. This solution is used in order to model successfully\nthe formation of peaks at the threshold of anode current and at excitation\npotentials, and to explain the dependence of the observed profiles on the\npressure and on the sign and magnitude of the potential across the detection\ncell.",
"arxiv_id": "physics/0402012",
"authors": [
"Peter Nicoletopoulos"
],
"categories": [
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"doi": "10.1088/0143-0807/25/3/005",
"journal_ref": "European Journal of Physics, vol. 25, iss. 3, pp. 373-383, (2004)",
"title": "The \"0.4 eV\" Shape Resonance of Electron Scattering from Mercury in a Franck-Hertz Tube",
"url": "https://arxiv.org/abs/physics/0402012"
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