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Journal of Physics B Atomic Molecular and Optical Physics

Electron energy distribution function in laser-excited rubidium atoms

M A Mahmoud

Published May 9, 2005• 11 citations
Publisher

Abstract

The electron energy distribution function (EEDF) in laser-excited Rb vapour at the first resonance transition 5S–5P and 5p– nl transitions is calculated numerically from the Boltzmann equation under the experimental conditions of Barbier and Cheret ( 1987 J. Phys. B: At. Mol. Phys. 20 1229 ). The calculations included all the interactions between electrons and ground or excited states of atomic rubidium. We have also studied the time evolution and the laser power dependences of the EEDF and the electron density which is created during the interactions. The energy spectra of the electrons emerging from the interaction contain a number of peaks corresponding to the low-energy electrons produced by the associative and Hornbeck–Molnar ionization in addition to the electrons created from the various excited states by the ionizing collisions (Penning ionization). The low-energy electrons are then heated by one or more superelastic collisions leading to further ionization. However the calculations indicated that, under the conditions of low power laser intensity and relatively low atom density, the dominant processes are collisional ionization and collisional excitation.

DOI
10.1088/0953-4075/38/10/012

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Abstract We have studied the formation of the molecular ion Rb2+ and the atomic ion Rb+. These are created in laser excited rubidium vapor at the first resonance, 5s–5p and 5p-nl transitions. A theoretical model is applied to this interaction to explain the time evolution and the laser-power dependence of the population density of Rb+ and Rb2+. A set of rate equations which describe: the temporal variation of the population density of the excited states; the atomic ion density; and the electron density, were solved numerically under the experimental conditions of Barbier and Cheret. In their experiment the Rb concentration was 1×1013cm−3 and the laser power was taken to be 50–500 mW at vapor temperature = 450 K. The results showed that the main processes for producing Rb2+ are associative ionization and Hornbeck-Molnar ionization. The calculations have also showed that, the atomic ions Rb+ are formed through the Penning Ionization (PI) and photoionization processes. Moreover, a reasonable agreement between the experimental results and our calculations for the ion currents of the Rb+ and Rb2+ is obtained.

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Cette thèse est une étude des divers processus d'Ionisation collisionnelle d'atomes de rubidium très excités, à énergie thermique (450° K).Dans une cellule, les atomes alcalins excités par laser sont ionisés par collision avec un partenaire excité ou dans l'état fondamental.L'analyse des courants ioniques atomiques et moléculaires met en évidence les réactions principales d'Ionisation Penning atomique et Hornbeck Molnar associative :Rb(nl) + Rb(5p) => Rb+ + Rb + e-Rb(nl) + Rb(5s) => Rb2+ + e-L'étude théorique de ces réactions confirme les taux de réaction mesurés,La formation d'ions négatifs est aussi observée. Ces ions sont issus de la réaction :Rb(nl) + Rb(5s) => Rb+ + Rb-Les mécanismes de formation de la paire d'ions dépendent de la position en énergie du niveau excité initial.Enfin la section efficace du processus inélastique d'association d'énergie a été mesurée et interprétée :Rb(5p) + Rb(5p) => Rb(5d) + Rb(5s)

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Computational Study of Resonantly Ionizing Rubidium Vapor by Nanosecond Laser Pulses

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An investigation of the resonant interaction of the rubidium atoms with an intensity (10 kWcm-2 ≤ I ≤ 2 MWcm-2) and a wavelength close to that of the D1 and D2 transitions of the rubidium atom (5S1/2 → 5P3/2 or 5S1/2 → 5P1/2, λD1 = 780 nm, λD2 = 795 nm), which has passes through rubidium vapor with density (1011 - 1014 cm-3) been studied theoretically. The system of equations describing the processes of Collisional ionization and multiphoton ionization of rubidium vapour resonantly excited with nanosecond pulsed laser is solved. The dependence of the ion density on the laser intensity and the atomic density of rubidium are considered. The result of calculations revealed that, both quadratic ion density dependence on laser intensity and linear behaviour of the ion density versus rubidium density for 5S1/2 → 5P3/2 transition is due to photoioization process. In contrast, for 5S1/2 → 5P1/2 transition, the ion density dependence is nonlinear and indicates that the collisional processes play the major contribution in the total ionization. Also, the obtained results showed reasonable agreement with the experimentally measured values of the ion density dependence given by Bakhramov et al. In addition, the analysis of mutual competition between the different ionization processes considered for the ion yield as a function of both laser intensity and atoms density are also presented this work.

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[Energy-pooling collisions of rubidium atoms: Rb (5P(J)) + Rb (5P(J))--> Rb (5S) + Rb (nl = 5D,7S)].

Baoxia Mu, Shuying Wang, Xiu-Hua Cui +4 more

An experimental study of rubidium energy pooling collisions, Rb(5P(J)) + Rb(5P(J))-->Rb(nlJ') + Rb(5S), at thermal energies, was carried out in a cell. Atoms were excited to either the 5P 1/2 or 5P 3/2 state using a single-mode diode laser. The excited atom density and spatial distribution were mapped by monitoring the absorption of a counter-propagating single-mode diode laser beam, tuned to either 5P 1/2-->5D 3/2 or 5P 3/2-->7S 1/2 transition, which could be translated parallel to the pump beam. The excited atom densities were combined with the measured fluorescence ratios to determine cross sections for the rubidium energy pooling process. For 5P 3/2 excitation the cross sections for nlJ' being 5D 5/2, 5D 3/2, and 7S 1/2 are (1.32+/-0.59) x 10(-14), (1.18+/-0.53) x 10(-14) and (3. 21+/-1. 44) x 10(-15) cm2, respectively. For 5P 1/2 excitation the cross sections for nlJ' being 5D 5/2 and 5D 3/2 are (6.57+/-2.96) x 10(-15), and (5.90+/-2.66) x 10(-15) cm2, respectively. The results were compared with those of other experiments.

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Superelastic electron scattering from the laser excited 52P3/2 state of rubidium

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Contained within this thesis are the collective theoretical and experimental methodologies required for the investigation of superelastic electron scattering from the laser excited 52P312 level of atomic rubidium. Superelastic electron scattering is the process by which an incident electron collides with an excited atom, in this case optically prepared rubidium, subsequently de -exciting the atom and gaining the relevant kinetic energy. By observing the different superelastic electron scattering rates as a function of laser polarisation, in conjunction with performing pseudo Stokes parameter analysis, the alignment and orientation of the rubidium 52P state caused by electron impact excitation is deduced. As a consequence of this experimental study, rubidium is at present the heaviest alkali to which the superelastic electron scattering technique has been applied. The motivation for performing an electron scattering experiment with a rubidium target, pertains to the possible relativistic effects that arise due to the heavy nucleus of the target atom. Recent fully relativistic first order distorted wave Born approximation (RDW) scattering calculations, for electron impact excitation have shown that rubidium has exhibited strong relativistic effects. As this calculation predicts radically different behaviour when compared to a conventional non relativistic first order distorted wave Born approximation (DWBA) calculation, an experimental investigation to determine the validity of each theory is justified A continuous wave Titanium Sapphire ring laser was used to provide the coherent single mode laser radiation that was resonantly tuned to excited the 52S1/2 - 52P3/2 rubidium transition. The laser excitation process, for both the 85Rb and 87Rb isotopes, was theoretically modelled using a full quantum electrodynamic (QED) model. This modelling of the rubidium atom within the influence of a resonant laser field was used to calculate values for the optical pumping parameters K, K' and K". These parameters are necessary as they provide information about the depolarisation of the excited 2P state caused by the laser. An unpolarised electron beam with an incident electron energy of 18.4eV was used to collisionally de -excite the optically prepared rubidium. Superelastic electron scattering measurements were made for an angular range of 5�-120�, allowing experimental determination of the Stokes parameters, the natural frame parameters and the collision frame parameters associated with electron impact excitation of the 52P state of rubidium. At small scattering angles the DWBA and RDW theories predict similar values for the aforementioned parameters. One of the key aims of this study was the collection of electron scattering data beyond 25�, an experimental limitation previously encountered on this superelastic apparatus. This aim was achieved and experimental data has been collected to maximum angle of 120�. A comparison between the experimental data and the DWBA and RDW scattering theories, reveals that while the RDW theory consistently outperforms the DWBA, there are areas where both theories do not agree with experiment.

•Jan 1, 1998•0 citations
The electron energy distribution function (EEDF) in laser-excited Rb vapour at the first resonance transition 5S–5P and 5p– nl transitions is calculated numerically from the Boltzmann equation under the experimental conditions of Barbier and Cheret ( 1987 J. Phys. B: At. Mol. Phys. 20 1229 ). The calculations included all the interactions between electrons and ground or excited states of atomic rubidium. We have also studied the time evolution and the laser power dependences of the EEDF and the electron density which is created during the interactions. The energy spectra of the electrons emerging from the interaction contain a number of peaks corresponding to the low-energy electrons produced by the associative and Hornbeck–Molnar ionization in addition to the electrons created from the various excited states by the ionizing collisions (Penning ionization). The low-energy electrons are then heated by one or more superelastic collisions leading to further ionization. However the calculations indicated that, under the conditions of low power laser intensity and relatively low atom density, the dominant processes are collisional ionization and collisional excitation.
Abstract We have studied the formation of the molecular ion Rb2+ and the atomic ion Rb+. These are created in laser excited rubidium vapor at the first resonance, 5s–5p and 5p-nl transitions. A theoretical model is applied to this interaction to explain the time evolution and the laser-power dependence of the population density of Rb+ and Rb2+. A set of rate equations which describe: the temporal variation of the population density of the excited states; the atomic ion density; and the electron density, were solved numerically under the experimental conditions of Barbier and Cheret. In their experiment the Rb concentration was 1×1013cm−3 and the laser power was taken to be 50–500 mW at vapor temperature = 450 K. The results showed that the main processes for producing Rb2+ are associative ionization and Hornbeck-Molnar ionization. The calculations have also showed that, the atomic ions Rb+ are formed through the Penning Ionization (PI) and photoionization processes. Moreover, a reasonable agreement between the experimental results and our calculations for the ion currents of the Rb+ and Rb2+ is obtained.
Cette thèse est une étude des divers processus d'Ionisation collisionnelle d'atomes de rubidium très excités, à énergie thermique (450° K).Dans une cellule, les atomes alcalins excités par laser sont ionisés par collision avec un partenaire excité ou dans l'état fondamental.L'analyse des courants ioniques atomiques et moléculaires met en évidence les réactions principales d'Ionisation Penning atomique et Hornbeck Molnar associative :Rb(nl) + Rb(5p) => Rb+ + Rb + e-Rb(nl) + Rb(5s) => Rb2+ + e-L'étude théorique de ces réactions confirme les taux de réaction mesurés,La formation d'ions négatifs est aussi observée. Ces ions sont issus de la réaction :Rb(nl) + Rb(5s) => Rb+ + Rb-Les mécanismes de formation de la paire d'ions dépendent de la position en énergie du niveau excité initial.Enfin la section efficace du processus inélastique d'association d'énergie a été mesurée et interprétée :Rb(5p) + Rb(5p) => Rb(5d) + Rb(5s)
Rb + and Rb 2 + formation in a laser-excited Rb vapour is extensively studied for s and d levels ranging from 5d to 11s levels. Collisional ionisation with a ground-state atom leads to Rb 2 + formation by Hornbeck-Molnar reaction with rate coefficients lying in the 10 -10 cm 3 s -1 range. This reaction is analysed theoretically. Penning ionisation occurs in collision with a resonant-state atom, Rb(5p), with a high efficiency (rate coefficient above 10 -8 cm 3 s -1 ). Associative ionisation between the 7s level and the 5p level is also observed (rate coefficient about 10 -10 cm 3 s -1 ). This reaction appears negligible for the neighbouring 5d level.
An investigation of the resonant interaction of the rubidium atoms with an intensity (10 kWcm-2 ≤ I ≤ 2 MWcm-2) and a wavelength close to that of the D1 and D2 transitions of the rubidium atom (5S1/2 → 5P3/2 or 5S1/2 → 5P1/2, λD1 = 780 nm, λD2 = 795 nm), which has passes through rubidium vapor with density (1011 - 1014 cm-3) been studied theoretically. The system of equations describing the processes of Collisional ionization and multiphoton ionization of rubidium vapour resonantly excited with nanosecond pulsed laser is solved. The dependence of the ion density on the laser intensity and the atomic density of rubidium are considered. The result of calculations revealed that, both quadratic ion density dependence on laser intensity and linear behaviour of the ion density versus rubidium density for 5S1/2 → 5P3/2 transition is due to photoioization process. In contrast, for 5S1/2 → 5P1/2 transition, the ion density dependence is nonlinear and indicates that the collisional processes play the major contribution in the total ionization. Also, the obtained results showed reasonable agreement with the experimentally measured values of the ion density dependence given by Bakhramov et al. In addition, the analysis of mutual competition between the different ionization processes considered for the ion yield as a function of both laser intensity and atoms density are also presented this work.
An experimental study of rubidium energy pooling collisions, Rb(5P(J)) + Rb(5P(J))-->Rb(nlJ') + Rb(5S), at thermal energies, was carried out in a cell. Atoms were excited to either the 5P 1/2 or 5P 3/2 state using a single-mode diode laser. The excited atom density and spatial distribution were mapped by monitoring the absorption of a counter-propagating single-mode diode laser beam, tuned to either 5P 1/2-->5D 3/2 or 5P 3/2-->7S 1/2 transition, which could be translated parallel to the pump beam. The excited atom densities were combined with the measured fluorescence ratios to determine cross sections for the rubidium energy pooling process. For 5P 3/2 excitation the cross sections for nlJ' being 5D 5/2, 5D 3/2, and 7S 1/2 are (1.32+/-0.59) x 10(-14), (1.18+/-0.53) x 10(-14) and (3. 21+/-1. 44) x 10(-15) cm2, respectively. For 5P 1/2 excitation the cross sections for nlJ' being 5D 5/2 and 5D 3/2 are (6.57+/-2.96) x 10(-15), and (5.90+/-2.66) x 10(-15) cm2, respectively. The results were compared with those of other experiments.
Contained within this thesis are the collective theoretical and experimental methodologies required for the investigation of superelastic electron scattering from the laser excited 52P312 level of atomic rubidium. Superelastic electron scattering is the process by which an incident electron collides with an excited atom, in this case optically prepared rubidium, subsequently de -exciting the atom and gaining the relevant kinetic energy. By observing the different superelastic electron scattering rates as a function of laser polarisation, in conjunction with performing pseudo Stokes parameter analysis, the alignment and orientation of the rubidium 52P state caused by electron impact excitation is deduced. As a consequence of this experimental study, rubidium is at present the heaviest alkali to which the superelastic electron scattering technique has been applied. The motivation for performing an electron scattering experiment with a rubidium target, pertains to the possible relativistic effects that arise due to the heavy nucleus of the target atom. Recent fully relativistic first order distorted wave Born approximation (RDW) scattering calculations, for electron impact excitation have shown that rubidium has exhibited strong relativistic effects. As this calculation predicts radically different behaviour when compared to a conventional non relativistic first order distorted wave Born approximation (DWBA) calculation, an experimental investigation to determine the validity of each theory is justified A continuous wave Titanium Sapphire ring laser was used to provide the coherent single mode laser radiation that was resonantly tuned to excited the 52S1/2 - 52P3/2 rubidium transition. The laser excitation process, for both the 85Rb and 87Rb isotopes, was theoretically modelled using a full quantum electrodynamic (QED) model. This modelling of the rubidium atom within the influence of a resonant laser field was used to calculate values for the optical pumping parameters K, K' and K". These parameters are necessary as they provide information about the depolarisation of the excited 2P state caused by the laser. An unpolarised electron beam with an incident electron energy of 18.4eV was used to collisionally de -excite the optically prepared rubidium. Superelastic electron scattering measurements were made for an angular range of 5�-120�, allowing experimental determination of the Stokes parameters, the natural frame parameters and the collision frame parameters associated with electron impact excitation of the 52P state of rubidium. At small scattering angles the DWBA and RDW theories predict similar values for the aforementioned parameters. One of the key aims of this study was the collection of electron scattering data beyond 25�, an experimental limitation previously encountered on this superelastic apparatus. This aim was achieved and experimental data has been collected to maximum angle of 120�. A comparison between the experimental data and the DWBA and RDW scattering theories, reveals that while the RDW theory consistently outperforms the DWBA, there are areas where both theories do not agree with experiment.