Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Superelastic electron scattering from the laser-excited 32P3/2 level of Na

Peter Mark Farrell

Published Jan 1, 1992• 0 citations
OpenAlex

Abstract

The atomic collision parameters ?, ?, ?, ?, P, |P| and |�| were determined from measurements of the pseudo Stokes parameters for superelastic scattering of 20 eV incident electrons at angles of 10� and 15� from the 32P312 excited state of sodium. Two depolarising factors K and K' for the pseudo Stokes parameters are defined for it and a laser excitation respectively to account for the depolarising influence due to optical pumping in the hyperfine structure of the 32P3t2 excited state. A theoretical model of the laser excitation of the sodium transition is developed to determine K and K'. The theory developed is a quantum -electrodynamic description of the resonant interaction of monochromatic light with the 32S in(F'=2) <-> 32P3a(F=3,2,1) hyperfine transitions of the sodium D2 line formualated in terms of the Heisenberg atomic operator. Off diagonal state coherences and all relaxation terms are included. It is found that the equations for the populations, optical coherences and certain state coherences form a closed subset of the total system of equations. This subset is sufficiently small to enable numerical computation. As well as K and K', the model is used to calculate the probability of occupation of the various atomic states and the polarisation of the sideways scattered fluorescence from the laser excited atoms. The results of this model are compared with the predictions of four other models, a rate equation model which includes only the F=3 excited state, a semiclassical model based on the density operator, a low light intensity approximation to the semiclassical model and a high intensity model which uses a transformed basis for the states. For both it and a laser excitation it is shown that the QED calculated values converge to the values predicted by the high and low intensity approximations in the appropriate limits.

Related papers

Superelastic Electron Scattering from Laser Excited States of Sodium

Sang, Robert

This thesis presents the results of a series of experiments in which electrons are superelastically scattered from various laser excited states of sodium. The atoms, once in the optically prepared state, are forced to relax via the superelastic collision with an electron. The rate of detection of superelastically scattered electrons was measured as a function of the laser polarisation which enabled pseudo Stokes parameters to be determined. These pseudo Stokes parameters are functions of both optical pumping parameters and atomic collision parameters. The optical pumping parameters describe the laser-atom interaction and the atomic collision parameters describe the electron-atom collision process. Three different laser excitation mechanisms were used to optically pump the atoms into various excited states. The first of these used a single laser tuned to the 32S 112(F'=2 hyperfine state)-~32P312 transition. The excited atoms underwent a superelastic collision with an electron leaving the atom in the ground state and pseudo Stokes parameters were measured as a function of both scattering angle and incident electron energy. The second superelastic experiment, utilised a folded step excitation mechanism which employed two lasers tuned from the two hypethne states of the 32S112 ground state respectively to the 32P312 excited state. Power broadening effects in the single laser experiment cause the atoms to be optically pumped into the F= 1 hyperfine ground state. The laser powers used were not great enough to power broaden the hyperfine ground states and as such the F'= 1 sublevel effectively acted as a sink. The folded step excitation method enabled the excited state population to be increased so that data at larger scattering angles could be obtained. Stokes parameters from both of these experiments which had an incident energy range of 10eV to 30eV and an angular range of 5°-25° were compared to three current electron-atom scattering theories and previous experimental data. Overall, fair to good agreement was found between theory and experiments for the individual Stokes parameters. Losses of coherence was observed at small scattering angles (50.200) at 20eV and 25eV incident electron energies which were poorly modelled by the three different theories. The third superelastic experiment involved the use of two lasers of specified polarisation to stepwise excite the atoms to the 32D512 excited state. Superelastic collisions with incident electron energies of 20eV from the 32D512-*32P312~312 collision were studied at three different scattering angles and pseudo Stokes parameters for the case where the polarisations of the radiation from the lasers were parallel were measured. The single step and folded step laser-atom interactions for it excitation were modelled using a full quantum electrodynamical treatment so that the optical pumping parameters from the single and folded step experiments could be investigated. Equations of motion were derived in the Heisenberg picture and it is shown that for the single laser case 59 equations of motion are required to fully model the interaction and for the folded step ease 78 equations of motion are required. The results of calculations demonstrated that the optical pumping parameters were sensitive to laser intensity, laser detuning and the Doppler width of the atomic beam. The theoretical quantum electrodynamical calculation results were in good agreement with the experimental results.

•Jan 1, 2007•0 citations

Electron superelastic scattering from states of atomic sodium and rubidium

B. V. Hall, Robert T. Sang, Max Shurgalin +3 more

This paper reports on the extension of the electron superelastic scattering technique to three new situations. The first considers scattering from the 32P3/2 level of Na that has been excited by two laser modes tuned, respectively, to the transitions from the two hyperfine states of the 32S1/2 ground level. Both coherent and noncoherent modes are treated in a full quantum electrodynamic model of the laser excitation. Under certain conditions, the time-averaged probability of finding an atom in the 32P3/2 level exceeds 0.5. The second situation is electron superelastic scattering from the 32D5/2 level of Na that has been resonantly excited from the ground level via a resonant intermediate level. With the first observation of superelastically scattered electrons from this higher lying level recently recorded, this paper considers the extension of the quantum electrodynamics (QED) model to describe the optical excitation process. Application of superelastic scattering to the 52S1/2–52P3/2 transition of Rb is the third situation considered. The superelastic scattering formalism is extended to allow for a nonzero spin flip cross section for this transition. The resulting optical pumping terms are calculated using the QED model and the method of their determination for the superelastic scattering experiment described. The experimental design necessary to measure all of the collision parameters for this transition is discussed.

Canadian Journal of Physics•Nov 1, 1996•4 citations

Quantum-electrodynamic calculation of hyperfine-state populations in atomic sodium

Peter M. Farrell, W. R. MacGillivray, M. C. Standage

A quantum-electrodynamic (QED) description of the resonant interaction of monochromatic light with the ${3}^{2}$${\mathit{S}}_{1/2}$(F'=2)\ensuremath{\rightarrow}${3}^{2}$${\mathit{P}}_{3/2}$(F=3,2,1) hyperfine transitions of the sodium ${D}_{2}$ line is formulated in terms of the Heisenberg atomic operator. Off-diagonal state coherences and all relaxation terms are included. It is found that the equations for the populations, optical coherences, and certain state coherences form a closed subset of the total system of equations. This subset is small enough to be computed numerically. The results of calculations with this model are compared with three previously developed semiclassical descriptions using the density operator. One of the semiclassical models was developed to describe the interaction of weak light with the atomic transition while another is suitable in the case of high-intensity light. For both \ensuremath{\pi} and \ensuremath{\sigma} excitation it is shown that the QED calculated values for the time-averaged, excited-level population probability converge to those of each of the semiclassical models in the appropriate limit of light intensity. For homogeneous broadening, results show that the optimum light intensity to obtain the largest fraction of atoms in the ${3}^{2}$${P}_{3/2}$ level after transversing a 1-mm-diam laser beam is 1.15 mW/${\mathrm{mm}}^{2}$ for \ensuremath{\pi} excitation and 1.43 mW/${\mathrm{mm}}^{2}$ for \ensuremath{\sigma} excitation.

Physical Review A•Jun 1, 1988•58 citations

Calculation of the optical pumping parameters for electron-superelastic-scattering experiments from the sodium 3 2 P3/2 level

Peter M. Farrell, W. R. MacGillivray, M. C. Standage

The optical pumping parameters that modify the pure-state pseudo-Stokes parameters in an electron-superelastic-scattering experiment are calculated for the 3 $^{2}$${\mathit{S}}_{1/2}$(F=2)--${3}^{2}$${\mathit{P}}_{3/2}$(F) transitions of Na. A QED model is used to describe the laser excitation. It is found, that while the magnitude of the pumping parameter K' associated with circularly polarized excitation is close to unity for other than weak laser intensities, the value of the parameter K, associated with linearly polarized light, differs significantly from unity and is dependent on such experimental conditions as laser intensity, laser detuning, laser beam profile, and the Doppler width of the atomic transition. Methods for measuring K are suggested.

Physical Review A•Aug 1, 1991•28 citations

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

Brenton Victor Hall

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

Resonance fluorescence line polarization studies of laser excited sodium transitions

Xian-Kun Meng

The resonant excitation of the sodium D2 transition by laser radiation was investigated experimentally in this thesis. Line polarization measurement of the resonance fluorescence was employed to investigate the excitation process. The sodium atoms, which were collimated in a very narrow beam, were excited by a monochromatic laser beam with the frequency tuned to resonance with the 32S 112(F=2) - 32P312 hyperfine transition. The direction of the laser beam was perpendicular to the atomic beam and the fluorescence photons were detected along a direction perpendicular to both the laser and atomic beams. The experimental measurements were performed to determine the effect due to the variation of the laser intensity and frequency on the line polarization. A theoretical expression of the line polarization as a function of density matrix elements of the upper excited hyperfine sub -states was derived. A full quantum electrodynamic theory was used to derive an atomic operator equation of motion which was needed to calculate atomic operator elements. These elements then yielded the corresponding density matrix elements. The experimental results and the theoretical modelling were in a good agreement. The first experimental results for the line polarization of the highly excited states, 42D512 and 42D312, are also presented. The use of two lasers enabled these highly excited states to be excited. The line polarization of the fluorescence for transitions from the 4D level down to lower states is derived in terms of the density matrix elements of the upper excited states. Two limiting cases for the theoretical predictions of the line polarization are considered.

•Jan 1, 1991•0 citations
The atomic collision parameters ?, ?, ?, ?, P, |P| and |�| were determined from measurements of the pseudo Stokes parameters for superelastic scattering of 20 eV incident electrons at angles of 10� and 15� from the 32P312 excited state of sodium. Two depolarising factors K and K' for the pseudo Stokes parameters are defined for it and a laser excitation respectively to account for the depolarising influence due to optical pumping in the hyperfine structure of the 32P3t2 excited state. A theoretical model of the laser excitation of the sodium transition is developed to determine K and K'. The theory developed is a quantum -electrodynamic description of the resonant interaction of monochromatic light with the 32S in(F'=2) <-> 32P3a(F=3,2,1) hyperfine transitions of the sodium D2 line formualated in terms of the Heisenberg atomic operator. Off diagonal state coherences and all relaxation terms are included. It is found that the equations for the populations, optical coherences and certain state coherences form a closed subset of the total system of equations. This subset is sufficiently small to enable numerical computation. As well as K and K', the model is used to calculate the probability of occupation of the various atomic states and the polarisation of the sideways scattered fluorescence from the laser excited atoms. The results of this model are compared with the predictions of four other models, a rate equation model which includes only the F=3 excited state, a semiclassical model based on the density operator, a low light intensity approximation to the semiclassical model and a high intensity model which uses a transformed basis for the states. For both it and a laser excitation it is shown that the QED calculated values converge to the values predicted by the high and low intensity approximations in the appropriate limits.
This thesis presents the results of a series of experiments in which electrons are superelastically scattered from various laser excited states of sodium. The atoms, once in the optically prepared state, are forced to relax via the superelastic collision with an electron. The rate of detection of superelastically scattered electrons was measured as a function of the laser polarisation which enabled pseudo Stokes parameters to be determined. These pseudo Stokes parameters are functions of both optical pumping parameters and atomic collision parameters. The optical pumping parameters describe the laser-atom interaction and the atomic collision parameters describe the electron-atom collision process. Three different laser excitation mechanisms were used to optically pump the atoms into various excited states. The first of these used a single laser tuned to the 32S 112(F'=2 hyperfine state)-~32P312 transition. The excited atoms underwent a superelastic collision with an electron leaving the atom in the ground state and pseudo Stokes parameters were measured as a function of both scattering angle and incident electron energy. The second superelastic experiment, utilised a folded step excitation mechanism which employed two lasers tuned from the two hypethne states of the 32S112 ground state respectively to the 32P312 excited state. Power broadening effects in the single laser experiment cause the atoms to be optically pumped into the F= 1 hyperfine ground state. The laser powers used were not great enough to power broaden the hyperfine ground states and as such the F'= 1 sublevel effectively acted as a sink. The folded step excitation method enabled the excited state population to be increased so that data at larger scattering angles could be obtained. Stokes parameters from both of these experiments which had an incident energy range of 10eV to 30eV and an angular range of 5°-25° were compared to three current electron-atom scattering theories and previous experimental data. Overall, fair to good agreement was found between theory and experiments for the individual Stokes parameters. Losses of coherence was observed at small scattering angles (50.200) at 20eV and 25eV incident electron energies which were poorly modelled by the three different theories. The third superelastic experiment involved the use of two lasers of specified polarisation to stepwise excite the atoms to the 32D512 excited state. Superelastic collisions with incident electron energies of 20eV from the 32D512-*32P312~312 collision were studied at three different scattering angles and pseudo Stokes parameters for the case where the polarisations of the radiation from the lasers were parallel were measured. The single step and folded step laser-atom interactions for it excitation were modelled using a full quantum electrodynamical treatment so that the optical pumping parameters from the single and folded step experiments could be investigated. Equations of motion were derived in the Heisenberg picture and it is shown that for the single laser case 59 equations of motion are required to fully model the interaction and for the folded step ease 78 equations of motion are required. The results of calculations demonstrated that the optical pumping parameters were sensitive to laser intensity, laser detuning and the Doppler width of the atomic beam. The theoretical quantum electrodynamical calculation results were in good agreement with the experimental results.
This paper reports on the extension of the electron superelastic scattering technique to three new situations. The first considers scattering from the 32P3/2 level of Na that has been excited by two laser modes tuned, respectively, to the transitions from the two hyperfine states of the 32S1/2 ground level. Both coherent and noncoherent modes are treated in a full quantum electrodynamic model of the laser excitation. Under certain conditions, the time-averaged probability of finding an atom in the 32P3/2 level exceeds 0.5. The second situation is electron superelastic scattering from the 32D5/2 level of Na that has been resonantly excited from the ground level via a resonant intermediate level. With the first observation of superelastically scattered electrons from this higher lying level recently recorded, this paper considers the extension of the quantum electrodynamics (QED) model to describe the optical excitation process. Application of superelastic scattering to the 52S1/2–52P3/2 transition of Rb is the third situation considered. The superelastic scattering formalism is extended to allow for a nonzero spin flip cross section for this transition. The resulting optical pumping terms are calculated using the QED model and the method of their determination for the superelastic scattering experiment described. The experimental design necessary to measure all of the collision parameters for this transition is discussed.
A quantum-electrodynamic (QED) description of the resonant interaction of monochromatic light with the 32{3}^{2}32S1/2{\mathit{S}}_{1/2}S1/2​(F'=2)\ensuremath{\rightarrow}32{3}^{2}32P3/2{\mathit{P}}_{3/2}P3/2​(F=3,2,1) hyperfine transitions of the sodium D2{D}_{2}D2​ line is formulated in terms of the Heisenberg atomic operator. Off-diagonal state coherences and all relaxation terms are included. It is found that the equations for the populations, optical coherences, and certain state coherences form a closed subset of the total system of equations. This subset is small enough to be computed numerically. The results of calculations with this model are compared with three previously developed semiclassical descriptions using the density operator. One of the semiclassical models was developed to describe the interaction of weak light with the atomic transition while another is suitable in the case of high-intensity light. For both \ensuremath{\pi} and \ensuremath{\sigma} excitation it is shown that the QED calculated values for the time-averaged, excited-level population probability converge to those of each of the semiclassical models in the appropriate limit of light intensity. For homogeneous broadening, results show that the optimum light intensity to obtain the largest fraction of atoms in the 32{3}^{2}32P3/2{P}_{3/2}P3/2​ level after transversing a 1-mm-diam laser beam is 1.15 mW/mm2{\mathrm{mm}}^{2}mm2 for \ensuremath{\pi} excitation and 1.43 mW/mm2{\mathrm{mm}}^{2}mm2 for \ensuremath{\sigma} excitation.
The optical pumping parameters that modify the pure-state pseudo-Stokes parameters in an electron-superelastic-scattering experiment are calculated for the 3 2^{2}2S1/2{\mathit{S}}_{1/2}S1/2​(F=2)--32{3}^{2}32P3/2{\mathit{P}}_{3/2}P3/2​(F) transitions of Na. A QED model is used to describe the laser excitation. It is found, that while the magnitude of the pumping parameter K' associated with circularly polarized excitation is close to unity for other than weak laser intensities, the value of the parameter K, associated with linearly polarized light, differs significantly from unity and is dependent on such experimental conditions as laser intensity, laser detuning, laser beam profile, and the Doppler width of the atomic transition. Methods for measuring K are suggested.
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.
The resonant excitation of the sodium D2 transition by laser radiation was investigated experimentally in this thesis. Line polarization measurement of the resonance fluorescence was employed to investigate the excitation process. The sodium atoms, which were collimated in a very narrow beam, were excited by a monochromatic laser beam with the frequency tuned to resonance with the 32S 112(F=2) - 32P312 hyperfine transition. The direction of the laser beam was perpendicular to the atomic beam and the fluorescence photons were detected along a direction perpendicular to both the laser and atomic beams. The experimental measurements were performed to determine the effect due to the variation of the laser intensity and frequency on the line polarization. A theoretical expression of the line polarization as a function of density matrix elements of the upper excited hyperfine sub -states was derived. A full quantum electrodynamic theory was used to derive an atomic operator equation of motion which was needed to calculate atomic operator elements. These elements then yielded the corresponding density matrix elements. The experimental results and the theoretical modelling were in a good agreement. The first experimental results for the line polarization of the highly excited states, 42D512 and 42D312, are also presented. The use of two lasers enabled these highly excited states to be excited. The line polarization of the fluorescence for transitions from the 4D level down to lower states is derived in terms of the density matrix elements of the upper excited states. Two limiting cases for the theoretical predictions of the line polarization are considered.