HAL Id: jpa-00208901
https://hal.archives-ouvertes.fr/jpa-00208901
Submitted on 1 Jan 1979
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Transitions between Rydberg levels of helium induced by electron and neutral collisions
F. Devos, J. Boulmer, J.-F. Delpech
To cite this version:
F. Devos, J. Boulmer, J.-F. Delpech. Transitions between Rydberg levels of helium in- duced by electron and neutral collisions. Journal de Physique, 1979, 40 (3), pp.215-223.
�10.1051/jphys:01979004003021500�. �jpa-00208901�
Transitions between
Rydberg
levels of helium induced by electron and neutral collisionsF. Devos, J. Boulmer and J.-F. Delpech (*),
Groupe d’Electronique dans les Gaz, Institut d’Electronique Fondamentale (**)
Bât. 220, Université Paris-XI, 91405 Orsay, France (Reçu le 26 juillet 1978, accepté le 2 novembre 1978)
Résumé. 2014 Nous donnons les résultats d’une étude expérimentale des transferts induits par collisions atomiques
et électroniques entre niveaux de Rydberg de l’hélium ayant des nombres quantiques principaux compris entre
8 et 17. La technique de fluorescence induite par laser a été utilisée pour suivre avec une résolution temporelle
suffisante le dépeuplement collisionnel du niveau pompé ainsi que les transferts entre niveaux de nombres quan-
tiques différents dans une post-décharge d’hélium de haute pureté dont les différents paramètres sont mesurés
avec précision. Nos observations montrent que les transferts entre sous-systèmes triplet et singulet sont négli- geables. Les transferts dus aux collisions avec les électrons suivent étroitement l’allure fonctionnelle prévue par la théorie hydrogénique classique de Mansbach et Keck, mais les valeurs expérimentales sont en moyenne plus petites d’un facteur 0,64. Les transferts induits par les collisions avec des atomes de 3He et de 4He sont en net désaccord avec la théorie classique de Flannery, qui utilise le modèle de la collision binaire ; cependant, le désaccord s’atténue pour les nombres quantiques principaux les plus élevés. Ce fait, joint à l’absence d’effet isotopique sur
les taux, indique qu’un modèle simple de collision binaire décrit mal les niveaux de Rydberg moyennement excités,
et qu’il est nécessaire de tenir compte des potentiels interatomiques dans un modèle moléculaire à deux centres, plus un électron excité.
Abstract. 2014 An experimental study of electron- and neutral-induced collisional transfer between Rydberg levels
of helium has been made for intermediate values (8 to 17) of the principal quantum number. The techniques of time-resolved, laser induced fluorescence spectroscopy were used to follow the collisional depopulation of the
laser pumped level as well as transfers between levels of different principal quantum number in a high purity,
well diagnosed helium afterglow. Transfers between singlet and triplet subsystems of atomic helium were found to be negligible. Electron-induced collisional transfer follows closely the functional variation of the Mansbach and Keck hydrogenic theory, but experimental values are on the average smaller by a factor of 0.64 than predicted.
Transfers induced by collisions with 3He and 4He atoms are in marked disagreement with Flannery’s classical binary-encounter theory for the smaller values of the principal quantum number, although disagreement is less pronounced for higher principal quantum numbers. This fact, and the absence of isotopic effect on rate coeffi- cients, indicate that a simple binary-encounter theory is not suitable for intermediate Rydberg levels, and that
interatomic potentials should be included in a two-centre, molecular model with an excited electron.
Classification Physics Abstracts
34.50 - 34.80
1. Introduction. - Rydberg levels, i.e. excited levels of intermediate or large principal quantum number with binding energies comparable to thermal energies,
are produced by collisions in many situations of
practical importance. They play dominant roles in many electronic recombination processes involving
atomic ions, and particularly in the complex inter- play between stepwise excitation and deexcitation processes which form an essential part of collisional- radiative recombination.
A detailed knowledge of collisional transfer mecha- nisms between Rydberg levels is thus of great funda- mental interest : for example, it will throw some
light on many characteristic features of collisions
at thermal energies. Precise and detailed measure- ments of rate coefficients for electron- and neutral- induced collisional transfers may thus be valuable. ,
However, up to now, most information has been theoretical - and somewhat contradictory - while experimental evidence was fragmentary and often
of an indirect nature.
In a recent paper [1] hereafter referred to as 1
we have reported for the first time laser fluorescence measurements of electron-induced collisional depo- pulation rates between Rydberg levels of helium.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01979004003021500
216
Broadly similar experimental techniques were used by other authors : Gounand et al. [2] have studied
the neutral-induced collisional depopulation of P
states of rubidium at thermal energies (principal
quantum numbers from 12 to 22) and, in a series of publications, Gallagher and his coworkers [3, 4, 5] .
have reported on neutral-induced collisional angular
momentum mixing of Rydberg states of sodium.
None of these studies gave any information on
the detailed rates of transfer between levels ; such
rates are however of paramount importance in many situations of interest in astrophysics and in laboratory plasma physics, which involve collisional-radiative
quasi-equilibria. The only information available was
of an indirect nature, deduced from comparisons
between observed and computed excited-state popu- lations in an unperturbed plasma [6, 7, 8]. In a recent development more precise, but still indirect infor- mation was deduced from observations in a plasma
where Rydberg states of neutral helium near the bottleneck for collisional-radiative recombination
were perturbed in a well-controlled manner by photo-
ionization with 10.6 1 tlm photons [9]. These obser-
vations were found to be in good agreement with
a collisional-radiative model of recombination in cold plasmas [10] using Mansbach and Keck rates [11] ]
of electron-induced transitions between hydrogenic levels, provided the influence of neutral-induced transitions was properly taken into account. _
With the current progress in experimental tech- niques, and particularly in pulsed dye lasers and in
time-resolved fluorescence measurements, it has now become possible to study directly transitions between
Rydberg levels of an atomic system induced by electron
and neutral collisions. The results presented here
were obtained in a helium afterglow [12] ; helium
may be expected to behave in a nearly hydrogenic fashion, when transfers between highly excited states
are concerned, and high-purity helium afterglows
are well suited to extremely precise and convenient control of experimental conditions.
2. Expérimental methods. - In the experiments reported here, intermediate Rydberg He (p IP)
sublevels are reached by direct photoexcitation from
the He (2 3S) metastable atoms present in sufficient concentration in a high purity, room temperature
stationary helium afterglow [12]. The light source
is a SOPRA dye laser ; after frequency doubling
with a temperature-tuned ammonium-dihydrogen- phosphate (ADP) crystal, the photoexciting UV pulse lasts about 3 ns, with a typical peak power of 500 W, a total spectral width of 0.025 A ; the repetition
rate is 50 Hz. Wavelength is tunable from 2 723 to 2 626 A ; levels 8 ’P to 17 ’P have thus been selectively pumped with good efficiency. These Rydberg levels
lie in what may be called the intermediate range of
principal quantum numbers, as distinct both from
the lower range (p 5) and from the higher range
(p > 20).
After cessation of the laser pulse, the population
of the He (q ’D) level is followed by fluorescence spectroscopy with a 3.5 ns resolution. The principal
quantum number q of the observed level ranges from 3 to 17 and may be equal to p, which will always designate the laser-pumped level ; He (q ’D) is optically connected to He (2 3P), and the wavelength
ranges from 5 876 A (q = 3) to 3 466 A (q = 17).
Other levels of the singlet and triplet subsystems,
as well as of the helium molecular system, have also been occasionally observed.
The general features of the experimental system have been described in detail elsewhere [13, 14]
and only a few specific remarks are needed. After wavelength selection, fluorescence light intensities
are measured with a RCA 8575 photomultiplier
calibrated from 3 000 Â to 7 000 A with a tungsten ribbon reference lamp and operated in the photon counting mode. The resulting photoimpulsions are
then analysed with a multichannel counter having
72 channels of 3.5 ns each, coupled to a minicomputer
and to suitable terminals.
An auxiliary, low-resolution monochromator was
also used to record the time-integrated fluorescence
signal at 3 889 Â on the He (3 3P-2 3S) transition ;
this was found, under constant experimental condi- tions, to be proportional to the laser energy and to the overlap between the laser line and the He (2 3S-
p ’P) line. It thus provides a convenient reference channel against which to normalize measured fluores-
cence intensities.
Residual nonlinearities of the light detection system may cause severe experimental problems in fast, transient fluorescence measurements [14]. Linearity
was carefully checked over the whole experimental
domain. Stability, reproducibility and noise immunity
of the complete system were such as to make efficient
use of the very weak laser-induced fluorescence
signals ; the useful sensitivity limit was about one
detected photon every 50 000 laser pulses.
Finally, plasma quantities, i.e. electron density
and temperature, were measured and, when necessary,
perturbed, using classical microwave techniques [9,12] .
3. Qualitative observations. - As in most fluores-
cence experiments, before detailed data taking and analysis, it is useful to first make a few qualitative
observations which will lead to a discussion of the main coupling mechanisms between the laser pumped
level and the other levels to which it may transfer its excitation.
Excited levels of atomic helium are of course not
exactly hydrogenic. They are distributed within singlet
and triplet subsystems, with negligible radiative coupling. Orbital sublevels with 1 = 0, 1 and 2 (S, P
and D) have non-zero quantum defects [15], res- pectively - 0.140, + 0.012 and - 0.0022 for singlets
and - 0.296, - 0.065 and - 0.0028 for triplets.
However, it should be noted that for relatively large principal quantum numbers energy differences cor-
responding even to the quantum defects of S levels
are quite small (31 cm -1 for 13 3 S and 14 cm -1 for
13 1 S, as compared to 90 cm -1 between the 13 and 14 hydrogenic levels ; energy différences are thus
substantially lower than thermal energy, i.e. 200 cm-1
near 300 K).
Figure 1 shows the typical population evolution
as a function of time of levels 10 3D and 10 3S after
photoexcitation of the 10 ’P level. Except at early times, where there is a slight discrepancy, the two
reduced populations are seen to be equal within
error bars ; this indicates that collisional transfers between S, P and D triplet states are sufficiently
fast for these levels to remain in statistical equilibrium.
Furthermore, levels with 1 > 2 should be effectively
mixed by the Stark broadening due to the quasi-
static Holtsmark field of the ions, as well as by colli-
sions with free electrons [16, 17] or by collisions
with helium atoms. (Gallagher et al. [14] have reported
cross-sections in the 103 Â 2 range for collisional 1-mixing of highly excited d states of sodium by
collision with helium atoms ; at 2 torrs, 300 K, this corresponds to mixing times of order 1 ns.)
Fig. 1. - Typical evolution of the populations of levels 10 3S and 10 3D after selective laser excitation of the 10 ’P level ; experi-
mental conditions : ne = 2.5 x 1010 cm- 3, no = 16.5 x 1016 cm - 3 and Te = 300 K.
It is thus reasonable to expect that the total popula- tion ni of any level of large enough principal quantum number i will always remain statistically distributed among its 1-sublevels of the same multiplicity accord- ing to their statistical weights. A possible, slight depletion of the 1 = 0 sublevel would have a negligible
overall effect.
On the other hand, coupling between levels of different multiplicities (i.e. in this case collisional formation of singlet states when triplet states are directly populated) should be expected to be very slow.
The argument goes as follows : the spin of the optical electron is conserved during the He (2 3S-
p ’P) pumping transition. Most of the population
of the p ’P states is then almost instantaneously
transferred to p 3L states with 1 > 2, which have dominant statistical weights. LS coupling being negligible for states of large angular momentum, the spin of the excited electron behaves essentially
as the spin of a free electron interacting with various collision partners (electrons, neutral atoms). Finally,
the spin of the excited electron is tested in relation to the spin of the core electron, as the atom radiates back to a lower level : it may for example give off
the radiation corresponding to the q ’D-2 1 P or to the q ’D-2 ’P transition, depending on whether the optical electron has exchanged spin with one of its
collision partners or not.
We may thus expect the rate of triplet-singlet
conversion among highly excited states to be compa-
ratively slow, roughly equal to the rate of spin exchange
of a free electron with one of its collision partners present in the experimental cell, taking the earth magnetic field into account.
This is experimentally supported : figure 2 shows
that triplet-singlet mixing occurs on a slow time scale compared with l-mixing within a given multi- plicity. Collisional coupling between levels of diffe- rent multiplicity may thus be ignored on the time scale typical of this experiment.
Associative processes [18] may result in coupling
between atomic and molecular states, i.e. in the for-
Fig. 2. - Typical evolution of the populations of levels 10 ’D, 101D and 10 1p after selective excitation of the 10 ’P level ; experi-
mental conditions : ne = 2 x 1011 cm- 3, no = 5 x 1016 cm - 3 and Te = 400 K. The apparent initial risetime of the triplet popu- lation is due to an instrumental integration time constant.
218
mation of molecular He2 ions or molecular He*
excited states. However, there is no particular reason
to expect that these processes will become important
for Rydberg states. In point of fact, no laser-induced fluorescence could be detected on the most intense molecular bands of helium, He2 (3,4 ’H g- 2 3Eu+)
after perturbation of the atomic triplet system. This indicates that in this experimental range collisional
coupling between atomic and molecular systems may be ignored.
Finally, direct photoionization of the Rydberg
levels by the laser pulse is possible. The temporal
resolution of the microwave electron density measure-
ment system would be inadequate to resolve electron
density relaxation on a nanosecond time scale ; however, its sensitivity is quite sufficient to detect
even minute perturbations of the integrated electron density in a 1 JlS temporal window overlapping
the laser pulse. Such perturbations were indeed
detected at low electron densities for peak laser
powers around 2 kW, but were always negligible
in the experimental range of concern here, where laser power never exceeded 500 W and was in most cases substantially attenuated to preserve the linearity
of the detection system.
4. Analysis of the experimental data. - It was
noted that in our experimental situation the triplet
system of atomic helium behaves for all practical
purposes as if isolated from the singlet and molecular
systems, while the total population ni of level i remains
always statistically distributed among its l-sublevels of the same multiplicity.
As a consequence, provided proper statistical
weights and photomultiplier calibration are taken into account, the global time evolution after cessation of the laser pulse of any observed level of principal
quantum number q can be deduced from the time evolution of the He (q 3D) sublevel, whether it coincides with the laser-pumped level (q = p) or
not.
Let i and j designate any principal quantum number of the helium atom, including the continuum, and
let ni and ni be the population densities of these levels. They will follow the master equation
where the summation includes an integration over
the ionization continuum. Pu is the probability per unit time of collisional-radiative transfer from level i to level j. It is a linear function of the electronic (k1j»
and atomic (ki(?» collisional transfer rate coefficients,
as well as of the radiative transfer probability Aij [10] :
ne and no being the electron and ground state neutral densities, respectively.
By charge neutrality, the electron density is equal
to the ion density, i.e. to the sum off over the ioniza- tion continuum. Eq. (1), with the Pij’s defined by
eq. (2), is thus in general nonlinear. However, the
laser perturbation is superimposed on the recombi-
nation quasi-equilibrium characteristic of an after-
glow plasma [12], and, as already noted, this pertur- bation is weak enough to induce negligible excess
ionization. The electron density ne thus remains
constant and the contribution of the recombination
quasi-equilibrium can be subtracted from eq. (1)
to yield the master equation for the density increases i§ and îîj of the i and j levels due to the laser excitation
pulse
where now the summation extends only to the relevant
bound states. The time evolutions fi;(t) are thus
solutions of a system of linear differential equations
with the initial condition that only level p be populated
at time t = 0 (the geometry of the experimental
system and the time scales involved are such that
no spatial transport term need be included in eqs. (1)
and (3)).
The first sum in eq. (3) is the global collisional- radiative depopulation probability per unit time of level i and may be written
where ki(e) and kO) are the electronic and atomic collisional depopulation rate coefficients. In practice,
radiative population transfers always remain negli- gible compared to collisional transfers over the electronic and neutral density range covered in these
experiments.
As a straightforward consequence of eqs. (2) and (4), note that
The ki’s and kij’s can be measured independently
with the experimental system and eq. (5) will provide
a useful consistency check.
After the end of the laser pulse, the laser pumped
level is gradually depopulated by collisions, while
other levels are populated. After a time, all levels
reach a relaxation quasi-equilibrium. A typical experi-
mental result is given on figure 3 ; it shows the tem-
poral evolution of levels 9 to 15 after almost instan- taneous selective population of level 13 by a laser pulse tuned on the 2 ’S-13 ’P transition (2 645 Â).
The relative position of each curve with respect
to the others is normalized by taking into account photomultiplier calibration, statistical weights, and
Fig. 3. - Temporal evolution of the populations of levels 9 to 15
after selective excitation of level 13 by a laser pulse tuned to the
2 3S-13 ’P transition at 2 645 z. The lines connect the experimental points for each level. Experimental conditions : ne = 2 x 1011 cm-3, no = 6.6 x 1016 cm-’ and T. = 400 K.
the relevant oscillator strengths of the observed helium transitions [19].
Such experimental results contain all the infor- mation needed to determine collisional depopulation
rates as well as transfer rates between the laser
pumped level and its neighbouring levels.
To a first approximation, after short time intervals,
one may consider that only the population excess np of the laser-pumped level is non-negligible at the
end of the laser pulse ; this means that îîj = 0 for
j :0 p in eq. (3) and thus
This simple procedure was used in 1 to determine P, as a function of electron density and thus kle).
It can be refined by taking into account indirect transfers, which become more and more important
at longer times, when the approximation n-, = 0
(j :0 p) becomes less and less valid. The probabilities Pp and Pj are then directly obtained from a multi- parameter least-squares fit to eq. (3) of the experi-
mental results for the population increases nl and for
their time derivatives dn¡jdt [14]. This procedure
was extensively tested on numerical simulations of the experimental results, including the effects of the finite response time of the experimental system, and was found to be satisfactory ; when properly
used, it leads to negligible systematic errors over
the range covered in this experiment.
Finally, the rate coefficients kpj and kp are obtained
from a bilinear least-squares fit to eqs. (2) and (4)
of the experimental probabilities Pj and Pp measured
at various electron and neutral densities. One such fit is shown on figure 4 at constant pressure and
varying electron density ; the statistical data scatter is typical.
Fig. 4. - Collisional-radiative depopulation probability of level
10 as a function of electron density at fixed electron temperature (400 K) and neutral density (5 x 1016 cm-3). The solid line is a
linear least-squares fit to the data.
This procedure was systematically repeated over
the whole experimental range : electron densities from 2 x 109 to 6 x 1011 cm- 3, neutral pressures from 1.5 to 9 torrs at 300 K, electron temperatures from 300 to 2 200 K ; the principal quantum numbers of the laser pumped levels range from 8 to 17 and fluorescence was measured for levels 5 to 17. This
corresponds to a total of approximately 20 million
laser shots, over which laser stability and repro-
ducibility were outstanding.
5. Results. - 5 .1 ELECTRON-INDUCED COLLISIONAL TRANSFER. - Measurements of the electron-induced collisional depopulation rate coefficients k(e) for laser
pumped levels of principal quantum number ranging
from p = 8 to p = 17 are summarized on figure 5.
They are compared to the theoretical hydrogenic predictions of Gryzinski [20], of Mansbach and
Keck [ 11 and of Johnson [21]. The increased sensiti-
vity and resolution of the experimental system and the more elaborate procedure to extract kp from
the data lead only to a slight upward revision, within
error bars, of the preliminary, less extensive results
reported in 1. As already noted in this first report,
they show unambiguously the inadequacy for inter-
mediate principal quantum numbers of the classical
binary-encounter theory of Gryzinski [20]. These
measurements are in satisfactory agreement, within
a factor of about 1.5, with the theoretical predictions
of Mansbach and Keck [ 11 ] and of Johnson [21 ],
which lead to almost undistinguishable depopulation
rate coefficients over this range. A similar agreement
