Book Title in 9 point bold
Editors: Editors name. In case of more than 3 editors use first name and et al.
Copyright © 2006, Narosa Publishing House, New Delhi, India
EXCITATION OF HELIUM ATOMS IN He-He COLLISIONS
S. Yu. Kurskov and A. S. Kashuba
Department of Physics, Petrozavodsk State University, 185910 Petrozavodsk, Russia
ABSTRACT
The present work is devoted to study of He I excitation in binary low energy He He collisions. The purpose of
this work is the investigation of mechanisms of atomic levels excitation at collision energies, corresponding the
conditions of adiabatic approximation. The results of the experimental investigation of the excitation cross sections
of He I 31P, 33P, 31D, 33D levels in the collision energy range from threshold up to 500 eV (cm) and degree of
polarization for 21S–31P, 23S–33P, 21P–31D and 23P–33D transitions in this energy range are represented. Also the
degree of polarization for 21P–n1D transitions as function of the main quantum number (3n12) at the fixed
collision energy of the particles is represented.
I Introduction
The importance of the study of non-elastic collisions of normal helium atoms was conditioned by their significant
role in different scientific and technical applications. Among the numerous research aspects of non-elastic collision
of neutral particles the determining of quantitative scattering characteristics in the conditions of a beam experiment
plays a considerable role. The low collision energy range is a special interest since the theoretical treatment of nonelastic processes at such energies is rather complicated and, therefore, the quantitative data as well as the
information on mechanisms of population of atomic states can be obtained in an experiment mainly. The
development of plasma physics, plasma chemistry, and astrophysics requires clarification of the idea of low-energy
atoms interactions, that is a significant interest of quantum theory of scattering.
Non-elastic scattering channels available for collision spectroscopy methods (ionization, excitation of resonance
and metastable states [1–3]) for the system He(1S0)+He(1S0) were investigated most thoroughly. The excitation
cross sections of some states He(1snl) with n=2–4 depending on the atomic collision energy were defined by optical
methods, excitation thresholds were measured for these states [4]. With the help of coincident equipment in papers
[57] simultaneous excitation of helium atoms into 2P states, and excitation into the states up to n=3 in paper [8]
were investigated.
Quantitative characteristics of atomic excitation processes of He I atoms under the interaction of a beam of fast
helium atoms in the ground state with a gas target are discussed below.
II Experimental Setup
The measurements of the excitation cross sections of interaction of an atomic beam with a gas target were carried
out by optical methods on CAMAC-based setup, controlled by computer [9]. Experimental setup outline is shown
on figure 1.
The neutral atoms beam was produced by means of charge exchange of He ions in the source gas in the
extending electrode channels of the ion source. The ions, remained in the atomic beam after neutralization, were
removed by deflecting plates. The energy spread of atoms (FWHM) measured by the time-of-flight method was
equal to 113 eV. The presence of the metastable atoms was controlled by the photoionization method. The quantity
of the metastable atoms of helium in 21S and 23S states in the beam of the fast particles was equal to 0.6%. The
density of the atom beam was defined by secondary electron emission from the detector surface. The dependence of
the secondary emission coefficient from the energy of atoms was measured [10]. The flux density of fast atoms in
the collision chamber reached 1016 particle/(m2s). The angular divergence of the neutral beam did not exceed
3·104 sr.
The target gas pressure was measured by the vacuum ionization gage. The target gas pressure in the collision
chamber was equal to 4.5·101 Pa, the residual gas pressure did not exceed 3·10 4 Pa. The gas pressure at the ion
source varied in the range 10–20 Pa.
Book Title in 9 point bold
Figure 1. Experimental setup:
1 – ion source; 2 – multi-channel charge exchange cell; 3 – gas target;
4 – detector of fast atoms; 5 – optical recording system.
The investigated area was at 123 mm distance from the extending electrode of the fast particle source and at 12
mm distance from the atom beam detector inlet. The distance between the detector target electrode and its input
aperture was equal to 47 mm. In determination of the flux density of fast atoms scattering of particles from the beam
was taken into account.
As a spectral device the diffraction grating spectrometer with changeable gratings was used, the width of the
device spread function did not exceed 2 Å. The observation zone and the spectrometer input slit were located at two
focal length distance from the quartz imaging lens. The vacuum chamber had the quartz output window with
thickness of 1 mm and diameter of 30 mm.
The emission of excited atoms was registered by photomultiplier tube in conditions of photon counting. The
photons were detected by the photomultiplier tube ФЭУ-106 that was cooled to –15 0C. The count rate of dark
pulses did not exceed 0.5 counts/s. Photomultiplier tube calibration was carried out according to standard procedure
by the registration of a certified tungsten band lamp spectrum. The storage time of a signal was chosen according to
the given error in the count rate and in the area of spectroscopic thresholds it reached 2 hours at one energy.
The analysis of polarization of emission was implemented using the film polaroid. The compensators from the
quarter-wave mica plates were applied to remove the influence of polarizing effect of the optical monochromator.
The permanent linear polarization did not exceed 0.005. In the measurement of the polarization degree for 2 1P–n1D
transitions against main quantum number (3n12) the compensators were not used. In this case the monochromator
transmission was measured on the wavelengths, which corresponded to those transitions, for light which was
polarized transversely and in parallel to the monochromator aperture.
The emission of exited particles was observed at right angle to the atomic beam, therefore radiating particles of
the beam and the target were not distinguished.
III Underlying Measurement Principles
The measurement procedure was described in detail in the work [10]. The emission cross section was measured
in the experiment directly. Note that the emission cross section is determined by measuring of the spectral line
intensity, the flux density of fast atoms and target particle density.
Without taking angular divergence of the dipole radiation into account, emission cross section is equal to
 ij 
4 S ( )
G
1
,
 K ( ) I p N t L 1  
where   a solid angle, defined by the optical system aperture; S ( )  photon count rate; K ( )  absolute
sensitivity of the registration system at the given wavelength; I p  beam intensity of the fast particles; N t  target
particle density, and L  observation zone length. The coefficient G considers the angular distribution of dipole
emission:
G
3 P
3(1  P cos 2  )
,
2
Excitation of helium atoms in He-He collisions
where P  a degree of polarization,   an angle between a beam of fast particles and an optical axis of system.
The degree of polarization is determined by the following expression
P  ( I par  I per ) /(I par  I per ) ,
where I par and I per  intensities of components which are polarized in parallel and transversely to the beam of
fast particles respectively. The value  takes into account a part of the excited fast atoms, which irradiate before
leaving the observed zone. It is equal to
x
  1  i exp( l / xi )(1  exp(  L / xi )) ,
L
where l  the distance between the point of fast particles enter the collision chamber before the observation zone
and xi   i , where   colliding particle velocity,  i  excited state life time. The multiplier 1 /  was obtained
from the condition that excitation cross sections of fast and slow particles in symmetric collisions are equal. The
atom beam intensity in the observation zone was defined in the following way:
Ip 
where J  detector current,
J
0
e ( E ) exp( s ( E ) N t d )
,
e – charge of electron,  0 ( E )  coefficient of secondary electron emission from the
detector surface under the action of fast atoms,  s (E )  cross section of decrease of fast atoms from atomic beam,
а d  distance from the observation zone up to the detector surface.
IV Results and Discussion
The excitation cross sections of He I 31P, 33P, 31D, 33D levels and the polarization functions for the 2 1S–31P,
2 S–33P, 21P–31D and 23P–33D transitions in the interaction of the ground states helium atoms are represented in the
figures 2–5, respectively. The dependence of the polarization degree for the 2 1P–n1D transition on the main quantum
number (3n12) at the fixed collision energy is represented in the figure 6.
The statistical error of the measurements for the excitation cross section did not exceed of 5% (with probability
of 95%). Taking into account the inaccuracy of measurements of the absolute spectral sensitivity, the inaccuracy of
the definition of the secondary electron yield from the detector surface of the fast particles, and the inaccuracy of the
definition of the gas pressure of the target the systematic error could reach ±60%. The statistical errors for the
polarization function are represented on the pictures.
Apparently from figures the polarization of the emission of the helium atoms depends not only on the orbital and
spin moments of atom, but also on the collision energy of the interaction particles. The most strong polarization of
the radiation is expressed at the singlet lines, which are corresponded to 2 1S–31P and 21P–n1D transitions. At the
triplet lines, which are emitted as a result of 2 3P–33D and 23P–33D transitions, the feature in the dependence of the
polarization degree on collision energy is observed. The figures 4–5 show that the pronounced oscillation structure
affects the general behavior of the dependence of the cross section on the energy.
3
Figure 2. He I 31P level excitation cross section (  ) and degree of polarization
for 21S–31P transition (  ) plotted against collision energy of He atoms.
Book Title in 9 point bold
Figure 3. He I 33P level excitation cross section (  ) and degree of polarization
for 23S–33P transition (  ) plotted against collision energy of He atoms.
Figure 4. He I 31D level excitation cross section (  ) and degree of polarization
for 21P–31D transition (  ) plotted against collision energy of He atoms.
Figure 5. He I 33D level excitation cross section (  ) and degree of polarization
for 23P–33D transition (  ) plotted against collision energy of He atoms.
The equidistance of the relative maximums and minimums on the excitation functions in the scale of the reverse
velocities of the system after the collision allowed to suppose that the observed features are the result of oscillations,
which are determined by the phase interference of the quasimolecule states of the He 2 system at the large
internuclear distances [11, 12]. The squares of the “loops”  UR  between the interfering quasimolecule states
and the initial phases of oscillations are defined [13].
Since the scattered atoms were not registered the excitation in that axially symmetric atom system (axis of
symmetry coincide with the direction of a beam of fast particles) is completely determined by two parameters: the
full cross section and the alignment parameter [14–17]. Using the expression for the alignment parameter it is
possible to find the formulas, which connect the excitation cross sections of corresponding sublevels with the
4
Excitation of helium atoms in He-He collisions
polarization degree of the emission, which is registered in the direction perpendicular to the beam of the fast atoms
[17–19].
According to this formulas for the axially symmetric system with orbital momentum L = 1 the knowledge of the
polarization degree of the radiation allows to determine the excitation cross sections of the magnetic sublevels
explicitly.
From these relations it is possible to show that in the case of the 3 1P level the relative partial excitation cross
sections of the magnetic sublevels with the M l = 0 and M l = 1 at the collision energy 250 eV (maximum of the
polarization function) is equal 0.48 and 0.26 correspondingly. With the increase of the collision energy they are
changed to 0.40 and 0.30 at 470 eV (minimum of the polarization function) respectively. In the case of the 3 3P level
the relative partial excitation cross sections of the magnetic sublevels with the M l = 0 and M l = 1 at the collision
energy 200 eV is equal 0.42 and 0.26 respectively, and at the energy 450 эВ – 0.30 и 0.35. The preferred population
of the magnetic sublevels with M l = 0 may be conditioned, for example, by the non-adiabatic radial coupling of the
g–'g states and also of the rotational coupling of the g–g–'g states of the quasimolecule He2. The probable
excitation mechanism of the 3 1,3P levels may contain, for example, following series of the transitions:
(1s g ) 2 (2 p u ) 2 X 1 g  (1s g ) 2 (2 p u ) 2 1  g  (1s g ) 2 2s g 4d g 1  g .
(Note that the sublevels with M l = 1 are mainly occupied at the interaction of helium ions with helium atoms
[20, 21]). Probably, the decrease of the polarization degree at the increase of the collision energy evidences of the
increase of the magnetic sublevels with M l = 1. It may be condition by the contribution to population of the
mentioned levels of transitions between the g–g, g–g–g and other states of a quasimolecule. The polarization
degree at the excitation of the level with spin, which is not equal zero, is not significant because the angular
distribution of photons “are smeared” because of presence of the spin-orbit interaction of electrons of the colliding
atoms. Besides, the cascade transitions from the n3S и n3D levels lead to the radiation depolarization.
We can only estimate the range of the possible magnitudes of the relative partial excitation cross sections of the
magnetic sublevels with M l = 2 for the He I 31,3D levels. The relative partial excitation cross sections of the
magnetic sublevels of the 31D level with M l = +2 or 2 at the polarization maximum (270 eV) may be estimated at
0.07 to 0.17, but at the polarization minimum (130 eV) may be estimated at 0.16 to 0.25. In the case of the 33D level
the relative partial excitation cross sections of the mentioned magnetic sublevels at the polarization maximum
(100 eV) may vary from 0.08 to 0.18, but at the polarization minimum may vary from 0.26 to 0.32.
However, the excitation of the magnetic sublevels with M l = 2 may be caused not only by the population g,
g and other states of the He2 quasimolecule but the deviation of the internuclear axis from the direction of the fast
atoms beam. In the last case the population of the sublevels with M l = 0 formed as a result of the g–'g transitions
in the center-of-mass system is transformed to the population of the sublevels with M l = 2 in the laboratory system
through the change of a scattering angle [22].
The oscillation structure presented on the dependence of the polarization degree of a radiation of the 2 1P–31D
transition on the collision energy of a particle is changed in the antiphase with oscillations in the full excitation cross
section of the 31D level. The mechanism of these oscillations is not clear.
Figure 6. The degree of polarization for the 2 1P–n1D transitions plotted against
main quantum number at 450 eV collision energy.
Book Title in 9 point bold
Concerning the dependence of the polarization degree for the 2 1P–n1D transitions from the main quantum
number (figure 6), possibly, the decrease of the polarization degree of a radiation is related with the shift of the
oscillation structure on the excitation functions of the high levels to the direction of the large collision energies [10].
Besides, the slow decrease of a polarization degree may be caused by the increase of amount of of the depolarization
collisions of particles at the states with a large main quantum number, since the increase of the n1D levels life time
from 16 ns at n=3 to 955 ns at n=12 leads to the increase of the effective thickness of the gas target for the atoms at
these states. The change of the orbital moment orientation in this case may be related with both the elastic scattering
of excitation atoms and the resonant exchange of the excitation between the mentioned atoms and gas target atoms.
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