Download Disalignment rate coefficient of neon excited atoms due to helium

INSTITUTE OF PHYSICS PUBLISHING
JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS
J. Phys. B: At. Mol. Opt. Phys. 36 (2003) 1885–1898
PII: S0953-4075(03)54875-1
Disalignment rate coefficient of neon excited atoms
due to helium atom collisions at low temperatures
M Seo1 , T Shimamura1 , T Furutani1 , M Hasuo1,3 , C Bahrim2 and
T Fujimoto1
1 Department of Engineering Physics and Mechanics, Graduate School of Engineering,
Kyoto University, Kyoto 606-8501, Japan
2 Department of Chemistry and Physics, Lamar University, Beaumont, TX 77710–10046, USA
E-mail: [email protected]
Received 24 September 2002
Published 24 April 2003
Online at stacks.iop.org/JPhysB/36/1885
Abstract
Disalignment of neon excited atoms in the fine-structure 2pi levels (in Paschen
notation) of the 2p5 3p configuration is investigated in a helium–neon glow
discharge at temperatures between 15 and 77 K. At several temperatures, we
plot the disalignment rate as a function of the helium atom density for Ne∗ (2p2 or
2p7 ) + He(1s2 ) collisions. The slope of this dependence gives the disalignment
rate coefficient. For both collisions, the experimental data for the disalignment
rate coefficient show a more rapid decrease with the decrease in temperature
below 40 K than our quantum close-coupling calculations based on the model
potential of Hennecart and Masnou-Seeuws (1985 J. Phys. B: At. Mol. Phys. 18
657). This finding suggests that the disalignment cross section rapidly decreases
below a few millielectronvolts, in disagreement with our theoretical quantum
calculations which predict a strong increase below 1 meV. The disagreement
suggests that the long-range electrostatic potentials are significantly more
repulsive than in the aforementioned model.
1. Introduction
The analysis of inter- and intra-multiplet transitions induced in atom–atom collisions within
the framework of a molecular theory has been discussed in many papers (e.g. [1]) and
textbooks (e.g. [2]). In order to test the accuracy of the molecular potentials between colliding
atoms proposed in theoretical models, a few elementary processes have been investigated
experimentally. In particular, the disalignment, which represents the angular momentum
relaxation of uniaxially polarized (aligned) atoms, due to atom–atom collisions gives a good
indication of the accuracy of anisotropic molecular potentials. More exactly, the disalignment is
3
Author to whom any correspondence should be addressed.
0953-4075/03/091885+14$30.00
© 2003 IOP Publishing Ltd
Printed in the UK
1885
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M Seo et al
60meV
3
-1
Potential ( x10 cm )
151.5
5meV
151.0
2p2
2p4
2p5
150.5
60meV
5meV
150.0
2p6
2p7
2p8
4
6
8
10
R (a0)
12
14
Figure 1. Some adiabatic potentials for the Ne∗ (2pi )–He system with = 1. is the quantum
number for the projection of the total electronic angular momentum on the internuclear axis. A
typical collision energy (60 meV) for our previous experiment [4] and another one, representative
of the present experiment (5 meV), are indicated by broken horizontal lines. The origin for the
adiabatic energies is the ground state of the neon atom, while the collision energy is given with
respect to the asymptotic limit 2pi of the molecular channel with i = 2 and 7.
defined as the relaxation of the alignment ρ02 /ρ00 of atoms, where ρ02 and ρ00 are the irreducible
tensor components of the atomic density matrix (for more details see [3]). Recently, both
experimentalists [4] and theorists [5] have analysed the disalignment of Ne∗ (2pi ) atoms (in
Paschen notation) due to thermal collisions with He atoms. Wakabayashi et al [4] have
measured the disalignment rate coefficient of excited neon atoms in the 2p2 and the 2p7
states of the 2p5 3p configuration due to neon or helium atom collisions in a discharge cell
for temperatures between 42 and 650 K. Bahrim et al [5] have performed full quantum
calculations of the disalignment cross sections based on the model potential of Hennecart
and Masnou-Seeuws [6], which describes the electrostatic interaction between Ne∗ (2p5 3p)
and He ground-state atoms, for the same range of temperatures. Figure 1 in [5] shows good
agreement between the theoretical disalignment rate coefficients and the experimental data
from [4]. However, at lower temperatures, the disalignment rate coefficient has neither been
calculated nor measured, until now. The investigation of the disalignment process at very low
collision energies is important because it provides a sensitive test for the long-range electrostatic
potentials between the colliding atoms.
In this paper, we report new experimental results in the low temperature range between 15
and 77 K, and compare them with full quantum calculations. In section 2, we briefly review
our quantum mechanical model for computation of the disalignment cross section and rate
coefficient, and we report new theoretical results. In section 3, we present our experimental
set-up, while our procedure to find the disalignment rate coefficient is described in section 4.
In section 5, we compare our theoretical results with our experimental data. Our conclusion
follows in section 6.
2. Quantum calculation of disalignment cross section and rate coefficient
In the present quantum mechanical calculations of disalignment cross sections, we use the same
model potential of Hennecart and Masnou-Seeuws [6] as in [5]. In the framework of this model
potential, the interaction between an excited neon atom and the ground-state helium perturber
Disalignment rate coefficient of neon excited atoms due to helium atom collisions
1887
is treated as a perturbation. Also, the complex multibody interaction between the two rare gas
atoms is simplified in three two-body problems: the interactions between the active electron
(3p) and each of the two cores, Ne+ (2p5 ) and He(1s2 ), at which the core–core interaction is
added. For slow collisions, such as those investigated here, the inner electrons of the Ne+ core
and the He atom are not perturbed. The electron-core electrostatic potentials are given in [6].
The core–core interaction is represented at long range by a polarization term, and at short
range by an empirical term fitted to reproduce the spectroscopic data for potential curves of the
HeNe+ molecular ion [7]. In figure 1, we present some molecular potentials of the Ne∗ (2pi )–
He system with = 1 (where is the quantum number of the projection of the total electronic
angular momentum on the internuclear axis). A complete picture of the molecular potentials
with = 1 includes the 2p9 and 2p10 states, too. But because they are much less relevant for
our discussion in section 5, we exclude them in figure 1. Of course, all the molecular states
of the Ne∗ (2p5 3p)–He system are included in our present calculations. The accuracy of the
model potential proposed by Hennecart and Masnou-Seeuws was tested in a wide range of
collision energies (between 10 and 1250 meV) by comparison with measurements of absolute
cross sections to describe polarization effects in Ne∗ atoms due to collisions with He ground
state atoms in experiments with crossed atomic beams [7], and disalignment effects due to
atomic collisions in gas cells [5, 8]. Excellent agreement between theory and experiment was
found in all cases.
In order to describe the Ne∗ (2pi ) + He collision, we choose a convenient diabatic
representation using as a basis set the unperturbed atomic wavefunctions. All 2p1 –2p10
fine-structure levels of the 2p5 3p configuration of neon are included, which generates 36
molecular channels for the Ne∗ (2p5 3p)–He system. Therefore for each collision energy
the total wavefunction of the system is expanded as a linear combination of all 36 diabatic
electronic states. The expansion coefficients correspond to the radial functions for the nuclear
motion. These radial functions are computed by numerical integration of the time-independent
Schrödinger equation using an improved version of the log-derivative method [7]. Both
open and closed molecular channels are included in our full quantum calculations. From
the asymptotic solutions of the coupled equations we calculate the collision S-matrix. In order
to guarantee the convergence of the S-matrix elements for very low collision energies, we
integrate the coupled equations up to an internuclear distance Rmax of 40 a0 , which is twice
as large as in our previous calculations [5, 7, 8]. In order to test our theoretical cross sections,
we have performed separate calculations in two reference systems:
(a) the space-fixed frame, where the quantization axis is chosen along the relative incident
velocity of the colliding atoms, and
(b) the body-fixed frame, where the quantization axis is chosen along the internuclear axis.
Details about the calculations in these two reference frames are given in section 3 of [7].
From the S-matrix elements computed at various collision energies E, we calculate the
isotropic intra-multiplet cross sections σm J ,m J (E) between the magnetic sublevels m J and m J
of the same fine-structure 2pi (J ) level of a neon atom by using equation (3) in [5], for the
2p2 (J = 1) and 2p7 (J = 1) levels. In figure 2, we show the energy dependence of our
theoretical cross sections σm J =1,m J =0 (thick full curves) for (a) the 2p2 and (b) the 2p7 levels
of neon. Finally, the disalignment cross section σ (E) is calculated as
σ (E) = 3σm J ,m J (E)
(1)
where the quantum numbers (m J , m J ) can be either (0, ±1) or (±1, 0). Because of the
symmetry relationships between the isotropic intra-multiplet cross sections σm J ,m J (which
means that σ1,0 = σ−1,0 = σ0,1 = σ0,−1 ) we can derive σ (E) by using in equation (1) the cross
section σ10 from figure 2.
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M Seo et al
30
σ10
vf14(E)
vf23(E)
vf32(E)
vf77(E)
vf300(E)
(a)
20
σ10 ( x 10
-20
2
m )
25
15
10
5
0
0
10
20
30
E (meV)
40
50
30
σ10
vf14(E)
vf23(E)
vf32(E)
vf77(E)
vf300(E)
(b)
20
σ10 ( x 10
-20
2
m )
25
15
10
5
0
0
10
20
30
E (meV)
40
50
Figure 2. The isotropic intra-multiplet cross section σ10 (thick full curve) of the Ne∗ atom on the (a)
2p2 and (b) 2p7 states induced by collisions with the He ground-state atom as a function of collision
energy. The multiplicative factor v f T (E) in equation (2) is indicated for several temperatures by
thin curves.
For the purpose of a direct comparison between theory and experiment, the disalignment
rate coefficient, K , is needed. Assuming that the energy distribution of atoms in a cell is well
described by a Maxwell function, f T (E), we find K (T ) as
∞
σ (E)v f T (E) d E,
(2)
K (T ) =
0
where E = mv 2 /2 (with v the relative asymptotic velocity and m the reduced mass of the
colliding atoms) and T is the temperature of atoms in the cell. Several examples of v f T (E) are
shown in figure 2. In order to obtain convergent results of K (T ) for T between 15 and 77 K,
the integration in equation (2) is done over an energy interval from 0.1 up to 200 meV. Our
theoretical results for the disalignment rate coefficient are shown in figure 3 (by full curves).
3. Experimental set-up
The experimental set-up and procedure are basically the same as described in [4], and therefore
in this section we will only briefly review them and emphasize the changes made to perform the
Disalignment rate coefficient of neon excited atoms due to helium atom collisions
6
4
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(a)
2
10
-16
3 -1
K (m s )
6
4
2
10
-17
6
4
Theory
Experiment [4]
Experiment (This work)
2
10
-18
2
3
10
10
4 5 6 7
2
3
4 5 6 7
100
T (K)
-15
8
6
(b)
3 -1
K (m s )
4
2
10
-16
8
6
Theory
Experiment [4]
Experiment (This work)
4
2
10
-17
2
10
3
4 5 6 7
2
3
4 5 6 7
100
T (K)
Figure 3. The disalignment rate coefficients K for (a) Ne∗ (2p2 ) + He and (b) Ne∗ (2p7 ) + He
collisions as a function of temperature from our quantum calculations (full curve), experimental
data from [4] (open circles) and the present experiments (full circles). The experimental error bars
are within twice the size of the symbols in (a) and within the size of the symbols in (b).
present measurements. A schematic diagram of the experimental set-up is shown in figure 4. A
tube made of fused quartz was filled with a mixture of neon and helium gases. A glow discharge
was produced with a DC of 0.1–0.4 mA. The structure of the discharge channel was similar
to that shown in figure 1 of [4] except for another slit and the viewing window as shown in
figure 2 of our preceding paper [9]. The two slits and windows were used for the self reabsorption measurements as explained in [9]. The temperature of the discharge channel below
77 K was produced by a continuous flow of evaporated helium gas from a liquid helium Dewar
through the temperature control layer surrounding the channel. This layer was surrounded by
a vacuum. By adjusting the current through a heater immersed in liquid helium, we stabilized
the flow of the cold helium gas from the Dewar. The temperature of the channel was measured
by a thermocouple attached to the outside wall of the channel. Fluctuations of the temperature
were less than 0.5 K during a series of measurements over 3 min. For the temperature of 77 K,
the temperature control layer was filled with liquid nitrogen.
We measured the gas pressure by a ceramic capacitance manometer (ULVAC CCMT100) at room temperature, which was calibrated against an oil manometer, assuming the same
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M Seo et al
Dichroic
Mirror
1064nm
YAG Laser
1064nm
SHG
532nm
ND Filter
Dye Laser
Aperture
(d=1mm)
Photo Diode
GTP
Polarizer
Digitizing
Signal
Analyser
(DSA)
PM
Liquid N2
(77K)
or
He gas
(17K~55K)
Monochromator
Fluorescence
Discharge
Cell
PC
x
z
y
Figure 4. A schematic diagram of the experimental set-up. SHG: second harmonic generator,
GTP: Glan–Thompson prism, ND filter: neutral density filter, PM: photomultiplier, PC: personal
computer.
pressure for the gas in the discharge channel at a low temperature. In situations where the
temperatures of parts of a system are different, the above assumption may not be justified due
to the thermal transpiration effect [10]. This effect is due to insufficient collisions between
the gas particles, and is pronounced at low densities. In our case, the inner diameter of the
discharge tube was 5 mm, which is several hundred times larger than the mean free path length
of the helium and neon atoms. Therefore this effect was considered insignificant and was
neglected.
The excitation light source was a dye laser (DCM in ethanol) pumped by a frequencydoubled YAG laser (Spectra Physics GCR-100). The laser pulse duration (measured as the
full width at half maximum and shown in figure 5(a)) was 6 ns, while the repetition rate
was 50 Hz. The spectral bandwidth was typically 0.01 nm. The laser light was linearly
polarized by a Glan–Thompson prism in the z direction shown in figure 4. A laser light pulse
of λ = 616.4 nm excited the neon atoms from the 1s3 (J = 0) level of the 2p5 3s configuration
to the 2p2 ( J = 1) state, while a λ = 653.3 nm pulse produced the 2p7 ( J = 1) atoms from
the same lower level. The energy of the laser light pulse was about 0.05 mJ. The diameter
of the light beam was 2 mm at the location of the observation. The direct fluorescence of
1s2 (J = 1) ← 2p2 (J = 1)(λ = 659.9 nm) and 1s4 (J = 1) ← 2p7 (J = 1) (λ = 638.3 nm)
transitions were observed for the 2p2 and 2p7 states, respectively. The fluorescence was
observed through the slit on the side wall of the discharge channel and the viewing window
along the x direction in figure 4. The x axis is perpendicular to the discharge channel axis.
We define the quantization axis along the polarization vector of the laser light (the z direction
in figure 4). We observed the fluorescence with the analysing polarizer located in front of the
monochromator (Nikon G-250). Thus we could measure separately the intensities of the π
and σ components. The entrance slit was parallel to the discharge channel axis. The width
and height of the entrance slit were 0.5 and 5 mm, respectively, and those of the exit slit were
Disalignment rate coefficient of neon excited atoms due to helium atom collisions
Intensity (arb.units)
1.0
1891
(a)
0.8
Iσ
77 K
Ne:He=1:100
Helium atom density
23
-3
= 4.81 x 10 m
0.6
laser
0.4
Iπ
0.2
0.0
0
20
40
60
Time (ns)
-0.6
(b)
-0.8
log( - A L )
-1.0
-1.2
-1.4
-1.6
-1.8
-2.0
0
20
40
60
Time (ns)
Figure 5. An example of the observed temporal developments for (a) the fluorescence 1s4 (J =
1) ← 2p7 (J = 1) (λ = 638.3 nm) intensities of the π and σ components (dots) and the temporal
development of the laser pulse (dotted curve) and (b) the longitudinal alignment.
0.5 and 10 mm. The temporal change of the output signal of the photomultiplier was recorded
by a transient digitizing signal analyser (Tektronix DSA601).
In order to determine the relative sensitivity of the π to the σ polarization component
in our detection system, we polarized the excitation light to the x direction. In this case,
the fluorescence intensity is independent of its polarization direction around the x axis. From
measurements of the fluorescence intensities for the π and σ polarization components, the
relative sensitivities were determined to be 0.670 and 0.698 for the wavelengths 659.9 and
638.3 nm, respectively.
In [4] the temperature of the metastable atoms was confirmed to be virtually equal with
the wall temperature of the discharge channel. At a low temperature of 20 K, we measured
the profile of the absorption line for the neon 1s3 (J = 0) → 2p7 (J = 1) transition (of
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M Seo et al
λ = 653.3 nm) using a single-mode CW diode laser. The line profile was found to be well
reproduced by a Voigt profile with a Lorentzian width of 12 MHz and a Gaussian width of
334 MHz. The Lorentzian width corresponds to the natural lifetime of the upper level. From
the Gaussian width the apparent temperature of the metastable neon atoms was found to be
22.4 K. We attribute the slight difference from the discharge tube temperature to the broadening
of the spectrum by the pump-over saturation effects discussed in [4]. We thus conclude that
the actual atom temperature is 20 K in this example.
4. Experimental results
Figure 5(a) shows an example of the temporal developments of the fluorescence intensities
with the π and σ components resolved. The intensities Iσ (t) and Iπ (t) were calibrated with the
relative sensitivity of the π to the σ polarization component in our detection system. Since the
excitation is done with π polarized light in the J = 0 → 1 transition, the initial population of
the upper level is produced only in the m J = 0 magnetic sublevel. In this case, the fluorescence
of the J = 1 ← 1 transition has only the σ component due to the selection rules. During the
lifetime of the upper level, excitation transfer from the m J = 0 magnetic sublevel to m J = ±1
magnetic sublevels, or disalignment, may take place due to atom collisions or trapped radiation.
As a consequence the π component appears in the fluorescence. The atomic processes involved
are: the laser light excitation, the excitation transfer, the radiative decay and the collisional
depopulation. The coupled rate equations are
dn 0 (t)
= −(2k + r )n 0 (t) + 2kn 1 (t) + l(t)
dt
(3)
dn 1 (t)
= kn 0 (t) − (k + r )n 1 (t),
dt
where n 0 and n 1 are the ‘populations’ of the m J = 0 and +1 (or m J = −1) magnetic sublevels of
the upper 2pi level, respectively. Because the magnetic sublevels m J = +1 and −1 are equally
populated (the disalignment process investigated here being isotropic), in equations (3) we
need to include the ‘population’ for the m J = +1 magnetic sublevel only. The rates k and
r correspond to the excitation transfer between the magnetic sublevels, m J = 0 and ±1, of
the same 2pi level and the total depopulation of the 2pi level, respectively. The latter process
consists of radiative decay and collisional depopulation. l(t) is the temporal development of
laser light excitation to the 2pi level.
The intensity of the polarized components of the fluorescence is given by
Iσ (t) = C 12 [n 0 (t) + n 1 (t)]
(4)
Iπ (t) = Cn 1 (t),
where C is a constant that depends on Einstein’s A coefficient of the observed transition, which
is the same for all the magnetic sublevels of the same 2pi level, and the detection efficiency
of the fluorescence. We define the longitudinal alignment for the emitted radiation, which is
proportional to the longitudinal alignment parameter of the 2pi level [3], as
1 n 1 (t) − n 0 (t)
Iπ (t) − Iσ (t)
A L (t) ≡
=
.
(5)
Iπ (t) + 2Iσ (t)
2 n 0 (t) + 2n 1 (t)
The second equality was found by introducing the intensities Iσ and Iπ from equation (4) in the
definition of A L (t). Figure 5(b) shows the temporal development of the longitudinal alignment
obtained from the fluorescence intensities presented in figure 5(a). After the cessation of the
laser pulse (for t > 20 ns in figure 5), the term l(t) in equation (3) vanishes and the longitudinal
alignment derived from the system of differential equations (3) becomes
(6)
A L (t) = − 21 e−3kt .
40
17K
35K
77K
30
10
40
0.5
1.0
1.5
2.0
2.5
24
-3
He atom density ( x10 m )
(b)
6
-1
20K
55K
300K
20
0
0.0
Disalignment rate ( x10 s )
1893
(a)
6
-1
Disalignment rate ( x10 s )
Disalignment rate coefficient of neon excited atoms due to helium atom collisions
30
17K
35K
77K
20K
55K
300K
20
10
0
0.0
0.5
1.0
1.5
2.0
2.5
24
-3
He atom density ( x10 m )
Figure 6. Experimental values for the disalignment rate of the 2p2 state of neon as a function of
the helium atom density. In (a) we present our direct measurements of disalignment rate, while in
(b) the effect of the radiation re-absorption (included in (a)) is separated [9]. The full lines in (b)
show the results of the linear fit within the least-squares method with the null intercept for each
temperature. The experimental error bars are within the size of the symbols.
From the slope of log[−A L (t)], we get the relaxation time, (3k)−1 , which is due to intramultiplet transitions within the same 2pi (J = 1) level. The term 3k due to He atom collisions in
equation (6) is related to the disalignment rate coefficient K defined in equation (2), 3k = n He K ,
where n He is the He atom density. By varying the He atom density in the discharged cell we
determine the disalignment rate coefficient K (T ).
The longitudinal alignment in figure 5(b) for t > 20 ns shows a single exponential decay
with time. The disalignment rate coefficient is determined by fitting the experimental data
points with equation (6). The result of this least squares fitting is indicated by the full line in
figure 5(b).
4.1. Disalignment of the 2 p2 state neon
Figure 6(a) shows the disalignment rate of the 2p2 state of neon as a function of the helium
atom density for several temperatures. The uncertainty of each data point is within the size of
M Seo et al
80
6
-1
Disalignment rate ( x10 s )
1894
60
40
15K
20K
32K
300K
20
0
0.0
0.2
0.4
0.6
0.8
He atom density ( x10
24
17K
26K
77K
1.0
1.2
-3
m )
Figure 7. Disalignment rate of the 2p7 state of neon as a function of the helium atom density. The
full lines are the results of a linear fit within the least-squares method. The experimental error bars
are within the size of the symbols.
the symbols in the figure. In our experiment we prepared the mixture of neon gas at 0.05 Torr
with helium gas of variable pressures at room temperature. The ratio of their partial pressures
was varied from 1:15 to 1:150.
In our cell experiment, disalignment due to electron collisions, neon atom collisions
and radiation trapping are always present together with helium atom collisions. Because the
electron density is of the order of 1016 m−3 in our experimental conditions [11], the disalignment
rate due to electron collisions is of the order of 104 s−1 [12] and therefore can be neglected.
Since we kept the neon density constant for all the helium densities at each T , the disalignment
rate due to neon atom collisions is constant for all the helium densities at each T . For the 2p2
state, the disalignment rate coefficient for Ne∗ + Ne collisions is almost the same as that for
Ne∗ + He collisions [4]. The disalignment rate due to Ne∗ + Ne collisions is estimated to be
about 2.5 × 105 s−1 for the 2p2 state at 77 K and therefore it can be also neglected.
Disalignment due to radiation re-absorption depends on the 1si (i = 2–5) populations in
the discharge channel, and therefore on the discharge conditions. Since at low temperatures the
increase in the disalignment rate with the increase in helium atom density is relatively small, the
determination of the disalignment rate coefficient due to helium atom collisions is sensitive to
the correction for the disalignment rate due to radiation re-absorption. In order to separate the
effect of radiation re-absorption, we measured the self re-absorption of relevant emission lines
by our discharge channel under the same conditions of the disalignment measurement. We have
evaluated the disalignment rate due to radiation re-absorption with a Monte Carlo simulation
program using the measured values of the self re-absorption. The method is explained in detail
in the preceding paper [9]. The disalignment rate due to radiation re-absorption is found to be
between 1 × 105 and 5 × 106 s−1 . Figure 6(b) shows the disalignment rate against the helium
atom density after this correction has been made. The full lines are the results of the linear fit
within the least-squares method with a null intercept. Finally we determine the disalignment
rate coefficient, K (T ), of the 2p2 state of neon for the collisions with the ground-state helium
atoms as the slope of each fitted line. The results for K (T ) are shown in figure 3(a). The
uncertainty of each data point is within twice the size of the symbols.
Disalignment rate coefficient of neon excited atoms due to helium atom collisions
1895
4.2. Disalignment of the 2 p7 state of neon
Figure 7 shows the disalignment rate of the 2p7 state of neon as a function of the helium atom
density for several temperatures. The uncertainty of each data point is within the size of the
symbols. In the experiment we prepared the mixture of neon gas of 0.1 Torr with helium gas
of variable pressure at room temperature. The ratio of their partial pressures was varied from
1:10 to 1:25.
As was the case for the 2p2 state, the disalignment rate due to electron collisions is
negligible for the 2p7 state, too. The disalignment rate due to Ne∗ + Ne collisions is estimated
to be about 3 × 106 s−1 for the 2p7 states at 77 K. Since we keep the neon density constant for
all helium densities for each T , the disalignment rate due to neon atom collisions is constant
and contributes to the intercept. We note that the disalignment rate coefficient for the 2p7 state
at low temperatures is about one order of magnitude larger than that for the 2p2 state. In this
case we expect the correction of the disalignment rate due to radiation re-absorption to have a
similar magnitude as for the 2p2 state, which is rather small. In fact, by adjusting the discharge
current we tried to make the disalignment effects approximately constant for each temperature.
We assume that the correction due to the radiation re-absorption is constant and contributes
to the intercept. Therefore we determined the disalignment rate coefficient of the 2p7 state of
neon due to the ground-state helium atoms as the slope of each linear fit (figure 7). The results
are shown in figure 3(b). The uncertainty of each data point is within the size of the symbols.
5. Comparison between theory and experiment
Figure 3 shows the disalignment rate coefficient for (a) Ne∗ (2p2 ) + He and (b) Ne∗ (2p7 ) + He
collisions as a function of temperature. The present results are consistent with our previous
measurements at higher temperatures [4]. However, in contrast to the excellent agreement
between theory and experiment above 77 K [5], the experimental disalignment rate coefficient
shows a more rapid decrease with the decrease in temperature below 40 K than is predicted by
our quantum calculations. This is more salient in the 2p2 case.
The analysis of the experimental data for the disalignment rate coefficient as a function
of temperature indicates that K (T ) varies as T 1.6 for the Ne∗ (2p2 ) + He collision and as
T 0.9 for the Ne∗ (2p7 ) + He collision below 40 K. Because the temperature dependence of the
multiplicative factor v f T (E) in equation (2) is T 0.5 , the collision energy dependence of σ (E)
may be E 1.1 for the 2p2 state and E 0.4 for the 2p7 state. This dependence suggests that the
strong increase in the theoretical cross section below a few millielectronvolts shown in figure 2
is absent, and that σ (E) converges to zero for E → 0.
At the present stage, the origin of the discrepancy between the quantum calculations
and experiment is not fully clear. Here we discuss possible sources of error. For quantum
calculations, the close-coupling method has a well-established conceptual basis in the
framework of atom–atom collision theory (for details see [7] and the references therein).
In particular, for the Ne∗ (2pi ) + He collisions, this method has been tested successfully in
order to explain various experiments [5, 7, 8]. However, such quantum calculations depend
on the accuracy of the molecular potentials which describe the atom–atom interaction. The
analysis of the adiabatic potentials presented in figure 1 indicates that, for collision energies of
about 60 meV, which are relevant for the domain of temperatures investigated by Wakabayashi
et al [4], the distance of closest approach is about 3.5 a0 for the Ne∗ (2p7 ) + He collision and
8 a0 for the Ne∗ (2p2 ) + He collision [5]. Therefore at higher temperatures the disalignment
rate coefficient is very sensitive to the influence of the short-range electrostatic potentials,
especially for Ne∗ (2p7 ) + He collisions. At temperatures below 40 K, the most significant
1896
M Seo et al
-1
Potential (cm )
400
Vσ
Vπ
Wcc
V 'σ
300
200
100
0
6
8
10
12
14
R (a0)
16
18
20
Figure 8. The electrostatic potentials for the Ne∗ (2p5 3p)–He system in the framework of the
model potential of Hennecart and Masnou-Seeuws [6]: Vσ and Vπ describe the e(3p)–He system
according to [13], Wcc is the polarization dipole term in the long-range core–core potential and Vσ
is a modified Vσ potential.
contribution to the rate coefficients K (T ) is given by collision energies below 10 meV. This
can be observed from figure 2, where the multiplicative factor v f T (E) in equation (2) is
indicated for several temperatures by thin curves. For E < 5 meV, the classical turning
point is located at internuclear distances, R, larger than 10 a0 for both systems. For R
between 11 and 13 a0 , the molecular potentials for the 2p2 and 2p7 states are repulsive, with
energies decreasing from about 40 to 10 cm −1 (these values are given with respect to the
asymptotic 2p2 and 2p7 atomic levels). At low collision energies, the long range interactions
dominate the collision, and very accurate long range electrostatic potentials (for R > 10 a0 )
are needed.
In figure 8, we show the long-range electrostatic potentials for the Ne∗ (2p5 3p)–He(1s2 )
system in the framework of the model potential of Hennecart and Masnou-Seeuws [6] for
internuclear distances between 6 and 20 a0 . In the present quantum calculations, we used
electrostatic potentials in a larger range of internuclear distances, between 2 and 40 a0 . The
core–core potentials, Wcc , were computed in [7] using accurate spectroscopic data for the
HeNe+ molecular ion. In our previous studies [7], we found that, for internuclear distances
larger than 6 a0 , the exchange interaction between the electronic wavefunction of the Ne+ (2p5 )
ion and the ground-state He atom is negligible. Therefore, for such distances we characterize
the core–core interaction by an electric dipole potential, αd /(2R 4 ) (where αd is 1.384 au and
represents the dipole polarizability of the helium atom). The e(3p)–He(1s2 ) system is described
by a model potential fitted to the low energy electron–helium scattering data by Valiron et al
[13]. The Vσ and Vπ potentials of the e(3p)–He system were included by Hennecart and
Masnou-Seeuws in their model potential [6] for internuclear distances up to 15 a0 . In our
present quantum calculations, we adopt the same Vσ and Vπ potentials and show them in
figure 8 for internuclear distances between 6 and 20 a0 . According to [6], Vπ vanishes for
R > 8.5 a0 . The Vσ potential is strongly repulsive, and for R > 9 a0 it can be fitted with a
simple exponential decay function: Vσ (R) = 171 687.78 exp(−R/1.493 92) (in cm−1), within
a maximum deviation of 25%.
The experimental results for K (T ) suggest that the long-range electrostatic potentials are
significantly more repulsive than in the model potential of Hennecart and Masnou-Seeuws [6].
Disalignment rate coefficient of neon excited atoms due to helium atom collisions
1897
This assumption would explain the rapid decrease of the experimental results for K (T ) with
the decrease in T , as shown in figure 3. Also, it suggests that σ (E) decreases rapidly with the
decrease in E below 1 meV, contrary to our quantum calculations.
The strong increase of the theoretical disalignment cross section at energies below 1 meV
(about 8 cm−1 ) can be explained by the overlap between the attractive asymptotic electrostatic
potentials and the repulsive centrifugal barrier. At energies below 1 meV, only the asymptotic
part of the Wcc potentials contributes to collisions. The overlap between the attractive dipole
potential, Wcc , and the repulsive centrifugal barrier (which is due to the rotation of the
internuclear axis) produces a potential well which is favourable to the formation of a resonance
in the scattering cross section. We tested this assumption by using various empirically modified
core–core potentials. However, calculations with modified Wcc do not solve the disagreement
between theory and experiment.
Our studies indicate that the disalignment cross sections for low collision energies is
sensitive to the repulsive Vσ potential for R > 10 a0 . We have done some test calculations
with modified Vσ potentials. In figure 8 we show an example of such a modified potential,
labelled by Vσ . Quantum calculations below 10 meV performed with Vσ change σ (E) by
only 10%, and do not solve the disagreement between theory and experiment. Tests with a Vσ
potential more repulsive than Vσ from figure 8 change σ (E) significantly for E > 10 meV,
and modify the agreement between theory and experiment for higher temperatures [5]. Such a
problem exists because, in our quantum calculations, the collision S-matrix depends on nonlocal electrostatic interactions (over a large domain of internuclear distances). The problem
becomes even more complex if we consider the influence of the rotational coupling. In
our quantum calculations, the rotational coupling between molecular channels was explicitly
included. The strong influence of the rotational coupling on the disalignment cross section
for higher temperatures was presented in figure 3 of [5]. At lower temperatures, the rotational
coupling has a similar contribution to σ (E).
In conclusion, our quantum calculations based on the model potential of Hennecart and
Masnou-Seeuws [6] fails to reproduce the present experimental data for collision energies
below a few millielectronvolts. New quantum calculations for very slow Ne∗(2p5 3p) + He(1s2 )
collisions require a new model for the description of the long-range atom–atom interaction,
with the inclusion of the asymptotic multipole interactions between the two colliding atoms.
Such models were recently proposed by Doery et al [14] for homonuclear diatomic systems of
heavy rare gas atoms. For the Ne∗ + He system, a similar model is somehow more difficult to
find because, in this case, different angular coupling schemes should be used for each colliding
atom. Indeed, the helium atom is described within the standard Russell–Saunders coupling
scheme, while the description of the Ne atom requires the non-standard coupling scheme which
corresponds to the Paschen notation.
Finally, we note that the effect of the short lifetime of the 2p2 and 2p7 states (of about 20 ns)
was not included in the theoretical model which leads to equation (1). However, a helium atom
having a speed of 70 m s−1 , which corresponds to a kinetic energy of about 1 meV, travels
about 1400 nm during its lifetime. This value is three orders of magnitude larger than the
internuclear distance considered here (40 a0 ) and therefore the effect of the short lifetime may
indeed be neglected.
6. Conclusion
Experimental results for the disalignment rate coefficients in Ne∗ (2p2 or 2p7 ) + He groundstate collisions at temperatures between 15 and 77 K are presented and compared with
quantum close-coupling calculations based on the model potential of Hennecart and Masnou-
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M Seo et al
Seeuws [6]. Contrary to the excellent agreement between theory and experiment above 77 K,
the experimental values for the disalignment rate coefficient show a more rapid decrease with
the decrease in temperature from 40 to 15 K than the theoretical results. Our experimental
data indicate that the disalignment cross sections vary as E 1.1 for Ne∗ (2p2 ) + He collisions
and E 0.4 for Ne∗ (2p7 ) + He collisions at energies below a few millielectronvolts, while our
quantum calculations predict a strong increase of the disalignment cross section below 1 meV.
Further investigations are necessary in order to clarify the origins of the discrepancy between
theory and experiment.
Acknowledgments
We would like to thank Professor F Masnou-Seeuws for her useful comments. This work
was partially supported by the Grant-in-Aid for Scientific Research (A) and Grant-in-Aid for
Exploratory Research of the Ministry of Education, Culture, Sports, Science and Technology
in Japan.
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