Polarization Fractions and Magnetic Sublevel Populations
Following Excitation and Ionization-Excitation of Helium by
Molecular Hydrogen (H2+ and H3+) Impact
H. Merabet, R. Bruch, and S. Fülling
Department of Physics, University of Nevada Reno, Reno, NV 89557 USA
Abstract. We present recent measurements of the degree of linear polarization following the extreme ultraviolet (EUV)
emission of helium in H2+ + He and in H3+ + He collision systems at impact velocities ranging from 1.4 to 4.5 a.u. and 1.4 to 3.5
a.u., respectively. The combination of these polarization fractions with our previous total EUV cross sections has enabled us to
determine the first experimental magnetic substate scattering angle-integrated cross sections, σ 0 and σ 1 for ML = 0, ±1,
following excitation of He (1s2) 1S to HeI (1s2p) 1Po levels and ionization-excitation to He+ (2p) 2Po for singly charged
molecular hydrogen (H2+ and H3+) impact. In addition, a comprehensive comparison of these spectropolarimetric data is given
for different collision processes together with our previous proton results at an extended velocity range (2.2 < v < 5.5 a.u.). Such
an experimental database is of great importance for astrophysical and laboratory plasma diagnostics.
radiation is dominated by the 584 Å emission arising
from the n=2 level.
INTRODUCTION
Research in the field of collision processes of
molecules and atoms has developed at an explosive rate
during the last two decades (1). The knowledge of
such collision processes is of great value and has
numerous applications from pure to applied physics. In
particular, most experiments have focused on twoelectron mechanisms in helium, since this is the
simplest target containing more than one electron, and
it is therefore ideally suited for achieving a better
theoretical understanding of the few-body problem (212). Furthermore, radiative emissions from neutral and
ionized helium play a major role in laboratory plasmas
driven by high-intensity, ultrafast femtosecond laser
interactions with gases and solid surfaces (13). The
created plasma is in many cases anisotropic with nonMaxwellian electron distributions leading to bright,
ultrafast X-ray production (13-14).
Simultaneous ionization-excitation of helium
leads to relatively small emission cross-sections (5)
making this mechanism very difficult to observe
experimentally. Such a process produces the singly
ionized He+ (2p) 2P state (also noted HeII (2p) 2P) in
the case of helium and gives rise to the emission of
Lyman-α radiation with a wavelength of 30.4 nm as
follows:
Hm+ + He (1s2) 1S → He+ (2p) 2Po + Hm+* + e|
→He+ (1s) 2S + hv. (2)
The quantity of interest in this class of experiments is
“the degree of linear polarization (P)”, also called
“polarization fraction” which is usually obtained by
measuring
the
emitted
photon
intensities
(perpendicular to the collision plane) that are
polarized parallel and perpendicular to the direction
of the emitted radiation (8). Assuming LS-coupling,
where L and S are the orbital and spin angular
momentum number of the excited levels, the degree
of linear polarization for L = 1 angular momentum
state, can be expressed as (15):
In the following, we draw attention to the
excitation and simultaneous ionization-excitation of
helium processes following proton and molecular
hydrogen singly charged ion (H2+ and H3+) collisions at
intermediate energies.
The dominant excitation
mechanism may produce HeI (1snp) 1Po states via
Hm++ He (1s2) 1S → He (1snp) 1Po + Hm+*
|
2 1
→He (1s ) S + hv, (1)
involving the extreme ultraviolet (EUV) emission of
radiation with wavelengths from λ=584 to 517 Å for
n=2 to 5, respectively, where m = 1-3. This type of
P (1 P o ) =
σ 0 −σ1
,
σ 0 + σ1
for HeI (1snp) 1Po (3a)
P (2 Po ) =
3(σ 0 − σ 1 )
,
7σ 0 + 11σ 1
for HeII (2p) 2Po
(3b)
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
180
where σ M L (ML= -1, 0 and 1) are the magnetic
second-Born cross section values for high velocities
impact (v=6.1 a.u.). The electron cross sections are
then renormalized to protons in a way that keeps
molecular hydrogen to proton cross section ratios the
same as those of Bailey et al. (5) for equi-velocity
projectile impact. The cross sections for the
excitation of He measured in this work were put on
an absolute scale by normalizing our measured high
velocity cross section data to the Bethe-Born cross
section values (9) for electron and proton impact
velocities v > 3.8 a.u. In addition, the obtained cross
section data have been corrected for alignment
effects (7).
sublevel angle-integrated excitation cross sections of
specific ML substates. The differential cross section
σ is given by the sum of the three magnetic sublevel
cross sections,
σ = σ 0 + 2σ 1
(4)
Thus σ M L can be obtained for excitation and
excitation-ionization when combining Eq. (3a) or
(3b) with Eq. (4).
In this work, we have utilized measurements of two
experimental techniques, namely EUV spectrometry
(5,9) and EUV polarimetry (8,15), to determine the first
experimental magnetic substate scattering angleintegrated cross sections, σ0 and σ1 for ML = 0, ±1, for
HeI (1s2p) 1Po and HeII (2p) 2Po excited states
following singly charged molecular hydrogen impact
(H2+ and H3+) at impact velocities ranging from 1.4 to
4.5 a.u. and 1.4 to 3.5 a.u., respectively. These
experimental spectropolarimetric data are compared
with corresponding proton results (17). Such
comparison may shed more light on the mechanisms
involved in molecular hydrogen impact on helium.
The statistical uncertainties of the measured line
intensities in this study were between 0.5% and 3%
over most of the range of impact energies. When
instrumental uncertainties related to energy
resolution of the Van de Graaff accelerator, target
pressure stability, polarization and charge
normalization are combined, the total uncertainty for
magnetic scattering angle-integrated substate cross
sections was found to be about 13% to 15% for HeI
(1s2p) 1Po and HeII (2p) 2Po states.
2
2
HeII (2p) P
He (1s) S
+
H3
+
RESULTS AND DISCUSSION
H2
0.2
Degree of Linear Polarization
The experimental setup used in this work has been
described in more detail elsewhere (5,8-9,16).
Therefore, we give here only a brief overview. This
apparatus is comprised of a target chamber housing
the MLM polarimeter, gas cell and a Faraday cup,
and a 1.5 meter grazing incidence monochromator.
A PC controlled data acquisition system has been
used to operate the apparatus and to record the data.
The polarimeter utilizes a molybdenum-silicon
(Mo/Si) multilayer mirror. The MLM and EUV filter
are fixed in a box that was shielded with aluminum
foils in order to prevent stray light and particles from
entering the polarimeter. Two different wedges were
used with this setup to provide an angle of 50E for
measuring Lyman-α (HeII (2p) 2Po) emission and an
angle of 40E used to measure HeI (1snp) 1Po
emissions. Since sufficiently strong magnetic fields
can lead to a depolarization of the observed radiation
by the Hanle effect, the gas cell used in this study
was mounted inside a cylindrical magnetic shielding.
With this shielding at the interaction region of the gas
target a magnetic field smaller than 0.05 Gauss have
been achieved. The corresponding total cross sections
σ measurements have been conducted using a 1.5 m
high resolution grazing incidence monochromator.
H
+
0.1
0.0
1
10
1
HeI (1snp) P
+
2 1
H3
He (1s ) S
+
H2
0.2
H
+
0.1
0.0
0.1
1
10
Target Pressure (mTorr)
FIGURE 1: Gas target pressure dependence of HeI and
HeII radiation following proton and molecular hydrogen
impact measured with the EUV-MLM polarimeter.
In order to maintain single-collision conditions, a
detailed pressure dependence of the emission from
both excited and ionized-excited helium was
investigated with the EUV grazing incidence
monochromator and the MLM polarimeter for
different projectile impact. In Figure1, we show the
degree of linear polarization as a function of the
target pressure for HeI and HeII states for protons
These HeII results have been put on the absolute
scale by renormalizing our proton data (17) to full
181
quite different from those of protons within the
velocity range investigated. Such distinction is
found to be further pronounced for H3+ projectiles.
On the other hand, the H2+ data exhibit a minimum at
1.5 a.u. followed by a gradual increase and then
decrease as a function of the velocity and the H3+
results have a constant decline. Since a more refined
theoretical description of this complex multicenter
collision processes does not currently exist, little can
be said about contributions to the total scattering
amplitude due to multicenter scattering and
interference effects in such complicated collision
systems. Nevertheless, a preliminary comparison of
the velocity dependence corresponding to the
polarization fraction for HeI and HeII measurements
indicates that, for excitation process, the H2+ and H3+
projectiles act on helium like two and three
independent protons, respectively. On the contrary,
for the ionization-excitation mechanism our EUV
results suggest taking into account electron-electron
interaction and/or other effects because the
polarization and therefore the angular distributions
are not just sensitive to the projectile charge but also
to its mass and structural complexity.
and molecular hydrogen ions. It is clearly seen from
this figure that the polarization fraction is constant
only below 1 mtorr for most projectile impact in the
case of HeI (1snp) 1Po states. Consequently, a gas
pressure of 1 mtorr was adopted for this type of
measurements. For HeII measurements higher gas
pressures were used (30 mtorr for protons) since
depolarization did not occur for helium pressures
under 40 mtorr. However, for molecular hydrogen
projectiles, a pressure of 10 mtorr was employed in
order to avoid dissociation of H2+ and H3+ prior to
encountering the emission region of the target cell.
A. Polarization Measurements
Our HeI (1snp) 1Po and HeII (2p) 2Po polarization
measurements following molecular hydrogen impact
(H2+ and H3+) are depicted in figure 2. The
corresponding, previously obtained proton data (17)
are also shown in this figure for comparison.
0.2
2
o
2
HeII (2p) P
o
He (1s) S
0.1
The HeI and HeII magnetic sublevel cross sections σ0
and σ1 are plotted in figure 3 and figure 4, respectively,
for different projectiles. We note that the general trend
0.0
1
HeI (1snp) P
o
2 1
o
He(1s ) S
150
2
o
2
HeII (2p) P
He (1s) S
0.1
2
cm )
+
+
H3
-20
0.0
-0.1
-0.2
H
+
H2
100
Magnetic Sublevel Cross Section σ0 (10
Degree of Linear Polarization
B. Magnetic Sublevel Cross sections
1
2
3
4
5
50
0
1250
Projectile Velocity (a.u.)
1
o
HeI (1s2p) P
2 1
He (1s ) S
1000
FIGURE 2. Polarization fraction for the HeI (1snp) 1Po and
HeII (2p) 2Po states as a function of projectile velocity for
proton and hydrogen molecular impact.
In the lower part of this figure, we note that the
degree of linear has the same velocity dependence.
In particular, the polarization fraction is zero for
protons at the same H2+ impact velocity and shows
almost identical values for H2+ and H3+ in the 1.4 to
2.5 a.u. velocity range. It is interesting to compare
these HeI findings with HeII measurements in order
to clarify diverse collision processes. The molecular
hydrogen polarization fractions for HeII seem to be
+
H
+
H2
750
+
H3
500
250
1
2
3
4
5
Projectile Velocity (a.u.)
FIGURE 3. Magnetic sublevel scattering angle-integrated
cross sections σ0 for HeI (1s2p) 1Po and HeII (2p) 2Po states
as function of projectile velocity.
182
In summary, we have measured the degree of
linear polarization of radiation from the decay of
excited HeI (1snp) 1Po (n=2-5) and HeII (2p) 2Po states
following proton and molecular ion (H2+ and H3+)
impact on helium at EUV wavelengths using an
optically characterized EUV polarimeter. The
measured polarization fractions appear to be insensitive
to the mass and geometry of the projectile since almost
all their values are equal within experimental
uncertainties for proton and molecular hydrogen (H2+
and H3+) induced excitation of helium whereas this is
not the case for the ionization-excitation mechanism.
This means that electron-electron interactions may play
an important role in the highly correlated ionizationexcitation process. We have also determined here
magnetic sublevel cross sections σ0 and σ1 for HeI
(1s2p) 1Po and HeII (2p) 2Po levels by combining
polarization fractions with total EUV cross sections for
Hn+ + He (m = 1-3) collision systems.
The
experimental results exhibit a similar behavior of the
sublevel cross sections σ0 and σ1 for each mechanism.
The present experimental database may serve as an
important prototype test case for future theoretical
calculations for such complex collision systems.
for σ0 and σ1 of is the same for HeI (1s2p) substates.
Similar behavior is observed for the HeII (2p)
sublevels. In addition, the σ0 cross sections are found
to be bigger than the σ1 results on the entire
investigated energy range for both excitation and
simultaneous ionization-excitation. From figure 3 and
figure 4 it can be seen that in the high-energy limit the
proton and molecular hydrogen data tend towards the
same asymptotic values. Alternatively, overall both σ0
and σ1 show alike velocity dependence for each
investigated projectile for HeI whereas these sublelvel
cross sections exhibit distinct velocity dependence for
H3+ ions when compared with H2+ and proton impact
results in the case of HeII emission. Indeed, all HeI
data start at their minima at a projectile impact velocity
of 1.4 a.u., then increase with increasing projectile
velocity until reaching their maxima between 2 and 2.5
a.u.; after that they decrease. However, HeII cross
sections for both proton and H2+ results have
continuous decline as function of the projectile velocity
impact while the H3+ sublevel cross sections behave
like the corresponding HeI measurements. The current
comparison between HeI and HeII suggests taking into
account more collisional effect like the electron
correlation for the process of ionization-excitation.
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2
+
H
+
H2
40
-20
Magnetic Sublevel Cross Section σ1 (10
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2
He (1s) S
2
cm )
o
HeII (2p) P
60
+
H3
20
0
1
o
2 1
HeI (1s2p) P
750
He (1s ) S
+
H
+
H2
500
+
H3
250
1
2
3
4
5
Projectile Velocity (a.u.)
FIGURE 4. Magnetic sublevel scattering angle-integrated
cross sections σ1 for HeI (1s2p) 1Po and HeII (2p) 2Po states
as function of projectile velocity.
183