We are carrying out a joint theoretical and experimental research program to study the broadening of alkali atom resonance lines due to collisions with helium and molecular hydrogen for applications to spectroscopic studies of brown dwarfs and extrasolar giant planets

Babb, J. F.

Kirby, K.

Shindo, F.

Zhu, C.

NASA Technical Reports Server

NASA LAW, February 14-16, 2006, UNLV, Las Vegas
Experimental and Theoretical Studies of Pressure Broadened
Alkali-Metal Atom Resonance Lines
F. Shindo, C. Zhu, K. Kirby & J. F. Babb
Harvard-Smithsonian Center for Astrophysics, Cambridge, MA
{fshindo, czhu, kkirby, jbabb}@cfa.harvard.edu
ABSTRACT
We are carrying out a joint theoretical and experimental research program to
study the broadening of alkali atom resonance lines due to collisions with helium
and molecular hydrogen for applications to spectroscopic studies of brown dwarfs
and extrasolar giant planets.
1. Introduction
The broadened resonance lines of sodium and potassium appear prominently in the
spectra of certain classes of brown dwarfs, and are expected to be present in the spectra
of certain extrasolar planets as well (Burrows et al. 2001; Sudarsky et al. 2003). Accurate
line-profiles, as a function of temperature and density, will be invaluable to astrophysicists
as diagnostics of the atmospheres of substellar mass objects. Our project currently consists
of an experiment to measure pressure broadening of potassium resonance lines by He and by
H2 at about 1000 K combined with theoretical calculations for other temperatures.
2. Description of the experiment
The critical elements in the absorption spectroscopy experiment include a Mach-Zehnder
interferometer and a 3 m Czerny-Turner grating spectrograph with CCD camera detector
(1024 × 256 pixels with a size of 26 µm) for dispersing and recording spectra. The spec-
trometer (McPherson model 2163) covers the wavelength range from 360 to 920 nm through
the use of a stepper controller enabling the rotation of a 1200 l/mm plane ruled grating at
116 different angles. As a background light source, we use a tungsten halogen lamp (250 W,
24 V) with the beam collimated through an arrangement of optics before entering the inter-
ferometer. A unique feature of the experiment is the accurate determination of the absorber
atom number density, which is obtained using the “hook” (or anomalous dispersion) method.
https://ntrs.nasa.gov/search.jsp?R=20060052431 2019-08-29T18:46:46+00:00Z
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To reproduce the conditions of the environments we want to study, the apparatus was
designed to allow measurements at different noble gas pressures, from 10 torr to 700 torr, and
at high temperatures (about 900 K). The cell was fabricated according to the design showed
in Fig. 1. The cell body is composed of three welded tubes of grade 330 stainless steel,
Fig. 1.— Cell design.
chosen for its resistance to the corrosive effects of alkali-metal gases at high temperature.
The middle tube (cold path-length l = 20 cm) is the gas chamber and it is closed by MgO
windows sealed with graphite gaskets. Each of the two tubes on the outside of the gas
chamber contains a cylinder and a spring to press the MgO window in, thereby allowing
the noble gas pressure in the gas chamber to reach values as high as 700 torr. The cell
ends are closed by quartz windows sealed with Viton O-rings. All of the cell body tubes are
independently connected to a vacuum line. The potassium sample is placed in a 330 grade
stainless steel reservoir attached to the cell by a Swagelok fitting allowing the reservoir to
be removed readily for sample replacement.
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The reservoir and the tube leading to the gas chamber are heated by homemade heaters
regulated through a commercial temperature controller. The gas chamber is inserted in a
specially designed split tube furnace that fits within our experimental size constraints. The
oven ensures that there is a uniform temperature along the path-length of the gas chamber
and facilitates the removal of the cell from the apparatus.
The system oven plus gas cell is situated in one branch of a Mach-Zehnder interferometer
whereas a pair of MgO windows and a pair of quartz plates are placed in the other arm to
compensate the windows of the gas cell. Then, the interferometer is adjusted at optical
zero path difference to produce a set of horizontal interference fringes at each wavelength
present in the light source. The fringe pattern is focused by a lens on the entrance slit of the
spectrometer. As each arm of the interferometer can be blocked by a shutter, we are able to
measure the spectrum arising from the gas cell, a reference spectrum and the fringe pattern.
The association of the interferometer and the spectrometer is essential to apply the so
called “hook” method (Rozhdestvenskii 1912), which provides a measurement of the atomic
number density of the absorbers vaporized in the gas chamber. This technique uses the
change in the refractivity in the vicinity of a resonance line which induces a distortion of the
fringe profile. By inserting an additional compensation plate into one of the interferometer
arms, the fringes are shifted to higher orders. Consequently, the fringes will appear slanted in
line-free spectral regions, whereas close to absorption lines the anomalous dispersion produces
maxima and minima in the fringe positions with wavelength, giving the characteristic hook
appearance near the lines. As the shape of the fringes is closely related to the number density
of absorbers, fitting the fringe distortion near the potassium doublet at 770 nm leads to the
determination of the potassium density number.
3. Theoretical work
Accurate calculations of the opacities due to pressure broadening in the wings of reso-
nance lines require accurate potential energy curves and transition dipole moments for the
alkali-metal atom and perturber gas atom (or molecule) interactions. Because satisfactory
data were not available in the literature for the K-He and K-H2 systems, the “Molpro” quan-
tum chemistry codes implementing a Multi-Reference Configuration Interaction method were
used to compute, at an unprecedented level of accuracy, all of the molecular states involved
in the line-broadening of the resonance lines (Santra and Kirby 2005).
The pressure broadening of Li, Na, and K by He in the wings of the resonance lines
was investigated using fully quantum-mechanical methods (Zhu et al. 2005, 2006) and the
calculated reduced absorption coefficients at several temperatures for Na-He and K-He are
presented in Fig. 2. Future experimental and theoretical work will focus on the K-H2 system.
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500 560 620 680 740
λ (nm)
10-41
10-40
10-39
10-38
10-37
10-36
α
ν 
(cm
-
1 s
-
1 H
z-
1 )
T=500K
T=1000K
T=2000K
670 730 790 850 910
λ (nm)
10-41
10-40
10-39
10-38
10-37
10-36
α
ν 
(cm
-
1 s
-
1 H
z-
1 )
T=500K
T=1000K
T=2000K
Fig. 2.— Absorption coefficients for a) (left view) Na-He and b) (right view) K-He at
temperatures of 500 K, 1000 K, and 2000 K.
This work is supported by NASA Grant NAG5-12751.
REFERENCES
Burrows, A., Hubbard, W. B., Lunine, J. I., and Liebert, J 2001, Rev. Mod. Phys., 73, 719
Rozhdestvenskii, D. S. 1912, Ann. Phys., 39, 307
Santra, R. and Kirby, K. 2005, J. Chem. Phys., 123, 214309
Sudarsky, D., Burrows, A., and Hubeny, I. 2003, ApJ, 588, 1121
Zhu, C., Babb, J. F., and Dalgarno, A. 2005, Phys. Rev. A, 71, 052710
Zhu, C., Babb, J. F., and Dalgarno, A. 2006, Phys. Rev. A, 73, 012506


Experimental and Theoretical Studies of Pressure Broadened Alkali-Metal Atom Resonance Lines

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