Complete spectral profile of the 6 1S0-6 3P 1 mercury line perturbed by argon

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Complete spectral profile of the 6 1S0-6 3P 1 mercury line perturbed by argon

D. Perrin, J.C. Jeannet

To cite this version:

D. Perrin, J.C. Jeannet. Complete spectral profile of the 6 1S0-6 3P 1 mercury line perturbed by argon. Journal de Physique, 1981, 42 (12), pp.1607-1610. �10.1051/jphys:0198100420120160700�.

�jpa-00209358�

Complete spectral profile ^{of the 6} 1S0-6 3P1 mercury line perturbed by argon

D. Perrin and J. C. Jeannet

Département de Recherches Physiques (*), Université Pierre-et-Marie-Curie, ^Tour 22, 4, place Jussieu, 75230 Paris Cedex 05, France

(Reçu ^{le 30} avril 1981, accepté ^{le 26 août} 1981)

Résumé.

Ce travail expose les résultats obtenus dans la région spectrale ^{dite «} intermédiaire ^» qui n’avait pas

encore été explorée. ^L’étude expérimentale ^est faite par spectroscopie laser, ^la largeur spectrale de la fonction

d’appareil ^étant de l’ordre de 2 GHz. On observe une évolution monotone du profil, différente selon que les fré- quences ^sont supérieures ^ou inférieures à la fréquence centrale 03BD0. On précise ^{les limites} expérimentales ^{de validité}

des lois observées antérieurement de part ^{et d’autre de ce domaine.}

Abstract.

The spectrum of Hg (61S0-6 3P1) perturbed by Ar is obtained in the so-called ^« intermediate frequency region ^{» which had not} yet ^been experimentally studied. We have used a tunable dye ^laser spectrometer apparatus the spectral ^{width of} which varies around 2 GHz. The spectral profile ^{does not} exhibit any undulation and the

shape ^{is different for} frequencies superior ^{to or inferior to the central} frequency 03BD0. We determine the experimental

limits of validity of the laws previously observed in the neighbouring regions.

Classification Physics ^Abstracts

32.70

34.20

1. Introduction.

The 6 ISo-63pl ^line shape ^of

mercury perturbed by ^noble gases has been studied

previously by ^different techniques ^{in our} laboratory

in order to get information about mercury-noble gas interaction potentials ^{for the two} mercury ^states involved in the transition [1-3].

The line core, explained ^{in the} impact approxima- tion, covers a narrow frequency range ; high ^resolu-

tion analysis is necessary and for this, magnetic scanning ^{was used.}

On the other hand, ^the wing region ^{where the} quasi-

static theory yields information useful for the poten- tials is much wider ; except ^{in some} parts, high ^reso-

lution was not necessary and a grating spectrometer

was quite sufficient.

Due to the lack of well-suited apparatus ^{we had}

not yet results in the frequency range between those

previously ^studied

typically between 20 and 90 GHz.

When the perturber ^{is helium, the line} shape ^{is the}

same lorentzian profile ^on both sides of this ^unex-

plored region ; this result could be expected ^because

the impact region ^is wide for this perturber.

For the other noble _gases, the shape ^{is not the same}

on both sides of the intermediate region. ^{In so far as} computations ^on the « whole » profile ^{are elaborat-}

ed [4-6] ^{we wish to obtain an accurate} determination of the spectrum ^{in this «} intermediate » region ^where

(*) Laboratoire associé au C.N.R.S. nO 71.

neither the impact approximation ^{nor the} quasi-

static approximation ^{is valid.}

The construction of a tunable dye ^laser spectrome-

ter apparatus, the width of which varies around 2 GHz in the spectral range concerned, ^{allows us to} complete ^our previous measurements.

Our work has been focused on the Hg-Ne ^{and the} Hg-A pairs ^{because the} previous ^results concerning

them were quite different in the wing region, ^{at the}

very time when they ^were qualitatively ^{the same when}

the perturber ^{was one of the} heavy ^noble gases [2, 3].

The results relating ^{to the} Hg-Ne pair ^{will be} published

in another _paper devoted to the light perturbers. ^We present here the results for the Hg-A pair ^{which has}

been choosen rather than the Hg-Kr ^{or the} Hg-Xe pairs because it was the more convenient for this

study : the value of the optical ^{cross section allowed}

us to expect ^a lorentzian profile beyond ^the frequency

range covered by ^the isotopic ^structure of the 2 537 A

mercury line, ^{i.e. a «} transition region » unperturbed by ^the impurities ^{of the} monoisotopic sample ^of

mercury.

2. Design ^{of the} apparatus.

^The apparatus ^has been mostly described in a previous paper [7]. ^The light ^{source is a} nitrogen pumped dye ^{laser; the} optical length ^{of the} cavity ^{is varied} using CO2 pres-

sure scanning ; ^the dye (coumarin 500) ^is circulating

in a cell. A crystal of lithium formate monohydrate

generates the second harmonic (around ^03BB

^{2 537} A)

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198100420120160700

1608

with angular phase matching ^{at room} temperature and no rotation is _necessary during ^a pressure scanning corresponding ^to about 400 GHz. When a Fabry-Perot

etalon is added inside the cavity, ^the apparatus ^func- tion is nearly ^{a Gauss} function, the width of which is about 2.1 GHz.

The U.V. beam is split up into two parts ^labelled (1)

and (2). (1) passes through ^a cell filled with a mixture of _argon and saturated _vapour of 202 mercury placed

inside an oven. (2) is the reference beam. These two beams are focused through UG5 filter glasses ^{on a}

detector (model 141 ^UV detector/preamplifier ^Molec- tron). ^The signal analysis device is the same as the

one described in reference [7]. ^Both signal (2) ^and signal (1)-to-signal (2) ^{ratio are measured on a chart}

recorder.

Part of the visible dye ^laser output ^{was sent into}

an « external » Fabry-Perot interferometer to provide

accurate frequency calibration markers during ^{a scan.}

This interferometer had a 5 mm fixed spacing.

A thin _mercury cell _may be inserted on beam (2) ;

the relevant signal ^{exhibits an} absorption peak ^{for a} specific frequency which is used as wave number reference.

By using successively three cells filled with mix- tures of _argon and saturated _vapour of 202 _mercury, the absorption profile ^can be studied in the whole

frequency range.

Analysis ^{of this} mercury sample has been made

previously by ^a spectroscopic method. The _argon pressures used were 200 torr and 400 torr for 20 cm

cell length, ^{and 700 torr for 1 cm} cell length. ^Different

atomic densities of _mercury were used by varying ^the

cell temperature. ^All experiments ^were performed ^bet-

ween 20 OC and 60 °C. Thus, the different absorption

measurements overlap ^{in the -130,} + 110 GHz fre- quency range (from ^{the line} centre).

Results are shown on figure ^1.

3. Results.

3.1 LINE coRE. - When the cell

length ^{1 and} the atomic _mercury and _argon densities

-

respectively ^{N and N’ - are} adjusted ^{so that the}

transmission of the cell is measured with reliability

over about 20 GHz on both sides of the minimum,

the absorption ^{curve exhibits an axis of} symmetry, the position of which is noted as vi.

In spite ^{of a rather} unprecise determination of the

position of this axis ^our shift measurement results are

consistent with the value 1.98 ± ^0.12 GHz/atm. given by J. Butaux [1].

Consequently this value was assumed to determine the position ^of vô, ^the perturbed ^{line centre. Ln} k(v’)

versus Ln (v’) (where

^{v -} v’0) ^is plotted ^on figure ^{1. It shows a} straight ^{line with a} slope ^measur- ing-2 ^{between 12} and 20 GHz on both sides of v0.

This corresponds ^{to a} Voigt profile becoming nearly

lorentzian sufficiently ^{far from} v’. ^A first estimate of the lorentzian half-width leads to about 7.8 GHz/atm.

The analysis ^{of the} curves can then be improved

thanks to theoretical computations ^of profiles ^{for the} v0 ± ^{30 GHz} range using this value and assuming

that k(v’) is the convolution of a Gauss function (appa- ratus) by ^a Voigt ^function

this latter being ^{itself the}

convolution of another gaussian (Doppler) by ^a

Lorentz function (Hg-A collisions; Hg-Hg ^collisions

are negligible ^{in these} experiments). Computations

have been performed ^{for different sets of} experiments taking ^{into account the} isotopic ^{structure and the} composition ^{of the} mercury sample, ^and varying ^the

width of the different functions around previously

determined values.

The agreement between the experimental ^{and com-} puted ^{curves allowed us to} conclude that the effect of collisions on the line shape ^{leads to a} lorentzian profile

shifted towards lower frequencies ; the half-width is :

and the corresponding optical ^cross section is

This description is limited to the v - v0 | 1 ^{18 GHz} frequency range ; this value is a little bit inferior to that obtained by ^{J. Butaux} (235 Â2) ; this last value had been considered less sure than that concerning

the other perturbers because of technical problems

encountered (difficulty of thermal equilibrium).

Writing ^the validity ^{condition of} impact approxi-

mation :

(V : ^{mean relative} velocity ^of perturbers), ^{we obtain}

this limit is superior ^{to the} experimental ^one.

3.2 THE ^NEAR WINGS.

Some results have been obtained previously ^{for the} 90 v | ^{150 GHz}

domain :

-

If v’ 0 (« ^{red »} wing) ^the experimental law ^for

the evolution of k(v’) is v’ |-3/2. ^{This can be related}

to the theoretical expression obtained in the quasi-

static theory when the difference between the two

isotropic levels involved in the transition is

and when Condon points ^{are real} [4, 8].

(a : ratio of the absorption coefficient to the intensity

distribution for this transition, ^N’ perturber density).

Consequently ^this region

so-called A in refe-

rence [2]

^{has been} interpreted ^{as a « static} wing »

connected with the existence of a potential ^difference

h AC6 ^{r 6 with} ~C6 ~ ^{1.65 x 10-32 s-l.cm6.} Taking

into account the 6 3p 1 ^level anisotropy (m

^{0 and}

1 m 1

1) ^{and the} frequency range implied, AC6

is a characteristic of the two potentials ~V1 (6’SO-6 3P1, | m |

1) ^{and AV °} (6 ISo-6 3P1, m

0)

which coexist and for which the adiabaticity ^condition

is probably ^{not fulfilled.}

-

For v’ > 0 (« ^{blue »} wing) ^a good agreement ^has been found between the experimental law and the theoretical expression obtained in the ^same _assump- tions as (1) ^{but with} complex ^Condon points :

with

vo is the most probable velocity, ^a and fl are ^numerical coefficients ; because of different approximations ⁱⁿ computations, their values slightly differ with the authors (a in reference [4] ^{has to be} multiplied by ^a

factor 2).

This spectral ^{range had been} interpreted ^{as an}

antistatic wing connected with the same pair ^off potentials ^as previously (v’ 0).

3.3 THE « INTERMEDIATE » REGION.

For v’ > 18 GHz, ^Ln k(v’) ^versus Ln 1 v’ has ^{not the same}

evolution for v’ > 0 and v’ 0.

-

v’ 0 : The slope gradually deviates from - 2 and monotonically ^tends towards -1.5 ; this limit is obtained beyond 60 GHz from v’. ^{We found} again

the previous qualitative ^and quantitative ^results

obtained in the near red wing ^and mentioned above (2).

Therefore we can assess the lower limit of « region ^{A »}

at about 60 GHz for our estimated temperatures. ^This value is less than the theoretical value

obtained by writing ^the quasistatic validity condition :

(perturber is still with respect ^{to the} emitting ^atom during the time of ^« interest »).

-

v’ > 0 : The decrease of k( v’) is much faster than in the other wing. ^The experimental points ^are plotted ^on figure 1 ; they ^{fall on to a} straight ^line,

the slope of which is ^{~ -} 2.4 (up ^{to 80} GHz and for temperatures ^{in the} vicinity ^{of room} temperature).

Previous results suggested ^{that we compare expe-}

rimental values to those deduced from relation (2).

We have plotted g( v’) ^{versus Ln v’ :}

Fig. ^2.

Expérimental ^and computed ^{functions g(v’) : x computed}

curve, Ref. [4] ; ²⁰²² computed curve, Ref. [8] ; - - - experimental

curve. In each case the experimental ^curve is translated by ^{Ln A}

along the vertical axis.

1610

(A : ^constant proportional ^{to a and} ~~C6). ^{This has}

been done for values of j8 proposed respectively by Tvorogov ^{and Fomin} [8] ^and by Szudy ^and Baylis [4],

for temperatures corresponding ^{to those of our} experiments (in ^{fact g(v’)} is insensitive to the small variation of T we had to consider) ^and assuming AC,6

^{1.65 x} lO- 32 s-1. cm6 (Fig. 2).

The agreement ^between experimental ^{curve and} g(v’) ^is fairly good beyond 25 GHz. But yet ^{the coef-} ficient A adopted ^{is about} 1.3 times the theoretical coefficient. This result is consistent with previous

results obtained in the farther wing. ^{It is} necessary to notice that the theoretical coefficient had been

computed assuming ^an isotropic difference of poten- tials, ^{and this} assumption ^{is not} fulfilled in our case.

4. Conclusion.

Several conclusions can be drawn from this study. ^{First, the} « intermediate region »

-

which is not subject ^{to the} restriction of either

impact ^or quasistatic approximation

^is very ^narrow and does not show _any undulation ofprofile.

Contrary ^{to what} happens ^with light perturbers [3]

k(v’) ^{loses its} lorentzian shape ^on both sides of vi ^for

the same frequency separation. ^The lorentzian region

so delimited fulfills the impact theory conditions.

The red wing ^becomes quickly ^{the same as the one} predicted by ^the quasistatic theory ^when

whereas the condition of validity ^{of the} theory ^{is not}

fulfilled. The identification arrives much faster ^{for the}

blue wing

^{at least} as concems the evolution law.

A computation ^{of real and} imaginary ^{cross section}

has been performed by ^{E. Leboucher} [9] using ^an analytical method and taking ^{into account} theoretical data and the Lennard Jones 6-12 or 6-9 potential proposed ^to explain ^the shape ^{of the} wings [2-3]. ^It

concerns the pairs Hg-Xe, Hg-Kr ^and Hg-A; ^the

results are in good agreement ^with experimental ^values given by ^{J. Butaux} except for the real cross section of

Hg-A (03C3opt), ^{which is inferior to the} experimental

value (157 ^A2 instead of 235).

This computation ^{shows that} broadening ^{of the}

line is _very critical on the short and intermediate range part ^{of the} potentials which have probably ^a larger weight ^{for the} light perturbers (such ^as argon).

The disagreement between theoretical and experi-

mental values comes probably from the fact that

repulsive ^{branches of the} potentials ^are badly depicted by empirical Lennard Jones models.

Acknowledgments.

^We would like to thank Professor R. Lennuier for his continuous interest in the present work, and Dr. E. Leboucher and Dr.

J. Butaux for helpful discussions.

References

[1] BUTAUX, J., Thèse, ^Paris (1972).

BUTAUX, J., SCHULLER, F., LENNUIER, R., ^J. Physique ³³ (1972)

635.

[2] ^BEN LAKHDAR, Z., PERRIN, D., LENNUIER, R., ^J. Physique ³⁷ (1976) ^{831 and 39} (1978) ^137.

[3] ^BEN LAKHDAR, Z., Thèse, ^Paris (1978).

[4] SZUDY, J., BAYLIS, ^W. E., J. Quant. Spectrosc. ^Radiat. Transfer

15 (1975) ^{641, 17} (1977) 269 and 681.

[5] ^{KIELKOPF, J. F., J.} Phys. ^{B 9} (1976) ^1601.

[6] LEBOUCHER, E., ^NGUYEN HOE, ^J. Physique ^{Lett. 41} (1980) ^L-57.

[7] BUTAUX, J., JEANNET, J. C., Opt. Commun. 28 (1979) ^81.

[8] TVOROGOV, ^S. D., FOMIN, ^V. V., Opt. Spectrosc. ³⁰ (1971) ²²⁸

and 31 (1971) 554; Appl. Opt. 12 (1973) ^584.

[9] LEBOUCHER, E., ^J. Physique ⁴² (1981) ^813.