Experimental study of the mercury 4 047 Å line (6 3P 0-7 3S1) absorption profile in the presence of foreign gases

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Experimental study of the mercury 4 047 Å line (6 3P 0-7 3S1) absorption profile in the presence of foreign

gases

Z. Ben-Lakhdar-Akrout, J. Butaux, R. Lennuier

To cite this version:

Z. Ben-Lakhdar-Akrout, J. Butaux, R. Lennuier. Experimental study of the mercury 4 047 Å line (6

3P 0-7 3S1) absorption profile in the presence of foreign gases. Journal de Physique, 1975, 36 (7-8),

pp.625-629. �10.1051/jphys:01975003607-8062500�. �jpa-00208295�

EXPERIMENTAL STUDY OF THE MERCURY 4 047 Å LINE

(6 3P0-7 3S1) ABSORPTION PROFILE IN THE PRESENCE OF FOREIGN GASES

Z.

BEN-LAKHDAR-AKROUT,

^J.

BUTAUX,

^{R. LENNUIER}

Département

de Recherches

Physiques (*),

Université Pierre et

Marie-Curie, 4, place Jussieu,

^Tour

22,

⁷⁵²³⁰ Paris Cedex

05,

^France

(Reçu

^{le 16 décembre}

1974, accepté

^{le 7 mars}

1975)

Résumé. ²⁰¹⁴ On étudie par

balayage magnétique

^le profil d’absorption de la raie 4 047 Å du mercure.

La cuve d’absorption contient soit un

mélange

^{de mercure et} d’azote, ^{soit un} mélange ^{de mercure}

et de _gaz noble, ^{avec une} petite quantité ^d’azote.

Abstract. ²⁰¹⁴ The absorption profile of the 4 047 Å line of mercury has been studied by ^{means of}

the magnetic

scanning

method. The

absorption

chamber contained either only mercury and nitrogen,

or a small amount of nitrogen ^{and a} perturbing noble gas.

Classification

Physics ^Abstracts

5.280

1. Introduction. ^- The

experiments reported

^here

were

performed

^{in order to measure the}

broadening

and the shift of the 4 047

Á

_mercury line

(6 3pO --+ 7 3S1

transition)

^{in the} presence of

foreign

gases

(N2, He, Ne, Xe).

^{We shall see that in order to} determine the

broadening,

it is also _necessary to obtain the

popula-

tion of the metastable level 6

3P0.

^{Atoms are}

brought

to this level

by

the classical

procedure :

^transition

6

1S0 --+

⁶

3p, by absorption

^{of the resonance 2 537}

^Á line,

^followed

by

the transition 6

3P1 --+

⁶

3Po

^induced

by

inelastic collisions between the _mercury atoms

3P1

^and

nitrogen

^molecules.

2.

Experimental arrangement.

^{- The}

experimental arrangement

^{is shown on}

figure

^1.

Spectral analysis

of the 4 047

Á

line was

performed using

^the

magnetic scanning

^method

[1, 2].

The source is a

monoisotopic

mercury

lamp (Hg 198) [3],

^{at ultra}

high frequencies (500 MHz) [4].

The

rotating chopper

^{S is used to} send either the reference

signal

^or the absorbed

signal

^{to the}

photo- multiplier.

^The

absorption

^{cell is 200 mm}

long,

15 mm in diameter and it is surrounded

by

^a

strongly

cooled helicoidal

exciting

^arc.

An

important difficulty

arises from the _presence of intense unwanted

light

^emitted

by

^the

exciting

^arc

for  ⁼ 4 047

Á.

In order to reduce that

contribution,

the

diaphragms D2, D3

^and

D4,

^{2 mm in}

diameter,

are also

included,

^as direct lock-in detection of the initial

signal

^{did not}

give good

^results.

D2

^and

D3

also

precisely

limit the fraction of the cell in which

absorption

^occurs.

(*) Laboratoire ^associé

au CNRS

^{no 71.}

FIG. 1. ^- Experimental set-up.

As will be mentioned

later,

^this

precaution

^is

necessary if the measurements are to be

correctly interpreted.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01975003607-8062500

626

3.

Principle

^of measurements. ^- Let us call

A(v - vB)

the normalized function

describing

^the

spectral profile

^{of the Zeeman}

scanning

component emitted when the source is in a

magnetic

^{field B.}

For each value

of B,

the measured transmission is :

T(v) being

the transmission of the cell for

frequency

^v.

3.1 THEORETICAL EXPRESSION FOR

T(v).

^{- The}

absorption

^{cell is filled} with natural mercury. For each

hyperfine component j

^{of a}

given isotope i,

and for each

point

^{M in} the cell which has reached

a

thermodynamical equilibrium

state, ^{it is}

possible

to define an

absorption

coefficient

kij(v, ^{M) :}

Bij ^being

Einstein’s coefficient :

N(M)

is the total

population density

^{in the 6}

3Po

state,

ai(M)

is the local relative abundance of the

isotope i, Fij(v, ^M)

is the normalized

spectral profile,

92 and _gl are the statistical

weights

^{of the final and}

the initial levels between which the transition takes

place.

Some

quantities

^{have a} non-uniform distribution in the

cell,

and it is _necessary to discuss this

point.

As a consequence of the reduction of the beam

by

the

diaphragms D2

^and

D3,

^the

M-dependent

quan- tities _vary little with distance

along

directions _per-

pendicular

^to the cell axis

(Oz axis)

^but

they

^can vary

strongly

with distance

along

this axis. This _occurs, in

particular,

^for

(X,ïCM) N(M),

^{which we} shall write

as

(X,i(z).N(z).

However,

^a very

important point

is that the

profile

Fij(v, ^M)

^can be considered as

independent

^{of M.}

For the present

experimental conditions,

^{it is reaso-}

nable to

write,

ⁱⁿ the examined

spectral region :

Fij(v, ^{M) = Gi(v, M) *} Lij(v, ^M)

G,(v, M)

is the Gaussian function related to

Doppler broadening

^and

Lij(v, ^M)

^{is a} Lorentzian function related to natural

damping

^and collisional relaxation.

The temperature ^{does not} vary ^more than a few

degrees

^{from one}

point

of the cell to

another, parti- cularly along

^{the Oz axis}

(mercury

^atoms

brought

to the 6

3Po

^level

by

^an inelastic collision are very

quickly

« thermalised

») consequently,

the Gaussian function has the same width at _any

point,

and will be written

Gi(v).

The Lorentzian function has a width

(Avl)ij

^which

depends

^{on the} temperature ^{and the}

population

density

^{N’ of the}

perturbers.

^{But N’ has the same value}

throughout

^{the whole}

^cell,

^{and T has} almost the same

value. So we shall consider that

(AVL)ij

^{does not}

depend

^{on M.}

ij

We can therefore write the

absorption

coefficient for the

(ij)

component ^{as :}

and the transmission

T(v)

^{for the cell}

(length : 1)

^{is :}

with

where

Generally,

^{for a}

given frequency

^{in the}

expression

of

T(v),

^{we have to take into account all}

isotopic

^and

hyperfine

components.

However,

^for

sufficiently

^low

perturber densities,

some of the components ^{have a} well-isolated

profile.

This will be the case for the

following

components : 199 A,

201 a,

^{201 c.}

3.2 DETERMINATION OF THE APPARATUS FUNC- TION

A(v - vB).

^{- The} Zeeman-shifted component has a

spectral profile A(v - VB),

the width of which is not

negligeably

^small

compared

^{to that of}

T(v).

^It

is then _necessary to

distinguish T’(vB)

^{as defined}

in

(1)

^{from the}

true-profile T(v).

^A considerable

simplification

^{occurs when}

A(v - vB)

^{does not}

depend

on the

magnetic

^{field B.} This is the case for the 2 537

A

line

[2]

^{but not for the 1 850}

^A

^{line of} mercury

(6 1S0 , 6 1P1) [5]

^{where it seems that the field}

dependence

is related ^to the strong

self-absorption

of the line. For the 4 047

A _line, self-absorption

^is

very

weak,

and it seemed reasonable to assume that

A(v - vB)

^{would be}

independent

^{of B. This}

hypo-

thesis has been used for the

interpretation

^{of the}

measurements. Under this

condition,

^{T’ is a convolu-} tion

product :

This

hypothesis

^{leads to coherent}

interpretations,

such that ^- when

extrapolated

^to

high perturbers

densities ^-

they

agree with

interpretations neglect- ing A.

We now have to determine

A(v - vB).

^{When the}

nitrogen

pressure is very low

(a

few tenths of a

torr)

and no other _gas is in the

cell,

^the

profile

^{is :}

LN being

^a Lorentzian

function,

determined

only by

^natural

damping.

^Both

LN

^and

Gi

^{can be} calculated.

We cannot calculate

T(v),

^{because we do not know}

anything

about the mean

populations

ai N. But it is

possible

^{to make a} reasonable

hypothesis

^{about the}

shape

^of

A(v - vB).

We

supposed

^that

A(v - vB)

^{was a Gaussian}

profile,

^{with a width}

AVD

considered as a parameter, the order of

magnitude

^of

OvD being

^{known. We}

computed

families of _curves, each one

corresponding

to a set of parameters

AVD,

ai N.

Comparison

^with

experimental

transmission ^{curves allowed an}

unique

choice for

AVD

^to be obtained

(AVD

^{is about 25}

mK ;

it

depends

^{of course on the}

^working

conditions of the

lamp).

3. 3 SHIFT MEASUREMENTS. ^- The

profile A (v - VB) being symmetrical

^{and narrow}

enough,

^the

magnetic scanning

^near the isolated components ¹⁹⁹

A,

²⁰¹ a, 201 _c, leads to

absorption profiles T’(v)

^{which are}

well isolated and also

symmetrical

^for

perturber

pressures smaller than about 100 torrs.

It is then

possible

^{to obtain}

directly

^{from these}

profiles T’(v)

^the

positions

^{of the}

absorption lines,

and hence the

corresponding

^shifts

Dij.

^{These measure-}

ments show that the shifts are the same for the three centers and are

proportional

^to

perturber density.

In order to determine the shifts for the other ^-

non isolated ^- components, it is necessary ^to compute the whole

profile,

^{as will be}

explained

^{in the next}

section. The final result is that the shift is found to be the same for all the components ^{at a}

given

pressure.

Zero-pressure extrapolation

^{of the}

plots giving

^for

each

perturber

^the

position

of the different _compo- nents, leads ^{to a} determination of the

isotopic

^and

hyperfine

^{structure of the 4 047}

^A

^{line. In table}

I,

we

give

^our results and _compare them to those obtained

by

Blaise and Chantrel. These authors used

a

Fabry-Perot

interferometer to carry ^out the

spectral analysis

^{of the} emission line from a

discharge lamp containing

^{a small amount of Ne}

[6].

3.4 DETERMINATION ^OF

T(v)

^AND

Fij(v)

^{PROFILES. -}

The direct deconvolution of T’ ⁼ A * T in order to

obtain T from T’

(since A

^is

known)

^{is a difficult}

task. We

prefered

^{to use a} substitution method.

Let us suppose that

Fij(v)

^{is a}

^{Voigt profile}

and let us suppose also that the Lorentzian width

(AVL)ij

^{is the same for all the} components

(this hypo-

thesis was very well verified in the case of the 2 537

A line).

^We compute ^the

profiles

^{A *}

T(ai N, OvL)

^and

compare them to the

experimental profile T’(v),

ⁱⁿ

order to look for the parameters oci N and

wL leading

to a

good

^fit.

Unfortunatly,

^{but not}

surprisingly,

many ^sets of parameters

give

^{similar T}

profiles.

^The

removal of the indetermination is

easily

^done

by performing

^several

experiments

^{with the same} pertur- ber

density (same AVL)

but with different 2 537

A

excitations.

Then,

the determination of

AvL

^and

W

^{is no}

longer ambiguous.

^An

example

^{of this}

procedure

^{is shown on}

figure

^2.

FIG. 2. ^- An example of the substitution method. The full lines represent ^the absorption profiles ^{for two} different 2 537 A exciting conditions, but for the same perturber density. ^The plots represent computed absorption profiles corresponding ^{to two different} populations for the metastable 6 3Po level, ^{but to the same lorentzian}

width.

It was verified that

wL

^is

proportional

^{to the} pertur- bers

density

^N’.

Of _course, we have to be _very careful as to the

conclusions,

since the determinations of

AVL

^and

ai N

depend

^{on the} apparatus ^function

A(v - VB).

But,

^{as we have}

already pointed

out, the method ^can be checked since the results obtained at

high

^densities

TABLE 1

628

(when

^{A can be}

neglected)

^{show no}

discrepancy

with those at low densities.

4. R esults. ^- 4.1 POPULATION OF THE 6

3Po

^LEVEL.

- 4. 1. 1 The

populating

^{of the}

3Po

^{level has pre-}

viously

been examined

by

several authors

[7-10].

First,

^{let us}

point

^{out that we did not intend to}

study

^the

populating

^of the metastable

3Po

^level

from the

3P1.

^Our

experiments give only

^mean

populations

ce; N for the different

isotopes.

^Further-

more, these mean values refer to

given

^excitation

conditions. These conditions are

reproducible,

^but

difficult to

analyse.

Transmission measurements were

performed

^under

constant excitation

conditions ; only

^the

nitrogen

pressure in the cell was allowed to vary

(no

^other

foreign

gas ^was

present).

^{The mean}

populations a i N

^increase

nearly linearly

^{from 0 to 45 torrs}

(nitrogen pressure) ;

^for pressures

higher

^{than 60} torrs,

they

remain constant. Under these

conditions,

^{for all}

of the

isotopes,

is about 7 ^x

1010 at.cm-3 (for

^the

lS0

^level

N ~ 5 x

1013 at.cm-3).

It should be

emphasized

^that

absorption

^measure-

ments at a

given frequency,

^{that is without}

spectral analysis

^{of the}

profile,

^would

easily

^{lead to incorrect}

conclusions. This is due to the line

broadening

^and

the line shift which occur when the

nitrogen

pressure increases.

4.1.2 In the course of this

study,

^we have observed

an effect that we

interpret

^{as a}

metastability

^transfer

between

isotopes.

^{In some of our}

experiments,

^the

exciting

^source

(producing

⁶

3P1 atoms)

is made of several

monoisotopic (Hg 198) lamps

^{so that in the}

cell, only

^{the 198 and 201 b} components ^{of the 2 537}

À

line are absorbed

by

^natural mercury. After inelastic collisions with

nitrogen molecules,

^{one would} expect that the 6

3po

^{level would be}

selectively populated

with the 198 and 201

isotopes.

^{In this} case, the 4 047

A absorption

line would be observed

only

for the follow-

ing

components :

201 a,

²⁰¹

b,

²⁰¹

c, 198.

^{As a matter} of

fact,

^we also observe

absorption corresponding

to the 199 A component ^{which is}

quite clear,

^{as this}

component

^is well-isolated and also

corresponding

to the

200, 202,

^{204 and 199 B} components. ^{For these} last mentioned components, ^{we have however to} obtain

T(v)

from ?" in order to

interpret

the results.

Taking

^{into account the}

isotopic composition

^of

mercury, the observed

population

^{of the}

63P0

^level

for the

199, 200, 202,

²⁰⁴

isotopes

is 0.8 of that of the 198-201

isotopes.

Excitation transfers between

isotopes resulting

from collisions between

6 3P1

^{and 6}

1 S,,

^{atoms are}

- according

^to Chéron and Saintout

[11] ]

^{of small}

importance.

^It seems more

likely

that the observed effect is due to the mechanism :

We further note that the addition of a noble _gas at pressures up ^to 0.5 atm to the

nitrogen/mercury

^does

not

significantly change

^the

population

^{of the meta-}

stable state.

However,

the addition of small amounts of

C02,

or CO

(

¹

torr)

^{results in a}

strong

decrease of the

population

^{of the 6}

3Po

^state.

4.2 RESULTS CONCERNING BROADENING AND SHIFT FOR VARIOUS GASES. ^- For

partial

pressures of

nitro-

gen up ^to p ⁼ 2 torrs, ^the

absorption

^can be measured under

good conditions,

while the

broadening

^and

the shift due to

nitrogen

^{itself are} very small.

For this _reason, the

experiments

^{were made with}

a

nitrogen

^noble gas mixture

(PN2

^{= 2 torrs,}

pgas

150 torrs).

Table II

gives

the values for

broadening B

^and

shift

S,

^{obtained as}

explained

above. The

proportiona- lity

^{of the}

broadening

and the shift to the

perturber density

is well verified.

TABLE II

We note

especially

^the blue shift in the case of

Hg-He

collisions.

The collision cross sections

ev :

^{mean relative}

velocity

^of

perturbers)

^{have been}

calculated. In table

III,

^we compare them to the

cross sections obtained for the 6

’SO-6 3P1

^transition

(Â

^{= 2 537}

Â).

TABLE III

We can try ^to

interpret

the order of

magnitude

^of

the ratio

’94047/’72-537 (the

^{case of He will not be}

considered).

Assuming straight

^line

trajectories

^{and a Lennard-}

Jones

interaction,

Hindmarsh’s results

[12]

^{lead to :}

(X4047 and _{a2 537} are obtained from the ratio : broaden-

ing/shift.

^{We now need to estimate}

and

In order to calculate this

dipole-dipole

interaction in the case of Ne and

Xe,

^{we use a} second-order

perturbation theory

and introduce for the energy differences a

unique

^{value AE}

(the

^rather

arbitrary

choice for DE does not matter

here,

^{since we are}

only

concerned with _energy

ratios).

For even

isotopes

^of mercury, the

interaction

energy ^can be written in the form

[13]

where

MJ

^{is the}

projection

^{of J on} the interatomic axis.

R,

^and

R2

represent

respectively

^{the mean}

values

of r2

for the 6s electron and for the other external electron of the _mercury atom.

The

anisotropic

contributions

f (L, S, J, MJ)

^are

equal

^{to zero} for the 6

1 S0,

⁶

3Po

^{and 7}

3S1

^states.

As for the 6

3P1

state, ^we shall take the mean value

R,

^and

R2

have been calculated

by

^{Dr J. Bauche}

(private communication), using

^a

Hartree-Fock

method [14].

^-

The results are listed in table IV.

TABLE IV

Using

^these

results,

^{we find :}

leading

^to

approximately

^{the same} value for the ratio

03C34047/03C32537

⁼ 2.3 for both Ne and Xe.

This result is in

good agreement

with the observed ratios

’74047/U2.537,

^{but we have to}

emphasize

^that

the theoretical

development

^{has been}

necessarily simplified.

Acknowledgment.

^{- We are} very much indebted to Dr J. Bauche for

computing the r2 >

^values.

References

[1] LAGARDE, D., BUTAUX, J., LENNUIER, R., PREVOT, J. Y.,

J. Physique Colloq. ²⁸ (1967) ^{C 2-243.}

[2] BUTAUX, J., ^Thèse Paris, ^1972.

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[4] THULIN, A., ^{J. Scient. Instrum. 32} (1955) ^257.

[5] LEBOUCHER, E., BOUSQUET, C., BRAS, N., Nouv. Revue Opt.

Appl. ⁵ (1974) ^121.

[6] BLAISE, J., CHANTREL, H., ^J. Physique ¹⁸ (1957) ^198.

[7] SCHEER, M. D., FINE, J., J. Chem. Phys. ³⁶ (1961) 15, ^1264.

[8] BIGEON, M. C., Thèse Caen, ^1966.

[9] BIGEON, ^M. C., ^J. Physique ²⁸ (1967) ^157.

[10] PITRE, J., HAMMOND, K., KRAUSE, L., Phys. ^{Rev. A 6} (1972) 6, 2101.

[11] CHERON, B., SAINTOUT, L., J. Physique ³² (1971) ^751.

[12] ^{HINDMARSH W.} R., PETFORD, ^A. D., SMITH, G., ^{Proc. R. Soc.}

(London) ^{A 297} (1967) ^298.

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

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[14] FR0152SE-FISCHER, C., Comput. Phys. ^{Commun 1} (1970) ^151.