Band profiles associated with induced dipole transitions in alkali-rare gas systems

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Band profiles associated with induced dipole transitions in alkali-rare gas systems

B. Sayer, J.P. Visticot, J. Pascale

To cite this version:

B. Sayer, J.P. Visticot, J. Pascale. Band profiles associated with induced dipole transitions in alkali- rare gas systems. Journal de Physique, 1978, 39 (4), pp.361-368. �10.1051/jphys:01978003904036100�.

�jpa-00208769�

BAND PROFILES ASSOCIATED WITH INDUCED DIPOLE

TRANSITIONS IN ALKALI-RARE GAS SYSTEMS

B.

SAYER,

J. P. VISTICOT and J. PASCALE

Service de

Physique Atomique,

^Centre d’Etudes Nucléaires de

Saclay,

B.P. n°

2,

^{91190 Gif sur}

Yvette,

^France

(Reçu

^{le 24 octobre}

1977, accepté

^{le 19 décembre}

1977)

Résumé. ²⁰¹⁴ Nous avons calculé les profils de bandes moléculaires de systèmes alcalin-gaz ^rare qui ^{sont associées aux} transitions dipolairement interdites entre l’état fondamental et le premier

état excité S ou D de l’alcalin. Ces calculs ont été effectués en utilisant la méthode quasi statique ^et

des données théoriques ^récentes concernant les potentiels adiabatiques ^et les forces d’oscillateur.

A partir ^des comparaisons ^{à des} profils expérimentaux, d’intéressantes informations ont été obtenues concernant

l’origine

des bandes observées et la validité des données

théoriques.

Abstract. ²⁰¹⁴ We have calculated the molecular band profiles of alkali-rare gas systems ^associated with dipole forbidden transitions between the ground ^state and the first excited S or D state of the alkali atom. These calculations use the quasistatic method and recent theoretical data relative to the adiabatic potentials and oscillator strengths. ^The comparison ^with

experimental profiles

provides interesting information about the origin of the observed band and the validity of the theoretical data.

Classification

Physics ^Abstracts

32.70 ^- 33.70 ^- 34.20

1. Introduction. ^- For a

long

time it has been known that the collisions between atoms broaden and shift the emission or

absorption lines ;

^{the colli-}

sions at small

impact

parameters, ^which

strongly perturb

the initial state of the

emitting

^or

absorbing

atom,

being responsible

^{for the}

profile

of the far

wings

of the lines. Under certain

circumstances, secondary intensity

^maxima

generally

called satellite bands _may appear in these far

wings.

^{Those associated}

with the lines of the alkali atoms which are

perturbed by

^rare gas ^atoms have often been studied.

The initial studies dealt with the bands associated with the resonance lines and, more

recently,

^with

those which have been associated with the

quadru- pole

transitions between the

ground

^{state nS and the}

first excited D state,

(n - 1)

D, of the alkali ^atom.

All these

experimental

^{data are} included in refe-

rence

[1].

^In the last few _years new bands have been observed and associated with the forbidden transi- tions between the

ground

^state and the first excited S state,

(n

⁺

1)

^S

[2]-[4].

A.

Gallagher

and collaborators

(see

^Ref.

[5]

^and

references

therein)

have studied in more detail the

profiles

of the far

wings

^{of the resonance lines and}

their variation with both the

temperature

^{and the} concentration of the rare gas

perturbers.

^{From these}

studies

they

determined the adiabatic

potential

^curves

of the alkali-rare _gas systems

associated,

ⁱⁿ the sepa-

rated atom limit, with the

ground

^state and the first ’P

state of the alkali atom.

The interaction between an alkali atom and a rare gas ^atom leads to a

mixing

of the alcali wave- functions. This affects

only slightly

^{the oscillator}

strengths

of the molecular transitions in the alkali-

rare gas system associated with the resonance lines, which

consequently

^can be assumed to be

independent

of the interatomic distance R. In contrast to

this,

the alkali wavefunction

mixing

makes the oscillator

strengths

of the molecular transitions associated with forbidden transitions in the alkali atom

strongly dependent

^{on R. This}

explains

the existence of bands associated with these forbidden transitions.

Obviously,

the structure of these bands is related both to the adiabatic

potentials

involved in the molecular transi- tion and to the variation of the oscillator

strength

with R.

Numerous

experimental

^data

concerning

^{the bands}

associated with the S-S and S-D electric

dipole

forbidden transitions have been related

only qualita- tively

^{to the} calculated adiabatic

potential

^curves

V(R)

because of the lack of

knowledge

of the relevant oscillator

strengths.

^These

comparisons

have neverthe- less led to

interesting

conclusions

[4]. Recently,

^the

oscillator

strengths f

^{for some} of these molecular transitions of the alkali-rare _gas

systems

^{have been} calculated as a function of R

[6].

^In this article we

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01978003904036100

362

use these data and those of the theoretical adiabatic

potentials [7]

^to calculate, in the framework of the

quasistatic

^{method, the band}

profiles

^associated

with the forbidden transitions between the

ground

state and the first excited S and D states of the alkali atom. We have limited our calculations to the cases

where

sufficiently precise experimental

data exist.

The

comparison

between the calculated

profiles

^and

those observed in the

experiments

of references

[4]

and

[8]

^{allows us to now make more}

significant

comments on the adiabatic

potentials

^{and to obtain}

new information liable to direct future

investigations.

2. Method of calculation of the band

profiles.

^-

2.1 THE QUASISTATIC ^{METHOD. -} The band

profiles

have been calculated

by

^the

quasistatic

^{method and}

by considering only binary

interactions. We

briefly

summarize the method which is described in detail elsewhere

[9]. According

^to the Franck-Condon ^‘

principle,

^the

wavelength Z

^{of a}

photon

^emitted

or absorbed

during

^the collision of two atoms is related to

Vu(R)

^and

Vl(R),

the adiabatic

potentials

of the _upper and lower states involved in the mole- cular transition,

by :

The

intensity I(À.)

of the emitted band is

given by :

where nu and nR

^are

respectively

^the concentration of the alkali atoms in the _upper state and that of the rare gas atoms ;

A (R )

^{is the} transition

probability

and

Pu(R)

is the distribution function of the rare gas atoms around the alkali atom in the _upper state.

The summation over different values

Ri

^{means that}

several interatomic distances _may

correspond

^to

emissions at the same

wavelength.

The

absorption

coefficient

k(Â)

^{is similar to}

Z) :

where the

concentration ni

and the distribution func- tion

Pl

^{are those}

corresponding

^to the alkali atom in the lower state,

and g

^are the statistical

weights.

In the

following

^we take the canonical distribution function

Pu.1

^{as :}

This distribution function is based ^on the

hypo-

thesis of a

thermodynamic equilibrium

between the

populations

^{of the} various states ; this will be dis- cussed latter on.

The observation of the emitted satellite band does not

directly give I(À)

^but,

taking

^the

apparatus

function F of the measurement system ^into account,

it

gives

the convolution

product I(À) * F(Â).

^In

the following

^we consider the normalized values

a(Â)

and

Ko,).

2.2 DISCUSSION OF THE METHOD. ^- More elaborate methods have been

proposed

^{for the}

calculation

^of

the band

profiles [10]-[12].

^The

profiles

^obtained

show little difference when

compared

^{to those}

given by

^the

quasistatic

^method,

except

^{in the}

region

^where

the

potential

^curves

Vu(R)

^and

Vi(R)

^are

parallel,

that is to say in the

neighbourhood

^{of a}

wavelength

extremum,

dÂ/dR

^{= 0}

[12].

^{At this}

point

^the

quasi-

static method presents ^a

discontinuity (see

^rela-

tion

(2))

^which

disappears

^{when a more refined}

treatment is used. However, the differences between

the

results

given by

^the various methods when

I(À)

is convoluted

by

^{a wide}

apparatus function,

^{as in} the case of the

experiments

considered

here,

^are small.

Two other

hypotheses

have been made in the calculation :

binary

interactions and

validity

^{of the}

canonical distribution function

Pu,,(R).

^These

^hypo-

theses have been discussed in detail in reference

[9],

and we will

only

consider them

briefly.

The interaction of an alkali atom with several

rare gas ^{atoms can}

always

^be

neglected

^{if the rare}

gas concentration is low

enough.

^{In order to estimate}

an upper limit for this concentration let us consider the distance

R,, beyond

^{which the rare} gas ^atoms do not

noticeably perturb

the alkali atom. If the

proba- bility

^of

finding

^{one rare} gas ^atom in a

sphere

^radius

of

Re

^is

^small,

^{that is to} say :

then, the

three-body

interactions can be

neglected.

If the adiabatic

potentials

^{are not too}

attractive,

the relation

(6)

^{leads to :}

Taking Re

^{= 20 a.u.}

(atomic units),

which appears to be reasonable in view of the calculated adiabatic

potentials

^{of reference}

[7],

^{we obtain :}

The

experiments

^{at which we refer to}

satisfy

^this

condition.

The classical distribution function which has been used

(see

^relation

(4))

^is

only ^valid,

^{in the case of}

an adiabatic

potential

^curve

having

^a

well,

^when the

thermodynamic equilibrium

between the free and the bound molecular states is reached. This

happens

^{when the}

frequency

of the collision which dissociate the molecular states is

large compared

^{to the}

inverse of the radiative time constant of these states.

Consequently,

the classical

expression of Pl

^{is valid}

in the case of

absorption by ground

^{state alkali}

atoms. For the emission spectra, ^{where the}

emitting

alkali atoms are in excited states, ^each

specific

^situa-

tion

might

be considered. Both the dissociation fre- quency, which is related to the

depth

^{of the}

potential well,

and the radiative lifetime

depend

^{on the}

pair

considered. In

practice,

^{when the rare} gas

density

^is

large enough

^for

maintaining

^the

equilibrium

^between

atomic and molecular states the band

profile

^becomes

independent

^{of the rare} gas

density.

This has been observed in the

study

of the far

wings

^{of the resonance}

lines

(see

^Ref.

[5]

^and references

therein).

These studies have shown that the

equilibrium

between the

popula-

tions of the free and bound states is reached for a

density

^{of rare} gas ^atoms close to one amagat ^for the lowest excited P states. The radiative lifetimes of the D and S states are

generally larger

than those of the P states and the

depth

^{of the}

potential

^{wells are}

not very different. Thus we suppose that the

equili-

brium is reached in the

experiments

^{that we consider}

here.

The distribution function

given by

^relation

(4) neglects

^the

quantization

of vibrational and rotational levels of the bound molecular states. When the _quan- tization of such levels is allowed

by

^the

shape

^{of the}

potential

^{curves, it can be}

responsible

^{for some}

undulations in the band

profile

^{which cannot be}

predicted by

^the present calculations.

3.

Comparison

^between calculated and

experimental profiles.

^{- The}

comparisons

between calculated and

experimental profiles

^{are limited to} some cases for which the most

interesting

information can be obtain- ed. We first make a few

general

^{remarks on the}

shape

of the calculated

profiles,

^{then we} consider the case

of S-S transitions in sodium and

potassium,

^and

finally

we deal with the case of S-S and S-D transitions for cesium and rubidium.

The calculations of band

profiles

^were

performed

with the

experimental

conditions referred to

(tempe-

rature, width of the

apparatus function).

^Because

of the absence of more

precise

information we have used a

triangular apparatus

^function

having

^{a half-}

width

equal

^{to that}

given by

^the

experimentalists.

3.1 GENERAL REMARKS. ^- The calculated

profiles j(J.)

^and

;)t(À-)

^{show two} types of maxima which

are

interesting

^to characterize before

comparing

them with the

experimental

^results.

a)

^One type of maximum is due to a

parallelism

between the relevant adiabatic

potential

^curves.

The

quasistatic

^method

gives

^an infinite value for

Io,)

^{as it} appears in relation

(2).

The convolution

product

^{with the} apparatus ^function

F(À-) gives

a maximum, ^{in whose}

neighbourhood

^the

shape

^of

the

profile

^{is close to} that of the apparatus ^function.

Further from the maximum the

profile

of the band is

asymetrical,

^{with a} steep

edge

^on the blue side

or the red side if

Vu(R ) - V1(R)

^{has a maximum or}

a minimum,

respectively.

^An

example

^{of this} type of

maximum

^{is shown}

by

^{the band}

BB

ⁱⁿ

figure

^1.

FIG. 1. ^- Normalized emission coefficients calculated for the

1/2(3

2S@/2)-1/2(4 2S1r2)

transitions in Na-rare gas systems for a gas temperature ^{T = 423 K and a} half-width of the apparatus ^function equal ^{to 3 À : -} Na-Xe, ^... Na-Kr, and - - - - Na-Ar.

The arrow indicates the position of the forbidden Na-line at 3 885 A.

It is this kind of maximum which

gives

the satellites bands associated with the allowed transitions

[14].

b)

^Another type of maximum appears in the ^case of the bands associated with forbidden transitions.

It arises because the oscillator

strength,

^{which is} very small when the

emitting

^or

absorbing

^{alkali atom}

is

isolated,

^{can become as}

large

^{as for an allowed}

transition when the alkali atom is close ^to a rare

gas ^atom

[6].

^{Such a maximum}

generally

^{leads to}

a band which is broader than that due ^to a

parallelism

between the adiabatic

potential

^{curves. An}

example

is shown

by

^{the band}

BR

ⁱⁿ

figure

^1.

3.2 S-S TRANSITIONS FOR SODIUM AND POTASSIUM.

- Bands have been observed in the emission

spectrum

of an electrical

discharge

^{in a} mixture of sodium

or

potassium

^with

^heavy

^{rare gases}

^(Ar,

^{Kr and}

Xe) [8].

These bands have been associated with the forbidden transition between the first excited S

364

state and the

ground

^state of the alkali atom. For each of the alkali-rare _gas systems, ^the calculation

gives

^similar

profiles

^{which show two well}

separated

bands

(see Fig.

^{1 in the case of}

sodium).

^{The band}

located at a few tens of

angstrôms

^on the blue side of the S-S forbidden line is due to a

parallelism

^of

the adiabatic

potential

^{curves which takes}

place

at an interatomic distance close to 10 a.u. for sodium and 13 a.u. for

potassium.

The other band has a

maximum which _appears a few hundreds of

angstrôms

on the red side of the

previous band ;

^{it comes from} the oscillator

strength

^{of the induced}

dipole

^mole-

cular transition which is

large

^{when the} alkali and the rare gas ^{atoms are}

separated by only

^{5 to 8 a.u.}

As shown in

figure

^{2, there is a narrow} range of inter- atomic distances in the

neighbourhood

^{of the}

posi-

tion of the well of the adiabatic

potential

^associated

FIG. 2. ^- Adiabatic potential ^{curves of the} Na-Ar, ^{Kr and Xe} 1/2(4

281/2)

^states and of the K-Ar, ^{Kr and Xe} 1/2(5

2S1/2)

^states

according ^{to Ref.} [7]. ^{The crosses} localize the interatomic distances where the bands BR ^{are maximum} (see Fig. 1). The thicker parts of the curves indicate the regions of interatomic distances where the emission intensities ^are greater ^than half of the maximum

intensities. T is 423 K for Na and 573 K for K.

with the _upper state which

correspond

^{to this}

^band.

Its

spectral

extension is wide because the final state of the molecular transition is the

ground

state, for which the adiabatic

potential

^{curve is} very

repulsive

in this range of interatomic distances.

In

figure

^{3, the}

position

of the maximum and the half-width of the calculated band

BR

^are

compared

with the

experimental

data of A. C. Tam et al.

[8].

A more detailed

comparison

of the band

shapes

would be

meaningless

in view of the

imprecision

of the

experimental profiles.

The overall agreement

FIG. 3. ^- Schematic comparison of the emission profiles ^{for Na-}

rare gas

1/2(3 2S1/2)-1/2(42S1/2)

transitions and for _{K-rare gas}

1/2(42S 1/2)-1/2(5 2S 1/2)

transitions. The scheme shows the position

of the band maxima and those on both sides of these maxima where the maximum intensities are halved. In each case the _upper

diagram corresponds ^{to the} experimental profiles ^{of Ref.} [8], ^the

lower one to the calculated profiles. ^The vertical lines indicate the

positions ^{of the} forbidden transitions 3S-4S in Na and 4S-5S in K.

T is 423 K for Na and 573 K for K.

is fair as A. C. Tam et al.

[8]

^{have estimated}

by

^consider-

ing

^the

shape

^{of the adiabatic}

potential

^curves.

However, ^we notice that the observed bands are

always

¹⁰⁰

^cm-1

^{to 400}

^cm-’

¹ further than those calculated from the

position

^{of the} forbidden line.

This _may be

explained

^either

by ground

^{state adia-}

batic

potential being

^more

repulsive

^than

predicted by

^the calculations, ^{or more}

probably, by

^a

potential

well for the first excited S state which is

deeper

^than

that calculated.

The calculated values of the normalized

intensities,

at the maxima of the bands

BR,

^are

respectively

^5,

1.25 and 0.25 x

10-9 cm2 S-1

for the Na-Xe, Kr and Ar systems ^{at T = 423} K ;

they

^are

respectively

6.32, ^{1.96 and 0.76 x}

10-10 cm2 S-1

for the K-Xe, Kr and Ar systems ^{at T = 573 K. Thus the}

intensity

of the band increases with the mass of the rare gas atom.

Unfortunately,

^{there is no}

experimental

^data

to compare with.

It should be noted that the bands

BB predicted by

the calculations have not been

observed, perhaps

because of their weak intensities.

3.3 BANDS OF THE CESIUM-RARE GAS SYSTEMS. ^-

The emission and

absorption spectra

^{of cesium}

vapor in the presence of ^rare gases

(Xe,

^{Kr, Ar and}

Ne)

^have shown the existence of a

yellow

^{band which}

has been associated with the

1/2(6 ’Sl/2)-1/2(7 2S 1/2)(1)

transition

[4], [15].

Bands have been also observed in the red

wings [16, 17]

and the blue

wings [1]

^{of the}

associated 6

2S-5 2D dipole

forbidden lines of cesium

(1) ^We adopt the notation Q (y) of references [6] ^and [7] ^for

molecular states, where Q is the absolute value of the projection

of the total angular ^momentum of the alkali-rare _gas system ^onto the internuclear axis taken as the quantization axis ; y is the set of the quantum numbers for the alkali state to which the mole- cular state is correlated at large internuclear distances. G. Moe

et al. [4] ^{use a} différent notation : their 4 dE and 5 dE states of Rb and Cs-rare _gas systems, respectively, correspond ^{to the} 1/2(4

2D3/2)

and 1/2(5

2DSi2)

^{molecular states in our notation.}

(6

^{849 and 6 895}

Â),

^{in the} presence of rare gases.

More

recently

^the

study

^{of the} spectrum ^emitted

by

an electrical

discharge

^{in a Cs-Xe} mixture has shown that the blue band _may be associated with an emission from the 5

2Ds/2

^state, the red band

being

^related

with the 5

2D3/2

^state

^[3].

^The calculated band

profiles

confirm these

results, indicating

that : the blue band

originates only

^{from the}

1/2(5 2D,,2)

^{state associated}

with a very

repulsive

^adiabatic

potential

curve;

the red band is due to the sum of the transitions from the

ground

^{molecular state to the}

3/2(5 2 D.5/2),

1/2(5 2D3/2)

^and

^3/2(5 2D3/2)

states, those associated with the 5

2D3/2 contributing

^{the most. We limit the}

comparison

between calculated and observed _pro- files to the blue

component,

which is the best known

experimentally

^{and whose}

origin

is associated with the

1/2(6 2S 1/2)-1/2(5 2Ds/2)

transition alone. The calculated

profiles

^are

compared

^{with the}

absorption profiles

^obtained

by

G. Moe et al.

[4].

The

experimental profiles

associated with S-S transitions

(see Fig. 4)

^{are all}

analogous

^{to those}

we have calculated for sodium and

potassium. They present

^{a narrow}

peak

^{close to the} forbidden line

(5

³⁹⁴

Á)

^{with a}

shape

^{similar to that} of the band

BB (see Fig. 1) ^and,

^{on the red}

side,

^{a broad band} similar to the band

BR.

^This

suggests

that the adiabatic

potential

^{curves of the}

1/2(7 2S1/2)

^state of the Cs-

rare gas systems ^{have a}

shape

^{similar to those asso-}

ciated with,

respectively,

^{the 4}

2S1/2

^{and 5}

2S 1/2

states of Na and K. However, the

profiles

^calculated

FIG. 4. ^- Comparison between the normalized absorption ^coeffi-

cients calculated for the 1/2(6

2S1/2)-1/2(7 2S1/2)

transitions of Cs-rare _gas systems (full lines) and those measured in the spectral

range between 5 100 and 5 800 Á (dotted lines) according ^{to Ref.} [4]

(Width of the instrument function 10

Â).

^{The arrows} indicate the

position of the forbidden 6S-7S Cs-line at 5 394 Á.

for the Cs-rare gas systems ^are very different from the

experimental

^results

(see Fig. 4).

^{These calculated}

profiles

^{exhibit two}

(Ne)

^{or three}

(Xe, Kr) peaks

^due

to

parallelisms

between the adiabatic

potential

^curves

involved in the transition.

Only

^{in the case of Ar does}

one observe a

profile

^{similar to those we have obtained}

for Na and K. Moreover, the calculated

profiles

^are

shifted towards the blue in

comparison

^{with the}

experimental profiles, particularly

^{in the cases of}

Xe and Ne.

For the

1/2(6 ’Sl/2)-1/2(5 2Ds/2)

transitions there is some

similarity

between calculated and

experi-

mental band

profiles (see Fig. 5), although

^{the calcu-}

lated

profiles

^{extend over a}

larger spectral

range. A broad band is

observed, presenting

^a

peak

^{on its blue}

side. From the

calculations,

^this

peak

appears ^to be due to a

parallelism

between the relevant adiabatic

potential

^{curves. However, as was} observed for the

1/2(62S1 /2)-1/2(7 2SJ /2) transitions,

^the calculated _pro- files extend further towards the blue than do the

experimental profiles, except

^{in the case of Ar.}

The remarks about the location of the bands associated with the S-S and S-D forbidden transitions have

already

led G. Moe et al.

[4]

^to notice that the calculated adiabatic

potential

^{curves for the}

1/2(5 2Ds/2)

^{state are}

^probably

^too

repulsive,

^and

that the well

depths

of the adiabatic

potentials

^of

the

1/2(7 2S 1/2)

^{state are}

^certainly

underestimated.

Our calculations enable us to make a few additional comments

arising

^{from the.}

approximate agreement

obtained in the case of Ar. If we consider the cal- culated adiabatic

potential

^curves

(see Fig. 6)

^we

notice that for Ar the

potential

^{curve of the}

1/2(5 2Ds/2)

state is the

least répulsive

^{and its} interaction with the

1/2(7 281/2)

^state is the least

apparent.

^{The weak}

dependence

^{of the}

shape

^{of the}

experimental

^band

profiles

^{on the rare} gases

(see Figs.

^{4 and}

5)

suggests that the adiabatic

potential

^{curves of the}

1/2(5 2Ds/2)

and

1 /2(7 2 S 1 r 2)

^{states are not} in themselves _very sensitive to the rare gases and are similar to those calculated for Ar.

Therefore,

^the

perturbations

^of

the

1/2(7 ’Sl,2)

^and

^1/2(5 2Ds/2)

^{states in the}

^neigh-

bourhood of the avoided

crossing

of their adiabatic

potential

^{curves are}

probably

weaker than indicated

by

the calculated curves

(see Fig. 6),

ⁱⁿ

particular

for Xe and Ne.

It is

interesting

^{to note that the band}

profiles

associated with the

1/2(6 281/2)-1/2(5 2Ds/2)

^transi-

tions

originate

^from

purely repulsive

^adiabatic

poten-

tial curves of the

1/2(5 2Ds/2)

state, and that ^no

potential

well is therefore necessary in order to obtain such a band

shape.

A last remark concerns the

comparison

^{of the}

absolute values of the

absorption

coefficients

K(Â).

Because of the considerable differences between the

experimental

and calculated

profiles,

^the

only comparison

^which may be

significant

is that of the

intégral Jo 0 ^Jt(l)

^{d which is}

^related, by analogy

366

FIG. 5. ^- Comparison between the normalized absorption ^coeffi-

cients calculated for the 1/2(6

281/2)-1/2(5 2D5/2)

transitions of Cs-rare gas systems (full lines) and those measured in the spectral

range between 6 000 and 6 850 À (dotted lines) according ^{to Ref.} [4].

The arrows indicate the position ^{of the} dipole forbidden 6

2S 1/2-

5

2D,/2

^{Cs-line at 6 849 Á.}

FIG. 6. ^- Adiabatic potential ^{curves of the} 1/2(7

’Sl/2)

^and

1/2(52Ds/2)

^states of Cs-rare _gas systems according ^{to Ref.} [7] : Cs-Xe ; ^... Cs-Kr ; - - - - Cs-Ar ; 2013 2013 2013 Cs-Ne.

with the

integrated absorption

coefficient of an atomic line to a mean oscillator

strength.

^{In the case of the}

1/2(6 2SJ /2)-1/2(7 ’Sl/2)

transitions the values of these

integrals

^{over the} calculated and

experimental

pro- files are not very

different, except

^for

Ne,

^{for which}

the calculated values are

noticeably larger. However,

for the

1/2(6 ’Sl/2)-1/2(5 2Ds/2)

transitions the compa- rison is the best for Ne, the calculated values

being

too small for the other ^rare _gases

(see Fig. 5).

^{If the}

above

comparison

^is

meaningful,

^this suggests ^that

generally

^the calculations underestimate the oscillator

strengths

^{for the}

1/2(6 281/2)-1/2(5’ 2dus/2)

transitions and overestimate them for Ne in the case of the

1/2(6 281/2)-1/2(7 281/2)

transitions.

3.4 BANDS OF THE RUBIDIUM-RARE GAS SYSTEMS. ^-

For rubidium the situation becomes more confused because of the small _energy

splitting (780 cm-1)

between the 5

2D

and 6

2S

levels of the Rb atom.

Consequently,

the bands associated with the transi- tions between these levels and the

ground

^{state can}

have

comparable wavelengths

^{which are difficult}

to

distinguish.

The

shape

of the calculated

profiles

^{is not very}

dependent

^{on the}

perturbing

^{rare gas, and three}

parts ^{are observed}

(see Fig. 7).

On the blue side there is a band

originating

^{from the}

1/2(5 ZS1/2)-

1/2(6 281/2) transition,

^which

presents

^{the same fea-}

tures as those

arising

^{from the}

1/2(6 ZSlj2)-1/2(7 2S 1/2)

transitions in the Cs-rare _gas

systems.

^{A second band} is located between the

positions

of the 5S-6S and 5S-4D ’ forbidden lines and

originates

^{from the}

1/2(5 2SJ/2)-1/2(4 2D3,2)

transition.

Finally,

^{on the}

FIG. 7. ^- Normalized absorption coefficients of Rb-rare _gas systems calculated for the transitions - - - - 1/2(5

2S1/2)-

1/2(6

2S 1/2),

^{- 1/2(5}

2Sl/2)-1/2(4 2 D3/2)

^{and for -.-.-.}

the sum of transitions from the 1/2(5

2S 1/2)

^{state to the 3/2(5}

2 D3/2),

1/2(5

2D,,2)

^{and 3/2(5}

2D5/2)

states ; and ^... coefficients measured by ^{G. Moe et al.} [4] ^{in the} spectral range between 4 300 and 5 800 A. On the present graph ^the intensity of the calculated

absorption coefficients have been multiplied by ^{3 so} that the cal- culated profiles ^{have a size} comparable ^to those of the experimental

results.

red

side,

^{there is a} band which comes from the transi- tions from the

1/2(5 ’sol/2) ^ground

^{state to the}

3/2(4 2D3/2), 1/2(4 2D5/2),

^and

3/2(4’D.5/2)

^states.

This band exhibits two maxima for the heaviest

rare gases.

The

experimental profiles

also shown three _sepa- rated bands

(see Fig. 7).

G. Moe et al.

[4]

attribute the band on the blue side to the

1/2(5 2S 1/2)-1/2(6 2S1/2)

transition;

the middle band to

1/2(5 2S1/2)-

1/2(4 2D3/2) ;

^{the band on} the red side to the transi- tions from the

ground

^{state to the other} components of the

4 2D

^{state. If this}

interpretation

is correct, it indicates that the adiabatic

potential

^{curves cal-}

culated for the

1/2(6 ’Sl,2)

^{states are much too}

repulsive. ^However,

^{a different}

interpretation

^{of this}

band

profile

^{has been}

recently given by

^{R. Granier}

et al.

[18]

for the Rb-Xe

system. They

attribute the whole observed band

profile only

^to the 5S-4D for- bidden transition. If this

interpretation

is correct, and valid for all the Rb-rare _gas

systems,

^small

changes

in the adiabatic

potential

^{curves associated}

with the 4 2D state, in the

range R L--

^{8-10 a.u. which}

contributes to the band

profiles,

would lead to a

satisfactory

agreement ^between calculated and

experi-

mental

profiles. ^Thus,

the observed blue band would have to be attributed to the

1/2(5 2S1/2)-1/2(4 2 D3/2)

transition alone and the observed middle and red bands to the

1/2(5 2S 1/2)-3/2(4 2D3/2), ^1/2(4 2Ds/2),

and

3/2(42Ds/2)

transitions. On the one

hand,

^if adiabatic

potentials

^more

repulsive

than those cal- culated for the

1/2(4 2D.,,2)

^states,

^by

about 100- 300

cm -1,

^were used in the calculations then the

positions

of the calculated and observed blue bands would be the same. On the other

hand, changes

ⁱⁿ

the adiabatic

potentials

différent for the

3/2(4 2D3/2), 1/2(4 2D,,2),

^and

3/2(4 2D,/2)

^{states are needed to}

obtain from the calculations the two observed middle and red bands.

Thus,

^{in order to have} _agreement between

experimental

and calculated

profiles,

^the

adiabatic

potentials

^{for the}

3/2(4 2D3/2) ^and/or 1/2(42Ds/2)

would have to be more

repulsive by

about 600-800

cm-1,

than those

calculated,

^{and the}

changes

^{in the}

remaining

^adiabatic

potential(s)

^asso-

ciated with the 4

2D

state would have to be of less

importance

than the latter.

In our

opinion,

^the

interpretation

of the whole band

profile

^{as due}

only

^to the 5S-4D forbidden transition is more

probable

^{than the one}

proposed by

^{G. Moe et}

^{al. ;}

^the bands associated with the

1/2(5 2S1/2)-1/2(6 2SJ 2)

transitions are located fur- ther towards the blue and their intensities are

probably

too weak to have been observed under the

experimen-

tal conditions of Ref.

[4]. However,

^further

experi-

ments are desirable to formulate a final conclusion about the

origin

of these Rb-rare _gas spectra.

4. Conclusion. ^- The

profiles

of the bands asso-

ciated with the forbidden atomic transitions between the

ground

^state and the first excited S and D states

of alkali atoms

perturbed by

^{rare gas atoms have}

been calculated

by

^the

quasistatic

^{method. For these}

calculations we have used the

only

^available theoretical data related both to the adiabatic

potentials [7]

^and

the oscillator

strengths

^{as a} function of the inter- atomic distance

[6].

The calculations have been carried out under the conditions

corresponding

^to

those for which both

expérimental

data exist

[4], [8]

and the

quasistatic approximation

^{is valid.}

The

calculated

profiles

^{exhibit two}

types

^{of struc-}

ture :

first,

^narrow bands which

originate

^from

parallelism

between the adiabatic

potential

^curves

of the states involved in the molecular

transition ; secondly,

broader bands which come from

large

values of the oscillator

strengths.

^{These two}

types

of

bands,

very easy ^to

distinguish,

^{are observed}

in the

experimental profiles

^and

help

in the inter-

pretation

of the results.

The calculated and

experimental profiles

^{are in}

fair

agreement

for the molecular transitions asso-

ciated with the S-S forbidden transition in sodium and

potassium ;

this leads us to believe that the calculated adiabatic

potential

^curves associated with the first excited S states of sodium and

potassium

are

reasonably

^{correct, even}

though

^the

depths

^of

the

potential

^{wells seem to be}

slightly

underestimated.

Absolute measurements of the transition

probabilities

or of the

absorption

coefficients would be useful for

testing

^the calculated values of the oscillator

strengths.

For the rubidium-rare _gas systems, because the 6S and 4D states of rubidium ^are close

together

^the

interpretation

^{of the}

existing experimental

^results

is uncertain.

For the cesium-rare _gas

systems,

^the

comparison

of the calculated and

experimental profiles suggest

that all the adiabatic

potential

^{curves of the}

1/2(7 ’Sl/2)

states have a

well,

^{which is}

deeper

^{than that}

calculated,

whose

shape

^is

probably

^{close to that calculated}

for the Cs-Ar

system.

^The

repulsive

^adiabatic

poten-

tial curves of the

1/2(5 2DSJ2)

^{states can}

^explain

^the

experimental profiles

^{of the}

1/2(6 ’Sl/2)-1/2(5 2Ds/2)

transitions. For these

transitions,

^the

comparison

between calculated and

experimental profiles

^indicate

that the calculated adiabatic

potential

^{curves for the}

1/2(5 2D,/2)

^{states are}

noticeably

^too

repulsive, except

for _argon. ^-

The

comparison

between the calculated and

experi-

mental

profiles

appears ^to be a very sensitive test of the

quality

of the theoretical data related to the rele- vant adiabatic

potentials

^and oscillator

strengths

of the molecular transition.

Acknowledgments.

^- The authors ^are

grateful

^to

Dr. J. Berlande and Dr. C. Manus for their conti-

nuous

support during

this work.

They

^{wish to thank}

Dr. J. Berlande for

helpful

discussions and valuable comments, and Miss A.

Taylor

^{for a careful}

reading

of the

manuscript.

368

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