Collisionally induced optical double resonance in I2 : rotational analysis of the D'(2g) - A'(2u) laser transition

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Collisionally induced optical double resonance in I2 : rotational analysis of the D’(2g) - A’(2u) laser transition

J.B. Koffend, A.M. Sibai, R. Bacis

To cite this version:

J.B. Koffend, A.M. Sibai, R. Bacis. Collisionally induced optical double resonance in I2 : rotational analysis of the D’(2g) - A’(2u) laser transition. Journal de Physique, 1982, 43 (11), pp.1639-1651.

�10.1051/jphys:0198200430110163900�. �jpa-00209545�

Collisionally ^induced optical ^double

^resonance

ⁱⁿ I2 :

rotational analysis ^{of the} D’(2g) - ^{A’(2u) laser transition}

J. B. Koffend, ^{A. M.} Sibai and R. Bacis

Université Claude-Bernard (Lyon I), Laboratoire de Spectrométrie lonique ^et Moléculaire, 43, boulevard du 11 Novembre 1918, 69622 Villeurbanne, ^France

(Reçu ^{le 9} juin 1982, accepté ^{le 27} juillet 1982)

Résumé. ^- La transition D’(2g)-A’(2u) de la molécule I2 ^{a été} excitée par double résonance optique induite par collisions. Une analyse rotationnelle correspondant ^à plus de 50 niveaux vibrationnels de l’état A’(2u) ^{a été effec-}

tuée. On a étudié le comportement de l’état A’ à longue distance internucléaire. L’énergie de dissociation de cet état a été déterminée : De = 2 505,7 ± 1,9 cm-1. ^{On a} montré que l’état D’ ^est l’état 03B1 de King ^{et al.} (Chem.

Phys. ⁵⁶ (1981)

145).

^Les énergies ^{de D’ et} A’ relatives à l’état fondamental X

1~g+(03BD

^{= 0, J = 0) ont été déter-}

minées comme étant T0 ⁼ 40 331,6 ± 1,6 ^{cm-1 et} T0 ^{= 9 988,7 ± 1,6 cm-1} respectivement. ^On discute le mécanisme de la double résonance. Un transfert collisionnel de grande efficacité vers l’état D’ a été observé, ^ce qui permet ^{de mieux} comprendre le fonctionnement du laser à iode D’-A’ pompé optiquement.

Abstract. ^- The I2 D’(2g)-A’(2u) transition has been excited by collisionally ^induced optical ^{double resonance.}

This system ^{has been} rotationally analysed ^{for more} than 50 vibrational levels of the A’(2u) ^{state. The} long range behaviour of the A’ state has been studied. The dissociation energy of this ^state has been determined to be

Dc ^{= 2 505.7 ± 1.9 cm-1.}

The D’ state has been identifed with the 03B1 state of King et ^al. (Chem. Phys. ⁵⁶ (1981) 145). ^The energies ^{of the D’}

and A’ states have been determined relative to X

1~g+(03BD

^{= 0, J = 0) to be T0 = 40 331.6 ± 1.6 cm-1 and}

To ^{= 9 988.7 ± 1.6} cm-1,

respectively. The mechanism of this double resonance is discussed. Efficient collisional transfer to the D’ state is observed and helps ^{to shed some} light ^{on the} operation ^{of the} optically pumped I2 D’-A’ laser.

Classification

Physics ^Abstracts

33.50 ^- 33.20L

1. Introduction. ^- The 340 nm transition in

I2

was

suggested

^{as a}

possible interesting

^{U-V laser}

by

McCusker and coworkers [1] ] and laser action was

originally

^obtained using ^electron beam excitation

[2-4].

^The

efficiency

^{of the} system ^was found however to be rather low and interest in it

quickly

diminished.

This transition has also been

optically pumped

ⁱⁿ

the presence of buffer _gases,

using light

^from

exploding

wires

[5].

^The

efficiency

^{of this} system however has also

proved

^to be low. But Zuev et al.

[6], pumping

with a conventional quartz

lamp,

^obtained

pulsed operation

^{with an} output energy of 10-50 mJ _per

pulse. Recently,

laser action was obtained using

optical

excitation with an ArF laser at 193 nm

[7]

with

surprising

^intrinsic energy conversion

efficiency

of

approximately

³⁰

%, equivalent

^{to a}

photon

^effi-

ciency

greater ^{than 50}

%.

Despite

^a number of studies of

I2

emission in the visible and UV _range

[1, 8-14],

little is known about the collisional transfer involved in this U-V laser.

A

spectroscopic study

of this transition was

performed by Tellinghuisen [ 11 ],

who attributed it to the

12 D(3 172g)>, A’(3 n 2u) (1)

system ^and gave ^an

isotopic

vibrational

analysis.

However, ^{he could not} locate the absolute

energies

of those two states. A more complete

analysis

^will

be

published by Tellinghuisen [11&].

The lower level of this transition is also of interest in

regard

^to the C.W. chemical atomic iodine laser

[ 15].

(1) ^As 12 ^{is a case c} molecule the transition will be noted

D’(2g)-A’(2u).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198200430110163900

The laser action is achieved on the

lPl/2-lP3/2

^tran-

sition of the iodine atom

by

energy transfer from the

1 d g

^or

1 Eg

metastable states of

02

^to

I2

^molecules

which results in

I2

dissociation.

Among

the various transfer schemes, ^the A’(2u) ^{state seems to}

play

^an

important

^role

(see

^Ref.

^[16]

and references

therein).

In order to elucidate this

point

^{the absolute} energy of this state must be determined.

In order to

study

these different

questions

^{we have}

undertaken a rotational

analysis

of this transition.

A priori, ^{this seems to be a difficult}

’problem.

^The

D’(2g)

state cannot be ^excited

directly

^{from the}

ground

^{state or} other accessible known states which

precludes

^{an absolute} energy measurement. More- over, the

D’(2g)-A’(2u)

transition has

always

^been

excited

through

collisional transfer and the

typical

pressure of inert gas

(a

few hundred

torr)

will broaden the lines and

complicate

^a

high

resolution

analysis.

In this report, ^we present ^a

study

^{of the}

I2 D’(2g)- A’(2u)

fluorescence excited

by collisionally

^induced

double resonance. We have

performed

^{a rotational}

analysis

^{of this} system. The observation of

high

vibrational levels of the

A’(2u)

^state allows the deter- mination of its dissociation _energy. Since the

A’(2u)

state shares the same dissociation limit as the

X(l E 9 ’)

state, ^the absolute

energies

^of the D’ and A’ states have been measured. This allows

important

^conclu-

sions to be made with respect ^{to the 342 nm laser} action and shows that the 2u state cannot be excited

directly

^from

O2(1 Ag).

2. Experiment ^{- In} the work of Shaw et al.

[7],

the

D’(2g)-A’(2u)

stimulated emission was obtained after ArF 193 nm

pulsed

excitation. The ArF laser excites the

D(O:)

^{state from the}

X(ll:’g+) ^ground

state

(see Fig. 1).

The inert buffer _gas causes transfer to the

D’(2g)

^state which results in D’-A’ laser oscil- lation.

In order to make a rotational

analysis

^{of the} spontaneous ^emission of the laser transition, ^the

excitation

by

^a continuous wave laser is

preferable.

As the direct excitation of the D state is

impossible

with

existing

^C.W. lasers, ^{we have}

attempted

^to

excite the D’-A’ transition

through

^{double resonance.}

The

E(Og )

^{state can be excited with two} C.W. lasers via the

B(O’)

^state

(Fig. 1).

^{We have} observed that very efficient

E(O’)-D’(2g)

collisional transfer can be

obtained, ^{which a} priori ^should

permit

^a spectros-

copic analysis

^{of the}

D’(2g)-A’(2u)

transition.

A schematic

diagram

^{of the}

experimental

^appa-

ratus is shown in

figure

^{2. The beams of a}

Spectra Physics

^{model 171 Ar + laser and a}

Spectra Physics

model 171 Kr’ laser were

superimposed using

^a

dichroic mirror and then focussed with an

f =10

^cm

lens into an

I2

cell. The

resulting I2

fluorescence

was observed with a 0.20 meter spectrometer

(Jobin

Yvon model

H-20) equipped

^{with an RCA 1 P28}

photomultiplier

^tube.

Higher

resolution studies were

performed by focussing

^the forward-scattered fluo-

rescence from the

I2

^{cell onto} the slits of a 3.4 meter

Fig. ^{1. -} Low-lying valence and charge ^{transfer states of} 12.

Potential energy ^curves for the

D(O:)

^and

F(O:)

^{states are}

estimated while others shown are RKR curves. Also shown

are the 193 nm pump and 340 ^nm laser transitions [7].

Atomic dissociation products ^{and molecular states which}

correlate to these limits are displayed ^{on the} right.

spectrograph

equipped ^{with a 1 200} lines/mm

grating

blazed at 1 300 nm. Filters were

placed

in front of each laser to isolate the laser lines and eliminate any interference from

plasma

lines from the

discharge.

Appropriate

band pass filters, ^inserted

just

^{after the}

I2

^{cell were used to isdlate}

particular spectral regions.

Kodak SWR film was used for U-V spectra ^while Kodak Tri-X was used for visible studies.

Typical

exposure times were six hours for the observation of faint lines, ^{but the more} intense U-V lines could be

photographed

^with exposure of the order of an

Fig. ^{2. - Schematic} diagram ^{of the} experimental set-up.

hour or less. Fe lines from an iron arc were used for

wavelength

calibration. The accuracy of the ^measu- rements is of the order of 0.05 cm - 1. The

I2

^cells

were evacuated to pressures below 10-’ torr with a

liquid N2

cooled cryopump. Reagent

grade I2,

^sub-

jected

^{to several}

freeze-pump-thaw cycles,

^{was intro-}

duced into the cells

by

distillation onto a

liquid N2

cooled

point

in the cell.

Argon

could be added to the cells and the argon pressure ^was determined

using

^{a Pirani} type gauge. In ^some

experiments,

^to

study

^the

D’(2g)

excitation mechanism, ^{the Ar+}

laser was

replaced by

^a

Spectra Physics

model 380-D

ring dye

^laser

operating

^{with Rhodamine 6-G.}

3.

Experimental

^{results. - In}

preliminary experi-

ments,

12 X(lEg )-B(Ou )

transition was excited

using

the 514.5 nm Ar + line which is known to be in reso- nance with a few lines of the B-X system

[17].

^We

tried to effect the second excitation step ^{with the} U-V or violet lines of a Kr+ laser in order to excite the

E(O:)

^{state as}

^high

^as

possible. Using

^{the 406.7 nm} line, strong

E(O:)-B(O:)

fluorescence was observed

indicating

^an E-B-X double resonance. It was found that upon addition of argon ^to the

I2

^{cell a new} system,

peaked

^{at 340 nm,}

appeared. Figure

^{3 shows}

several low resolution spectra ^{near 320-340 nm taken} with different argon pressures. As

already

^{seen in}

the spontaneous emission of the

D’(2g)-A’(2u)

^tran-

sition

[7],

the increase of argon pressure

strongly

favours emission at 340 nm. We observed the same

behaviour

giving

^us confidence that collisional transfer from the

E(O:)

^{state leads to the}

preferential

popu- lation of the

D’(2g)

^{state as was the case with the}

D(O:)

^state in reference

[7].

^The

peak appearing

^at

325 nm

(Fig. 3)

^{is due to the}

D(0")-X(lEg )

^transi-

tion. Thus a small part ^{of the} collisional transfer from

E(O:)

results in the

population

^{of the}

D(Ou)

state.

High

resolution spectra ^of

I2

^{with 2 torr argon}

excited

by

the 514.5 nm and 406.7 ^nm laser lines

were recorded in the _range 315-345 nm and in the

region

^of

expected E(O:)-B(O:)

fluorescence (408-

435 nm). ^Several

E(O:)-B(O;)

transitions were assi-

gned, indicating

^{that the}

E(O’)

^{state was involved.}

However, ^{even at a}

reciprocal dispersion

^of

0.04 nm/mm, the 330-345 nm U-V spectrum appear- ed continuous with few discrete features

barely

visible in the continuum

background.

The excita- tion of

high

vibrational levels of the

D’(2g)

^state

mainly give

^{emission to} the continuum of the A’(2u)

state. An

interesting

result from these spectra ^{is that} the E state can be

easily

^excited

through

collisional double ^resonance excitation. An

example

^{is shown in}

figure

^4.

Argon-I2

collisions transfer

population

^to

a

large

^{number of B states levels near the}

initially

excited levels. Thus, ^{numerous B state} rovibrational levels are

populated

and since the

density

^{of E-B}

lines is _very

high (higher

than in the B-X

system)

there is a

high probability

^that any discrete laser line with sufficient _energy will excite some rovibra- tional level of the E state.

If the 454.5, 457.9, 465.8, 472.7 and 476.5 lines of

an Ar + laser were used for the second excitation step in

conjunction

with either the 514.5

nm Ar+,

^520.8

or 530.9 nm Kr+ lines

(first step),

^{a discrete} spectrum

was observed in the D’-A’

region

^{with Ar buffer} gas.

That collisional

population

^of many B state levels

occurs is confirmed

by

the observation of the same

D’-A’ spectra when either 514.5, 520.8, ^{or 530.2 nm}

are used as the first step.

We have also noted that if care is not taken in

preparing

^the

I2

cells, ^D’-A’ spectra ^are obtained,

even in the absence of Ar. This _may be due to traces of water in the

I2

which will be condensed as well onto the

liquid

nitrogen ^cooled

point

ⁱⁿ the cells.

Fig. ^{3. -} Spectra ^of 12 excited with 200 mW 406.7 nm and 1 500 mW 514.5 nm.

QO.3

^torr 12 ^{+ 100 torr} Ar;

Q)0.3

^torr

12 ^{+ 12 torr} Ar;

(3) 0.3

^torr 12 ^{+ 1 torr Ar;}

(4)0.3

^torr 12.

Fig. ^{4. -} Energy ^level diagram showing ^observed example

of

E(O+) -->

^D’(2g) collisional transfer.

Thus, ^{the cross} section for E-D’ transfer _may be

large

for collisions of excited

I2

^with

H20. Figure

⁵

shows a low resolution spectrum ^{of the}

D’(2g)-A’(2u)

fluorescence obtained with 530.9 nm Kr+ line as a

first step and various Ar+ ^{lines as a} second step.

Some fluorescence lines of the D-X transition were

observed in the 320-325 nm range with 454.5 nm and 457.9 nm as seen in

figure

^{5. No} spectra ^{of either} the D’-A’ or the D-X transitions were obtained

using

^{Ar +} lines with

wavelengths

greater ^than 476.5 nm.

4. Analysis ^{of the data. - The}

spectroscopic

^ana-

lysis

of the fluorescence lines was

complicated by

the

superposition

^{of numerous} fluorescence series,

large

Franck-Condon gaps in

(V2g, V2.)

^{series, and}

overlapping

of the D-X transition in the 320-330 nm

range. Furthermore, ^{for the most} intense series no

rotational relaxation lines were observed. Hence the series appear ^as groups of two lines

(P

^and

R)

for _{every v2u} level. That no Q ^{lines were detected}

eliminates a Af2 :0 0 transition

(in particular 1 g-2u).

Among

^{the numerous} series observed about 15 of the more intense were selected for the measurements.

The observed line

positions

^{were least} squares fitted to the

expression :

where v is the transition

frequency, G(v)

^{is the rota-}

tionless energy for v’ ^or v", ^{X =}

J ( J

⁺

1),

^and B, D, ^{H and L are} the usual rotational constants. Since few lines for each vibrational band

(v’, v")

^{were mea-} sured, the distortion constants for the 2u state were

fixed at calculated values in the fit. Thus, ^{an iterative}

fitting procedure

^{was used. First, the distortion}

constants were set to zero and the

resulting G(v")

and

B(v")

obtained from the fit were used to construct an RKR curve for the 2u state. Then the distortion constants were calculated from the RKR

potential using

^a program

by

^Hutson

[19, 20].

^{These values}

were used in a second fit and the

procedure

^was

repeated

^{until no}

significant change

in the successive fits was observed. The results for the 2u ^{state are}

presented

^{in table I a. These constants} result from

a

weighted

^fit of 720 lines and the RMS ^error of the fit is 0.07 cm - 1. Table I b

displays

coefficients for the

polynomial expansions

^{of these constants in}

- Fig. ^{5. -} Spectra ^of 12 emission when excited by ^{530.9 nm}

and 454.5, 457.9, 465.8, 472.7, ^{or 476.5 nm} laser lines. Spectra

were obtained with 0.3 torr I2. Arrows show

emission observed using 454.4 and 457.9 nm as the second step.

Table I a. ^- A’(2u) spectroscopic ^constants.

e) ^{All constants} given ^{in cm - 1. 2 a} estimates in parentheses. Constants for ^{v =} 0, 1 extrapolated ^{from data.}

(b) Calculated (see text).

Table I a

(continued).

^- A’(2u) spectroscopic ^constants.

Table I b. ^-

A’(2u)

expansion parameters ^valid

for

^{v = 0-59.}

(a) Expansion ^{of the form :}

G(v) = £

Yio(v ⁺

2)‘.

t=i 1

(b) Expansion of the form :

B(v) = L

^{Yil (v +}

i)‘.

i=O

(C) Expansion of the form : In

(F(v)) = Y

^{Ki(v +}

^t)i,

^{where F(v) =} D(v), - H(v), ^{or -} L(v).

i=o

Table II. ^-

D(OU )

parameters.

(a) Values of the parameters ^obtained from 5 fluorescence series G(v ⁺ 4) ^{has been obtained} using B(v ⁺ 4) ^estimated

0.020 6 cm-1. Values given ^{are in cm-1.}

powers of v + 1/2. The J’ values

ranged

from 14-120 for v" ⁼ 2 - 12, ^from 36-90 for v" ⁼ 19-39, ^and from 36-40 for v" ⁼ 40-59.

In some cases, there was

enough

information to fit

D(v")

^{for some 2u levels. The} fitted values of

D(v")

are

generally

ⁱⁿ agreement with those calculated from the RKR

(see

^table

II).

However, ^{in a few cases}

the agreement ^is

questionable.

^{This is}

probably

^due

to the fact that few lines of

high

^{J" were measured}

for these A’ vibrational levels.

In order to understand the emission in the

region

320-330 nm a few

D(O +)-X(’Z +)

fluorescence series

were

analysed.

The results are

given

^{in table II for}

the

D(O:)

parameters determined. The

X(E 9 ’)

^vibra-

tional levels cover the _range v ⁼ 53-63 for the most intense lines.

5. Near-dissociation behaviour of the A’(2u) ^state.

- As no

perturbations

^{were observed in the} spectra, the

only

way of

fixing

^{the absolute} energy of the

A’(2u)

state with respect ^{to the}

ground

^{state is}

by extrapola-

tion of the

positions

^{of the}

higher

vibrational levels to the dissociation limit. Le

Roy’s theory [21-22]

is

particularly

well suited for this

extrapolation.

^From

the relative values of the

energies G(v")

^{of the}

A’(2u)

vibrational levels, ^this

theory

^{allows a}

precise

^extra-

polation

^to the dissociation limit. Since the

A’(2u)

state has the same dissociation limit as the

X( 1 E g+ )

state, its value is

precisely

^{known. It has been deter-}

mined

directly

from Fourier Transform

Spectros-

copy measurements

[23]

^to be 12 440.083 ± 0.145 cm - ’

(with

respect ^to

X(1 E g+)

^{v = 0, J =}

^0).

This value is in excellent agreement with the indirect determination

Do

⁼ 12 440.086 ± ^0.023

cm-1,

taken from the dissociation limit of the iodine

B(O:)

^state

(20 ^043.063 ± ^0.020

cm -1 )

[24] and the atomic

I 2 P 1 J2-

2P3/2

^energy

separation

(7 ^602.977 ± ^0.003

cm-1) [25].

An

example

^{of this}

extrapolation procedure

^can

be found in reference

[23].

The interaction

potential

of the two atoms in the

long-range region

^is

approxi-

mated

by :

where

Do

^is the dissociation limit, ^{R is} the inter- nuclear distance,

C,,

^{is a} constant, and n is ^some

weighted

average (in

general non-integer)

^{of the}

powers of the

locally important

^terms.

The _energy G(v) of the vibrational levels may then be

expressed

^as [21, 22,

26]

where _VD is the effective vibrational index at the disso- ciation limit and

Xo(n)

^is

given by :

where T is the gamma function

and p

is the reduced

mass.

The observed values of G(v) ^{were least} squares

Fig. ^{6. -} 12 A’(2u) long- range parameters obtained from least squares fits ^to equation (3). The abcissa displays ^the

range of vibrational levels included in the different fits.

fitted to equation (3) ^{for the}

highest v"

^{levels measured}

to obtain the parameters ^n, vD,

C.,

^and

G(vD). Figure

⁶

shows the results from several fits where the number of v" levels used is varied from v" ⁼ 42-59 to v" ⁼ 54-59.

This

procedure

^{allows us to} fix the absolute

positions

of the

D’(2g)

^and A’(2u) ^{states relative to v =} 0, ^{J = 0} of the

X 1 Eg+

^{state with a}

^precision

^{of 1.6 cm -1.}

At

long

range the interaction

potential

^is

expected

to be of the form

Values of

and

have been calculated from iodine atom

properties

[27, 28]. ^{When one} compares the theoretical value of

CS

calculated

by

Saute and Frecon

[27]

^{for the}

I2 B(Ou )

state, ^{3.59 x} 105 AS

cm-1,

^{with the}

experimental

value of

Danyluk

^and

King [24], 2.89

^{x 105 AS}

cm-1,

the theoretical value is a factor of 1.2 times

larger.

Since the atomic contribution to

CS

^{is identical for}

all

I2

^{valence states, a more} reasonable value for

C.

for the

A’(2u)

^{state is}

C5 -

^{1.68 x 105 A5 cm-1.}

The order of

magnitude

^{of the}

respective

contribution of

C5, C6

^and

C8

in the 6.5 A-7 A _{range for}

A’(2u)

^are

shown in table IV.

C8

^was

roughly

estimated from

C6 using

^the

C8lC6

^{= 15.3 A2} ratio determined in

[24].

Displayed

^{in table III are the constants}

Cn,

^n, vD, and

G(VD)

deduced from the fits to

equation

(3)

along

with

Te

^and

De.

The results ^{are a}

weighted

^{mean of}

the fits with v"

spanning

50-59, 51-59, 52-59, ^{and 54-59.}

The values obtained for n and

Cn

^are in reasonable agreement ^{with the data}

presented

^{in table IV, i.e.}

the dominant contribution to the

binding

energy is due to

C6

in the 6.5-7 A _range.

To test the

previous analysis,

the values of G(v)

from the

experiment

with their correct absolute ener-

Table III. ^- Long-range parameters

of

^the

A’(2u)

state.

Estimated errors are two standard deviations. For definition of parameters ^{see text.}

(a) Experimental ^data adjusted ^to give known value of

G(v,) (see text).

(’) Te ^{is defined as} the energy difference between the minima of the A’(2u) ^and

X(lEg )

^{potential energy curves.}

The

X( 1 Eg )

^{(v = 0, J = 0)} level lies 107.107 cm -1 above the minimum of the

X(lEg )

^{curve [38].}

Table IV. ^- Contribution to binding ^energy

of long-range

potential parameters

for

^the A’(2u) ^state.

(a) ^From references [24] ^and [28] (see text).

(b) ^{From reference} [28].

(C) The value of C8 ^is only roughly estimated from reference [24] ^as explained ^{in the text. However the deduced contri-}

butions are in agreement ^{with the} remaining binding energy determined from the RKR ^outer turning points when the cal- culated Cs ^and C6 contributions are subtracted.

gies

^with respect ^{to v =} 0, ^{J = 0 of the}

X(ll’g+)

^state

were fitted to the

expression :

where AG(v) ⁼ G(v ⁺ 1) -

G(v)

^and

K 5

^{is a cons-}

tant which

depends only

upon the value of

C5

^{and the}

reduced mass.

Equation

(6) results from the

theory

of Le Roy [21,

22]

^{when the}

leading

^term of the inter- atomic

potential

^at

long

range is n ⁼ 5, ^{as is the case} for the A’(2u) ^{state of}

I2.

^The

plot

is shown in

figure

^7.

The value

of Do

^{= 12 440.8 ± 4.0 cm-1 is in} agree- ment with that

displayed

^{in table III.} The value of

C s

Fig. ^{7. - Fit of} experimental ^{data to} equation (6). ^Error

bars denote two standard deviations.

determined from this fit, (3.9 ±

1. 0) - 10’ A’ cm - ,

is too

large, probably

since in the _range of R

sampled C.

^is

really

^{closer to}

C6,

because in

equation

(2) n - ⁶ (see ^{Tables III and} IV). However, the

experimental

vibrational

energies,

^as is often the case

[39], obey

^the

limiting

near-dissociation

equations

^{even when the}

leading

^term (here

CS/R 5)

^is

responsible

^for

only

^a

fraction of the

binding

energy. ^We have also tested the results of table III in an

extrapolation procedure

of the A’ RKR curve which is discussed in the next section.

6. RKR curves. ^- The positions ^{of the D’ and A’}

states have been fixed relative to ^{v =} 0, ^{J = 0 of} the

X( 1 E g+ )

^{state from the}

^long

^range

^analysis

^{of the A’}

state. Table V shows a

comparison

^{of constants for}

the D’ state obtained

along

^{with the constants for the}

a-state in the work of

King et

^al.

[ 18].

^We have decreas- ed the vibrational

numbering

of reference

[ 18] by

^seven.

This has been

suggested by Tellinghuisen [llb]

^and

in our case this was necessary ^to reach agreement between Franck-Condon factors calculated from RKR

curves and our observed

D’(2g)-A’(2u)

fluorescence intensities. The agreement between the values of G(v)

for the D’ state seen in table V is of the order of 0.3

cm -1,

^which suggests ^{that our estimated 2 a error} in the

positions

^{of the D’ and A’ states} (1.6

cm -1 )

is

probably

^too

large.

We used the data of reference

[18]

^{with the new}

vibrational

numbering

^{for the} a-state to construct

Table V. ^-

D’(2g)

spectroscopic ^constants.

All G(v) ^{relative to X}

1 Eg (v

^{= 0, J = 0).}

(a) ^{This work} (2 ^Q estimates in parentheses).

(b) ^Reference [18] ^observed.

0 ^Reference [18] calculated (Te ⁺ we(v ⁺

t) -

We xe(v ⁺

t)2).

(d) ^Reference [18] calculated (Be - ae(v

+’t)).

Table VI b. ^-

D’(2g)

state constants.

Constants determined from data of reference [18] ^with

v numbering ^decreased by ^seven (levels ^{used were v =} 1-14).

an RKR curve for the

D’(2g)

^{state. Table VIa}

(2)

presents ^{the RKR curve} and table VIb

displays

^the

molecular constants for the D’ state. It should be ^men- tioned that the

D’(2g)

^RKR

potential

^{had to be shifted}

by -

^{0.030 A so} that calculated intensities _agree with our observed 2g-2u fluorescence intensities.

This shift is

compatible

^{with the}

poorly

defined values of B(v) in reference

[18]

(see for instance Table V).

The RKR curve for the A’(2u) ^{state is}

reported

ⁱⁿ

table VIIa

(2). Equilibrium

^{constants are}

presented

in table VIIb. There is excellent agreement ^{with the} RKR curve

given by Tellinghuisen [ 11 bJ

^{and the}

observed D’-A’

intensity

distribution is

reproduced

Table VII b. ^- A’(2u)

equilibrium

^constants.

Estimated errors are two standard deviations.

(2) Tables VIa and VIIa are too lengthy ^{to be} published here, ^but they ^{may be obtained on request to} Les Editions de Physique ^or the authors.

when Franck-Condon factors are determined. As a

second check of the consistency ^{of our}

long-range

treatment of the A’ state, the ^outer turning

points

^were

extrapolated

using equation (5) ^{for R} > 9 A

(the C8

term is

negligible

^{in that}

range).

The program of Hutson

[20]

^{was then used to} calculate the molecular constants for all bound levels of the A’ state. Two

extrapolations

^were

performed,

^one

using

^{the value}

of

Cs

from the work of Saute and Frecon

[27,

28]

and the other

using Cs

^{= 1.68 x 10S AS}

cm-’,

^which

we consider to be the better value. In both _cases, the value of

C6

from reference

[28]

^was used. Table VIII presents these results. The constants for the last two bound levels (v ⁼ 68, 69) ^{were not found}

by

^Hutson’s

program and were determined

by extrapolation using

the

long-range

theory ^{of Le} Roy. ^The

energies

^{of the}

levels v ⁼ 60-67 were fitted to the

expression :

Table IX. ^-

D’(2g)-A’(2u)

Franck-Condon

factors.

2 6 estimates in parentheses.

(") Frequencies given ^{are for band} origins.

Table VIII. ^- A’(2u) ^molecular constants at large internuclear distance.

e) ^{This work} (2 ⁶ estimates in parentheses).

105 106 ⁶ CM-1

(b) Calculated from RKR curve having CS ^{= 2.09 x 105 AS cm-1 and} C6 ^{= 1.95 x 106 A6 cm-1} (see text).

(C) Calculated from RKR curve having Cs ^{= 1.68 x 105 AS cm-’ and} C6 ^{= 1.95 x 106 A6 cm-1} (see text).