High density self-broadening of the first xenon and krypton resonance line

LE JOURNAL DE TOME JANVIER 9PHYSIQUE 40, 1979,
Classification
AbstractsPhysics
- 32.70 34.20
density High self-broadening
of the first xenon and resonance line krypton (*)
P. and H. Laporte Damany
de C.N.R.S. Cours 42023 Saint-Etienne France158bis, Fauriel, Cedex, Equipe Spectroscopie, (LA 171) (**),
le 3 le 2 octobre (Reçu juillet 1978, accepté 1978)
2014 nm et nm du est étudié dans le domaineRésumé. des raies du xénon L’autoélargissement 146,96 123,58 krypton
1-100 x 1019 2014 1021 Les sont obtenus à desde densité amagat (2,7 2,7 at. cm-3). profils d’absorption partir
Les critèresmesures du facteur de réflexion au d’une méthode de Kramers-Krönig specialement adaptée. moyen
à dans mesure on est en de validité des théories existantes sont discutés en détail de façon préciser quelle pré-
de forces résonnantes. On montre en du sence d’effets multiples et/ou purement particulier que l’hypothèse plus
voisin en théorie demeure dans les ailes. De là il est a densité possible, croissante,proche quasi statique justifiée
de forces forces de dede mettre en evidence les effets des différents resonance, spécifiques types impliquées :
Van der on trouve en l’état excite une faiblementainsi, Waals, répulsives ; particulier, que 1u présente partie
attractive et pour Xe2 Kr2.
2014 Abstract. of the 146.96 nm xenon line and 123.58 nm line is studied in the densitySelf-broadening krypton
1-100 x 1019 2014 2.7 1021 The is deduced from reflectionrange amagat (2.7 at. cm-3). absorption profile
a modified A detailed discussion of the criteria for of availableexperiments by Kramers-Krönig analysis. validity
theories is the determination of the extent to which the cases studied are related to given, allowing many-body
in the nearest isinteractions resonance forces. The and/or pure quasistatic theory, neighbour approximation,
shown to be valid for the far Thus it is at to underline the interpreting wings. possible increasing density, specific
to effect of the various kinds of forces : Van der Waals and and the excited stateresonance, repulsive, specify 1u
which is found attractive for and potential weakly Xe2 Kr2.
1. Introduction. - While studies have been has been studied at densities 1 many beyond amagat [3-6] (1).
withdevoted to atomic line collisions On the other rare have their resonanceby hand, broadening gases
in the low or the in either lines the vacuum ultraviolet and the lack of trans-density highforeign gas,
few are in the materials work on linedensity range, experiments reported parent prevents quantitative
field of most of them in the low below 105 self-broadening [1] profiles nm ; thus, high density investiga-
tions are now restricted to the first resonance linesdensity range.
be both theore- of Such a situation and xenon the may explained by krypton and, although experi-
difficulties. mental conditions remain recent instrumentaltical and difficult, experimental
of when oneFrom the theoretical allow accurate measurements.view, point improvements fairly
whole at tries to the Another more fundamental lies in theprofile high density,interpret difficulty
arises from the well-known non-the main at the line centre of a problem very strong absorption pure
additive character of the resonant interaction [2]. transmissionhigh density gas (§ 5). Accordingly,
line studies of atomic measurements cannot the whole broadeningExperimental yield profile, although
several to metallic are for the shift be attained unusual restricted, reasons, vapours may by
or rare Pure metallic such a gases. vapours require high techniques 11]. Actually, [10, strong absorp-
and and only mercurytemperatures high pressures
31 n the case of 1 2.706 7 x 101 Y at CM-3 ( 1 ) xenon, amagat ==
and in the case of [7]), krypton,(Ref. Work done in at Laboratoire des Interactions molé-(*) part
culaires et des Hautes Pressions Centre Universitaire 3 (C.N.R.S.), 1 2.695 3 x 101 y aLcm - amagat - (Ref. [8]) .
av. J.-B. 93430 France.Paris-Nord, Clément, Villetaneuse,
de Laboratoire et For a definition of the for instance Jer-(**) Spectrométrie Ionique Moléculaire, general unit, see, amagat
associé au Universités de et de St-Etienne. rard et al. C.N.R.S., Lyon [9].
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01979004001090010
- tion is associated with the so-called selective or tation of the data. Note thatpresent experimental
- in a first observed the width reflection, phenomenon density specular range implied, Doppler may
which consists of a coherent diffusion be with the Wood effectsby [12], neglected compared broadening
of the incident at sufficient of the absorb- of atomic interactions.light density
of the selective reflectionmedium. The Theories have two developed ing properties mainly along lines,
are well-known in the reflectance and theories [13-15], particular, namely impact [20] quasistatic [21, 22],
of the medium be as a function of to may expressed corresponding complementary frequency ranges
index Fresnel’s formula below its refractive we are led to distin-by (see § 3.2). complex Accordingly,
at normal between the line centre and the which, incidence, yields guish wings.
-2.1 LINE CENTRE. - 2.1.1 Loii’ case. densitv
valid at low theories, and in theImpact density
of the line a Lorentzian vicinity centre, predict shape
whatever the considered so thatpotential [23], n - ik the refractive index of thebeing complex
measurements in the line centre a test of aprovide medium and n’ the real refractive indexabsorbing
kind of curves rather than an actual deter-potential window of the cell. The indexof the transparent
mination of these [24-27].of k is related to the coeffi-absorption absorption In the case a of transition with a oscillator
= high cient a the relation k Te. But inter-by Àa/4 any
the effect of forces other than resonancestrength f, of the data the ofpretation requires knowledge
is and the law is negligible broadening given by (2)n and k which have to be deduced from R-data by
This is main a mathematical the differenceanalysis.
as with direct transmittance measurements.compared
At normal incidence the method based on Kramers-
as theKrônig suitably modifiéd, integrals, appears
where N is the /11 thé electronie massdeiisity, aiid (1, of mathematical treatment which does notonly type
and X is a constant whosecharge respectively ; rest on an a chosen model. As far as we know,priori
value is somewhat the variousdependent upon never this has been to line broa-procedure applied
theoretical approaches (Table I).studies and R-data have been treated dening [3, 4, 14]
in term of the semi-classical dispersion formulae,
- based on the harmonic oscillator model Table I. Theoretical K.(Lorentzian values for
for shape nk).
The normal incidence reflec-present paper reports
tance measurements on xenon and performed krypton
at in the of their first reso-densities, high vicinity
nance lines. It has been to possible study experi-
the xenon ’line from the mentally continuously gas
= to the phase up liquid phase 16.60°C,[16]-(Tc
= 58.40 bar and to observe the onset ofPc [17])
fluid excitonic in the dense (appearancephenomena
180 We will restrict ourselvesdensity - amagat).
100 where here to densities below amagat interpre-
tation in terms of interatomic is potentials possible.
the whole is obtained fromAt each density, profile
R-data the above mentioned by Kramers-Krônig
analysis.
recalled the main theoretical deve-Having briefly
we discuss their tolopments, applicability according
the of force the considered, type frequency range
and the This allows us to define therange. density K function of the limit to the (*) Nf (from quasistaticimpact extent which interactions to have to bemany-body limit).
taken into account. we show that a Finally, large
of the be in the frame ofpart profile may interpreted
Low line centre measurements show a fairdensity the in the nearest quasistatic theory (QST) neighbour
with the more recent values ofagreement impact Thus valuable informationapproximation (NNA).
K in the some[40] ; large discrepancies appearing about excited can interatomic be obtainedpotentials
cases have reviewed Exton been critically by [41].from data.wing
full In the we shall between the width(2) following distinguish
- the2. In this we recall section, half-width at half-Theory. briefly at half-maximum and the (FWHM) A v 1/2
main theoretical results to be for the maximum used (HWHM) interpre- ôvl/2.11
The situation where resonance The treatment is much if it is furtherforces is a simplified prevail
one since a Lorentzian is in assumed that the is dictated thespecific shape predicted perturbation by
the as as in well the limit the nearest impact quasistatic (in neighbour [21] (nearest neighbour approxi-
nearest mation referred to as Then the neighbour NNA). intensityapproximation).
distribution is toproportional
- 2.1.2 density case. In the High density range
1 the fails p > amagat, impact approximation (§ 3)
and the line centre must be described intoby taking
account effects. of reso-many-body Non-additivity
nance forces is a and the major difficulty problem are distances where the difference ri potential
has to be tackled in a fromvery general way. Apart
the work of Holtsmark based on too crudeearly [42]
an various haveapproximation [43], approaches is to hv and are the equal (3) ai respective probabilitiesbeen tried either the resolvent method orusing [44] excited states.of the implied
many-body techniques [34, 39, 45-48]. However, Then the index of is related toabsorption directly
most of them remain formal or as a thefind, limit, P(v) byresult. The recent work of Zaidi theory impact [49],
founded on the of shielded interactions andconcept
the use of thepropagator techniques, represents
first to solve the resonant case.attempt high density
be It leads to a Lorentzian for written, Eq. (6) may using eq. (5)generalized expression
the of the mediumsusceptibility absorbing
where are for the sake of introduced, generality,
term Z4 the Boltzmann factor and the where the Lorentz shift cor- (00 )(see 5.2.3) ; B (§ 3. 3) (r)/ A dL is § C3
the relative variation of the transi-to the resonant r- 3 term of the inter- which responds represents C3
tion moment with internuclear distance.atomic and is related to the oscillatorpotential dipole
an infinite at r valuesthe formula Eq. (5) predicts intensity strength by following (2) :
a where vanishes (satellite bands), physi-d(AV)/dr
result which can be correctedcally meaningless
either into account the collision time by taking [50-52]
Thisor a Franck-Condon [53, 54]. by approach
a to is referred as a realistic satellite withoutZ(Acv) complex term, leads to self-energy, shape procedure
whose is the cause of the its Another feature ofimaginary part principal affecting position noticeably.
of Im from a Lorentzian (x) satellite bands is a decrease of departure shape. sharp intensity beyond
Two main features are in this work : in it is often the maximum so predicted that, possiblepractice,
the contribution of the various molecularto A rate of versus smaller separate (i) broadening density,
states involved than the linear law in the where the (see § 5).range binary
When the différence is a collision is no valid. potential d V (r) single-approximation longer
one-to-onevalued function NNA a of r, A correlative of the yields (ii) asymmetrical development
from which follows acorrespondence I (v) H 0 V (r) line shape.
and direct method of determination of thesimple resonance i.e. Unfortunately, only forces, long
différence which recent workspotential, upon many distance forces are taken into and sinceaccount, to self-are based The method can be [55-61]. applied Van der Waals forces are known to a play major studies as shown NNAbroadening since, below, in short distance this asinteractions, part appears remains valid in selected For thisspectral ranges. a severe limitation to the to real situa-applicability it is convenient to the followingpurpose adopt tions. Thus transitions can be dealtonly strong of the différence expression potential :with simultaneous interactions willsince, otherwise,
set at densities where the influence of Van derup
Waals forces extends to the line centre up (see §3.4).
= = = with 2 if M 0 and 1 if M 1+
- YBMI = - YIMI 2.2 LINE In of WINGS. the the line,wings the the reso-(M being magnetic quantum number) ; fail theories but are they by impact relayed quasi- added to the well-nant term has been C3/r 3 YIMI static ones which the and(QST) disregard trajectory Lennard-Jones This allows known potential. simplecollision below the atomsThen, concepts (see § 3). calculations and also takes into in a realisticaccount,
considered at the line is determinedrest, being shape
the statistical distribution of the distances ofby
atoms the excited one. In the the of will be taken at surrounding (3) following origin frequency v,,.12
the effect of Van der Waals the the way, triple resonance, is suchreported experiments, broadening
and order forces in the interatomic that the of the is in the higher overlap major part profile validity
involved in our distance of the range experiments. range quasistatic assumption.
- NEAREST
- 3.3 NEIGHBOUR APPROXIMATION. IlIn 3. criteria. we recalled2, Validity paragraph
the NNA is most often literature, restricted to lowand evoked the ofsome theoretical aspects validity
densities. In Kuhn the first enough fact, various in terms of and gave quanti-approximations frequency
tative discussion of the and showed question The of the section is to that,density. purpose present
in the frame of the the QST, larger shift,discuss more the of frequency ranges quantitatively validity
the the that the beof higher probability perturbation these approximations.
induced one instead of several by perturbers [21].
- 3. 1 BINARY COLLISION (DENSITY RANGE). Binary on that we the Relying result, propose following
collision can be retained at densitiesapproximations criterion for the ofsimple validity frequency range
where one atom at most lies in the Weisskoff sphere NNA :
the active atom. In the case of surrounding strong
transitions values of this is unam-(large C3) sphere
defined its radius by biguously [20]
where A is the value of the difference Vn potential
at the mean interatomic distance. Inequality (11)
means that one need consider a simply where V is the mean frequencyof the atoms. As verifiedvelocity
to a from arange corresponding large departure a in our Van der Waals forces canposteriori cases,
fixed a situation where Kuhn’sregular distribution, be in the definition of disregarded pW.
result is applicable.From in 5. 1 and fromf-values given paragraph
In the criterion does not cover allfact, preceding we eq. (4), find,
situations and must be amended thepossible by
considerations :following
The Boltzmann factor(i)
Such values to the interatomiccorrespond average
in distance at a a gas density NL ~ pW 3 1 amagat. introduces a cut off in the distance betweenapproach
we conclude that the condition for Thus, may binary atoms in their state. Let a be the distance ofground
collision is never fulfilled in theapproximation the the turning corresponding frequency.point and v(1
of our measurements.density range the Boltzmann1, For frequencies v such that 1 vi> 1 v (1
factor decreases the that the
- strongly probability 3.2 RANGE. to Hol-FREQUENCY According
be induced a atperturbation by simple perturber stein’s and Sobel’man’s theoriesworks, [62] [63] impact
short so that Kuhn’s distance reasoning may pro-in the line whereas apply centre, quasistatic
fail at gressively increasing 1 v 1 (> 1 v (1 1).in the also Then a,apply wings (see Gallagher [57]).
Another case illustrated in 1.occur, (ii) may figure is thefrequency limit 1 VL 1 introduced, making
For a such as the is M, point frequency v positivebetween the two Such aseparation descriptions.
and does not fulfill the condition (blue side) (11) ;result comes out from the discussion of thedirectly
NNA is valid because the whole bluenevertheless, behaviour of the the Fourierintènsity, given by square
side to close distancecorresponds ônly approach of the time in the twoamplitude varying oscillator,
and B no restrictive plays part.where iscases v > and v « opposite 1/1:c 1/1:c, 1:c
the Thus we see when + NNA duration of a the cases that, (thereafterQST typical collision. vL 1, in
an controlof interest to is well defined referred to as is a into account NNQST) used, us, posteriori by taking
of the of interatomic distance resonance forces alone range corresponding
to the data has to be done.interpreted wing
in Let us now illustrate the above condition two
cases of monotonic curves :particular potential
- Resonant interactions. The a) C3 r-’ potential
It is found 4 x 10-3 nm for boththat law 1 .1ÀL l ’" from yields eq. (11)
Xe 147 nm and Kr 123.6 nm lines (4).
As will be shown later in the ofon, density range
the in this HWHM is fromAs, case, typically
and and table 1eq. (2) (4)
because of the in term from(4) Actually, the factor y arising
resonance forces différent limit could be(eq. (8)), frequencies
introduced for the red and blue but in a discussion of sides, validity
this distinction be criteria, may forgotten.13
= = Since G/4 nC3)3/2, eq. (10) yieldsNL pW 3
1and most of the will be relevant to the profile quasi-’
static with effects assumption many-body typically
above the in the line as illus-centre, half-maximum,
trated in 2. Due to the value reached figure high by
- in which NNA is valid the condition1. A case although Fig.
not fulfilled.1 is ! v ! [ a ) A VQ5fh
We writemay
- Waals interactions. Then we haveVan der b)
The true is the profile approximated by quasistatic
thegiven by Disregarding profile Margenau [22].
blue of this physically meaningless wing profile (no
2. - The various situations in resonanceFig. at v > we then write for the red occurring pure intensity vo), wing
, broadening. (a) impact region ; (b) quasistatic (a’) many-region ;
nearest’ bo4i’ general case ; (b’) many-body (b")
neighbour quasistatic region.
the maximum it is ofabsorption (§ 5.2.2) worthy
note that the can be studiedmany-body range only
reflection. Now an additional arises.by question
to For both NNA is becases, expected particular Can we Van der Waals forces in the lineneglect
of the line.valid to the half-maximum up nearly centre at densities ? To answer this high question,
from the theoretical back-Consequently, very simple = let us consider for instance 10 ThenNH NL.
of it is to account for theground NNQST possible
in a of a density gas large properties high spectral
- of force is whatever kind acting resonance,range,
the Van der Waals or other. Following NNA, frequencies + B)HbV1/2(R,
are associated with distances :
- 3.4 HIGH DENSITY RESONANT CASE > As(N NL).
said the collision previously (§ 3. 1) binary for the blue andapproxi- wing,
= mation fails in the line core if N > For N NL. NL
the HWHM is typically
for the red wing .14
we then obtain From and (9) (21) eq. for rH
be studied ifPure resonant case could high density
From and we therefore write theeqs. (22) (23)
condition
- 4. Reflectance of the fluorideFig. spectrum xenon-magnesium To an order of let us take someget magnitude,
interface. 33 instrumental width : 0.05 Density amagat ; nm.typical values C 6 =’ 1 0 - 3 1 cm 6 . S - 1 , V = 4 x 104 cm . s - 1 ;
we obtain :
known with the of the of state help equations (Xe [65] ;
Kr [8]).
or
- 4.2 KRAMERS-KRÔNIG ANALYSIS. In order to
obtain the true the ofabsorption profile, analysis
normal incidence reflectance data has to be performedSuch a condition is not fulfilled in the really present without the choice of model. This ispreliminary any and we conclude that a study may pure high density allowed in principle by Kramers-Krônig analysisresonant case has to be studied for high f-values. the is whole reflection known.provided spectrum
a restricted is observedUsually only spectral range 4. data discussion. -Experiment, analysis, so that the method is combined with somealways
- 4.1 EXPERIMENT. The methods andexperimental extrapolation procedure [66, 67].have been described So weapparatus already [16]. an idea of Bachrach and Brown Following [68],
mention them briefly. Ahrenkiel has a substractive [69] developed proce-
are V.U.V. measurements Quantitative performed dure well suited to the of a limited analysis spectralwith a double beam modifiedphotometer [64] suitably since it a more of therange gives rapid convergence for reflectance measurements This (Fig. 3). photo- in of the unobserved the integral spectrum.part meter is attached to a monochromator whose reso-
We have Ahrenkiel’s method to the caseadapted is lution of the order of 0.04 the source isnm ; light where the index k vanishes in the farabsorption
a deuterium a lamp emitting pseudo-continuum.
on both sides of the atomic line, wings by adoptingA reflectance curve is on 4.typical presented figure a substractive testsdoubly procedure [6]. Systematic
is from measureddetermined, Density accurately on with performed synthetic spectra, parametersand ambiant temperature ( ~ temperature),pressure close to real have demonstrated the ones, good
of the even when the method, accuracy integration
is to ten the of the limited times half-width broadened
line.
4.3 DlscussloN. - Before letfurther, proceeding
us discuss the two whichpart played by specific effects
occur in reflectance measurements.may high density
- 4. 3 .1 Wall First of one all, imagineeffect. may
the surface orrare atoms adsorbed on gas getting
the even into the bulk of transparentmigrating
window. Such should broad phenomena yield absorp-
tion bands rather insensitive to which ispressure,
not observed.
one wonder whether the windowSecondly, may
has influence from either a collisional or a staticany
of at the line the view, since, centre, point penetration
- 3. The with the reflection cell. S : exit slit ofFig. photometer 15 nm of is light typically - (§ 5.2.2).depth
the toroidal imonochromator ; M1, M2, M3 : mirrors ; Wl, W2 : at fixed collisions with the windowIf, temperature, sodium coated G : Th : ther-windows ; tube ; salycilate gas filling
were the main the den-physical process, increasing R : reflection C : circuitmocouple ; cell ; cooling jacket (cooling
not should not but shown here). sity basically change,the process only15
its the half-increase collisions. This would the molecularrate, leaving corresponding by explain why
width which is not observed. On the thancontribution to the is much weaker unchanged, spectrum
other we have in our hand, the one.density range computed
- 5. results and Illus-Expérimental interprétation.
trations of the obtained are absorption profiles given
= NV is the number of atoms where 1 /4 collidingnp in 5 and 6 for xenon and in 7 for figures figure krypton.with the window second and unit andper area, Similar features are observed for both lines :
N2 vV is the number of atom-atom colli-Jtp§ nC ~
even in the low second in a volume V of (i) Unsymmetrical wings, densitysions unit section andper
with a red and a blue one.range, long wing to the steep which doesheight equal penetration depth,
and of a far blue(ii) Appearance development not with Thuschange significantly density (§ 5.2.2).
at intermediate densities.wing we conclude even whén the that, may penetration
is collisions with the window contri-minimum, depth
a amount to the bute observed broadenednegligible
line.
Let us now look at the static of view : ifpoint
of the atoms the the window is domi-by perturbation
it will be on the atom-windownating, only dependent
as the of does notdistances ; depth penetration
with the line change significantly density, shape
on an distribution ofwould unchanged depend
with i.e. the halfincreasing density perturbation
width would be which is not observed.constant,
- 4.3.2 Molecular It is well known thateffects.
attractive state leads toa weakly ground potential
the existence of bound the free atoms. 5. - 146.96 nm xenon line pairs among Fig. absorption profile : density
20.4 20 °C.amagat, The molecular for Xe and Kr temperature corresponding spectra
have been observed at low and [70-74] density par-
The of molecules can betially analysed. proportion
calculated at low As a crudeonly density [75]. very
of such a calculationapproximation, extrapolation
from 1 to 100 bound indicates that, amagat, pairs
could 1 to 50 of the whole atoms forrepresent %
xenon and from 0.5 to for 30 % (room tempe-krypton
we also effects from mole-rature) ; may expect coming
cular trimers... In the complexes, fact, experiment
does not reveal molecular effect soany important
that the above estimation doubtful.may appear
we must in these molecules arebear mind that Actually,
bound - the well is 196.3 cm-1weakly potential depth
- for Xe and 140.3 cm -1 for Kr so that are[76] they
6. -146.96 nm xenon line 70 Fig. ama-dissociated thermal collisions room absorption profile ; density (at easily by
20 C.gat, temperature k T - 300 Consider now thetemperature, 3/2 cm-1).
collision at 100 for an frequency le amagat approach
= distance d re :
to the classical vibration ofCompared frequency
the molecule [77-79]
is of the same order of as f, magnitude co,,.
This casts some doubt on the nature ofspecific
bound at densities as with thepairs high compared 7. - 123.58 nm line Fig. krypton absorption profile ; density
free since their lifetime much be reduced 80.2 ones, may 20 C.amagat, temperature
- LE JOURNAL DE N° PHYSIQUE. T. 40. I. JANVIER 197916
- The first 5 .1 INTEGRATED AREA. information we not contribute The well-known relationsignificantly.
these is the can from between area and oscillator is inprofiles integrated area,get integrated strength
far obtained almost since dovery wings based on the of Lorentziancompletely principle assumption
We nevertheless tabulated the profiles. f-values
- deduced from this relation for various densities. NoTable II. Oscillator associated with thestrengths
nm line and nm variation is observed with and the146.96 xenon 123.58 line as systematic density krypton
are in fair determined various values both lines averaged by investigators. of f for agreement
with other determinations found in thé ’1literature
Thus we are inclined to at (Table leastII). think,
for these allowed transitions and in thestrongly
internuclear distance our by experimentsrange implied
Tables III and variation ofthat no (see IV), important
the transition moment in withoccurs, agreement
Mulliken’s estimation in the case of xenon. We[94]
shall in the therefore, adopt following A (r) JA ( oo) =1
(eq. (7)).
- IV. Table Numerical values of intermolecular poten-
tials at the dissociation (origin respective limit).of Kr2
- Table III. Numerical values of intermolecular poten-
tials at the dissociation (origin limit).of Xe2 respective
Evolution the 5.2 LINE CENTRE. - 5 . 2 .1 of half
- width. The the half-width versusevolution of
is in 8 and 9. Note the density given figures asymmetry
of the line in the whole indensity range, especially
the case of xenon.
results obtained from data for theUsing wing
excited curves we relate thatpotential (§ 5.3), may
to the effect of Van der Waalsasymmetry increasing
forces to reduce the bluewhich, according QST,
width are substractive with to (they respect repulsive17
resonant theand to f-value (smaller broadening)
lower of measurements at accuracy corresponding
shorter wavelengths.
5.2.2 Evolution the maximum the indexof kM of
- In order to an idea of the evo-of absorption. get
establish a lution of let us first general propertykM,
of Lorentzian for a of identical atoms.profiles gas
The index of writtenabsorption
maximuma yields
In resonant the case, eq. (2) gives
8. - 146.96 nm xenon line half-width versus Circles :Fig. density.
curve : blue dashed FWHM ; triangles : HWHM ; extrapolation
= the theoretical resonance for K 2.07.of broadening
Hence
From table we see for I, that, impact broadening,
= the value K 2.07 leads totypical
= 0.837km
which to a of 1 - corresponds depth penetration Â/10.
the determination ofReciprocally, experimental
the whereas thewithout yields K knowledge of f, kM
broadening yields Kf.
On the other in the case of weak oscil-hand, very
Van lator der Waals strength, impact broadening
dominates and from Lindholm’s lawbroadening
9. - 123.58 nm line Cir-half-width versus Fig. krypton density.
cles : blue dashed curve : extra-FWHM ; HWHM ; triangles :
of the theoretical resonance for K = 2.07.polation broadening
one would obtain
= M andresonance forces associated with ± 1)
= M increase the red (additive effect, 0).
a Our are at densities whereAs already pointed out, quantitative interpreta- experiments performed
tion of the exceeds the the interaction is no broadening present possibility two-body assumption longer
of on account of the simultaneous valid. We observe both a smaller thanpresencetheory broadening
in this case. the of two kinds of forces resonance many-hody extrapolated two-body broadening
In the case of in the 1-20 and a of the far Bothxenon, density range (§ 5.2.1) development wings.
we note the limited effects balance each other to a certain extent as farthat, resolvingamagat, despite
the the is below as the behaviour of is considered. Between 1broadening extrapolatedpower, kM
result obtained for resonance and 20 the linear values of obtainedpure amagat, average impact kM
Such a we could be are 0.88 for Xe 147.0 nm and 0.8 for Kr 123.5 behaviour, believe, broadening. nm,
deve-connected to the shielded interaction which are not far from the aforementioned theore-concept
effect of which is a reducedZaidi the tical value 0.837 valid at lower densities.by (§ 2), loped
25 the decrease of can bebroadening. Beyond amagat, km
The line does not exhibit so clear an ascribed to Van der Waals forces in akrypton qualitatively
its smallerwhat be ascribed both to A iseffect, may QST description. quantitative interpretation 18
conceivable since both resonance andnow for the xenon transmission data arehardly line, especially
Van der Waals forces contribute via two distinct a error due to affected residual theby systematic
molecular states below of the line.(see § 5.3). asymmetry
- From a theoretical of several mecha-view, In 10 and 11 are point 5.2.3 presentedShift. figures
to nisms have be evoked :from reflectance measurementsshift data obtained
as well as from transmission studies Note Resonant shift.that,[11]. (i)
Lorentz shift.(ii)
Van der Waals statistical shift.(iii)
The of existence a resonant shift has notpure
been laid on a firm in the yet ground impact approxi-
null or red shifts mation, blue, being predicted by
the various authors in low table I. At quoted density,
in the a null shift is favoured impact case, by experi-
mental data [95].
At the well-known local fielddensities, higher
correction in the frame of the classical dispersion
the shift shift following theory yields (Lorentz [96])
thewhere the term in takes into account parentheses
case of dense medium and was not [97] originally
included. first to solids theAlthough applied [98]
in the Lorentz shift has also been considered case
In the of theof gases [99, 100]. approach Zaidi,
Lorentz term but its influence is reduced onappears
account of the shielding effect.
shift is smaller thanThe observed clearly actually
the Lorentz shift at densities below 40 amagat.
10. - 146.96 nm xenon line shift versus Circles : the shift exhibits a Fig. density. Furthermore, quasiquadratic
transmission reflectance measurement ; triangles : measurements ; to the conclusion that the dependence leading gene-
curve Van der Waals shift for(a) : quasistatic ralized Lorentz shift Zaidi is not the mainby given
= 14.5 x in our case.10 32 c1116. S 1 ;C6 physical process
If one now in a rather crude imagines, approxima-curve Lorentz shift 0.27.(b) : for f =
that the effects of resonance forces associatedtion,
molecular states with the two involved next (see §),
in cancel each other as far as the shiftopposite sign,
is the shift can be as concerned, expressed (22) :
over the two states.where is an value average C6
The fit in 10 and 11.appears figures corresponding
The obtained values are close to the finalfairly C6
value deduced from so that the observeddata, wing
der Waalsshift seems related to Van effectively
forces.
- We with a 5.3 LINE WINGS. begin qualitative
discussion of our results with the of availablehelp
theories and known estimations of the potential
curves and of Xe2 Kr2.
Il. - 123.56 nm line shift versus Circles :Fig. density. krypton for Potential curves the first excited states of xenon
transmission reflectance measurements ; triangles : measurements ;
and have been estimated Mulliken krypton by curve Van der Waals [94,shift for(a) ; quasistatic
Barr et al. Four mole-101] and by [102] respectively.
= 10 X lU 32 cm6.S 1;C6 cular states are correlated with the0:, 1 u, Og 1g,
curve Lorentz shift 0.21. first excited state i.e. 6 for Xe(b) : for f = here, implied s(3/2)’