Stark broadening of neutral and singly ionized gallium and indium lines

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Stark broadening of neutral and singly ionized gallium and indium lines

M. N’Dollo, M. Fabry

To cite this version:

M. N’Dollo, M. Fabry. Stark broadening of neutral and singly ionized gallium and indium lines.

Journal de Physique, 1987, 48 (5), pp.703-707. �10.1051/jphys:01987004805070300�. �jpa-00210488�

703

LE JOURNAL DE PHYSIQUE

STARK BROADENING OF NEUTRAL AND SINGLY IONIZED GALLIUM AND INDIUM LINES

M. N’DOLLO and M. FABRY

Laboratoire de Physique des Milieux Ionisés (C.N.R.S., ^U.A. 835),

Faculté des Sciences de Nancy, ^B.P. 239,

54506 Vandoeuvre-lès-Nancy Cedex, ^France

(Regu le ^{18 novembre} 1986, accepte Ie ¹⁹ fivrier 1987)

Résumé : Les élargissements Stark de raies du gallium ^et de l’indium neutre (Ga I, ^In I) ^et

une fois ionisé (Ga ^{II, In} II) ^{sont calculés à partir} d’une méthode semiclassique ^{et mesurés. Les}

déterminations expérimentales ^sont déduites de l’observation spectroscopique d’un arc à cathode

liquide ^{utilisant un} mélange sodium-indium ou potassium-gallium, la densité electronique pouvant varier de 1014 à 2 1015 cm-3 et la temperature électronique ^étant voisine de 3300K.

Abstract : Stark widths for lines of neutral and singly ^ionized gallium and indium are both calcu- lated and measured. Calculations are based on a semiclassical method. Measurements are carried out by observing ^{the emission of a} low-pressure sodium-indium or potassium-gallium ^{mixture in}

a liquid ^{cathode arc. The electron} density ranged ^{from 1014 to 2 x 1015 cm-3} and the electron temperature ^{was close to 3300K.}

J. Physique ⁴⁸ (1987) ^{703-707 MAI 1987,}

Classification

Physics ^Abstracts

32.70J - 52.70K

1. Introduction.

Stark broadening parameters ^of spectral ^lines

will be useful in the characterization of plasmas. ^Nu-

merous measured and calculated Stark widths have been reported for neutral and singly ionized elements but no data are available for gallium and indium.

In this _paper we report calculated and measured Stark widths for some lines of neutral or singly ^ion-

ized gallium ^and indium. Measurements consist in the spectroscopic observation of a potassium-gallium

or a sodium-indium ^arc. In the plasma, ^{electron den-} sity ranges from 1014 - 2 x 1015cm-3 for an electron temperature of about 3300K. G.B.K.O. theory [1] ^is

used for the calculations which was proved ^successful

in predicting ^{the widths of isolated} lines for neutral atoms [2 - 3]. ^{We used} semi-empirical ^relations [4]

for ions ; indeed, experimental works show that the

G.B.K.O. widths ^are often too small by ^{a factor 2 to}

10 for ion lines [5 - 71.

2. Theory.

The broadening of emission lines is treated by using ^the substantial difference in equilibrium ^veloc-

ities for electrons and ions. For the slow moving ions, ^the quasistatic theory ^{can be} used : ions are as-

sumed to be motionless while the perturbation ^acts,

which significantly ^{alters the atomic} Hamiltonian. It results in a shift of the levels by ^the Stark effect.

The electron impact theory requires ^{that strong col-}

lisions ^are well separated ^{in time while} overlapping

collisions ^are weak and can be treated by ^{means of}

the second order perturbation approximation. ^The

effect can be reduced to calculation of the scattering

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01987004805070300

704

matrix for a single collision. Averaging ^{over the} pos- sible electron configurations ^is required. ^Electrons

are assumed to have a Ma,xwellian velocity distribu- tion, ^{to be} randomly distributed in _space and to have

straight trajectories.

The broadening calculations are greatly simpli-

fied when only isolated lines are considered. This

means that neighbouring energy levels do not over-

lap. The electron impact ^{width we} and shift d of an

isolated line with upper state i and lower state f can

be obtained from G.B.K.O. theory by [1] :

in terms of the S-matrix for collision of a single ^elec-

tron with an atom. The curly brackets , ^indicate

an angular average, the thermal _average being ^com- pleted by integration ^over velocities v. The minimum

impact parameter pmin is obtained by :

and the cut-off in the integration ^{over the} parameter

,

P ^at pax is given by pax ⁼ 1.123pD ^where /9D is the

Debye ^radius. Note that the electron impact ^width

we can be obtained from semi-empirical theory using Baranger’s ^relation [8] :

where Ne ^{is the} density ^of perturbing (free) electrons,

ai,i and af,f ^are the inelastic cross-sections for transi- tions to levels i’ ( f’) ^{from initial i} (final f) ^{level, fi and}

f f ^{are elastic} scattering amplitudes ^{for the two states}

of the perturbed system ; ^the integral ^{is over scatter-} ing angles, ^df) being the element of solid angle ^and

the average 8Y is calculated over electron velocity ^v.

The scattering S-matrix is expanded ^to second-order in perturbation, dipole (Ol = ±1) ^{and quadrupole} (Ot ^{= 0,} :J:2) ^terms being retained in the multipole expansion. The atomic matrix elements which ap- pear in relations (1) ^and (3) ^{may be estimated using}

approximate wavefunctions in the Coulomb _approx- imation [9].

3. Experiment

The liquid ^{cathode arc} generator has been de-

scribed previously [10 - 111. Its essential characteris- tics are as follows: the plasma is initiated in the _pres-

ence of _argon between a copper anode and a water cooled cathode ; ^different elements, ^{such as low melt-} ing point metals, may be used as cathodes. In cre-

ating gallium ^{or indium} plasmas ^{we use} potassium- gallium ^or sodium-indium mixtures as the cathode.

This avoids non-conducting ^oxide coating ^{of the} pure metal which would prevent initiation of the plasma

[11]. ^The optical system consists in a T.H.R. mono-

chromator and an optical multichannel analyser ^with

a vidicon tube or a photomultiplier ^{detector. The}

monochromator has ^a 2400 grooves/mm holographic grating ^which gives ^a resolving power of about 250000 ;

a tungsten ^ribbon lamp is used for the detector cal- ibration. The instrumental width is determined to be 0.004 nm. Details of the optical apparatus ^and performances ^are given in reference [12].

Electron density Ne is measured from the Hp profile, ^{a small} quantity ^of hydrogen being ^{added to}

the auxiliary gas. (argon ^{in this} case) ; electron den-

sity may vary from 1014 to 1016cm-s according ^to

pressure and arc current. In order to have a suf- ficient stability ^and reproducibility ^of experimental conditions, ^an upper limit to the _range of 1015cm-3 is used in the present study. ^In addition, ^{L.T.E. is}

obtained under these conditions [13]. ^{Electron tem-}

perature Te is deduced from relative intensities of 3P-nD lines for sodium or 4P-nD lines for potassium, using known oscillator strengths [14] ; ^{electron tem-}

perature depends weakly ^on plasma conditions and

typical ^{values are} Te N ^3300K [15]. Stark half-half widths Alas ^are deduced from recorded line profiles by taking instrumental width and Doppler ^broaden- ing ^{into account.}

4. Results and discussion

Numerical calculations are carried out for iso- lated neutral and singly ^ionized gallium ^{and indium}

lines situated in the visible region. ^{Tables I to IV}

list half-half widths _wc as a function of tempera-

ture from 2500 to 40000K and for electron density Ne = ^1016cm-S for neutral species (Ga ^{I and In} I) ^{and Ne = 1017cm-S for ions} (Ga II and In II).

The election impact contribution we is predominant

but an ion contribution is present ^{in the} given ^Stark widths, ^the total width being given by [16] :

where ^a represents the relative importance ^{of ion} broadening and rdetermines the Debye shielding ^and

the ion-ion correlations.

Table I.- Calculated half-half ^{widths We} (nm) ^{Ga I} multiplets ^at Ne =1016cm-3 using equations (1) ^and (f).

Table II.- Calculated half-half ^widths wc(nm) for ^{In I} multiplets ^at Ne =1016cm-3 using equations (1) ^{and (2).}

Table IIL-Cajculated half-half ^{widths We} (nm) for ^{Ga II} multiplets ^at Ne ⁼ 1017 cm-3 using equation (3).

Table IV.-Calculated half-half ^widths We (nm) for ^{In II} multiplets ^at Ne = 1017 cm-3 using equation (9).

The approximations ^{in the} calculations of Stark half widths are well justified for neutral atom lines

even if some deviations are due to uncertainties in ra-

dial matrix elements obtained by ^the Bates-Damgaard

method.

In the calculated Stark widths or ionized ele- ments, ^the principal difference lies in the _presence of the long range Coulomb interactions between ra-

diators and charged perturbers. Compared ^{with the} straight ^classical path result, the contribution of _qua-

drupolar interaction using hyperbolic trajectory ^as- sumption,will be increased. However, this effect re-

mains limited compared ^to the dominant dipole ^con-

tribution.

Measured Stark widths _wm are given ^{in table}

V and only ^concern lines which are of sufficient in-

tensity ; other lines are too feint and measured _pro- files lead to substantial uncertainties. In table V the transitions with corresponding wavelengths, ^{the the-}

oretical widths _wc and experimental ^widths wm ^nor- malized to Ne ⁼ 1016cm-s for neutral species, Ne ⁼ 1017CM-*3 for icas and the ratio wm/wc ^{are listed.}

The experimental ^data given ^{are average values over}

measurements carried out at various electron densi- ties. Uncertainties take the different sources of ex-

perimental ^{error and} dispersion between different re-

sults into account. The _average ratio between _exper- imental and theoretical widths is 1.1, comparable ^to

the limits of experimental ^error (typically ^{20 %} ).

No experimental ^{data are} given ^{for the 52P - 6’S.}

In I multiplet (410.29 ^{and 451.20} nm) ^{because re-} absorption of these intense resonance lines has been established in some experiments. ^The necessity ^of operating ^at high ^electron density ^{in order to ob-}

tain accurate determination of weak Stark broaden-

ing ^is incompatible ^with reabsorption ^{effects. The}

same phenomenon has also been observed for the 42p - 52S Ga I multiplet (403.41 ^{and 417.32} nm)

but without hindering correct measurements.

5. Conclusion

We report ^Stark broadening parameters ^{of iso-} lated gallium ^and indium lines in the visible region.

From the results given ^{in table V, it appears that the}

measured Stark widths are in good agreement ^with the theory, ^the average ratio between experimental

and theoretical values being ^1.1. Nevertheless, ^mea-

sured values are limited to a few lines because of

experimental difficulties.

706

Table V.-Stark broadening parameters for gallium ^and indium lines : _We are theoretical values (the ⁼ 5000K ; Ne ⁼ 1016cm-3 for ^neutral species ^and Ne ^{= 1017cm 3} for ions) ; ^{wm are the} corresponding experimental ^values.

Reference

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