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Collision broadening and shifts in the spectra of neutral and singly ionised magnesium, calcium and strontium

View the table of contents for this issue, or go to the journal homepage for more 1982 J. Phys. B: At. Mol. Phys. 15 2871

(http://iopscience.iop.org/0022-3700/15/17/020)

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J. Phys. B: At. Mol. Phys. 15 (1982) 2871-2880. Printed in Great Britain

Collision broadening and shifts in the spectra of neutral and singly ionised magnesium, calcium and strontium

R G Giles and E L Lewis

Department of Atomic Physics, The University, Newcastle upon Tyne, N E 1 7RU, England

Received 8 July 1981, in final form 21 May 1982

Abstract. The broadening and shift induced by helium and argon in the singlet neutral resonance line and the resonance doublet of the first ionised stage of magnesium, calcium and strontium are reported. The pressure-broadened components were extracted from predominantly Gaussian profiles by full numerical analysis and the resulting cross sections are discussed in the context of other data for these transitions.

1. Introduction

The broadening and shift of spectral lines of neutral atomic species have been intensively studied by high resolution spectroscopic techniques and in recent years have provided critical tests of sophisticated calculations of interatomic forces (Lewis 1980). Much of this work has concentrated on the resonance lines of the alkali metals since they are experimentally convenient and the one-electron configurations involved are amenable to theoretical treatment. The isoelectronic singly-ionised group I1 metals have received much less attention although they are important for an understanding of stellar spectra in which their lines are often the most prominent absorption features.

In the present work we have aimed at a survey of the broadening and shifts of the resonance lines of the lighter group I1 metals in their first ionised stage. In comparison with the neutral alkalis, the states of the group I1 ions are much more strongly bound so that the resonance lines lie in the near uv rather than the visible. In addition, all except the magnesium ion have D3/2,5/2 levels lying below the resonance levels P1/2,3/2. Other previous experimental work has been limited to shock tube studies of the Ca' resonance lines (Hammond 1975, Baur and Cooper 1977). While these have necessarily rather lower precision than our work, they are complementary to our investigation since shock tube temperatures are significantly higher than ours.

Conventionally, the 2P1/2-2S1/2 and 2P3/2-2s1/2 resonance lines of CaC are referred to by the Fraunhofer nomenclature as the H and K lines. In this paper we shall for convenience use this nomenclature for the analogous lines of Mg+ and Sr'.

The high ionisation potentials of the group I1 metals mean that they are not accessible to absorption methods at laboratory temperatures, but their spectra must be obtained in emission. We have used a flow lamp light source and scanning Fabry-Perot etalon to obtain line profiles. These techniques were previously applied to lines of Ca+ by Bowman and Lewis (1978).

2 2

0022-3700/82/172871+ 10$02.00 @ 1982 The Institute of Physics 287 1

2872 R G Giles a n d E L Lewis 2. Experiments

2.1. Optical system

An etalon was used in the centre spot scanning mode with the pressure of the gas in the etalon chamber varied at a closely linear rate. Light from the flow lamp was focused through the system on to the sampling pinhole at the entrance of a mono- chromator. Light from a standard lamp could also be passed through the optical system by means of reflection from the front surface of a quartz plate inserted at 45O to the optic axis before the etalon. After the fringe-forming lens, a second beamsplitter was inserted so that the fringes could be focused on to the slits of two separate monochromators. For shift measurements, one of the lines recorded was that from the standard lamp. The central intensity of the fringe system was recorded as the pressure of carbon dioxide in the etalon chamber increased. Photomultiplier signals were amplified by Keithley picoameters and the output voltages were recorded both graphically on a two pen chart recorder and, after digitisation, as numbers on paper tape. Digitisation of the voltage was via a microcomputer based on the MK3850 microprocessor (Mostek Corporation).

Three sets of etalon plates were required for the range of lines studied. The dielectric coatings were maximised for the regions 2900,4000 and 8500 A, the coatings being eleven layers PbF-Jcryolite, five layers ZnS/cryolite and six layers cryolite/ZnS, respectively. The choice of etalon spacer was largely determined by the Doppler widths of the lines studied which, for the uv and blue lines, almost always dominated the linewidth. For the final measurements, a spacer of 0.512 cm was used for the uv and blue lines and a 1.014 cm spacer for the calcium infrared triplet.

2.2. T h e flow l a m p

The flow lamp source is described in detail elsewhere (Bowman and Lewis 1979). It basically consists of a quartz tube of rectangular cross section constructed from a precision quartz cell, through which the carrier gas flows. Metal vapour is diffused into the helium or argon carrier gas from a pyrophylite oven and the discharge is microwave excited in the section of tube encased in a cavity. Carrier gas pressures are typically form 10 to 200 Torr. Light is extracted from a small aperture in the end cap of the microwave cavity, whose image on the monochromator slit was slightly larger than the sampling pinhole.

The resonance lines of the ionised and neutral species were obtained from the discharge with high intensity and some care was taken to minimise self-absortion.

The effects of discharge power, depth of discharge in the line of sight, and density of metal diffused into the flowing gas, were all investigated. Eventually the discharge was confined to a rectangular section quartz tube with a depth of 5 mm in the line of sight and this could not be further reduced without sacrifice of discharge stability.

Oven temperatures were held steady so as to inject metal into the carrier gas at densities which kept self-absorption below 3%, the worst case being that of magnesium.

At that level, effects of self-absorption were negligible for profiles with such large

Gaussian components at our level of precision (Lewis and Stacey 1969). This was

confirmed by analysis of computer-generated profiles with varying degrees of self -

absorption. The gas temperature was monitored by a thermocouple which could be

traversed along the axis of the quartz tube through the region of the discharge, and

Collision broadening in calcium, magnesium and strontium 2873

- z

+ 5

f -

_z

. .

5 -

m

the pressure was measured by McLeod and U-tube gauges attached close to the discharge.

In addition to these parameters, it is important to determine, at least approximately, the electron density and temperatures of the discharge under typical operating condi- tions so as to assess the contributions of Stark broadening to the profiles. As an indicator of the discharge conditions we investigated the ratio of the intensities of the ionised metal resonance lines to that of the neutral atomic resonance lines (i.e. IH,K/IN)

as a function of the discharge power and pressures. Our analysis was an extension to a two-component plasma of the Saha equations for LTE given by Griem (1964).

As an example we show in figure 1 a plot of I J I N calculated on that basis and experimental points. The fit has been obtained by reducing the theoretical ratio by a factor four. To the first approximation this factor can be accounted for by allowing for the radiative decay of the ionised resonance levels which competes with the electron collisions. Experimental values of both radiative decay and electron de-excitation rates are available for Ca' (Smith and Gallagher 1966, Crandal et a1 1974). Radiative rates are known for the other ions (Smith and Gallagher 1966, Lurio et ^a1 1964).

1 6 - - 1 0

1 2 - - 0 6 --

0 8 - - 0 2

__

04---02

Microwave power ( W )

0 40 80 120 160 200

0 1 - 0 6 il'

Electron temperature I K 1

Figure 1. Variation of the ratio of the intensities of the K resonance line of the ion (IK) to that of the resonance line of neutral magnesium in an argon carrier gas. The points are experimental and the full curve is calculated from Saha equations.

Drawin (1961, 1962) gives an expression from which electron collision rates can be

estimated and which reproduces the Ca+ and Mg+ data very well. This was used to

estimate collision rates which were relevant but not yet measured. On this basis, we

conclude that the ion resonance levels are strongly coupled to the ion ground state

with very little coupling to higher excited states. The ratios of K-resonance level

population NK to that of the ion ground state, No, is then modified from the LTE

2874 R G Giles and E L Lewis value according to

where A K is the Einstein coefficient for the K level and (uKue) is the averaged rate for electron de-excitation. This yields Ne - ^{6 x 1013} cmV3 from the data for mag- nesium-argon discharges, given in figure 1, and establishes T e - 10 000 K.

The contribution of Stark broadening to the linewidth of the Mg' ion lines can therefore be estimated from the experimental data of Fleurier et a1 (1977) as 1.3 mK.

Similar values result for other metal-carrier-gas combinations.

2.3. Profile analysis

Typically 4-5 orders of interference were recorded for each pressure together with background signals, of scattered light and dark current, taken for each channel immediately before and after the recording of the interference profiles. The digital record was analysed in two stages on the NUMAC 370/168 computer. In the first stage, residual non-linearities of the time scan and any intensity drifts of the lamp were corrected for. Traces were only acceptable if the intensity drifts were monotonic and less than 10% overall. Each channel was then reduced to a single averaged order of interference. Relative positions of the peaks in the two channels were extracted at this stage to provide shift data. The averaged profile was then fitted to a calculated profile consisting of a convolution of the Airy function and a Gaussian function. A least-squares fit was performed based on the NAG routine E 0 4 F A F and the analysis yielded a Gaussian halfwidth corresponding to the temperature of the emitting atoms or ions and an Airy function whose width is related to the sum of the pressure- broadened width, radiation width and the instrumental contribution which depends on the etalon reflectivity.

Natural calcium consists essentially of a single isotope while magnesium and strontium, although both predominantly a single even isotope, have admixtures at the 10% level of other isotopes. Our detailed analysis of the profiles required that these admixtures should be taken into account. Data on the isotope shifts and hyperfine structure of the lines studied were taken from Crawford et a1 (1949) for MgC, Kelly (1957) for the Mg resonance line, and for Sr+ from Heilig (1961) and Heyden and Kopferman (1938). Four-component profiles were fitted to the profiles of the Mg' and Sr+ resonance lines and a three-component profile to those of the neutral magnesium line. Figure 2 show the quality of the fit for a profile of the Sr+ H line perturbed by helium, the residuals being magnified by one order of magnitude.

3. Results and discussion

3.1. Broadening and shift constants

We combine our results with those previously presented by Bowman and Lewis (1978)

for calcium. The two investigations essentially provide a complete set of data for

broadening and shifts due to helium and argon in the singlet resonance line of the

neutral species and the resonance doublet of the ionised species of magnesium, calcium

and strontium. Practical difficulties in obtaining a stable discharge in a magnesium-

Collision broadening in calcium, magnesium and strontium 2875

. . ..

. . . .

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..*. ...

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20 40 60 80 100 120

Channel number

Figure 2. Numerical fit to the profile of strontium A =4215 8, in argon at density 4 x 1017 ~ m - ~ , Lower curve shows the residuals multiplied by ten. Wavenumber runs from right to left, 7.63 mK/channel.

helium mixture resulted in a lack of data for the H and neutral resonance lines for that combination. In addition to the resonance lines of Ca+, the two stronger com- ponents of the infrared triplet, which shares the upper level with the resonance doublet, were also investigated.

Our analysis of the interference profiles, as described above, yielded Gaussian

components which had halfwidths as high as 1 6 0 m K for magnesium whereas the

largest Lorentzian halfwidths were approximately 80 mK. Only a full analysis of the

profiles can yield the pressure broadening from such admixtures with any degree of

confidence. The Lorentzian components showed a linear variation with the number

density of the carrier gas, the latter being obtained from the measured pressure and

the thermocouple temperature for the discharge region. The broadening and shift

constants were derived from this linear variation, any Stark broadening being within

the experimental error. The Lorentzian component, extrapolated to zero density,

provides a value of the instrumental contribution to the profile together with the small

radiation width. An independent determination of the instrumental contribution

obtained by studying the profiles of standard lines obtained with various spacers

(Bowman and Lewis 1979) agreed well with these intercepts. The Gaussian contribu-

tion to the profile due to etalon plate deviations from flatness was small so that the

Gaussian width could be used directly to obtain Doppler temperatures. These were

in the range of 870-1500 K and for a given combination of line and carrier gas and

showed no significant variation with number density during a run. Measured gas

temperatures were always close to 500K. The excited atom and ion temperatures

are therefore intermediate between those of the carrier gas and of the electrons. This

is consistent with the departures from LTE discussed in 82.2. We interpret the

temperature derived from the Gaussian component of the profile T D as the temperature

of the emitting ions and atoms which are in collision with rare-gas carrier atoms whose

temperature, TG, is that measured by the discharge thermocouple. In table 1 we

quote the temperature to which our broadening measurements apply, as

2876 R G Giles and E L Lewis

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Collision broadening in calcium, magnesium and strontium 2877

where

This table also contains all other work on these lines reported in the literature.

and mG are the masses of the emitting species and the rare gas, respectively.

3.2. Broadening and shifts of the singlet resonance lines

Our measurements of the broadening and shift of the singlet resonance lines of the neutral species were largely intended as a check on our understanding of the discharge conditions; the other data being essentially absorption measurements. The most intensively studied of these is the 4227 8, calcium line and our most direct comparison is with the work of Smith (1972). For broadening by helium there is close agreement between the two sets of data and combining with the shock tube results of Driver and Snider (1976) we obtain a temperature dependence (B ^E T a ) of

^(Y

= 0.36(4) which can be interpreted as an inverse power potential ( E R - ” ) with 6.5 G n G 11. The lower temperature result of Chen and Lonseth (1971) is rather qualitative but is consistent with the other sets of data for both broadening and shift whereas the hook method result Jf Penkin and Shabanova (1968) appears to be considerably too small.

For the same line perturbed by argon, the data is less consistent in that while there is general agreement on the shift constant to within the quoted errors, the hook method result is again lower and, more seriously, the value quoted by Smith is almost a factor two larger than our result. In his survey of the broadening by all the rare gases, Smith (1972) ficds the result for argon to be larger than that for krypton. We know of no other line for which this has been observed and feel justified in discounting his value for argon.

From strontium 4607 A, the results of Penkin and Shabanova (1968) again appear to be considerably too small in that the other two results are just consistent with a physically possible temperature dependence. In the case of magnesium 2852 8,) our result is in agreement with that of Zhuvikin et a1 (1977).

This survey indicates an unsatisfactory situation in that there is no consistency between the existing data against which we can judge the reliability of our measure- ments. We feel, however, that the hook method measurements of Penkin and his co-workers should be viewed with suspicion, and that otherwise our measurements fit in satisfactorily with the more direct absorption measurements.

3.3. Broadening and shifts of the ionised resonance lines

Considering first the results with helium as the perturbing gas, we see that for Ca’ a combination of our results and those of Hammond (1975) gives a temperature dependence with

(Y

= 0.40 (13) which is closely similar to that for the neutral resonance line. This is also close to the calculated value of Lwin et a1 (1977) for the light alkali resonance lines perturbed by helium. Similarly for broadening by argon, a combination of our measurements with those of Baur and Cooper (1977) gives a = 0.31 (07) which is in agreement with the trend obtained by Lwin er a1 (1977) and is essentially the van der Waals result.

The broadening constant B can be expressed as a cross section via the relationship

where 6 = (8kTAv/7rp)”* and a similar expression holds for shift cross sections. The

R G Giles and E L Lewis

velocity dependence of the effects are thus largely removed in the cross section data of table 2 which are consequently more indicative of,the interatomic forces involved.

For helium, the broadening cross sections are approximately the same for the three ions while the shift cross sections show a trend from large negative values for Mg' to a positive value for Sr+. A similar trend was observed by Lwin et a1 (1977) for the D lines of the light alkalis perturbed by helium. It is more common, however, for helium to produce positive (blue) shifts, reflecting the predominantly repulsive potentials which are more pronounced for the excited rather than the ground state.

The trend we observe suggests that for the lighter ions the contrary case applies and that the ground state has a more repulsive potential than the resonance states.

The ratio of the broadening cross sections for the H and K lines for all the ions differ significantly from unity, both for helium and argon perturbers. This indicates that the fine structure is not significantly decoupled at the interatomic separations which determine the cross sections. Taking a typical Weisskopf radius at 10 8, and d - ^{4 x lo3 m s-',} we obtain a collisional phase change of unity for interactions of only 1.5 cm-' which is much less than the fine-structure splitting even for Ca' (60.7 cm-').

In contrast to the helium results, we see that for argon the shifts are approximately independent of line and ion while the broadening cross sections increase significantly with ion mass. The latter trend would be expected for van der Waals forces since the polarisability of the ion excited states increases in this way. Indeed, calculations of the broadening constants from the well known expression of Unsold (Lewis 1980) gives agreement with experiment in the 10-15% region with the exception of the Mg'-He combination. Shifts calculated on this basis, however, are generally too small by about a factor two. The calculation of Giusti-Suzor and Roueff (1975) for the broadening of the H and K resonance lines by argon underestimates the broadening by about 30%. However, since these authors use an essentially repulsive potential, their calculation gives good agreement with the observed temperature dependence.

On the basis of earlier work, Bowman and Lewis (1978) pointed out that the broadening of the infrared lines of Ca' which share common upper levels with the H and K resonance lines exhibit closely similar broadenings. This is in contrast to the Unsold formula which is sensitive to the difference in polarisability between the ground state and the metastable 2D3/2,5/2 states.

The forces between ions and perturbing atoms which arise specifically from the ion charge must be virtually identical for all states of the ion. Thus the line broadening, which depends on differences of potentials in the ions, should depend to the first approximation on van der Waals terms in a very similar manner to neutral atom interactions. The level of agreement for broadening based on van der Waals forces is better than that commonly obtained in such comparisons. Shifts obtained from the Unsold expression are, however, a factor two too large and for Sr+ helium of the wrong sign.

4. Conclusions

Our measurements of the broadening and shifts of the ionic resonance doublets of

magnesium, calcium and strontium show trends which are familiar from line broadening

studies of the isoelectronic neutral alakalis. While the van der Waals theory is closer

to experiment than is commonly the case, the disagreement as to shifts indicates that

Collision broadening in calcium, magnesium and strontium

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2879

R G Giles and E L Lewis

considerably more sophisticated potentials will be required to explain our measure- ments.

Acknowledgments

We are pleased to acknowledge the generous assistance of Mr C Goodwin and Dr D N Stacey of the Clarendon Laboratory, Oxford, and of discussions with numerous colleagues both at Newcastle and Meudon (France). RGG acknowledges the award of an SERC studentship during this work which was also supported by SERC and in part by Nato (Grant No 1198).

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- 1979 J. Phys. E: Sci. Instrum. 12 126-8

Chen S Y and Lonseth A J 1971 Phys. Rev. A 3 946-50

Crandal D H, Dunn G H, Gallagher A, Hummer D G, Kunasz C V, Leep D and Taylor P 0 1974 Crawford M F, Kelly F M, Schawlow A L and Gray W M 1949 Phys. Rev. 76 1527-8

Drawin H W 1961 2. Phys. 164 513

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Heyden M and Kopferman H 1938 Z. Phys. 108 232-43

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Lwin N, McCartan D G and Lewis E L 1977 Astrophys. J. 213 599-603 Penkin N P and Shabanova L N 1968 Opt. Specktrosk 25 446-7 Smith G 1972 J. Phys. B: A t . Mol. Phys. 5 2310-19

Smith W W and Gallagher A 1966 Phys. Rev. 145 26-35

Zhuvikin G V , Penkin N P and Shabanova L N 1977 Opt. Spektrosk. 42 134-6

Astrophys. J. 191 789-93