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Oscillator strengths of the resonance lines of the rare gases—I. Krypton
J. Qunnr..S~CCIIOSC. Radiat.TransYeer. Vol.5,pp. 503410. Pergamon Press Ltd., 1965. Printedin Great Britain
OSCILLATOR
STRENGTHS OF THE RESONANCE THE RARE GASES-I. KRYPTON* P. G.
E. 0. Hulburt
WILKINSON
Center for Space Research, U.S. Naval Research Washington, D.C., 20390 (Receiced
LINES OF
Laboratory,
14 October 1964)
Abstract-The oscillator strengths of the resonance lines of krypton at 1164 A and 1236 8, have been measured by an optical absorption technique. The results give f ~4 = 0.135 and AZ36 = 0.158. The corresponding lifetimes are T(‘P~) = 4.55 x 10m9 set and TV = 4.38 x 10e9 sec. The values for the oscillator strengths do not agree well with those obtained by refractive dispersion, but do agree well with electron scattering data. I. INTRODUCTION THE oscillator strengths of the resonance transitions of the rare gases are of interest experimentally in the interpretation of discharge processes in the rare gases(l), for comparison with optical dispersion data (see below), and for comparison theoretically, where such calculations have been made. From the oscillator strengths, one obtains also the mean life-times of the resonance levels. TABLE
l.*
WAVELENGTHS
Atom
He Ne Ar Kr Xe *
B.
AND
WAVENUMBERS FOR THE RESONANCE RARE GASES
LINES OF THE
IP,”
Y
3P10
Y
(a
(cm- ‘)
(A)
(cm- ‘>
584.334 735.895 1048.219 1164.867 1295.586
171,135.0 135,889.0 95,399.g 85,846*7 77,185.2
743.718 1066.659 1235.838 1469.610
EDLJ'?N,Reports Prog. Php
134,456.O 93,750.7 80,916.8 68,045*3
26, 181 (1963).
Table 1 lists the wavelengths and wavenumbers for transitions involving the ground state and the two lowest resonance levels (except for helium). L-S (Russell-Saunders) notation is used here in spite of the fact that strongj-j coupling is present, especially for xenon and krypton. The general experimental methods for determining oscillator strengths in atomic and molecular systems are (I), optical absorption (2); (2), optical refractive dispersionC3); (3), small angle scattering scattering methodC6);
of electronsC4’; (4), eerenkov radiation and (6), atomic beam methodsC7).
methodC5);
(5), Rayleigh
* Sponsored jointly by the Office of Naval Research and the National Science Foundation. 503
P. G. WILKINSOK
504
Absorption
coefficients
of krypton in the number of pm-ionized lines as well as the for each transition can be obtained from GARTON(~) and HUFFMAN rt al.‘“’
have been measured by PERY-THORNE and region from 500 A to 900 A which contains a ionization continuum. The oscillator strengths graphical integration:
f = 4.19 x 1O-8 ‘k,ds, Li
(1)
with k, and v measured in cm-l.clo) The only experimental oscillator strengths for the resonance lines of krypton are those by KoCH’rl’ from optical dispersion data. His result gives f-r = Jz = 0.266 fog the 1164 A and 1236 A lines. In the present paper, the oscillator strengths of the krypton resonance lines have been measured by the optical absorption technique. II. EXPERIMENTAL The absorption data for the resonance lines of krypton were obtained on a Baird monochromator’12), modified at the U.S. Naval Research Laboratory (NRL). In Fig. 1. A and B are the entrance and exit slits, respectively; C is a Pyrex tube through which argon flows at a pressure of about 350 mm (purified by a molecular sieve cold trap) and is excited inside the microwave cavity, D, powered by a Raytheon microwave generatot (PG 104A, Model CMD-10) which operates at 2450 MC/S and 125 W. An ASCOP Model 340-0, 14-stage photomultiplier, E, is mounted in air behind a glass window coated with sodium salicylate. The absorption cell, F, (length 5.72 cm) carries a lithium fluoride window near the exit slit. B. The monochromator is equipped with a Bausch & Lomb replica diffraction grating (600 grooves,‘mm); in the present Lvork, slit widths of _ 50/f (bandpass _ 0.8 A) were used. The microwave excited argon source emits a continuous emission from 1070 A to of its operation treated 1650 A. This source has been described’13’ and the mechanism theoretically(r). Krypton gas pressures from 4 to 22 mm were read simultaneously on a McLeod gage and a mercury manometer. The accuracy of the gas pressure measurements is estimated at i 3 per cent or less; the accuracy of the photomultiplier current readings is probably & 2 per cent. 111. MEASUREMENT
OF ABSORPTION LINE OPTICAL SPECTROSCOPY
INTENSITIES
BY
A complete discussion of the method of measurements of the absorption line intensity of a monatomic gas is given in reference 2. There are four types of line broadening which need be considered here: (1) natural line broadening; (2) Doppler broadening, due to the gas kinetic velocities of the atoms; (3) pressure broadening due to collisions with other absorbing krypton atoms (Holtzmark broadening); and (4), broadening due to absorption by Kr, molecules in a state of van der Waals attraction. If the absorbing gas pressure is below about 0.01 mm, broadening due to (3) and (4) above is quite small and may be ignored. In many experiments, including the present ones, such small pressures are not practical as the absorption cell would be inconveniently long (furthermore, the exit beam in the Baird monochromator is divergent).
Oscillator strengths
of the resonance
lines of the rare gases-I.
Krypton
505
Since the instrument width (0.8 A) exceeds by far the natural line width (O*OOl A), we must now consider a method of measuring the total energy absorbed by a resonance line that is not completely resolved. LADENBURG and REICHE(~~~*) have defined the total absorption, AG:
A,
=
2nq[l -exp(
-k,l)]
dv
m
= 2~r (1 -I:‘&) s
dv,
(2)
0
where
v
is the frequency
in set-l
and the other quantities
are related
Z/Z, = exp[ -kJ]
as follows: (3)
where ZOis the incidence intensity, I is the transmitted intensity, k, the absorption coefficient at 298°K for an atmosphere in a path of I cm. It may be shown’2115’ that the relations among oscillator strength,f, the unperturbed wavelength, X0, of a resonance line and the lifetime, T, of a resonance level, can be represented :
(4) where m = electron g, are the statistical AlsoC2’:
rest mass, c = velocity of light, e = electron weights (= 2 J+ 1) of the upper and ground
to
A; = rrxl,:c = 4n2
1
charge, and g, and states, respectively.
2
(1 - Z;‘Z,) dv
,
(5)
where u = 8n2e2Nf/mT
= 2.000 x 10lONf/~
(6)
In the above, I is the cell length, and v is the frequency in set- l; N is the number density (atoms/cm3). Also, as described in reference 2, the oscillator strength may be obtained from the contour of the wings of the absorption lines. This method fails at gas pressures where pressure broadening is appreciable and where absorption by Kr, molecules causes considerable distortion in the shape of the wings. Also, in this spectral region, strong absorption bands of H,O, present as a minute impurity, distort the shape of the wings of the lines. Accordingly, it is preferable to evaluate the integral, AG [equation (2)] for a series of 4
506
P. G.
WILKINSON
pressures, calculate an apparent 7 for each pressure, and extrapolate the proper values for g,/'g,and A, in equations (4), (5) and (7):
to p = 0. Using
“fi236= 6.93 ~lO-~~,~secc~
(da)
.JJ
%
59.2 x 1030
=
-2
Ii
‘( 1 - I I,) dl, I
.u 0
with v in cm- * %I236 = 13.86 N ‘~a Similarly,
(7a)
for the 1164 A line: .I’rIE4 = 6.14 x 1O-1o 7 set-l
(4b)
X1164 = 12.28 N,?.
(7b)
Equation (5a) can. of course be used for both lines. It should be mentioned here. that, within limits, the measurements
of
03 ‘(1 -I/lo) I ‘n
dv
is independent of the slit width. MINKOWSKI ‘IS) has shown that correct values of the oscillator strength and corresponding lifetimes of the excited atoms may be obtained in this way even though the absorption line is not completely resolved. IV.
RESULTS
The experimental function, 1 -/iI,, plotted against v is given in Fig. 2 for the 1164 A line with krypton pressures of 8.40 mm, 12 mm, and 15 mm. The relative wavelength
0.0 A
O,I
A
B
B 0.2
c
-
..
-.
._
*.
:
. . ..
0.3
..
‘ .
. .
Cl.0 -
FIG. 2.
85600
Experimental
85700
.
.I. ;_..”
85800
85900
d
Icm ‘1
values of (I -I/In)
I
-.
_~~ .C
2
--
.
.J
Kr
86000
86100
86200
for the krypton resonance line at 1164 A.
Oscillator strengths
of the resonance
lines of the rare gases-I.
Krypton
507
measurement is good only to + 0.1 A (+ 8 cm- “); therefore, the apparent shift in the line center is not quantitatively significant. The asymmetry toward smaller wavenumbers (longer wavelengths) should be noted as this is due primarily to molecular (Kr,) absorption. Very similar curves are given in Fig. 3 for the 1236 A line of krypton.
FIG. 3. Experimental
values of (1 -Z/lo) for the krypton resonance
line at 1236 A.
Applying the appropriate equations (4a, 4b, 5a, 5b, and 7a, 7b), the apparent oscillator strengths, f, and the apparent lifetimes, 7, may be calculated and these are given in Table 2 for 1164 A and Table 3 for 1236 A. If our experimental methods are correct, the function Ac/2xc against (Nf)’ should yield a straight line. Such tests are shown in Fig. 4 resulting in a straight line at low values of (NY): but showing a slight upward curvature at higher values. The slope of the straight line portion is proportional to (l/~)l, where 7 is the true lifetime and is, of course, a constant.
cc
(1 -Z/lo) dv against (Nf)t showing a linear relationship for s > 0 low values of (Nf)i. f here is the apparent oscillator strength. See text for discussion. FIG. 4. Plot of Ac/Znc
(
=
508
P. G. WILKINSON
A more effective way of estimating the true lifetime, 7, is to plot the apparent 7 (Tables 2 and 3) against y: and extrapolate tol>” = 0. This should eliminate both pressure TABLE 2. EXPERIMENTALQUANTITIESUSEDTV COMPUTEf Pressure
(mm) 4.04 4.97 8.40 12.0 15.0 22.0
AND
T
AT 1164 8,
Nx 10” (cm- 3)
f (apparent)
Ac:27X (cm ‘)
7 I: IO” set (apparent)
(Nf)' ( :
1.429 1 .I57 7.97 4.24 5.30 7.77
0.166 0.146 0.261 0.320 0.403 0.522
46.59 45.56 105.x 155.5 218.1 356.2
3.70 4.20 2.35 1.92 I ,52 I.18
1.54 1.60 2.78 3.55 4.60 6.36
TABLE 3. EXPERIMENTALQLJAKTITIES USED70 COMPUTL/ AND T AT 1236 A Pressure (mm)
Nx IO’; (cm-y
f (apparent)
4.04 4.97 8.40 12.0 15.0
I .429 I.757 2.97 4.24 5.30
0,237 0.242 0.304 0,395 0,475
.4,:,12w (cm
'1
62.58 70.8 1 115.7 179.6 241.5
IO” see (apparent) 2.92 2.865 2.28 1.755 I.460
( ,Vf’): ( :
broadening and molecular absorption effects. This has been done in Fig. 5 for the 1164 A and the 1236 A lines. The results are given in Table 4 along with the true oscillator strength, f, calculated from equations (4a) and (4b).
FIG. 5. Plot of apparent lifetime (7) against p’(mm) for the 1164 A and 1236 A lines. Extrapolation to pi = 0 gives the true lifetime of ‘P In and 3P1’ (see text and Table 4).
Oscillator strengths TABLE
of the resonance
lines of the rare gases--I.
509
Krypton
4. LIFETIMES OF Kr ‘PIO AND 3P~o AND OSCILLATORSTRENGTHSOF THE RESONANCE LINES State
7 (set x log)
8,
lP,O 3P/
4.55 4.38
1164 1236
* KOCH, Kungl. 4%~. Siillskapets
0.135 0.158 -__ S = 0,293
0.266 0.266 S = 0.532*
Lund Ferh. 19, 173 (1949).
Theoretically, the index of refraction, the expression :(17) II-1
f Optical dispersion
f Oscillator strength
n, of a gas in regions =--
2N
of transparency
is given by
h
2rrmc2 ~2 2 -v2’
(7)
where e is the electron charge, N is the number of atoms (or molecules)/cm3, m is the rest mass of the electron, c is the velocity of light, andyi is the oscillator strength, or the associated with transitions corresponding to a reson“number of dispersion electrons” ance frequency, vi. In actual practice, the refractive data are taken at wavelengths in the near ultraviolet and it is possible only to utilize two or three terms of equation (7). KocH’s(~~) results for krypton givesf, = f2 = 0.266 for wavelengths near the resonance lines, Our results (Table 4) indicate values only about one-half of that. However, PERY-THORNE and GARTON (O), have estimated that the sum of the oscillator strengths in krypton should be about 0.36. Also, theoretical calculations of the oscillator give a value for the sum of the two resonance lines of 0.249. This strengths in argon’l” is about one half that obtained from the optical dispersion data (0.420). Other discrepancies of this sort have been noted in the past. They are probably due to the fact that refractive dispersion measurements at wavelengths far removed from the strong far ultraviolet transitions are not particularly sensitive and do not pin-point each strong transition. it was pointed out that while the g-values of the 3P1” and In a previous paper(l), lPlo states of Ne and Ar show that these states approach closely L-S (Russell-Saunders) coupling conditions, these same states in Kr and Xe are described best by j-j or j-1 coupling. The observed g-values for the 3P10 and ‘PI0 states of Kr are 1.242 and 1.259 respectively. For pure j-j coupling, the g-values would be I.167 and 1.333. In view of these comparisons, it is not surprising that the oscillator strengths of the two resonance lines should be about equal. It means that in the heavier atoms, as is well known, the spin intercombination selection rule (&S = 0) no longer has any meaning. Acknow/edgement-It is a pleasure to acknowledge the very considerable help of Mr. R. NABERand Mr. V. FRANKLIN in the construction of the equipment and in the preparation of the figures. I am indebted to Professor R. S. MLJLLIKENof the University of Chicago for an interesting discussion on the Landi g-values of rare gas atoms. Note added in proof: J. GEIGER[Z. Phys. 177, 138 (1964)I has obtained the sum of the oscillator strengths, fi+tf2, by an electron scattering method. His result, 0.346kO.06, is in good agreement with the sum obtained here (0.293).
510
P. G. WILKINSON REFERENCES
I. P. G. WILKINSON,J. C/?e/?l. P/IJX. (submitted). 2. A. C. G. MITCHELL and M. W. ZEMANSKY, Resonance Radintiot7 and Excited Atom, Macmillan. New York (1962) 2nd Edition. 3. J. H. JAFFE, M. A. HIRSHFELDand S. &MEL, J. Che/?~. Pllys. 29, 675 (1958); F. W. HEINCKES and A. BATTAGLIA, Physica 24, 589 (1958); P. G. WILKINSON,/. Opt. Sot. An7ev. 50, 1002 (1960). 4. E. N. LASSETTREand S. A. FRANCIS. J. C/7em. Ph~3. 40, 1208 (1964). 5. D. W. 0. HEDDLE, R. E. JENNINGSand A. S. L. PARSONS.1. Opt. Sot. A717er. 53, 840 11963). 6. P. GILL and D. W. 0. HEDDLE, Unpublished. 7. R. B. KING, /QSRT3, 299 (1963). 8. ANNE PERY-THORNE and W. R. S. GARTON, Proc. Roy. Sac. 76, 833 (1960). 9. R. E. HUFFMAN, Y. TANAKA and J. C. LARRAREE,Appl. Opt. 2, 947 (1963). 10. The factor 4.19 x 1O-s is derived from w?Nirnc, with e = electron charge, N = no. atoms,‘cn+. 177= electron mass, and c = velocity of light. I 1. J. KOCH, Kungl. Fys. Siihkapets Lund Forh. 19, 173 (1949). 12. R. T~USEY, F. S. JOHNSON, J. RICHARDSON and N. TORAN. J. Opt. Sot. A777er. 41, 696 (19.51). 13. P. G. WILKINSON and E. T. BYRAM, Appl. Opt. (submitted). 14. R. LADENBURGand R. REICHE. Ann. P/t.w. 42, 181 (1913). 15. R. LADENBURG, Z. Phys. 4, 451 (1921). 16. R. MINKOWSKI, 2. Plzys. 36, 839 (1926). 17. See, e.g. R. S. MULLIKEN and C. A. RIEKE, Rept. Prog. Phys. 8, 231 (1941). 18. R. S. KNOX, Phys. Rep. 110, 375 (1958).
OSCILLATOR
STRENGTHS OF THE RESONANCE THE RARE GASES-I. KRYPTON* P. G.
E. 0. Hulburt
WILKINSON
Center for Space Research, U.S. Naval Research Washington, D.C., 20390 (Receiced
LINES OF
Laboratory,
14 October 1964)
Abstract-The oscillator strengths of the resonance lines of krypton at 1164 A and 1236 8, have been measured by an optical absorption technique. The results give f ~4 = 0.135 and AZ36 = 0.158. The corresponding lifetimes are T(‘P~) = 4.55 x 10m9 set and TV = 4.38 x 10e9 sec. The values for the oscillator strengths do not agree well with those obtained by refractive dispersion, but do agree well with electron scattering data. I. INTRODUCTION THE oscillator strengths of the resonance transitions of the rare gases are of interest experimentally in the interpretation of discharge processes in the rare gases(l), for comparison with optical dispersion data (see below), and for comparison theoretically, where such calculations have been made. From the oscillator strengths, one obtains also the mean life-times of the resonance levels. TABLE
l.*
WAVELENGTHS
Atom
He Ne Ar Kr Xe *
B.
AND
WAVENUMBERS FOR THE RESONANCE RARE GASES
LINES OF THE
IP,”
Y
3P10
Y
(a
(cm- ‘)
(A)
(cm- ‘>
584.334 735.895 1048.219 1164.867 1295.586
171,135.0 135,889.0 95,399.g 85,846*7 77,185.2
743.718 1066.659 1235.838 1469.610
EDLJ'?N,Reports Prog. Php
134,456.O 93,750.7 80,916.8 68,045*3
26, 181 (1963).
Table 1 lists the wavelengths and wavenumbers for transitions involving the ground state and the two lowest resonance levels (except for helium). L-S (Russell-Saunders) notation is used here in spite of the fact that strongj-j coupling is present, especially for xenon and krypton. The general experimental methods for determining oscillator strengths in atomic and molecular systems are (I), optical absorption (2); (2), optical refractive dispersionC3); (3), small angle scattering scattering methodC6);
of electronsC4’; (4), eerenkov radiation and (6), atomic beam methodsC7).
methodC5);
(5), Rayleigh
* Sponsored jointly by the Office of Naval Research and the National Science Foundation. 503
P. G. WILKINSOK
504
Absorption
coefficients
of krypton in the number of pm-ionized lines as well as the for each transition can be obtained from GARTON(~) and HUFFMAN rt al.‘“’
have been measured by PERY-THORNE and region from 500 A to 900 A which contains a ionization continuum. The oscillator strengths graphical integration:
f = 4.19 x 1O-8 ‘k,ds, Li
(1)
with k, and v measured in cm-l.clo) The only experimental oscillator strengths for the resonance lines of krypton are those by KoCH’rl’ from optical dispersion data. His result gives f-r = Jz = 0.266 fog the 1164 A and 1236 A lines. In the present paper, the oscillator strengths of the krypton resonance lines have been measured by the optical absorption technique. II. EXPERIMENTAL The absorption data for the resonance lines of krypton were obtained on a Baird monochromator’12), modified at the U.S. Naval Research Laboratory (NRL). In Fig. 1. A and B are the entrance and exit slits, respectively; C is a Pyrex tube through which argon flows at a pressure of about 350 mm (purified by a molecular sieve cold trap) and is excited inside the microwave cavity, D, powered by a Raytheon microwave generatot (PG 104A, Model CMD-10) which operates at 2450 MC/S and 125 W. An ASCOP Model 340-0, 14-stage photomultiplier, E, is mounted in air behind a glass window coated with sodium salicylate. The absorption cell, F, (length 5.72 cm) carries a lithium fluoride window near the exit slit. B. The monochromator is equipped with a Bausch & Lomb replica diffraction grating (600 grooves,‘mm); in the present Lvork, slit widths of _ 50/f (bandpass _ 0.8 A) were used. The microwave excited argon source emits a continuous emission from 1070 A to of its operation treated 1650 A. This source has been described’13’ and the mechanism theoretically(r). Krypton gas pressures from 4 to 22 mm were read simultaneously on a McLeod gage and a mercury manometer. The accuracy of the gas pressure measurements is estimated at i 3 per cent or less; the accuracy of the photomultiplier current readings is probably & 2 per cent. 111. MEASUREMENT
OF ABSORPTION LINE OPTICAL SPECTROSCOPY
INTENSITIES
BY
A complete discussion of the method of measurements of the absorption line intensity of a monatomic gas is given in reference 2. There are four types of line broadening which need be considered here: (1) natural line broadening; (2) Doppler broadening, due to the gas kinetic velocities of the atoms; (3) pressure broadening due to collisions with other absorbing krypton atoms (Holtzmark broadening); and (4), broadening due to absorption by Kr, molecules in a state of van der Waals attraction. If the absorbing gas pressure is below about 0.01 mm, broadening due to (3) and (4) above is quite small and may be ignored. In many experiments, including the present ones, such small pressures are not practical as the absorption cell would be inconveniently long (furthermore, the exit beam in the Baird monochromator is divergent).
Oscillator strengths
of the resonance
lines of the rare gases-I.
Krypton
505
Since the instrument width (0.8 A) exceeds by far the natural line width (O*OOl A), we must now consider a method of measuring the total energy absorbed by a resonance line that is not completely resolved. LADENBURG and REICHE(~~~*) have defined the total absorption, AG:
A,
=
2nq[l -exp(
-k,l)]
dv
m
= 2~r (1 -I:‘&) s
dv,
(2)
0
where
v
is the frequency
in set-l
and the other quantities
are related
Z/Z, = exp[ -kJ]
as follows: (3)
where ZOis the incidence intensity, I is the transmitted intensity, k, the absorption coefficient at 298°K for an atmosphere in a path of I cm. It may be shown’2115’ that the relations among oscillator strength,f, the unperturbed wavelength, X0, of a resonance line and the lifetime, T, of a resonance level, can be represented :
(4) where m = electron g, are the statistical AlsoC2’:
rest mass, c = velocity of light, e = electron weights (= 2 J+ 1) of the upper and ground
to
A; = rrxl,:c = 4n2
1
charge, and g, and states, respectively.
2
(1 - Z;‘Z,) dv
,
(5)
where u = 8n2e2Nf/mT
= 2.000 x 10lONf/~
(6)
In the above, I is the cell length, and v is the frequency in set- l; N is the number density (atoms/cm3). Also, as described in reference 2, the oscillator strength may be obtained from the contour of the wings of the absorption lines. This method fails at gas pressures where pressure broadening is appreciable and where absorption by Kr, molecules causes considerable distortion in the shape of the wings. Also, in this spectral region, strong absorption bands of H,O, present as a minute impurity, distort the shape of the wings of the lines. Accordingly, it is preferable to evaluate the integral, AG [equation (2)] for a series of 4
506
P. G.
WILKINSON
pressures, calculate an apparent 7 for each pressure, and extrapolate the proper values for g,/'g,and A, in equations (4), (5) and (7):
to p = 0. Using
“fi236= 6.93 ~lO-~~,~secc~
(da)
.JJ
%
59.2 x 1030
=
-2
Ii
‘( 1 - I I,) dl, I
.u 0
with v in cm- * %I236 = 13.86 N ‘~a Similarly,
(7a)
for the 1164 A line: .I’rIE4 = 6.14 x 1O-1o 7 set-l
(4b)
X1164 = 12.28 N,?.
(7b)
Equation (5a) can. of course be used for both lines. It should be mentioned here. that, within limits, the measurements
of
03 ‘(1 -I/lo) I ‘n
dv
is independent of the slit width. MINKOWSKI ‘IS) has shown that correct values of the oscillator strength and corresponding lifetimes of the excited atoms may be obtained in this way even though the absorption line is not completely resolved. IV.
RESULTS
The experimental function, 1 -/iI,, plotted against v is given in Fig. 2 for the 1164 A line with krypton pressures of 8.40 mm, 12 mm, and 15 mm. The relative wavelength
0.0 A
O,I
A
B
B 0.2
c
-
..
-.
._
*.
:
. . ..
0.3
..
‘ .
. .
Cl.0 -
FIG. 2.
85600
Experimental
85700
.
.I. ;_..”
85800
85900
d
Icm ‘1
values of (I -I/In)
I
-.
_~~ .C
2
--
.
.J
Kr
86000
86100
86200
for the krypton resonance line at 1164 A.
Oscillator strengths
of the resonance
lines of the rare gases-I.
Krypton
507
measurement is good only to + 0.1 A (+ 8 cm- “); therefore, the apparent shift in the line center is not quantitatively significant. The asymmetry toward smaller wavenumbers (longer wavelengths) should be noted as this is due primarily to molecular (Kr,) absorption. Very similar curves are given in Fig. 3 for the 1236 A line of krypton.
FIG. 3. Experimental
values of (1 -Z/lo) for the krypton resonance
line at 1236 A.
Applying the appropriate equations (4a, 4b, 5a, 5b, and 7a, 7b), the apparent oscillator strengths, f, and the apparent lifetimes, 7, may be calculated and these are given in Table 2 for 1164 A and Table 3 for 1236 A. If our experimental methods are correct, the function Ac/2xc against (Nf)’ should yield a straight line. Such tests are shown in Fig. 4 resulting in a straight line at low values of (NY): but showing a slight upward curvature at higher values. The slope of the straight line portion is proportional to (l/~)l, where 7 is the true lifetime and is, of course, a constant.
cc
(1 -Z/lo) dv against (Nf)t showing a linear relationship for s > 0 low values of (Nf)i. f here is the apparent oscillator strength. See text for discussion. FIG. 4. Plot of Ac/Znc
(
=
508
P. G. WILKINSON
A more effective way of estimating the true lifetime, 7, is to plot the apparent 7 (Tables 2 and 3) against y: and extrapolate tol>” = 0. This should eliminate both pressure TABLE 2. EXPERIMENTALQUANTITIESUSEDTV COMPUTEf Pressure
(mm) 4.04 4.97 8.40 12.0 15.0 22.0
AND
T
AT 1164 8,
Nx 10” (cm- 3)
f (apparent)
Ac:27X (cm ‘)
7 I: IO” set (apparent)
(Nf)' ( :
1.429 1 .I57 7.97 4.24 5.30 7.77
0.166 0.146 0.261 0.320 0.403 0.522
46.59 45.56 105.x 155.5 218.1 356.2
3.70 4.20 2.35 1.92 I ,52 I.18
1.54 1.60 2.78 3.55 4.60 6.36
TABLE 3. EXPERIMENTALQLJAKTITIES USED70 COMPUTL/ AND T AT 1236 A Pressure (mm)
Nx IO’; (cm-y
f (apparent)
4.04 4.97 8.40 12.0 15.0
I .429 I.757 2.97 4.24 5.30
0,237 0.242 0.304 0,395 0,475
.4,:,12w (cm
'1
62.58 70.8 1 115.7 179.6 241.5
IO” see (apparent) 2.92 2.865 2.28 1.755 I.460
( ,Vf’): ( :
broadening and molecular absorption effects. This has been done in Fig. 5 for the 1164 A and the 1236 A lines. The results are given in Table 4 along with the true oscillator strength, f, calculated from equations (4a) and (4b).
FIG. 5. Plot of apparent lifetime (7) against p’(mm) for the 1164 A and 1236 A lines. Extrapolation to pi = 0 gives the true lifetime of ‘P In and 3P1’ (see text and Table 4).
Oscillator strengths TABLE
of the resonance
lines of the rare gases--I.
509
Krypton
4. LIFETIMES OF Kr ‘PIO AND 3P~o AND OSCILLATORSTRENGTHSOF THE RESONANCE LINES State
7 (set x log)
8,
lP,O 3P/
4.55 4.38
1164 1236
* KOCH, Kungl. 4%~. Siillskapets
0.135 0.158 -__ S = 0,293
0.266 0.266 S = 0.532*
Lund Ferh. 19, 173 (1949).
Theoretically, the index of refraction, the expression :(17) II-1
f Optical dispersion
f Oscillator strength
n, of a gas in regions =--
2N
of transparency
is given by
h
2rrmc2 ~2 2 -v2’
(7)
where e is the electron charge, N is the number of atoms (or molecules)/cm3, m is the rest mass of the electron, c is the velocity of light, andyi is the oscillator strength, or the associated with transitions corresponding to a reson“number of dispersion electrons” ance frequency, vi. In actual practice, the refractive data are taken at wavelengths in the near ultraviolet and it is possible only to utilize two or three terms of equation (7). KocH’s(~~) results for krypton givesf, = f2 = 0.266 for wavelengths near the resonance lines, Our results (Table 4) indicate values only about one-half of that. However, PERY-THORNE and GARTON (O), have estimated that the sum of the oscillator strengths in krypton should be about 0.36. Also, theoretical calculations of the oscillator give a value for the sum of the two resonance lines of 0.249. This strengths in argon’l” is about one half that obtained from the optical dispersion data (0.420). Other discrepancies of this sort have been noted in the past. They are probably due to the fact that refractive dispersion measurements at wavelengths far removed from the strong far ultraviolet transitions are not particularly sensitive and do not pin-point each strong transition. it was pointed out that while the g-values of the 3P1” and In a previous paper(l), lPlo states of Ne and Ar show that these states approach closely L-S (Russell-Saunders) coupling conditions, these same states in Kr and Xe are described best by j-j or j-1 coupling. The observed g-values for the 3P10 and ‘PI0 states of Kr are 1.242 and 1.259 respectively. For pure j-j coupling, the g-values would be I.167 and 1.333. In view of these comparisons, it is not surprising that the oscillator strengths of the two resonance lines should be about equal. It means that in the heavier atoms, as is well known, the spin intercombination selection rule (&S = 0) no longer has any meaning. Acknow/edgement-It is a pleasure to acknowledge the very considerable help of Mr. R. NABERand Mr. V. FRANKLIN in the construction of the equipment and in the preparation of the figures. I am indebted to Professor R. S. MLJLLIKENof the University of Chicago for an interesting discussion on the Landi g-values of rare gas atoms. Note added in proof: J. GEIGER[Z. Phys. 177, 138 (1964)I has obtained the sum of the oscillator strengths, fi+tf2, by an electron scattering method. His result, 0.346kO.06, is in good agreement with the sum obtained here (0.293).
510
P. G. WILKINSON REFERENCES
I. P. G. WILKINSON,J. C/?e/?l. P/IJX. (submitted). 2. A. C. G. MITCHELL and M. W. ZEMANSKY, Resonance Radintiot7 and Excited Atom, Macmillan. New York (1962) 2nd Edition. 3. J. H. JAFFE, M. A. HIRSHFELDand S. &MEL, J. Che/?~. Pllys. 29, 675 (1958); F. W. HEINCKES and A. BATTAGLIA, Physica 24, 589 (1958); P. G. WILKINSON,/. Opt. Sot. An7ev. 50, 1002 (1960). 4. E. N. LASSETTREand S. A. FRANCIS. J. C/7em. Ph~3. 40, 1208 (1964). 5. D. W. 0. HEDDLE, R. E. JENNINGSand A. S. L. PARSONS.1. Opt. Sot. A717er. 53, 840 11963). 6. P. GILL and D. W. 0. HEDDLE, Unpublished. 7. R. B. KING, /QSRT3, 299 (1963). 8. ANNE PERY-THORNE and W. R. S. GARTON, Proc. Roy. Sac. 76, 833 (1960). 9. R. E. HUFFMAN, Y. TANAKA and J. C. LARRAREE,Appl. Opt. 2, 947 (1963). 10. The factor 4.19 x 1O-s is derived from w?Nirnc, with e = electron charge, N = no. atoms,‘cn+. 177= electron mass, and c = velocity of light. I 1. J. KOCH, Kungl. Fys. Siihkapets Lund Forh. 19, 173 (1949). 12. R. T~USEY, F. S. JOHNSON, J. RICHARDSON and N. TORAN. J. Opt. Sot. A777er. 41, 696 (19.51). 13. P. G. WILKINSON and E. T. BYRAM, Appl. Opt. (submitted). 14. R. LADENBURGand R. REICHE. Ann. P/t.w. 42, 181 (1913). 15. R. LADENBURG, Z. Phys. 4, 451 (1921). 16. R. MINKOWSKI, 2. Plzys. 36, 839 (1926). 17. See, e.g. R. S. MULLIKEN and C. A. RIEKE, Rept. Prog. Phys. 8, 231 (1941). 18. R. S. KNOX, Phys. Rep. 110, 375 (1958).