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Radiative-lifetime measurements for ions of nitrogen and oxygen
NUCLEAR INSTRUMENTS
A N D M E T H O D S 90
0970) 9 3 - 1 o 2 ; © N O R T H - H O L L A N D
PUBLISHING
CO.
RADIATIVE-LIFETIME MEASUREMENTS FOR IONS OF NITROGEN AND OXYGEN E. H. PINNINGTON*
Department of Physics, University of Alberta, Edmonton, Canada This report discusses lifetime measurements by the photoncounting method. A focusing-scanning chamber is described, which permits measurements of the intensity of a spectrum line as a function of the distance along the beam from the exciting foil without moving the foil. The resulting simplification of the target chamber permits other features to be included in it, and one such possibility, the direct measurement of the beam velocity
is discussed. A parameter is derived which may be used to estimate the accuracy of the lifetime derived from a particular set of data points. From this derivation it is shown that the ideal statistical uncertainty in an experimental lifetime is given by 60/A½%, where A is the peak line intensity (number of photon counts). Recent data for ions of nitrogen and oxygen are presented.
1. Introduction In this report I will discuss some of the results obtained by J. A. Kernahan, C. C. Lin and myself from a series of experiments during the past year. Since the general principles involved in photoelectric measurements of radiative lifetimes by the beam-foil method are now well known and well described in the literaturel-3), I will restrict myself mainly to a few specific points which have, to my knowledge, no.t been previously discussed in detail elsewhere. I will then present some of our more recent data and compare them with those obtained by other workers.
2.2. THE FOCUSING-SCANNINGCHAMBER The usual practice in measuring decay curves photoelectrically is to move the foil. This produces problems in normalizing the recorded signal for a fixed number of ions arriving at the charge collector. While these problems can certainly be overcome by moving the charge collector with the foil, or by monitoring the total optical intensity of the beam by an additional photomuttiplier, further practical difficulties can arise. For example, the mechanism required to move a holder with many interchangeable foils along the target chamber, together with the mounting for either the Faraday cup or the monitor photomultiplier, while maintaining a reasonably high vacuum, can become rather complex. Furthermore, there still remains the necessity of focusing the light at the spectrometer slit, if a useful intensity is to be obtained for a reasonable slit-width. It occurred to me that both the required scanning action and the focusing action could be performed by a single optical device involving a paraboloidal mirror with a plane mirror at its focus. The basic principle of the device is shown in fig. 1. From the P L A N it is readily seen that all rays leaving the ion beam perpendicular to the ion motion are focused at the rectangular plane mirror at the focal point of the paraboloid. Rotation of the plane mirror then focuses different sections of the beam on the monochromator slit. The departure of the paraboloid from a sphere is sufficiently small that a sharp horizontal focus still results, i.e. a vertical section through the beam is focused to a vertical line at the slit. No loss of definition is apparent when the device is used to focus a slit which is 50 #m wide. The situation is worse for the vertical focus, but, since the slit length is longer than the width of the beam image, a sharp vertical focus is not essential. The dimensions of the rectangular plane mirror are chosen to match the monochromator aper-
2. Experimental method 2.1. GENERAL ARRANGEMENT
A beam of positive ions was accelerated by a model A K 60 Van de Graaff generator from High Voltage Engineering, Inc., which had been made available for these experiments by the Radiation Research Laboratory at the University of Alberta. Following low resolution mass-analysis by a bending magnet, capable of producing deflections of 7 ° for a 2 MeV O + beam, the ions struck a carbon foil of thickness 10 _+ 2/zg/cm 2 (obtained from the Yissum Research Development Co.). The light emitted by the beam after passing through the foil was examined by a model 1500, f/6.8, 0.75-m focal-length spectrometer of the in-plane Ebert type from Spex Industries, fitted with an EM[ 6256S photomultiplier. For the results to be discussed later in this report, beams of N + and O + ions having energies of 0.8 MeV and 1.2 MeV were used for the radiative-lifetime measurements. In addition, energies from 0.5 MeV to 1.8 MeV were used for recording the spectrum emitted in order to determine how each line varied in intensity with beam energy. Further details of this equipment are available in the literature3). * Presented the paper.
93 II. LIFETIMES AND T R A N S I T I O N P R O B A B I L I T I E S
E. H. PINNINGTON
94
FOCUSINgDEVICE
Poruboteid ~---
I'/---~---------~~:P
....
. Carbon Foil I Rodiating Ion Beem
PLAN
Fig. 1. Basic principle of t h e focusing device u s e d to s c a n the i m a g e o f t h e b e a m across the spectrometer slit.
ture. The paraboloid must of course be masked to a rectangular area to avoid vignetting. Two possible masks are shown in fig. 2, one giving a 7.5 x 7.5 cm square section and the other a 2.5 x 12.5 cm rectangular section. If the plane mirror width is such that light from a section of the paraboloid 2.5 cm wide enters the monochromator, then the square section of the paraboloid permits 5 cm of beam to be scanned, while the rectangular section allows a 10 cm scan at one third the intensity. The linearity of the scan with rotation of the plane mirror through constant angular increments is better than _ ½%. The resolution limit imposed by Doppler effect broadening is about 2 ~. The system was used in a photon-counting mode. The plane mirror was kept fixed and the photo.
5'O
I / ! c£'o Fig. 2. T w o possible m a s k s for t h e paraboloidal mirror to avoid vignetting (3" x 3" = 7.5 c m x 7.5 cm, a n d 1" x 5" = 2.5 c m x 7.5
cm).
multiplier output was integrated for a certain integrated beam charge, the integration time being typically 45 sec. The mirror was then rotated through a known angle (which, from the geometry of the system, was equivalent to moving a known distance downstream in the beam) and the signal was again integrated for the same integrated beam charge. Thus the intensity was recorded for each line as a function of distance from the foil. (The system can in principle be used down to 1100 It, as all the optics are MgF2-overcoated, but in practice the two reflections in the focusing chamber and the three reflections in the spectrometer make the system too slow below 1800 A. We plan to try the device on a 1-m McPherson instrument, which involves only one reflection, and hopefully this will permit us to use the scanning telescope at lower wavelengths.)
PLane
Parab°[/°id~ Spectrometer Entrance SLit
L
j
X-~F0it HoLder
Fig. 3. S c h e m a t i c d i a g r a m of the target a n d focusing-scanning chambers.
2.3. THE TARGETCHAMBER Having removed the necessity of moving the foil, it becomes possible to modify the target chamber for additional measurements. Fig. 3 shows schematically the target chamber attached to the focusing-scanning chamber. The mirrors M1 and M2 can be moved to position M~ and M~ to collect the radiation leaving the beam at 10 ° and 30°~ to the direction of motion. The resulting Doppler shifts of the recorded spectrum lines enable the velocity of the beam particles to be determined directly, and avoids estimating the energy loss occurring in the foil. By scanning the entire spectrum at 30 °, we are able to check that all the lines come from particles having the same velocity, which is a valuable check that the beam incident on the foil contains only one significant component. This is particularly important in our case because of the rather low resolution of our analyzing magnet. Fig. 4 shows a section of the oxygen spectrum around 4350 A ob-
RADIATIVE-LIFETIME
MEASUREMENTS
017 Lines 4367 4378
4348/49 ,b
90 °
4/45/17
/
F O R I O N S OF
N2
95
AND 0 2
current, using pulse counter C. Counter B simply records the time for which photon-counting has continued. A change in this value during the recording of the decay curve for a given transition indicates that some change in the beam has occurred. The cause of this change must then be located (usually the foil has punctured) and the set of counts for that transition repeated.
3. Data analysis 3.1. COMPUTER TECHNIQUES
Two main types of computer program have been used to assist in the analysis of the data obtained. First, the decay curves have been fitted by a least-squares technique, following correction for background, to the expression I = A e x p ( - ax) + B exp( - bx), (1)
~-Hg
30 °
I<
33,&
,1
DOPPL ER-SHIFTE]::) SPECTRA lO~" beam at1.2 NeV) Fig. 4. Section o f the s p e c t r u m a r o u n d 4350 d~ obtained f r o m a 1.2 M e V 02 + beam, s h o w i n g that the lines viewed at 30 ° to the b e a m direction are shifted by a b o u t 33 • with respect to those viewed at 90 ° .
where x is the distance from the foil. This allows for the possibility of line-blending or cascade repopulation of the radiating level. For lines giving B ~ 0, a = 1/vr, where r is the radiative lifetime of the radiating level and v is the beam velocity. This program also gives an estimate in % of the accuracy of the resulting v, by means of the parameter which I will discuss in a moment. The second kind of program is used to assign lines not previously classified, and simply lists in order the reciprocals of the wavenumber differences for all allowed transitions between known energy levels. 3.2.
tained from an O + beam at 1.2 MeV viewed at 90 ° and 30 ° to the beam direction. The mercury line at 4358 A comes from a small mercury lamp outside the chamber. The Doppler shift produced on each of the four O I I lines at 4346/49 •, 4367 ]t, 4378 ~ and 4415/17 A is about 33 ~.
UNCERTAINTY ESTIMATES IN LIFETIME MEASUREMENTS
Very few published lifetimes have had meaningful
Current Integrator PuLse Output)
Faraday Cup
High VoLtage SuppLy
2 . 4 . T H E PHOTON-COUNTING ELECTRONICS
Fig. 5 shows schematically the electronic equipment used in the photon-counting technique. Each primary photoelectron in the photomultiplier results in a pulse of about 10 -t2 C. This pulse is used to trigger a pulse generator, which in turn emits a pulse to be recorded by pulse counter A. This permits a significant reduction in the number of noise pulses counted, since a pulse originating from one of the later dynodcs in the photomultiplier will be smaller than 10-12 C and will not trigger the pulse generator. Counting is continued at each setting of the plane mirror for the same total number of ions, as measured by the integrated beam
BLOCK DIAGRAM Of Photon Counting Technique used in Lifetime Measurements.
Timing Pulse Generator (I per secJ
- -
[{0n-ii:s~e } Counter C
.....
Fig. 5. Schematic d i a g r a m o f the electronics used in p h o t o n c o u n t i n g m e a s u r e m e n t s of radiative lifetimes. II. L I F E T I M E S
AND TRANSITION
PROBABILITIES
96
E. H. PINNINGTON
error limits attached to them. While it may be agreed that at present photoelectric measurements of radiative lifetimes by the beam-foil method are generally accurate to within about -4-10%3), nevertheless in any given report there may be some " g o o d " lines, which give lifetimes which are much better than + 10%, and some " b a d " lines which give values less accurate than this. In comparing one set of data with another, it is obviously necessary to know which lifetimes in a given paper are more reliable and which are less reliable. However, the normal practice has been to quote a typical accuracy to be applied equally to all the values reported, without indicating which values are more accurate than this and which are less, and even this is more than many authors have been prepared to do. Since [ am in agreement with various journal referees who have indicated that accuracy estimate must be made in lifetime measurements, I will discuss in detail the justification for one accuracy parameter, and attempt to convince you that it does have some meaning. It is well known 4) that the mean square deviation of the number of photons counted per second is related to the average number counted per second, fi, by the relation
An 2 = ~.
(2)
(There is, in principle, a second term arising from stimulated emission, but this is negligible if hv ~>kT, which is generally the case in beam-foil spectroscopy for transitions below 10000 A coming from an approximately mono-energetic beam.) Hence, for an ideal decay curve, where photons are counted for a given integrated beam current at N equally spaced points along the beam,
1 L (A hi) 2
-1.
(3)
The value of c~ can be calculated from the least-squares program. Decays giving c~~ 1 can then be considered to be more reliable than those for which c~> 1. We have calculated the value of c~for our decay curves and have found that those curves which appear to have relatively little scatter do give values of e close to 1, in agreement with eq. (3), while those curves which looked bad when plotted gave values of e significantly greater than 1. The parameter, ~, can thus be used to indicate which lines should be considered more reliable and which less. It is, however, not a very useful parameter for specifying the accuracy of the lifetime, z, which is obtained from the curve. This can be seen
Fig. 6. Two simulated decay curves giving the same value for ~, showing that the ~age uncertainty in T is proportional to the reciprocal of the square root of the line intensity. (See discussion in text.) from fig. 6. The lower curve represents data giving accurate to ___20%. The upper curve is obtained from the lower curve by increasing the n-values by a factor of 100, and An, the deviation from the "theoretical" straight line, by a factor of 10. Both curves therefore give the same value for e. However, the uncertainty in the lifetime of the upper curve is obviously much less than ___20%, and is actually about + 2%. This effect may be readily understood as follows. The distance on the graph paper which a given point falls from the straight line is given by
Al= log(n+An)-log(n) = log(1 +An~n) ~ An~n,
(4)
since (~--~z)~~ n ~, and (~--~2)~~ An, hence
A l a n -~.
(5)
Thus the deviation on the graph from the linear decay varies as n --~, and therefore the uncertainty in the slope of the line obtained from a set of experimental points is proportional to the reciprocal of the square root of the intensity of the signal, for a given value of ~.. This is just the result obtained from the curves in fig. 6. We can include this factor in our expression for the parameter which specifies the accuracy of the lifetime obtained from an experimental decay curve by dividing ~¢ by the square root of the mean intensity of the par-
R A D I A T I V E - L I F E T I M E MEASUREMENTS FOR IONS OF
N2 AND
97
0 2
TABLE 1 Radiative lifetimes for transitions giving a single-exponential decay curve. Wavelength (~) Obs. Listeda
Ion
Upper term
2445 2455
2445.55 2454.99
OII O IiI
3p' 2D° 3p 1S
2510
2509.35 +
O III
4p aDo
2983
2983.78
O III
3350
3350.68 3350.99
3p JD
Radiative lifetime (nsec) Measured (AP) Theory b 3.72 1.78 3.82 3.38
0.29 0.38 0.13 0.25
4.36 3.50
0.14 0.12
2.5 C 4.5 C
O III
3p 5p0
10.15
0.56
6.7 C
3384.95 3450.94 3455.12 3774.00 3973.26 4072.16 4075.87 4085.12 4094.18 4119.22 4185.46 4253.74 4253.98
O lii O Iii O ilI O IiI O Ii OII OII OII OiI O iI OiI
3d 5D 3d SF 3d aF 3p ZD 3p 2p0 3d 4F 3d 4F 3d 4F 3d 4F 3d 4D 3d" 2G
15.23 7.60 6.29 6.50 6.01 7.76 8.61 8.82 9.64 4.46 8.47
0.09 0.04 0.16 0.39 0.45 0.06 0.07 0.12 0.57 0.24 0.05
4.8 C 6.0 C 6.0 C 9.3 C 6.8 C 5.1 C 5.1 C 5.1 C 5.1 C 4.5 C 4.0 C
O II
4f" ZH°
6.19
0.29
3.8 C
4275.52 4313.43 4345.56 4349.43 44.14.91 4416.97
OII OII OII O Ii
4f 4f 3p 3p
4.22 2.98 7.05 7.69
0.39 0.43 0.12 0.06
4.7 4.7 9.5 9.5
O li
3p 2D°
9.92
0.16
8.8 C
O I1 OII O I1 OII
3p 2D° 5p 4D°(?) 3p" 2F° 4f 4F°(?)
8.83 2.7l 14.16 6.30
0.21 0.51 1.03 0.75
8.8 C 9.0 C 4.7 C
4639
4452.38 4530.59 + 4590.97 4610.14 4638.85 4641.81
OII
3p aDO
29.77
0.74
9.8 C
4649
4649.14 4650.84
O Ii
3p 4D°
40.31
0.24
9.8 C
4660 4676 4701
4661.63 4676.23 4699.2l
OI[ OII OII
3p 4D° 3p 4D° 3d' 2F
11.91 14.53 0.81
0.69 1.64 0.57
9.8 C 9.8 C 0.38 D -
3385 3450 3455 3773 3973 4072 4075 4087 4096 4119 4185 4253 4276 4313 4345 4349 4415 4452 4533 4592 4610
4F° 4F°(?) 4po 4p0
C C C C
a C. E. Moore, " A Multiplet Table of Astrophysical Interest", and "An Ultraviolet Multiplet Table", U.S. Department of Commerce, National Bureau of Standards. ( + = assignment from our computer prograrn.) b W. L. Wiese, M. H. Smith and B. M. Glennon, "Atomic Transition Probabilities", vol. 1, U.S. Government Printing Office, NSRDS-NBS 4 (1966). (C = accurate to 25~, D = accurate to 50~.)
ticular
decay curve, nav, i.e. accuracy parameter
= fi = e/nav, which may be written
=,..
/,
(6)
By running a series o f test curves through the same program, we have found that fl may be converted to an estimate of the ° a g e uncertainty in the lifetime by the expression P = %age uncertainty in • = 20 fi,
(7)
where A is the value of the coefficient obtained from the least-squares fit ( = number of photons counted at t = 0). This procedure is strictly only valid for curves requiring only a single exponential, i.e. where blending or cascading is absent. However, the same program will tabulate values for c~ and fi for curves requiring the second exponential, and larger values for these parameters indicate lower accuracy for the derived lifetimes. As the ratio of the coefficients A / B increases, so eq. (7), becomes more valid as an estimate of the II. LIFETIMES AND T R A N S I T I O N P R O B A B I L I T I E S
98
Z. H. P I N N I N G T O N
accuracy of the lifetime associated with the A-coefficient. I should stress at this p o i n t that all we have calculated is the c o n t r i b u t i o n to the total experimental error which comes from the analysis of the actual decay curve. To this m u s t be added the other sources of experimental error, such as the uncertainty i n the b e a m velocity a n d in the correct b a c k g r o u n d to be subtracted from the observed signal, b o t h of which in our case c o n t r i b u t e a b o u t 1% to the total u n c e r t a i n t y in the lifetime value. It is interesting to note, however, that we can n o w estimate the highest accuracy possible if all the other sources of error could be eliminated. I n this case, ~ = 1, so that P = 20(nay) -~, a n d thus, for the case where the decay curve is c o n t i n u e d until the signal has fallen to 1% of its peak value giving nay = A/IO, we o b t a i n M i n i m u m %age error
Peak line intensity A (counts)
-I- 10 -t- 1 +__0.1
40 4 × 103 4 x 10 5
This may prove useful to certain m e a s u r e m e n t s as it
allows the experimenter to estimate h o w m a n y counts he needs, a n d therefore for how long he m u s t c o u n t at each p o i n t on his decay curve, in order to o b t a i n a given accuracy in the resulting lifetime. The o p t i m u m would be to take enough c o u n t s to reduce the statistical error that we have been discussing to the same size as the c o m b i n e d error from other sources.
4. Some specimen results 4.1. OXYGEN IONS Table 1 lists the radiative lifetimes we have obtained for oxygen lines giving a decay curve in which the coefficient B in eq. (1) was ~ 0. The listed wavelengths are from M o o r e ' s Multiplet Tables. The accuracy p a r a m e t e r (AP) is given by eq. (6) a n d m a y be converted to a percentage estimate of the u n c e r t a i n t y by multiplying by 20. The theoretical values have been calculated from the t r a n s i t i o n probabilities listed i n vol. 1 of " A t o m i c T r a n s i t i o n Probabilities" by Wiese et al. A cross ( + ) indicates that the assignment has been m a d e using our c o m p u t e r program. Table 2 lists the o u t p u t f r o m our p r o g r a m for lines giving decay curves requiring a non-zero value for B.
TABL~2 Computer analysis of decay curves requiring a second exponential. Wavelength (•) Obs. Listed
ion
Upper term
4379
3043.02 3047.13 3260.93 3693.70 3727.33 3734.80 3754.67 3759.87 3791.2,5 4140.74 4153.30 4189.7"7 4366.90 4378.01 4378.41
4434 4447
4437.24+ 4448.21
OII O IX
5p 4p0(?) 3d' 2F
4467 4475 4516 4592
4513.61 + 4590.97
O II O Ii, O I11 O II(?) O Ii
? 9 5p 4D(?) 3p' 2F0
4649
4649.14 4650.84
O II
3045 3250 3700 3726 3736 3754 3759 3791 4140 4151 4189 4366
A
ra (nsec) B
Computer analysis ~B (nsec)
(AP)
O III O II1 O III OII O III O III O III O III O 1I OII OII OiI
3p 3p 3d aF° 3p 5D° 3p 4S° 3p 5D° 3p aD 3p ZD 3p 8D 3d 4p(?) 3d 4p(?) 3d' 2G 3p 4p0
320 647 1393 670 878 1069 823 579 289 200 316 372
2.52 4.97 7.65 4.80 5.40 5.00 7.09 6.99 7.20 9.28 64.84 11.27
- 94 -277 -782 -242 - 453 -433 -259 --248 445 145 574 190
0.06 2.13 3.01 2.09 3.31 1.66 2.25 1.68 1.82 1.97 5.59 2.23
0.41 0.14 1.139 0.14 13.33 0.35 0.03 0.17 0.44 0.18 0.05 0.08
O II
4f' ZF0(?)
753
11.27
781
2.16
0.11
242 256 253 1151 105 160 1085 1198 224 1087 584
1.78 8.19 7.44 6.74 19.31 1.48 9.50 10.75 12.03 21.13 22.75
270 150 151 -- 378 150 86 -- 52"7 -- 445 -- 74 -- 350 -- 127
16.25 1.05 0.75 2.30 2.72 33.28 3.83 5.36 4.14 3.75 4.61
0.13 0.07 0.1 l 0.24 0.09 0.37 0.04 0.23 0.41 1.85 0.07
3p 4D0
RADIATIVE-LIFETIME
MEASUREMENTS
F O R I O N S OF
N2
99
AND 0 2
TABLE 3 Experimental transition probabilities for s o m e oxygen lines o f astrophysical interest. Listed wavelength ( ~ )
ion
U p p e r term
3759.87 4072.16 4075.87 4085.12 4119.22 4153.30 [430.09 4185.46 4189.79
O II1
3p aD
OII
3d 4F
OII
3d 4D
OII
3d 4p
OII
3d' ~G
OII O II
4 f ' ~H ° 4f 4F°
OII
3p 4po
OII
3p 2D°
O II O [I
3d' 2F° 3p 4D°
4253.74 4253.98 4275.52 4345.56 4349.43 4366.90 4414.91 4416.97 4452.38 4448.21 [445.62 4649.14
T r a n s i t i o n probability (10 s sec - t ) Observed Theoretical 1.44 1.03 1.20 0.29 1.48 ? 5.1 1.39 1.43
B B+ B* B+ C
1.62 2.36 0.96 0.80 0.54 1.06 0.88 0.14 9 10.3 0.39
C C C C C B B B
C CC-
BD
1.07 1.70 1.98 0.48 1.48 0.77 39 2.43 2.51
C C C C C C D-] C C
2.63 2.12 0.89 0.74 0.50 1.15 0.95 0.15 0.57 26 1.04
C C C C C C C C C D-] C
TA~L~ 4 C o m p a r i s o n with previously published data. Ion
Radiative lifetime (nsec) O t h e r values Ref. a Ref. b
Upper term This work
0 1I
0 III
3p 2D°
9.5
_+ 5(2)
-
3p 4po
8.8
+ 1.8(3)
-
3p" 2F°
10.5
_+ 1.2(4)
-
3d 4F
8.4
+ 0.5(4)
3d' 3d' 4f' 3p
0.92 7.0 6.2 3.9
_+ 0.10(3) + 1.5(2) + 0.9(1) _+ 0.4(2)
3~ ap
2.5
+_ 0.4(1)
30 aD 3p 5p0
6.9 10
-± 0.6(4) + 2(1)
3d aF°
5.0
-& 0.5(1)
2V 2G ~H ° tD
3d aD 3d aF
15 7.3
q_- 2(1) + 0.7(2)
Theory Ref. c
11.85 8.54 7.7
8.8 C
9.0 C
-
12.8 c 4.18 c 5.29 c
0.64 3.25 2.20 3.36
5.05 c 4.35 c 3.37 3.71 3.35
4.67 ¢ 22.8 c 4.80 5.13
9.5 C
5.0 C 0.36 D 4.0 C 3.8 C 4.5 C 4.9 C
-
9.3 C 6.7 C
5"04c
4.8 C
25.2 c
2.12 1.44 2.84 c
4.8 C
7.61 9.00
-
6.0 C
ReL a. M. R. Lewis et al., Phys. Rev. 178 (1959) 49. Ref. b. M. D r u e t t a a n d M. C. Poulizac, Phys. Letters 29A (1969) 651. Ref. c. W. L. Wiese et al., A t o m i c T r a n s i t i o n Probabilities, vol. 1 (U.S. G o v e r n m e n t Printing Office, N S R D S - N B S 4, 1966). II. L I F E T I M E S
AND TRANSITION
PROBABILITIES
100
E. H. PINNINGTON TABLE5 Lifetime measurements of some N l I levels. Wavelength (~) Obs. (+ 2 ~) Listed 3995
Upper level This work
Radiative lifetime (nsec) Others
3995.00 5041.32 4043.54 4145.76 4176.16 4241.79 4432.74 4530.40 4607.16 4630.54 4991.22 5001.13 5001.47
3p 1D
6.3 _+ 10~
4f 3G 3p 5S° 4f IF 4f 8F 4f 8D 4f 1G 3p ap 3p 5p 3p apo
3.8* + 10~ 6.0 + 3 ~ 5.4 _+ 4 ~ 3.2* + 10~ 3.9* + 10~ 4.3* + 10~ 3.3"/11.0" 6.0* + 10~ 12.0 _+ 10~
5.3 a, 5.8P, 9.0~ 10.5r, 5.7a 3.5d, 5.9P 2.8 ~ 2.80 -
3d ZF°
16.7 ___3 ~
13.0a
5003 5005
5005.14
3d ZF°
18.4 + 2 ~ 14.0 + 5 ~
-
8.2 8.2
5012
5011.24 5012.03
3p ~po
14.1 __. 3 ~
-
13.0
5179.50 5535.39
3d 5F 3d 5D 3p 5D°
5.2 _+ 7 ~ 17.0 + 3 ~
4042 4146 4176 4241 4433 4531 4607~ 4631 4992 5001
5179 5535
7.0a, 6.1P
Theoryt 6.3 2.9 7.3 3.9 4.7 5.4 3.9 9.5 9.5 13.0 8.2
7.3f, 17.4d
9.8 12.1 12.8
* Cascading present. t Computer fit gives two equal contributions with lifetimes listed. A. Denis et al., C. R. Acad. Sci. 266B (1968) 64; Proc. Beam-Foil Conference, U. of Arizona (1967) 341. f U. Fink et al., J. Opt. Soc. Am. 58 (1968) 475. P E. I-L Pinnington and C. C. Lin, J. Opt. Soc. Am. 59 (1969) 717. Theoretical values have + 25~ accuracy. Table 3 lists the t r a n s i t i o n probabilities which can be o b t a i n e d f r o m the experimental lifetimes for these oxygen lines which we have f o u n d listed in the spectra of certain B-type starsS). T h e theoretical t r a n s i t i o n probabilities are t a k e n f r o m the c o m p i l a t i o n by Wiese et al., who estimate their accuracy according to the scheme: B = accurate to within +__10%, C = accurate to within ___25%, D = accurate to within __ 50%. We have also used this scheme to represent our estimate of the accuracy of our experimental values for the t r a n s i t i o n probabilities derived according to the relation
1 (Aij)e~p = (Aij)th%xpZ(Aij)th,
(8)
where (Aij)th = theoretical p r o b a b i l i t y for the t r a n s i t i o n f r o m level i to level L %xp = our m e a s u r e d lifetime for level i, (A,~)th = s u m of the theoretical probabilities for all possible radiative transitions from the level i.
This m e t h o d assumes that only the transitions listed by Wiese et al. c o n t r i b u t e significantly to the dep o p u l a t i o n of level i, a n d that the theoretical b r a n c h i n g ratios are correct. F o r all except two of the transitions listed in table 3, the u p p e r level only makes transitions to levels of one lower electron configuration, so that for these cases our m e t h o d of estimating the t r a n s i t i o n p r o b a b i l i t y has some meaning. F o r two cases, however, strong transitions are possible to levels of two lower electron configurations, a n d in each case one of these transitions lies in the far ultraviolet region of the spectrum, a n d therefore has a relatively high t r a n s i t i o n probability, for which the theoretical value has a large estimated uncertainty. I n these two cases, shown inside square brackets [ ] i n table 3, our Iifetime m e a s u r e m e n t gives a value for the t r a n s i t i o n probability for the short wavelength line only. The fact that a radiative-lifetime m e a s u r e m e n t in the visible region can be used to o b t a i n t r a n s i t i o n probabilities on the far ultraviolet is one of the advantages of this type of technique, a n d should n o t be overlooked. Table 4 presents a c o m p a r i s o n of our radiative lifetime values with other m e a s u r e m e n t s to be f o u n d in the literature. The value given in the c o l u m n "This w o r k "
RADIATIVE-LIFETIME
MEASUREMENTS
I01
F O R I O N S OF N 2 A N D 0 2
TABLE 6 Lifetime m e a s u r e m e n t s o f s o m e N III levels. Wavelength (~) Obs. (+_ 2 A) Listed
Upper term This w o r k
Lifetime (nsec) Others
3354
3353.78 3354.29
3p ap
5.3 ___ 1 0 ~
5.7 l, 5.8P
3367 3373 3771 4098 4103 4200
3367.36 3374.06 3771.08 4097.31 4103,37 4100.02
3p 3p 3p 3p 3p 3p
5.4 7.3 8.9 4.7 5.0 2,2
5.841, 5.4P, 5.2 a 9.8 f, 5.671 14.6 I, 9.01, 8.8 a 4.3 I, 4.2 a 4,11 2.39, 1.71, 3.0 f, 2.1 a
4290 4378 4456 4510 4515 4860 4862 4867
4288"72m 4290.8 m 4379.09 ¢ 4510.92 4514.89 4858.74 4861.33 4867.18
4p ap 4S 2p0 zp0 2D -
5g 2G 3p 4D 3p 4D 3d 4F° 3d 4F° 3d 4F°
+ 5~ + 10~ _+ 3 ~ _+ 3 ~ + 5~ _+ 3 ~
1.5'/10.7"
4.2 I, 3.3 a
2.7 ~ + 1 0 ~ 2.4 e + 1 0 ~ 31.0 _ 3 ~ 31.7 + 3 ~ 19.1 + 5 ~ 21.8 ___ 5 ~ 15.7 + 1 0 ~
4.0 I, 4.11, 3.3 a 24.0 a 24.0 d I6.9 a I6.7~
Theory t
5.7 5.? 5.7 8.1 10.4 10.4 10.0 14.3 14.3 15.9 15.9 15.9
m Listed in M o o r e ' s tables but n o t classified. * C a s c a d i n g with equal c o n t r i b u t i o n s giving values listed. ¢ Unclassified b u t listed as N III by U . Fink, J. Opt. Soc. A m . 58 (1968) 937. c C a s c a d i n g present. a A. D e n i s et al., C. R. Acad. Sci 266B (1968) 64; Proc. B e a m - F o i l Conference, U. o f A r i z o n a (1967) 341. U. F i n k et al., J. Opt. Soc. A m . 58 (1968) 475. 1 M. R. Lewis et al., Phys. Rev. 164 (1967) 94. P E. H. P i n n i n g t o n a n d C. C. Lin, J. Opt. Soc. A m . 59 (1969) 717. t Theoretical values have _+ 2 5 ~ accuracy.
is tile weighted mean with its probable error of all values we have obtained for that particular upper term, and the number in brackets is the number of such values from which the mean has been calculated. A superscript c with values taken from ref. a indicates that cascading may be present which has not been corrected, but with values from ref. b that an allowance for cascade effects has been made. It is noteworthy that the only significant discrepancies between the various values occur when cascading is present. 3d 4F, O II. The factor of almost 2 between our data and that listed by Druetta and Poulizac is difficult to explain. Our value comes from the mean of values obtained from 4 cascade-free decays, including the two most intense lines in the muttiplet, whereas Druetta and Poulizac have two values from cascadeaffected decays. However, this level must be reinvestigated before an accurate experimental lifetime can be established. 3d SD, O III. Lewis et al. (ref. a, table 4) have discussed this transition, pointing out that the line at 3384.95 /~ was blended in their measurements (pre-
sumably with the O IV-line at 3385.55 A). Druetta and Poulizac did not observe this multiplet at all, but made their measurements with less intense lines belonging to the 3p 5D°-3d 5D multiplet at 3065 A, 3075 A, lines which were not seen by either Lewis et al. or us. More recent work by Druetta has given a lifetime of 8.6 nsec for the O III transition at 3384.94 A (M. Druetta, private communication, January 1970). Further discussions of our oxygen data are to be published shortly 6' 7). 4.2. N I T R O G E N IONS
Tables 5 and 6 present radiative lifetimes for some levels belonging to ions of nitrogen, which are derived from decay curves recorded only two weeks prior to my departure for this meeting. The data are therefore somewhat preliminary. However, the lifetime values have been derived from our computer program by means of the parameter fl discussed earlier. The quoted errors should therefore have some significance for those lines where no cascading was present. All values derived from lines where significant cascading was II. L I F E T I M E S A N D T R A N S I T I O N
PROBABILITIES
102
E.H. P I N N I N G T O N
p r e s e n t , as i n d i c a t e d b y a l a r g e v a l u e o f the B-coefficient c a l c u l a t e d by o u r p r o g r a m , h a v e b e e n a s s i g n e d a n a r b i t r a r y e r r o r o f _ 10%. T h a n k s are d u e t o t h e staff o f t h e R a d i a t i o n R e s e a r c h L a b o r a t o r y f o r t h e i r willingness to serve b e y o n d t h e n o r m a l call o f d u t y , a n d to M r . E. A . F o s t e r f o r d e s i g n i n g a n d c o n s t r u c t i n g t h e v a r i o u s c h a m b e r s used in t h e s e e x p e r i m e n t s . M i s s S. D o r p e r a n d M r . G. F i n l e y are to b e t h a n k e d f o r t h e i r assistance in recording the data and preparing the diagrams Finally, g e n e r o u s f i n a n c i a l s u p p o r t m u s t be a c k n o w l e d g e d f r o m the Province of Alberta and the National Research Council of Canada
References J) S. Bashkin, D. Fink, P. R. Malmberg, A. B. Meinel and S. G. Tilford, J. Opt. Soc. Am. 56 (1966) 11364. 2) W. S. Bickel, Appl. Opt. 7 (1968) 2367. 8) E. H. Pinnington and C. C. Lin, J. Opt. Soc. Am. 59 (1969) 717. 4) M. Garbuny, Opticalphysics (Academic Press, New York and London, 1965) p. 418.
5) K. O. Wright, E. K. Lee, T. V. Jacobson and J. L. Greenstein, PuN. D.A.O. Victoria XII, no. 7 (1964). 6) E. H. Pinnington, J. A. Kernahan and C. C. Lin, Astrophys. J. 161 (1970) 339. v) j. A. Kernahan, C. C. Lin and E. H. Pinnington, J. Opt. Soc. Am. (L) 60 (1970) 986.
Discussion WHALING': Can you rely on the theoretical branching ratios in calculating the transition probabilities? PINiNG.TON: This depends on the nature of the coupling. In light elements you are not in too bad a position. WHALING': Are there any experimental measurements of branching ratios? PINNING-TON: There are some rough measurements available. BERRY: There is a problem in O III where some two-electron transitions are quite strong. P1NNINGTON: if yOU vary the oscillator strengths, you are not going to improve the agreement with theory, since if some of the values are adjusted to give a better agreement, then the others must be adjusted to give a worse agreement, in order to preserve the observed value for the lifetimes. WHALING':TO measure the beam velocity to 1% with the Doppler shift, how accurately must you locate the line centers? PINNING,TON: Each Iine can give you 2-3 % accuracy. The question is how many lines can you measure. The broadening without blending is about 2 A, and with 10 measurements you can get 1% accuracy.
A N D M E T H O D S 90
0970) 9 3 - 1 o 2 ; © N O R T H - H O L L A N D
PUBLISHING
CO.
RADIATIVE-LIFETIME MEASUREMENTS FOR IONS OF NITROGEN AND OXYGEN E. H. PINNINGTON*
Department of Physics, University of Alberta, Edmonton, Canada This report discusses lifetime measurements by the photoncounting method. A focusing-scanning chamber is described, which permits measurements of the intensity of a spectrum line as a function of the distance along the beam from the exciting foil without moving the foil. The resulting simplification of the target chamber permits other features to be included in it, and one such possibility, the direct measurement of the beam velocity
is discussed. A parameter is derived which may be used to estimate the accuracy of the lifetime derived from a particular set of data points. From this derivation it is shown that the ideal statistical uncertainty in an experimental lifetime is given by 60/A½%, where A is the peak line intensity (number of photon counts). Recent data for ions of nitrogen and oxygen are presented.
1. Introduction In this report I will discuss some of the results obtained by J. A. Kernahan, C. C. Lin and myself from a series of experiments during the past year. Since the general principles involved in photoelectric measurements of radiative lifetimes by the beam-foil method are now well known and well described in the literaturel-3), I will restrict myself mainly to a few specific points which have, to my knowledge, no.t been previously discussed in detail elsewhere. I will then present some of our more recent data and compare them with those obtained by other workers.
2.2. THE FOCUSING-SCANNINGCHAMBER The usual practice in measuring decay curves photoelectrically is to move the foil. This produces problems in normalizing the recorded signal for a fixed number of ions arriving at the charge collector. While these problems can certainly be overcome by moving the charge collector with the foil, or by monitoring the total optical intensity of the beam by an additional photomuttiplier, further practical difficulties can arise. For example, the mechanism required to move a holder with many interchangeable foils along the target chamber, together with the mounting for either the Faraday cup or the monitor photomultiplier, while maintaining a reasonably high vacuum, can become rather complex. Furthermore, there still remains the necessity of focusing the light at the spectrometer slit, if a useful intensity is to be obtained for a reasonable slit-width. It occurred to me that both the required scanning action and the focusing action could be performed by a single optical device involving a paraboloidal mirror with a plane mirror at its focus. The basic principle of the device is shown in fig. 1. From the P L A N it is readily seen that all rays leaving the ion beam perpendicular to the ion motion are focused at the rectangular plane mirror at the focal point of the paraboloid. Rotation of the plane mirror then focuses different sections of the beam on the monochromator slit. The departure of the paraboloid from a sphere is sufficiently small that a sharp horizontal focus still results, i.e. a vertical section through the beam is focused to a vertical line at the slit. No loss of definition is apparent when the device is used to focus a slit which is 50 #m wide. The situation is worse for the vertical focus, but, since the slit length is longer than the width of the beam image, a sharp vertical focus is not essential. The dimensions of the rectangular plane mirror are chosen to match the monochromator aper-
2. Experimental method 2.1. GENERAL ARRANGEMENT
A beam of positive ions was accelerated by a model A K 60 Van de Graaff generator from High Voltage Engineering, Inc., which had been made available for these experiments by the Radiation Research Laboratory at the University of Alberta. Following low resolution mass-analysis by a bending magnet, capable of producing deflections of 7 ° for a 2 MeV O + beam, the ions struck a carbon foil of thickness 10 _+ 2/zg/cm 2 (obtained from the Yissum Research Development Co.). The light emitted by the beam after passing through the foil was examined by a model 1500, f/6.8, 0.75-m focal-length spectrometer of the in-plane Ebert type from Spex Industries, fitted with an EM[ 6256S photomultiplier. For the results to be discussed later in this report, beams of N + and O + ions having energies of 0.8 MeV and 1.2 MeV were used for the radiative-lifetime measurements. In addition, energies from 0.5 MeV to 1.8 MeV were used for recording the spectrum emitted in order to determine how each line varied in intensity with beam energy. Further details of this equipment are available in the literature3). * Presented the paper.
93 II. LIFETIMES AND T R A N S I T I O N P R O B A B I L I T I E S
E. H. PINNINGTON
94
FOCUSINgDEVICE
Poruboteid ~---
I'/---~---------~~:P
....
. Carbon Foil I Rodiating Ion Beem
PLAN
Fig. 1. Basic principle of t h e focusing device u s e d to s c a n the i m a g e o f t h e b e a m across the spectrometer slit.
ture. The paraboloid must of course be masked to a rectangular area to avoid vignetting. Two possible masks are shown in fig. 2, one giving a 7.5 x 7.5 cm square section and the other a 2.5 x 12.5 cm rectangular section. If the plane mirror width is such that light from a section of the paraboloid 2.5 cm wide enters the monochromator, then the square section of the paraboloid permits 5 cm of beam to be scanned, while the rectangular section allows a 10 cm scan at one third the intensity. The linearity of the scan with rotation of the plane mirror through constant angular increments is better than _ ½%. The resolution limit imposed by Doppler effect broadening is about 2 ~. The system was used in a photon-counting mode. The plane mirror was kept fixed and the photo.
5'O
I / ! c£'o Fig. 2. T w o possible m a s k s for t h e paraboloidal mirror to avoid vignetting (3" x 3" = 7.5 c m x 7.5 cm, a n d 1" x 5" = 2.5 c m x 7.5
cm).
multiplier output was integrated for a certain integrated beam charge, the integration time being typically 45 sec. The mirror was then rotated through a known angle (which, from the geometry of the system, was equivalent to moving a known distance downstream in the beam) and the signal was again integrated for the same integrated beam charge. Thus the intensity was recorded for each line as a function of distance from the foil. (The system can in principle be used down to 1100 It, as all the optics are MgF2-overcoated, but in practice the two reflections in the focusing chamber and the three reflections in the spectrometer make the system too slow below 1800 A. We plan to try the device on a 1-m McPherson instrument, which involves only one reflection, and hopefully this will permit us to use the scanning telescope at lower wavelengths.)
PLane
Parab°[/°id~ Spectrometer Entrance SLit
L
j
X-~F0it HoLder
Fig. 3. S c h e m a t i c d i a g r a m of the target a n d focusing-scanning chambers.
2.3. THE TARGETCHAMBER Having removed the necessity of moving the foil, it becomes possible to modify the target chamber for additional measurements. Fig. 3 shows schematically the target chamber attached to the focusing-scanning chamber. The mirrors M1 and M2 can be moved to position M~ and M~ to collect the radiation leaving the beam at 10 ° and 30°~ to the direction of motion. The resulting Doppler shifts of the recorded spectrum lines enable the velocity of the beam particles to be determined directly, and avoids estimating the energy loss occurring in the foil. By scanning the entire spectrum at 30 °, we are able to check that all the lines come from particles having the same velocity, which is a valuable check that the beam incident on the foil contains only one significant component. This is particularly important in our case because of the rather low resolution of our analyzing magnet. Fig. 4 shows a section of the oxygen spectrum around 4350 A ob-
RADIATIVE-LIFETIME
MEASUREMENTS
017 Lines 4367 4378
4348/49 ,b
90 °
4/45/17
/
F O R I O N S OF
N2
95
AND 0 2
current, using pulse counter C. Counter B simply records the time for which photon-counting has continued. A change in this value during the recording of the decay curve for a given transition indicates that some change in the beam has occurred. The cause of this change must then be located (usually the foil has punctured) and the set of counts for that transition repeated.
3. Data analysis 3.1. COMPUTER TECHNIQUES
Two main types of computer program have been used to assist in the analysis of the data obtained. First, the decay curves have been fitted by a least-squares technique, following correction for background, to the expression I = A e x p ( - ax) + B exp( - bx), (1)
~-Hg
30 °
I<
33,&
,1
DOPPL ER-SHIFTE]::) SPECTRA lO~" beam at1.2 NeV) Fig. 4. Section o f the s p e c t r u m a r o u n d 4350 d~ obtained f r o m a 1.2 M e V 02 + beam, s h o w i n g that the lines viewed at 30 ° to the b e a m direction are shifted by a b o u t 33 • with respect to those viewed at 90 ° .
where x is the distance from the foil. This allows for the possibility of line-blending or cascade repopulation of the radiating level. For lines giving B ~ 0, a = 1/vr, where r is the radiative lifetime of the radiating level and v is the beam velocity. This program also gives an estimate in % of the accuracy of the resulting v, by means of the parameter which I will discuss in a moment. The second kind of program is used to assign lines not previously classified, and simply lists in order the reciprocals of the wavenumber differences for all allowed transitions between known energy levels. 3.2.
tained from an O + beam at 1.2 MeV viewed at 90 ° and 30 ° to the beam direction. The mercury line at 4358 A comes from a small mercury lamp outside the chamber. The Doppler shift produced on each of the four O I I lines at 4346/49 •, 4367 ]t, 4378 ~ and 4415/17 A is about 33 ~.
UNCERTAINTY ESTIMATES IN LIFETIME MEASUREMENTS
Very few published lifetimes have had meaningful
Current Integrator PuLse Output)
Faraday Cup
High VoLtage SuppLy
2 . 4 . T H E PHOTON-COUNTING ELECTRONICS
Fig. 5 shows schematically the electronic equipment used in the photon-counting technique. Each primary photoelectron in the photomultiplier results in a pulse of about 10 -t2 C. This pulse is used to trigger a pulse generator, which in turn emits a pulse to be recorded by pulse counter A. This permits a significant reduction in the number of noise pulses counted, since a pulse originating from one of the later dynodcs in the photomultiplier will be smaller than 10-12 C and will not trigger the pulse generator. Counting is continued at each setting of the plane mirror for the same total number of ions, as measured by the integrated beam
BLOCK DIAGRAM Of Photon Counting Technique used in Lifetime Measurements.
Timing Pulse Generator (I per secJ
- -
[{0n-ii:s~e } Counter C
.....
Fig. 5. Schematic d i a g r a m o f the electronics used in p h o t o n c o u n t i n g m e a s u r e m e n t s of radiative lifetimes. II. L I F E T I M E S
AND TRANSITION
PROBABILITIES
96
E. H. PINNINGTON
error limits attached to them. While it may be agreed that at present photoelectric measurements of radiative lifetimes by the beam-foil method are generally accurate to within about -4-10%3), nevertheless in any given report there may be some " g o o d " lines, which give lifetimes which are much better than + 10%, and some " b a d " lines which give values less accurate than this. In comparing one set of data with another, it is obviously necessary to know which lifetimes in a given paper are more reliable and which are less reliable. However, the normal practice has been to quote a typical accuracy to be applied equally to all the values reported, without indicating which values are more accurate than this and which are less, and even this is more than many authors have been prepared to do. Since [ am in agreement with various journal referees who have indicated that accuracy estimate must be made in lifetime measurements, I will discuss in detail the justification for one accuracy parameter, and attempt to convince you that it does have some meaning. It is well known 4) that the mean square deviation of the number of photons counted per second is related to the average number counted per second, fi, by the relation
An 2 = ~.
(2)
(There is, in principle, a second term arising from stimulated emission, but this is negligible if hv ~>kT, which is generally the case in beam-foil spectroscopy for transitions below 10000 A coming from an approximately mono-energetic beam.) Hence, for an ideal decay curve, where photons are counted for a given integrated beam current at N equally spaced points along the beam,
1 L (A hi) 2
-1.
(3)
The value of c~ can be calculated from the least-squares program. Decays giving c~~ 1 can then be considered to be more reliable than those for which c~> 1. We have calculated the value of c~for our decay curves and have found that those curves which appear to have relatively little scatter do give values of e close to 1, in agreement with eq. (3), while those curves which looked bad when plotted gave values of e significantly greater than 1. The parameter, ~, can thus be used to indicate which lines should be considered more reliable and which less. It is, however, not a very useful parameter for specifying the accuracy of the lifetime, z, which is obtained from the curve. This can be seen
Fig. 6. Two simulated decay curves giving the same value for ~, showing that the ~age uncertainty in T is proportional to the reciprocal of the square root of the line intensity. (See discussion in text.) from fig. 6. The lower curve represents data giving accurate to ___20%. The upper curve is obtained from the lower curve by increasing the n-values by a factor of 100, and An, the deviation from the "theoretical" straight line, by a factor of 10. Both curves therefore give the same value for e. However, the uncertainty in the lifetime of the upper curve is obviously much less than ___20%, and is actually about + 2%. This effect may be readily understood as follows. The distance on the graph paper which a given point falls from the straight line is given by
Al= log(n+An)-log(n) = log(1 +An~n) ~ An~n,
(4)
since (~--~z)~~ n ~, and (~--~2)~~ An, hence
A l a n -~.
(5)
Thus the deviation on the graph from the linear decay varies as n --~, and therefore the uncertainty in the slope of the line obtained from a set of experimental points is proportional to the reciprocal of the square root of the intensity of the signal, for a given value of ~.. This is just the result obtained from the curves in fig. 6. We can include this factor in our expression for the parameter which specifies the accuracy of the lifetime obtained from an experimental decay curve by dividing ~¢ by the square root of the mean intensity of the par-
R A D I A T I V E - L I F E T I M E MEASUREMENTS FOR IONS OF
N2 AND
97
0 2
TABLE 1 Radiative lifetimes for transitions giving a single-exponential decay curve. Wavelength (~) Obs. Listeda
Ion
Upper term
2445 2455
2445.55 2454.99
OII O IiI
3p' 2D° 3p 1S
2510
2509.35 +
O III
4p aDo
2983
2983.78
O III
3350
3350.68 3350.99
3p JD
Radiative lifetime (nsec) Measured (AP) Theory b 3.72 1.78 3.82 3.38
0.29 0.38 0.13 0.25
4.36 3.50
0.14 0.12
2.5 C 4.5 C
O III
3p 5p0
10.15
0.56
6.7 C
3384.95 3450.94 3455.12 3774.00 3973.26 4072.16 4075.87 4085.12 4094.18 4119.22 4185.46 4253.74 4253.98
O lii O Iii O ilI O IiI O Ii OII OII OII OiI O iI OiI
3d 5D 3d SF 3d aF 3p ZD 3p 2p0 3d 4F 3d 4F 3d 4F 3d 4F 3d 4D 3d" 2G
15.23 7.60 6.29 6.50 6.01 7.76 8.61 8.82 9.64 4.46 8.47
0.09 0.04 0.16 0.39 0.45 0.06 0.07 0.12 0.57 0.24 0.05
4.8 C 6.0 C 6.0 C 9.3 C 6.8 C 5.1 C 5.1 C 5.1 C 5.1 C 4.5 C 4.0 C
O II
4f" ZH°
6.19
0.29
3.8 C
4275.52 4313.43 4345.56 4349.43 44.14.91 4416.97
OII OII OII O Ii
4f 4f 3p 3p
4.22 2.98 7.05 7.69
0.39 0.43 0.12 0.06
4.7 4.7 9.5 9.5
O li
3p 2D°
9.92
0.16
8.8 C
O I1 OII O I1 OII
3p 2D° 5p 4D°(?) 3p" 2F° 4f 4F°(?)
8.83 2.7l 14.16 6.30
0.21 0.51 1.03 0.75
8.8 C 9.0 C 4.7 C
4639
4452.38 4530.59 + 4590.97 4610.14 4638.85 4641.81
OII
3p aDO
29.77
0.74
9.8 C
4649
4649.14 4650.84
O Ii
3p 4D°
40.31
0.24
9.8 C
4660 4676 4701
4661.63 4676.23 4699.2l
OI[ OII OII
3p 4D° 3p 4D° 3d' 2F
11.91 14.53 0.81
0.69 1.64 0.57
9.8 C 9.8 C 0.38 D -
3385 3450 3455 3773 3973 4072 4075 4087 4096 4119 4185 4253 4276 4313 4345 4349 4415 4452 4533 4592 4610
4F° 4F°(?) 4po 4p0
C C C C
a C. E. Moore, " A Multiplet Table of Astrophysical Interest", and "An Ultraviolet Multiplet Table", U.S. Department of Commerce, National Bureau of Standards. ( + = assignment from our computer prograrn.) b W. L. Wiese, M. H. Smith and B. M. Glennon, "Atomic Transition Probabilities", vol. 1, U.S. Government Printing Office, NSRDS-NBS 4 (1966). (C = accurate to 25~, D = accurate to 50~.)
ticular
decay curve, nav, i.e. accuracy parameter
= fi = e/nav, which may be written
=,..
/,
(6)
By running a series o f test curves through the same program, we have found that fl may be converted to an estimate of the ° a g e uncertainty in the lifetime by the expression P = %age uncertainty in • = 20 fi,
(7)
where A is the value of the coefficient obtained from the least-squares fit ( = number of photons counted at t = 0). This procedure is strictly only valid for curves requiring only a single exponential, i.e. where blending or cascading is absent. However, the same program will tabulate values for c~ and fi for curves requiring the second exponential, and larger values for these parameters indicate lower accuracy for the derived lifetimes. As the ratio of the coefficients A / B increases, so eq. (7), becomes more valid as an estimate of the II. LIFETIMES AND T R A N S I T I O N P R O B A B I L I T I E S
98
Z. H. P I N N I N G T O N
accuracy of the lifetime associated with the A-coefficient. I should stress at this p o i n t that all we have calculated is the c o n t r i b u t i o n to the total experimental error which comes from the analysis of the actual decay curve. To this m u s t be added the other sources of experimental error, such as the uncertainty i n the b e a m velocity a n d in the correct b a c k g r o u n d to be subtracted from the observed signal, b o t h of which in our case c o n t r i b u t e a b o u t 1% to the total u n c e r t a i n t y in the lifetime value. It is interesting to note, however, that we can n o w estimate the highest accuracy possible if all the other sources of error could be eliminated. I n this case, ~ = 1, so that P = 20(nay) -~, a n d thus, for the case where the decay curve is c o n t i n u e d until the signal has fallen to 1% of its peak value giving nay = A/IO, we o b t a i n M i n i m u m %age error
Peak line intensity A (counts)
-I- 10 -t- 1 +__0.1
40 4 × 103 4 x 10 5
This may prove useful to certain m e a s u r e m e n t s as it
allows the experimenter to estimate h o w m a n y counts he needs, a n d therefore for how long he m u s t c o u n t at each p o i n t on his decay curve, in order to o b t a i n a given accuracy in the resulting lifetime. The o p t i m u m would be to take enough c o u n t s to reduce the statistical error that we have been discussing to the same size as the c o m b i n e d error from other sources.
4. Some specimen results 4.1. OXYGEN IONS Table 1 lists the radiative lifetimes we have obtained for oxygen lines giving a decay curve in which the coefficient B in eq. (1) was ~ 0. The listed wavelengths are from M o o r e ' s Multiplet Tables. The accuracy p a r a m e t e r (AP) is given by eq. (6) a n d m a y be converted to a percentage estimate of the u n c e r t a i n t y by multiplying by 20. The theoretical values have been calculated from the t r a n s i t i o n probabilities listed i n vol. 1 of " A t o m i c T r a n s i t i o n Probabilities" by Wiese et al. A cross ( + ) indicates that the assignment has been m a d e using our c o m p u t e r program. Table 2 lists the o u t p u t f r o m our p r o g r a m for lines giving decay curves requiring a non-zero value for B.
TABL~2 Computer analysis of decay curves requiring a second exponential. Wavelength (•) Obs. Listed
ion
Upper term
4379
3043.02 3047.13 3260.93 3693.70 3727.33 3734.80 3754.67 3759.87 3791.2,5 4140.74 4153.30 4189.7"7 4366.90 4378.01 4378.41
4434 4447
4437.24+ 4448.21
OII O IX
5p 4p0(?) 3d' 2F
4467 4475 4516 4592
4513.61 + 4590.97
O II O Ii, O I11 O II(?) O Ii
? 9 5p 4D(?) 3p' 2F0
4649
4649.14 4650.84
O II
3045 3250 3700 3726 3736 3754 3759 3791 4140 4151 4189 4366
A
ra (nsec) B
Computer analysis ~B (nsec)
(AP)
O III O II1 O III OII O III O III O III O III O 1I OII OII OiI
3p 3p 3d aF° 3p 5D° 3p 4S° 3p 5D° 3p aD 3p ZD 3p 8D 3d 4p(?) 3d 4p(?) 3d' 2G 3p 4p0
320 647 1393 670 878 1069 823 579 289 200 316 372
2.52 4.97 7.65 4.80 5.40 5.00 7.09 6.99 7.20 9.28 64.84 11.27
- 94 -277 -782 -242 - 453 -433 -259 --248 445 145 574 190
0.06 2.13 3.01 2.09 3.31 1.66 2.25 1.68 1.82 1.97 5.59 2.23
0.41 0.14 1.139 0.14 13.33 0.35 0.03 0.17 0.44 0.18 0.05 0.08
O II
4f' ZF0(?)
753
11.27
781
2.16
0.11
242 256 253 1151 105 160 1085 1198 224 1087 584
1.78 8.19 7.44 6.74 19.31 1.48 9.50 10.75 12.03 21.13 22.75
270 150 151 -- 378 150 86 -- 52"7 -- 445 -- 74 -- 350 -- 127
16.25 1.05 0.75 2.30 2.72 33.28 3.83 5.36 4.14 3.75 4.61
0.13 0.07 0.1 l 0.24 0.09 0.37 0.04 0.23 0.41 1.85 0.07
3p 4D0
RADIATIVE-LIFETIME
MEASUREMENTS
F O R I O N S OF
N2
99
AND 0 2
TABLE 3 Experimental transition probabilities for s o m e oxygen lines o f astrophysical interest. Listed wavelength ( ~ )
ion
U p p e r term
3759.87 4072.16 4075.87 4085.12 4119.22 4153.30 [430.09 4185.46 4189.79
O II1
3p aD
OII
3d 4F
OII
3d 4D
OII
3d 4p
OII
3d' ~G
OII O II
4 f ' ~H ° 4f 4F°
OII
3p 4po
OII
3p 2D°
O II O [I
3d' 2F° 3p 4D°
4253.74 4253.98 4275.52 4345.56 4349.43 4366.90 4414.91 4416.97 4452.38 4448.21 [445.62 4649.14
T r a n s i t i o n probability (10 s sec - t ) Observed Theoretical 1.44 1.03 1.20 0.29 1.48 ? 5.1 1.39 1.43
B B+ B* B+ C
1.62 2.36 0.96 0.80 0.54 1.06 0.88 0.14 9 10.3 0.39
C C C C C B B B
C CC-
BD
1.07 1.70 1.98 0.48 1.48 0.77 39 2.43 2.51
C C C C C C D-] C C
2.63 2.12 0.89 0.74 0.50 1.15 0.95 0.15 0.57 26 1.04
C C C C C C C C C D-] C
TA~L~ 4 C o m p a r i s o n with previously published data. Ion
Radiative lifetime (nsec) O t h e r values Ref. a Ref. b
Upper term This work
0 1I
0 III
3p 2D°
9.5
_+ 5(2)
-
3p 4po
8.8
+ 1.8(3)
-
3p" 2F°
10.5
_+ 1.2(4)
-
3d 4F
8.4
+ 0.5(4)
3d' 3d' 4f' 3p
0.92 7.0 6.2 3.9
_+ 0.10(3) + 1.5(2) + 0.9(1) _+ 0.4(2)
3~ ap
2.5
+_ 0.4(1)
30 aD 3p 5p0
6.9 10
-± 0.6(4) + 2(1)
3d aF°
5.0
-& 0.5(1)
2V 2G ~H ° tD
3d aD 3d aF
15 7.3
q_- 2(1) + 0.7(2)
Theory Ref. c
11.85 8.54 7.7
8.8 C
9.0 C
-
12.8 c 4.18 c 5.29 c
0.64 3.25 2.20 3.36
5.05 c 4.35 c 3.37 3.71 3.35
4.67 ¢ 22.8 c 4.80 5.13
9.5 C
5.0 C 0.36 D 4.0 C 3.8 C 4.5 C 4.9 C
-
9.3 C 6.7 C
5"04c
4.8 C
25.2 c
2.12 1.44 2.84 c
4.8 C
7.61 9.00
-
6.0 C
ReL a. M. R. Lewis et al., Phys. Rev. 178 (1959) 49. Ref. b. M. D r u e t t a a n d M. C. Poulizac, Phys. Letters 29A (1969) 651. Ref. c. W. L. Wiese et al., A t o m i c T r a n s i t i o n Probabilities, vol. 1 (U.S. G o v e r n m e n t Printing Office, N S R D S - N B S 4, 1966). II. L I F E T I M E S
AND TRANSITION
PROBABILITIES
100
E. H. PINNINGTON TABLE5 Lifetime measurements of some N l I levels. Wavelength (~) Obs. (+ 2 ~) Listed 3995
Upper level This work
Radiative lifetime (nsec) Others
3995.00 5041.32 4043.54 4145.76 4176.16 4241.79 4432.74 4530.40 4607.16 4630.54 4991.22 5001.13 5001.47
3p 1D
6.3 _+ 10~
4f 3G 3p 5S° 4f IF 4f 8F 4f 8D 4f 1G 3p ap 3p 5p 3p apo
3.8* + 10~ 6.0 + 3 ~ 5.4 _+ 4 ~ 3.2* + 10~ 3.9* + 10~ 4.3* + 10~ 3.3"/11.0" 6.0* + 10~ 12.0 _+ 10~
5.3 a, 5.8P, 9.0~ 10.5r, 5.7a 3.5d, 5.9P 2.8 ~ 2.80 -
3d ZF°
16.7 ___3 ~
13.0a
5003 5005
5005.14
3d ZF°
18.4 + 2 ~ 14.0 + 5 ~
-
8.2 8.2
5012
5011.24 5012.03
3p ~po
14.1 __. 3 ~
-
13.0
5179.50 5535.39
3d 5F 3d 5D 3p 5D°
5.2 _+ 7 ~ 17.0 + 3 ~
4042 4146 4176 4241 4433 4531 4607~ 4631 4992 5001
5179 5535
7.0a, 6.1P
Theoryt 6.3 2.9 7.3 3.9 4.7 5.4 3.9 9.5 9.5 13.0 8.2
7.3f, 17.4d
9.8 12.1 12.8
* Cascading present. t Computer fit gives two equal contributions with lifetimes listed. A. Denis et al., C. R. Acad. Sci. 266B (1968) 64; Proc. Beam-Foil Conference, U. of Arizona (1967) 341. f U. Fink et al., J. Opt. Soc. Am. 58 (1968) 475. P E. I-L Pinnington and C. C. Lin, J. Opt. Soc. Am. 59 (1969) 717. Theoretical values have + 25~ accuracy. Table 3 lists the t r a n s i t i o n probabilities which can be o b t a i n e d f r o m the experimental lifetimes for these oxygen lines which we have f o u n d listed in the spectra of certain B-type starsS). T h e theoretical t r a n s i t i o n probabilities are t a k e n f r o m the c o m p i l a t i o n by Wiese et al., who estimate their accuracy according to the scheme: B = accurate to within +__10%, C = accurate to within ___25%, D = accurate to within __ 50%. We have also used this scheme to represent our estimate of the accuracy of our experimental values for the t r a n s i t i o n probabilities derived according to the relation
1 (Aij)e~p = (Aij)th%xpZ(Aij)th,
(8)
where (Aij)th = theoretical p r o b a b i l i t y for the t r a n s i t i o n f r o m level i to level L %xp = our m e a s u r e d lifetime for level i, (A,~)th = s u m of the theoretical probabilities for all possible radiative transitions from the level i.
This m e t h o d assumes that only the transitions listed by Wiese et al. c o n t r i b u t e significantly to the dep o p u l a t i o n of level i, a n d that the theoretical b r a n c h i n g ratios are correct. F o r all except two of the transitions listed in table 3, the u p p e r level only makes transitions to levels of one lower electron configuration, so that for these cases our m e t h o d of estimating the t r a n s i t i o n p r o b a b i l i t y has some meaning. F o r two cases, however, strong transitions are possible to levels of two lower electron configurations, a n d in each case one of these transitions lies in the far ultraviolet region of the spectrum, a n d therefore has a relatively high t r a n s i t i o n probability, for which the theoretical value has a large estimated uncertainty. I n these two cases, shown inside square brackets [ ] i n table 3, our Iifetime m e a s u r e m e n t gives a value for the t r a n s i t i o n probability for the short wavelength line only. The fact that a radiative-lifetime m e a s u r e m e n t in the visible region can be used to o b t a i n t r a n s i t i o n probabilities on the far ultraviolet is one of the advantages of this type of technique, a n d should n o t be overlooked. Table 4 presents a c o m p a r i s o n of our radiative lifetime values with other m e a s u r e m e n t s to be f o u n d in the literature. The value given in the c o l u m n "This w o r k "
RADIATIVE-LIFETIME
MEASUREMENTS
I01
F O R I O N S OF N 2 A N D 0 2
TABLE 6 Lifetime m e a s u r e m e n t s o f s o m e N III levels. Wavelength (~) Obs. (+_ 2 A) Listed
Upper term This w o r k
Lifetime (nsec) Others
3354
3353.78 3354.29
3p ap
5.3 ___ 1 0 ~
5.7 l, 5.8P
3367 3373 3771 4098 4103 4200
3367.36 3374.06 3771.08 4097.31 4103,37 4100.02
3p 3p 3p 3p 3p 3p
5.4 7.3 8.9 4.7 5.0 2,2
5.841, 5.4P, 5.2 a 9.8 f, 5.671 14.6 I, 9.01, 8.8 a 4.3 I, 4.2 a 4,11 2.39, 1.71, 3.0 f, 2.1 a
4290 4378 4456 4510 4515 4860 4862 4867
4288"72m 4290.8 m 4379.09 ¢ 4510.92 4514.89 4858.74 4861.33 4867.18
4p ap 4S 2p0 zp0 2D -
5g 2G 3p 4D 3p 4D 3d 4F° 3d 4F° 3d 4F°
+ 5~ + 10~ _+ 3 ~ _+ 3 ~ + 5~ _+ 3 ~
1.5'/10.7"
4.2 I, 3.3 a
2.7 ~ + 1 0 ~ 2.4 e + 1 0 ~ 31.0 _ 3 ~ 31.7 + 3 ~ 19.1 + 5 ~ 21.8 ___ 5 ~ 15.7 + 1 0 ~
4.0 I, 4.11, 3.3 a 24.0 a 24.0 d I6.9 a I6.7~
Theory t
5.7 5.? 5.7 8.1 10.4 10.4 10.0 14.3 14.3 15.9 15.9 15.9
m Listed in M o o r e ' s tables but n o t classified. * C a s c a d i n g with equal c o n t r i b u t i o n s giving values listed. ¢ Unclassified b u t listed as N III by U . Fink, J. Opt. Soc. A m . 58 (1968) 937. c C a s c a d i n g present. a A. D e n i s et al., C. R. Acad. Sci 266B (1968) 64; Proc. B e a m - F o i l Conference, U. o f A r i z o n a (1967) 341. U. F i n k et al., J. Opt. Soc. A m . 58 (1968) 475. 1 M. R. Lewis et al., Phys. Rev. 164 (1967) 94. P E. H. P i n n i n g t o n a n d C. C. Lin, J. Opt. Soc. A m . 59 (1969) 717. t Theoretical values have _+ 2 5 ~ accuracy.
is tile weighted mean with its probable error of all values we have obtained for that particular upper term, and the number in brackets is the number of such values from which the mean has been calculated. A superscript c with values taken from ref. a indicates that cascading may be present which has not been corrected, but with values from ref. b that an allowance for cascade effects has been made. It is noteworthy that the only significant discrepancies between the various values occur when cascading is present. 3d 4F, O II. The factor of almost 2 between our data and that listed by Druetta and Poulizac is difficult to explain. Our value comes from the mean of values obtained from 4 cascade-free decays, including the two most intense lines in the muttiplet, whereas Druetta and Poulizac have two values from cascadeaffected decays. However, this level must be reinvestigated before an accurate experimental lifetime can be established. 3d SD, O III. Lewis et al. (ref. a, table 4) have discussed this transition, pointing out that the line at 3384.95 /~ was blended in their measurements (pre-
sumably with the O IV-line at 3385.55 A). Druetta and Poulizac did not observe this multiplet at all, but made their measurements with less intense lines belonging to the 3p 5D°-3d 5D multiplet at 3065 A, 3075 A, lines which were not seen by either Lewis et al. or us. More recent work by Druetta has given a lifetime of 8.6 nsec for the O III transition at 3384.94 A (M. Druetta, private communication, January 1970). Further discussions of our oxygen data are to be published shortly 6' 7). 4.2. N I T R O G E N IONS
Tables 5 and 6 present radiative lifetimes for some levels belonging to ions of nitrogen, which are derived from decay curves recorded only two weeks prior to my departure for this meeting. The data are therefore somewhat preliminary. However, the lifetime values have been derived from our computer program by means of the parameter fl discussed earlier. The quoted errors should therefore have some significance for those lines where no cascading was present. All values derived from lines where significant cascading was II. L I F E T I M E S A N D T R A N S I T I O N
PROBABILITIES
102
E.H. P I N N I N G T O N
p r e s e n t , as i n d i c a t e d b y a l a r g e v a l u e o f the B-coefficient c a l c u l a t e d by o u r p r o g r a m , h a v e b e e n a s s i g n e d a n a r b i t r a r y e r r o r o f _ 10%. T h a n k s are d u e t o t h e staff o f t h e R a d i a t i o n R e s e a r c h L a b o r a t o r y f o r t h e i r willingness to serve b e y o n d t h e n o r m a l call o f d u t y , a n d to M r . E. A . F o s t e r f o r d e s i g n i n g a n d c o n s t r u c t i n g t h e v a r i o u s c h a m b e r s used in t h e s e e x p e r i m e n t s . M i s s S. D o r p e r a n d M r . G. F i n l e y are to b e t h a n k e d f o r t h e i r assistance in recording the data and preparing the diagrams Finally, g e n e r o u s f i n a n c i a l s u p p o r t m u s t be a c k n o w l e d g e d f r o m the Province of Alberta and the National Research Council of Canada
References J) S. Bashkin, D. Fink, P. R. Malmberg, A. B. Meinel and S. G. Tilford, J. Opt. Soc. Am. 56 (1966) 11364. 2) W. S. Bickel, Appl. Opt. 7 (1968) 2367. 8) E. H. Pinnington and C. C. Lin, J. Opt. Soc. Am. 59 (1969) 717. 4) M. Garbuny, Opticalphysics (Academic Press, New York and London, 1965) p. 418.
5) K. O. Wright, E. K. Lee, T. V. Jacobson and J. L. Greenstein, PuN. D.A.O. Victoria XII, no. 7 (1964). 6) E. H. Pinnington, J. A. Kernahan and C. C. Lin, Astrophys. J. 161 (1970) 339. v) j. A. Kernahan, C. C. Lin and E. H. Pinnington, J. Opt. Soc. Am. (L) 60 (1970) 986.
Discussion WHALING': Can you rely on the theoretical branching ratios in calculating the transition probabilities? PINiNG.TON: This depends on the nature of the coupling. In light elements you are not in too bad a position. WHALING': Are there any experimental measurements of branching ratios? PINNING-TON: There are some rough measurements available. BERRY: There is a problem in O III where some two-electron transitions are quite strong. P1NNINGTON: if yOU vary the oscillator strengths, you are not going to improve the agreement with theory, since if some of the values are adjusted to give a better agreement, then the others must be adjusted to give a worse agreement, in order to preserve the observed value for the lifetimes. WHALING':TO measure the beam velocity to 1% with the Doppler shift, how accurately must you locate the line centers? PINNING,TON: Each Iine can give you 2-3 % accuracy. The question is how many lines can you measure. The broadening without blending is about 2 A, and with 10 measurements you can get 1% accuracy.