Physica X, no 7
J u l i 1943
T H E R E L A T I V E P R O B A B I L I T I E S OF T R A N S I T I O N S IN T H E ZINC ATOM*) b y J. W. S C H U T T E V A E R and J. A. SMIT Communication from the Physical Ipstitute of tile University of Utrecht
Summary I n o r d e r t o d e t e r m i n e t h e r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s (t.p.) of t h e zinc a t o m , w e m e a s u r e d t h e i n t e n s i t i e s of lines ~tnd b a n d s in t h e s p e c t r u m of a d.c. c a r b o n a r c in air w i t h one e l e c t r o d e c o n t a i n i n g a m i x t u r e of Z n O a n d MgCO 3 o r MgO. I n t a b l e I t h e r e l a t i v e i n t e n s i t i e s of t h e c o m p o n e n t s w i t h i n s e v e r a l t r i p l e t s a r e g i v e n . T h e s e i n t e n s i t y r a t i o s are in g o o d a g r e e m e n t w i t h t h e m u l t i p l e t i n t e n s i t y rules. T h e m e a n v a l u e s of t h e p r o d u c t of t . p . a n d s t a t i s t i c a l w e i g h t of t h e u p p e r l e v e l for t h e m e a s u r e d s i n g l e t a n d t r i p l e t lines are s h o w n in t a b l e I I . I n o r d e r t o o b t a i n t h e a p p r o x i m a t e a b s o l u t e v a l u e s in sec -1 t h e v a l u e s of t a b l e I I h a v e t o be m u l t i p l i e d b y ca. 4,6 . l0 s.
§ 1. Method, and checking o/the method. Transition probabilities of spectral lines can be determined by measuring their intensities in a radiating gas with known populations of the energy levels. In the column of an arc these populations correspond, under suitable conditions, to thermal equilibrium, so that they can be computed from the temperature of the gas ~[). Accordingly we measured the intensities of Zn lines, emitted b y an arc containing Zn vapour. The temperature of the gas in the positive column of the arc was determined with the aid of the intensity ratio of CN bands, which were also present in the spectrum. In order to obtain populations of the high Zn levels, that were sufficiently large for our purpose, high arc temperatures (ca. 6000°K) had to be applied. We used a d.c. carbon arc, current 3,5--6 A, in air of atmos*) For full experimental details comp. J. W. S c h u t t e v a e r: ,,Relatieve waarschijnlijkheden van overgaugen in het Ca-, Zn- eu Sr-atoom" (thesis Utrecht 1942). t) For references see the paper of K e r s t e n ~ ) .
502
R E L A T I V E P R O B A B I L I T I E S OF T R A N S I T I O N S IN T H E ZiNC ATOM 5 0 3
pheric pressure, of which the electrodes had a n ' o u t e r d i a m e t e r of 4 mm. In the lower one, the anode, a hole of 1--2 m m d i a m e t e r contained a m i x t u r e of ZnO and MgCQ. The relative intensities of the Zn lines a n d of the CN bands have been measured according to the p h o t o g r a p h i c - p h o t o m e t r i c m e t h o d 2). As a s t a n d a r d lightsource we used a tungsten b a n d lamp with absolutely calibrated spectral brightness as a function of the lamp current. This b a n d lamp was used in the same position as the positive column of the arc, of which an image was formed on the slit of a q u a r t z - s p e c t r o g r a p h with auto-collimation, made in the workshop of the institute. The time of exposure varied between 2 and 40 seconds. F o r the d e t e r m i n a t i o n of the t e m p e r a t u r e of the arc we used the first three bands of the CN b a n d sequence Av = - - 1 (X = 4216 A, etc.). The relation between the t e m p e r a t u r e and the intensity-ratio of the bands has been calculated b y V ij v e r b e r g and b y S p i e r and S m i.t ~). We used the curves of S p i e r. F o r the lines u n d e r investigation our arc must be a B o 1 t zm a n n radiator. I t was shown b y 0 r n s t e i n a n d B r i n kin a n 4) t h a t an e l e m e n t a r y volume in the column of a d.c. carbon arc in air sufficieiatly a p p r o x ! m a t e s a B o 1 t z m a n n r a d i a t o r with respect to a spectral line, provided t h a t : 1°. there does not occur disturbing self-absorption for the line, 2 ° . the axial electric field-strength is low enough, 3 ° . the mean n a t u r a l life time for the u p p e r level of the line, with respect to radiation, is high enough. The influence of self-absorption was checked b y measuring the int e n s i t y ratios of the components of the triplets, which ratios were in good agreement with the multiplet intensity rules (table I) and did not change systematically with the concentration of Zn. Moreover, for these triplet c o m p o n e n t s and for the singlet lines we have c o m p a r e d the i n t e n s i t y of such a line with the intensity of the black b o d y radiation of the same t e m p e r a t u r e and wavelength in a wavelength interval equal to the D o p p l e r width of the lineS). We have only used such exposures where this ratio Q was smaller t h a n 0,1, corresponding to a m a x i m a l intensity loss, due to self-absorption, of 4°/~. T h e exact Value of this loss c a n n o t be calculated since t h e cross-
504
J. W. SCHUTTEVAER AND J. A. SMIT
section for d a m p i n g collisions, which differs from element to element a n d from transition to transition, is not k n o w n here. In our arc, with 16 % ZnO, measured at currents i between 4 and 6 A, the electric fieldstrength E (in Volt/cm) was f o u n d to be related to i b y E = 5 + 70/i. Consequently E varied in our arc between 16 and 25 V/cm, so it is less t h a n in the corresponding pure carbon arc (23,5 - - 30,5 V/cm) which is a l r e a d y thermic. Ornstein and B r i n k m a n h a v e suggested t h a t the n a t u r a l m e a n life time of a level should be g r e a t e r t h a n 10 -8 sec in order to be sure of the t h e r m a l equilibrium of its population. I n c o m plete t h e r m a l equilibrium would cause s y s t e m a t i c variations of the d e t e r m i n e d values of the t.p. with the ten~perature. A r a t h e r rough calculation of t h e absolute t.p. of our lines, with the aid of the m e a s u r e d relative t.p. o f the resonance , i n t e r c o m b i n a t i o n line 43P1 - - 41So X = 3076 A and of the absolute t.p. of this line which is d e t e r m i n e d b y o t h e r investigators (further details § 4), showed t h a t the smallest n a t u r a l m e a n life time a m o u n t e d to 4 , 4 . 10 -9 sec for the 43D3,zl levels. The n e x t was 7,1 . 10 -9 for the 5351 level, whereas the o t h e r m e a n lifetimes were g r e a t e r t h a n 10 -8 sec. F o r the lines 53S1 - - 43P0 X = 4680 A and 43D1 - - 43P0 3282 A we have d e t e r m i n ed the ratio Ag (3282)/Ag (4680) at different t e m p e r a t u r e s (A = t.p., g = statistical weight of the u p p e r level of the line). The ratio appears to be i n d e p e n d e n t of the t e m p e r a t u r e (fig. 1), from which we conclude t h a t , t h o u g h the n a t u r a l m e a n life times are smaller t h a n 10 -8 sec, our d e t e r m i n a t i o n of the t.p. is permissible.
10 A.g(~.3282) i . (~.4 8o)
11f!i 6-
I
•
5000
•
T ..____........ ~ -
5500
Fig. 1. T h e r a t i o of t h e m e a s u r e d .4g v a l u e s of t h e t r a n s i t i o n s 43D1 - 43P0 X = 3282 A a n d 53S1 - - 43Po 4680 A p l o t t e d a g a i n s t t h e a b s o l u t e temperature.
At a high t e m p e r a t u r e in the centre of the arc the Zn atoms might ionize to a considerable degree. This ionization would cause a concav i t y in the centre of the radial intensity distribution of the Zn a t o m i c
RELATIVE PROBABILITIES OF TRANSITIONS IN THE ZINC ATOM 5 0 5 ¢
lines. The CN bands have their intensity maximum in the centre of the arc and therefore give the temperature of the Zn vapour in this centre, but the greater part of the measured intensity of a Zn atomic line would have been emitted then in the outer region. Since the ionization potential of Zn is 9,35 eV and our arc temperaturc generally was somewhat lower than 6000°K, we did not expect such an effect here in view of a rather rough calculation with the aid of the ionization formula of S a h a 6). This conclusion was in good agreement with measurements of the radial intensity distribution of some Zn atomic lines, at an (rather low) arc temperature of 5200°K, by K r u i t h o f, who for this purpose made a ,,cross-spectrogram" 7). Furthermore we made some exposures in the ultraviolet region with 100 °/o ZnO and exposure times up to one minute, showing the absence of Zn ion lines such as 52S,/2 - - 42p,/, 2558 A and 52S,I, - - 42p,I, 2502 A.
§ 2. Measurements in the triplet system. In most of the following work, except those plates on which we made exposures of arcs with different relative concentrations of ZnO, we determined the temperature from the CN bands of each spectrum separately, after which the average of these temperatures from a plate was used for the lines in all the spectra of that plate. The deviations of these (10--15) temperatures from their average were less than 150°K, that is about the error of measurement. Some of the Zn-lines were lying in a background, for which the necessary corrections always have been applied. Though the dispersion of our spectrograph was 0,0513 mm/A at 5000 A and 0,443 mm/A at 2500 A it was impossible to resolve the three, respectively two, components of the 3D3,2,1- - 3 P 2 and 3D2,I - - 3 . P 1 transitions. We therefore were not able to check the multiplet intensity rule that gives the intensity ratios of all six components of 3D _ 3p, but we could compare the three main groups with the theory. For these groups agreement was found (table I), so that this may also be expected for the separate lines. The triplets 53Si--43p2,1,0 and 43D3,2,1--43P2,1,o have been measured together in the d.c. arc with 2--16 ~o ZnO and temperatures between 4700 and 5800°K at an arc current of 3,5 A. As it is necessary to use the same exposure time both for the density marks and for the spectra, we diminished the intensity of the spectra by
506
j.w.
SCHUTTEVAER
AND J. A. SMIT
means of a rectangular diaphragm of variable height. This diaphragm reduced the height of the lightspot on the lens that focusses the arc on the slit, without causing a change in the resolving power or in the relative light-loss in the spectrograph. The obtained values of the relative t.p. showed no systematical influcnce of the t e m w r a t u r e . The energy difference between the upper levels of these triplets is 1,12 eV. The triplet 6aS1--4aPzl,0 was measured relative to the line 43D1 - - 43Po (arc current 5 #2, temperature 5885 ° K, 16 ~o ZnO). The CN bands and the line 4 3 D ~ - 43Po being relatively strong, it was necessary to diminish their density by means of two weakeners of platinized quarts placed into the spectrograph just in front of the plate. The weakest line of the triplet, 3018,3 A, was disturbed by the Fe lines 3019,0 and 3018,1 A. It therefore was necessary to analyse these three lines and to make some exposures of the same arc, but without ZnO, for the interpolation of the background. In the triplet 53D3,2,1--43P2,1,0 only 5332,1"--43P 1 could be measured without difficulties. We used an arc with a current of 5 A and with a mixture of MgCQ and ZnO in the ratio of 10 : 1. The line 5aDt - - 4aP0 2756,4 A has not been measured since it was disturbed by a strong Fe line 2756,3 A. 53D3,2.1-43p2 2801 A was disturbed b y the Mg ion line 2802,7 A. We made again exposures without ZnO and have compared the logarithmic intensity diagram of both types of exposures *), in order to correct for the intensity of the violet wing of the disturbing Mg ion line. The two triplets lines have been measured with respect to 6aSl - - 43Pt. Owing to the great dispersion of the spectrograph, it was impossible to photograph these lines together with the CN bands on one plate. We therefore made two plates, one with exposures in behalf of the CN bandsequence and one containing the Zn lines, under the same arc conditions but with different adjustment of the spectrograph. This method was admissible since the temperature of the arc was approximately constant and since the energy differences betv~een the upper levels of all lines measured in this way are relatively small. As the following lines are much weaker then those mentioned be-fore, it was necessary to increase their intensity relative to the background. This was effected by increasing the relative concentration of *) F o r f u r t h e r d e t a i l s a b o u t t h i s m e t h o d see K e r s t e n t).
R E L A T I V E P R O B A B I L I T I E S OF TRANSITIONS IN THE ZINC ATOM 5 0 7 ¢
ZnO up to 200/0 . In this w a y it was possible to measure the two strongest components of the triplet 7 3 S 1 - 43P2,1,o and the components of the triplet 6aD3,zl - - 43Pzl,o relative to 6aS1 - - 4aPzl,o . In order to measure the 83S1--43Pzl,o, 9as1--4aP2,t,o and 7aDa,z~- 4apzl,o transitions, we had to use pure ZnO in a hole of 1,5 m m diameter and at an arc current of 5 A. In spite of the fact t h a t we used the largest possible slitwidth of the spectrograph (1,5 mm) the density marks for these short wavelengths appeared to require so long times of exposure, t h a t we had to weaken the arc spectra in order to obtain comparable exposure times; for this purpose a rectangular d i a p h r a g m was used again. Of the triplet 8as1 - - - 4aPzl,0 only 8aS1 - - 43P~ has" been measured, 8aS1 - - 4aP2 being to strong and 8aSl - - 4aPo 2530,0 A being disturbed by the Fe line 2529,8 A. The lines 9 3 S 1 - 4aP1 and 93S1 - - 4aPo were weak and fell at the end of the plate. The triplet 7 a D a , z t - 4aPzl,o yielded no measurable lines as t h e y were all disturbed by other lines. The first one 7aDa,2,1- 4aP2 2515,8 A b y a v e r y strong line, probably a Si line 2515,1 A. The other two by the Fe lines 2491,4 and 2479,8 A. For these triplet lines it was only possible to give an upper limit for the relative t.p. The last three triplets have been measured relative to the triplet 7 3 S 1 - - .43p2,t,0 . In table I a survey is given of the relative intensities of the components of the measured triplets. The fourth column gives the intensities of the third column to which the 44 correction is applied. It will be seen t h a t the deviations from the 5 : 3 : I ratio, which is approximately predicted by theory, do not surpass 10 °/o s). Upon the reality of these deviations we generally can give no opinion, since the error of measurement too a m o u n t s to 10 %.
§ 3. Measurements in the singlet system. First the line 41D2--4tPi 6362 A was measured with respect to 5 a S t - 4aPz~,0 . In order to obtain a measurable density for these lines together with the CN bands we mostly used a red filter placed in front of the slit of the spectrograph. The arc was operated at a current of 5 A and the hole in the anode contained different amounts of ZnO varying between 5 and 16°./o. The temperatures of these arcs lay between 5000 and 6000°K. No systematical influence of these different temperatures on the values of the measured relative t.p. was observed (fig. 2). 51D2 - - 41Pt 4630 A was very weak and could only be measured
] . W. SCHUTTEVAER
508
A N D J, A. SMIT
relative to 4 1 D 2 - 41_PI if the intensity of the latter was weakened by means of a blue filter placed in front of the slit of the spectrograph and if the CN band sequence was photographed through a platinized quartz weakener. TABLE I I n t e n s i t y ratios in the aS - - ap and ~D - - 3p transitions of zinc *) Transition
[ )'vac in X
[
I
I/v'
-- 4'P.~ -- 4sp, -- 4spo
4810,5 4722,1 4680,1
5 3,03 4- 0,03 1,01 4- 0,02
5 2,81 0,91
68Sa
-- 4spo
63Si 6sS]
-- 4sp, -- 4SPo
3072,0 3035,7 3018,3
5 3,27 -4- 0~06 1,05 4- 0,02
5 3,13 0,99
7sSt
7sS,
- - 4spo.. -- 4sp,
7sS,
-- 4apo
2712,4 2684,1 2670,5
5 3,27 4- 0,06 1,02 ~ 0,03
5 3,16 0,96
3346 3303 3282,3
5 3,08 i 0,04 0,98 + 0,02
5 2,92 0,91
5 3,11 4- 0,17
5 2,99
5 2,98 :k 0,07 0,98 -- 0,04
5 2,87 0,93
8sSi 5sS, 5sSt
4'D3, 2, t - - 4sp~. 4aD2, I - - 4aP* 4SD,
-- 4sPo
5'D2, I
-- 4'P,
2801 2771
5SD,
- - 43p0
2756,4
58D~, ~., i -- 4aP~.
6aDa, 0., * - - 43P0. 6aD-., I - - 4aP* 6aDl -- 4spo
2609 2582 2569,8
A.g(~.631S2)
A,g ( ~. 468o) 4
3'
' 5000
,
,
,
,
I 5500
I
I
•
6OOO
I
F i g . 2. T h e r a t i o o f t h e m e a s u r e d A g v a l u e s o f t h e t r a n s i t i o n s 4 1 D 2 - 41P1 ), = 6 3 6 2 J~ a n d 53S1 - - 4 3 P 0 4 6 8 0 A p l o t t e d a g a i n s t t h e a b s o l u t e temperature.
*) The choice of 5,00 as the value of the strongest component is arbitrary.
R E L A T I V E P R O B A B I L I T I E S OF T R A N S I T I O N S IN T H E ZINC ATOM ~ 0 9 t
The next line of this series 6tD2 - - 41P1 4112 A just lay in the CN band sequence so t h a t only an upper limit for the t.p. could be determined. In the 'So - - 4 ' P , series the first transition, with upper level 5'S0, had to be dropped out on account of its wavelength of 11055 A. The second line 61S0 - - 41P, is very weak and has been measured together with 5 1 D 2 - 4tP, which, as we have seen above, is very weak too. The measurement was possible by using pure ZnO and exposing 30 seconds. The next member of this series was still weaker and could not be measured; only a perhaps far to high upper limit of the relative t.p. was determined. § 4. The resonance intercombination line 4aPl - - 41So ~ = 3o75,9 o ,4. The resonance intercombination line first has been measured relative to the triplet 5as, - - 4aP2a,0 under the same conditions as mentioned in § 2. The line was heavily disturbed by the Fe line 3075,92 A. This disturbance, caused by impurities of the carbon electrodes, could not easily be diminished. It was necessary to make exposures of spectra without ZnO in order to determine the intensity-ratio between a free Fe line and the disturbing one. We used the Fe line 3067 A with practically the same heigth of the upper level. L a p o r t e 9) states t h a t 3075,7 A__corresponds to the_ transition d3~--/1a and 3067 to d ~ - - / ~ with v*(d a) -----7768,9 and v*(d~) = 8030,4, whereas the ground level of Fe, d 1, has a term value v* of about 48000 cm -1. The intensity ratio I(3075,9)/I(3067) was found to be 0,7. By means of this ratio the intensity of the disturbing line could be determined and subtracted from the measured sum of the intensities. The intensity that had to be subtracted varied between 10 and 80 per cent of the original intensity. The ratio which we find for the t.p. of the Zn-lines 4ap1 - - 41S0 and 5aSl - - 4aP0 is very sensitive to errors in the determination of the temperature, owing to the great energy difference of their upper levels (2,62 eV). At an arc temperature of 5000°K an error of 150°K yields an error of 20~/o in the relative t.p. of these lines. We have also determined the relative t.p. of the resonance intercombination line together with 6aS~ - - 4aP2 3072 A. The latter has in the occurring temperature region a ten times greater intensity and was therefore measured in a part of the spectrum, which was weakened by means of platinized quartz.
510
J.W.
SCHUTTEVAER
AND J. A. SMIT
With another way of measuring the upper electrode, in this case the anode, was a copper rod of 7 mm diameter, whereas the cathode, with a diameter of 8 mm, was a carbon one again. The hole in the cathode, 5 mm diameter, contained MgO and ZnO in the ratio 40 : 1. The arc current was 5 A and the axial electric field-strength amounted to 25 V/cm. Exposures of this arc without ZnO showed the absence of the Fe line 3067 A from which we concluded that the disturbance caused by the Fe line 3072 A could amount to 2,5 o/ /o at most. The results of these methods were in good accordance.
§ 5. Results, and determination o] the absolute t.p. In table II the results are given. Ag means the product of the relative t.p. of the line and the statistical weight of its upper level. The figures between brackets have not been measured but were computed from a measured component by means of the theoretical ratio given by the intensity rules. T A B L E II Relative
Transition
Ag
values
of z i n c a t o m
transitions
*)
(~) A g
Number of measurements
),vacin .~
g
4810,5 4722,1 4680,1
3 3 3
511 304 100
17 17 17
3072,0 3018,3
3 3 3
176,5 114 36,5
9 30 19
3 3 3
90,5 5g,6 18,2
19 9 9
5sS~
- - 4apo
5aS1 5aSx
- - 4ap~ - - 4apo
6aSl 6aSt 6aSt
-- 4ap 2 - - 4spx - - 4spo
7ast 7sSz
- - 4sp,, -- 4spz
7aSI
- - 43Po
2712,4 2684,1 2670,5
8sSx 8sSx 8sSl
- - 4sp2 -- 4spl - - 4spo
2567,8 2542,3 2530,0
3 3 3
(48,6} 30 (9,6)
9ss~ 9sSx 9sSl
- - 4sp.~ - - 4spx - - 4spo
2493,3 2469,3 2457,8
3 3 3
(t4)
4SDa, 2, l - - 4 s p . ,
3346 3303 3282,3
7, 5, 3 5, 3 3
4SD*., ~ --4sP~ 4SDt
- - 4spo
3o~5,7
23
(4,5) 4140 2800 896
*) T h e c h o i c e of 100 a s t h e Ag v a l u e of 4680,1 .~ is a r b i t r a r y .
14 14 19
RELATIVE
PROBABILITIES
Transition
kva c
OF TRANSITIONS IN THE ZINC ATOM
in A
SAD3, 2, t - - 4aPe 5aD2, t - - 4aPl 5SDl - - 43po
2801 2771 2756,4
6aDa, .~, I - - 4aP2 6aDo, i - - 43Pt 6aD~ - - 4apo
7aD2, i 7aDt
(~) Ag
I
N u m b e r of measurements
5,3 i, 3 3
1450 896 (286)
II 19
2609 2583 2569,8
5, 3 i, 3 3
795 468 152
18
43p~ - - 4aP~ - - 4a.P.
2515 2491 2479,7
5,3 i, 3
<500 < 300 < lO0
61So 7~So
- - 4tp) - - 4ty'~
5182,0 4292,9
11,4 <2
5
4 t D~
--
51D2 6tD.~
- - 4tp1 - - 41p:
6362,4 4629,9 4113,0
397 28,1
10 21
43P1
- - 4LSo
3075,9
73Da,
~, ~ - -
41Pt
0,244
51 l
8
10
24
The absolute t.p. of the resonance i n t e r c o m b i n a t i o n line can be d e t e r m i n e d in several ways, which have led to somewhat different results 10). W. B i l l e t e r determined, b y means of an absorption m e t h o d . . . . . . . . . . . . . . 3,79. 104 sec -1 P. S o l e i l l e t derived from the material of Billeter the value . . . . . . . . . . . . 4,76 . . . . . J. A u s l i i n d e r determined, b y means of an absorption method, the absolute value of the resonance line 4 1 P l - 41So 2138,6 A being 4,38. 108 sec -1. With this value and the ratio A(res.)/ A(int.) = 15.000, d e t e r m i n e d b y F i l l i p o v , we obtain . . . . . . . . . . . . . . . . . . 2,92 . . . . . Assuming with \V. P r o k o f j e w , t h a t the oscilatorstrength is I, 19 just as for Cd and Hg, we find A ( r e s . ) = 5,73. 108. With the ratio 15.000 this gives . . . . . . . . . . . . . . . . . . 3,81 . . . . . H.C. Wolfe a n d G . W. K i n g a n d J . H. van Vleck calculated A ( r e s . ) / A ( i n t . ) and found 13.500 and 14.100 respectively. These values combined with A(res.) = 4,38. 108 sec -1 give . . 3,24 . . . . .
512
R E L A T I V E P R O B A B I L I T I E S OF T R A N S I T I O N S IN T H E ZINC ATOM
and . . . . . . . . . . . . . . . . . . . . w h e r e a s t h e c o m b i n a t i o n w i t h A (res.) = 5 , 7 3 . 10s gives . . . . . . . . . . . . . . . . . . . . and . . . . . . . . . . . . . . . . . . . . F o r t h e absolute v a l u e we h a v e used t h e a v e r a g e of these 8 v a l u e s . . . . . . . . . . . . . . . a n d t h e r e f o r e A g ( i n t . ) = 1,12. l0 s sec -1. T h e v a l u e s of t a b l e I I t h e n h a v e to be m u l t i p l i e d b y 1,12. 105/0,244 = 4 , 6 . 10s. in order to o b t a i n t h e absolute A g values.
3, I 1 . . . . . 4,24 . . . . .
4,06 . . . . . 3,74 . . . . .
W e wish to t h a n k Prof. Dr. J. M. W. M i 1 a t z for his interest in this work. Received April 24th, 1943.
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