Relative oscillator strengths for lines of Fe I

Aarts, J. Harting, D. Bakker, C. J. 1954

Physica X X 1250-1258

R E L A T I V E OSCILLATOR STRENGTHS FOR LINES OF Fe I b y J. A A R T S , D. H A R T I N G a n d C. J. B A K K E R Zeeman Laboratorium, Universiteit van Amsterdam, Nederland

Synopsis The relative intensities of 80 emission lines in 16 multiplets of iron, in the spectral region A 3800/1_--5300 A have been measured. Light source is a King furnace with a graphite tube at a temperature of 2800°K as heating element. The spectrograph is a concave grating in Wadsworth mounting, the recording apparatus a photomultiplier with a linear amplifier and tube voltmeter. The f-values derived from the measured intensities are compared with the/-values obtained by R. B. and A. S. K i n g from measurements in absorption. 1. I n t r o d u c t i o n . a. T h e m e t h o d s for the m e a s u r e m e n t of s p e c t r a l intensities can be divided into t w o classes: the emission a n d the a b s o r p t i o n m e t h o d . D u r i n g the last t h i r t y years several a t t e m p t s to m e a s u r e spectral intensities in Fe I h a v e been described in literature. The earliest w o r k was done b y V a n M i 1 a a n 1) a n d F r e r i c h s ~). I n their e x p e r i m e n t s , emission lines of Fe I were excited in an electric arc b e t w e e n iron electrodes a n d p h o t o g r a p h i c a l l y recorded. R e l a t i v e intensities of spectral lines belonging to the s a m e m u l t i p l e t were obtained, b u t as neither t e m p e r a t u r e nor d i s t r i b u t i o n function were known, calculation of the line s t r e n g t h s was not possible. Moreover, self a b s o r p t i o n m a r r e d t h e i r results in c o m b i n a t i o n s w i t h the lowest e n e r g y levels. H o w e v e r , t h e i r results showed t h a t the s u m m a t i o n rule for m u l t i p l e t s was at least a p p r o x i m a t e l y o b e y e d in the s p e c t r u m of

Fe 1 8). V a n D r i e 1 4) working along the s a m e lines, b u t u n d e r conditions which were, t h r o u g h the w o r k of O r n s t e i n S ) and Brinkman on the electric arc, b e t t e r known, c o n f i r m e d a n d e x t e n d e d their results. A . S . K i n g 6) a n d collaborators p h o t o g r a p h e d the a b s o r p t i o n s p e c t r u m p r o d u c e d in an electric resistance furnace, a n d succeeded in o b t a i n i n g relative oscillator s t r e n g t h s of 160 iron lines belonging to a n u m b e r of different m u l t i p l e t s with u p p e r t e r m s b e t w e e n 4200 a n d 26000 c m - l o v e r the ground level. F i n a l l y in 1949 W. C a r t e r 7) published a n u m b e r of •-values of iron lines m e a s u r e d in emission; he used a K i n g furnace as a light source a n d a p h o t o t u b e with g a l v a n o m e t e r as a recording a p p a r a t u s . - - 1250 - -

RELATIVE OSCILLATOR STRENGTHS FOR LINES OF F e I

1251

It seemed w o r t h while repeating a n u m b e r of the measurements in emission to compare the results and e v e n t u a l l y to e x t e n d this m e t h o d to higher energy levels. b. Method of K i n g to d e t e r m i n e / - v a l u e s in absorption. The relative absorption is given b y the relation

A a --

Iv

y(e2 l --

e--Em[kT Ng.,/m,,---

mc

Ut

where I , = intensity of the entering light beam per unit of frequency. A = absorbed energy per cubic c e n t i m e t e r and per second. N = n u m b e r of neutral atoms per cubic centimeter of the vapour. l = length of the light p a t h in the absorbing vapour. g,,, = statistical weight of the lower state. [ ..... = oscillator strength o r / - v a l u e for the transition in question. E,, ---- energy of the a t o m in the lower state m. T ---- absolute temperature. Ut -----p a r t i t i o n sum. The equivalent width A2 of an al;sorption line is given by : AI

A/In

=

where I n is the intensity of the entering light beam per unit of wavelength, hence AJl = ( A / I , ) (~2/c) = a ~2/c and we m a y write: A 2 . ~ 4 2 g,, /,,,,, exp ( - - E , , / k Y ) . A~I can be determined b y measuring the curve of growth, t h a t is the relation between the total absorption and the concentration. K i n g finally calculated the r e l a t i v e / - v a l u e s as:

gl/l__

(A2)l

~

e(El--gz)lkT.

c. D e t e r m : i n a t i o n of /-values in emission. The energy r a d i a t e d per cubic centimeter per second in case of the transition n -+ rn is given b y I = N,, A .... hv = Ng,, e -En/kT". gm g~

8n2e2v2 mc 3 /,,,,,. hv

where N, A,,, v E,,

---- n u m b e r of atoms per cubic centimeter in the upper energy state n. = transition probability with regard to the transition n -+ m. = f r e q u e n c y of the radiation. = energy of the atom in the upper energy state n.

We m a y write I ~-. g,,,/,,,,,# e -~n/kr, hence the intensity ratio of 2 spectral

1252

j . AARTS, D. HARTING AND C. J. BAKKER

fines is given b y 1,/12 = can be calculated from

07,/~,~).(gt L/g2/2)ecE=-~ll/*~ and g2/2

the relative

/-value

"Is"

43"

2. Apparatus. a. A King furnace 8) was used as a light source with a graphite tube as a heating element. This tube is 150 mm long, 7 mm inner diameter, 11 mm outer diameter, clamped in two copper electrodes, which are cooled b y running water. The heated part of the tube is 75 mm long, and surrounded b y a carbon jacket with inner diam. 23 mm and outer diam. 30 mm. In the jacket there is a mixture of iron and carborundum that is heated b y theradiation of the graphite tube. Through a slit in the length of the tube, iron vapour diffuses inwardly, where the temperature has a well determined value between 2500 ° and 2900°K (fig. 1).

/

it

E

Gt i

[

Cj

Carbon jacket

I

iron-carborundum

Gt S

graphite tube slit-(70mm long)

E d

electrodes diaphragm

Fig.1

mixture..

Section of furnace

Tube, jacket and electrodes are enclosed in a chamber with an argon atmosphere of 10 cm Hg pressure. The life time of the tube is about I0 hours of operation. The furnace is fed b y an alternating current of about 500 A, supplied from a transformer with a power output of 4.5 kW at a tube temperature of 2800°K. In the primary circuit of the transformer a variable resistor and a regulating transformer are inserted; the latter is fed b y a variac. Temperature variations can be kept within 5°C b y means of a thermopile, receiving the radiation emitted b y the inner tube surface. The thermopile voltage regulates the heating current through the tube by means of a galvanometer, photocel relay, arrangement (fig. 2). b. Optical arrangement. The vapour volume inside the graphite tube is imaged on the slit of a grating spectrograph. Diaphragming prevents continuous light of the inner tube surface from entering the spectrograph.

RELATIVE OSCILLATOR STRENGTHS FOB LINES OF

Fe I

1253

Before failing on the slit, light emitted by the iron vapour is interrupted at a frequency of 200 c/s by a rotating disc. The spectrograph contains a 20 foot, 7500 lines/inch grating in Wadsworth mounting; in the first order the dispersion amounts to 10 A/mm and the resolving power to 45000. Along the focus of this spectrograph a photomultiplier with a second vertical slit in front of it, is moved. c. T h e photomultiplier (RCA I P21) converts the interrupted light into an alternating current of 200 c/s. The voltage over the anode-resistor is proportional to the intensity of the light falling through the slit of the photomultiplier. This voltage is amplified 10000 times by a tuned push-pull

/ Graphite- ~1 Th.... tube

~ Compensat Voltage ingH

Gal.....

arrangement

meter

pile

Main transformer

Fig.2

Regulating

H

"

Varia¢

transformer

H

relay

I.I

Circuit for regulating temperature of the furnace.

pre-amplifier

Furnace motor

mounting

with

Lamp 25 watt

Motor

Photocell

int .

. . .

prop

disc"

2OO°/s

_~[

Photo tube for reference voltage

~.~

amplifier t H

Phase-

Amplifier demodulator

f Fig.3

Schematic diagram of component the apparatus.

parts of

Tube

volt-

meter

amplifier (band:width 20 c/s). The amplified voltage is applied to a phasedemodulator, the reference voltage being supplied by another photo tube, on which light falls that is interrupted by the same rotating disc that modulates the beam under investigation. The resulting direct voltage is measured by means of a tube voltmeter, the reading of which varies linearly with the intensity of the incident light (fig. 3). The time constant of the voltmeter is between 5 and 10 sec. d. Details. The widths of the entrance slit and the second slit are 0,2 and 0,1 mm respectively. The optimum sensitivity of t h e multiplier tube RCA 1P21 occurs at 4200 A, diminishing to 50% of the maximum at 5500 A and to 10% at 6100 A. The photomultiplier tube is mounted in a glass pipe, supplied with a flat

1254

j . AARTS, D. HARTING AND C. J. BAKKER

quartz window. The glass pipe is surrounded b y solid carbondioxide. Using this refrigeration the signal-to-noise ratio is about 15 times better than at room temperature. A heating-wire is wound around the quartz-window preventing this from becoming dimmed (fig. 4). The output voltage of the photo tube can be regulated b y ~¢arying the anode resistor in the ratio 1 : 100 in 8 steps. Adjustment of the second slit along the spectrum can be made with an accuracy of 0,01 mm. The lowest light level measurable with an accuracy of 5% is about 10 4 photons per sec. between 3500 and 5000 A.

i

Fig.4

Schematic

i -

insulating

wall

q

quartz Window

S

slit

h

heating elements

A

amplifier

C Ph

chamber for CO 2 phot0multiplier ="

g

glasspipe

R

rail

diagram of the multiplier tube arrangement.

3. M e t h o d o / m e a s u r e m e n t . The entrance slit of the spectrograph is 0,20 mm and so is the width of the image in the focus of the spectrograph.. The slit of the photomultiplier is smaller, viz 0,10 mm. If this slit is adjusted to be at the centre of the image the phototube receives a quantity of light that is proportional to the total intensity of the spectral line, and independent of the line shape. At a stated wavelength the intensity I is given b y I = u. s where s~is the spectral sensitivity of the photomuttiplier and u is the reading of the voltmeter, s is determined b y means of a tungsten bandlamp of known temperature, from which the emission is known as a function of wavelength. The slit of the phototube is adjusted alternately on the reference line and on lines under investigation. The relative intensity of a line with regard to the reference line can be derived from I/IR = u . sluR. sR. The temperature of the inner surface of the graphite tube is determined by imaging this surface on the slit of the spectrograph; right after that the

R E L A T I V E OSCILLATOR S T R E N G T H S FOR L I N E S OF

Fe I

1255

calibrated tungsten bandlamp is imaged. The ratid of the voltmeter readings caused b y both radiations, equals the ratio of the brightnesses of tube surface and bandlamp; so from the known energy emission of the bandlamp that of the tube surface follows. The temperature of the graphite tube is calculated from the radiated energy b y means of the radiation law of Wien. The tube temperature is practically equal to the temperature of the vapour in the tube. Experimentally this was tested and proved b y R e i n d 1 9). Corrections are introduced for the absorption b y the backwindow of the furnace and b y the lens between this window and the bandlamp. 4. Results and discussion. In table I the wavelengths of the iron lines are shown in the first column; the second column gives the multiplet to which the line belongs and the third gives the measured [-values. These values are relative; they have been converted to the same arbitrary scale as that used b y King. The values obtained by King in absorption are placed in the last column. From gill[g2[2 ~ el~l-~21/kr. I1/I2 it follows that the inaccuracy in the determination of temperature has an increasing influence on the possible error in the/-values if the difference between the upper energy levels of the line under investigation and the reference line increases. In the measurements described this difference is at most 9000 c m - l ; the average value of k T = 1800 cm -1, hence a deviation of 1~/o in the determination of the temperature gives an inaccuracy of 5% in the relative/-values. Taking the inaccuracy in the measurements of the intensities into account, the possible error in the •-values can be fixed at 10~/o at the utmost. Most of the difficulties are caused by self absorption. Light emitted by an atom can be absorbed b y atoms of the same kind, which are in the lightpath. By this the line intensity is reduced; the reduction is a function of the intensity at the line centre: strong lines are reduced more than weak ones. V a n d e r H e 1 d 10) concludes that self absorption in a gas, where the temperature in:the lightpath is constant (and in the furnace this is approximately true), is less than 5% if the total line intensity It < 0,1. E. b where E = intensity of the continuous spectrum at the wavelength of the line in question, emitted b y a black body of the same temperature as the emitting gas and 2b~/2 = the Doppler width of the line. The highest line intensity that can be measured without violating the condition given above for small self absorption is only a small, nearly constant, fraction of the continuous radiation at the same wavelength and temperature. At wavelengths below 3500 A the continuous radiation of the furnace is so weak that this highest allowable intensity falls below the limit of sensitivity of the apparatus which is determined by the noise of the photo-

11256

j . AARTS, D. H A R T I N G AND C. J. B A K K E R

tube. Therefore below 3500 A measurement is not possible without the occurrence of increasing self absorption. The emission method enables us in principle, in contrast to the absorption method, to measure intensities of transitions between energy levels of higher excitation. To get further results in this region it is necessary to have at our disposal a light source that produces vapour temperatures over 3000°K under the same favourable conditions as those existing in a graphite tube TABLE I Wavelength

tl I"

Multiplet

Measured /-value

King's /-value 15 13 11 4.6 12 7.3 11 8.6 12

5269.54 5328.04 5371.50 5397.13 5405.78 5429.70 5434.53 5446.92 5455.62 5497,52 5501.47 5506.78

aSFs--zSD"4 aSF4--zSD% aaFs--zSD% aSF4--zSDO4 aSFt--zSDO t aSFs--z6D% a6Fl--zSO% a6Ft--zSD% a6Fl--z6DO, a6F4--#D% aSFa--zSD% a~Ft--zSD%

15.6 14.9 12.1 4.0 9.8 7.2 10.2 9.7

5171.60

aaF,--ztFJ4

7.1

II

5227.19 5167.49

aS.Fs--zSD~z aSF4--zSD%

36.0 35.0

33 29

5254.96 5250.21 5247.07 5225.53 5204.58 5168.90 5166.29 5110.41

a'Do--z~D., aSDs--z'DO s aSDz--z~Da, a6D,--z'DO 2 aSD,--z'D% aSm4--zTD% a~D4--z~D o,

5150.84 5142.93 5127.36 5123.72 5083.34 5079.74 5051.64 5041.07 5012.07 4994.13 4939.69

aSF2--#F% aSF3--zSF% a6F4--zSFO5 aSF,--z6F% aSFa--z6Fa a a6F2--zSF ~, aSF4--zSFa, aSF,--zSF% aSFs--z6F% a6F4--z6F% a6Fs--zSF%

0.71 0.53 0.31

4602.94 4592.66 4531.15

aSF,--y'*FO 6 a*Fs---y6F% aaF,--ySF%

3.34 2.30 3.87

11.2

2.24 0.65 1.45

0.034 0.068 0.014 0.031 0.067 0.086 0.039 0.098

0.052

0.076 0.039 0.084

1.54

0.72 0.64 0.84 0.78 0.99 0.47 0.21

1.o0

13

R E L A T I V E OSCILLATOR STRENGTHS FOR L I N E S OF

Fe I

TABLE I (continued) Wavelength

Multiplet (i-values)

Measured /-value

4489.74 4482.17 4466.55 446|.65 4435.15 4427.31 4389.24 4375.93

aSDo--z~Fq

0.60

0.63

aSD,--zTF'2 aSDx--z~F% aSD2--zTF% a~D~--zTF~,

0.57

0.54

a~Da--zTF"~ a~Da--zTF.** a~D,--zTF.~

4415.13 4404.75 4383.55 4337.05 4294.13

anF~--zSGna a~Fa--zSGO4 aaF4--zSG% aaFa--zSG"a aSFa--zSG%

4291.47 4258.32 4216.19 4206.70

a~Ds--zTP%

4325.77 4307.91 4271.76 4250.79

a, F.--zaGL'a aSFs--zaG% a'F4--zaG% a*Fa---zaG%

840 540 350 120

760 470 270 130

4143.87 4132.06 4071.74 4063.60 4045.82 4005.25 3969.26

aaFa--yaF1, aSFi--y3FOa a'F,--y'F% a*Fa--ySFJa aSF4--ySFJ, aaFs--yaF% a~F4--y;F'a

194 220 850 690 836 159 179

200 220 760 610 670 170 170

3872.50 3865.53 3849.97 3834.23

a,~Fs--ySD ', aSFt--ySDh aSFt--ynD*o aSFa--ySDa,

102 166 224 264

82 140 170 210

1 3902.98 3888.52 3827.83 3815.84

aaFa--y~D% aSFz--Y aD ~z aaFa--y~D', aaFi--ySD%

226 215 564 460

260 240 670 580

3930.30 3927.92 3922.91 3920.26 3906.48 3899.71 3895.66 3859.91 3856.37 3824.44

a~D.--zSD"a a6Dt--z~D'.. a,Ds--zSD~4 a~D,--z6D~t aSDl--z~D~t aSDs--zSDe.. a~Dl--#D~o aSD,--zSD*4 aSDa- z S D '2 a6D4--zSD~

a~Dz--zTP% aSD4--z~p,' 4 a6Da--z~P.'.~

King's /-value

0.080 0.63 0.046 0.62 0.041

I

0.I0

0.58 0.048 0.61

0.034 0.49

0.53 220

200 430 650

456 730

19

14.9 42

42 0.064 0.076 0.24 0.086

0.076 0.066 0.197 0.089

i

14.6 24.4 10.9 68 8.3

14.0 16.9 30 17.6 10.6

16 23 8.3 48 6.3

14 17

! I I

29 16 9.7

1fi57

1258

RELATIVE OSCILLATORSTRENGTHS FOR LINES OF

Fe I

urnace, viz. a c o n s t a n t t e m p e r a t u r e a n d a c o n s t a n t c o n c e n t r a t i o n of the •a d i a t i n g v a p o u r . T h e i n v e s t i g a t i o n is being c o n t i n u e d in this direction. T h e a u t h o r s wish to t h a n k Mr P. J. V a n d e r R o e s t, technical chief ~f the Z e e m a n l a b o r a t o r y a n d Mr H. R. S c h a n s, i n s t r u m e n t m a k e r , for :heir v a l u a b l e technical services. Yeceived 23 September 1954.

REFERENCES 1 2) 3,) 4) 5) 6) 7) 8) 9) 10)

V a n ,M i 1 a a n, J. B., Z. Phys. 34 (1925) 922. Frerichs, R., Ann. Physik 8 ! (1926) 807. Burger, H . C . and D o r g e l o , H . B . , Z . Phys. 23(1924) 258. Van Driel, H., Dissertation, Utrecht 1935. Ornstein, L . S . and B r i n k m a n , H., P h y s i c a l (1934)~797. K i n g , R. B. and K i n g , A. S., Astr. J. 82 (1935) 377; Astr. J. 87 (1938) 24; Astr. J. 95 (1942) 78. Carter, W. W., Phys. Rev. 76 (1949) 962. K i n g, A. S., Astr. J. 56 (1922) 318. R e i n d l, H. P., Dissertation, Utrecht 1946. V a n d e r H e l d , E. F. M.,Z. Phys. 70 (1931) 508.