June 1966

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 56, NUMBER 6

Studies of the Zeeman Effect Using Strong Pulsed Magnetic Fields*t

SAM H. LOTT, JR., CHARLES E. Roos, AND MARSHALL L. GINTERt

Department of Physics, Vanderbilt University, Nashville, Tennessee 37203

(Received 4 December 1965)

Pulsed magnetic fields of -270 kG which are repeatable to <1% from pulse to pulse have been usedto produce the Zeeman effect in a number of electronic transitions for 0 II, 0 III, Si I, Si III, Si iv, Cu II,C I, C III, Ca II, Mg I, Mg II, and B I. The reliability of the method has been checked by comparison of theresulting experimental g values both with theoretical Land6 g factors and, when data exist, with earlierZeeman work performed using conventional field strengths (-25 kG). A total of 109 previously unpublishedg values are reported, with the listings for the above, oxygen and silicon species being the more complete.The over-all uncertainty in the reported g values is believed to be in the range 1%-3%. While the magnethas been used above 400 kG in other experiments, assymetries were becoming apparent below 300 kG. There-fore, data for this work was restricted to 270 kG where strong LS coupling was observed to hold with fewexceptions (primarily 3d terms of 0 II). It is believed the method described should be of most utility in thedetermination of atomic transition types from their characteristic Zeeman patterns.INDEX HEADINGS: Atomic spectra; Zeeman effect; Silicon; Copper; Carbon; Oxygen; Calcium; Magnesium;B oron.

INTRODUCTION

W E present here a simple and convenient methodfor the observation of atomic Zeeman patterns

using strong pulsed magnetic fields. Such pulsed-fieldmethods first were employed by Kapitsa,' who createdpulsed (half sine wave) magnetic fields of -200-

* Work supported by the U. S. Army Missile Command contract#DA-33-008-AMC-131(Z) and the National Science Foundation.

t Based on a dissertation (SHL) submitted in partial fulfillmentof the requirements for a PH.D. degree at Vanderbilt University(1965). Preliminary discussion of the results given at APS Wash-ington meeting; S. H. Lott, C. E. Roos, and M. Ginter, Bull. Am.Phys. Soc. 8, 300 (1963).

t Present address: Department of Physics, University of Chi-cago, Chicago, Illinois 60637.

1 P. Kapitsa, Proc. Roy. Soc. (London) A167, 1 (1938).

320 kG by momentarily short-circuiting a large, low-impedance generator across a helical air-core magnet.In Kapitsa's work, each spectroscopic exposure utilizedthe light from a single spark or flash. However, withthe present methods, fields of -400 kG can be producedwhich are reproducible to < 1% from pulse to pulse-with which Zeeman patterns can be obtained for spec-troscopic transitions of even relatively low intensity.In addition, high magnetic fields make it feasible toobtain well-defined patterns with a spectrograph of rela-tively high aperture and modest dispersion. Thus, themethods to be discussed are especially adaptable forgeneral diagnostic purposes in the assignment of tran-sition types, and the determination of atomic g valuesto within a few percent.

775

JUNE 1966

LOTT, ROOS, AND GINTER

EXPERIMENTAL PROCEDURES

The most important features of the experimental sys-tem are the magnet, electronic control circuits,2 spec-troscopic source, and spectrograph. The magnet coreconsists of about 100 overlapping copper-alloy disksfitted together to form a continuous helical coil. Thinmeline disks are used to insulate neighboring turns. Afiberglass-epoxy cylinder is placed around the coil anda 2-in.-thick meline disk is placed over each end of thecoil for insulation. The coil and surrounding insulationare then put in a 1-in.-thick stainless-steel cylinder with11-in.-thick end plates for containment. Steel bolts4X 12 in. are used to pull the steel end plates togetherand make a tight package. The oil-cooled magnet usedin the majority of the experiments has an i.d. of 1.2 cm,a field uniform to better than 2% over a 5.5-cm length,and an inductance of - 10 /iH. The pulsed currents usedto produce the magnetic fields were provided by a 4-kV,4.3-mF capacitor bank; all switching was done byignitrons. The half-period of the magnetic field wasapproximately 700 gsec.

The spectroscopic source was a 6-mm-i.d. Pyrex flashtube with copper electrodes designed so that the flashwas localized in the uniform portion of the axial mag-netic field. The electrical pulse to the flash tube, lasting-25 ,tsec, was produced by discharging 3 AF at 2000-

3000 V through the tube. In order to use the light froma number of flashes on a single spectroscopic exposure,it is critically necessary (a) that each flash occur exactlyat the peak of the field intensity and (b) that the peakfield value remain constant from pulse to pulse. Condi-tion (a) was fulfilled by use of electronically controlledtime delays (between the initiation of the pulse to themagnet and the pulse to the flash tube) which werestable to 1 gsec. Condition (b) was fulfilled by accuratelycontrolling the time intervals between pulses to themagnet so that the charging time for the magnet capa-citors was the same from one pulse to the next (i.e.,presenting an identical voltage to the magnet circuitat each discharge). These procedures yielded magneticfields which are reproducible to better than 1%.

The majority of the spectra were photographed usinga Jarrell-Ash 3-m Wadsworth spectrograph (recip. disp.-11 A/mm in the first order). Iron-arc lines were used

for wavelength standards, while values for the mag-netic fields were determined' to - 1% from the Zeemanpatterns of the Cu i lines at 3273.957 A and 3247.540 Ain combination with the accurate g values of Kiess4 and

2 Only a brief outline of the methods and results are given here.A complete discussion, including details of construction of appa-ratus and the original experimental data, can be found in thethesis of Sam H. Lott, "High Field Zeeman Studies" (1965),which can be obtained from the Joint University Library, Vander-bilt University, Nashville, Tennessee 37203 or from UniversityMicrofilms, Ann Arbor, Michigan.

I The magnetic fields also were measured to within -4% usingpickup coils; the results were used as a check of the field strengthsdetermined from the Zeeman patterns of Cu i.

4 C. E. Moore, Atomiiic Energy Levels (National Bureau ofStandards, Washington, D. C., 1949), Vol. I; (1952), Vol. II.

of Ting and Lew.' All measurements were made by thesupcrposition of optical-density profiles using a Grantphotoelectric scanning comparator. Spectral-line quality(from the 3-m spectrograph) and line width (the flashlamp produced relatively broad lines) were the majorfactors in the over-all experimental errors.

As a check on the over-all reliability of the method,Zeeman patterns were analyzed for approximately 120electronic transitions of 0 ii, 0 iII, Si i, Si iII, Si Iv, andCu II. Most of the g values obtained for 0 II and 0 iIIcould be compared with values calculated from the dataof Mihul,6 while those for Cu ii could be compared tovalues calculated from Shenstone's7 data. In general,the disagreement between the g values determined fromprevious works and those obtained from the presentexperiments was in the range 1%-3%.

DISCUSSION

Since the experimental arrangements described abovepreclude observations perpendicular to the magneticfield, g values were determined only for Zeeman patternswhich were symmetric (within experimental errors)about their zero-field line.8 Both resolved and unresolvedZeeman patterns were used to determine g values. Re-solved patterns were treated according to the method ofBack and Lande9 while the procedures of Shenstone andBlair' 0 and of van den Bosch" were employed for un-resolved patterns.

As mentioned in the previous section, a number ofZeeman patterns for 0 II and 0 iII were observed byMihul6 using a conventional dc magnet with field of-26 kG. In the present work, Zeeman patterns for 32lines of the 0 ii spectrum and 25 lines of the 0 iII spec-trum were recorded2 using magnetic fields up to 266 kG.For resolved patterns, the g values determined from thetwo sets of data are in good agreement. Since almost nog values have been reported for these species, the datawere combined to produce the "best" set of experimentalvalues listed in Tables I and II. Except where indicated,the experimental g values in these tables are averagesof the valuesufrom Mihul's data and the present work,the deviation from the average being in the range40.01-0.02. Theoretical Land6 g values,4 based on the

assumption of LS coupling, are also listed. It is immedi-

5 Y. Ting and H. Lew, Phys. Rev. 105, 581 (1957).6 C. Mihul, Ann. Phys. 9, 294 (1928).7A. G. Shenstone, Phys. Rev. 29, 380 (1927); Phil. Trans. Roy.

Soc. (London) A235, 195 (1936).8 Except when a given Zeeman pattern is completely sym-

metrical about the zero-field line, both the a and 7r components(from observations parallel and perpendicular to the magneticfield, respectively) must be used in the determination of g (see Ref.9). The magnet used here has been utilized in other experimentsto generate fields above 400 kG. This work was purposely limitedto 270 kG.

9 E. Back and A. Land6, Zeeiizaneject and Multiplett-Strukturder Spektrallinien (Julius Springer, Berlin, 1925).

"A. G. Shenstone and H. A. Blair, Phil. Mag. 8, 765 (1929).1'J. C. van den Bosch, in Encyclopedia of Physics (Springer-

Verlag, Berlin, 1957), Vol. 28, pp. 296-332.

776 Vol. 56

ZEEMAN EFFECT USING STRONG PULSED FIELDS

TABLE I. g Values for 0 II.,

Desig.b J Land6 Exp.c Desig.b J Land6 Exp.,

3s" 2 S 2 2.00 (1.97) 3d' 2S 4 2.00 2.03*d3s 2 2 4 0.67 0.68 3d 2P 4 0.67 0.67e3s 4P 2 2.67 2.69 3d'MI 2 0.67 0.70d3s 2P 14 1.33 1.33 3d 4P I 2.67 1.90d~f3s'1 D 1- 0.80 0Q84d 3d 4

D I 0.00 0.77d.f3s 4P 12 1.73 1.74 3d 2p 14 1.33 1.33e3s1 'D 22 1.20 1.17d 3d 2P 14 1.33 1.38d3s 4P 22 1.60 1.60 3d 2D 12 0.80 0.803p IS' 4 2.00 2.02e 3dI D 14 0.80 0 .83d3p 2p0 4 0.67 0.66 3d 4P 14 1.73 1.6 0d3p/2pO 4 0.67 0.69d 3d 4F 11- 0.40 0.42d3p" '2PO 4 0.67 (0.63) 3d 2D 22 1.20 1.203p 4P0 4 2.67 2.65 3d' D 21 1.20 1.16d3p

4D

0 4 0.00 0.03 3d"'D 24 1.20 (1.06)3p2 P0 14 1.33 1.34 3d2F 24 0.86 1.06*d3p'2'PI 14 1.33 1.37d 3d' F 24 0.86 0.8 6d3p" 2P0 14 1.33 (1.27) 3d 4P 22 1.60 1.57°

3p 'DI 14 0.80 0.79 3d 4D 24 1.37 1.31*d3p' 2D° 14 0.80 0.82d 3d 4F 24 1.03 1.lO*d3p 4S° 12 2.00 2.000 3d 'F 34 1.14 1.16*3p 4P0 14 1.73 1.74 3d'2F 34 1.14 1.lOd3p 4D° 14 1.20 1.19 3d' 2G 34 0.89 (0.97)3p 2D° 24 1.20 1.20 3d 4D 34 1.43 1.43d3p'2D° 22 1.20 1.19d 3d 4F 314 1.24 1.18*d3p' 'F° 24 0.86 0.86d 3d' 2G 44 1.11 (1.12)3p 4P° 24 1.60 1.60 3d 4F 42 1.33 1.32*3p 4D0 24 1.37 1.37e 4s 2P 14 1.33 1.383p' FF 34 1.14 1.13d 4s 4P 21 1.60 1.6103p 4

D0 32 1.43 1.43d

a For a complete listing of the original spectroscopic data, see Ref. 2.The data are grouped by configurations. Values marked by an asterisk (*)were obtained from unresolved patterns only. Parentheses indicate valuescalculated from the g-sum rule (see text). The theoretical Lande valuesassume pure LS coupling.

b The designations of atomic states are those of Moore (Ref. 4).o Except where indicated, the quoted experimental values are the averages

of g calculated from both Mihul's data and the present work. In general,the deviations from the average value are in the range :1=0.01-0.02.

d From Mihul's data only.o From the present work only.f The apparent g values for these states differ considerably from the

theoretical Lande values, indicating departure from LS coupling. However,the theoretical and experimental g sums involving these terms differ by onlyI%.

ately evident from Tables I and II that, with the excep-tion of a few terms from the 3d configurations of 0 I, theexperimental and the theoretical g values agree withinthe experimental errors (i.e., 3% or better) indicating

TABLE II. g Values for 0 III.0

Desig.b J Land6 Exp.' Desig.b J Land6 Exp.'

3s 'P 1 1.00 1.01 3d 3P0 2 1.50 1.52d3s 3P° 1 1.50 1.51 3d 3D° 2 1.17 1.18d3s 'P 0 2 1.50 1.50 3d 3F

0 2 0.67 0.66*03p'P 1 1.00 1.03d 3d'FF 3 1.00 1.003p 3S 1 2.00 1.99d 3d 3D' 3 1.33 1.35d3p 'P 1 1.50 1.51d 3d 'F0 3 1.08 1.08d3p ID 1 0.50 0.51 3d 3F° 4 1.25 1.24*d3p 'D 2 1.00 1.01 4p 3D 3 1.33 1.30*d3p 3P 2 1.50 1.49 3s 3P 2 1.50 (1.48)d3p 3D 2 1.17 1.17 3s 5P 2 1.83 1.85*d3p 'D 3 1.33 1.33d 3s 5P 3 1.67 1.70d3d 1P] 1 1.00 1.03d 3p 5]P 3 1.67 1.70d3d 3P° 1 1.50 (1.45)d 3p 'D0

4 1.50 1.35*-3d 3D° 1 0.50 0.52d 3d IF 5 1.40 1.34*-3d 'D0 2 1.00 (0.98)

a See footnote a of Table I.b See footnote b of Table I.c See footnote c of Table I.

d From the present work only.e From Mihul's data only.

TABLE III. g values for Si I, Si III, and Si IV.0

Species Desig.b J Land6 Exp.

Si I 3p2 3P 1 1.50 1.523p2 'D 2 1.00 1.013p2 3P 2 1.50 1.504s 'P0 1 1.00 0.994s 3P

0 1 1.50 1.524s'P 0 2 1.50 1.493d 'P0 1 1.00 1.003d ID' 2 1.00 1.02

Si III 3p2 ID 2 1.00 0.98

3p 1'P 1 1.00 0.983d ID 2 1.00 0.994s 'S 1 2.00 2.004p 'P0 1 1.00 1.014p3P' 1 1.50 1.554p3P0 2 1.50 1.494d' D 2 1.00 1.00

Si IV 4s 2S - 2.00 1.984p 2PO 1 0.67 0.722p 4'P 14 1.33 1.344d 'D 24 1.20 1.16*5p 2P

0 14 1.33 1.34*

3 For a complete listing of the original spectroscopic data see Ref. 2.Values marked by an asterisk (*) were obtained from unresolved patternsonly.

b See Ref. c of Table I.

strong LS coupling even for fields of 270 kG. Thus, italso follows that the g sums 12 are in agreement with thetheoretical values. In cases where only one g value in agiven g sum was undetermined experimentally, the theo-retical sum and the sum of the known experimental g'swere used to calculate the remaining "experimental" gvalue. Such calculated g values appear in the tablesenclosed in parentheses.

As a further check on the method, g values were de-termined from the Zeeman patterns2 for 9 lines of the

TABLE IV. Miscellaneous g values.a

Species Desig.b i Land6 Exp.

Cu II 4s2 "G 4 1.00 0.98

C I 3s 'P0 1 1.00 0.97

C III 2p 'PI 1 1.00 1.012p2 'D 2 1.00 1.01

Ca II 4s2S - 2.00 2.014p 22) 4 0.67 0.664p 2p0 14 1.33 1.34

Mg I 3p 'PO 1 1.00 1.00

Mg II 3S 2S 2 2.00 1.9603p 2PO 1 0.67 0.6903p 2'P 14 1.33 1.33'

B I 3s'S 4 2.00 1.92'2p 2P] 4 0.67 0.6702p 2p' 14 1.33 1.30'

3 See Ref. a of Table I.b See Ref. b of Table I..Any deviation from the theoretical Lande values is of questionable

significance, since the field patterns used in the determination of this gvalue are in the transition from Zeeman to Paschen-Back patterns.

12 E. U. Condon and G. H. Shortley, The Theory of Atomnic Spec-tra (Cambridge University Press, Cambridge, 1951).

777June 1966

LOTT, ROOS, AND GINTER

Si I spectrum, 7 lines of the Si in spectrum, and 6 linesof the Si iv spectrum. While no other Zeeman data havebeen published for these species, the theoretical (assum-ing LS coupling) and experimental g values can be com-pared in Table III. The agreement between theory andexperiment is better than -202%, indicating that thecoupling of the atomic states of Si i and Si iII listed inTable III is LS within our experimental error. It is notparticularly enlightening to speak of LS coupling in thecase of Si iv, since (for the configurations observed inour experiments) we are dealing with a simple one-electron spectrum. It should be noted that the lines ofthe Si iv spectrum were especially broad and difficultto measure accurately, so that the uncertainties in theg values for Si iv are roughly a factor of two larger thanthose for the other measurements discussed here.

In addition, a few Zeeman patterns for a varied as-sortment of atomic species were observed in conjunctionwith the spectra discussed above. In this miscellaneousgroup, the most prominent species was Cu ii, for whicha number of Zeeman patterns have been previously re-ported by Shenstone.7 Shenstone's patterns were thebasis for the g values for Cu ii reported by Moore.4 The28 patterns observed in the present work2 provided onlyone g value in addition to those already reported. Thisvalue is listed on Table IV, together with several pre-viously unreported g values for six other species. Itshould be noted that McNally"3 has published the ratioof two of the g values for Ca ii reported in Table IV.McNally reports g(2SO)/g(P i) = 1.5013 while thesame ratio taken from Table IV is 1.50.

Although we have emphasized that Zeeman patternsobtained from the present methods can be used to cal-culate reliable g values, we should re-emphasize thatwe used only patterns symmetric about the zero-fieldline. With the experimental arrangements describedabove, it is not possible to obtain reliable g values in thepresence of the Paschen-Back effect or other strong per-turbations because only the a components of the fieldpatterns are observed.8 However, this feature does not

13 J. R. McNally, Jr., Phys. Rev. 73, 1130 (1948).

impair the usefulness of the onservec patterns as aidsto assignment of atomic-transition types. The methodsdiscussed above are particularly well adapted to the useof high-aperture, moderate-dispersion spectrographs,and hence to studies of relatively low-intensity transi-tions. The experimental system could be modified easilyfor study of transitions occurring in the vacuum ultra-violet, a relatively unfavorable region for the resolutionof conventional field-strength Zeeman patterns.

The parallel polarization might be extracted witha mirror arranged at an angle with the tube axis andsufficiently long to receive light from the length of thetube. This modification would necessitate a larger-boremagnet and would yield lower light levels than the end-on system employed in the present work. Helical mag-nets have also been made with a port cut in the side forviewing perpendicular to the field; however, the avail-able light from this arrangement would be even less thanfrom the mirror system described above.

Line widths possibly could be improved by utilizinga constant discharge exposed only during peak mag-netic fields by means of a Kerr cell. A similar systemalso could be used for studying Zeeman effects in ab-sorption. In either case, a major advantage resultingfrom the use of a Kerr cell would be greater freedom tovary the excitation conditions, and hence, the possi-bility of studying a greater variety of atomic or molecu-lar species. However, a system utilizing a Kerr cellwould have several disadvantages. The Kerr cell wouldreduce the light intensity at least by half even if it isassumed that a discharge can be produced which oper-ates continuously and yields emission intensities com-parable to those from flash tubes. In addition, the Kerrcell would be limited to observation in the visible regionbecause of its absorption characteristics.

ACKNOWLEDGMENTS

The authors are indebted to Professor K. K. Innesfor the use of his laboratory facilities and for many help-ful discussions. Also, the suggestions and continued in-terest by Dr. John Barach, Dr. C. W. Mathews, andDr. J. E. Parkins, are gratefully acknowledged.

78 Vol. 56