S12−P12 - Lambshift in the n=5 state of ionized helium

Volume 43A, number 2

S112

PHYSICS LETTERS

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26 February 1973

LAMBSHIFT IN THE n5 STATE OF IONIZED HELIUM M. BAUMANN and A. EIBOFNER University of Tubingen, Germany Received 2 January 1973

Radio frequency induced transitionsbetween the 5 S1,2 (m1/2) and the 5 P3,2 (m—1/2) state in He+ have been detected and a value for the 5 S112 — 5 P112 - Lambshift of (909.2 ±7) MHz has been deduced, which agrees well with the theoretical value of 906.0 MHz.

The S1~2 P112 Lambshift in the n5 state of hydrogenlike systems has so far been measured in two experiments. The results were (64.6 ±5.0) MHz for hydrogen [1] and (1098 ±147) MHz for ionized helium [2] The theoretical values are 68.1 and 906 MHz, respectively [3]. In this paper we report on a measurement of the 5 S112 5 P1~2shift in He~by means of a radio frequency method. The experimental arrangement was similar to that in our former investigations [4]. The Zeeman sublevels of the n=5 state of He+ were populated by collisions between neutral helium atoms (pressure 5 X i0~torr) and 300 eV electrons (20 mA), which travelled parallel to the magnetic field. By an electric r.f. field perpendicular to the magnetic field, and the 5 P transitions between the 5 S1,2 (m1/2) 312 (m=—1/2) sublelvels have been induced, resulting in a change of the intensity of the 3203 A line (n=5-+n=3). This spectral line was selected with a monochromator and detected by a photomultiplier. For the lock-in detection of the resonance signal, the electric r.f. field was square wave modulated. The magnetic field was swept through the resonance at a fixed r.f.The frequency. positions of the resonance signals are displaced by the static electric field in the interaction region, which consists of several parts: the motional electric field seen by the ions moving perpendicularly to the magnetic field, the space charge field and stray fields. In order to account for these displacements, the dependence of the energy of the Zeeman sublevles involved in the experiment on the electric field components Er and E~perpendicular and parallel to the magnetic field, respectively, was computed by diagonalization of the Hamiltonian of the n5 state of He~.The elec—

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tric field components were determined from the experiment as follows: R.f. transitions at the magnetic field strengths Ha and Hb on both sides of the crossing of the two undisturbed Zeeman levels have been detected (fig. 1 a). Ha and Hb are displaced towards each other approximately proportional to E~,the shift of R~slightly exceeding that of Hb. In our special case, the component E~is much less effective. To obtain the component Er we compared the experimental difference L~H=(Ha —Hb) with the corresponding theoretical difference ~H’ for Er E~= 0. The difference ~H’ is practically independent of the Lanbshift (S1,2 P1~2)and of the fine structure splitting (P3~2 P1~2).From the deviation (i.~H’—~R) (about 4 G in the experiment) Er can be 11b~480 deduced.pairs To determine the positions ofHa and of signalcurves have been measured at eight frequencies of the r.f. field varying from 600 to 1000 MHz (fig. Ib). In order to reduce the data and to improve the signal to noise ratio, groups of five signal curves obtained under comparable conditions have been summed up (fig. lc) and fitted with a Lorentzian function. From the deviation (~H’ ~H), obtained. a value The squared 2 has been E~ (26 ± 12) (V/cm) motional electric field was computed to be (38 ±15) (V/cm)2 assuming a gas temperature of (400±lOO)°K. Consequently the other contributions to E~are small compared to the motional electric field. With the monochromator used in the experiment the 3203 A line could not be separated totally from the spectral lines close by. Therefore the possibility disturbing resonance signals was considered. But within the precision of the experiment there was no indication for the existence of such effects. For evaluation of the measurements the experimen—

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Volume 43A, number 2 V

PHYSICS LEUERS

26 February 1973

G with a statistical 3o error of 1 .7 G. This value has

1GHz)

:J~:::;~::~ s;

Kb

as

1j~i:I/2)

H0

been corrected for the dependence of the transition matrix element on the magnetic field, for the small superposition of the two resonance curves, for Zeeman curvature and for the uncertainty of Er and E~.For a maximum value of 5 V/cm was assumed. Each of thesewas(—0.1 tion corrections ±2.0)G. was less than 0.15 G, the total correcWith regardthe to experimental these corrections difference between and the the average theoretical value for (ILa + 11b)12 is (—1.7 ±3.7) G equivalent to (—3.2 ±7) MHz. This corresponds to a 5 P 3,2 —5 S1,~2

Er~3O 0 V/cm Er~

I

6~5,

5

H (kG)

splitting of (10 328.7 ±7) MHz. By accepting a theo-

retical fine structure splitting 5 P3,,2 5 P1,,2 of 11 237.9 MHz, the result for the 5 S1,,2 5 P112 Lambshift is (909.2 ±7.0) MHz (theory 906 MHz). —

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1,

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4.5

I

s

We like to thank Professor H. Kruger for his interest and the continuous support of this work. I

s.s

H (kG)

Fig. 1. a) Energy diagram of the Zeeman sublevels for Er = 0 and Er = 30 V/cm. In the experiment, Er was about 5 V/cm and the shift of Ha and Hb were much smaller. b) Typical signal curve (time constant 10 sec). c) Average of five signal curves (arbitrary units).

2 have been compared with tal values the theoretical for (Ha ones. + Hb)/ The average deviation was 1.6 —

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References [1 C.W. Fabian, F.M. Pipkin and Lett. 26 (1971) 347.

M. Silverman, Phys. Rev.

[2] E.G. Kessler and F.L. Roesler, J. Opt. Soc. Am. 62 (1972)

440. [3] J.D. Garcia and J.E. Mack, J. Opt. Soc. Au. 55 (1965) 654. (slightly corrected according to: T. Appelquist, S.J. Brodsky [4] A.Phys. Eibofner, Z. Physik (1971) 58, 73; Rev. A2 (1970) 249 2293). M. Baumann and A. Eibofner, Phys. Lett. 34A (1971) 421.