HAL Id: jpa-00218388
https://hal.archives-ouvertes.fr/jpa-00218388
Submitted on 1 Jan 1979
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
THE LAMB SHIFT IN HYDROGENLIKE ARGON
Harvey Gould, Richard Marrus
To cite this version:
JOURNAL DE PHYSIQUE
Colloque
C1,suppldment au n
O2,
Tome 40, fdvrier 1979, page C1-30
THE LAMB SHIFT IN HYDROGENLIKE ARGON
Harvey Gould and Richard Marrus
Materials and Molecular Research Division, Lawrence Berkeley Laboratory and Department of Physics, University of California, Berkeley, CA 94720
Resume. Le deplacement Lamb S dans l'argon hydrogenoide (Z=18) a btb mesa6 dans une expeience de temps de vol avec quenching en champ Blectrique. Nous trouvons S=(38,0+_0,6) THZ 05 l'erreur inclut 1'errew statipe la de 0,35 THZ et une erreur systematique es- timee 2 0.48 THz.
Abstract. The Lamb shift
S
in hydrogenlike argon (Z=18) has been measured by a motional electric field quenching time-of-flight experiment. We find S = (38.0+
0.6) THz where the error includes 10 statistical error of 0.35 THz and an estimated systematic error of 0.48 THz.INTRODUCTION
The comparison between theory and experi- ment of the Lamb shift is the most rigorous and precise test of the quantum electrodynamic corrections to the binding energy of a charged particle in a Coulomb field [l]. Experiments in hydrogenlike atoms of high nuclear charge Z test the theory for a strong Coulomb field and in the region where the higher order corrections to the binding energy are relatively more important
[I].
If one writes the Lamb shifts as a power series in a and Za (wherea
is the fine structure con- stant), then the largest terms have the form:The term c4a(za)' is the highest order term which has so far been calculated in the series expan- sion. At Z=1 it contributes 0.016% but accounts for 12% of the Lamb shift at Z=18. Even allowing for the greater experimental precision attainable at Z=1 current experiments [2] at Z=1 and Z=18 are of comparable sensitivity to deviations in this term. In testing still higher order terms, a high Z measurement offers a substantial advant- age in sensitivity. The slow convergence of the series expansion has prompted theoreticians to seek- alternate approaches to the calculation of the Lamb shift. One by Erickson [3] is an analytic app,roximation to the uncalculated terms in the series expansion. Another by Mohr
[4J
is a direct numerical evaluation of the selfenergy to all orders in ZQ. The two calculations yield slightly different values. The difference
6
scales roughly as Z
.
To date, Lamb shift measure- ments on hydrogenlike ions through Z=9 have been reported [2]. In this talk we report a measure- ment of the 2SIl2-
2PlI2 energy splitting (Lamb shift) of hydrogenlike argon (Z=18). We find S = (38.0*
0.6) THz which may be compared to values of S = (39.0 f 0.16) THz calculated by Erickson [3] andS
= (38.25 ? 0.025) THz calculated by Yohr [4]. This comparison constitutes the most rigorous test of QED at high field strengths El].EXPERIMENTAL METHOD
Our experiment is performed by measuring the electric field quenched lifetime of the meta- stable 2SlI2 state. At Z=18 the unperturbed state decays predominantly by the simultaneous emission of two electric dipole photons. A decay rate [5]
8
of 2.76 x 10 sec-I is associated with this mode. There is also a relatively slow, single-photon magnetic dipole channel with a rate [5] A = 9.08
6 -1
x 10 sec
.
The frequency distribution of the emitted photons therefore consists of a continuous spectrum centered about 1659 eV falling rapidly to zero at the end points plus a small peak at the 2SlI2-
1SlI2 energy separation of 3318 eV.The application of an external electric field mixes the wavefunctions of the 2s state
112 with the nP states. Since P states decay by fully allowed electric dipole radiation, the 2SlI2 lifetime is shortened. To lowest order the decay
rate R o f t h e 2Slf2 s t a t e a s a f u n c t i o n o f e l e c t r i c f i e l d i s g i v e n by [ 6 ] :
where Rs and R a r e t h e n a t u r a l 2 s and 2P decay P
r a t e s , S i s t h e Lamb s h i f t i n r a d i a n s p e r second and V i s t h e r e l a t i v i s t i c e l e c t r i c d i p o l e m a t r i x element: V = 0.992
6
eEa / Z where e i s t h e e l e c t r o n c h a r g e , E t h e e l e c t r i c f i e l d i n e s u and a. t h e Bohr r a d i u s . An e l e c t r i c f i e l d i n t h e atom's r e s t frame i s produced by p a s s i n g atoms a t a v e l o c i t y o f v = 4 x 10' cm/s t h r o u g h a homogeneous magnetic f i e l d . A t a f i e l d o f B =5
1 6 kGauss, t h e 6 . 5 x 1 0 V/cm e l e c t r i c f i e l d produces a quench r a t e comparable t o t h e n a t u r a l 2SlI2 decay r a t e . The Lamb s h i f t c a n t h u s b e d e t e r m i n e d by measuring t h e v e l o c i t y , m a g n e t i c f i e l d and quenched l i f e t i m e .
The magnetic f i e l d i s measured w i t h a n i n t e g r a t i n g f l u x m e t e r c a l i b r a t e d a g a i n s t a n u c l e a r m a g n e t i c r e s o n a n c e Gauss m e t e r . The v e l o c i t y i s d e t e r ~ i n e d t o 3 few p a r t s p e r thousand. by measuring t h e beam e n e r g y ( a p p r o x i m a t e l y 340 MeV) w i t h s u r f a c e b a r r i e r d e t e c t o r s which h a v e been c a l i b r a t e d a g a i n s t a m a g n e t i c a l l y a n a l y z e d a r g o n beam o f 346 MeV. E r r o r s from t h e s e v e l o c i t y and magnetic f i e l d measurements make no s i g n i f i c a n t c o n t r i b u t i o n t o t h e Lamb s h i f t e r r o r .
L i f e t i m e s o f t h e 2 s s t a t e a r e 112
measured by beam-foil t i m e - o f - f l i g h t . Bare 9 a r g o n n u c l e i , a t v e l o c i t i e s of 4 x 1 0 cm/s o b t a i n e d from t h e Lawrence B e r k e l e y L a b o r a t o r y
2 SuperHILAC a r e p a s s e d through 8 ug/cm c a r b o n f o i l l o c a t e d i n a homogenous magnetic f i e l d ( F i g . 1 ) . Among t h e n u c l i i which c a p t u r e e l e c t r o n s t h e r a t i o o f h y d r o g e n l i k e atoms t o h e l i u m l i k e atoms is 1 7 : l . The l i t h i u m l i k e f r a c t i o n i s t o o s m a l l t o d e t e c t i n o u r a p p a r a t u s , however, from t h e known c a p t u r e c r o s s s e c t i o n and f o i l t h i c k n e s s we e s t i m a t e t h e r a t i o of h y d r o g e n l i k e a r g o n t o l i t h i u m l i k e a r g o n t o b e a t l e a s t 5 0 0 : l . X-rays from d e c a y s i n . f l i g h t o f t h e e x c i t e d s t a t e s a r e o b s e r v e d a t a d i s t a n c e o f a p p r o x i m a t e l y 0 . 6 m e t e r s from t h e beam by a p a i r of S i ( L i ) x-ray d e t e c t o r s . A t y p i c a l p u l s e h e i g h t s p e c t r a i s shown i n F i g . 2. The raw d a t a f o r t h e 2 s decay c u r v e s i s t h e
112 p u l s e - h e i g h t s p e c t r a measured a s a f u n c t i o n o f x-ray d e t e c t o r p o s i t i o n downstream of t h e f o i l . The i n t e n s i t y is normalized t o t h e i n t e g r a t e d
Magnet pole t i p 4
n
7ncmX-ray
I
\Movable
SI (Li) x-ray detector
\
11
JOURNAL
DE
'PHYSIQUE1500 eV the sensitivity of the detector drops rapidly to zero. In addition to the 3318 eV line from ly decay of hydrogenlike Ar there are weaker lines at 3126 eV and 3104 eV from decays
3 3
of 2 P2 and 2 S1 states of heliumlike Ar. The hydrogenlike line can be separated from the heliumlike lines by computer fit.
current obtained by stopping the beam in a Faraday cup. The comparable intensities in the quench peak and two-photon spectra enable us to con- struct decay curves from either portion of the spectra.
ANALYSIS OF DATA
The raw data must be corrected for deflection of the beam in the magnetic field. In addition to the change in solid angle and change in length of the beam viewed, there is a large change in brightness due to the motion of the deflected beam toward (or away from) the detectors [7]. Our model was tested by deflecting beams of heliumlike argon in the long lived 2 3 ~ 1 state, so that changes in count rate were
primarily due to deflection effects rather than population depletion. At current levels of accuracy the uncertainties in the geometrical corrections make a negligible contribution to the experimental error.
Most of the hydrogenlike argon forms in the ISll2 ground state or low lying excited states. Among the atoms formed in highly excited states, few cascade through the 2SlI2 state, because decay chains which populate the 2s
112 state are far more likely to decay to the 1s
112 state due to a much larger energy separation. Furthermore, atoms undergoing transitions in which the principle quantum number n decreases more rapidly than the orbital angular momentum
R
have a high probability of reaching states of maximumR
= n-1 which are long-lived and decay through. the chain....
4F, 3D, 2P, 1s.An
upper limit to the cascading to the 2s state can be112
made from examination of the spectra (Fig. 2) as follows. Assume that all of ,the counts in the (240 eV Gaussian width) region 4000 eV
-
4700 eV are from (Doppler shifted) decays nP + 1s (n>
2). The branching ratio 181 nP + 1S:nP -t 2s (n > 2)is about 7.5:l. By comparing the number of counts in the two-photon continuum with the (n > 2)P + 1s. rate we find an upper limit of 0.2% of the observed two-photon counts orginating from cascades to the 2SlI2 state, an insignificant contribution. At larger foil-detector separations the upper limit is much smaller. We emphasize that this upper limit is derived from purely experimental quanti- ties and is model independent. The large energy gap between the series limit of the Balmer series at 1100 eV and the beginning of the Lyman series at 3318 eV assures the absence of interfering lines in this region of the two-photon spectra.
In the observation of single photon decay of the 2SlI2 state interference between the unresolved spectra lines 2s 9 ISll2 and the
cascade fed 2P + 1s result in a large
312,112 112
systematic error in determining the 2SlI2 decay rate. In measurements of unquenched 2s life-
1/2 times in hydrogenlike argon and hydrogenlike iron (Z=26) we observe
a
significant number of counts arising from cascades through the 2P state. In the absence of information about the populations of the different nR states this cascade data is not directly applicable to quenching experiments as the electric field causes appreciable mixing of states of different parity. For the present, we base our Lamb shift determination only upon 2SlI2 decay rates obtained by observing the two- photon decay channel.Heliumlike argon, present in the beam
3
in small quantities has metastable states 2 P
3 2
and 2 S whose decay produces x-rays at 3126 eV 1
and 3104 eV respectively
191.
(Counts from these lines can be separated from the 3318 eV line from hydrogenlike argon by a careful computer fit to the spectra using the measured x-raydetector response function.) However, the two- photon decay (2E1) of the 2 l ~ state in the argon
0
is a continuum and can not be distinguished from the two-photon decay spectra of the 2SlI2 state of hydrogenlike argon. From observed population
3
ratios 2s :2 P in this experiment and population 31/2 2
ratios 2 P2:2 S in experiments on heliumlike 0
argon performed by Marrus and Schmieder[9], we 1
find the initial population of 2 So to be 0.03 f
0.01 of the initial 2SlI2 population. The un- 1
L i f e t i m e s were measured o v e r a n a v e r a g e o f 2.5 decay l e n g t h s i n e l e c t r i c f i e l d s f ( 5 . 9 3 , 5 7.14, 8.06, 8.60) x 1 0 V/cm w i t h two d e t e c t o m f o r a t o t a l of 1 6 decay c u r v e s . P o s i t i o n dependent background (which a p p e a r s t o b e t h e r e s u l t o f gamma r a y s , Compton s c a t t e r e d i n t h e d e t e c t o r ) was measured a s a f u n c t i o n o f d e t e c t o r p o s i t i o n ( s e e F i g . 1 ) w i t h t h e f o i l 0.75 meter upstream t o a l l o w t h e 2 s s t a t e t o d e p o p u l a t e b e f o r e 112 r e a c h i n g t h e d e t e c t o r s . The d a t a was s o r t e d t o y i e l d Lamb s h i f t v a l u e s a s a f u n c t i o n o f f i e l d s t r e n g t h and p o l a r i t y , d i r e c t i o n o f beam b e n d i n g , d i r e c t i o n o f d e t e c t o r t r a v e l and c o u n t r a t e . No s y s t e m a t i c d i f f e r e n c e s were observed. RESULTS The r e s u l t f o r t h e Lamb s h i f t i s 38.0 f 0.6 THz. C o n t r i b u t i o n s t o t h e e r r o r a r e s t a t i s t i c s a t t h e
l a
l e v e l o f 0.35 THz which i s m o s t l y due t o v a r i a t i o n i n t h e background; 0.45 THz, from 1 u n c e r t a i n t y i n t h e 2 So f r a c t i o n , and 0.15 THz m i s c e l l a n e o u s . ACKNOWLEDGBMENT Nany p e o p l e made c o n t r i b u t i o n s b o t h l a r g e and s m a l l t o t h i s e x p e r i m e n t . We thank them a l l , b u t most e s p e c i a l l y we t h a n k o u r e n g i n e e r , Douglas MacDonald, who c o n t r i b u t e d t o a l l a s p e c t s of t h e t e c h n i c a l d e s i g n . T h i s work was s u p p o r t e d by t h e D i v i s i o n of Chemical S c i e n c e s , O f f i c e of B a s i c Energy S c i e n c e s , U.S. Department o f Energy.REFERENCES
111
S. J. Brodsky and P. J . Mohr, "Quantum E l e c t r o d y n a m i c s i n S t r o n g and S u p e r c r i t i c a l F i e l d s " i n T o p i c s i n C u r r e n t P h y s i c s , Vol. 5 , e d i t e d by I.A. S e l l i n ( S p r i n g e r - V e r l a g , B e r l i n , 1 9 7 8 ) , p.3.[ 2 ] S. R. Lundeen and F. M. P i p k i n , Phys. Rev. L e t t .
x,
1368 (1975); D. A. Andrews and G. Newton, Phys. Rev. L e t t .37,
1254 ( 1 9 7 6 ) ; H. W. Kugel and D. E. Murnik, Rep. Prog. Phys. 40, 297 (1977).-
[ 3 ] G. W. E r i c k s o n , Phys. Rev. L e t t .
2,
780 (1971); J. Phys. Chem. Ref. Data6,
8 3 1 (1977). [ 4 ] P. J. Mohr, Phys. Rev. L e t t .24,
1050 (1975);Ann. Phys. (N.Y.)
88,
26 (1974); I n Beam-Foil S p e c t r o s c o p y , e d i t e d by I . A . S e l l i n and D . J . Pegg (Plenum P r e s s , N.Y., 1 9 7 6 ) , p.89. [ 5 ] W. R. Johnson, Phys. Rev. L e t t .29,
1 1 2 3(1972).
[ 6 ] M. H i l l e r y and P. J. Mohr, p r i v a t e communi- c a t i o n ; C. Y. Fan, M. Garcia-Munoz, and I. A. S e l l i n , Phys. Rev.
161,
6 (1967).[71 V. F. Weisskopf, Phys. Today
13,
24 (1960);J. T e r r e l l , Phys. 9ev.
e,
1 0 4 1 ( 1 9 5 9 ) . [ 8 ] H. A. Bethe and E. E. S a l p e t e r , QuantumMechancis o f One- and Two-Electron Atoms, ( S p r i n g e r - V e r l a g , B e r l i n , 1 9 5 7 ) , S e c t . 63. [ 9 ] R. Y a r r u s and R. Schmieder, Phys. Rev.
