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R.F. OPTOGALVANIC DETECTION OF RYDBERG AND AUTOIONIZING LEVELS OF RARE GASES :
DIAMAGNETIC BEHAVIOUR OF XENON RYDBERG STATES
J. Lemoigne, J. Grandin, X. Husson, H. Kucal
To cite this version:
J. Lemoigne, J. Grandin, X. Husson, H. Kucal. R.F. OPTOGALVANIC DETECTION OF RYD- BERG AND AUTOIONIZING LEVELS OF RARE GASES : DIAMAGNETIC BEHAVIOUR OF XENON RYDBERG STATES. Journal de Physique Colloques, 1983, 44 (C7), pp.C7-209-C7-216.
�10.1051/jphyscol:1983717�. �jpa-00223274�
JOURNAL
DEPHYSIQUE
Colloque C7, supplement au nO1l, Tome 44, novembre 1983 page C7-209
R , F , OPTOGALVANIC D E T E C T I O N OF RYDBERG AND A U T O I O N I Z I N G L E V E L S OF RARE GASES
:
D I A M A G N E T I C BEHAVIOUR OF XENON RYDBERG STATESJ.P. Lemoigne, J.P. Grandin, X. Husson and H. Kucal
Laboratoire de Spectroscopie ~ t o m i ~ u e ' , Universite' de Caen, 14032 Caen Cedez, France
RESUME
Quand un oscillateur R.F. est utilise pour produire une ddcharge dans une cel- lule contenant un gaz, le regime et donc la consommation de l'oscillateur peuvent Ctre tr2s sensibles aux variations d'impddance du plasma, telles que celles rdsul- tant de l'excitation laser de transitions entre niveaux d'excitation dlectronique de l'Ql6ment considere. Ceci constitue le principe de la methode de ddtection R.F.
optogalvanique que nous appliquons 1 llQtude de niveaux de Rydberg et autoionisants du krypton et du xenon. On montre dans le cas de niveaux de Rydberg du x6non que la methode s'applique particulisrement bien 3 la d6tection en presence d'un champ ma- gndtique fort.
ABSTRACT
When a R.F. oscillator is used to produce a discharge in a gas cell, the rate and hence the power consumption of the oscillator may be very sensitive to impedance variations of the plasma, such as those induced by laser transition between electro- nic excitation levels of the considered element. This is the basis of the R.F. opto- galvanic detection method which we apply to the study of Rydberg and autoionizing levels of krypton and xenon. It is shown in the case of xenon Rydberg states that the method is especially suitable for detection in presence of a strong magnetic field.
INTRODUCTION
The wealth of experimental opportunities offered by the development of tunable dye lasers has impulsed a recrudescence of interest towards highly excited atomic levels. On the other hand the importance of the problem of the behaviour of such levels submitted to a strong magnetic field is attested by the proceedings of the 1982 meeting in Aussois(1). We report here about some experiments of optogalvanic spectroscopy performed on krypton and xenon Rydberg and autoionizing levels in zero and strong magnetic field.
A part from the fact that optogalvanic methods come immediatly to the mind for the detection of levels which ionize easily, their use in the case of rare gases arises naturallysince laser excitation of these atoms in the vicinity of their ionization
limits requires the previous population of their lowest excited levels by the mean of a discharge.
EXPERIMENTAL PRINCIPLE
A) Energy levels and excitation scheme (figure 1)
The ground state of a rare gas atom corresponds to a ns2np6 configuration.
The only excited configurations i< which we are interested here are obtained by 'the excitation of a p electron thus giving rise to two sets of levels built on the two
2 2
possible states p3,2 and pIl2 of the np5 ionic core and to two corresponding ioni- 'assoeig au C.N.R.S. No 19
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983717
C7-210 JOURNAL DE PHYSIQUE
z a t i o n l i m i t s . The l e v e l s a r e l a b e l l e d ~ ' R ( K ) J o r n l R ' ( ~ ) ~ , f o l l o w i n g t h e Racah cou- p l i n g scheme,then t h e y a r e i s s u e d from a np5 nlR c o n f i g u r a t i o n and t h e y belong t e s - p e c t i v e l y t o s e r i e s converging towards 2 i o n i z a t i o n l i m i t (J
P3/2 Or '1/2 E
2p( ,/,) limit
being t h e i r t o t a l a n g u l a r momentum and K t h e momentum o b t a i n e d by coupling t h e
h
c o r e a n g u l a r momentum 312 o r 1/2 w i t hI I 1
t h e o r b i t a l momentum R of t h e e x t e r n a l ."series e l e c t r o n ) . The f i n e s t r u c t u r e i n t e r v a l limit
-2p,12 of t h e c o r e i s l a r g e 5000cm-l f o r krypton, 10000cm-~ f o r xenon) s o t h a t a l o t of a c c e s s i b l e n'g' l e v e l s a r e s i t u a t e d above t h e f i r s t
I
I \ I I V . U . V . transitions
\ I
I
I \\ i
( 2 i o n i z a t i o n l i m i t and become au- t o i o n i z i n g l e v e l s s i n c e t h e y a r e cou- p l e d t o t h e a d j o i n i n g continuum. The l e v e l s of t h e f i r s t e x c i t e d configura- t i o n s np ( n + l ) s , ( n + l ) p o r nd (n=4 5 f o r krypton, n=5 f o r xenon) a r e t h e ones which can be s u f f i c i e n t l y popu- l a t e d by an R.F. d i s c h a r g e t o allow h i g h r e s o l u t i o n l a s e r e x c i t a t i o n of h i g h l y e x c i t e d l e v e l s .
1 1
n ~ ~ < ' s , , B) Experimental s e t up ( f i g u r e 2)The s t u d i e d atoms a r e contained i n a c u b i c c e l l of Icm edge connected t o a 1OOmR r e s e r v o i r f i l l e d a t a p r e s s u r e F i g u r e 1 of about . l t o .4 t o r r s . This c e l l may S i m p l i f i e d energy l e v e l s diapram be placed i n t h e gap of an electromagnet
of r a r e g a s e s p r o v i d i n g f i e l d s up t o 2.2 t e s l a s and it i s coupled t o t h e R.F. o s c i l l a t o r by t h e mean of two 5mm diameter e x t e r n a l e l e c t r o d e s s t i c k e d on o p p o s i t e s i d e s of t h e cube. The lamp R.F. o s c i l l a t o r i s analogous t o t h e one d e s c r i b e d by Lyons and ~ o l l J 3 )
r Electrodes
;
Cell0
. F . oscillatorL
,PhotodiodeIodine cell
w
aver Supply
F i g u r e 2 E x p e r i m e ~ t a l s e t U?
It works a t a frequency of about 30 Mhz and a power of about 100 t o 200 mwatts i s n e c e s s a r y t o produce i n t h e c e l l a v e r y f a i n t and n o i s e l e s s d i s c h a r g e having t h e appearance of a 3mm diameter sphere. The l a s e r beam i s focused i n t o t h e c e l l , not i n t h e c e n t e r of t h e d i s c h a r g e where t h e s t u d i e d s p e c i e s would be submitted t o i m - p o r t a n t p e r t u r b a t i o n s due t o t h e g r e a t d e n s i t y of i o n s and e l e c t r o n s , b u t s l i g h t l y upwards o r downwards i n r e g i o n s where t h e d e n s i t y of p e r t u r b e r s i s much lower. I n t h e s e c o n d i t i o n s provided t h a t s u f f i c i e n t l y long l i v i n g s t a r t i n g l e v e l s a r e chosen e x c e l l e n t s s i g n a l t o n o i s e r a t i o s a r e g e n e r a l l y obtained.The l a s e r used i s a com- m e r c i a l C.W. r i n g dye l a s e r p r o v i d i n g 100 t o 500 mW w i t h a bandwidth of about lOMhz and allowing monomode p r e s s u r e scans of 150 Ghz (5cm-I)in t h e range 540-680m. Laser induced t r a n s i t i o n s a s e i t h e r t h e wavelength A o r t h e magnetic f i e l d B a r e swept, a r e d e t e c t e d through v a r i a t i o n s of t h e regime of t h e o s c i l l a t o r due t o changes of t h e d i s c h a r g e impedance.A r e s i s t o r R h a s t h e r e f o r e been i n s e r t e d i n t h e anode c i r c u i t of t h e o s c i l l a t o r and a s t h e observed v a r i a t i o n s a r e small (10 -2 t o I O - ~ of t h e to- t a l c u r r e n t ) t h e l a s e r beam i s chopped and t h e v o l t a g e a c r o s s t h e r e s i s t o r i s de- t e c t e d by a lock-in a m p l i f i e r . The s i g n a l from t h e lock-in a m p l i f i e r can be recor- ded t o g e t h e r with t h e i o d i n e a b s o r p t i o n spectrum allowing a 10 mK p r e c i s i o n i n t h e wave number c a l i b r a t i o n by r e f e r e n c e to(2).The v a l u e s of t h e magnetic f i e l d a r e determined by N.M.R. w i t h an e x c e l l e n t accuracy.
EXPERIMENTS I N ZERO MAGNETIC FIELD A) Krypton
Using a sample of i s o t o p i c a l l y e n r i c h e d 8 6 ~ r ' we were a b l e t o d e t e c t a g r e a t number of Rydberg and a u t o i o n i z i n g l e v e l s e x c i t e d from l e v e l s of 4p5 5p and 4p5 4d c o n f i g u r a t i o n s w i t h a v e r y good s i g n a l t o n o i s e r a t i o . We were p a r t i c u l a r l y i n t e r e s - t e d i n t h e l e v e l s of t h e nf s e r i e s which could be e x c i t e d f o r n = 9 t o 32 from l e - v e l s of 4p5 4d c o n f i g u r a t i o n . T h e s e s e r i e s a r e s t r o n g l y p e r t u r b e d by t h e l e v e l s of 4p' 7p' c o n f i g u r a t i o n and t h e study of t h e e v o l u t i o n o f t h e i x f i n e s t r u c t u r e allowed us t o o b t a i n p r e c i s e ~ o s i t i o n s f o r t h e s e l e v e l s nobs served s o f a r . The energy l e v e l s p o s i t i o n s f o l l o w indeed t h e Rydberg formula
L being t h e p o s i t i o n of t h e i o n i z a t i o n l i m i t R t h e Rydberg c o n s t a n t
6 t h e quantum d e f e c t
For unperturbed s e r i e s ( f i g u r e 3) 6 remains c o n s t a n t
For p e r t u r b e d s e r i e s on t h e c o n t r a r y 6 v a r i e s r a p i d l y i n t h e v i c i n i t y of t h e per- t u r b i n g l e v e l .
We could a l s o o b t a i n a v a l u e f o r t h e Zp3,2 i o n i z a t i o n l i m i t of krypton L = 112914.48(.02) cm- 1
This v a l u e f a l l s i n a very good agreement with a v a l u e p r e v i o u s l y determined by D e l s a r t and c o l l ( 4 )
The agreement between our r e s u l t s i s very s a t i s f a c t o r y f o r us s i n c e indeed the- s e a u t h o r s determined t h e i r v a l u e by e l e c t r i c f i e l d i o n i z a t i o n d e t e c t i o n of Ryd- b e r g l e v e l s e x c i t e d i n an atomic beam : a method which would i n p r i n c i p l e allow very p r e c i s e measurements.
JOURNAI- DE PHYSIQUE
Figure 3
Quantum defects 6 for the levels of the nf series of krypton ver- sus prZncipa1 quantum xiumber n.
A - . - .
- A-A-A-A
B)
Xenon
Using a sample of isotopically enriched 1 3 6 ~ e and as a preliminary to the experiments in strong field described below,we could observe nf(3/2)1 series of xenon excited from 4d(1/2)0 level up to n = 60 determining thus a value of the
CI
Lp312 ionization limit for that atom :
This value is also in good agreement with the one obtained by Labastie and c011(~)
in anoptogalvanic spectroscopy experiment allowing extrapolation of the line positions at zero pressure and discharge intensity.
We could at last determine a new value of the pIl2 ionization limit of xenon 2
improving by the way of about one order of magnitude the precision on this value by the recording of the nf '(5/2)2,3 and nft(7/2)3, 4 fine structure doublets excited from 5df(3/2)2 and 5dt(5/2)3 levels for n = 7 to 31.
As a conclusion for this
resent at ion
of our zero field experiments we shall state that R.F. optogalvanic spectroscopy can lead to precise experimental results provided that low pressures and low dischar~e intensities are used.STRONG FIELD EXPERIMENTS
The problem of Rydberg atoms submitted to a strong magnetic field has been the subject of various theoretical and experimental works in the recent years (1).
Important experimental advances were achieved by Gay and coll (6.7) and Castro and coll (8). Gay particularly pointed out the advantapes of performing high reso- lution experiments on quasi hydrogenic series. Optogalvanic spectroscopy of nf series of xenon ( 6 %.055) offers the opportunity for such an experiment.
The hamiltonian describing an hydrogen atom placed in a magnetic field may be written in spherical coordinates in the followin2 way :
m and e being the electron mass and charge
The magnetic field being directed along oz and the proton mass supposed to be in- finite.
The four members of this hamiltonian are respectively,the term of kinetic energy, the Coulomb term and two terms of interaction with the maynetic field : the para- magnetic term linear in B and the diamagnetic term quadratic in B.
The diamagnetic term varies as r2 that is to say as n4 and thus rapidly do- minates the paramagnetic term for hiqh n levels, it may even become comparable or greater than the Coulomb term itself,leading to inportant alterations of the usual hydrogenic spectrum. Due to the lack of a complete theoretical treatment for the problem of an hydrogen (or quasi hydrogenic) Rydberg atom submitted to a stronr:
magnetic field, the interpretation of experimental results is limited to some specific cases for which approximate treatments are available
.
Two cases will therefore be considered below, on the one hand the case where the effect of the diamagnetic term is small in front of the energetic intervalLR
between two suc-n 5
cessive Rydberg levels, on the other hand the case where the problem is restricted to the interpretation of the dominant lines of the spectra.
In the first case perturbation theory may be used since levels with diffe- rent principal quantum number n are not mixed and diagonalization of the diamagnetic term may be done inside each n level. Figure 4 shows the evolution of 3lf(3/2) 1 le- vel excited from 5d(1/2)0 level in 0 polarization for values of the magnetic field going from 0 to 2 teslas
.
On figure 5 the theoretical positions of mR= '3 odd parity components of n = 31 levels are given as a function oflet let
us notice that in the particular case of the studied transitions the sum of spin and orbital para- magnetic terms cancels for mR = 23 components so that the observed deviations are pureiy diamagnetic).The coincidence between these positions and the dominant lines of figure 4 is obvious. The smaller lines observed on figure 4 correspond to mR values of 0,1 or 2. The wavefunctions corresponding to the fourteen components of figure 5 are linear combinations of n = 31 mk = 3' R=3 to 29 odd parity states.The most intense line in the experimental spectra corresponds to the component which re- tains the major part of the 2 = 3 mE==*3 states. At low field due to the small quantum defect of nf(3/2)1 series this component lies below the hydrwgenic manifold, as the field is increased a series of anticrossings allows the R = 3 mp = 3' cha- racter to be transfered progressively to the upper component of the man~fold, so that for a field of two tesla the situation reached is analogous to that which would be obtained in a purely hydrogenic case.
The fact that the dominant lines of the recorded spectra correspond to 9, = 3 mR = +3 components gives the key for an approximate theoretical approach allowins at least the interpretation of the positions of these lines for arbitrary field values. The R = 3 mR = *3 components are indeed the ones for which the wavefunction is localized in the vicinity of the xOy plane and it is well known otherwise (6) that the Bohr Sommerfeld quantization formula allows to determine the general beha- viour for the levels of an hydrogenic atom in a strong magnetic field,if the move- ment of the electron is supposed to be limited to the xOy plane perpendicular to the magnetic field. Figure 6 gives the results of a computation realized on the basis of this approximation,together with a set of experimental points obtained
JOURNAL DE PHYSIQUE
Figure 5
Theoretical positions for m% = 3 odd
~arity com~onents of 31f(3/2)1 level.
The stars correspond to experimental data obtained from figure 4. For each field value the black star indicates the position of the more intense com- ponent.
f Figure 4
Evolution with the magnetic field of the s~ectrum of 5d( l /2)0-31 f (3/2) 1 transitior.
he
arrows indicate the positions of components. (relatives amplitudes and positions of the various spectra are without significations on this figure).forthe nf(3/2)1 series excited from 5d(1/2)0 level in o polarization. The agreement between theoretical l k e s and experimental points can be considered as satisfactory taking into account the roughness of the approximation used. At zero energy the
~n~ = constant law characteristic of the quasi Landau regime is observed and reso- nances are followed up to about 25cm-l beyond the zerofield ionization limit.
Excitation from the 5d(7/2)3 level even allowed us to excite:discrete resonances up to l00cm-' above the ionization limit. Figure 7 shows an aspect of the quasi Landau spectrum obtained for such an excitation at an energy corresponding to the zerofield ionization limit. The fact that no decrease of the signal to noise ratio is observed as the field is increased indicates that the detection method would probably work for higher values of B.
+ Figure
5
Theoretical positions of the do- minant components of the spectra.
The stars are obtained from the positions of the dominant lines in the experimental spectra. Black stars correspond to spectra recor- ded at a fixed value of the magne- tic field B by scanning the laser wavelength A. White stars to spec-
tra recorded at fixed A while scanning B.
Figure 7 -f
Quasi Landau spectrum obtained in a magnetic field scanning at the zerofield 2~3,2 ionization limit by excitation from the 5d(7/2)3 level.
JOURNAL DE PHYSIQUE
CONCLUSION
Our experiments demonstrate that reliable results may be obtained from R.F.
optogalvanic detection method which appears as an interesting tool for the study of highly excited states of rare gases in zero and strong magnetic field.
Simplicity and high sensitivity are the main advantapes of this method, the first one results from the use of electrodeless cells which may be of small dimen- sions, the second one allows to realize excitations
start in^
from a great number of levels and not only from metastable levels. At last the fact that this method works with very small R,F.powers allows to minimize the influence of parasitic effects due to ions and electrons.REFERENCES
1 "Atomic and molecular physics close to ionization thresholds in high fields"
J. Phys. Paris
3,
1982, colloque C 22 Gerstenkorn S. and Luc P. 1978 "Atlas du spectre d'absorption de la molCcule d'iode (Paris Editions du CNRS).
3 Lyons D.R., Schawlow A.L. and Yan G.Y. Opt. Comnun.
38,
1981, 35.4 Delsart C., Keller J.C., Thomas C. J. Phys. B 14 ; 1981, 4241.
5 Labastie P., Biraben F., Giacobino E., J. Phys. B 15, 1982, 2595.
6 Gay J.C., Delande D. and Biraben F. J. Phys.
B,
1980, L 729.7 Delande D., Gay J . C . , Physics Letters
82,
1981, 399.8 Castro J.C., Zimmerman M.L., Hulet G., Kleppner D. and Freeman R.R., Phys. Rev.
Lett. 45, 1980, 1780.
