Z. Phys. D 38, 201—209 (1996)
CW laser spectroscopy of autoionising 6p 3/2 nl states of Barium
G.J. Kuik, W. Vassen, W. Hogervorst
Laser Centre Vrije Universiteit, Department of Physics and Astronomy, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
Received: 21 June 1996
Abstract. 6pnl states of Ba with l55, excited with two
narrowband, tunable CW lasers have been studied. In the
first excitation step 6snl states were populated from metastable states of the 5d2 configuration: to 6s40h (l"5)
states in the absence, and to parabolic 6pnk (n"30, 35, 40)
states in the presence of an electric field. The atomic
motion was used to adiabatically reduce this field to zero
before applying the second excitation step to high-l 6p nl
3@2
states (Stark-switching). A slow decrease in the
autoionisation rate for increasing value of l and, in case of
6pnh, a dependence on the fine-structure state was measured. The narrowest autoionisation linewidth observed is
113(11) MHz, relatively close to the 20 MHz linewidth
corresponding to the radiative lifetime of the 6p state of
the Ba`-ion.
PACS: 32.80.Dz; 32.70.Jz; 31.50.#w
1 Introduction
Doubly-excited Rydberg states of two-electron atoms
have been the subject of investigation by several theoretical and experimental groups. The studies on doubly-excited Rydberg states of alkaline-earth atoms partly focus
on the understanding of autoionisation processes [1—6]
and partly on effects of correlated electron motion [7—11].
High angular momentum Rydberg states received special
attention as in this case the Rydberg electron does not
penetrate the orbit of the inner (excited) electron, thus
reducing autoionisation rates. To populate high angular
momentum l-states from a low-l ground state in a onephoton excitation step a Stark switching technique can be
applied. In pulsed laser excitation Stark switching is performed by excitation of a first electron in the presence of
a strong electric field, followed by adiabatical reduction of
the field to zero.
A Rydberg electron excited in the presence of a sufficiently strong electric field is hydrogenic and may be
characterized with a parabolic wavefunction (with parabolic quantum number k). It can be expressed as a sum of
spherical harmonic functions with l"0 to l"n!1. The
relative contributions of the spherical harmonics depend
on the electric field strength. In the presence of an electric
field in principle each parabolic quantum state k may be
excited provided that the angular momentum l that can be
reached in the one-photon transition is sufficiently strongly mixed into the k parabolic wave function. When the
electric field is reduced to zero the composition of the
k parabolic wave function changes to a pure single spherical harmonic function with l equal to k!1. In the present
experiment, we use a Stark switching technique in an
excitation process with CW lasers which does not allow to
use the technique of simply changing a voltage over a set
of two capacitor plates in time. The technique we applied
is described in paragraph 2 of this paper.
The application of CW lasers to populate doublyexcited Rydberg states is not obvious. In general, to reach
doubly-excited states, powerful pulsed lasers are required
which have a relatively broad bandwidth. Usually this is
not a problem as fast autoionisation often results in broad
resonances as well. However, in the case of doubly-excited
high angular momentum Rydberg states the autoionisation rates may be strongly reduced and the high spectral
resolution of a CW laser experiment becomes attractive.
To demonstrate the use of CW lasers in the study of
doubly-excited high angular momentum states we investigated 6p nl states with l55. These states, if sufficiently
3@2
narrow, may then be used for further excitation to e.g.
7dn@l@. The high resolution may provide new insights in
a regime where spectra become extremely complicated
[8].
2 Experiment
The experimental setup is an extension of the setup used in
earlier studies of the properties of 6snh Rydberg states of
Barium [12—14] and is shown schematically in Fig. 1. In
the experiment we use a well-collimated atomic beam, in
which metastable states of the 5d2 configuration are populated by running a DC discharge between the bariumfilled tantalum oven and a heating wire. A fraction of
202
Fig. 1. Experimental setup (E.M.,
electron multiplier; P.D., photo
diode; W.P., Wollaston prism). E.M.
1 is used to detect the autoionising
states whereas E.M. 2 is used to lock
the first step
about 10~4 of the atoms is transferred to the metastable
5d2 1G state at 24696.278 cm~1. The atomic beam is
4
perpendicularly intersected by narrow band (\1 MHz)
laser light to eliminate Doppler effects to a large extent
(\10 MHz). Due to configuration interaction this 5d2 1G
4
state has some 6s5g character, allowing for the direct
excitation of 6snh Rydberg levels using a single Rhodamine 6G laser around 580 nm (ionization limit at
42034.902 cm~1). We used a CW frequency stabilized ring
dye laser (Spectra Physics 380D) with an output power of
typically 500 mW for good signal strength. In zero electric
field both the 6snf and 6snh states are excited; however,
excitation of 6snf states is an order of magnitude weaker.
In the presence of a sufficiently strong electric field (perpendicular to the laser polarisation) all components of an
angular momentum manifold originating from the 6snh
state can be resolved and individually excited. The high
J-value of the metastable state prevents selection of
a single M-value.
In two-step excitation experiments to 6pnl states the
first laser was frequency locked on the transition to 6snh
(field-free excitation) or to a selected angular momentum
manifold component (excitation in an electric field). For
this purpose we used a system with three well-shielded and
separated interaction regions (see Fig. 2). In the first region a capacitor plate was mounted to generate a homogeneous electric field for the excitation of manifold peaks.
The excited, long-lived Rydberg atoms leave the field
adiabatically because of their relative slow motion in the
gradually decreasing static electric field. This ensures that
the atoms remain in the same state when the field decreases to zero. Downstream, in a second, well-shielded
field-free interaction region the inner 6s electron is excited
to 6p
with a Stilbene 3 ring dye laser operating at
3@2
a wavelength of 450 nm (also Spectra Physics 380D). The
excited nl electron is a spectator in this isolated-core
excitation process. The zero-field excitation of the
6p 40h-multiplet was performed using only the second
3@2
and third chamber, with both lasers spatially overlapping.
Electrons released by autoionisation decay of 6pnl states
will diffuse through a grounded wire mesh and are
counted with an electron multiplier. In a third interaction
Fig. 2. Interaction Region: [1] First excitation in
a homogeneous electric field; [2] Field-free inner-core
excitation after Stark switching; [3] Field-ionisation of
singly-excited atoms for locking the first laser to the
atomic transition. (E.M."electron multiplier)
203
Fig. 3. Calculated energies as a function of the electric field strength
for the n"40, DMD"4 manifold. The arrow at 1.5 V/cm shows the
fixed laser frequency to excite the k"21 state. When the electric
field is reduced to zero the character of the k-wavefunction changes
until in zero field the l"k!1 state results. This is schematically
depicted by the arrows pointing towards zero field along the k"21
electric field line
Fig. 4. Calculated 6s40k Stark manifold at 1.5 V/cm. The individual
lines are convoluted with a Gauss function (50 MHz FWHM)
region the atoms left in the 6snl Rydberg state are field
ionised and counted with a second electron multiplier.
This signal is used to lock the laser for the first excitation
step on the transition. For this purpose the laser frequency
is modulated at 10 Hz and the ionisation signal demodulated using a computer controlled lock-in technique.
The first laser may be frequency-locked to any component
of the angular momentum manifold originating from the
6snh configuration in the presence of the electric field
(linear Stark effect). The excited atoms leave the diverging
field adiabatically over a distance of 12 mm, corresponding to a time of \30 lsec (atomic velocity \450 m/sec).
A manifold state in the field, labelled with the parabolic
quantum number k, obtains a pure l-character (with
l"k!1) when the electric field gradually reduces to zero.
This is illustrated in Fig. 3, where for n"40 a calculated
6snk manifold as a function of the electric field F is shown
for M"4 only. In zero electric field (F"0 V/cm) the
experimental spectrum consists of pure 6snl states (l"0
to 39 for M"0 and l"4 to 39 for M"4), separated in
energy E by the quantum defect d : E"I!R/(40!d )2
l
l
(I"42034.902 cm~1 and R"109736.88 cm~1). Only the
singlet fraction of Rydberg states is excited from the
5d2 1G state. As barium has a large core with s-, p- and
4
d-electrons the quantum defects of the 1S, 1P and 1D series
are large, respectively 4.210, 4.033 and 2.699. Due to
mixing with levels of 5dn@l@ series many perturbations
occur, leading to singlet-triplet mixing and a strong variation of the quantum defect over the Rydberg series.
However, we studied only a small energy range
(n"30—40) where the quantum defects are constant. For
increasing l the Rydberg states change their coupling from
¸S (for l43) to jj (for l'3). This e.g. leads to the excitation of both 6snh (weak) and 6snh
(strongest) states
9@2
11@2
from the 5d2 1G state. Other relevant quantum defects
4
are 0.0368 for the perturbed 6snf 1F series (value for
3
n"40), 0.0522 and 0.0560 for 6sng and 6sng respec9@2
7@2
tively, and 0.0179 and 0.0187 for 6snh
for 6snh
11@2
9@2
respectively. For even larger l the quantum defect reduces
to zero with a l~5 dependence.
For non-zero electric field the energy positions are
calculated by diagonalisation of the Stark Hamiltonian in
a jj-coupled basis. 6snl states with l-values lower than 5 do
not mix strongly into the 6snk states at the relatively weak
electric fields applied in our experiments. Fig. 3 shows the
calculated manifold energy levels as a function of the
electric field strength. At field strengths below 1 V/cm
low-l values are not yet mixed into the manifold. At a field
of 1.5 V/cm all levels with l54 are strongly mixed into
the manifold. In the excitation from 5d2 1G at zero field
4
6s40f 1F and 6s40h
are primarily populated. There3
11@2
fore inside the manifold the f- and h-fractions in the
different k-levels determine the oscillator strength distribution. In Fig. 4 a calculated manifold (folded with
a 50 MHz line width profile) is shown, assuming that the
M"0!5 components are excited equally strong. For
the electric field used, i.e. 1.5 V/cm, the M'2 spectra are
almost hydrogenic, whereas the M42 spectra are influenced by 6snl (l42) levels not yet mixed into the
manifold. Therefore at the low-frequency side of the spectrum different M-values for one k-value are non-degenerate and vary considerably in intensity. In the middle of the
manifold the small field dependence results in near degeneracy. At the high-frequency side of the manifold the
larger field dependence results again in an M-splitting.
With an experimental resolution of about 10 MHz it
204
3 Results and discussion
3.1 6p3 2 40h states
@
Fig. 5. The 6s40k manifold recorded as a function of frequency for
F"1.5 V/cm
follows from Fig. 4 that a field of less than a few V/cm is
already sufficiently strong to resolve most k-components.
This is shown in Fig. 5, where the experimental 6s40k
manifold, recorded in the same field of 1.5 V/cm, is reproduced. In the spectrum six different M-values are excited.
For k around 20 even the small M-dependence of manifold peak positions is still visible. The good agreement
between experiment (Fig. 5) and calculation (Fig. 4) shows
that the spectra are well understood. It is obvious that any
k-value '7 may be selected for Stark switching.
In the second excitation region the blue ring dye laser
is scanned over the 6s!6p
ionic transition for each
3@2
setting of the first laser. The resulting autoionisation signal and the signal of a calibrated Fabry-Perot interferometer are recorded and stored on a computer which
also controls the scanning of the laser.
We recorded 6p 40h spectra in two-step excitation from
3@2
the metastable 5d2 1G state via the 6s 40h
J"5
4
1@2 11@2
bound Rydberg states in a field-free configuration (in
Sect. 2 of the excitation chamber shown in Fig. 2). In
Fig. 6 a spectrum of the 6p 40h multiplet is shown as
3@2
a function of the frequency of the second, blue laser. The
three multiplet components with K"13/2 (strongest),
11/2 and 9/2 (weakest), difficult to separate in a pulsed
laser experiment, are well resolved. We use a ( jl) K-coupling scheme to assign the resonances. From these spectra
intensities, quantum defects, multiplet splitting and
autoionisation widths of part of the 6p 40h configura3@2
tion could be determined accurately. The experimental
data are collected in Table 1. The absolute quantum defect
of the 6p 40h [K"13/2] state was determined from
3@2
absolute frequency measurements using the 6p ionisa3@2
tion limit (at 63987.324 cm~1) and the 5d2 1G level
4
(at 24696.278 cm~1).
The 6p nl-multiplet splitting follows from the elec3@2
trostatic repulsion between the two valence electrons. It
can be calculated from [2]:
¼ "S6p nlKJD»D6p nlKJT.
(1)
K
3@2
3@2
To evaluate the matrix elements of (1) the Coulomb repul1
1
sion term of the operator »" ! is expanded in
r
r
12
1
multipoles:
= rk
(2)
" + : C(k) C(k).
rk`1 1 2
12 k/0 ;
Here C(k) and C(k) are spherical harmonic operators, and
2
1
r (r ) is the larger (smaller) of the radial positions of both
; :
electrons (r , r ). The zero-order terms cancels the 1/r
1 2
1
term in ». The first non-trivial term (k"1) gives the
screening effect of the 6p electron and is not relevant for
1
r
Fig. 6. Experimental spectrum of the
6s40hP6p 40h transition
3@2
205
Table 1. Experimental quantum defects
d with respect to the 6p ionisation
l
3@2
limit, experimental and theoretical
position DE (in GHz) and intensity
I relative to the K"13/2 component, and
autoionisation line width C in (GHz) for
the 6p 40h configuration
3@2
Label
6p 40h
3@2
6p 40h
3@2
6p 40h
3@2
6p 40h
3@2
6p 40h
3@2
d
DE
%91
DE
5)
0.027 (1)
0.0
0.0
2.93!,
3.09!,
4.11!,
4.33!,
l
K"13/2, J"6
K"9/2, J"4
K"9/2, J"5
K"11/2, J"5
K"11/2, J"6
H 0.051 (1)
H 0.065 (1)
2.4 (2)
3.9 (2)
2.63"
2.76"
3.68"
3.88"
I
%91
I
5)
C
%91
C
5)
1.0
1.0
0.3
0.5
0.3
0.6
1.10 (5)
0.65
0.50
0.50
0.42
0.42
0.2
0.6
0.67 (2)
0.80 (2)
!Calculated with the bound-bound matrix element S6pDr2D6pT of Pruvost et al. [4]
"Idem with value of Jaffe et al. [16]
Table 2. Bound-bound matrix elements Sn l DrkDn l T
00
22
n l
00
k
n l
22
Value (au)
Ref.
5d
5d
6s
6p
6p
1
3
1
2
2
6p
6p
6p
6p
6p
2.522
81.43
3.781
33.95
30.44
[3]
[3]
[3]
[4]
[16]
the multiplet splitting. The second term leads to the quadrupole splitting:
¼ "S6pDr2D6pTSnlDr~3DnlT
Q
]Sp lKJDCM (2) ·CM (2) Dp lKJT.
(3)
3@2
1
2 3@2
The matrix element S6pDr2D6pT has been calculated by
Jaffe et al. [16] and Pruvost et al. [4] and is given in
Table 2. The hydrogenic value of SnlDr~3DnlT equals
(n3(l#1) (l#1/2) l)~1 [15]. The angular part can be
calculated using standard techniques [15]. In Table 1 the
multiplet splitting, calculated with the quadrupole term,
is given relative to the K"13/2 energy. Using the data
on singlet—triplet mixing in the 6s40h
state [14]
11@2
the transition probabilities to the different 6p 40h
3@2
K-components were obtained. These values are, together
with the observed values, included in Table 1 as well.
From the oscillator strength distribution it is clear that
the 6p 40h K"13/2, J"6, 6p 40h K"9/2, J"5,
3@2
3@2
and 6p 40h K"11/2, J"6 components are excited pre3@2
ferably, and, although weaker, 6p 40h K"9/2, J"4
3@2
and 6p 40h K"11/2, J"5. It should be noted that the
3@2
calculated oscillator strength distributions do not directly
correspond to the measured peak heights due to the different autoionisation rates for the different K-components.
The calculated relative energies and intensities of the
observed K-components compare well with the low-n
(n"7—13) members of the 6p nh states investigated by
3@2
Bente and Hogervorst [2] and Pruvost et al. [4]. The
quantum defects of the 6p 40h K-states are slightly lar3@2
ger than the quantum defects for the low-n states close to
the 6p -limit observed by Bente and Hogervorst [2].
1@2
Their quantum defects for the low-n members differ significantly from the quantum defects for the same states
calculated by Pruvost et al. [4]. It has to be noted that
these calculated quantum defects were derived with
a model potential to determine the Ba` matrix element
S6pDr2D6pT. Its value differs from the one reported by Jaffe
et al. [16]. For comparison both calculated values for the
matrix elements are listed in Table 2. As shown in Table
1 the calculated multiplet splitting with the matrix element
of Jaffe et al. [16] compares best with the experimental
values. Pruvost et al. [4] did not report accurate experimental data to compare energies of resonances. The calculated positions and intensities of the K-components are
in good agreement with the experimental data, confirming
our assignment. The J-splitting of each K-doublet due to
the spin-orbit interaction of the Rydberg electron could
not be resolved.
The observed autoionisation linewidths differ for the
various K-components. The autoionisation rate into the
n l el continuum can be expressed as [6]:
00
C "2nDSn l elKJD»Dn l n l KJTD2.
(4)
K
00
22 11
For the 6p nh state (n "6, l "1, n "n, l "5) as well
3@2
2
2
1
1
as for the continuum states the inner electron at r is
2
assumed always to be closer to the core than the outer
electron at r . Furthermore, ignoring configuration inter1
action, single configuration wave functions can be used.
The exchange contributions to the matrix elements are
neglected as the outer electron is in a high-l state and the
overlap with the inner electron will be small.
With these assumptions the autoionisation rate for
an atom in a ( jl ) K-coupled doubly-excited n l n l
22 11
state ionising into a n l el continuum may be expressed
00
as [3]:
C "2n[l , l , l , l, j , j ]
K
2 1 0 0 2
] + Sn l DrkDn l T2SelDr~k~1Dn l T2
00
22
11
k51
l k l 2 l k l 2
2
1
] 0
0 0 0
0 0 0
A
G
BA
HG
B
H
l s j 2 j l K 2
0
0
·
(5)
] 0
j k l
l j k
2
2
1 2
Here [l , l , 2 ] stands for (2l #1) (2l #1) etcetera.
2 1
2
1
The autoionisation rate is independent of J for a given Kvalue. The bound-bound matrix elements for the barium
ion have been calculated by Poirier [3] and by Pruvost
et al. [4] by numerical integration of the one-electron
Schro~ dinger equation taking core-polarization effects into
account. These values are included in Table 2. The boundfree matrix elements can be calculated by numerical integration as well [3]. The outer Rydberg electron is
206
represented by a hydrogenic wave function and the continuum wave function of the ejected electron by a regular
Coulomb wave function.
Three different K-components of the 6p 40h mul3@2
tiplet were observed. The K"13/2-component may
autoionise into the 5d eg, 5d ei, 5d ek, 5d ei,
5@2
5@2
5@2
3@2
5d ek, 6p ej and 6s ei continua, the K"11/2-com3@2
1@2
1@2
ponent into 5d eg, 5d ei, 5d ek, 5d eg, 5d ei,
5@2
5@2
5@2
3@2
3@2
6p eh and 6s ei and the K"9/2-component through
1@2
1@2
dipolar coupling into 5d ed, 5d eg, 5d ei, 5d eg,
5@2
5@2
5@2
3@2
6p eh and 6s eg.
1@2
1@2
In Table 3 the calculated bound-free matrix elements
are given. In Table 1 the calculated autoionisation rates
are included, whereas in Table 4 branching ratios to the
different continua are given. The scaled linewidths
(C]n*3) (FWHM, n* is the effective quantum number) of
the different K-components for n"40 are of the same
order of magnitude as those deduced from the line widths
observed by Bente and Hogervorst [2], for low n. A detailed comparison is not possible due to the large scatter
in these scaled linewidths data. Comparison of the experimental autoionisation widths with the theoretical calculations shows agreement within a factor of 2. We conclude
that the model explains the dominant autoionisation
mechanism but calculations in all cases underestimate the
measured widths. The neglect of the exchange interaction
and the use of hydrogenic wavefunctions cannot account
for the extra broadening. However, two effects may have
an influence on the observed linewidths:
— a small admixture of e.g. 7sNl or 6dNl character
into the 6p 40h wavefunction. 7s and 6d are highly3@2
excited states in Ba`, so admixture of states with a
low N-value is possible. The polarisation of the 6p
electron by the Rydberg electron through dipole
coupling allows for such small admixtures despite the
fact that these states lie far away in energy. This effect
becomes of interest when the total ionisation rate
significantly depends on a quadrupole coupling between
the bound and continuum state. The contribution of
quadrupole coupling to the autoionisation decay rate
can be of the same order as two dipole—dipole couplings.
In the case of 6p 40h a large fraction (up to 40%)
3@2
autoionises into 6p el continua through quadrupole
1@2
coupling. A similar effect was observed by Luc-Koenig
et al. [17] for the 5d5g states of barium. As the rk
matrix elements (see 5) scale as 1/N3 small admixtures
may have a large effect on the autoionisation width of
6p 40l. The influence of this effect is extremely difficult to
3@2
assess.
— a small admixture of 6p 40g and/or 6p 40f. As
3@2
3@2
these low-l states have much larger autoionising
linewidths (see Table 5) a small admixture may induce
considerable broadening. We calculated the effect of
a stray electric field of 10 mV/cm on the 6s40h
level
11@2
and conclude that this will result in an admixture of
0.02% 6s40g (and 0.2% 6s40i) character into the 6s40h
wavefunction at the intermediate level. This induces a negligible broadening of the 6p 40h states. However, the
3@2
weak stray electric field may mix the 6p 40h with
3@2
6p 40g (and 6p 40f ) directly. Several K- components of
3@2
3@2
6p 40h, 6p 40g and 6p 40f resonances partly overlap
3@2
3@2
3@2
at their high frequency sides, but the amount of mixing
Table 3. Bound-free matrix elements SelDr~k~1D40hT
Continuum
e (au)
l
k
K
Value (au)
6p ej
1@2
5d eg
5@2
5d eg
5@2
5d ei
5@2
5d ei
5@2
5d ek
5@2
5d ei
3@2
5d ei
3@2
5d eg
3@2
6s ei
1@2
6p eh
1@2
5d ed
5@2
5d eg
5@2
5d eg
5@2
5d ei
5@2
5d ei
5@2
5d eg
3@2
5d eg
3@2
5d ei
3@2
5d ei
3@2
6s eg
1@2
6p eh
1@2
5d eg
5@2
5d eg
5@2
5d ei
5@2
5d ei
5@2
5d ek
5@2
5d eg
3@2
5d eg
3@2
5d ei
3@2
5d ei
3@2
6s ei
1@2
0.1216
0.3843
0.3843
0.3843
0.3843
0.3843
0.3937
0.3937
0.3937
0.4466
0.1216
0.3843
0.3843
0.3843
0.3843
0.3843
0.3937
0.3937
0.3937
0.3937
0.4466
0.1216
0.3843
0.3843
0.3843
0.3843
0.3843
0.3937
0.3937
0.3937
0.3937
0.4466
7
4
4
6
6
8
6
6
8
6
5
2
4
4
6
6
4
4
6
6
4
5
4
4
6
6
8
4
4
6
6
6
2
1
3
1
3
3
1
3
3
1
2
3
1
3
1
3
1
3
1
3
1
2
1
3
1
3
3
1
3
1
3
1
13/2
13/2
13/2
13/2
13/2
13/2
13/2
13/2
13/2
13/2
9/2
9/2
9/2
9/2
9/2
9/2
9/2
9/2
9/2
9/2
9/2
11/2
11/2
11/2
11/2
11/2
11/2
11/2
11/2
11/2
11/2
11/2
7.873]10~6
1.867]10~5
4.695]10~7
8.034]10~5
7.290]10~7
6.637]10~7
7.686]10~5
7.111]10~7
6.666]10~7
6.468]10~5
1.260]10~5
1.286]10~8
1.867]10~5
6.637]10~7
8.034]10~5
7.290]10~7
2.771]10~5
6.666]10~7
7.686]10~5
7.111]10~7
1.275]10~5
1.260]10~5
1.867]10~5
4.695]10~7
8.034]10~5
7.290]10~7
6.637]10~7
2.771]10~5
4.561]10~7
7.686]10~5
7.111]10~7
6.468]10~5
Table 4. Branching ratios of 6p 40h states calculated for autoionisation into the 6p el, 5d el,3@25d el, and 6s el continua
1@2
5@2
3@2
1@2
State
K"13/2
K"9/2
K"11/2
6p continuum
5d1@2 continuum
5d5@2 continuum
6s 3@2 continuum
1@2
25.2%
11.8%
4.6%
58.5%
40.7%
53.1%
4.8%
1.4%
28.0%
38.7%
7.9%
25.4%
Table 5. Autoionisation widths (in GHz) for 6p 40l states. Data for
3@2
lO5 were deduced using a l~5 scaling of the 6p 40h K"13/2
3@2
autoionisation width, except for l"3
6p 40l
3@2
l"3! l"4 l"5 l"6 l"7 l"8 l"9 l"10
Width
33
3.5
1.1
0.44
0.2
0.1
0.06
0.03
! Ref. [20]
cannot be determined directly. A very small field-induced
admixture of 6p 40g (and 6p 40f ) character could ex3@2
3@2
plain the observed widths (see also Sect. 3.2).
207
nl states
3@2
3.2 6p
Using the Stark-switching technique discussed in Sect.
2 we studied the 6p nl configuration for n"30, 35 and
3@2
40 for various values of l (or k, see Fig. 5). We investigated
for a given n the l-dependence of the autoionising
linewidth. For these high-l states the wave function of the
Rydberg electron is localized in a region well outside the
classical turning point of the 6p electron at 4a (a "
0 0
0.53 As ) [2]. For this reason it is expected that the
autoionisation decay will be completely suppressed for
high-l states. In that case the decay is dominated by the
radiative transitions 6p!5d and 6p!6s in the Ba`-ion,
corresponding to a linewidth of 20MHz. From a simple
polarisation model, incorporating non-penetrating Rydberg electrons, a l~5 dependence for the autoionisation
linewidth is expected for a given n-value. In Table 5 measured and extrapolated autoionisation widths for 6p 40l
3@2
are given for l"3 to 10. For l'10 the autoionisation
decay rate is expected to be lower than the radiative decay
rate of the 6p electron, resulting in an expected decrease in
signal strength at constant linewidth. Poirier [3] calculated autoionisation rates for barium 6p 24l states
3@2
with l"2, 4, 6, 8. His data show that for l58 the
autoionisation linewidth becomes comparable to the
radiative linewidth. Jones et al. [1] report autoionisation
rates for 6p nl states (n"11—13, l"4—11) using a satu1@2
ration broadening technique which confirms that the
autoionisation rate drops below the radiative decay rate
for lK8.
In Fig.7 one measurement using the Stark-switching
technique is presented. In this case 6s40k"21 is excited in
the first step (connected to l"20 in zero field). We observe indeed a significant decrease in autoionisation width
compared to the l"5 case (Fig. 6). Only a single peak is
observed as the K-splitting is expected to decrease rapidly
with l, see (3), while the coupling changes from jK to jj.
This was also observed by Pruvost et al. [4]. We, however,
do not observe the expected radiative linewidth. We find
a more or less constant linewidth independent of the
k-value (for k'10). For n"30, 35 and 40 autoionisation
widths vary slightly: the average linewidths were 250, 160
and 160 MHz for n"30, 35 and 40 respectively (averaged
for k'10). The smallest width we observed was
113 (11) MHz exciting 6s35k"20.
We investigated several processes to understand the
observed autoionisation linewidths.
— Firstly, the influence of black body radiation during
the Stark switching process was considered. The rate of
absorption of black body radiation is determined as the
inverse of the black body lifetime qB by [18]:
n
1
4a3k ¹
¹
B "6.79]104·
"
s~1,
(6)
qB
3n*2
n*2
n
where a is the fine structure constant, k Boltzmann’s
B
constant, ¹ the temperature and n*"n!d the effective
quantum number. At a temperature of 300 K for
n"30, 35, 40 the black body radiative lifetimes are approximately 45 lsec, 60 lsec, and 80 lsec respectively.
During the Stark switching time (30 lsec) some excitations/de-excitations may take place due to black body
Fig. 7. Autoionisation spectrum recorded in a two-step experiment
with the first laser locked to the 6s40k"21 component shown in the
Stark-manifold of Fig. 5
radiation. However, this will be at a limited scale, and
moreover, most probably to other high-l Rydberg states.
Therefore this process can not be responsible for the
observed autoionisation widths.
— Secondly, admixture of low-l character into the
wave function of the 6snl Rydberg state may occur when
the electric field is not zero after the Stark switching at the
time of the inner-core 6s!6p excitation. This is likely to
be the case in our experiment. Although the excitation
chambers have been carefully designed and every percaution was taken to limit stray electric fields, the residual
electric field in the second excitation chamber used for the
inner-core 6s!6p excitation is estimated to be 5 to
10 mV/cm. As the high-n, high-l Rydberg states are extremely sensitive to electric fields even residual electric
fields of this order of magnitude induce lower- and higher-l character to be mixed into their wave functions. This
has been confirmed through calculations of wave function
compositions of high-l Rydberg states in electric fields of
the order of 5 to 10 mV/cm using a direct diagonalization
procedure. For l"20 at 10 mV/cm all higher-l values mix
into the wavefunction, but admixtures of l-character with
l(10 are extremely small. The effect on the calculated
autoionisation linewidth, using the data provided in Table
5, is such that at most 1 MHz would be added to the
radiative decay rate. Lower-l 6snl Rydberg states, obtained after Stark switching using low k-manifold components show a similar behaviour. For example, for l"9 the
total width is calculated to be 36 MHz and for l"6 the
calculated width is 261 MHz, in both cases the extra
broadening is 1 MHz only.
— Thirdly, the adiabaticity of the Stark switching process may be questioned. The adiabaticity condition for
208
ture of about 0.3% suffices to understand the '100 MHz
width of the observed states.
4 Conclusions
Fig. 8. Schematic drawing of overlapping 6p 40l resonances (l"3,
3@2
4 and 5) with autoionisation line widths of 45, 5 and 0.7 GHz
respectively. (For clarity the oscillator strength of the 6p 40h
3@2
state is taken as one fifth of the oscillator strengths of the other two
states
Stark switching, i.e. the reduction of the electric field
to zero on a time scale such that the character of the
k-wavefunction gradually changes to a well defined
l-wavefunction in zero field without ‘hopping’ to another
k field line (see Fig. 3), is determined by the relation (in
a.u.) [4]:
A B
dF
2
(7)
; n~8(d !d )2
l
l`1
dt F/0
3
where d and d
are the quantum defects of 6snl and
l
l`1
6sn(l#1) states respectively. (dF/dt)"1.4 · 10~30 a.u. for
a field of 1.5 V/cm reducing to zero in 27 lsec. Using the
l~5 scaling law of Freeman and Kleppner [19] to determine the quantum defects for high-l values, the right-hand
side of (7) becomes 2.8 · 10~24 a.u. for n"40 and l"20.
So the adiabaticity condition is easily met.
— Finally, assuming that the Stark switching is correct
and that for k"20 indeed primarily l'10 6s40l states
are excited, a 10 mV/cm stray electric field may induce
mixing of 6p 40l with 6p 40f (and 6p 40g) states. The
3@2
3@2
3@2
6p 40f autoionising states of barium are extremely broad
3@2
(33 to 45 GHz) [20]. The quantum defects of the 6p 40f
3@2
states vary from 0.15 to 0.30. The 6p 40g (quantum
3@2
defects between 0.07 and !0.01 and autoionising widths
between 3.5 to 5 GHz) [16] and 6p 40h resonances (this
3@2
work) both lie on the high frequency wing of 6p 40f (see
3@2
Fig. 8). As 6p 40l states with l'5 have small quantum
3@2
defects and are nearly degenerate with 6p 40h states it is
3@2
probable that 6p 40l states with l'3 do acquire an
3@2
admixture of 6p 40f in a small electric field. An admix3@2
We have measured in high resolution a spectrum of the
6p 40h state with a well resolved fine structure splitting.
3@2
The autoionisation widths for the different fine structure
components compare reasonably well with calculations
assuming a ( jl) K-coupling scheme. The Rydberg electron
may be described with a hydrogenic wave function. Only
the direct integrals have to be taken into account. The fine
structure splitting within the multiplet is understood calculating the electrostatic quadrupole energies in a ( jl)
K-coupling scheme as well.
We have demonstrated the Stark switching technique
in a static electric field and have studied 6p nl Rydberg
3@2
states with high-l values which still show autoionisation.
The residual stray electric fields in the interaction region
where the core electron is excited are of the order of 5 to
10 mV/cm. These residual fields may induce a coupling
with the very broad 6p nf states. A small admixture of
3@2
this configuration is the most probable explanation for the
observed autoionisation of the high-l 6p nl Rydberg
3@2
states.
Although the linewidth could not be reduced down to
20 MHz (corresponding to the radiative decay rate of the
Ba`6p state), the observed resonances are sufficiently narrow and 6p nl states may be used as intermediates for
3@2
further CW excitation to states just below the Ba2`-limit.
This was one of the reasons to investigate the 6p nl
3@2
states at high resolution. A positive aspect of the fact that
the 6p nl states still weakly autoionise is that this pro3@2
vides an electron signal which can be used to lock the
second dye laser to an atomic transition as well.
The authors are indebted to Jacques Bouma for his technical assistance. We would like to thank Robert van Leeuwen for valuable
discussions. Financial support from the Foundation for Fundamental Research on Matter (FOM) and the Netherlands Organization for the Advancement of Research (NWO) is gratefully
acknowledged.
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