Journal of the Physical Society of Japan
Vol. 71, No. 11, November, 2002, pp. 2681–2686
#2002 The Physical Society of Japan
Common Window Resonance Features in K and Heavier Alkaline Atoms Rb and Cs
Michi K OIDE, Fumihiro K OIKE1 , Tetsuo N AGATA2 , Jon C. LEVIN3 , Stephan FRITZSCHE4 , Ralf W EHLITZ5 ,
Ming-Tie H UANG5 y, Brett D. D EP AOLA6 , Shunsuke O HTANIz and Yoshiro A ZUMA5
Institute for Laser Science, University of Electro-Communications, Chofu, Tokyo 182-8585
1
School of Medicine, Kitasato University, Sagamihara, Kanagawa 228-8555
2
Department of Science and Technology, Meisei University, Hino, Tokyo 191-0042
3
Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996-1200, U.S.A.
4
Fachbereich Physik, Universität Kassel, Heinrich-Plett-Str. 40, D-34132 Kassel, Germany
5
Photon Factory, Institute for Materials Structure Science, KEK, Tsukuba, Ibaraki 305-0801
6
Physics Department, Kansas State University, Manhattan, Kansas 66506, U.S.A.
(Received April 30, 2002)
A previous study of subvalence s-shell photoionization of potassium [Koide et al.: J. Phys. Soc. Jpn. 71
(2002) 1676] has been extended to the cases of heavier alkaline atoms Rb and Cs. We have measured the
photoion time-of-flight spectra using monochromatized synchrotron radiation. Dual windows resonance
structure previously observed in K was also found in Rb and Cs, suggesting that thouse structure are
general features in alkaline atoms. We have observed also the Rydberg series of resonances that appear in
dual windows. Our data analysis shows that the resonance widths are broad when compared with its rare
gas neighbors. Based on multiconfiguration Dirac–Fock calculations, the Rydberg series of resonances
were assigned to the 4s1 4p6 5s5p excitations embedded in the 4p5 5s continua for Rb and to the
5s1 5p6 6s6p excitations embedded in the 5p5 6s continua for Cs.
KEYWORDS: photoionization, alkaline vapor, window resonance
DOI: 10.1143/JPSJ.71.2681
1.
Introduction
Window resonances in the inner shell photoionization
processes of many electron atoms have been studied
extensively for a few decades, since Fano’s pioneer work
in early 1960’s.1,2) In the vacuum ultraviolet region,
transitions to the ionization continua in the inner-shell
photoexcitations are the dominant processes. When a
discrete state is embedded in a continuum, they interact
with each other and give rise to characteristic structures in
the absorption spectra, which are called Fano profiles. For
example, the subvalence s-shell photoexcitation of rare gas
atoms gives window resonances. The target gas becomes
partially transparent for photons near the resonance energy.
Earlier studies of Fano profile were carried out mainly for
the light rare gas atoms; they normally have peak-like
resonance structures. However, the recent development of
tunable high-brilliance light sources, such as synchrotron
radiation, and of high-performance computers made it
possible to gain detailed information about the interaction
of atoms with light. In the last decade, the window
resonances have been studied extensively both experimentally and theoretically;1–20) Kþ and heavier alkaline atoms
exhibit window resonances16–19) in the inner s-shell photoabsorption spectra. All these resonances lie in the 20–40 eV
photon energy regions. While, in this region, we have a
considerable direct photoionization probability, the inner sshell photoabsorption probabilities are generally small. The
resonance shape shows a dip structure called the window
resonance. In this cross section region, the depth of the
window resonance is not sensitive to the oscillator strength
Present address: Synchrotron Radiation Center, 3731 Schneider Dr.,
Stoughton, WI-53589, U.S.A.
y
Present address: Physics Department, Saginaw Valley State University,
7400 Bay Road, University Center, MI 48710, U.S.A.
z
E-mail: [email protected]
of the discrete state but rather sensitive to the ratio of the
interference of the continuum cross section with the discrete
state and the total cross section. The window resonances of
rare gases,4–13) their isoelectric alkaline or alkaline earth
ions16–19) have been studied extensively. The studies for the
window resonances were mostly on closed shell atoms or
ions as the targets. For open shell atoms, an early study of
window resonances of alkaline atoms has been reported by
Mansfield.15) He observed a large window structure due to
the first subvalence s-shell hole state in the photoabsorption
spectrum of alkaline atom. Due to the restriction of the early
experimental method, however, he found the spectral
structures similar to the one in rare gas atoms, except the
broadness of the resonance.
Now, we note here that we have observed very interesting
features in a recent experiment; in which the 3s1 3p6 4s4p 4 P
state creates a deep window structure in K photoabsorption
resonances.20) The dual window resonance, which is a large
4
P window with a subsidiary small 2 P window structure has
been reported. We now have to be concerned whether this
feature is general in alkaline atoms. To compare K and the
other heavier alkaline atoms, Rb and Cs, we observed
charge-state resolved photoion-yield spectra for the ðm 1Þs ! np resonance of Rb (m ¼ 5) and Cs (m ¼ 6). MultiConfiguration Dirac–Fock (MCDF) calculations21) were
performed in order to understand the spectral structure.
2.
Experimental Details and Results
Photoion-yield spectra were measured at beamline BL-3B
of the 2.5-GeV electron storage ring of the Photon Factory,
KEK in Tsukuba, Japan. The beam line is composed of a
prefocusing toroidal mirror, a spherical grating monochromator (24-m SGM) with a movable exit slit, and refocusing
mirrors.22,23) The photon energy range covered by the
200 lines/mm grating, which was used in this experiment, is
10–80 eV. The entrance and exit slits of the monochromator
2681
J. Phys. Soc. Jpn., Vol. 71, No. 11, November, 2002
M. KOIDE et al.
N2 trap
n
toio
Pho
SR
P
MC
Atom
eter
trom
ec
F sp
TO
Ion
ller
repe
Metal vapor oven
Fig. 1. Sketch of the experimental setup and measurement system.
were set to 100 m each resulting in an estimated bandpass
of 50 meV.22)
Figure 1 shows a sketch of our collision chamber and the
relevant electronic components. The vacuum system was
evacuated by two independent pumping systems with a turbo
molecular pump and a rotary pump. Monochromatized
synchrotron radiation of 28–45 eV crosses a beam of alkaline
atoms created by a metal vapor oven mounted on the
collision chamber. The metal vapor oven was composed of a
thermocoaxial heater wound around a stainless steel furnace
and a three-fold radiation shield. The temperature of the
oven was monitored by a thermocouple attached to the
bottom of the furnace. The operating temperature for K is
145–150
C, and the vapor pressure is estimated to be 4.0–
5:5 104 Torr in the furnace. This pressure ensured that
single–collision conditions applied in the chamber. The
operating temperatures for Rb and Cs were about 133
C, and
120
C, respectively, which were chosen so that the vapor
pressure is the same for all three samples. The background
pressure in the experimental chamber is 1:0 107 Torr.
12
65x10-3
3s 3p 4s4p
Rb+ Intensity (arb. u.)
11
10
9
8
K
7
36.4
36.8
0.125
5s15p66s6p
6
37.2
37.6
Photon energy (eV)
1
6
4s 4p 5s5p
60
55
+
1
K+ Intensity (arb. u.)
The collision region is surrounded by a copper plate cooled
with liquid nitrogen to trap the metal vapor after crossing the
collision region.
This study was carried out using a TOF mass spectrometer24) as an ion detector mounted in a direction
perpendicular to both the atomic and photon beams. The
TOF spectrometer consisted of an ion repeller, an extraction
plate, a field-free drift tube25) and a microchannel plate
(MCP) detector. The alkaline ions produced in the interaction region were pushed into the TOF tube by periodic
voltage pulses applied to the ion repeller. The pulses were
provided by a pulse generator having an amplitude of
+100 V, a width of 4 s, and period of 50 s. The pulse
generator also triggered a time-to-amplitude converter
(TAC). Photoions were counted and their number saved on
a computer at each given photon energy after a fixed
acquisition time. The photoion counts are normalized by the
photon flux of the synchrotron radiation monitored during
measurement. Here, the photon flux was obtained by
converting a photo emission currents from the downstream
mirror of the monochromator into the flux at the interaction
region. The conversion factor was determined separately as a
function of the photon energy. In order to calibrate the
conversion factor, a Heþ ion-yield spectrum was measured
in the same energy region as for the alkaline ðm 1Þs ! np
measurements. The photon energy was calibrated by taking
photoion-yield spectra across the He K-edge,26) He 2s np
double-excitation,14) K 3p ! nl excitation,27) Ar 3s ! np
excitation,9,10) Kr 4s ! np excitation7) and Kr 4p ! nl
excitation.8) Total photoion-yield spectra obtained by
summing over the charge-resolved photoion-yield spectra
of singly-charged and doubly-charged photoions.
Figure 3 shows our photoion-yield spectra for K, Rb, and
Cs atoms, respectively. By comparing the spectra shown in
Figs. 3(b) and 3(c) with 3(a), we find several common
features. They are due to the similarity of their shell
structures and binding energies. Three common features
appear in the singly-charged photoion-yield spectra: (i) the
lowest predominant window and subsidiary shallow window
are both formed by the first subvalence s-electron excitation,
Cs Intensity (arb. u.)
2682
50
0.120
0.115
0.110
0.105
0.100
45
Rb
32.4 32.8 33.2 33.6 34.0 34.4
Photon energy (eV)
Cs
0.095
26.8
27.2
27.6
28.0
Photon energy (eV)
Fig. 2. The first excitation resonance of ðm 1Þs1 ðm 1Þp6 msmp along with a fit curve according to eq. (3). Because the two window
resonances are very close together, both were fitted simultaneously.
J. Phys. Soc. Jpn., Vol. 71, No. 11, November, 2002
+
12
n=4
(a)
0.16
6 789
5
n=4
0.14
6 (7) 8 9
5
(4snp 1P) 2P
10
0.12
8
0.10
Double
Ionization
Limit
6
0.08
0.06
4
K2+ Intensity (arb. u.)
K Intensity (arb. u.)
14
M. KOIDE et al.
0.04
2
36.0
37.0
38.0
39.0
Photon energy (eV)
40.0
41.0
2.2x10-3
n=5
(b)
7 8
n=5
(6)
2.0
1.8
7 8
2+
Rb
1.6
60
1.4
50
1.2
+
Double
Ionization
Limit
40
1.0
Intensity (arb. u.)
Rb Intensity (arb. u.)
70x10-3
6
0.8
0.6
30
31.0
32.0
33.0
34.0
35.0
36.0
Photon energy (eV)
37.0
12x10-3
0.14
n=6
n=6
(c)
7
10
8
2+
1
2
8
Double
Ionization
Limit
+
6
4
0.06
Intensity (arb. u.)
(6snp P) P
0.10
0.08
2
0.04
27
28
29
30
31
32
Photon energy (eV)
33
34
Fig. 3. Partial photoion-yield spectra of (a) K, (b) Rb, and (c) Cs. Singlycharged photoion yields are shown as dots and doubly-charged photoion
yields are shown as a solid line. Our calculated ðm 1Þs np resonance
energies and two ðm 1Þs ionization threshold energies, 3 S and 1 S are
shown in the upper part of the panel. The energies of the doubleionization thresholds were obtained from other data.30–32)
ðm 1Þs ! mp. (ii) A higher Rydberg series does not
appear clearly in the singly-charged photoion-yield spectrum. However, several peaks corresponding to the higher
Rydberg series were observed in the doubly-charged
photoion-yield spectrum. Because the Cs2þ spectrum is
strongly affected by the 4d giant resonances due to the 4th
order light of the monochromator grating, we could not
verify the presence of the resonance structures as in the other
alkaline spectra. (iii) The resonance widths are broader than
the ðm 1Þs ! np excitations of their neighboring rare
gases.
3.
from multiconfiguration Dirac–Fock (MCDF) computations.
However, a concrete reasoning were rendered to the
succeeding studies on the question of why an optically
forbidden level appears to play an important role for the
formation of such large window structures in the 3p direct
photoionization spectrum.
When a discrete state configuration is embedded in a
continuum, the discrete and the continuum interact each
other to form a single quantum state. As has been shown by
Fano1,2) the wave function of the system is described by a
linear combination of a discrete state wave-function and
continuum wave-functions. In the present case, the discrete
state corresponds to the intermediate state ðm 1Þs1 ðm 1Þp6 ms np and the continuum state corresponds to the final
ionic state ðm 1Þs2 ðm 1Þp5 ms þ e . The dominant direct
ionization processes are ðm 1Þp ! s; d in the energy
region of interest. Here, we note that the strength for a direct
s-shell valence photoionization is negligible when compared
with the ðm 1Þp photoionization. The actual photoionization is the sum of the excitations to the relevant resonance
states and the direct continuum which has no interaction
with discrete configurations. Then the Fano profile is given
by the following formula
2
2
2 ðq þ Þ
ð1Þ
ðEÞ ¼ T 1 þ1 ;
2 þ 1
8
Cs
Cs Intensity (arb. u.)
0.12
7
2683
Analysis and Discussion
In a recent work,20) we have suggested that a part of the
window resonances of K 3s ! np photoexcitation were of
the 4 P configurations. The grounds for this argument was the
very good agreement of the experimental data with results
where E, Er , and are the incident photon energy, resonance
energy, and resonance width (FWHM), respectively. The
quantity is the reduced energy in unit of half the resonance
width ðE Er Þ= 12 . And the parameter T (¼ a þ b ) is the
total photoabsorption cross section, which is the sum of the
cross sections for the excitations to the resonance state, a ,
and the non-resonant state, b . The parameter q is called
profile index or Fano parameter, and this parameter
characterizes the shape of the resonance spectrum. In the
single channel case, the profile index q is given by the
following equation,
hdjzjgi
q ¼ pffiffiffiffiffiffiffiffiffiffiffi
:
ð2Þ
1=2hcjzjgi
In the numerator is the matrix element of the excitation from
the ground state jgi to a discrete state jdi, and in the
denominator is the matrix element of the excitation from the
ground state jgi to a continuum state jci. Although the
present case is not valid for a single channel, we can still
consider q as a profile index in a formal treatment of the
spectral shape. A close to zero q-value and a large a result
in a window resonance. At the resonance energy, the
resonant part of the absorption cross section almost vanishes.
The window depth is determined by the ratio of a to a þ
b (often defined as 2 ¼ a =ða þ b Þ).
In order to obtain the profile parameters from the
measured spectra, equation (1) was modified by taking into
account a monochromator bandpass WBP ¼ 50 meV,28)
0 2
02 ðq þ Þ WBP
ð3Þ
ðEÞ ¼ T 1 þ1 :
02 þ 1 Here, 0 ¼ ð1 þ WBP =Þ1 , ¼ ðE Er Þ= 12 , and 0 ¼
ð1 þ WBP =Þ1 . The energy difference of ðm 1Þs states
with different total angular momenta J ¼ 1=2 and 3=2, is
2684
J. Phys. Soc. Jpn., Vol. 71, No. 11, November, 2002
M. KOIDE et al.
Table I. Calculated energies (eV) for ðm 1Þs hole states and the
ionization limit of K, Rb, and Cs. The right two columns show the
observed energies. Values shown in brackets are tentative values obtained
using the quantum defect law of the series.
4
Main config.
Pð93%Þ þ2 Pð7%Þ
1/2
4
Pð7%Þ þ2 Pð93%Þ
3/2
Obs.
1/2
3/2
Lower Higher
K
3s1 3p6 4s4p
36.71
36.71
37.14
37.16
36.72 37.45
3s1 3p6 4s5p
38.93
38.93
39.52
39.52
38.89
—
3s1 3p6 4s6p
3s1 3p6 4s7p
39.57
39.86
39.57
39.86
40.12
(40.12)
40.12
(40.12)
39.68
39.9
—
—
3s1 3p6 4s8p
40.02
40.02
40.55
40.55
40.02
—
3s1 3p6 4s9p
40.11
40.11
40.65
40.65
40.08
—
40.3
40.7
3s1 3p6 4sp
40.40
40.78
Rb
4s1 4p6 5s5p
33.42
33.45
33.89
33.93
4s1 4p6 5s6p
4s1 4p6 5s7p
35.65
36.26
35.66
36.26
(36.13)
36.84
(36.13)
36.84
4s1 4p6 5s8p
36.53
36.53
37.11
37.1
4s1 4p6 5sp
37.03
37.54
33.36 33.97
35.44
36.14
—
—
—
—
37.0
37.4
Cs
5s1 5p6 6s6p
27.48
27.53
27.94
28.03
5s1 5p6 6s7p
29.61
29.61
30.17
30.17
—
—
5s1 5p6 6s8p
5s1 5p6 6sp
30.19
30.17
30.7
30.71
—
—
—
—
—
—
27.42 27.76
very small. For example, the splitting between 3s1 3p6 4s4p
4
P1=2 and 4 P3=2 , which is the largest J splitting of the series,
is 5.9 meV according to our calculation (see Table I). Hence,
the two J states merge within the resonance width. Therefore
we fit all the fine structure states 4 P1=2 and 4 P3=2 as a single
width. As the first excitation states, the dual windows are too
close to fit separately, they are fitted simultaneously. The
results of a least-squares fit are shown in Fig. 2 and Table II.
One statistical error is included in the results. All of the q
values are positive and almost all q values are less than 1.
Regarding the dual windows, the value of the first window
is broader than the second one.
We have also performed Multiconfiguration Dirac Fock
(MCDF) calculations for the observed resonances utilizing
the General purpose Relativistic Atomic Structure Program
(GRASP) 92.21) Because our calculation is relativistic, the
spin multiplicity of the state cannot be of our primary
concern. However, it is convenient to gain a relationship of
the present relativistic calculation to the conventional nonrelativistic LS-scheme of representation. We used also an
older version of GRASP code (GRASP2) for the nonrelativistic symmetry indices such as the total spin S and the
total orbital angular momentum L, which are useful to refer
the configuration state functions expressed in terms of nonrelativistic scheme of conventions. The energies obtained for
each level are shown in Table I and shown as bars in Fig. 3.
We have calculated the total energy of the excited states,
ðm 1Þs1 ðm 1Þp6 ms np with m ¼ 5 for Rb and m ¼ 6 for
Cs, which have three open shells and six different terms
according to the LS coupling scheme and the total angular
momenta J. The terms are as follows: ðm 1Þs1 ðm
1Þp6 ms np 4 P1=2;3=2 , ðm 1Þs1 ðm 1Þp6 ms np 2 P1=2;3=2 , and
another 2 P1=2;3=2 .
The number of configuration state functions (CSF) used
for the subvalence s-shell hole states were 1675 for K, 3264
for Rb, and 2963 for Cs. The accuracy of our calculations
were assessed by calculating the well known binding
energies. For example, we obtained 24.63 eV for the Kþ
3s2 3p5 4s 3 P2 state relative to the K ground state, and
24.75 eV for 3 P1 , 24.89 eV for 3 P0 , and 25.11 eV for 1 P1 . We
obtained 4.18 eV for the energy to create Kþ 3s2 3p6 from the
K ground state, and 35.53 eV to create K2þ 3s2 3p5 (See
Koide20) Table III). The good agreement of these values
with previous data27,31) supports the reliability of the present
calculation. Hence, our calculation accuracy is estimated to
be about 0.5 eV. It is accurate enough to identify the
resonances in the question.
Although computations have been carried out for three
different alkaline atoms, the results are very similar because
their sub-valence shells have the same electronic structure
and their inner electrons below the sub-valence shell are
tightly bound. In all the cases of K, Rb, and Cs, a pair of the
energetically lowest entries of ðm 1Þs1 ðm 1Þp6 ms np
states consists of 93% 4 P and 7% 2 P configurations, and a
pair of the second lowest entries is of 7% 4 P and 93% 2 P
configurations. Therefore, we may, for convenience, call the
lowest entry as of 4 P state and the second lowest entry as of
2
P state. There is still a pair of the energetically highest
entries in ðm 1Þs1 ðm 1Þp6 ms np states. We note that the
2
P symmetry dominates this pair and sits a couple of
electron volt above the second lower entries, and further, this
pair is more or less dipole unfavored, providing us with no
contribution to the photoexcitation spectrum.
Table II. Fano parameters as derived from eq. (3). For the first excitation states ðm 1Þs1 ðm 1Þp6 msmp both the 4 P and the 2 PðÞ
term are given. For the other states, parameters are given only for the 4 P term.
K
n
4
4
5
6
7
8
9
Er (eV)
36.72(5)
37.4(6)
38.90(8)
39.6(1)
39.91(8)
40.0(2)
40.1(1)
(eV)
0.21(5)
0.15(9)
0.16(8)
0.09(9)
0.07(9)
0.06(9)
—
q
0:23 0:01
0:6 0:1
0:14 0:03
1:0 0:2
0:8 0:1
0:8 0:1
0:6 0:3
n
5
5
6
7
Er (eV)
33.36(1)
34.0(1)
35.45(2)
36.1(1)
(eV)
q
0.16(5)
0:11 0:05
0.1(2)
0:4 0:1
0.10(3)
0:12 0:02
0.1(1)
0:3 0:08
Rb
Cs
6
6
Er (eV)
27.42(1)
27.8(1)
(eV)
q
0.15(1)
0:26 0:01
0.06(1)
0:5 0:1
J. Phys. Soc. Jpn., Vol. 71, No. 11, November, 2002
Our computations shows that, in general, the ionic core
state of the sub-valence s hole is strongly affected by
configuration mixing with the p2 $ sd conversion. The
dominant configuration mixing is the conversion of p2 $ sd
at the main configuration states ðm 1Þsðm 1Þp6 ms np.
More precisely, the mixing ratio of ðm 1Þs2 ðm 1Þp4 ðm 1Þd in the ðm 1Þs1 ðm 1Þp6 are 25% for K, 28% for Rb,
and 32% for Cs. This is in agreement with other recent
investigations.10,15)
In Rb, the 4f mixing lowers the ground state total energy
by 1.17 eV, and the first subvalence s-shell state energy by
0.18 eV, respectively. And in Cs, the corresponding values
are 1.09 eV and 0.26 eV. Although these effects are small
compared to those by the mixing of d-orbitals, they cannot
be ignored; the consideration of these effects are indispensable to carry out the identification of the levels of
current interest.
To compare the observations and the calculations (see
Fig. 3), the predominant window and subsidiary small
window correspond to the first subvalence s-hole states ðm 1Þs1 ðm 1Þp6 ms mp 4 P and 2 P. Following the small window
resonances at higher energies, there are higher members of
the Rydberg series (n m þ 1). The higher doublet states,
ðm 1Þs1 ðm 1Þp6 ms np 2 P1=2;3=2 , have almost the same
energy as of the ðm 1Þs1 ðm 1Þp6 msðm þ 1Þp states.
In Fig. 3(a), dual windows corresponding to the
3s1 3p6 4s4p are found in the K spectrum at 36.7 eV and
37.4 eV. The energy splitting between 3s1 3p6 4s4p 4 P and 2 P
is reproduced well by theory within our calculation
accuracy. Higher energy windows may be assigned to a
Rydberg series of 4 P. The calculated energies of higher 4 P
states with n ¼ 5, 6, and 7 almost agree with the observed
window positions. In Fig. 3(b), new dual windows
corresponding to the 4s1 4p6 5s5p were observed in the Rb
spectrum, too. On the analogy of the K case, the first
predominant window, at 33.36 eV, and subsidiary small
window in the Rbþ spectrum could be assigned to
4s1 4p6 5s5p 4 P and 2 P, respectively. Higher energy windows
may be assigned to a Rydberg series of 4 P. The energy
splitting between 4s1 4p6 5s5p 4 P and 2 P was reproduced well
by the calculation. The calculated energies of higher 4 P
states with n ¼ 6 and 7 are good in agreement with our
observations. In the spectral curve of doubly charged ion
Rb2þ in Fig. 3(b), a window is observed at 33.4 eV. Such a
window was not observed clearly in the K2þ spectrum. The
origin of difference is not clear. It might be of interest to
make clear if such a feature is common to the alkaline atoms.
Fig. 3(c) shows the first window at 27.42 eV and subsidely
small window at 27.76 eV in the Csþ spectrum. These
resonances are assigned to 5s1 5p6 6s6p 4 P and 2 P, respectively. The energy splitting between 4 P and 2 P is reproduced
well by the calculation. The calculation results show that a
part of the following small structures may be assigned to
5s1 5p6 6s np 4 P with n 7.
Although the K double-ionization threshold was not
observed, the Rb double-ionization threshold was observed
clearly in the Rb2þ spectrum. The Rb double-ionization limit
of 31.50 eV, which was derived empirically by Catalán and
Rico,32) is in good agreement with our observation. In
contrast to the singly-charged photoion-yield spectra, the
doubly-charged ion-yield spectra show some additional
M. KOIDE et al.
2685
peaks. In the Rb2þ spectra, two peak structures were
observed at 34.1 eV and 35.5 eV. They can be assigned to
4s1 4p6 5s5p 2 P and to 4s1 4p6 5s6p 2 P, respectively. The next
peak at 36.2 eV may be 4s1 4p6 5s7p 2 P. In the K2þ , 2 or 3
peaks can be identified. The peak at 39 eV may be attributed
to 3s1 3p6 4s4p 2 P. The following peaks are members of a
Rydberg series 3s1 3p6 4s np 2 P (n 5). 3s1 3p6 ½4s np 3 P 2 P
(n 6). The first peak due to a 3s ! 4p 2 P excitation was
not observed clearly, but a small peak is expected to be
present in analogy to the peak observed in the Rb spectrum.
As the Cs2þ spectrum strongly suffers the fourth order light
contribution, the large background structure below 32 eV has
no relation to the 5s ! np resonances. Here, we only like to
point out that the photoexcitation spectrum of Cs has the
same dual window as the other alkaline atoms.
The series limits could not be observed in the singlycharged photoion spectrum, but were clearly observed in the
doubly-charged spectrum. We also calculated the energy
limits and they agree fairly well with our measurements.
There are two limits, namely ðm 1Þs1 ðm 1Þp6 ms 1 S and
ðm 1Þs1 ðm 1Þp6 ms 3 S. The 3s ionization thresholds of K
are 40.4 eV (3 S) and 40.8 eV (1 S) from our calculation. The
large structure beginning at 40.3 eV and its shoulder at
40.7 eV correspond to the respective energy limits.
The 4s ionization thresholds of Rb are 37.03 eV (3 S) and
37.54 eV (1 S) from our calculation. The Rb2þ spectrum has a
large structure starting at 36.4 eV and it has two shoulders at
37.0 eV and 37.3 eV. The higher energy points of the
shoulders correspond to the two 4s ionization limits, 3 S and
1
S, respectively. The first point of the broad structure, at
36.4 eV photon energy, may not be the series limit of the
window resonances. The binding energy of Sr I 5s4f is
0.89 eV.30) This energy should be almost the same as for the
Rb I 4s1 4p6 5s4f binding energy considering the effective
nuclear charge for the valence electron. For example, we
have measured an energy difference between Rb I
4s1 4p6 5s5p 4 P and Rb II 4s1 4p6 5s 3 S of 3.6 eV and the
energy difference between Sr I 5s5p 3 P and Sr II 5s is
3.9 eV.30) Utilizing this similarity, we can assume that the
foot of the broad structure at 36.4 eV in the Rb2þ spectrum
may be formed by double Auger transition from the excited
states 4s1 4p6 4f 5s.
4.
Summary
The window resonances of heavy alkaline atoms formed
by subvalence s-shell photoabsorption were observed
utilizing the monochromatized synchrotron radiation and
the TOF spectroscopy technique. The presence of dual
window resonances is verified also in heavier alkaline atoms
such a Rb and Cs. We performed a series of MCDF
calculations and assigned all the levels observed. We
obtained the energy positions of excited states, the profile
index q, the resonance width , and the resonance energies
Er . We identified the every structure based on the
comparison in the our calculation to the observation results.
In the doubly charged photoion yield spectra, we observed
the 2 P series as peak like structures and obtained subvalence s-shell ionization thresholds.
We point out that the speculations in a previous study on
the K atom can be extended to cover the heavier alkaline
atoms such as Rb and Cs. For all the alkaline atoms, K, Rb,
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J. Phys. Soc. Jpn., Vol. 71, No. 11, November, 2002
and Cs, which we studied so far, we found a dual window
structure that can be attributed to the ðm 1Þs1 ðm
1Þp6 ms np resonances. Energetically good agreement has
been obtained between experiment and theory when we
assign the energetically lower entry as of the 4 P configuration dominating state and the upper entry as of the 2 P
configuration dominating state. Although the present assignment for the dual window resonance structures is not
completely solid, we would note that all the investigations in
the present paper support the assignment. We should, then,
suggest the necessity of further extensive study both
experimentally and theoretically to realize a clear feature
of the mechanism of the dual window structures.
Acknowledgment
Support to R.W. from the Japan Society for the Promotion
of Science is gratefully acknowledged. This work was
performed under the approval of the Photon Factory
Program Advisory Committee (Proposal No. 98G028).
Discussions with Dr. X.-M. Tong, Dr. D. Kato, Prof. Y.
Suzuki, Prof. C. Yamada, and Prof. T. Watanabe are
appreciated.
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