8 September 1995
ELSEVIER
CHEMICAL
PHYSICS
LETTERS
Chemical Physics Letters 243 (1995) 94-101
Emission spectra of calcium dimer. The A
+
u-X
+
l Xg
system
M.A. Gondal, M.A. Khan, M.H. Rais
Laser Research Section, Energy Resources Division, Research Institute, King Fahd University of Petroleum and Minerals,
Dhahran 31261, Saudi Arabia
Received 8 February 1995; in final form 13 July 1995
Abstract
The AIX~+-X 1Xg+ spectral system of Ca 2 has been studied in two independent experiments. The collision-induced
fluorescence due to this band was investigated following the resonant excitation of the 4s4p 3P1 metastable state of calcium
using a Nd : YAG laser pumped dye laser. In another experiment, a low current glow discharge in calcium vapor was used.
We have assigned 86 spectral lines to this band system for vibrational quantum numbers (v'= 10-13 and v"= 0) by
applying a Dunham type analysis. The A 1Xu+ state dissociation energy D~ is estimated to be ~ 8693.6 + 1 cm-1. The
processes involved in the collisional excitation of the upper molecular state are discussed.
1. Introduction
The alkaline earth metal dimers form a weakly
bound van der Waals ground state and are therefore
potential candidates for metal vapor excimer lasers.
The weakly bound van der Waals character of the
2 2
X 1~; ground state of Ca is due to the tr_~tr,
valence electron configuration with two bonding (~rg)
and two antibonding (tr.) electrons. Studies have
been carded out in the past to investigate the red and
green system arising due to A - X and B - X transitions in the vapor phase using the laser-induced
fluorescence technique [1-5]. However conclusions
differed regarding the ground state as well as the
excited states [1-5].
Belfour and Whitlock [1] recorded the first highresolution absorption spectra of Ca 2 and assigned the
green system as A IE~+-X 1 ~ . They estimated the
ground state dissociation energy D~' to be 1075 + 150
cm -1, while the upper state dissociation, D', is of
the order of 6000 c m - l , assuming the state corre-
lates in the long range to 1S + l p calcium atoms.
Vidal confirmed these vibrational assignments from
the laser-induced fluorescence measurements of the
green system using an argon ion laser [2]. He improved the molecular constants by extending the
term value data and calculated RKR (RydbergKlein-Rees) and IPA potential curves for both
molecular states. He concluded that the green system
upper state dissociated to 1S + 1 0 and that the ground
state dissociation energy is -- 1095 ± 1 cm -1 while
the excited state has D " - - 3 9 8 0 c m - 1 . Subsequent
studies have, however, introduced considerable confusion into this issue. Earlier, Andrews and coworkers conducted absorption, LIF and laser excitation experiments on calcium dimer in rare gas matrices and assigned the red system as A 1 Eu+ - X 1 Eg+
arising from the 1S + 1p atomic limit [6-9]. Wyss [3]
reported gas-phase observations of the Ca 2 red system and gave the value of D~' = 2075 cm-1 close to
the matrix value. Since this value is quite large
compared with the value of 1075 cm-1 reported by
0009-2614/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved
SSDI 0 0 0 9 - 2 6 1 4 ( 9 5 ) 0 0 8 1 2 - 8
Mdi. Gondal et al. / Chemical Physics Letters 243 (1995) 94-101
Balfour and Whitlock for the green system, Wyss
suggested new assignments for the red and green
calcium dimer systems similar to what was proposed
by Sakurai and Broida [10]. They suggested that the
red system involves transitions from the ground state
itself, while the green system must involve transitions between two excited electronic states. Theoretical calculations [11] and recent experimental studies
by Hofmann and Harris [5] have shown two bound
1Eu states correlating to i s +~P and ~S+~D calcium atoms. The red system upper state is A 1~u+
which correlates adiabatically to 1S + 1D atoms. This
state is stron~!y perturbed by the a 3IIu that correlates to S + P atoms. The green system upper state
is B 1 Eg+ which correlates adiabatically to ~S + 1p
calcium atoms. This was also confirmed from LIF
studies of calcium dimer by Bondybey and English
[4]. In spite of numerous theoretical as well as
experimental studies by different groups, the value of
T~ for this state has an error range of about 1000
cm -1 [11] and similarly the value of D, varies
between 9200 and 1000 cm -1 [4,5,11]. These are the
reasons which motivated us to investigate the spectra
of Ca dimer in more detail.
We have studied the red system corresponding to
the A 1~ u+- X 1~g+ transition in two different but
complementary experiments. In the first, the dimer
spectra were measured in resonant laser excitation of
the 4s4p 3p~ state of atomic calcium. The same
spectra were reproduced when a low current glow
discharge in calcium vapor was employed. The population mechanism and the assignment of the observed spectral lines to this band system are presented using the Dunham coefficients recently available [2,4,5]. The value of the dissociation energy D~
and the band origin energy V0o for the A 1~u+ state
is estimated from the recorded spectra and by fitting
all 86 observed transitions.
2. Experimental details
The experimental arrangement for obtaining the
laser-induced fluorescence of calcium dimer is identical to that described in earlier publications [12-17].
A schematic diagram is given in Fig. 1. The calcium
dimers are generated in a stainless-steel tube having
inner diameter of 25 mm and a length of 300 mm
95
Ilrror
i
ergy
mp
r I .........
|
Fig. 1. Schematic diagram of the experimental apparatus used for
the study of collision-induced emission spectra of Ca 2.
containing high-purity calcium ( = 99.99%). The
central 80 mm portion of the tube could be heated to
950°C using resistance heaters. The oven was operated around 875°C with 825 mbar of argon as buffer
gas in the present experiment. The system was baked
at 350°C for many hours to remove any water vapor
from the walls of the stainless-steel pipe and calcium
sample. During this baking out period, argon gas was
back filled into the system and pumped out several
times. Prior to the loading of the heat-pipe with Ca,
the system was baked at 900°C for several hours.
This procedure can reduce impurities such as Call
and CaO. We used a N d : Y A G (Quanta Ray DCR
2A) pumped dye laser (Quanta Ray PDL2) to excite
the 4s 2 1So-4S4p 3P1 transition of calcium. The collision-induced fluorescence was collected in the
backward direction using an off-axis lens and a
mirror. This was important to avoid the detection of
scattered laser radiation. The fluorescence was observed by means of a grating monochromator (Spex
Compudrive CD 2A) with a theoretical resolution of
96
M.A. Gondal et al. / Chemical Physics Letters 243 (1995) 94-101
0.4 cm -1, and detected with a thermoelectrically
cooled photomultiplier (Thorne EMI 9558B). The
electrical signal generated by the photomultiplier
was fed into a Box-car averager (EG&G 4421) and
processed by a signal processor (EG&G 4402). The
detection system averaged the 20 pulses per sample
point.
In order to record the dimer spectra in a glow
discharge, a similar arrangement was used as described in an earlier publication [18]. Ca vapor was
again produced in the heat-pipe oven by maintaining
a temperature of the order of 825°C with Ar as a
buffer gas. A low current glow discharge was created
in the vapor by applying a voltage of the order of 20
V on a central coaxial rod (2.5 mm diameter) using a
stabilized power supply (HP model 6186C). The
main body of the pipe was grounded. Typical discharge current was of the order of 200 IxA. The light
emitted by the glow discharge was collected by a
lens and focused on the entrance slit of the scanning
monochromator and photomultiplier as described
previously. The output of the photomultiplier was
fed into a chart recorder (HP 7132A)
of fluorescence spectra. As illustrated in the figure,
the 4s4p 3P1 state is prepared by resonant excitation
from 4s 2 ZS0 ground state of atomic calcium using a
Nd:YAG pumped dye laser tuned to 657.278 nm.
The 4s4p 3P1 state is metastable (r = 350 Ixs) and
can combine with atoms in the 4s 2 1S0 ground state
to ~ive the molecular states such as 3Eu, 3II_, 3I-I
-~'
3
~
u
or Eg. From these states, only the II~ state has the
proper symmetry to perturb homogeneously the
neighboring A 1E~+ state. This is because the gerade
states cannot perturb ungerade states. This seems to
be the most probable channel of energy transfer in
our case, where population from the optically prepared 3p state is transfered first to a 3IIu state and
then through collisions or level crossing to the A 1Eu+
state. Collision-induced triplet to singlet population
transfers can be highly efficient and have been studied extensively in alkali dimers [19-21]. The a 31-IX 1E ÷ is not an allowed transition while A 1 +
X ~E
--gg+ is allowed as evidenced by the high intensity
and short lifetime of the red system. The various
possible processes involved in the excitation and
subsequent emission are
Ca 4s 2 1S0 + hv(657.278 nm) o Ca 4s4p 3P1,
(1)
3. Results and discussion
Fig. 2 shows a schematic of the Ca 2 energy levels
of interest as well as for calcium atoms together with
the pumping scheme involved in the excitation of the
upper levels of A 1E u+ responsible for the generation
Ca 4s4p 3P1 + Ca 4s 2 150 ~-~ Ca2(a 31-I),
Ca2(a 31-I) + M o Ca2(A 1E~+) + M + AE,
(2)
(3)
Ca2( m l~u+ ) (...>Ca2( x 1 ~ ; ) .~_ h1.'(620-640 nm),
(4)
~I
Ca2
25
/Cottisi ..... d/or C. . . . Crossing
"~1o
o
or
Ca
I$ ,0
~l E
k~
~
x,r;
I
J
g-I
I
I 1
's. 's
Fig. 2. Energyleveldiagramof selectedstates of Ca 2 showingthe
collision-inducedexcitationscheme followingresonantexcitation
of the 4s4p 3P1 state of Ca.
Ca 4s4p 3P1 + M o Ca 4s3d XD2 + M,
(5)
Ca 4s3d 1D2 + as 2 1So o Ca2(A 1E~+),
(6)
where M - - C a , argon, and AE = change in kinetic
energy. Most of these collision-induced processes in
Ca vapor are efficient in transferring population from
lower atomic states to higher states and have been
investigated in our laboratory, as described in recent
publications [13,15,16].
Fig. 3 shows a part of the collision-induced spectra due to Ca dimer in the range 16062-15936 cm -1
following resonant excitation of the Ca 4s4p 3P1
metastable state recorded at 875°C. The total pressure inside the heat pipe = 825 mbar. The same
spectra in the 16065-15625 cm -1 region at higher
M~A. Gondal et al. / Chemical Physics Letters 243 (1995) 94-101
resolution were reproduced by creating a low current
glow discharge inside the Ca vapor. To achieve
higher resolution, the slit width on the monochromator was reduced to 10 Ixm and the resolution achieved
was 0.98 cm -1. The high-resolution spectra could be
recorded only in the glow discharge and were not
possible with laser-pumped vapor. This is due to two
reasons. First the discharge fills the entire volume of
the vapor while the laser beam is only 5 mm in
diameter, hence the detected fluorescence is weaker
in the case of the laser pumped vapor; second the
laser does not excite the upper molecular state
(A 1 ~ ,+ ) directly and this level is populated through
collisions later on while in the case of a discharge,
the electrons transfer the population more efficiently
from the ground state to upper excited states of the
molecule.
Figs. 4a and 4b show typical examples of highresolution spectra in the 16065-15977 and 1586815794 cm -1 region. The 620-640 nm (16129-15625
cm -1) region is virtually without any lines from
atomic calcium. This puts some constraints on the
accuracy of the measured wavelengths in the observed spectra due to the non-availability of frequency markers. An independent calibration spectrum was recorded using a hollow cathode calibration lamp (Cathodean model 3QQAY-C610) containing argon and calcium. The monochromator scanning
speed and the chart recorder speed were kept the
same as in the original experiment. A number of
transitions from Ar were available here for use as
97
Ii
(a)
I
,i
I j
'i
I
i
16060
16040
16020
16000
15980
Wavenumber(cm-1)
(b)
I
. b
15860
I
: .If ,! Jl,l
15840
15820
. i
15800
Wavenumber(cm-1)
Fig. 4. Examples of the spectra recorded at 825°C in a low current
glow discharge: (a) in the 16065-15977 cm -1 region; (b) in the
15868-15794 cm -1 region. The discharge current was 200 I~A at
argon buffer gas pressure of 825 mbar. Here the slit width = 10
p~m and the achieved resolution was 0.98 c m - 1 .
standards and a dispersion curve for the region of
interest was obtained. The assignment of the observed line frequency ' v ' was done using
v=T'(v', J') -T"(v", J"),
(7)
where v is the observed frequency, and T'(v', J')
and T"(v", J") are the term values of the excited
and ground state respectively, where
T(v, J) = Eaik(v+O.5)i[J(J+
1)] k.
(8)
i,k
.,
16060
.
.
.
.
,
. . . . .
16020
,
.,
,
.
,
15980
,
. . . . . .
i .
15940
Wmvenumber(cm-1)
Fig. 3. Collision-induced spectra of Ca 2 A 1 2 , - X 12g system
recorded in the 16062-15936 cm -1 region at 875°C following
laser excitation of the 4s4p 3P 1 state. Here the argon pressure =
825 mbar. The slit width = 120 p,m and the resolution about 3
c m - 1.
Aik
are the Dunham coefficients taken from previously published data [2,4,5]. A search program based
upon Eqs. (7) and (8) was developed to identify the
quantum numbers of the measured line. For every
measured line the program calculated all the lines
within the given range of quantum numbers which
fall into a given search interval A vs around the
MA. Gondal et al. / Chemical Physics Letters 243 (1995) 94-101
98
Table 1
Term values of the identified vibrational-rotational transitions for A lY-u+ (v', J ) - X lX~(v", J"). The observed term values have been
corrected to vacuum
Observed term
value
( c m - 1)
Calculated term
value
(cm 1)
Difference
( c m - 1)
Source
16062.5
16058.5
16055.3
16046.9
16044.0
16030.9
16028.5
16026.6
16016.9
16014.8
16000.8
15998.5
15989.5
15985.0
15982.6
15976.5
15972.5
15962.0
15954.7
15947.1
15933.1
15929.3
15919.2
15906.2
15891.3
15888.8
15881.2
15876.2
15872.4
15865.0
15863.6
15860.6
15857.3
15853.5
15842.2
15838.5
15834.9
15828.4
15823.4
15819.7
15816.6
15814.2
15812.4
15806.7
15804.7
15800.9
15798.9
15795.4
15791.7
15786.7
16061.8
16058.5
16054.5
16047.0
16043.6
16030.9
16028.2
16026.5
16017.8
16015.6
16001.6
15998.9
15960.2
15984.8
15983.5
15976.4
15971.7
15961.4
15953.8
15946.2
15932.3
15929.5
15918.7
15906.6
15892.0
15889.1
15882.2
15876.1
15872.5
15865.2
15864.3
15860.1
15857.1
15853.0
15841.9
15837.5
15834.9
15827.4
15822.6
15818.7
15816.0
15813.2
15813.2
15806.7
15805.1
15800.1
15798.5
15796.3
15791.2
15786.0
- 0.7
0
- 0.8
0.1
-0.4
0
- 0.3
- 0.1
0.9
0.8
0.8
0.4
0.7
- 0.2
0.9
- 0.1
- 0.8
- 0.6
- 0.9
- 0.9
- 0.8
0.2
- 0.5
0.4
0.7
0.3
1.0
- 0.1
0.1
0.2
0.7
- 0.5
- 0.2
- 0.5
- 0.3
- 1.0
0
- 1.0
- 0.8
- 1.0
-0.6
- 1.0
0.8
0
0.4
- 0.8
- 0.4
0.9
- 0.5
- 0.7
D
D
L
D,
D
D,
D
L
D
D,
D,
D
L
D
L
L
L
L
L
L
D,
D
D
D,
D,
D,
D,
D,
D,
D
D,
D,
D
D,
D,
D,
D,
D,
D,
D,
D,
D
D,
D,
D
D
D
D
D
D
Assignment
v'
J'
v"
J"
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
11
11
11
11
11
11
11
11
103
101
100
96
95
89
88
87
82
81
74
73
68
66
64
61
59
52
47
41
100
98
94
88
81
80
76
74
72
70
67
66
64
62
55
53
50
46
42
39
36
34
I00
98
97
96
95
93
92
90
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
102
100
99
95
94
88
87
86
81
80
73
72
67
65
63
60
58
51
46
40
99
97
93
87
80
79
75
73
71
69
66
65
63
61
54
52
49
45
41
38
35
33
99
97
96
95
94
92
91
89
-
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
M.A. Gondal et al. / Chemical Physics Letters 243 (1995) 94-101
99
Table 1 (continued)
Observed t e r m
value
(cm - 1)
Calculated term
value
15780.5
15778.5
15773.0
15770.0
15759.3
15754.6
15740.5
15736.7
15735.2
15728.8
15723.4
15719.0
15713.0
15704.1
15701.6
15698.4
15692.8
15688.6
15684.4
15681.7
15679.7
15674.8
15671.1
15669.4
15667.2
15665.0
15661.1
15656.4
15653.0
15651.2
15646.6
15643.2
15640.7
15638.3
15634.8
15632.9
15780.5
15778.7
15772.3
15770.7
15760.0
15754.7
15740.3
15736.5
15735.4
15728.0
15724.0
15718.4
15712.8
15703.7
15701.5
15697.6
15692.4
15688.0
15684.7
15681.8
15680.3
15675.5
15670.6
15669.6
15667.6
15665.6
15660.1
15655.5
15653.3
15652.1
15647.3
15642.7
15640.0
15637.4
15634.8
15633.0
Difference
(cm- 1)
Source
( c m - 1)
-
-
-
-
-
0
0.2
0.7
0.7
0.7
0.1
0.2
0.2
0.2
0.8
0.6
0.6
0.2
0.4
0.1
0.8
0.4
0.6
0.3
0.1
0.6
0.7
0.5
0.2
0.4
0.6
1.0
0.9
0.3
0.9
0.7
0.5
0.7
0.9
0
0.1
D
D
D
D
D
D
D
D
D
D
D
D,
D,
D,
D,
D,
D,
D,
D,
D,
D,
D,
D,
D
D
D,
D,
D,
D
D,
D,
D
D,
D
D,
D
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
Assignment
v'
J'
v"
J"
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
87
86
84
82
77
75
68
66
65
62
58
56
52
46
44
42
37
100
98
97
96
94
93
92
91
90
89
87
85
84
82
81
80
79
77
76
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
86
85
83
81
76
74
67
65
64
61
57
55
51
45
43
41
36
99
97
96
95
93
92
91
90
89
88
86
84
83
81
80
79
78
76
75
D: transitions observed in the discharge; L: transitions observed by laser excitation.
measured line. For our Ca 2 data, typical values of
A vs have ranged from + 1 to - 1 cm -x. In this
manner we have identified most of the observed
lines which belong to the strongest bands with vibrational quantum numbers v ' = 10-13 and v"= O.
These are listed in Table 1. In principal, the upper
state J level should remain the same as prepared
originally but due to collisions and the broader line
width of the pump laser (0.2 c m - l ) , many levels of
the A state are excited. Both the v' and J' of
collisionally excited states may differ from the v'
and J' prepared initially. The effect of collisional
excitation transfer is to produce satellite fluorescence
series with a J' and/or v' other than in the main
series with no strict requirements on Av', but with
the strong requirement that rotational states remain
symmetric 's' or antisymmetric 'a' in collision.
Hence a collision may change J' by an arbitrary
integer without a change from 'a' to 's'. It is worth
mentioning that the thermal energy of the collisional
partners (molecules/atoms) -- 764 cm-1 at heat-pipe
oven temperature --- 825°C which could help in trans-
100
M,4. Gondal et al. / Chemical Physics Letters 243 (1995) 94-101
ferring population among various rotational levels.
The change in the value of J ' due to collisions has
been observed in Na 2 by Kush and Hessel [22]
where J ' varies from 16 to 64, 90 to 104 and 139 to
162 for various series observed by them.
Since the A 1E u+ state dissociates into
Ca(4s3d 1D 2) and Ca(4s 2 1S 0) states, the dissociation energy of the A 1E,+ can be derived as follows:
De(A 1]~+ )
= Te(Ca(4s3d 1D2)) + De(X 1 ~ - ) _ T¢(A 1~+ )
= 21849.6 + 1095 -- 14251 + 1 cm -1
= 8693.6 + 1 c m - 1 .
This value of D'e is in reasonable agreement with
that predicted theoretically [11] and within the limits
observed experimentally [5]. The value of De' =
8693.6 cm-1 as compared with the dissociation energy of the X 1]~- ground state which is 1095
cm -1, shows that the excited A 1?~u+ state is eight
times more tightly bound than the ground state. This
is true for van der Waals molecules like Ca 2 in
which the excited state A 1Eu+ is basically built by
three bonding and one antibonding electrons having
a (4SCrg)2(4ScruX4dcrg) electronic configuration and
the ground state X 1E~ is built by two bonding and
two antibonding electrons having (4Strg)2(4Styu) 2
electronic configuration.
The observed red fluorescence is assigned to the
molecule of C a 2 for the following reasons:
(1) The vibrational spacing and the dissociation
energies of the observed states agree well with the
theoretical and experimental values [2,4,11].
(2) The spectrum is not due to impurities such as
Call, CaOH or CaO and CaCl. In fact with our best
efforts, we were unable to detect any line which
could be identified as due to Call, CaOH or CaO but
we observed some of the CaCl bands by tuning the
laser frequency carefully to those bands. For example when we tuned the laser to the 0 - 0 band of CaCl
at 621.116 nm, the spectrum of A - X , B - X bands of
CaC1 becomes stronger while the spectra due to Ca 2
disappear. This is a clear indication that the observed
spectra are not due to CaC1. As mentioned earlier,
we took all necessary precautions to avoid impurities.
(3) The same spectra have been reproduced
through three different sources such as laser resonant
excitation of the 4s4p 3p1 metastable state of Ca, by
creating a discharge in Ca vapor and from the hollow
cathode lamp having Ca and Ar. The reproduction of
spectra by three sources is strong evidence that the
spectra are not due impurities.
4. Conclusions
Two independent experimental techniques: pulsed
laser excitation and low current glow discharge are
applied to study the emission spectra of calcium
dimers. The spectra were assigned to the A 1~ u+X 1Eg+ transitions. The new assignment confirms the
value of V0o and D" to be = 14251 _ 1 and 8693.6
+_ 1 c m - 1 , respectively, for the A 1E u+ state.
Acknowledgement
This work is a part of the Laser Research Program
(Project: 12043) supported by the Research Institute,
KFUPM. The authors are thankful to Dr. H.A. Yamani and Dr F.F. AI-Adel for their continuing support and encouragement.
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