10 September 1999
Chemical Physics Letters 310 Ž1999. 471–476
www.elsevier.nlrlocatercplett
X1 q
1
Observation of the y 1 P g –cX14 Sq
u and k P g –c 4 S u systems of N2
Arno de Lange ) , Wim Ubachs
Department of Physics and Astronomy, Vrije UniÕersiteit, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
Received 25 June 1999
Abstract
X 1 q
1
We observed the L-doublet of both parity components of the Ž1, 0. band of the y 1 P g –cX4 1 Sq
u and k P g –c 4 S u
systems of molecular nitrogen in an extreme ultraviolet ŽXUV. q infrared ŽIR. double resonance experiment. The Ž e .
components as well as the Ž f . components are observed up to J s 21 in the case of the y state and up to J s 17 in the case
of the k state. Apart from mutual interaction between y 1 P g and k 1 P g , the Ž e . components undergo additional
perturbations giving rise to predissociation. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction
The y 1 P g state is the upper state in Kaplan’s
. and second Ž y 1 P g –w 1Du . sysfirst Ž y 1 P g –aX 1 Sy
u
tems in N2 . Though the first observation of the
second system was by Duncan in 1925 w1x, it was
Kaplan who recognized the structure in the series
w2–4x. Lofthus and Mulliken w5x remeasured and
added several bands to Kaplan’s first and second
systems and assigned 1 P g symmetry to the y state.
The low intensity of the lines involving Ž e . components of y Ž Õ s 0. and the total absence of the Ž e .
components of y Ž Õ s 1. in emission was ascribed to
predissociation. An interaction with a 1 Sq
g state was
proposed as the predissociation mechanism, since
any other singlet gerade species would also affect
the levels of the Ž f . component.
)
Corresponding author. Fax: q1-31-20-444-7999; e-mail:
arno@nat.vu.nl
The k 1 P g state is the upper state in Carroll–Sub. and II Ž k 1 P g –w 1Du . sysbaram I Ž k 1 P g –aX 1 Sy
u
tems, observed for the first time in 1975 w6x. The y
Ž Õ s 0, 1, 2. states were also observed and it was
found that the y 1 P g and k 1 P g states exhibit a very
strong mutual homogeneous interaction, which explains the strong perturbation in the rotational structure, especially for the Õ s 1 vibrational level, as
was previously observed in the y state by Lofthus
and Mulliken w5x. In the case of the k state a similar
predissociation process was observed as in the case
of the y state; low intensities for the Ž e . components
of Õ s 0 and a total absence of the Ž e . components
of Õ s 1. An indirect predissociation mechanism was
postulated involving the lowest excited 1 Sq
g state
converging to the dissociation limit 2 D q2 D and the
dissociation continuum of the 3 Sy
g state correlating
with 4 S q2 P.
Whereas the experiments mentioned above involved emission spectroscopy, multi-step laser excitation is used in the present Letter. The Ž1, 0. band of
the y–cX4 and k–cX4 systems have been observed in
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 7 7 8 - 2
472
A. de Lange, W. Ubachsr Chemical Physics Letters 310 (1999) 471–476
the near infrared Ž l f 867 nm., with the cX4 1 Sq
u
state used as intermediate. Both parity components
of the Õ s 1 vibrational level of the y and k states
are observed and further evidence is found for the
indirect predissociation process suggested by Carroll
and Subbaram w6x.
2. Experiment
The y 1 P g Ž Õ s 1. and the k 1 P g Ž Õ s 1. states
are investigated in a extreme ultraviolet ŽXUV. q
infrared ŽIR. double resonance scheme, with the
Ž Õ s 0. state as an intermediate. The excitacX4 1 Sq
u
tion scheme as well as the potential curves of relevance for the present Letter are depicted in Fig. 1.
The general features of the apparatus are similar to
the one used for the investigation of double resonance spectra in molecular hydrogen w7x. Wave-
Fig. 1. Excitation scheme and potential energy curves for N2 . The
X 1
1 q
transition c 4 Sq
u – X Sg is induced by a XUV laser and the
X 1
X 1 q
1
transitions y 1 P g – c 4 Sq
u and k P g – c 4 S u are driven by a
temporally overlapped IR laser. A third laser at 532 nm is used to
ionize molecular nitrogen from the y and k excited states. The
curve of the 1 Sq
g state is based on ab initio calculations from
Dateo w16x, whereas the curve of the 3 Sy
g is based on ab initio
calculations from Partridge w17x.
length-tunable XUV radiation around 96 nm is used
to drive the transition from the X 1 Sq
g electronic
ground state to a rotationally selected level of the
Ž Õ s 0.
lowest Rydberg state in nitrogen, the cX4 1 Sq
u
state. To induce transitions from the cX4 1 Sq
state
to
u
the y 1 P g and k 1 P g states, a second laser, tunable
in the infrared near 867 nm, is used. The pulses of
the XUV and IR lasers, each of 3–5 ns duration, are
temporally overlapped in the interaction region in
view of the short lifetime Ž- 1 ns. of the cX4 1 Sq
u
intermediate state w8x. A third laser at l s 532 nm is
used to ionize N2 from the y or k state, and hence
the detection of Nq
2 ions can be used to record the
double resonance spectra, in this case of the y 1 P g –
Ž1, 0. and k 1 P g –cX4 1 Sq
Ž1, 0. bands. For
cX4 1 Sq
u
u
further details on the generation of tunable XUV
radiation and its application to the spectroscopy of
N2 we refer to Ref. w9x.
The level energies of the cX4 state are known with
an accuracy of ; 0.03 cmy1 w10x and therefore only
the radiation from the second dye laser needs to be
wavelength calibrated to obtain level energies of
y 1 P g Ž Õ s 1. and k 1 P g Ž Õ s 1. rotational states
Ž Õ s 0, J s 0. ground
with respect to the X 1 Sq
g
state. Since no standard reference is available around
867 nm, the infrared light was frequency-doubled to
record a Te 2-absorption spectrum Ž5108C. simultaneously with the double resonance spectra of N2 .
Through fitting of the Te 2 resonances with Gaussian
profiles and assigning the peak positions with the
Te 2 atlas w11x, an accurate frequency scale was constructed for the infrared. At low intensities of the
infrared radiation, the linewidth of the N2 absorption
lines was ; 0.08 cmy1 , equal to the laser linewidth
of the second laser.
The effects of predissociation in laser excitation
experiments can in principle be observed through
line broadening. However, if the bandwidth of the
lasers exceeds the Fourier-transform limit, as in the
present Letter, even predissociation yields of up to
99% cannot be observed via line broadening. The
present three-laser configuration provides two methods to derive quantitative information on the excited
state lifetimes and predissociation rates. First, pulses
from the third laser, used to ionize the y 1 P g and
k 1 P g excited state population, can be subject to a
variable delay. From this procedure we deduce that
the lifetime of the Ž f . components of both y 1 P g
A. de Lange, W. Ubachsr Chemical Physics Letters 310 (1999) 471–476
473
strating that the Ž e . components are shorter lived. As
previously explained in more detail w13x the line
intensities in resonance enhanced multi-step excitation decrease if predissociation becomes a competitive process. Indeed for the higher J levels of the Ž e .
component of both y 1 P g Ž Õ s 1. and k 1 P g Ž Õ s 1.
states, such intensity decrease, even to the extent of
missing lines, is observed.
3. Results and discussion
X 1
Ž Õ s 0, J s
Fig. 2. A double resonance spectrum with the c4 Sq
u
5. as the intermediate state. The intensity of the second laser is
reduced to avoid saturation broadening; the linewidth equals the
laser bandwidth Ž ; 0.08 cmy1 ..
and k 1 P g is about 20 ns, in agreement with the
value found by Hummer and Burns w12x. For signal
recording in excitation via the Ž e . components the
third laser had to be temporally overlapped, demon-
In Fig. 2 a typical double resonance spectrum is
Ž Õ s 0, J s 5. intermediate
depicted for the cX4 1 Sq
u
state. In the case of electric dipole transitions, up to
three transitions within one band can be observed in
such a spectrum, each corresponding to one of the P,
Q and R branches. Double resonance spectra have
two advantages over single photon spectra; blending
of lines will be avoided in most cases and the
identification of the upper level is less complex as
Table 1
X 1
X 1 q
1
y1
Observed line positions in the y 1 P g –c 4 Sq
. The estimated uncertainty in the transition
u and k P g –c 4 S u systems. Values in cm
y1
frequencies is 0.03 cm .
J
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
X 1
Ž .
y 1 P g –c 4 Sq
u 1, 0
X 1
Ž .
k 1 P g –c 4 Sq
u 1, 0
PŽ J .
QŽ J .
RŽ J .
PŽ J .
QŽ J .
RŽ J .
–
–
11543.60
11539.19
11534.62
11529.65
11524.38
11518.82
11512.93
11506.82
11501.08
11488.99
11482.63
11474.21
–
–
11456.47
11444.36
–
–
–
11415.28
–
–
11550.75
11550.08
11549.08
11547.88
11546.44
11544.64
11542.81
11540.79
11539.21
11531.52
11529.87
11526.54
11522.70
11518.49
11513.95
11509.05
11504.04
11498.82
11493.55
11488.18
11555.12
11558.48
11561.53
11564.32
11566.67
11568.70
11570.36
11571.59
11572.43
11572.78
11573.57
–
–
–
11573.65
11568.86
11564.71
11559.92
11552.59
–
–
–
–
–
11606.28
11601.85
11597.22
11592.26
11587.25
11582.03
11576.65
11571.26
11566.65
–
–
11548.67
11542.60
11537.11
11531.92
–
11522.10
–
–
–
–
–
11613.56
11612.93
11612.00
11610.97
11609.79
11608.57
11607.34
11606.20
11605.90
11599.80
11600.09
11599.27
11598.44
11597.68
11597.12
11596.85
–
–
–
–
11617.81
11621.17
11624.21
11626.96
11629.58
11631.81
–
11636.09
11638.00
11639.86
11641.41
–
–
11646.94
11649.12
–
–
11657.26
–
–
–
–
A. de Lange, W. Ubachsr Chemical Physics Letters 310 (1999) 471–476
474
the total angular momentum J may differ up to one,
with respect to the known intermediate state. The
Ž1, 0. and
observed lines of the y 1 P g –cX4 1 Sq
u
Ž
.
k 1 P g –cX4 1 Sq
1,
0
bands
are
listed
in
Table
1. The
u
level energies of both states, with respect to the
Ž Õ s 0, J s 0. ground state, are obtained by
X 1 Sq
g
adding the infrared transition frequencies to the calculated level energies of the rotational states of
Ž Õ s 0.. Level energies up to J s 19 can be
cX4 1 Sq
u
computed from the molecular constants with deviations between observed and calculated energies of
; 0.04 cmy1 when the mutual homogeneous interŽ Õ s 1. state is taken into
action with the bX 1 Sq
u
account w10x. Since this model for the level structure
Ž Õ s 0. breaks down for J ) 19 the obof cX4 1 Sq
u
served values are used for J s 20 and J s 21 w10x.
The resulting level energies for the y 1 P g Ž Õ s 1.
and k 1 P g Ž Õ s 1. states are listed in Table 2.
As discussed by Carroll and Subbaram w6x the
y 1 P g and the k 1 P g states undergo a strong mutual
homogeneous interaction. The energy levels of both
the y and k states are fitted simultaneously to eigenvalues of the matrix
ž
Ey
Hy k
Hy k
Ek
/
,
Ž 1.
where H y k represents the J-independent matrix element for a homogeneous interaction between the y
and k states, and E y and Ek represent the deperturbed energy levels of the y and k states respectively, given by the formulae:
E y s n 10, y q B y J Ž J q 1 . y L2
y Dy J Ž J q 1 . y L 2
2
,
Ž 2.
Ek s n 10, k q Bk J Ž J q 1 . y L2
y Dk J Ž J q 1. y L2
2
,
Ž 3.
where n 10 represents the band origin, B the rotational constant and D a centrifugal distortion parameter. The values for Dy and D k are kept fixed at
calculated values. If for the potential function a
Table 2
The obtained level energies of the Ž e . and Ž f . components of the y 1 P g Ž Õ s 1. and k 1 P g Ž Õ s 1. states, with respect to the X 1 Sq
g
Ž Õ s 0, J s 0. ground state. Deviations between experimentally determined energies and the ones calculated from the molecular constants
y1
y1
given in Table 3 are given in the columns under Doc . All values in cm . The estimated uncertainty in the level energies is 0.04 cm .
J
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
y 1 P g Ž e.
y 1Pg Ž f .
k 1 P g Ž e.
k 1Pg Ž f .
energy
Doc
energy
Doc
energy
Doc
energy
Doc
115877.79
115884.98
115895.78
115910.10
115927.86
115949.13
115973.84
116001.92
116033.34
116067.97
116105.82
116146.49
–
–
116298.93
116350.86
116407.15
116466.39
116526.66
116612.54
–
0.09
0.12
0.20
0.24
0.19
0.12
y0.01
y0.24
y0.59
y1.14
y1.86
y3.13
–
–
3.53
0.27
y1.92
y4.44
y9.21
8.36
–
–
115884.97
115895.86
115910.26
115928.31
115949.92
115975.06
116003.72
116035.90
116071.46
116110.57
116153.06
116198.82
116247.99
116300.52
116356.39
116415.52
116478.11
116544.02
116613.14
116685.43
–
y0.02
0.02
y0.03
y0.02
y0.01
y0.01
y0.01
0.02
y0.03
0.04
0.08
0.01
y0.01
y0.01
y0.01
y0.07
0.01
0.09
0.06
y0.11
115940.47
115947.65
115958.41
115972.71
115990.75
116012.30
116037.56
116066.40
116098.84
116134.97
116173.67
116220.95
116267.89
116319.19
116374.39
–
116496.17
116563.73
–
–
–
y0.03
y0.02
y0.02
y0.09
y0.04
y0.11
y0.12
y0.24
y0.39
y0.71
y2.15
1.22
0.45
0.23
0.09
–
y0.32
0.40
–
–
–
–
115947.77
115958.71
115973.19
115991.40
116013.28
116038.89
116068.26
116101.31
116138.16
116178.85
116223.28
116271.55
116323.73
116379.72
116439.57
116503.32
–
–
–
–
–
y0.03
0.01
y0.05
y0.05
y0.06
y0.03
0.02
0.01
0.02
0.08
0.05
0.02
0.04
y0.01
y0.07
y0.11
–
–
–
–
A. de Lange, W. Ubachsr Chemical Physics Letters 310 (1999) 471–476
475
power series around the equilibrium distance R e is
used, it can be shown w14x that
DÕ s
4 Be3
ž / ž
ve2
1q
8 ve x e
ve
y
5ae
Be
y
a e2ve
24 Be3
= Ž Õ q 12 . .
/
Ž 4.
With this formula and the constants taken from Ref.
w6x Dy was determined to be Dy s 6.7 = 10y6 cmy1.
This procedure cannot be used to determine D k , as
only two vibrational levels, Õ s 0 and Õ s 1, have
been observed up to now. Since the k state is a
Rydberg state in a series converging towards the
electronic groundstate of Nq
2 , D k was kept fixed at
D k s 6.6 = 10y6 cmy1 , which is the value of the
2 q Ž
Nq
Õ s 1. state. Resulting parameters from
2 X Sg
a least-squares fitting procedure are tabulated in
Table 3 while the deviations between observed and
calculated levels are included in Table 2.
In Fig. 3 it can be seen that the levels of the Ž f .
component Žopen markers. fit very well to the above
formulae with Eobs y Ecalc f 0.04 cmy1 . The levels
of the Ž e . component Žfilled markers., however,
deviate strongly from the calculated values for both
k Žcircles. and y Žsquares. states, such that no
consistent analysis could be given on the basis of a
two-state interaction model. The rotational B parameter derived for the Ž e . components is lower than for
the Ž f . components and is represented here by a
parameter q for the L-doubling as B Ž e . s B Ž f . q q.
The ordering of the energy levels of the Ž f . component as a function of J Ž J q 1., as depicted in Fig. 3,
shows anti-crossing patterns that are indicative of
additional perturbations by bound states. In fact the
q parameters as given in Table 3 for both k and y
Table 3
Molecular constants of the y 1 P g Ž Õ s1. and k 1 P g Ž Õ s1.
states, as derived from a least squares fit. All values in cmy1 .
n 10
B
q
D
Hy k
a
y 1 P g Ž Õ s1.
k 1 P g Ž Õ s1.
115905.33Ž7.
1.7127Ž2.
y0.021a
6.7=10y6 a
31.40Ž2.
115905.71Ž8.
1.9122Ž3.
y0.023 a
6.6=10y6 a
Estimated; kept fixed.
Fig. 3. Level energies plotted as a function of J Ž J q1.. For
clarity 1.8= J Ž J q1. is subtracted from the level energies. The
circles correspond to the k 1 P g Ž Õ s1. state and the squares to the
y 1 P g Ž Õ s1. state. The Ž f . components are indicated with open
markers and the Ž e . components with filled markers. The solid
lines represent the fitted values with parameters given in Table 3
and the short-dashed lines correspond to the deperturbed energy
levels of the Ž f . components. Also, the predissociated perturber is
tentatively drawn Žlong-dashed..
states are set at values such that the anti-crossing
patterns appear symmetric.
Ž1, 0. and k 1 P g –
In both the y 1 P g –cX4 1 Sq
u
X 1 q
c 4 S u Ž1, 0. bands, the intensities of the P and R
lines, representing the transitions to the Ž e . component, decrease much faster with increasing J, compared to the Q transitions probing the Ž f . component. In a REMPI experiment this is an indication of
predissociation w9x. The intensities reach a minimum
around the avoided crossings and in the case of the
y 1 P g state J s 13 and J s 14 are missing. Beyond
the avoided crossings the intensities of the Ž e . components tend to grow again towards the same signal
strength as the Ž f . components. This strongly suggests that the perturbations in the energy levels are
linked to predissociation.
Carroll and Subbaram w6x did not observe the Ž e .
component of Õ s 1 and to explain this; it was
suggested that this component was predissociated by
a 1 Sq
g state. However, the lowest dissociation limit
2
2
to which a 1 Sq
g state can converge, is D q D at
4
4
Ž
14.522 eV besides the S q S at 9.756 eV, the
.
dissociation limit of the X 1 Sq
g ground state , 0.151
eV above the k state. Therefore, an indirect predissociation mechanism was proposed, involving the low-
476
A. de Lange, W. Ubachsr Chemical Physics Letters 310 (1999) 471–476
est excited 1 Sq
state converging to the 2 D q2 D
g
dissociation limit and the 3 Sy
g state converging to
the 4 S q2 P dissociation limit Žsee also Fig. 1.. As
argued by Carroll and Subbaram w6x the 3 Sy
g causes
predissociation in the 1 Sq
state
through
an
intersysg
tem interaction. This 1 Sq
state
was
first
studied
g
theoretically by Michels in 1970 w15x and it was
found to be a valence state containing bound levels.
Recently ab initio calculations were performed by
Dateo w16x and the 1 Sq
g curve presented in Fig. 1 is
derived from this Letter. The y 1 P g and k 1 P g states
as well as the 1 Sq
g valence state have bound levels
and therefore avoided crossings are to be expected.
As can be seen in Fig. 3, avoided crossings seem to
be present between J s 11 and J s 12 in the k state
and between J s 12 and J s 15 in the y state. If the
same state is responsible for both crossings, then the
rotational B constant can be estimated graphically to
be B ; 0.49 cmy1 . The perturber is tentatively drawn
in the same figure. It is calculated, using the potenŽ Õ ; 35. level
tial curves by Dateo w16x, that the 1 Sq
g
falls in the energy region of the k and y states. The
estimated value for the rotational constant of B ;
0.49 cmy1 is in reasonable agreement with the calculated value of B s 0.53 cmy1 derived from the ab
initio curve.
A second perturbation appears to be present at
higher values of J for the Ž e . components of both y
and k states. For the y 1 P g Ž Õ s 1. state large level
shifts are observed near J s 19, while in the k 1 P g
Ž Õ s 1. state a line is missing at J s 16, a clear
indication of an accidental predissociation. The vibrational level spacing in the 1 Sq
g state, causing the
perturbations at lower J, is calculated at 340 cmy1
near the excitation energy of k, y Ž Õ s 1. w16x. This
value cannot be matched consistently with the energy separation between the two regions of interaction in the k and y states. Hence it is postulated that
another state causes the perturbation effects at higher
J.
time. The observed anti-crossings in the Ž e . component of the y and k states indicate that the perturbing
state is a 1 Sq
g species, supporting bound levels. The
behaviour of the line intensities around the anticrossings proves that the level shifts are linked to
predissociation. The suggestion, made by Carroll and
Subbaram w6x, that the Ž e . components of the y 1 P g
Ž Õ s 1. and k 1 P g Ž Õ s 1. states are indirectly predissociated by a 1 Sq
g state, is verified. The present
experimental Letter shows that excitation of gerade
Rydberg states in molecular nitrogen is feasible in
XUV q IR double resonance laser excitation. This
method may in future be applied to uncover the
entire manifold of highly excited gerade states in
nitrogen.
Acknowledgements
The authors wish to thank H. Partridge and C.
Dateo for making available results on an ab initio
calculation prior to publication. They wish to acknowledge The Netherlands Foundation for Fundamental Research on Matter ŽFOM. for financial support.
References
w1x
w2x
w3x
w4x
w5x
w6x
w7x
w8x
w9x
w10x
w11x
w12x
w13x
4. Conclusion
w14x
1
The Ž1, 0. band of the y 1 P g –cX4 1 Sq
u and k P g –
X 1 q
Ž
.
c 4 S u systems and the e components of y 1 P g
Ž Õ s 1. and k 1 P g Ž Õ s 1. are observed for the first
w15x
w16x
w17x
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