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Laboratory astrophysics
I. Qurmt. Spdmsc.
R&at.
Tranafkr. Vol. 2. pp. 433-439. Perpmon
LABORATORY
Pma Ltd.. Printed in 0-t
bit&
ASTROPHYSICS
R. W. NICHOLLS Department of Physics, University of Western Ontario, London, Canada Ahatraet-The great need for laboratory work on astrophysical problems is discussed and illustrated by the current research programme in this field at the University of Western Ontario. As an example of the experimental work in progress, a critical review ls given of intensity measurements on twenty band systems. The dependence upon transition parameters of the degree of variation of the electronic transition moments for these systems is discussed. The variation with internuclear separation of the electronic perturbation integral in excitation and ionisation transitions is also discussed. As an example of the theoretical work in progress, arrays of Franck-Condon factors calculated to high vibrational quantum numbers for the following eleven vacuum ultraviolet band systems and nine excitation transitions are presented. Ns: Lyman-BirgtHopfield, Vegard-Kaplan, Birge-Hopfield Ns+ : Janin d’lncan, Second Negative 0s: Schumann-Runge co: Fourth Positive, Cameron, Hopfield-Birge u, Hopfield-Birge 6 +: First Negative ::&fi $) -Ns@II~, As X,, BsII~, 0%) -N;(X%;, A*&, BYZ;;, “IIs, CsX) Finally, a study of the geometry in the u’-u” plane of loci of the local maxima of Franck-Condon factors is reviewed. This has immediate application to identification of molecular spectra.
I. INTRODUCTION UNTIL fairly recently the only seriously sustained demand for a precise knowledge of the
parameters and processes of atomic physics was from astronomers and astrophysicists. They have a continual need for such quantities as excitation cross sections (and related parameters) of atomic collision processes, and oscillator strengths (and related parameters) of radiative transitions, for unambiguous interpretation of their observations on extraterrestrial radiation. It was not until after the second World War, when interest in upper atmospheric physics revived, and later with the advent of what is now called Space Physics, that laboratory programmes and theoretical work specifically in support of astrophysical phenomena were started in a number of laboratories. Some aspects of one such programme, which has been running since 1948 are described below. Current activities include : Experimental Spectroscopic intensity measurements(l), (ii) Production of atlas of molecular spectra(s*s), (iii) Ion beam spectroscopy@), 433
R. W. NICHOLLS
434
(iv) (v) (vi) (vii)
Shock tube spectroscopy (shock excitation of powdered solids)(s), Plasma jet spectroscopy(*), Corona spectroscopy(7) Ablation studies in shock tubes and free flight pellet rangds).
Theoretical (i) Calculation of molecular vibrational wavefunctions and the derived quantities Franck-Condon factors and r-CentroiddQ) (ii) Study of molecular potential@) (iii) Calculation of cross-sections of elementary collision processes(i1J2). Its intention is to provide basic data (transition probabilities and excitation crosssection and wavelengths) on atomic and molecular excitation and radiation processes. Emphasis is mainly on diatomic molecules. In this paper, after a brief review of necessary basic theory and concepts, the intensity measurement programme is discussed to illustrate experimental work. The theoretical programme is illustrated by recently calculated arrays of Franck-Condon factors for excitation and radiation of vacuum ultra violet band systems. They are presented and discussed. A brief review is also given of some recent work on molecular potentials. II.
BASIC
CONCEPT&
In the wor.k to be described we are primarily concerned with the excitation of and radiation from molecules. A more detailed discussion of some of the material of this section has been given by NICHOLLSand STEWART( 2.1 Molecular potentials, vibkational levels and wave function Consider three electronic states (Ground (X), Upper (B) and Intermediate (A)) of a molecule whose respective potentials are l+(r), VB(r) and VA(r). Each of these potentials possess energy levels E, and associated vibrational wave functions &(r) which are solutions of
d2+v
87Sm
-dF+ -
h2
L-
W)Ih(r) = 0
(1)
2.2 Excitation processes If the molecule is excited by electron collision from vibrational levels (Y”‘) of the ground state to levels (0’) of the ‘upper state, the excitation probability Pxs per collision is proportional to the matric element 1~I,~x~wJ~~~GxB~~~~~~ dr 12,(14Js). integral GxB~#*‘~, is given by
The perturbation
1
X
ISII*(XIR~,r)#BIR~,r)Ce”“-~“.Rrn
@&I
(2)
435
Laboratory astrophysics
of the incident and scattered electron respectively. The of the states X and B. Rm is the position of the mth molecular electron and r is the internuclear separation. Thus if GXB is a relatively slowly varying function of internuclear separation r, we may assert (see discussion leading to equation 11) The k’s are the momenta
$‘s are the molecular electronic wavefunctions
PXB
The Franck-Condon
=
const GxB~(~~~~,~,)~S~X~,,~~E~~ dr 1s.
(3)
factor qu- &XB) for the excitation transition is qvw( XB) =
~~$b”~X~v’B
(4)
dr12
As we shall see later, from somewhat’comparable reasoning in the case of radiation, ?, , I svJXB) is the r-centroid of the excitation transition ~v*v( XB) =
dr/j&&~~x’dr
jyhB&YXr
(5) It is clear from equation (3) that the excitation probability PXB is somewhat influenced by an electronic factor GXB which is probably relatively slowly varying with r. However the dominating influence on PXB and on its variation from level to level are the FranckCondon factors qc,, sv,, tables of which will thus be of value in the study of excitation processes. Some are available from the work of COOLIDGE, JAMES and PRESENJQ~), BATES(16),WACKSand KRAU&~) and NICHOLLS@).Further extensive tables are presented here to high vibrational levels for many states of Ns and N2+. The rate of excitation PXB, which is proportional to i c Nx, in a steady electron beam current ic through a low pressure gas of ground state concentration NX is often balanced by the rate of radiation
c
NBPBA =
v”
c
IBA
___
V”
EBA
from the upper vibrational level of B. ZBA is the intensity of the Zv~v~~(BA)band, and E v j2,I JBA) is its energy quantum. Equating the two rates Const
G2v,.sv,(X& fv,,,v,) = --
iJVx
1 qvv
Zv,v,*( BA) c o,,
Evv(
BA)
(6)
It is thus possible to study G as a function off and of electron energy through equation 6. G is thought to be linear with energy excess above threshold for electron excitation, and to behave as a step function for photon excitation(l7). Use of this equation is discussed in section 3.2. 2.3 Radiation processes The integrated intensity Zvjvfz(BA) of the v’, VI’ band is Z,Y( BA) = Const N,,( B)Pv~n-(BA)Ev~v-(B A) where P,,,,#(BA) = Const E~V~V~~(BA)~JySu~(B/r)~,~~(A/r)Rc(BA/r) drj2 is the Einstein A coefficient.
(7) (8)
436
R. W. NICHOLLS
The band strength
po~@A) = I~~&wR&) and the electronic transition moment
dr12
&Jr) = JY&)A1*(~)~cd7e
(9)
(10)
where # &4), # &3) are the molecular electronic wavefunctions and MC is the dipole moment operator, T c are the molecular electron coordinates. FRASER(~@ has pointed out that in (9) it is possible to take account of the dependence of R c(r) upon r by the r-centroidos) concept. Thus from (9) pvw
= Rc2(Fv~w~~)~j&&~~ dr12 = Rc2(fv*,v,)qv,u,,
(11)
where the Franck-Condon factor qojv, I is defined in an analagous way to equation (4) and the r-centroid ?, ,Vjsis defined analagously to equation (5). Equation (7) thus becomes I,,,,,( BA) = Const N,( B)E&~( BA)R,2(~‘,,,,,)q,~,~~(BA)
(12)
in which the influences upon 1, TvIS of purely molecular parameters (E, R,(r), +‘v”, ~,,~,~~)and of source conditions (NV@)) are seen. Some applications of equation (12) are discussed in section (III) below. It is clear from equations (6) and (12) that as much information as possible on the molecular parameters should be obtained in order that spectroscopic observations on astrophyscial and laboratory light sources can be interpreted in terms of source conditions and mechanisms.
III.
Intensity Measurements
EXPERIMENTAL
on Molecular Band Systems and their Interpretation
Electronic transition and moment band strengths
The previous section shows that band intensity measurements of important systems should be made for the determination of both excitation and radiative transition probabilities. For this reason, a continuing programme of intensity measurements (A1000 8L-20,000 A) upon band systems of importance in astrophysics and the physics of the upper atmosphere has been in progress in our laboratories for a number of years. The band systems which have been and are currently studied are summarised in Table 1. The integrated intensities IVPVI I of as many bands of each of these systems as are accessible are measured either photoelectrically or photographically. Details of the measurements can be found in the papers cited in Table 1. It is sufficient to mention here that the measurements of IV,,,, , are first interpreted (through equation (12)) by plots of (~~,v,,h4,,v,,/qv,v,,)t vs Fv,v,* for each v’ progression. Each of these plots represent iV,,W, R e(r) vs r. The plots are resealed to a common ordinate scale to represent the smooth variation of the electronic transition moment R c(r) with internuclear separation (r) for each system. Intensities for all measured bands of a system are thus used to delineate the behaviour of R c(r) with r. This information is then used, with equation (11) to produce, for each system an array of “ smoothed ” relative band strengths puCvS,.
437
Laboratory astrophysics TABLE1. BAND SYSTEMS Molecule Ns
N+z 02
OZf NO OH co co+
CZ CN BO SiN BN
WHOSE
INTENSITIES
HAVE
System First Positive (BaHI-AsZ~) Second Positive (cSH,- B’WJ Lyman-Birge-Hopfield (allI #+ X1 S:) First Negative (Bs 5: - Xe X1 ) Meinel (A2H, - X2 Z ) Schumann-Runge (5s Si -xS xi) Second Negative (AsHI, - XW #) Beta (B2H - XsH) Gamma (As S+ - XslI) Violet (A2 Z+ - XsH) Angstrom (Bl Cf --AeLI) Third Positive (bs EC+ -aaH) Fourth Positive (ArTI- Xr 8+) Comet Tail (AW - X2 Z+) Swan (AsILo - XHI,) Red (#II -X2 Z+) Violet (g2 C+ - C2 C+) Alpha (A211 - XsZ+) Beta (Pa Z+ - x2 Z+) Violet (B2 C+ - Xs S+) Violet (A3H - XW)
BEEN
MEASURED
References (20, 21, 22) (23) (2425) (23) (25) (1, 26) (29) (29) (29) (26) (29) (29) (24) (30) (26) (30) (30) (31) (31)
The smoothing comes about from the use of all of the IV,2)I I in the determination of R &). When the values of n4/N for each band are used in equation (12) to determine Re2q there is a relatively large variation in error from band to band. From a practical standpoint, the I, ,VI I were measured either from the area under the contour of unblended bandsf2s), or from selected rotational line intensities of blended bands (1332). The programme reviewed above is currently being extended into the vacuum ultraviolet. Somer observations in emission on the 0s Schumann-Runge system(r) have been cited, and a Hilger 3 m vacuum spectrograph is currently being used to study intensities in emission systems of vacuum ultraviolet Ns, Ns+; CO and CO+(as). In cases where eye estimates of intensity alone are available it is sometimes possible to draw semiquantitative conclusions from them on the behaviour of R c(r) with r(22). In particular it was recently pointed out (24) that early eye estimates of intensity of the vacuum ultraviolet Ns Lyman-Birge-Hopfield and CO Fourth Positive systems indicated that R e was probably relatively independent of r for these systems and thus that putv~’ was probably well represented by qv zvI ,. While one primary aim of the intensity measurement programme is the provision of band strength arrays, sufficient band systems have now been measured, to study, at least empirically, which of the characteristics of the transition appear to influence the strength of the dependence of RG(r) upon r. Ba-rns(r‘J)has suggested that Rc(r) should vary more strongly with r for perpendicular band systems (AA = of: 1: the electron charge cloud changes significantly) than for parallel band systems (AA = 0: the electron charge cloud does not change drastically). In addition to a dependence upon the perpendicular or parallel character of the elec-
R. W. NICHOLLS
438
tronic transition, which dominates much of the molecular architecture, one would also expect a significant dependence of R, (r) upon the total change in r involved in the transition. To investigate this effect a dimensionless parameter AReI2Re = (Rc,,, - Re,,,,,)I(Re,B, + Re,J was chosen to represent the relative change in R e over the transition. dimensionless parameter
Similarly the
Are/2fe = (re,,,,, - re,J(re,,,,, f re,(,) was chosen to represent the change of iv .ernuclear separation involved. The plot of AR c/2R e vs Ar e/2f e for the twenty band systems studied is displayed in Fig. 1.
!a? N .
z
0
2
3
4
5
6
I 7
Fig. 1. Dependence of the ielative variation of the electronic transition moment of band systems upon the relative change of equilibrium internuclear separations and upon the character of the transitions.
In this figure it is noticed: (i) that there is an apparent separation between regions in which points representative of perpendicular band systems lie, and regions in which points representative of parallel band systems lie. (ii) that both parallel and perpendicular band systems appear to exhibit a very approximately linear relationship between the relative change in Rp and the relative change of re. (iii) for a given change in re, the perpendicular band systems appear to exhibit a larger relative ,change in Re than the parallel ones as was suggested by Bates.
Laboratory astrophysics
439
Although no detailed.quantitative theoretical explanation of Fig. 1 can yet be made, it is eminently plausible on general principles to suppose that the c0meQnent.s .of R&) (electronic wavefunctions and the dipole moment see equation (10)) willbe depenl dent upon (i) the parallel ot perpendicular character of the electronic transition (and thus the relative, change in electron charge cloud) arid (ii) the relative total change in r. Further, Fig. 1 indicates that Franck-Condon factor arrays will be more likely to approximate band strength arrays for parallel than for’perpendicular transitions. 3.2 Excitation functions Experimental work using electron beam tubes, has only recently started in our laboratories to apply the methods outlined in section 22 with specific reference to equation (6) to determine the manner by which the perturbation integral Gv ,,,,,, for excitation varies with internuclear separation. Some idea qf the results to be expected may be obtained however from an analysis of the photographic intensities of N2 and N2+ spectra excited by electron beams by LANGSTROTH(~~~J) and discussed by CRAGGS and MASSEY(15). For comparison with equation (a), Table 2 represents in multiple entry form relative ZvPv,, and /\r.v,, for bands of the Nz+ First Negative System together with qvsssv,, rw ,,‘,,, and $,I,.,Y.h,.,.P.
TABLE2.EXCITATIONDATA FORTHENsf FIRSTNEGATIVEBANDS
V
,,
0
V’
0
59 3914
2
1
16 4278
3
2,5 091 4709 5288
Q”“‘,V’ (u,,, = 0)
1
rpp(A)
(",,, = 0)
r, I”Q)A,.,~~
q”,,‘“’ “”
0,891
1,091
337
1
2,2 2,2 0,5 3,2 3582 3884 4237 4652
0,107
1,186
299
2.
0 3308
0,018
1,394
204
091 3564
0 3858
0 4199
Upper entry: Z,,v*,(arb units); Lower entry: &,w (A). Note-Iv~v** from CRAGGSand MA.SEY’S@) discussion of LANGSTROTH’S(~~) work.
The Franck-Condon factors qvs I svs and r-centroids iv ,,,v, used for the ~“‘4 excitation transition are discussed more fully in section (IV) where more extensive tables are presented. A plot is given in Fig. 2a of 1 qv-3’
which although containing smoothly decreasing trend.
only three points (corresponding
to w’ = 0, 1, 2) shows a
440
R. W. NICHOLLS
Similarly, data of LANCZWROTH~cited by CRAGGSand MMSEYW for the Ng second positive system excited in an electron beam is given in Table 3, and the 1
Iv,.- &r- vs i~*+~, 4u”‘U ct),, plot is shown in Fig. 2b.
Fig. 2a Relative variation of the electronic perturbation integral Gv-,v, with internuclear separation in the excitation of the Ns+ First Negative System.
50,,v'=2 40-
=> 2 5 .? $I 4
30-
20-
IO-
Fig. 2b. Relative variation of the electronic perturbation integral Gu-,~, with internuclear separation in the excitation of the Ns Second Positive System.
0
1
__f-1.112
1
1
1
6.3335-2
2
3
l.D65+GM
4
5
7
0
TABLE 7. FRANCK--CONDON 6
10
12
13
5.4636-23.6545~ 2.27494
11
FACTORS TO HIGH VIBRATIONAL QUANTUM 9
-la-1.2626-l-1.1596-1_9.7609+-7.567~
15
6
,
A
Q
,o
9.
4,
ID
1.132+2
::;z
3.06~
1.1593-2
16
3.5585-3
17 1.69+3
3.cm2-4
19
Ll44f-4
20
co2op5
21
BANDSYSTEM
la
(&r~-P$)
7.4095-4
7.73494
7.4354-2 Gqp49lx 2.294pd
6.01454
9.6300-3
1.3aoq
22
3.929I-6
23
24
l~W-6
25
2.7565-7
26
1.34~
27
1.4loW
3.o929+
6.0629-3
5.2537-2
1.7123-2 8.343~3
2.9919-3
4.3574-i6 4.a24n6 l.b,rtr L55i43-i3 ,.a94645 3..9!39O+ l.lamo 2.343H2
2.70135
6.676H6
3.z
2.O+l6
l-a*?5
2‘
4.9335~6
2.OtlH6
')r
U55H
3.6013-3
P.WiWl6
3.3641-e
9.6,7546
2q28H6
1.595446
1.2,29-i5
4.593p16
,.036o15
r.l287-,7 2.,*6
2.346446
2.29+i6 I.~o)(H~
r.,n6-,5
4.3lXH6 ,.pf7+
9.1,79-,7 ,.n31-?9
7.64*6 8.116645
1.611562 9.2i681
3.42481
3.468916
6.qss-s
6dQm6
,.3674-l, 2.69Ol-l3 X5744-,5 2.8iy-9 6.a39Ml l.nZna
P.ca24-4
3.~14
1.*3
9.9X0-5
a.425n7
,.0952-i6 1~,646+5
9.44721
6.36~~
2.5055Q
6.94&-2
19
4.199616 6.2zmo 8.999',+
l-1693-3 4.lCQ2-4
42qW?
T-5&-2
48807-2
3.01~17
SYSTEM
3.7O&%?+
6.638.S
9.2%
3.241.~ 1.9411~ 1.~42~ 5.3367-32.46C&3 l.O4le-34.051+4 1.44-J 47207+ lM3S-5 3&!9M
3.8353-2 6.4377-2
1.5O'XW
1.2237-3 -1.96c.5+ 3.8065-e
7.6065-2
7.93434 6.634%~ 4.9fM-2 3.2Ce3-21.8737-29.8863-3472%-3 2.0452-38.039l-4Z&6+4
5.7621-3
2‘
*
2.367644
LYMAN-BIRGE-HoPFIELD(~~II,-X~$)
>I
1'1
l.a3(zwz
3.36lnS
OF THENZ
22 9.9345-u
2,
16
7."ioM, ::rs
20
15
r.9606+
4.11oM2
:::z
8.6253-S
1.2W-iO
:::G
6.yDSiO 7.7a7w :I&:
::z
,"::tz
7.57F2
23
1.1~11
1.2993-10
3.93w3
g.q66-12l.W.3
1.7366114 1.836+,5
1.9734-14 1.25~0-16 2.*,6
BANDSYSTEM
22
4.959613
2.4953-9
(A3$-X~l$)
l.l23~11
3.7194%
2.Yl7-lO
21
21
3.794+9
2.0707-S
6.OB9-16
2.OWHO
4.390+7
~6
20
49422-0
25 2.88X-9
4.14955
24
1.96o4-4 3.1q
4.4467-6 5.19671
19 ri2c6-5
18
9@lc-4
1,
~.4,7s-l
t:z
,
16
1.841-4
1.6993-5 2.5662-6 3.2317-7 3.4106s 1.34le2
1.6352-4
cw-3
VEGARD-KAPLAN
?$z
3.567N
3.4033-3 a.62914
9.449-5
::z
15
4.oKe+
BANDS
2.835l-3 2.49&~.401+2
1
FOR
5.0315-3
I
II
.
NUMBERS FOR THE N2 BIRGE-HOPFIELD 14 1.3195~2 7.1357-3
5.0917~21.616%? 2.57lW .3.441+33.37334 6.285% s.3730-29.037;i98.3427-26.77~2-24.92SW
2.637p4
F-50-2
3.6W2-e
9.693&'45375~ 1-5.1715-Q
1.4221-5
,,
2.8178Q
4.63+2<%
(0
VIBRATIONAL QUANTUM
1.2613-2 <0168-4
6.7057-4 2.1221-2
3.84332
I)
46355Q
5.73263 44362-3 3.214% 5.7932Q 2.wpI+z 3.6agW 9.8873-37.276p5 1.28%~ LIZ0-2 6.6116-2 8.0369+? --k
1
-9799-2
2.6639~2 j.52W
,
FACTORS TOHIGH
1.24124
2.95Sl.Q2.3413-4
3.46433.8936-2
6
TABLE ~.FRANCK-CONDON
1~,1.6834-,-
5
TABLE~.FRANCK-CONDONFACTORSTOH~GHVIBRATIONALQUANTUMNUMBERSFORTHEN~
1.6781+
5
40231-3
1.7303-2 4.2692-2
412854 1.943l-5
>.6653-2&64+2
1
3.6592~
3
3.96.34-2 4B
3
9.7769-4
2
1.4443Q
2
9.4229-3
d
e
9.6915Q
0 435sl-3 1.5565Q 3.531H 6.14spQ 0.9245-e
z +'
0
7.2.m
1 2.65W-2 2
r'+
0
*4ih?
5.3372-3 2.2atB-2 6.166+2
2.5Clb)
r’+’ 5.9CC44
16 r.@ti
0
12 6.9375-2 9.0~3-3 13 6.O71O-2 1.8172-2
/"
O
1
2
3
TABLE 4
3. i534-4
4.5631-5
6.8078-3
2.2076-3
3.7824-4
4e 141@-2
2.3862-2
9.5282-3
l.sf391-3
7*o5o+2 <.92aW
5.4504-2
2.8202-2
7.4508-3 *
8.26io-2
6.0064-2
2.1156-2
FORTHE
i 2.wo-5 1.1560-3 1.4749-2
BAND SYSTEM
1 8.9184-5 2.9916-3
3.5009-z
Nz JANIN-D'INcAN(?~II~- A!%,)
10. FRANCK-CONDONFACTORSTOHIGHVIBRATIONALQUANTUMNUMBERS
2
2.6757-4 6.1377-3
7.2809-3
TABLE
3 6.3704-4 I .o631-2
2.62466
4 I .2a la-3
2.5665-4
0
5 1.6167-2
9.5858-3
2.2671-3
6.36853
6
4.4007-2
2.2167-2
4.982 4 -2
3.62O6-3
2.2668-2 /
7
5.4221-5
2.7933-2/J.
2 .a745-2
5.3222-3
162-2
a
4.6287-2
5.2964-3
2.972&i!
3.28/ 17-2
3.939)_2
3.0464-3
7.305!+3
3.6342-2
11
12
13
4.5014-4 1.50525 6.413%
15
9.6299-g 6.6542-e
14
NEGATIvE(C~&-_X~$)
1.4926-2
9 9.4703-3
10
10
NUMBERS FOR THE N~SECOND
2.0408-2
6.4951-4
9
VIBRATIONAL QUANTUM
1.aoG2
3.0981-2
/
3.8269-2
1.1694-2 ’
a
11
7
FACTORSTOHIGH 6
11. FRANCK-CONDON 5
L3900Q
16
BAND SYSTEM
17
la
19
20
l&258-10 2.1918-12 0.3932-13 1.614~13 2.39*15
21
1.1200-14
4.6165-g 2.4059-g
Wja6-6
1.29758
7.1138-12 g.668?12
2.040610
2.207*
3.92896
6.q4w
3.3795lb 6.1355-10 3.3646=11 3.32O0-12 1.4079-12 1.415514
l-5531-4 1.5201-5 2.7376-6
4.34+!5
Ma58-3
2.2691-4
3.6834-3
g-4673-4
0
v=
1 2 3 4 5 6 7 8
9 la 11 l2 l.3 14 15 16 17 l2 19 P P
+
Y”
0
0
1
2
2.w
3
3
5
6
7
TABLE ~~.FRANCK-COND~NFACTORSTOHIGH 4
5
6
7
TABLE 13. FRANCK-CONDON
zlhua 1.62224 1.l299-2 7.17-3 w3 1.8359-3
A
9
9
lo
11
VIBRATIONALQUANTIJMNIJMBERSFORTHE 6
10
FACTORS TO HIGH VIBRATIONAL 8
QUANTUM
11
12
NUMBERS
13
l3
lb
l5
A6
02 SCHUMANN-RIJNGE(B~Z~---X~X;~)BAND 12
FOR THE
IA
CO
FOURTH
-15
17
la
POSITIVE (AIII-XX'Z+)~~~~
16
n
SYSTEM
SYSTEM
19
20
l6
21
l9
22
m
23
24
a
8.5997-3 3&ll-3 2axs-2 5.32bl-2 a&n4 ,L2Vl4-L6b+l~L~+l-LSlhl-~-7.2lW2 4-m m &nzI-3 3.363m 9.w Lm33-5 -3 LB%-2 Lm54 3.m --ZGG, -Ll2wl*%5mk2 cl.3754 Llm-l-Lm9-l 7.0861-5 9.27c4-24zG 6.*564 zwh2 1.@w+ Lm4-2 l.O2l9& 2w93-2 b.3-w LQ3a-6 Lw5-5 24076) I-=%3 -7.00364 ,Ll82&l-L2#M iziG L53554 6.6987~c7.al9w-5.swi-2 zaoch2 7.3533-7 2.lB5-2 6m32-2-&%?JM'3.5W-2 5.72s7-6 baa-5 ?..l.m+? &u+2 c5l%-4 7-3 zuob7 L9m2-3 c6949-2 ?zGz 5.9376-2-5.97lb-2'LrrOW t121W Ln6b-2 3.64@3 3.54364, 5.6l65-2 Lo4m-6 2.26324 %ZLlsJ 2.03&3 L3659-3 L-2 3.89Q-2 6A09Q-2' 'z?G-zzzz &.17624!,6.4757-2-2.m24 2-3 bm57-2~ixzG L5l92-3 3.357w 4.55l3-2 Lns7-2 3.5bw-2 3-L7884 6.79oM 6.WU-b 3.3m-3 5.960-2,,6.ll76-2 3.936s-2 6-3 &e&k3 hxm-2 4.76l5-2'2.2365-2 EGG ?zi!iG 3.3m-2 LWY-2 3.ll96-3 34w-2,3.6l%G 2.3054-3 2.96&6-2,Lm3w "iJiG= 9.6380-b 1.7Uo-h L3745-3 6.55s)_3 4.223s-2 5.65u-2 6.2679-2 Loa7-2 & plxs2~Llbu-2 b&53 bJ7O9-2~3.lm~ Lb* --izG L-3 2.9l944,3.o5ol-z L4l5+2 6.92584 4.76684 l.WA5-2 24519-5 2&!52*,3.75&-2 2.3224-5 3.73554 2.6435-3 LKK-2 8.6u7s3 3.05ls-2~Lm9-2 3&373-2~cow-3 c99563 2.O5e-2, 3.w Loll+3 Lpy-2 69nl-5 7.2622-4 4.6605-3 L&E& zO9jM 3aOs-7 2.22W-3 0.95x-3 3.m6-2 3.wwz cm 5.726+3 3.2BoFz~-izG d9w-3 ~ 3.w 3.om-2/ LOl3w um6-2 7.a%l-3 0.~3 LOW 9.6625-5 l.a8163 7.m3 2.3a2/2J3295-2 %lm-3 LBOl-2 2.w 'w7-2 7&W 3.%x&3 3.lw-2 zm9d -37-3 ' L33E-2 9-3 5a9o-4 2al5-2,L~ 1.0652-2 2.9097-2 1-3 2.ul9-2'iziG 1.73l2-4 2.m3 1.m 2.9m-2 8.7s95-3 2.w 2.=U-3 l.79sM /L9LYlMz 5.5wm-3 cllsn-4 2.5U6-2~iEz 1.95x-3 1.m 2.24tea cwso-4 1.7lllD-2 9.a 1.9035-2/ 2.43+2 2.a9w 3.1-3 L71c9-1 1.193o-2, tsO-2 Lb39h-2 Lntu 2.23ll-2'7~3 6.4555-3 2.3319-7 1~750-3 Lw-2,Laz&.2 7.99c1-c 2Alm-2 1.90&3 2.48094 4.55ll-4 6.5367-3 1-3-2 L3329-1 9.75664 2.l2zl-2 Lm76-2 3.Us-2~ 6.896+3 CU9+3 l-l?+3 1.7U6-2' L49w Ls6774 ' 9.73x4-3 L556l-3 z2z+2 l.l75&2,iziG l-0693 Leo49-j 2.19?3w 3.69.0-2 3.w3 s.ozcn-) 2-w 6.79W-4 a-3 1.1*3 1.l258-2 ,2.37+2 ,Le53x L5m.4 1.69@-2,9.3670-3 5.3m3pw2 LlUw 6-3 7.2mb-4 1-m5-2- 6xf@-3 Lbls2 l.zox-4 1.7bu-2/ 1.v 9.b76QL L4795-5 L5fm2/L3367-2 7.~3 8.zKG3 L7w-2 7.w LM7-3 bs56+3 1.w6-2 9.sw-5 L5X-2 s.w-3 2.5052-3 2.WW 9.9999-3 2.2996) L2983-2 L-3 9.9~3 2.0X%2 1.74363 1.192+2 3.56l7-3 b&VU-3 3.2772-3 7.mzl-b Ll390-2/ 1.69384 2.39934 2.2239-3 1.1854-2 2.~44-2 1.0546-5 Lbw-2 1~986-2 5.33764 1.53654 4.6-3 znls-3 1.5639-2 2.932W ,GEGasoaJ l3.363z+3/8.ml-3 3-3 L-3 2.5359-3 1.3271-2 3.2679-5 lZ22-2 LGl9+2/7.%3+3 Lool&3 l&v&2 7.02k,w 3.09sb3 m a&67-4 1.n99-2 2.eD674 3.m3 Laxs!/5.O?7+3 -3 L2497-2 9.4ou-6 LZ73-2 L695>3 r.w2-3 2.90b7-3 &91763/&9m-3 6.&S-3 LW?0-2 dOm-5 Las-2 wo5+7-3 L6601-2 3.us*3 Lml-3/zGzLu5a-L Lt)94a 26om4 pU-2 LO= 3.9232-3 SJlW3/8.395&3 5.42~7-3/~5u2-2 7.74564 94~~9-3/ s.pS5-3 LW3,L235W 3.U74-4 l.Lz6-2 686274 9.42353 Lsw-3~Llls2=2 9.aw3 E55s7-3 5.99063 aw9-3 3.~3 9.95l7-3 ZaapJ 22&x Ll.359-2 4.4-3 c-3 7.7552-3 L270-2
2
4.4975-3 L9wo-2
1
L0074-12 9.6394-14 1.9682-15 1.~450-16 6.9579-16 0.446~l0 4.n)~16 2.298-162.3193-17 8.472%lo 4.0175d 2.2i316420.0603-143.5241-155.578H6 1.054~161.259cM6p@02-16 1.20OO-79.0300-9 6.325~~10 3.4137-U 1.59~12 5.34O3-14 6.426~16z-14+16 5.7173-19
W w M S-7+9 ~~tl~~~~O2.)44~142.094615 2.0572-4 4.1650-54.9963-6 4.9572-7 4.O797-0 2.7859-9 1.5695-10 7.2000-12 3.CBSf3 4.6004-3 9.0orr-4 1.6515-42.2666-5 2.5551-6 2.3757-7 1.0248-81.156fi-9 6.0027-11
_
7
0
8.1812-3 2.63519
6
a
9
IO
11
11
12
12
14
,*
If
1.256+7
,r;
2.934% 1.33m
l.QM~
1.1~I6
7.0X-16
2.674%16 Z&YZZ-~~ ldX5I-tb
Z-3604-16 LcB79-16 3.4-17
2.~192-16 2&3o-l8
22
l.O+ls
7.2728-16
3.3262-134.367%15 l.Of2616 1.551+16
21
9.0660-9 1.5554-10 1.~l2
2.6360-9 4.C84Wl
SYSTEM
8.15fm-6 3.362*
BAND
20
24 19
Z-4669-10
18
23 17
20
21
22
3.2290-9 1.6529-9 8.618MO
6572610
16
SYSTEM
6.432~9
BAND
1.3V@+l
X1X+)
I8
24
2.2754-3 1.2623-8
a @‘2X+-
17
r.9p3-7
16
l.0549-5 imq-6
1.5862-9
2.6541-4
4.402+4 7.5i575 9.843%
1.65i55 1.93186 1.84951
2.308W
1.9963% l-5991-9 9.950t-114.7007-12
2.6929-4 5.W2-5
5.2609-4 i&02&4
19
7*oOe7-3 2.H~3
1.8202-5 2.5033-z 2.759W
23
5.7736% 2.717~
3.504c+3 1.o540-3 4.367t-e I.%+
b (b28+ -x1X+)
5.3693+
3.052+11 3.5373-13 1.645Fl5 6.2277~1 1.7772-164.3996-17 1.6740-1766459-17 2.2771-17 1.5732-102.0134-12 1.627z_14 1.5746-17 1.6023-W 1.9767-171.06Wl6 3.536W6
5.11)9+14 1.1047-15 1.m16
1.337+16 5.~3010-177.9066-W 1.1713$+16 2.525W7
NUMBERS FOR THE CO CAMERON (a211 - X1 C+) BAND SYSTEM
13
i?
8.0765Q
2.3997-Q 9.%55+3 j.W+i
1.2390-i 9.5266-2 5.3726+ 2.)23l+? 7.070&3 2.1-3
5.3W2-2 2.3701-e &49i7-3
2.4580-3 5.7598-4 w095-4 1.051yz
1.9331-e 5.9642-3 M20M
6.5CczW 2.7W
3.06)2-e 1.383~~ 3.7544-3
7.2666-2 1.2225-I im
4.02ly2
6.8427+ 2.1514-2 1.6357-3 4.77&>l,
-73
2.1733-3 5.4351-e a
3.6135-2 1.8984-e 6~007-3
3.3234-2 1.119!~6 a3.6733-2 zs
6.0%
4.Qolrr9
1.0572+ I.55052
1.7414+2 6.4357-3 5.6= 5.0622-e 3.2717-3 Z-4945+? 9.678>1.25~1 9.4a36e _V 6.2729-3 1.93&%57+ 3.215?n? 6.1712-4 5.3937Q>l%Fi =4.7619-e
2.2661+
1.1284-e 9.0294-3 ~9263~
.CZoOQ 2.3437-4
a.o79hrp075+
10
FACTORS TO HIGH ‘WBRA~ONAL QUANTUM NUMBERS FOR THE CO HOPF[ELD-BIRGE 7
r.q98-I l.5i~i~.734~~~.64ltl~.)wB-l
5
6.~9~
4
2.2458-6 l.lo53-6 5.5355-7 2.0241-7 I.46681 7*75itH 4166W
QUANTUM NUMBERS FOR THE CO HOPFIELD-BIRGE
FACTORS TO HIGH VIBRA~ONAL QUANTW
9
FACTORS TO HIGH. VIBRA~ONAL
TABLE 14. FRANCK-CONDON
6
TABLE 15. FRANCK-CONDON 5
1.775W4 6.3613-5 2.3683-5 9.1523-6 3.65886 1.5093-S 6.4123-7 2.80w-7
4 5.19374
3.5504-3 1.4335-3 5.9018-4 2.4870-4 1.0136-4 4.7436-5 2.14375
1
1.< M-i
1.62
6.i653-2 9.7334-3 5.906C-3 5.4248-2
i.wa-i
,.033ti
9.76+3
1.6i2N? 6=9i5t3 -5.59%
2.8151-e 2.8l8~3 8.2878-4 3.37OiQ _
9.255i-5 3.69~~
9.9033-6 4.67146
1 6*832+2 1.16724 5.0662-3 lGW7-3 B-928*3
i&77-3
1.9768+ 7.126~,&-2
9.2253-2s
4 3-w
TABLE 16. FRANCK-CONDON
1*5516-l 6.03164 2.289lQ
0
3369oe
3
1.0167-3 ae25-3
MW-4
48226-2
2.4930-2 6.914+2
2
0
L903l-3
++'
I
9.90~3
5 4.8277-Q a. 12-4 2.2752-2 P 2.4015-3 2.36%1-3
1
7.69~~
3
2
6 6.3lw
&%3fCT 5.7QMQ
7 a 1.651
IO
9
TABLE 17. FRANCK-CONDON FACTORS TO HIGH VIBRATIONAL QUANTUM NUMBERS FOR THE CO+ FIRST NEGATIVE @2X+-PE+) BAND SYSTEM
+ 6
+*
0
i)
.c%L
2.495
f? 43305
1 1.9mO-i
2 3 1 2.13P-(~.4033-Ll.447y-l_6$+2
3.47
4344
4
5
5
6 2.m92-2
6
, 5.295F3
7
l.YA-5 1
FACTORS
11 12 1.905z-6 1.43447
TABLE 19.FRANCK-CONWN ¶ 1.622wl
14
1.6111617
2.7 2-m
-N~BaII,
24 4788~9
l.aU?-i?
NaXI$
23 7-4979-S
2.67OY-17 5.4264-l? 1.3E+l8
NUMBERS
21 22 1.a?7o-f6 S-OiQ316
1.vm
LW6
26 7&?e-i6
2.66?8-l6 1.589W9
1.4532-15 6s299(16
47034-l?
25 6.288M6 2.234ll6
2.6-6
4.lEY+i6
I9 20 2d3675-l? 7.215W6 w-6
2.645Wl5
4U4%l6
la ?.368+l6
5.'3937-l21.395ll3
3.Wfl5
4444616
l6 17 ~049p1319289l5 2-Q)3WO
2.#2-f6
1.yCS-16
l.i?6H4
26
27
.3.6255_0 9.5439-U
25
1.248~12
24
3.?W?-iQ
2.545116
1.0596-17 2.2748-16 3.919+l? 5.0147-l78.218W7
6.5443-i?
6.6456-16 l.5734-152.3324-l6
5.8588-17 2.6576-19 7.4692-l? 2.055217 7.8407-i? 2.918t-16 4.3697-i? l.694H6
2.2885+5
2.033C-S
2.6229-16 46436-16 0.456~6
8.0164-16 3.92X+
27 3s?xe+ ,.(o)t+$
7.125216
1.8993-15 1.6829-16 l.l646-16 l.187~16 7.647817 5.4631-17 7.62?6-17 7.6926-17 l.62)(w 1.17C@-+5 3.875~$6
7.662W6
6.0421-17 2.2@6-l6
l.42Ot-16 7.1770-16 1.5894-15 4.0335-f? 1.26~615 r.763tl5 6&07-l?
1.833~8
23
1.W4%
48xLw5
22
5.6336-H
1.8001-16 1.943516
432QH3
26 5 2.&7 2.627~7 ,~y,j6m,5 ,.-5
i6 20 n m (P 1 ?.5?'67+'3l.Y?H6 3-5&-V 4.834m 2*36#-l6 4&8-q I.691616 4.1~4-16 ?.32?+l6 &.9,42-q 2.-S ,.o#.M
22 23 24 3.49X-i? l.Wti6 3.47rw? 4.6~6 4.i679-,6 6.5@2+7 2.WC-i5
1s 3.496M7
21
1.625+9
4645Pl7
1.3554-V 1.6#8-15 49124-16 8.2W-S
20
2.4W
18
NaXlB: -NK%, 17
l.3309-0 l.23W-15 3.777H6
5.0273-i4 6.0233-16 1.805~l5
9.5536-17 1.0175-16 l&63-16
9.4977-11 1.2O?t12 1.35~~14
4.3692-M
l9
+61126
15
lb
4.3668%
QUANTUM
7.754~
TO HIGH VIBRATIONAL
l3
2.74C9-9
8.286812
1.2719-15 6.(937-166.3666-l? 5.566216
12
l.O4h-f,
4.6513-3 0.C~65-4 1.046W
11
6.2924-2 2.0@2+
10
FACTORSTOHIGHVIBRATIONALQUANTUMNUMBERS
9
i.m
5.714MO
3.2027-9 5.7236fl 6.?248-13 9.12C.S-i5
a
TABLE~O.FRANCK-CONDON
a m462-3
8.4645-5 3.9092-6 1.30??1
2.11354q 5.3959.9
2.801%
0.9436-S
6.304%
WM-6
2.8174-16 .9.703f-i7 2.221~f6
1.283S4
W325-3
2.4CQO-5 9.n30-7
3.5596-0 7.504~IO 1.1359-11
1.6630-p I.&Xl-3
WM4-2
4.W5P4
2.9774-5 1.215%
2.6605-I 9.3C8W
6.V82-2
4.7X7-3
7.4&j
w713-1
2.295>2=
1.4736-l 3-Wp-2
3.7225-2 l&p .
6.Sn5-2
1.6538-3>21d
I_
1.2282-U 2.SJB-l)
9 Y.CW-i7
TABLE 21.FRANCK-CONDON FACTORSTOHIGH VIBRATIONAL QUANTUM NUMBERS NzX'C~--N~PC~ 6 , l.2664-l4 42175-S
6
l&-w
1.9569-1 4.5640-Q 6.0537-3 5.14254
1.343l-2 l&XC-3
3
2.1147Q
9.1279%
2
3.2652-3 1.41W
7.6067-4 5.536+3 4057W
I
5.4873-l-3.449&1
0
0
1.0516-l \ e
3.07'b
++I 1
?.zz26-3 7.7427%
8.28669 >a
2 3 4
5
2.6656-W 2.??2W3
I
2.942911
11 13 la t2 U 5.4893-i6 2.2925-16 5.2217-l? i.407t16 2.27OWY
41KBtl
5.425W
3.0295-Z 4.8W-6
8.m
3.395~
4.*)6~6
6.7-
4m6x+
~.3m+i5
1.~5
4.345~5
3-5
r&34+
6.~~16
~~&-i6
3.35-b
1.215n5
2.W+l6
1.663215 l-5
l.509MY
6.WC6
4.0m7+6 2.16Vj-l6 I.-5
3.,?5t,~
2.4?3Y-i6 8.6Q33-V
6tSS-i4
r&74+
2.0348-V
y&6016
4.094617
1.213tl5 3.631645 2.630517 4.OCM6
l.551(15 3.646416 1.On0-15 2.24136+5 3.30Ca-16 3&?w?
1.&Y++
4'39-5
h-5
6.416515 1.172444
1.46~
6.W0-13
,.4695+
497YWl
l.&337-g6 9.6,30tl6 1.6-5
l.?W%
&9x+
1.639~
~-5
1.W
Wd+i
1.3597-13 40474d
1.1fln6
1.354Gi5 3.m
3~~5
3.465t3
S-3.l3P-l
6.W-l
6.24W-Y
4299l-M
l.3?48+
8.6y24+
6.206WO
6.47W
l.24y5.i0 43uv-10
1.906nO
3.l8OS-7 3.05~6-9 l.??93+1 1.23cz-i1 8.9267-e 43?+~
km6-3
3.7KM
1.69m-2
1+4+3
1.wl-f
2.gg*s
3.0427+5 3.5025-l5 l.yi24q
2.&,~5
l-&X?-iS 6q54W7
1.~92115 3.-p+, Li46+l5
7.557~
l+3+i5
3&a++
4~361~4
-74n6
2-2424-U
l.ol74-15 6.78Se-rs l&60-j6
2Jpz-fi
2.09lM6
16Si6+
a.-
l-25l7-l 6.47Y-10 6.3~0+
I&U-U cnw 3.524tl5 1.~374~3
9.4)966
7.41~~5 5.9~
40455-Y
7.933~5 tat-(~
4.1794~
4.96YMs 6.452~
4.27654
3d?n6 m
9.785W
1~9207-w i-m5 1.931gl5 ~3-5
2d2W-4
W0?-S 5q66y+5
1.W2-1
~23~6 l-n5+U
5.3qy-t~
3.6Cq-?$ 2.3460-$4 5.7565.+3 2.r567-e
6.Wt3
2.551M5 wUR~~
46425q
3. 4fl
1-6764+1 6-CW-U 4-9302-9 cxpcI1
wgps?
?dY@W
6qS-7
E'EICCU
8.9~~4
W+W
7.37CW5
2.4q7-~
2.9974-7 1.J#+
l.Wti5
6d91H4
1.31~3
?.5U%l6
665ow
I-905Fl
1.042bKI 2.7661U4 Wosru
6mS-U
7.7@=-4
3+4ti5
l.6556-l 2-l96TQ
2d!WS
6.8%3+
1.4992Q
*alw
2dW%
3.295H3
3.&974-~3 7.0622-U 2.?05.U3 2.@67-i2 ?&OH
1.s+i 1.2~2.62931 _
l*54tl*3C&f-l-~ l.6334~1~
Lm 3.33lOe
45345-2
4%38+
'.u*
2-m
~247-y
l.WYW?
2.W8-U
,>:j:s+ 2.3+CO+
~2.8356-l
7.4564-5
'-m
l.4*
S.WnO
1.6957~3 i..9162--ll&Z?%
1.8a?4-3 L591W
1.49CQQ
2.l6$-3
3.4253-3
I.-
6.7YCM
8.3XQ-4
5.2831-4 6..?29M
r.ufe.3
2.4!+3
2.19234
1.75wd
CqEl64
1.23~3
3.v
#e236t2
5.87yb
1.1393-2 6.6-S-4
(.3?st2
2.254~1
40344-4
4-SW-Q--RL~
9.W2-2
46724-!2
7.674&l, 6-1
7dll5-3
2.3W-4
7.2-5
3.M l.WH 6.w
4.*l4-3
?.@I+3
f.W*-(
G&Pz.676c-l
43-3
1.11~1
W4yB-3
5.2939-Y l.l637-f* l-Y@-l3
rnsw
Y-*1316
4.0194-4
&W2?-4
s53?%l
1.0136)
l.5363e
1.2-
1.8266-3 46(cp-I, 6.04281
4 3.24OY-7 3.Q316l
2.283ti 2.76w5
6.W
le
2.5207-I 5.6225-Q
3.~3oge
5 3.0~
s
6 5.0548% 4.656%
c.1433q 2.264% 1.34Ol-4 9.94U-4
C'W'I-3 1.540-5
l.5q4-S
5.=3M
2.50Y6-4
l.1697-l l.4sYm
r.&?yk? M7U2.d
5.45'20-6 4.93C7-7
6.34031
3.xX%% 2.7OVX
3.5107-7 3.p2+6 l.616tY
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Tranafkr. Vol. 2. pp. 433-439. Perpmon
LABORATORY
Pma Ltd.. Printed in 0-t
bit&
ASTROPHYSICS
R. W. NICHOLLS Department of Physics, University of Western Ontario, London, Canada Ahatraet-The great need for laboratory work on astrophysical problems is discussed and illustrated by the current research programme in this field at the University of Western Ontario. As an example of the experimental work in progress, a critical review ls given of intensity measurements on twenty band systems. The dependence upon transition parameters of the degree of variation of the electronic transition moments for these systems is discussed. The variation with internuclear separation of the electronic perturbation integral in excitation and ionisation transitions is also discussed. As an example of the theoretical work in progress, arrays of Franck-Condon factors calculated to high vibrational quantum numbers for the following eleven vacuum ultraviolet band systems and nine excitation transitions are presented. Ns: Lyman-BirgtHopfield, Vegard-Kaplan, Birge-Hopfield Ns+ : Janin d’lncan, Second Negative 0s: Schumann-Runge co: Fourth Positive, Cameron, Hopfield-Birge u, Hopfield-Birge 6 +: First Negative ::&fi $) -Ns@II~, As X,, BsII~, 0%) -N;(X%;, A*&, BYZ;;, “IIs, CsX) Finally, a study of the geometry in the u’-u” plane of loci of the local maxima of Franck-Condon factors is reviewed. This has immediate application to identification of molecular spectra.
I. INTRODUCTION UNTIL fairly recently the only seriously sustained demand for a precise knowledge of the
parameters and processes of atomic physics was from astronomers and astrophysicists. They have a continual need for such quantities as excitation cross sections (and related parameters) of atomic collision processes, and oscillator strengths (and related parameters) of radiative transitions, for unambiguous interpretation of their observations on extraterrestrial radiation. It was not until after the second World War, when interest in upper atmospheric physics revived, and later with the advent of what is now called Space Physics, that laboratory programmes and theoretical work specifically in support of astrophysical phenomena were started in a number of laboratories. Some aspects of one such programme, which has been running since 1948 are described below. Current activities include : Experimental Spectroscopic intensity measurements(l), (ii) Production of atlas of molecular spectra(s*s), (iii) Ion beam spectroscopy@), 433
R. W. NICHOLLS
434
(iv) (v) (vi) (vii)
Shock tube spectroscopy (shock excitation of powdered solids)(s), Plasma jet spectroscopy(*), Corona spectroscopy(7) Ablation studies in shock tubes and free flight pellet rangds).
Theoretical (i) Calculation of molecular vibrational wavefunctions and the derived quantities Franck-Condon factors and r-CentroiddQ) (ii) Study of molecular potential@) (iii) Calculation of cross-sections of elementary collision processes(i1J2). Its intention is to provide basic data (transition probabilities and excitation crosssection and wavelengths) on atomic and molecular excitation and radiation processes. Emphasis is mainly on diatomic molecules. In this paper, after a brief review of necessary basic theory and concepts, the intensity measurement programme is discussed to illustrate experimental work. The theoretical programme is illustrated by recently calculated arrays of Franck-Condon factors for excitation and radiation of vacuum ultra violet band systems. They are presented and discussed. A brief review is also given of some recent work on molecular potentials. II.
BASIC
CONCEPT&
In the wor.k to be described we are primarily concerned with the excitation of and radiation from molecules. A more detailed discussion of some of the material of this section has been given by NICHOLLSand STEWART( 2.1 Molecular potentials, vibkational levels and wave function Consider three electronic states (Ground (X), Upper (B) and Intermediate (A)) of a molecule whose respective potentials are l+(r), VB(r) and VA(r). Each of these potentials possess energy levels E, and associated vibrational wave functions &(r) which are solutions of
d2+v
87Sm
-dF+ -
h2
L-
W)Ih(r) = 0
(1)
2.2 Excitation processes If the molecule is excited by electron collision from vibrational levels (Y”‘) of the ground state to levels (0’) of the ‘upper state, the excitation probability Pxs per collision is proportional to the matric element 1~I,~x~wJ~~~GxB~~~~~~ dr 12,(14Js). integral GxB~#*‘~, is given by
The perturbation
1
X
ISII*(XIR~,r)#BIR~,r)Ce”“-~“.Rrn
@&I
(2)
435
Laboratory astrophysics
of the incident and scattered electron respectively. The of the states X and B. Rm is the position of the mth molecular electron and r is the internuclear separation. Thus if GXB is a relatively slowly varying function of internuclear separation r, we may assert (see discussion leading to equation 11) The k’s are the momenta
$‘s are the molecular electronic wavefunctions
PXB
The Franck-Condon
=
const GxB~(~~~~,~,)~S~X~,,~~E~~ dr 1s.
(3)
factor qu- &XB) for the excitation transition is qvw( XB) =
~~$b”~X~v’B
(4)
dr12
As we shall see later, from somewhat’comparable reasoning in the case of radiation, ?, , I svJXB) is the r-centroid of the excitation transition ~v*v( XB) =
dr/j&&~~x’dr
jyhB&YXr
(5) It is clear from equation (3) that the excitation probability PXB is somewhat influenced by an electronic factor GXB which is probably relatively slowly varying with r. However the dominating influence on PXB and on its variation from level to level are the FranckCondon factors qc,, sv,, tables of which will thus be of value in the study of excitation processes. Some are available from the work of COOLIDGE, JAMES and PRESENJQ~), BATES(16),WACKSand KRAU&~) and NICHOLLS@).Further extensive tables are presented here to high vibrational levels for many states of Ns and N2+. The rate of excitation PXB, which is proportional to i c Nx, in a steady electron beam current ic through a low pressure gas of ground state concentration NX is often balanced by the rate of radiation
c
NBPBA =
v”
c
IBA
___
V”
EBA
from the upper vibrational level of B. ZBA is the intensity of the Zv~v~~(BA)band, and E v j2,I JBA) is its energy quantum. Equating the two rates Const
G2v,.sv,(X& fv,,,v,) = --
iJVx
1 qvv
Zv,v,*( BA) c o,,
Evv(
BA)
(6)
It is thus possible to study G as a function off and of electron energy through equation 6. G is thought to be linear with energy excess above threshold for electron excitation, and to behave as a step function for photon excitation(l7). Use of this equation is discussed in section 3.2. 2.3 Radiation processes The integrated intensity Zvjvfz(BA) of the v’, VI’ band is Z,Y( BA) = Const N,,( B)Pv~n-(BA)Ev~v-(B A) where P,,,,#(BA) = Const E~V~V~~(BA)~JySu~(B/r)~,~~(A/r)Rc(BA/r) drj2 is the Einstein A coefficient.
(7) (8)
436
R. W. NICHOLLS
The band strength
po~@A) = I~~&wR&) and the electronic transition moment
dr12
&Jr) = JY&)A1*(~)~cd7e
(9)
(10)
where # &4), # &3) are the molecular electronic wavefunctions and MC is the dipole moment operator, T c are the molecular electron coordinates. FRASER(~@ has pointed out that in (9) it is possible to take account of the dependence of R c(r) upon r by the r-centroidos) concept. Thus from (9) pvw
= Rc2(Fv~w~~)~j&&~~ dr12 = Rc2(fv*,v,)qv,u,,
(11)
where the Franck-Condon factor qojv, I is defined in an analagous way to equation (4) and the r-centroid ?, ,Vjsis defined analagously to equation (5). Equation (7) thus becomes I,,,,,( BA) = Const N,( B)E&~( BA)R,2(~‘,,,,,)q,~,~~(BA)
(12)
in which the influences upon 1, TvIS of purely molecular parameters (E, R,(r), +‘v”, ~,,~,~~)and of source conditions (NV@)) are seen. Some applications of equation (12) are discussed in section (III) below. It is clear from equations (6) and (12) that as much information as possible on the molecular parameters should be obtained in order that spectroscopic observations on astrophyscial and laboratory light sources can be interpreted in terms of source conditions and mechanisms.
III.
Intensity Measurements
EXPERIMENTAL
on Molecular Band Systems and their Interpretation
Electronic transition and moment band strengths
The previous section shows that band intensity measurements of important systems should be made for the determination of both excitation and radiative transition probabilities. For this reason, a continuing programme of intensity measurements (A1000 8L-20,000 A) upon band systems of importance in astrophysics and the physics of the upper atmosphere has been in progress in our laboratories for a number of years. The band systems which have been and are currently studied are summarised in Table 1. The integrated intensities IVPVI I of as many bands of each of these systems as are accessible are measured either photoelectrically or photographically. Details of the measurements can be found in the papers cited in Table 1. It is sufficient to mention here that the measurements of IV,,,, , are first interpreted (through equation (12)) by plots of (~~,v,,h4,,v,,/qv,v,,)t vs Fv,v,* for each v’ progression. Each of these plots represent iV,,W, R e(r) vs r. The plots are resealed to a common ordinate scale to represent the smooth variation of the electronic transition moment R c(r) with internuclear separation (r) for each system. Intensities for all measured bands of a system are thus used to delineate the behaviour of R c(r) with r. This information is then used, with equation (11) to produce, for each system an array of “ smoothed ” relative band strengths puCvS,.
437
Laboratory astrophysics TABLE1. BAND SYSTEMS Molecule Ns
N+z 02
OZf NO OH co co+
CZ CN BO SiN BN
WHOSE
INTENSITIES
HAVE
System First Positive (BaHI-AsZ~) Second Positive (cSH,- B’WJ Lyman-Birge-Hopfield (allI #+ X1 S:) First Negative (Bs 5: - Xe X1 ) Meinel (A2H, - X2 Z ) Schumann-Runge (5s Si -xS xi) Second Negative (AsHI, - XW #) Beta (B2H - XsH) Gamma (As S+ - XslI) Violet (A2 Z+ - XsH) Angstrom (Bl Cf --AeLI) Third Positive (bs EC+ -aaH) Fourth Positive (ArTI- Xr 8+) Comet Tail (AW - X2 Z+) Swan (AsILo - XHI,) Red (#II -X2 Z+) Violet (g2 C+ - C2 C+) Alpha (A211 - XsZ+) Beta (Pa Z+ - x2 Z+) Violet (B2 C+ - Xs S+) Violet (A3H - XW)
BEEN
MEASURED
References (20, 21, 22) (23) (2425) (23) (25) (1, 26) (29) (29) (29) (26) (29) (29) (24) (30) (26) (30) (30) (31) (31)
The smoothing comes about from the use of all of the IV,2)I I in the determination of R &). When the values of n4/N for each band are used in equation (12) to determine Re2q there is a relatively large variation in error from band to band. From a practical standpoint, the I, ,VI I were measured either from the area under the contour of unblended bandsf2s), or from selected rotational line intensities of blended bands (1332). The programme reviewed above is currently being extended into the vacuum ultraviolet. Somer observations in emission on the 0s Schumann-Runge system(r) have been cited, and a Hilger 3 m vacuum spectrograph is currently being used to study intensities in emission systems of vacuum ultraviolet Ns, Ns+; CO and CO+(as). In cases where eye estimates of intensity alone are available it is sometimes possible to draw semiquantitative conclusions from them on the behaviour of R c(r) with r(22). In particular it was recently pointed out (24) that early eye estimates of intensity of the vacuum ultraviolet Ns Lyman-Birge-Hopfield and CO Fourth Positive systems indicated that R e was probably relatively independent of r for these systems and thus that putv~’ was probably well represented by qv zvI ,. While one primary aim of the intensity measurement programme is the provision of band strength arrays, sufficient band systems have now been measured, to study, at least empirically, which of the characteristics of the transition appear to influence the strength of the dependence of RG(r) upon r. Ba-rns(r‘J)has suggested that Rc(r) should vary more strongly with r for perpendicular band systems (AA = of: 1: the electron charge cloud changes significantly) than for parallel band systems (AA = 0: the electron charge cloud does not change drastically). In addition to a dependence upon the perpendicular or parallel character of the elec-
R. W. NICHOLLS
438
tronic transition, which dominates much of the molecular architecture, one would also expect a significant dependence of R, (r) upon the total change in r involved in the transition. To investigate this effect a dimensionless parameter AReI2Re = (Rc,,, - Re,,,,,)I(Re,B, + Re,J was chosen to represent the relative change in R e over the transition. dimensionless parameter
Similarly the
Are/2fe = (re,,,,, - re,J(re,,,,, f re,(,) was chosen to represent the change of iv .ernuclear separation involved. The plot of AR c/2R e vs Ar e/2f e for the twenty band systems studied is displayed in Fig. 1.
!a? N .
z
0
2
3
4
5
6
I 7
Fig. 1. Dependence of the ielative variation of the electronic transition moment of band systems upon the relative change of equilibrium internuclear separations and upon the character of the transitions.
In this figure it is noticed: (i) that there is an apparent separation between regions in which points representative of perpendicular band systems lie, and regions in which points representative of parallel band systems lie. (ii) that both parallel and perpendicular band systems appear to exhibit a very approximately linear relationship between the relative change in Rp and the relative change of re. (iii) for a given change in re, the perpendicular band systems appear to exhibit a larger relative ,change in Re than the parallel ones as was suggested by Bates.
Laboratory astrophysics
439
Although no detailed.quantitative theoretical explanation of Fig. 1 can yet be made, it is eminently plausible on general principles to suppose that the c0meQnent.s .of R&) (electronic wavefunctions and the dipole moment see equation (10)) willbe depenl dent upon (i) the parallel ot perpendicular character of the electronic transition (and thus the relative, change in electron charge cloud) arid (ii) the relative total change in r. Further, Fig. 1 indicates that Franck-Condon factor arrays will be more likely to approximate band strength arrays for parallel than for’perpendicular transitions. 3.2 Excitation functions Experimental work using electron beam tubes, has only recently started in our laboratories to apply the methods outlined in section 22 with specific reference to equation (6) to determine the manner by which the perturbation integral Gv ,,,,,, for excitation varies with internuclear separation. Some idea qf the results to be expected may be obtained however from an analysis of the photographic intensities of N2 and N2+ spectra excited by electron beams by LANGSTROTH(~~~J) and discussed by CRAGGS and MASSEY(15). For comparison with equation (a), Table 2 represents in multiple entry form relative ZvPv,, and /\r.v,, for bands of the Nz+ First Negative System together with qvsssv,, rw ,,‘,,, and $,I,.,Y.h,.,.P.
TABLE2.EXCITATIONDATA FORTHENsf FIRSTNEGATIVEBANDS
V
,,
0
V’
0
59 3914
2
1
16 4278
3
2,5 091 4709 5288
Q”“‘,V’ (u,,, = 0)
1
rpp(A)
(",,, = 0)
r, I”Q)A,.,~~
q”,,‘“’ “”
0,891
1,091
337
1
2,2 2,2 0,5 3,2 3582 3884 4237 4652
0,107
1,186
299
2.
0 3308
0,018
1,394
204
091 3564
0 3858
0 4199
Upper entry: Z,,v*,(arb units); Lower entry: &,w (A). Note-Iv~v** from CRAGGSand MA.SEY’S@) discussion of LANGSTROTH’S(~~) work.
The Franck-Condon factors qvs I svs and r-centroids iv ,,,v, used for the ~“‘4 excitation transition are discussed more fully in section (IV) where more extensive tables are presented. A plot is given in Fig. 2a of 1 qv-3’
which although containing smoothly decreasing trend.
only three points (corresponding
to w’ = 0, 1, 2) shows a
440
R. W. NICHOLLS
Similarly, data of LANCZWROTH~cited by CRAGGSand MMSEYW for the Ng second positive system excited in an electron beam is given in Table 3, and the 1
Iv,.- &r- vs i~*+~, 4u”‘U ct),, plot is shown in Fig. 2b.
Fig. 2a Relative variation of the electronic perturbation integral Gv-,v, with internuclear separation in the excitation of the Ns+ First Negative System.
50,,v'=2 40-
=> 2 5 .? $I 4
30-
20-
IO-
Fig. 2b. Relative variation of the electronic perturbation integral Gu-,~, with internuclear separation in the excitation of the Ns Second Positive System.
0
1
__f-1.112
1
1
1
6.3335-2
2
3
l.D65+GM
4
5
7
0
TABLE 7. FRANCK--CONDON 6
10
12
13
5.4636-23.6545~ 2.27494
11
FACTORS TO HIGH VIBRATIONAL QUANTUM 9
-la-1.2626-l-1.1596-1_9.7609+-7.567~
15
6
,
A
Q
,o
9.
4,
ID
1.132+2
::;z
3.06~
1.1593-2
16
3.5585-3
17 1.69+3
3.cm2-4
19
Ll44f-4
20
co2op5
21
BANDSYSTEM
la
(&r~-P$)
7.4095-4
7.73494
7.4354-2 Gqp49lx 2.294pd
6.01454
9.6300-3
1.3aoq
22
3.929I-6
23
24
l~W-6
25
2.7565-7
26
1.34~
27
1.4loW
3.o929+
6.0629-3
5.2537-2
1.7123-2 8.343~3
2.9919-3
4.3574-i6 4.a24n6 l.b,rtr L55i43-i3 ,.a94645 3..9!39O+ l.lamo 2.343H2
2.70135
6.676H6
3.z
2.O+l6
l-a*?5
2‘
4.9335~6
2.OtlH6
')r
U55H
3.6013-3
P.WiWl6
3.3641-e
9.6,7546
2q28H6
1.595446
1.2,29-i5
4.593p16
,.036o15
r.l287-,7 2.,*6
2.346446
2.29+i6 I.~o)(H~
r.,n6-,5
4.3lXH6 ,.pf7+
9.1,79-,7 ,.n31-?9
7.64*6 8.116645
1.611562 9.2i681
3.42481
3.468916
6.qss-s
6dQm6
,.3674-l, 2.69Ol-l3 X5744-,5 2.8iy-9 6.a39Ml l.nZna
P.ca24-4
3.~14
1.*3
9.9X0-5
a.425n7
,.0952-i6 1~,646+5
9.44721
6.36~~
2.5055Q
6.94&-2
19
4.199616 6.2zmo 8.999',+
l-1693-3 4.lCQ2-4
42qW?
T-5&-2
48807-2
3.01~17
SYSTEM
3.7O&%?+
6.638.S
9.2%
3.241.~ 1.9411~ 1.~42~ 5.3367-32.46C&3 l.O4le-34.051+4 1.44-J 47207+ lM3S-5 3&!9M
3.8353-2 6.4377-2
1.5O'XW
1.2237-3 -1.96c.5+ 3.8065-e
7.6065-2
7.93434 6.634%~ 4.9fM-2 3.2Ce3-21.8737-29.8863-3472%-3 2.0452-38.039l-4Z&6+4
5.7621-3
2‘
*
2.367644
LYMAN-BIRGE-HoPFIELD(~~II,-X~$)
>I
1'1
l.a3(zwz
3.36lnS
OF THENZ
22 9.9345-u
2,
16
7."ioM, ::rs
20
15
r.9606+
4.11oM2
:::z
8.6253-S
1.2W-iO
:::G
6.yDSiO 7.7a7w :I&:
::z
,"::tz
7.57F2
23
1.1~11
1.2993-10
3.93w3
g.q66-12l.W.3
1.7366114 1.836+,5
1.9734-14 1.25~0-16 2.*,6
BANDSYSTEM
22
4.959613
2.4953-9
(A3$-X~l$)
l.l23~11
3.7194%
2.Yl7-lO
21
21
3.794+9
2.0707-S
6.OB9-16
2.OWHO
4.390+7
~6
20
49422-0
25 2.88X-9
4.14955
24
1.96o4-4 3.1q
4.4467-6 5.19671
19 ri2c6-5
18
9@lc-4
1,
~.4,7s-l
t:z
,
16
1.841-4
1.6993-5 2.5662-6 3.2317-7 3.4106s 1.34le2
1.6352-4
cw-3
VEGARD-KAPLAN
?$z
3.567N
3.4033-3 a.62914
9.449-5
::z
15
4.oKe+
BANDS
2.835l-3 2.49&~.401+2
1
FOR
5.0315-3
I
II
.
NUMBERS FOR THE N2 BIRGE-HOPFIELD 14 1.3195~2 7.1357-3
5.0917~21.616%? 2.57lW .3.441+33.37334 6.285% s.3730-29.037;i98.3427-26.77~2-24.92SW
2.637p4
F-50-2
3.6W2-e
9.693&'45375~ 1-5.1715-Q
1.4221-5
,,
2.8178Q
4.63+2<%
(0
VIBRATIONAL QUANTUM
1.2613-2 <0168-4
6.7057-4 2.1221-2
3.84332
I)
46355Q
5.73263 44362-3 3.214% 5.7932Q 2.wpI+z 3.6agW 9.8873-37.276p5 1.28%~ LIZ0-2 6.6116-2 8.0369+? --k
1
-9799-2
2.6639~2 j.52W
,
FACTORS TOHIGH
1.24124
2.95Sl.Q2.3413-4
3.46433.8936-2
6
TABLE ~.FRANCK-CONDON
1~,1.6834-,-
5
TABLE~.FRANCK-CONDONFACTORSTOH~GHVIBRATIONALQUANTUMNUMBERSFORTHEN~
1.6781+
5
40231-3
1.7303-2 4.2692-2
412854 1.943l-5
>.6653-2&64+2
1
3.6592~
3
3.96.34-2 4B
3
9.7769-4
2
1.4443Q
2
9.4229-3
d
e
9.6915Q
0 435sl-3 1.5565Q 3.531H 6.14spQ 0.9245-e
z +'
0
7.2.m
1 2.65W-2 2
r'+
0
*4ih?
5.3372-3 2.2atB-2 6.166+2
2.5Clb)
r’+’ 5.9CC44
16 r.@ti
0
12 6.9375-2 9.0~3-3 13 6.O71O-2 1.8172-2
/"
O
1
2
3
TABLE 4
3. i534-4
4.5631-5
6.8078-3
2.2076-3
3.7824-4
4e 141@-2
2.3862-2
9.5282-3
l.sf391-3
7*o5o+2 <.92aW
5.4504-2
2.8202-2
7.4508-3 *
8.26io-2
6.0064-2
2.1156-2
FORTHE
i 2.wo-5 1.1560-3 1.4749-2
BAND SYSTEM
1 8.9184-5 2.9916-3
3.5009-z
Nz JANIN-D'INcAN(?~II~- A!%,)
10. FRANCK-CONDONFACTORSTOHIGHVIBRATIONALQUANTUMNUMBERS
2
2.6757-4 6.1377-3
7.2809-3
TABLE
3 6.3704-4 I .o631-2
2.62466
4 I .2a la-3
2.5665-4
0
5 1.6167-2
9.5858-3
2.2671-3
6.36853
6
4.4007-2
2.2167-2
4.982 4 -2
3.62O6-3
2.2668-2 /
7
5.4221-5
2.7933-2/J.
2 .a745-2
5.3222-3
162-2
a
4.6287-2
5.2964-3
2.972&i!
3.28/ 17-2
3.939)_2
3.0464-3
7.305!+3
3.6342-2
11
12
13
4.5014-4 1.50525 6.413%
15
9.6299-g 6.6542-e
14
NEGATIvE(C~&-_X~$)
1.4926-2
9 9.4703-3
10
10
NUMBERS FOR THE N~SECOND
2.0408-2
6.4951-4
9
VIBRATIONAL QUANTUM
1.aoG2
3.0981-2
/
3.8269-2
1.1694-2 ’
a
11
7
FACTORSTOHIGH 6
11. FRANCK-CONDON 5
L3900Q
16
BAND SYSTEM
17
la
19
20
l&258-10 2.1918-12 0.3932-13 1.614~13 2.39*15
21
1.1200-14
4.6165-g 2.4059-g
Wja6-6
1.29758
7.1138-12 g.668?12
2.040610
2.207*
3.92896
6.q4w
3.3795lb 6.1355-10 3.3646=11 3.32O0-12 1.4079-12 1.415514
l-5531-4 1.5201-5 2.7376-6
4.34+!5
Ma58-3
2.2691-4
3.6834-3
g-4673-4
0
v=
1 2 3 4 5 6 7 8
9 la 11 l2 l.3 14 15 16 17 l2 19 P P
+
Y”
0
0
1
2
2.w
3
3
5
6
7
TABLE ~~.FRANCK-COND~NFACTORSTOHIGH 4
5
6
7
TABLE 13. FRANCK-CONDON
zlhua 1.62224 1.l299-2 7.17-3 w3 1.8359-3
A
9
9
lo
11
VIBRATIONALQUANTIJMNIJMBERSFORTHE 6
10
FACTORS TO HIGH VIBRATIONAL 8
QUANTUM
11
12
NUMBERS
13
l3
lb
l5
A6
02 SCHUMANN-RIJNGE(B~Z~---X~X;~)BAND 12
FOR THE
IA
CO
FOURTH
-15
17
la
POSITIVE (AIII-XX'Z+)~~~~
16
n
SYSTEM
SYSTEM
19
20
l6
21
l9
22
m
23
24
a
8.5997-3 3&ll-3 2axs-2 5.32bl-2 a&n4 ,L2Vl4-L6b+l~L~+l-LSlhl-~-7.2lW2 4-m m &nzI-3 3.363m 9.w Lm33-5 -3 LB%-2 Lm54 3.m --ZGG, -Ll2wl*%5mk2 cl.3754 Llm-l-Lm9-l 7.0861-5 9.27c4-24zG 6.*564 zwh2 1.@w+ Lm4-2 l.O2l9& 2w93-2 b.3-w LQ3a-6 Lw5-5 24076) I-=%3 -7.00364 ,Ll82&l-L2#M iziG L53554 6.6987~c7.al9w-5.swi-2 zaoch2 7.3533-7 2.lB5-2 6m32-2-&%?JM'3.5W-2 5.72s7-6 baa-5 ?..l.m+? &u+2 c5l%-4 7-3 zuob7 L9m2-3 c6949-2 ?zGz 5.9376-2-5.97lb-2'LrrOW t121W Ln6b-2 3.64@3 3.54364, 5.6l65-2 Lo4m-6 2.26324 %ZLlsJ 2.03&3 L3659-3 L-2 3.89Q-2 6A09Q-2' 'z?G-zzzz &.17624!,6.4757-2-2.m24 2-3 bm57-2~ixzG L5l92-3 3.357w 4.55l3-2 Lns7-2 3.5bw-2 3-L7884 6.79oM 6.WU-b 3.3m-3 5.960-2,,6.ll76-2 3.936s-2 6-3 &e&k3 hxm-2 4.76l5-2'2.2365-2 EGG ?zi!iG 3.3m-2 LWY-2 3.ll96-3 34w-2,3.6l%G 2.3054-3 2.96&6-2,Lm3w "iJiG= 9.6380-b 1.7Uo-h L3745-3 6.55s)_3 4.223s-2 5.65u-2 6.2679-2 Loa7-2 & plxs2~Llbu-2 b&53 bJ7O9-2~3.lm~ Lb* --izG L-3 2.9l944,3.o5ol-z L4l5+2 6.92584 4.76684 l.WA5-2 24519-5 2&!52*,3.75&-2 2.3224-5 3.73554 2.6435-3 LKK-2 8.6u7s3 3.05ls-2~Lm9-2 3&373-2~cow-3 c99563 2.O5e-2, 3.w Loll+3 Lpy-2 69nl-5 7.2622-4 4.6605-3 L&E& zO9jM 3aOs-7 2.22W-3 0.95x-3 3.m6-2 3.wwz cm 5.726+3 3.2BoFz~-izG d9w-3 ~ 3.w 3.om-2/ LOl3w um6-2 7.a%l-3 0.~3 LOW 9.6625-5 l.a8163 7.m3 2.3a2/2J3295-2 %lm-3 LBOl-2 2.w 'w7-2 7&W 3.%x&3 3.lw-2 zm9d -37-3 ' L33E-2 9-3 5a9o-4 2al5-2,L~ 1.0652-2 2.9097-2 1-3 2.ul9-2'iziG 1.73l2-4 2.m3 1.m 2.9m-2 8.7s95-3 2.w 2.=U-3 l.79sM /L9LYlMz 5.5wm-3 cllsn-4 2.5U6-2~iEz 1.95x-3 1.m 2.24tea cwso-4 1.7lllD-2 9.a 1.9035-2/ 2.43+2 2.a9w 3.1-3 L71c9-1 1.193o-2, tsO-2 Lb39h-2 Lntu 2.23ll-2'7~3 6.4555-3 2.3319-7 1~750-3 Lw-2,Laz&.2 7.99c1-c 2Alm-2 1.90&3 2.48094 4.55ll-4 6.5367-3 1-3-2 L3329-1 9.75664 2.l2zl-2 Lm76-2 3.Us-2~ 6.896+3 CU9+3 l-l?+3 1.7U6-2' L49w Ls6774 ' 9.73x4-3 L556l-3 z2z+2 l.l75&2,iziG l-0693 Leo49-j 2.19?3w 3.69.0-2 3.w3 s.ozcn-) 2-w 6.79W-4 a-3 1.1*3 1.l258-2 ,2.37+2 ,Le53x L5m.4 1.69@-2,9.3670-3 5.3m3pw2 LlUw 6-3 7.2mb-4 1-m5-2- 6xf@-3 Lbls2 l.zox-4 1.7bu-2/ 1.v 9.b76QL L4795-5 L5fm2/L3367-2 7.~3 8.zKG3 L7w-2 7.w LM7-3 bs56+3 1.w6-2 9.sw-5 L5X-2 s.w-3 2.5052-3 2.WW 9.9999-3 2.2996) L2983-2 L-3 9.9~3 2.0X%2 1.74363 1.192+2 3.56l7-3 b&VU-3 3.2772-3 7.mzl-b Ll390-2/ 1.69384 2.39934 2.2239-3 1.1854-2 2.~44-2 1.0546-5 Lbw-2 1~986-2 5.33764 1.53654 4.6-3 znls-3 1.5639-2 2.932W ,GEGasoaJ l3.363z+3/8.ml-3 3-3 L-3 2.5359-3 1.3271-2 3.2679-5 lZ22-2 LGl9+2/7.%3+3 Lool&3 l&v&2 7.02k,w 3.09sb3 m a&67-4 1.n99-2 2.eD674 3.m3 Laxs!/5.O?7+3 -3 L2497-2 9.4ou-6 LZ73-2 L695>3 r.w2-3 2.90b7-3 &91763/&9m-3 6.&S-3 LW?0-2 dOm-5 Las-2 wo5+7-3 L6601-2 3.us*3 Lml-3/zGzLu5a-L Lt)94a 26om4 pU-2 LO= 3.9232-3 SJlW3/8.395&3 5.42~7-3/~5u2-2 7.74564 94~~9-3/ s.pS5-3 LW3,L235W 3.U74-4 l.Lz6-2 686274 9.42353 Lsw-3~Llls2=2 9.aw3 E55s7-3 5.99063 aw9-3 3.~3 9.95l7-3 ZaapJ 22&x Ll.359-2 4.4-3 c-3 7.7552-3 L270-2
2
4.4975-3 L9wo-2
1
L0074-12 9.6394-14 1.9682-15 1.~450-16 6.9579-16 0.446~l0 4.n)~16 2.298-162.3193-17 8.472%lo 4.0175d 2.2i316420.0603-143.5241-155.578H6 1.054~161.259cM6p@02-16 1.20OO-79.0300-9 6.325~~10 3.4137-U 1.59~12 5.34O3-14 6.426~16z-14+16 5.7173-19
W w M S-7+9 ~~tl~~~~O2.)44~142.094615 2.0572-4 4.1650-54.9963-6 4.9572-7 4.O797-0 2.7859-9 1.5695-10 7.2000-12 3.CBSf3 4.6004-3 9.0orr-4 1.6515-42.2666-5 2.5551-6 2.3757-7 1.0248-81.156fi-9 6.0027-11
_
7
0
8.1812-3 2.63519
6
a
9
IO
11
11
12
12
14
,*
If
1.256+7
,r;
2.934% 1.33m
l.QM~
1.1~I6
7.0X-16
2.674%16 Z&YZZ-~~ ldX5I-tb
Z-3604-16 LcB79-16 3.4-17
2.~192-16 2&3o-l8
22
l.O+ls
7.2728-16
3.3262-134.367%15 l.Of2616 1.551+16
21
9.0660-9 1.5554-10 1.~l2
2.6360-9 4.C84Wl
SYSTEM
8.15fm-6 3.362*
BAND
20
24 19
Z-4669-10
18
23 17
20
21
22
3.2290-9 1.6529-9 8.618MO
6572610
16
SYSTEM
6.432~9
BAND
1.3V@+l
X1X+)
I8
24
2.2754-3 1.2623-8
a @‘2X+-
17
r.9p3-7
16
l.0549-5 imq-6
1.5862-9
2.6541-4
4.402+4 7.5i575 9.843%
1.65i55 1.93186 1.84951
2.308W
1.9963% l-5991-9 9.950t-114.7007-12
2.6929-4 5.W2-5
5.2609-4 i&02&4
19
7*oOe7-3 2.H~3
1.8202-5 2.5033-z 2.759W
23
5.7736% 2.717~
3.504c+3 1.o540-3 4.367t-e I.%+
b (b28+ -x1X+)
5.3693+
3.052+11 3.5373-13 1.645Fl5 6.2277~1 1.7772-164.3996-17 1.6740-1766459-17 2.2771-17 1.5732-102.0134-12 1.627z_14 1.5746-17 1.6023-W 1.9767-171.06Wl6 3.536W6
5.11)9+14 1.1047-15 1.m16
1.337+16 5.~3010-177.9066-W 1.1713$+16 2.525W7
NUMBERS FOR THE CO CAMERON (a211 - X1 C+) BAND SYSTEM
13
i?
8.0765Q
2.3997-Q 9.%55+3 j.W+i
1.2390-i 9.5266-2 5.3726+ 2.)23l+? 7.070&3 2.1-3
5.3W2-2 2.3701-e &49i7-3
2.4580-3 5.7598-4 w095-4 1.051yz
1.9331-e 5.9642-3 M20M
6.5CczW 2.7W
3.06)2-e 1.383~~ 3.7544-3
7.2666-2 1.2225-I im
4.02ly2
6.8427+ 2.1514-2 1.6357-3 4.77&>l,
-73
2.1733-3 5.4351-e a
3.6135-2 1.8984-e 6~007-3
3.3234-2 1.119!~6 a3.6733-2 zs
6.0%
4.Qolrr9
1.0572+ I.55052
1.7414+2 6.4357-3 5.6= 5.0622-e 3.2717-3 Z-4945+? 9.678>1.25~1 9.4a36e _V 6.2729-3 1.93&%57+ 3.215?n? 6.1712-4 5.3937Q>l%Fi =4.7619-e
2.2661+
1.1284-e 9.0294-3 ~9263~
.CZoOQ 2.3437-4
a.o79hrp075+
10
FACTORS TO HIGH ‘WBRA~ONAL QUANTUM NUMBERS FOR THE CO HOPF[ELD-BIRGE 7
r.q98-I l.5i~i~.734~~~.64ltl~.)wB-l
5
6.~9~
4
2.2458-6 l.lo53-6 5.5355-7 2.0241-7 I.46681 7*75itH 4166W
QUANTUM NUMBERS FOR THE CO HOPFIELD-BIRGE
FACTORS TO HIGH VIBRA~ONAL QUANTW
9
FACTORS TO HIGH. VIBRA~ONAL
TABLE 14. FRANCK-CONDON
6
TABLE 15. FRANCK-CONDON 5
1.775W4 6.3613-5 2.3683-5 9.1523-6 3.65886 1.5093-S 6.4123-7 2.80w-7
4 5.19374
3.5504-3 1.4335-3 5.9018-4 2.4870-4 1.0136-4 4.7436-5 2.14375
1
1.< M-i
1.62
6.i653-2 9.7334-3 5.906C-3 5.4248-2
i.wa-i
,.033ti
9.76+3
1.6i2N? 6=9i5t3 -5.59%
2.8151-e 2.8l8~3 8.2878-4 3.37OiQ _
9.255i-5 3.69~~
9.9033-6 4.67146
1 6*832+2 1.16724 5.0662-3 lGW7-3 B-928*3
i&77-3
1.9768+ 7.126~,&-2
9.2253-2s
4 3-w
TABLE 16. FRANCK-CONDON
1*5516-l 6.03164 2.289lQ
0
3369oe
3
1.0167-3 ae25-3
MW-4
48226-2
2.4930-2 6.914+2
2
0
L903l-3
++'
I
9.90~3
5 4.8277-Q a. 12-4 2.2752-2 P 2.4015-3 2.36%1-3
1
7.69~~
3
2
6 6.3lw
&%3fCT 5.7QMQ
7 a 1.651
IO
9
TABLE 17. FRANCK-CONDON FACTORS TO HIGH VIBRATIONAL QUANTUM NUMBERS FOR THE CO+ FIRST NEGATIVE @2X+-PE+) BAND SYSTEM
+ 6
+*
0
i)
.c%L
2.495
f? 43305
1 1.9mO-i
2 3 1 2.13P-(~.4033-Ll.447y-l_6$+2
3.47
4344
4
5
5
6 2.m92-2
6
, 5.295F3
7
l.YA-5 1
FACTORS
11 12 1.905z-6 1.43447
TABLE 19.FRANCK-CONWN ¶ 1.622wl
14
1.6111617
2.7 2-m
-N~BaII,
24 4788~9
l.aU?-i?
NaXI$
23 7-4979-S
2.67OY-17 5.4264-l? 1.3E+l8
NUMBERS
21 22 1.a?7o-f6 S-OiQ316
1.vm
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26 7&?e-i6
2.66?8-l6 1.589W9
1.4532-15 6s299(16
47034-l?
25 6.288M6 2.234ll6
2.6-6
4.lEY+i6
I9 20 2d3675-l? 7.215W6 w-6
2.645Wl5
4U4%l6
la ?.368+l6
5.'3937-l21.395ll3
3.Wfl5
4444616
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27
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1.248~12
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2.545116
1.0596-17 2.2748-16 3.919+l? 5.0147-l78.218W7
6.5443-i?
6.6456-16 l.5734-152.3324-l6
5.8588-17 2.6576-19 7.4692-l? 2.055217 7.8407-i? 2.918t-16 4.3697-i? l.694H6
2.2885+5
2.033C-S
2.6229-16 46436-16 0.456~6
8.0164-16 3.92X+
27 3s?xe+ ,.(o)t+$
7.125216
1.8993-15 1.6829-16 l.l646-16 l.187~16 7.647817 5.4631-17 7.62?6-17 7.6926-17 l.62)(w 1.17C@-+5 3.875~$6
7.662W6
6.0421-17 2.2@6-l6
l.42Ot-16 7.1770-16 1.5894-15 4.0335-f? 1.26~615 r.763tl5 6&07-l?
1.833~8
23
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5.6336-H
1.8001-16 1.943516
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22 23 24 3.49X-i? l.Wti6 3.47rw? 4.6~6 4.i679-,6 6.5@2+7 2.WC-i5
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20
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l.3309-0 l.23W-15 3.777H6
5.0273-i4 6.0233-16 1.805~l5
9.5536-17 1.0175-16 l&63-16
9.4977-11 1.2O?t12 1.35~~14
4.3692-M
l9
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lb
4.3668%
QUANTUM
7.754~
TO HIGH VIBRATIONAL
l3
2.74C9-9
8.286812
1.2719-15 6.(937-166.3666-l? 5.566216
12
l.O4h-f,
4.6513-3 0.C~65-4 1.046W
11
6.2924-2 2.0@2+
10
FACTORSTOHIGHVIBRATIONALQUANTUMNUMBERS
9
i.m
5.714MO
3.2027-9 5.7236fl 6.?248-13 9.12C.S-i5
a
TABLE~O.FRANCK-CONDON
a m462-3
8.4645-5 3.9092-6 1.30??1
2.11354q 5.3959.9
2.801%
0.9436-S
6.304%
WM-6
2.8174-16 .9.703f-i7 2.221~f6
1.283S4
W325-3
2.4CQO-5 9.n30-7
3.5596-0 7.504~IO 1.1359-11
1.6630-p I.&Xl-3
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4.W5P4
2.9774-5 1.215%
2.6605-I 9.3C8W
6.V82-2
4.7X7-3
7.4&j
w713-1
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3.7225-2 l&p .
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9 Y.CW-i7
TABLE 21.FRANCK-CONDON FACTORSTOHIGH VIBRATIONAL QUANTUM NUMBERS NzX'C~--N~PC~ 6 , l.2664-l4 42175-S
6
l&-w
1.9569-1 4.5640-Q 6.0537-3 5.14254
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