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Photodissociation of Li+2 ions
CIIkIXIICAL
Volume 65. number I
PHOTODlSSOCIATION
PIlYSlCS
LM-T1-:RS
OF Lit IONS
T. UZER * and A. DALGARNO Ilan ord&ni~hwttia~~ Ccnfcr for Aslmph.rsics. Canrbri&c.
Hccehed
Massacltcrscrrs
16 April
1979:
02138.
in litul
US.4
form
I1 \lay
1979
Calculations JIG presented of the cffcctivc cross ulated by abrorplion from (hc B ’ 11, skate of Liz.
sections
Disroci3tivc phoroioniz;ltion of cscinlcr rnolrcules by multiphoton 3bsorption c3n le3d to I3rge isotope fractiomtions. A substmtia! isotope frxrionarion h3s been dernoustr3rcd in the sequentid tao-photon ionization of Li, [ I]. Using 3 high-powered pulsed dye laser. Nitz et al. [I?] h3ve studied tile resonmt two-photon ioniL3rion of N3? 3rd the subsequcnc dissociariou of Nat by a third photon. This rhrccpIloton process nlusl 3lso led 10 isotope fractionstion. WC present here c3lculstions 3ppropri3tc to the intcrprctatiorl of similar csperinicnts on !_i,.
2. Theory T!IC direr-photon process consists of absorprion frotll the u = 0 vibrJtion3t le\cl of the ground X 15; state of Liz lo 3 distribution of vibra~ima! levels u’ in the escitrd B 1Ii, staI(: followed by photoionimtion into vibra~iona! I~vcls II: of Liz which then undergo photodissoci~tion inro Li 3rd ri+ [I]_ We suppose 10 be ulur3ted. the R ’ II,-?< 1’; trmsition The vibr3Gonal distribution in the 2X; is 3ccur3w ly represcnM by the Fran&-Condon f3ctors = I(x,.Ix,;~l”
the p!wtodissuciJtion
of
-: ions in vibrational Lt_
Icxcls pop-
where
1. Introduction
(I,.,;
for
,
xU. is tlw nuclear vibr3tion31 eigcnfunction of the u’ vibr3riund level of the B 1II, s131e of Liz md x”: is rhc nuclem vibrational cigcnfunction of the ui vidration3l level of tllc X 2X; st31e of !-it. We delerniined x,. by uumerica! inrtgmioa of the racikt! wtw equalion using rhe empiric31 KKK porenIi31 curve of ticsse! mc! Vi&! [3] for the B 1II, state 3nd the nlodel potenti curve of Cerjm et 31. [4] for tile X 1x; S13Ic\. The c3lcul3red VJhleS Of ‘I,.,.. far u’ = 0 10 u’ = 5 wllicll x5 1101less Ilwn 0.00 I jr, given in mblc 1. Rlotodissoci3tion cross sections for absorption from rhc ui = 0 !c\ci of !_i: h3ve been c3lcul3td by Kirby-Dockcn CI al. [ 51. I\,= have csrcndal tlw cdcul3tiom to hi$er vibrarional lcvcls and rhc cross sections o(ui) for vibration31 lcvcls ui = 0, I. 2 and 3 for photons of energy less than 3.5 eV are sllo\\*n in fig. I _The behavior is similar 10 rhsl for XI; 161. The projccrcd c~pCrilllcIki would nlcilsurc 311 3wr33~2cross secrion for absorpticll by the Icwl of u’ of the B 1II, stale, 3pprosinl3wly given by the fornuh E(u’)
= XII
u;
“‘“I +J,)
-
Fig. r! illustrates 3s 3 function \Kwflength. 5000 .&. die cross scclions 3rc of the order of 3 X I O-l7 cn12. conIpzr3blc to tllosc of x.13. Our cross sections. which were calculnred for 7 I-i<. \\i!! not be rnuc!~ changced by isotopic subsrituriuns but significant isotope effects cm he produced by 311 appropriate selection of the wm~elength of tllc photons that are initially absorbed into tlw U 1II, state.
Volume Trblc
65. number
CIiEM:CAL
I
LETTERS
1 August
1979
I
frmck-Condon
factors 4”‘~; for transitions ..---.
-
u;
i
= c
v’ - I __----.--0.335 0.178 0.254 0.144 0.059 0.021 0.007 0.002 0.001
6 7 8 9 IO II I2 13 I4 IS __
._
-.
Liz(B
_--_-
0.614 0.265 0.086 0.0?5 0.007 0.002
0 I 2 3 4 5
ktwccn
-_--.--
-.-_.-...--_-_---
___.___.
PHYSICS
_._.
.-___
_-_
’ tlu) and Lii (X ‘Xp*) ---u’ = 3 -----
0.049 0.443 0.03 1 0.175 0.158
0.001 0.111 0.454
0.003 0.169
0.000 0.099 0.143 0.100 0.052 0.023
0.434 0.006 0.048 0.117 0.103 0.063
0.009 0.003 0.001
0.032 0.014 0.006 0.002 0.001
0.086 0.037 0.014 0.005 0.002 0.001
..-
.._-
u’ = 4
u’ = 2
_-..
--.-..._--.
.-._-.
-
u’ = 5
0.004 0.217 0.414 0.017 0.019 0.089 0.097 0.069 0.039 0.020 0.009 0.004 0.002 0.001 _-.-.
-.._.------
-
6.C
SC
“E0 rT
0 J -
‘i-
4c
3c
-
lb
hv (eV) f-i& I. Photodisocia:ion 7
cross sections
o(ui) from the u; vibrational
level of Lt.; as J function
of incident
photon
energy in eV.
Volume
65. number
Cllt%lC~L
I
PllYSlCS
I Au+usI
LEITLRS
1979
lb IO-
5000
4030
5000
Acknowledgement This work was supported III part by the Department of Energy under Contract EY-76.SO?-7887.
References
[I I k.\V. Hothc. 1c11rrs
M.P. Wthur 53 (1978) 74.
and G.P.
RML.
Cncm.
HI)%.
6000
D.C. F;IIT. P.M. Ilogan. L.1). Shcarcr t’hyr 1112 (1979) LIO3. 51.11. llrrrrl and C.H. \‘~&l. ptn~tc
and S.J. Snwh.
J.
ccrmntunacafion
(197s). C.J. CCrJW-,. );. K~rb\~L)uc~rn xv_! ,\. DJ~~NW. ~Wnl. phys. Lcrrcrr 38 (1976) -lOI. K_ K~rt~~~LJocLrn. C.J. C’zr~~n Jnd A. IMgrno. Clwn. Phyr Lcrtrtr JO (1976) 205. 1. Uzcr and t\. I)aI~~fno, (‘hctn. Phy,. LCIICI~ 61 (1979) 213.
Volume 65. number I
PHOTODlSSOCIATION
PIlYSlCS
LM-T1-:RS
OF Lit IONS
T. UZER * and A. DALGARNO Ilan ord&ni~hwttia~~ Ccnfcr for Aslmph.rsics. Canrbri&c.
Hccehed
Massacltcrscrrs
16 April
1979:
02138.
in litul
US.4
form
I1 \lay
1979
Calculations JIG presented of the cffcctivc cross ulated by abrorplion from (hc B ’ 11, skate of Liz.
sections
Disroci3tivc phoroioniz;ltion of cscinlcr rnolrcules by multiphoton 3bsorption c3n le3d to I3rge isotope fractiomtions. A substmtia! isotope frxrionarion h3s been dernoustr3rcd in the sequentid tao-photon ionization of Li, [ I]. Using 3 high-powered pulsed dye laser. Nitz et al. [I?] h3ve studied tile resonmt two-photon ioniL3rion of N3? 3rd the subsequcnc dissociariou of Nat by a third photon. This rhrccpIloton process nlusl 3lso led 10 isotope fractionstion. WC present here c3lculstions 3ppropri3tc to the intcrprctatiorl of similar csperinicnts on !_i,.
2. Theory T!IC direr-photon process consists of absorprion frotll the u = 0 vibrJtion3t le\cl of the ground X 15; state of Liz lo 3 distribution of vibra~ima! levels u’ in the escitrd B 1Ii, staI(: followed by photoionimtion into vibra~iona! I~vcls II: of Liz which then undergo photodissoci~tion inro Li 3rd ri+ [I]_ We suppose 10 be ulur3ted. the R ’ II,-?< 1’; trmsition The vibr3Gonal distribution in the 2X; is 3ccur3w ly represcnM by the Fran&-Condon f3ctors = I(x,.Ix,;~l”
the p!wtodissuciJtion
of
-: ions in vibrational Lt_
Icxcls pop-
where
1. Introduction
(I,.,;
for
,
xU. is tlw nuclear vibr3tion31 eigcnfunction of the u’ vibr3riund level of the B 1II, s131e of Liz md x”: is rhc nuclem vibrational cigcnfunction of the ui vidration3l level of tllc X 2X; st31e of !-it. We delerniined x,. by uumerica! inrtgmioa of the racikt! wtw equalion using rhe empiric31 KKK porenIi31 curve of ticsse! mc! Vi&! [3] for the B 1II, state 3nd the nlodel potenti curve of Cerjm et 31. [4] for tile X 1x; S13Ic\. The c3lcul3red VJhleS Of ‘I,.,.. far u’ = 0 10 u’ = 5 wllicll x5 1101less Ilwn 0.00 I jr, given in mblc 1. Rlotodissoci3tion cross sections for absorption from rhc ui = 0 !c\ci of !_i: h3ve been c3lcul3td by Kirby-Dockcn CI al. [ 51. I\,= have csrcndal tlw cdcul3tiom to hi$er vibrarional lcvcls and rhc cross sections o(ui) for vibration31 lcvcls ui = 0, I. 2 and 3 for photons of energy less than 3.5 eV are sllo\\*n in fig. I _The behavior is similar 10 rhsl for XI; 161. The projccrcd c~pCrilllcIki would nlcilsurc 311 3wr33~2cross secrion for absorpticll by the Icwl of u’ of the B 1II, stale, 3pprosinl3wly given by the fornuh E(u’)
= XII
u;
“‘“I +J,)
-
Fig. r! illustrates 3s 3 function \Kwflength. 5000 .&. die cross scclions 3rc of the order of 3 X I O-l7 cn12. conIpzr3blc to tllosc of x.13. Our cross sections. which were calculnred for 7 I-i<. \\i!! not be rnuc!~ changced by isotopic subsrituriuns but significant isotope effects cm he produced by 311 appropriate selection of the wm~elength of tllc photons that are initially absorbed into tlw U 1II, state.
Volume Trblc
65. number
CIiEM:CAL
I
LETTERS
1 August
1979
I
frmck-Condon
factors 4”‘~; for transitions ..---.
-
u;
i
= c
v’ - I __----.--0.335 0.178 0.254 0.144 0.059 0.021 0.007 0.002 0.001
6 7 8 9 IO II I2 13 I4 IS __
._
-.
Liz(B
_--_-
0.614 0.265 0.086 0.0?5 0.007 0.002
0 I 2 3 4 5
ktwccn
-_--.--
-.-_.-...--_-_---
___.___.
PHYSICS
_._.
.-___
_-_
’ tlu) and Lii (X ‘Xp*) ---u’ = 3 -----
0.049 0.443 0.03 1 0.175 0.158
0.001 0.111 0.454
0.003 0.169
0.000 0.099 0.143 0.100 0.052 0.023
0.434 0.006 0.048 0.117 0.103 0.063
0.009 0.003 0.001
0.032 0.014 0.006 0.002 0.001
0.086 0.037 0.014 0.005 0.002 0.001
..-
.._-
u’ = 4
u’ = 2
_-..
--.-..._--.
.-._-.
-
u’ = 5
0.004 0.217 0.414 0.017 0.019 0.089 0.097 0.069 0.039 0.020 0.009 0.004 0.002 0.001 _-.-.
-.._.------
-
6.C
SC
“E0 rT
0 J -
‘i-
4c
3c
-
lb
hv (eV) f-i& I. Photodisocia:ion 7
cross sections
o(ui) from the u; vibrational
level of Lt.; as J function
of incident
photon
energy in eV.
Volume
65. number
Cllt%lC~L
I
PllYSlCS
I Au+usI
LEITLRS
1979
lb IO-
5000
4030
5000
Acknowledgement This work was supported III part by the Department of Energy under Contract EY-76.SO?-7887.
References
[I I k.\V. Hothc. 1c11rrs
M.P. Wthur 53 (1978) 74.
and G.P.
RML.
Cncm.
HI)%.
6000
D.C. F;IIT. P.M. Ilogan. L.1). Shcarcr t’hyr 1112 (1979) LIO3. 51.11. llrrrrl and C.H. \‘~&l. ptn~tc
and S.J. Snwh.
J.
ccrmntunacafion
(197s). C.J. CCrJW-,. );. K~rb\~L)uc~rn xv_! ,\. DJ~~NW. ~Wnl. phys. Lcrrcrr 38 (1976) -lOI. K_ K~rt~~~LJocLrn. C.J. C’zr~~n Jnd A. IMgrno. Clwn. Phyr Lcrtrtr JO (1976) 205. 1. Uzcr and t\. I)aI~~fno, (‘hctn. Phy,. LCIICI~ 61 (1979) 213.