A coupldchannl calculation o th B 3 Σ u X 3 Σ g spctrum o S 2 Stv Gibson Stvn Cavanagh Brnton Lwis Glnn Stark 2 Rsarch School o Physical Scincs and Enginring, Th Australian National Univrsity, Canbrra ACT 2, Australia 2 Physics Dpartmnt, Wllsly Collg, Wllsly, MA 248, USA Ovrviw: Background Coupldchannl Schrödingr quation Rsults S 2 Conclusions ANU
Background S 2 UV absorption obsrvd in th atmosphrs o Jupitr and IO. K. S. Knoll t al. Scinc 267, 37 (99); J. R. Spncr t al. Scinc 288, 28 (2). highicincy lamps S 2 isovalnt with O 2 : VUV B X spctrum is wll undrstood in trms o CSE modl. Apply a similar modl to S 2. B. R. Lwis t al. Phys. Chm. Earth(C) 26, 9 (2). VoyagrJupitrIOLokiplum (NASA) EETD Lawrnc Brkly National Laboratory
Modl radial Schrödingr quation F (R) + 2µ 2 [E W(R)] F(R) = intraction matrix radial wavunctions V (R) V V 2... F (R) F (R)... F Nopn (R) V (R) V 2... F (R)... B. @. C. AB C @. A V NN (R) F N (R)... F NNopn (R) PE B. R. Johnson, J. Chm. Phys. 69, 4678 (978). Normalization F. H. Mis, Mol. Phys. 4 93 (98). scattring matrix F S (R) R i ikr i ikr S Photoabsorption cross sction σ v J νj = 2π2 ν 3ɛ F M F i 2 lctronic transition momnt rotational matrix lmnt σ γv J νj Fγ M F i + F γ M F i +... 2 opn channl Total cross sction P (2J + )σ γv σ γ(ν, T) = J νj E V J /kt P (2J + ) E v J /kt σ R
Modl coupldchannl Schrödingr quation (CSE) F (R) + 2µ 2 [E W(R)] F(R) = intraction matrix radial wavunctions V (R) V V 2... F (R) F (R)... F Nopn (R) V (R) V 2... F (R)... B. @. C. AB C @. A V NN (R) F N (R)... F NNopn (R) PE B. R. Johnson, J. Chm. Phys. 69, 4678 (978). Normalization F. H. Mis, Mol. Phys. 4 93 (98). scattring matrix F S (R) R i ikr i ikr S Photoabsorption cross sction σ v J νj = 2π2 ν 3ɛ F M F i 2 lctronic transition momnt rotational matrix lmnt σγv J νj Fγ M F i + F γ M F i +... 2 opn channl Total cross sction P (2J + )σ γv σ γ(ν, T) = J νj E V J /kt P (2J + ) E v J /kt σ Intnsity borrowing Intrrnc lin shap asymmtry R
O 2 B 3 Σ u X 3 Σ g σ( 9 cm 2 ) E(V) Exprimntal 29K CSE J= 2 Rydbrg 3 Σ u S. T. Gibson and B. R Lwis JESRP 8, 9 (996). Valnc 3 Σ u 8 O( D)+O( 3 P) 6.. 2. 2. M/a o Singl Rydbrgvalnc intraction rproducs th main aturs o th spctrum, including th Tanaka bands. Rydbrg transitions borrow intnsity. 2 4 6.. Wavlngth (Å) R(Å)
O 2 B 3 Σ u X 3 Σ g σ( 9 cm 2 ) E(V) Exprimntal 29K CSE J= 2 Rydbrg 3 Σ u S. T. Gibson and B. R Lwis JESRP 8, 9 (996). Valnc 3 Σ u 8 O( D)+O( 3 P) 6.. 2. 2. M/a o Singl Rydbrgvalnc intraction rproducs th main aturs o th spctrum, including th Tanaka bands. Rydbrg transitions borrow intnsity. 2 4 6.. Cross Sction (cm 2 ) 2 2 22 23 24 2 26 (6,) Wavlngth (Å) (4,) R(Å) CSE xp. 4 6 7 8 9 2 Wav numbr (cm ) K. Yoshino t al. Plant. Spac Sci. 4, 8 (992). B. R Lwis t al. Phys. Chm. Earth (C) 26, 9 (2). CSE modl rproducs psudo continuum btwn rovibrational lins.
S 2 B 3 Σ u X 3 Σ g CSE modl B prdissociatd by B 3 Π u, Π u. ( Σ u mployd by Whlr is orbiddn to intract with B 3 Σ u ), Π u and 2 3 Σ + u. Modl paramtrs or 32 S 2 : potntial nrgy curvs (PEC), coupling constants (spinorbit B B 6 cm, B Π cm, B Π 9 cm, b X 44 cm, rotational coupling btwn 3 Σ and 3 Σ stats) and th transition dipol momnts M (R) (ab initio ) shown as inst within igur. M. D. Whlr t al. J. Chm. Phys. 8, 694 (998). Potntial nrgy abov Xstat minimum ( 4 cm ) A. D. Pradhan and H. Partridg, Chm. Phys. Ltt. 2, 63 (996). 6 4 3 2 S 2 3 Σ 2 + u B 3 Σ S( D)+S( 3 P) u 2 B" 3 Π u b + Σ g X 3 Σ g S( 3 P)+S( 3 P) 2 3 4 R 2 3 4 6 Intrnuclar distanc R(Å) X, b, B, B RydbrgKlinRs (RKR) curvs Π, Π and 2 3 Σ u rom ab initio calculations (Whlr), shitd to th corrct dissociation limit. M(R) B X BX
S 2 oscillator strngths or an isolatd Bstat 2 v 3 4 CSE Pradhan 6 q v 2 3 CSE Andrson 7 Incrasing dviation rom publishd thortical valus. Valus snsitiv to th shap o th Bstat PEC. Improv by including 3 Σ u Rydbrgvalnc intraction which inluncs th high v lvls, as is th cas or O 2 B X. 6 2 v 2 3 4 6 Intrnuclar distanc R(Å) A. D. Pradham and H. Partridg, Chm. Phys. Ltt. 2, 63 (996). Q. R. Andrson t al. J. Chm. Phys. 7, 82 (979). Potntial nrgy abov Xstat minimum ( 4 cm ) 6 4 3 2 B" 3 Π u 2 3 Σ + u S 2 B 3 Σ u X 3 Σ g S( D)+S( 3 P) S( 3 P)+S( 3 P) 4 2 v
Rsults S 2 UV photoabsorption spctrum Partial cross sctions Cross sction calculation or lvl rotational maniold at 3 K. Cross sction ( 6 cm 2 ) 9 3K lvls ( ) v= 2 3 total B" 3 Π u 36 38 4 42 Wavnumbr (cm ) Potntial nrgy abov Xstat minimum ( 4 cm ) N J 8 8 8 7 8 9 6 6 6 6 7 4 4 4 3 4 2 2 2 2 3 6 4 3 2 B" 3 Π u 2 3 Σ u + S 2 B 3 Σ u X 3 Σ g S( D)+S( 3 P) S( 3 P)+S( 3 P) 2 3 4 6 Intrnuclar distanc R(Å) B 3 Σ u F 3 F F 3 F F 3 F F 3 F P R3 R P3 P R 3 3 P R 2 2 R R P R Q2 Q32 N J P Q2 P Q23 T R3 N P3 6 4 F F 3 3 3 3 4 3 2 F 3 X 3 Σ g
32 S 2 B 3 Σ u X 3 Σ g Comparision with xprimntal data CRDS M. D. Whlr t al. J. Chm. Phys. 8, 694 (998). (,) (2,) lvls ( ) lvls (F ) 3 lvls (F 3 ) total 38 39 36 36 Wavnumbr (cm ) 362 363 364 36 Wavnumbr (cm ) (3,) (4,) 366 367 368 Wavnumbr (cm ) 37 37 372 Wavnumbr (cm )
Conclusions CSE calculations provid a physically basd quantum mchanical modl o photodissociation. Application to B X transition o S 2 clarly idntiis th rol o ach prdissociating stat: ssntial or undrstanding th complxitis o th spctrum..g. (, ) band prdissociatd by 3 Π u, whras (3, ) prdominantly Π u intraction. Calculations agr wll with publishd data but data is limitd. Furthr improvmnts to CSE modl through adjustmnt o modl paramtrs, PECs, couplings and transition momnts. Prliminary study, plannd masurmnts o S 2 and clustrs using a astbam photoragmnt spctromtr.