Spectra of Diatomic Molecules: From Cold to Hot

Transcription

1 Spctra of Diatomic Molculs: From Cold to Hot obrt M. uc rislav Horvatić Mladn Movr Zagrb Croatia

2 Outlin Diatomic molculs hav bn an objct of vry intnsiv invstigation for diffrnt physical conditions. I shall discuss thortical aspcts of som invstigations in a wid rang of tmpraturs. Ovrviw of thortical mthods usd in th analysis of spctra of diatomic molculs Formation of ultracold molculs in magntooptical traps using photoassociation mthod = 0-4 K Spctroscopy of alkali diatomic molculs adsorbd on th surfac of hlium droplts = 0.7 K Optical spctra of carbon monoxid molcul at room tmpratur 00 K Spctroscopy of hot vapors > 00 K Potassium rsonanc lins prssur broadnd by hlium atoms Absorption and thrmal mission of suprhatd csium vapor at high tmpraturs K

3 Introduction h absorption cross sction from a rovibrational stat of th lowr lctronic stat v J to th rovibrational stat of th uppr lctronic stat v J Lam t al. 977 Chung t al. 999 is givn by v`j `` v``j ```` 8 hc w J ` ` S J `` `` J `` v``j ```` D v`j `` g tr and th spontanous mission rat from th stat v J to v J is A 4 J ` ` vj 64 S J `` `` v` J `` w ` J v``j ```` D hc v`j `` D is th lctronic transition dipol momnt µ th molcular rducd J `` mass g tr th lin-shap function S J ```` th Hönl-London factor 0 ` htr Ev J Ev J th transition nrgy and w th statistical 0 factor dpndnt on th symmtry of lctronic stats. h nrgis E and radial wav functions v J vj can b obtaind from th Schrödingr quation J J d E V 0 d whr V is th potntial of th lctronic stat Λ.

4 j i i i j i j i J J V j i j i ij j i i H 8 If on of th transition stats is a fr continuum stat instad of unitynormalizd wav functions Φ vjλ th nrgy-normalizd wav functions Φ εjλ ar usd. In th Fourir grid Hamiltonian mthod rovibrational wav functions ar rprsntd on a finit numbr of grid points i i= N uniformly spacd by Δ. h Hamiltonian is rprsntd by an NxN matrix h infinit st of rovibrational stats is rprsntd on th grid by a finit st of stats whos nrgis E vjλ and wav functions Φ vjλ ar th ignvalus and ignvctors of th Hamiltonian matrix. h continuum of fr stats is rprsntd by a discrt st of unity-normalizd wav functions having a nod at th outr grid boundary N = N Δ.

5 h absorption cofficint Kν is obtaind by avraging ovr initial rovibrational lvls with wighting factors v`` J `` `` and summing ovr all transitions multiplid by th molcular numbr dnsity N A. Z K N A v`j `` v`` J`` `` Z v``v `J ``J ` v``j ```` whr is th partition function of th molcular stat Λ h mission cofficint εv is obtaind by avraging ovr uppr rovibrational lvls with wighting factors v` J ` ` and summing ovr all transitions. vj N v J A A Z v`j `` v``v`j ``J ` Assuming thrmodynamic quilibrium th wighting factor is: v J J D EvJ E J xp k D EvJ E J xp whr ω J is a statistical factor dpndnt on nuclar spin I with th valus I/I + for vn J and I + /I + for odd J D Λ is th dissociation nrgy of th stat Λ and E V Z J v J Z v J v J k

6 According to th mass action law at thrmodynamic quilibrium N A S / N N S L S L k A N A is th atom numbr dnsity S A is spin L A th angular momntum of atom A. h absorption cofficint Kv: h mission cofficint εv: N C A K 8 hc 4 64 hc A A w w N ` xp E k C C N v``v `J ``J ` v``v`j ``J ` S S L A A ~ Z v J J `` A J ` J D k / S L k E J xp h thrmal mission from a uniform layr of thicknss L is rlatd to th absorption cofficint K v by Kirchhoff s law of thrmal radiation [Horvatić t al. 05]. Spctral radianc Iν can b writtn as I Z Ev ``J `` `` k Ev ` ` `` k J S S J `` J ```` J `` J ```` k vj h xp LK v xp hv / k v c xphv / k v``j ```` v``j ```` D D v`j `` v`j `` g ij g tr

7 Ultracold = 0-4 K

8 Formation of ultracold Cs molculs M.Pichlr W.C.Stwally.uc and G.Pichlr. Phys. v A 69 : At ultracold conditions 00 µk in a magnto-optical trap MO cold molculs can b producd by two-photon photoassociation procss of colliding atom pairs. I shall dscrib on of th scnarios for th formation of cold Cs molculs by photoassociation. From th ultracold fr stat dscribd by th wav function ΦEX Σ g+ that scattrs within th ground X Σ g + stat nrgy of th fr stat corrsponds to th avrag rlativ kintic nrgy of th collision of 00 μk th absorption of a photon producs xcitation into th bound vibrational stat v of th xcitd Σ u + lctronic stat photoassociation. y spontanous photon mission Σ u + X Σ g + transition th bound vibrational stats v of th ground lctronic stat X Σ g + ar producd.

9 h ground lctronic stat potntial curv for J>0 has a long-rang barrir so only th colliding pairs of atoms with J=0 can rach th shortrang rgion. h probability of photoassociation P PA Ev from th fr ΦEX Σ g+ stat into th bound v Σ u + stat is proportional to th squar of th modulus of th matrix lmnt for th lctronic transition dipol momnt D for this transition h probability of spontanous mission from bound stats v of th xcitd lctronic stat Σ u + into bound stats v of th ground lctronic stat X Σ g + u g PA v D X E v E P u g SE v D X v v v P 6 6 J J C J V

10 Probability of formation of ultracold molculs in v stats of th ground lctronic X Σ g + stat in dpndnc of photoassociation into bound stats v of th xcitd lctronic Σ u + stat P E v v P PA E v P SE v v E v ' v '' 00 0 Molculs formd in th ground lctronic X Σ g + stat by photoassociation ar translationally and rotationally cold bcaus only low partial-wav collisions s-wav and p-wav of cold atoms contribut to th procss. Howvr gnrally thy ar not vibrationally cold.

11 Cold = 0.7 K

12 Csium dimr spctroscopy on hlium droplts W.E.Ernst;. Hubr; S. Jiang;. uc; M. Movr; G. Pichlr: J. Chm. Phys Cold nanodroplts of about 0 4 hlium atoms provid a wakly intracting low-tmpratur nvironmnt cryostat of 0.7 K for th formation and spctroscopy of molculs. Csium atoms pickd up by a bam of hlium nanodroplts rmain on th hlium surfac whr thy skat and form molculs in cold collisions. Enrgy of xcitd rovibrational stats is rlasd into th surrounding hlium clustr and causs vaporation of hlium atoms on hlium atom for vry 5 cm of nrgy. As a rsult hlium droplts loadd with wakly bound molculs a Σ + u ΔE vib =0.8 cm - ar obsrvd at largr abundanc downstram in th hlium clustr bam than droplts loadd with strongly bound molculs X Σ + g ΔE vib =44.8cm Enrgy cm triplts v=0 E=-4 cm - v=0 E=-68 cm - ohr singlts X g x u

13 All adsorbd Cs molculs ar in v =0 vibrational stat. Only a fw rotational lvls within th lowst vibrational lvl ar populatd. In that cas on can safly nglct th J dpndnc of th matrix lmnts and put J = J = 0. h small vibrational spacings in th bands of th havy alkali diatoms ar usually not rsolvd bcaus of th hlium-inducd lin broadning and w rplac th summation ovr v with an intgral ovr nrgy. Using th rflction approximation [uc t al. 007] on gts th absorption cofficint in th form: ` `0 `` 00 ` 8 ij v v hc g D w N K h E w c w D w N K / position of ground stat minimum V V g w V V E g

14 Intnsity cts/s Lasrpowr Intnsity cts/s Lasrpowr Normalisd intnsity arb.u u 600 cm - E=67 cm - g 6684 cm- + u 756 cm - + u 7 cm - Normalisd intnsity arb.u u cm - 4 g cm - g 857 cm Wavnumbr cm Wavnumbr cm - Spctra of csium molculs on hlium droplts h6g and h0 dy lasr. Uppr panls show obsrvd spctra of lasr-inducd fluorscnc and th simultanously rcordd rlativ lasr intnsity. Lowr panls show normalizd spctra and Gaussian fits to th band maxima as wll as th positions of th bands. All obsrvd spctral faturs ar idntifid by comparison with thortical spctra simulations basd on th simpl rflction formula.

15 oom tmpratur 00 K

16 Spctra of th CO molcul CO is th scond most common molcul aftr H in th intrstllar mdium. h CO molcul spctra hav bn th subjct of many studis of Earth atmosphr spcially grnhous gas rmdiation. W calculatd th quantum-mchanical absorption and mission spctra for th Σ + A Π Angström transition of CO molcul at room tmpratur 00 K. his transition is suitabl for plasma diagnostics in th study of cold and lowdnsity plasmas prformd by th group of S. Milošvić at my Institut.

17 In ordr to simulat th plasma mission spctra in non-le condition th rovibrational lvls wighting factor can b aproximatd by th rlation v J vib rot h mission intnsity is I vib rot 4 ~ Z vib rot J Evvib EvJrot J xp J `` J ` k vib v J vib k rot rot S J `` J ```` v``j ```` D v`j `` g tr ~ Z vib rot v J vib rot v J whr E v vib and E vj rot ar vibrational and rotational nrgis of th rovibrational stat and and rot ar th vibrational and rotational tmpraturs. vib

18 Hot > 00 K

19 Potassium rsonanc lins prssur broadnd by hlium atoms. uc G. Pach M. Movr. Horvatić; X SAC 06 AApr? Potntial curvs diffrnc potntial curvs dashd lins of th ground X Σ + and th xcitd Σ + and A Π stats. Potntial curvs ar prdominantly rpulsiv xhibiting just a shallow wll. X-A transition has a monotonic diffrnc potntial curv and contributs to th rd wing of th first rsonant lin. X- transition has a diffrnc potntial curv with on maximum and contributs to th blu wing and th blu satllit band.

20 In LE assuming th Q-branch approximation ΔJ=0 and ω J =/ th absorption cofficint has th form Chung t al. 00 uc t al. 0: K 4 hc w C v``v `J `` J Ev ``J `` `` k v``j ```` D g In th cas of a K-H dimr th fr-fr transitions dominat th optical spctra and th motion of th atoms can b dscribd by a classical trajctory t. Using th smiclassical approximation and th standard stationary phas approximation on obtains: K 6 4 w C xp c n c Summation is ovr th Condon points c c c c Divrgnc at th diffrnc potntial xtrms can b rmovd by uniform Airy approximation [Sando t al. 97 Szudy t al 975 uc t al. 99] i D c c V i k v`j V V ` ij h V D V xp D xp k 4 K c w C h Ai x 0 x / / x dx V D D 6 6 k k 4/ 8m g h Ai x 0 k h x / x 4 h g dx / k

21 absorption mission K N K N H W calculat th rducd absorption cofficint and th rducd mission cofficint N K N H using th fully quantum-mchanical and th smiclassical approach in th wid rang of tmpraturs K typical for th atmosphrs of brown dwarfs and giant xoplants.

22 Absorption and thrmal mission of csium vapor at high tmpraturs Pichlr G Makdisi Y Kokaj J homas N Mathw J and uc J. Phys. 06; Pichlr G Makdisi Y Kokaj J Mathw J akić M and uc J. Physi: Conf. Sris 07 Absorption and thrmal mission of suprhatd csium vapor was studid in th all-sapphir cll at vry high tmpraturs K. h masurd spctra of th Cs diffus band around 70 nm wr compard with thortical simulations.

23 hr groups of optical transitions contribut to th mission and absorption in th spctral rgion btwn 680 nm and 740 nm; two triplt transitions and on singlt transition. Potntial curvs of ths lctronic stats givn by [Spis 989] ar shown in Fig. a. Diffrnc potntial curvs for th rlvant transitions ar shown in Fig b. All diffrnc potntials of triplt transitions hav two xtrma minima and maxima. In Fig c w prsnt th rlvant transition dipol momnts calculatd without th spin-orbit intraction [Allouch t al. 0].

24 Absorption spctra K 4 hc w C k v``v ` Ev ``0 `` k v``0 `` D v`0 ` g ij caus of th small vibrational and rotational nrgy splitting in th Cs molcul in our calculations w usd th smiquantum approach [uc t al. 0]. In ordr to valuat th absorption cofficint on nds to know th vibrational nrgis and th corrsponding wav functions for J = 0 only. If svral lctronic transitions contribut to th absorption in th sam frquncy rang th total absorption cofficint is K K i j i j

25 hr ar two distinct contributions to th masurd mission spctra. h first on is th mission of suprhatd csium vapor and th scond is th blackbody radiation of th ovn hatr and sapphir cll. Paramtrs A and ar optimizd in ordr to obtain th bst fit to th obsrvd mission profil. / / / xp k h k h k h LK c h c h A I Emission spctra

26 Acknowldgmnts h prsnt work was supportd by th Croatian Scinc Foundation HZZ undr th projct numbr 75. I am gratful for th coopration to: Gillian Pach Univrsity Collg London London Goran Pichlr Slobodan Milošvić Institut of Physics Zagrb G Pichlr Y Makdisi J Kokaj N homas J Mathw Kuwait Univrsity Kuwait Wolfgang Ernst Institut fur Exprimntalphysik U Graz William C. Stwally Marin Pichlr Univrsity of Concticut Storrs

27 hank you for your attntion