Contains reports on three research projects.U.S. Air Force - Office of Scientific Research (Grant AFOSR-76-2972)National Science Foundation (Grant CHE79-02967)National Science Foundation (Grant PHY79-09743

Ahmad-Bitar, Riad N.

Becker, Christopher H.

Brunner, Timothy A.

Durand, Marie

Gottscho, Richard A.

Havey, Mark D.

Kinsey, James L.

Lapatovich, Walter P.

Morales-Mori, Alejandro

Moskowitz, Warren P.

Pritchard, David E.

Scott, Thomas P.

Serri, John A.

Smith, Neil

DSpace@MIT

V. ATOMIC RESONANCE AND SCATTERINGAcademic and Research StaffProf. D. KleppnerProf. D.E. PritchardDr. R.N. Ahmad-BitarDr. C.H. BeckerDr. R.W. ClineL.R. BrewerT.A. BrunnerJ.C. Castro NetoR.G. HuletA.W. KarpM.M. KashDr. T.W. Ducas*Dr. R.A. GottschoDr. S. HarocheDr. M.D. HaveyGraduate StudentsW.P. LapatovichA.L. MigdallP.E. MoskowitzW.P. MoskowitzT.P. ScottJ.A. SerriDr. M.G. LittmanDr. A. Morales-MoriDr. J.R. RubbmarkDr. A. Spielfiedel+Dr. M.L. ZimmermanD.A. SmithN. SmithW.P. SpencerA.G. VaidyanathanR.E. WalkupG.R. Welch1. STUDIES OF ROTATIONAL ENERGY TRANSFERU.S. Air Force - Office of Scientific Research (Grant AFOSR-76-2972)Timothy A. Brunner, Marie Durand, David E. Pritchard,Thomas P. Scott, Neil SmithThe most probable type of inelastic collision involving molecules is RotationalEnergy Transfer (RET), an important process in high-power gas lasers and interstel-lar clouds. We have measured rate constants for the RET processNa2(j o ) + X - Na2(j0 +A) + X - AE, (1)where the * indicates that the Na2 is in an electronically excited state, X is thetarget atom, jo is the initial rotational quantum number, A is the change in rota-tional quantum number, and AEr is the increase in rotational energy.Since at typical temperatures roughly 100 rotational levels are populated, thereare thousands of rate constants, k(j j +A), needed to characterize the system. Use00oAssistant Professor at Wellesley College.+Visiting Scientist from Observatoire de Paris, France.PR No. 122(V. ATOMIC RESONANCE AND SCATTERING)50 I I+ A > 00 A<0LINE ECS-PO0004+J =16++  =38+ 0=66 +0 100+0 26IAJFig. V-1. Measured Na2-Xe rate constants, k(jo -jo+A), versus JAI forjo = 4, 16, 38, 66, 100. The lines connect points generatedby the ECS-P fit.of a computerized data-acquisition system and data-analysis programs have made pos-sible accurate measurements of typically 50 to 100 level-to-level RET rate constantswith jo ranging from 4 to 100 and JA < 28 for each of eight target gases: X = He,Ne, Ar, Kr, Xe, H2, N2, and CH4. Figure V-1 illustrates the (apparently) complexdependence of the rate constants on j , JA I, and the sign of A.This unprecedented wealth of accurate data has made it possible for us to searchsystematically for fitting laws1 - laws which express the hundreds of rate constantsin terms of a few physically significant parameters. We have found a highly success-ful fitting law which combines the theoretically predicted Energy Corrected Sudden(ECS) scaling law with our empirically discovered2 Power (P) law. The resultingfitting law, ECS-P, can fit 100 experimental rate constants with only 3 variablePR No. 122k (cvp)2-It------ -- ) - -A--LIS+(0 //6-+ /0----- o-- +4.0.0 l+6 .- - - -- 4-*-0 -+* 0 0 * -8---- +IO* 0 0 +16Jo= 38Jo---160--~0.. r1 r2it 2The normalized rate constants plotted versus the relativevelocity vr in units of a thermal velocity s .PR No. 122Fig. V-2.Vr /S,(V. ATOMIC RESONANCE AND SCATTERING)parameters3 to within our experimental error of =10%. In Fig. V-1 the ECS-P fit tothe data, represented by the solid lines, reproduces the "complex" dependence of therate constants on Jo and A. A comprehensive set of fits to various fitting laws ofboth our measurements and other accurate data has demonstrated the wide applicabil-ity of ECS-P.4We have recently demonstrated 5 a new technique to measure the velocity depen-dence of the rate constants of process (1) which takes advantage of the Dopplereffect. By simply tuning the laser, we can vary the mean-square collisional veloc-ity (temperature) by more than an order of magnitude because when the laser is ex-actly tuned to line center it excites slow molecules, but when it is tuned slightlyoff-resonance, then only fast molecules are Doppler-shifted into resonance.The results of our measurements for Na2 colliding with Xe are shown in Fig, V-2where the normalized rate constant is plotted versus the relative velocity vr inunits of a thermal velocity s . The Jo = 38 data rise rather linearly with increas-ing velocity, indicating that the cross sections are fairly independent of velocity.For jo = 66 the rates rise faster than linearly so the cross sections are risingwith increasing velocity. These results seem to confirm the naive notion that thefaster the molecules collide the more RET will take place. Surprisingly, the jo = 16rates actually fall off with increasing velocity, more so for the larger changesin angular momentum A. A possible explanation for this surprising behavior is thatthe long-range attractive intermolecular potential can suck slow-moving atoms in toundergo "hard" collisions more easily than fast atoms.References1. M. Wainger, I. Al-Agil, T.A. Brunner, A.W. Karp, N. Smith, and D.E. Pritchard,J. Chem. Phys. 71, 1977 (1979).2. T.A. Brunner, R.D. Driver, N. Smith, and D.E. Pritchard, J. Chem. Phys. 70, 4155(1979).3. T.A. Brunner, N. Smith, and D.E. Pritchard, J. Chem. Phys. Lett., to be publish-ed (May 1980).4. T.A. Brunner, "Scaling Laws for Rotational Energy Transfer," Ph.D. Thesis, De-partment of Physics, M.I.T., January 1980.5. N. Smith, T.A. Brunner, A.W. Karp, and D.E. Pritchard, Phys. Rev. Lett. 43, 693(1979).PR No. 122(V. ATOMIC RESONANCE AND SCATTERING)2. LEVEL-TO-LEVEL ENERGY-TRANSFER DIFFERENTIAL CROSS SECTIONSUSING DOPPLER VELOCITY ANALYSISNational Science Foundation (Grant CHE79-02967)John A. Serri, Alejandro Morales-Mori, Warren P. Moskowitz,David E. Pritchard, Christopher H. Becker, James L. Kinsey[James L. Kinsey is Professor in the Department of Chemistry, M.I.T.]We have recently measured differential cross sections for rotational level-changing collisions in ground-state Na2 with Ar :Na2 (v"=O, j i=7) + Ar - Na2 (v"=O, jf) + Ar.Measurements range in Aj(jf-ji) from -4 to 80 and in e from 0 to 7i.The experiment is performed in a new differentially pumped crossed-beams appara-tus capable of producing intense molecular beams with narrow velocity spreads (10%FWHM) and internal temperature (typically 500 K). The Ar and Na2 intersect at 900.Two cw dye lasers make the level-to-level measurements: one laser (called the pump)modulates by optical-pumping the initial level population (v"=O, ji); the otherlaser (called the analysis) measures the angular distribution of the final level(v"=O, jf) using the ADDS method in which the angle of scattering is inferred fromthe Doppler shift. 2 '3  Level-to-level scattering signals are isolated by phase-detecting the fluorescence from (v"=O, jf) at the pump-modulation frequency.Level-to-level cross sections, a. .j(), are shown in Fig.V-3. All cross sec-tions display a steep rise from zero to a maximum with a gradual decrease at largerangles. This maximum follows the empirical relation 1.4 Aj + 20. The scattering isdominated by the repulsive core of the intermolecular Na2-Ar potential. Our obser-vations can be qualitatively understood classically as follows: For a given molec-ular orientation and impact parameter there is an associated Aj and e. When theimpact parameter is small, the repulsive force is large, producing a large deflec-tion 6 and large integrated torque (i.e., Aj). As the impact parameter increases,the force decreases and so must e and Aj. The maximum in a(6) for a particular Ajarises because there is, for a particular Aj, a minimum deflection angle with respectto orientation, and all orientations near this one give roughly the same deflection,PR No. 122900 1200 1500 1800+1l -IThe level-to-level cross sections j.f (6) for ji = 7 are givenin counts/sec vs e (upper x-axis) and vs frequency offset or cos 0(lower x-axis). Each a(e) from 0 to T consists of approximately 40data points; typical points with their error bars are shown. The ex-istence of signal outside the nominal 0 < 0 < F range is due to im-perfect resolution.Legend:* Aj = 2; + Aj = -4; o Aj = 16; x Aj = 28; A Aj = 40; 0 Aj =48; V Aj = 80.PR No. 122Fig. V-3.0 300 600(V. ATOMIC RESONANCE AND SCATTERING)causing the maximum. We call this phenomenon a "halo" in analogy to the atmosphericoptical phenomenon.We plan to extend the present measurements to more initial levels and to dif-ferent collision energies. Trends in the data will provide insight into the colli-sion process, and the data itself should provide a sound basis for tests on differentpotential surfaces and current approximation methods used for calculating inelasticdifferential cross sections. The same experimental method can be extended to vibra-tional-energy transfer. Preliminary measurements will soon be under way.References1. J.A. Serri, A. Morales-Mori, W.P. Moskowitz, D.E. Pritchard, C.H. Becker, andJ.L. Kinsey, J. Chem. Phys. Lett., to be published (June 1980).2. W.D. Phillips, J.A. Serri, D.J. Ely, D.E. Pritchard, K.R. Way, and J.L. Kinsey,Phys. Rev. Lett. 41, 937 (1978).3. J.A. Serri, R. Mittleman, A. Morales-Mori, D.E. Pritchard, C.H. Becker, andJ.L. Kinsey, M.I.T. RLE Progress Report No. 121, January 1979, pp. 17-19.4. W.J. Humphreys, Physics of the Air (Dover, New York, 1964).3. MOLECULAR SPECTROSCOPYNational Science Foundation (Grant PHY79-09743)Walter P. Lapatovich, Riad N. Ahmad-Bitar, Philip E. Moskowitz,Richard A. Gottscho, Mark D. Havey, David E. PritchardThe van der Waals group has been involved in laser spectroscopic studies ofalkali-rare gas diatomics formed in a supersonic molecular beam. These weakly boundmolecules (DeeX 1 meV) are interesting theoretically and experimentally. Specialconditions are necessary to produce the molecules (supersonic beam), and the poten-tial energy surfaces extracted from the data serve as a check for theoretical cal-culationsI and provide insight into interpretation of line broadening 2 and scatter-ing experiments.3Earlier work4 done on NaNe has been expanded to include analysis of the B2 +state. A more definitive vibrational assignment of the A21 - X2Z + manifold hasbeen developed using long-range theories.5'6 A deperturbation analysis whichPR No. 122(V. ATOMIC RESONANCE AND SCATTERING)involves fitting the data to a model Hamiltonian and calculating RKR potentials, andthen deducing Franck Condon factors is in progress.7Laser excitation of NaAr formed in a beam has yielded A2IT - X2 +(v,o) for 10 <v < dissociation, and several B2 + - X2 + bands. Analysis and application of long-range theories corroborates work done elsewhere8 and provides new information onboth the A2H and B2 + states.rCurrently, using two photons of different energy, we are searching for a Rydbergstate in NaAr which correlates to Na(52S) + Ne(lS) in the separated atom limit. Thesestates have potentials of theoretical interest but have never been observed before.References1. K.T. Tang and J.P. Toennies, J. Chem. Phys. 66, 1496 (1977).2. R. Scheps et al., J. Chem. Phys. 63, 1052 (1975).3. F. Masnov et al., J. Phys. B 12, 4065 (1979).4. R. Ahmad-Bitar et al., Phys. Rev. Lett. 39, 1657 (1977).5. R.J. Leroy and R.B. Bernstein, J. Chem. Phys. 52, 3869 (1970).6. W.P. Lapatovich et al., to be published.7. R.A. Gottscho et al., to be published.8. R.E. Smalley et al., J. Chem. Phys. 66, 3778 (1977).PR No. 122

Atomic Resonance and Scattering

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Atomic Resonance and Scattering

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