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Hot Cold Molecules: Collisions at Astrophysical Temperatures Frank C. De Lucia Ohio State University Atom Envy, Molecule Envy: [the Grass is Greener on the Other Side of the Fence] Atom Envy: Science: Rotational and Vibrational Partition Function Dilution of Oscillator Strength Complexity of ‘Open’ Collisional Channels hard theory classical results Preclusion of many cooling techniques Technology: Photon >> kT Molecule Envy? THE ENERGETICS Temperature Atoms and Molecules kT (300 K) = 200 cm-1 E (electronic) ~ 50000 cm-1 kT (1.5 K) = 1 cm-1 E (vibrational) ~ 1000 cm-1 kT (0.001 K) = 0.0007 cm-1 E (rotational) ~ 1 cm-1 E (fine structure) ~ 0.01 cm-1 Fields qE (electron) >> 100000 cm-1 mE (1 D) ~ 1 cm-1 mB (electronic) ~ 1 cm-1 mB (nuclear) ~ 0.001 cm-1 Radiation UV/Vis > 3000 cm-1 IR 300 - 3000 cm-1 FIR 30 - 300 cm-1 MW 1 - 30 cm-1 RF < 1 cm-1 Overview Why have we been interested in ‘hot’ cold molecules? What are the techniques we have developed? What kinds of science have we done? What is the physics in the regime where kT ~ hnr ~Vwell? What kinds of results have been obtained? A fundamental experimental - theoretical gap? Why Have We Been Interested? To explore new experimental regime A regime in which ‘exact’ calculations are possible A regime where the results are quantal and interesting Collisions in the Astrophysical Regime COLLISION COOLING: AN APPROACH TO GAS PHASE STUDIES AT VERY LOW TEMPERATURES Typical Spectra - HCN Other Systems INELASTIC CROSS SECTIONS Low Temperature System Polarizing Grid Collisional Cooling Cell Polarizing Grid 4.2 K InSb Detector Klystron Driven Harmonic Generator Preamplifiers 1 MS/s analog input board Ferrite Switch 118-178 GHz BWO Synthesizer Computer QUANTUM COLLISIONS L 300 K 1K L ~ 30 J ~ 10 L~2 J 1 __________________________________ b 2Em Correspondence Principle The predictions of the quantum theory for the behavior of any physical system must correspond to the prediction of classical physics in the limit in which the quantum numbers specifying the state of the system become very large. CROSS SECTIONS FOR CO-He Why Low Temperature Collisions are Interesting COLLISIONS 100 broadening cross section shift cross section CO (0 1) - He Cross Section (Å2) 80 60 40 20 0 -20 0 100 200 300 Temperature (K) 400 500 Calculated Pressure Broadening Cross Sections for HCN - He AN ATOM-MOLECULE COLLISION Before Before During During After After R Elastic R R R R R J=1 J=1 R Inelastic R R R R R 2B MOLECULAR ENGINEERING - TEST Rotational Spacing Decreased by 5% (dashed) 500 P ressure Broadeni ng 400 J=1-0 2 J=1-0 Pressure Broadening 400 J=0-1 Cross Section (Å ) 2 Cross Section (Å) 500 Well Depth Increased by 2% (dashed) 300 200 100 J=0-1 300 200 100 0 0 0 1 2 3 E nergy (cm-1) 4 5 6 0 1 2 3 -1 Energy (cm ) 4 5 6 H2S - He COLLISION CROSS SECTIONS Pressure broadening (open squares) and inelastic (solid circles) cross sections for the 110 - 101 transition HCN 10 Elastic Cross Section CO-He CROSS SECTIONS J = 1 0 J = 2 1 100 2 Broadening Cross Section (Å ) 2 Broadening Cross Section (Å ) Comparison of Experiment with Theory for CO in Collision with Helium 80 60 40 20 0 4 6 8 2 4 6 8 10 100 Temperature (Kelvin) 2 2 Lineshift Cross Section (Å ) 10 0 -10 -20 2 4 6 8 2 4 6 8 10 100 Temperature (Kelvin) 2 60 40 20 0 1 20 1 80 4 2 Lineshift Cross Section (Å ) 1 2 100 4 2 4 2 4 6 8 2 4 6 8 2 4 6 8 2 4 6 8 2 4 10 100 Temperature (Kelvin) 20 10 0 -10 -20 1 XC(fit) Prediction TKD Prediction Experiment 10 100 Temperature (Kelvin) Doppler Width Are the molecules cooled to the same temperature as the walls of the cell? What Underlies the Difference between Experiment and Theory? The Theory Quantum Scattering Calculations Impact Approximation THE JOURNAL OF CHEMICAL PHYSICS 105, 4005 (1996) Linewidths and shift of very low temperature CO in He: A challenge for theory or experiment Mark Thachuk, Claudio E. Chuaqui, and Robert J. Le Roy Intermolecular Potential ab initio from Quantum Chemistry Inversion of bound state energy levels The Experiment The Pressure - Transpiration The Frequency Measurements The Temperature Measurements Department of Chemistry, The University of Waterloo A Hint? - Contributions To sPB COLLISIONAL COOLING APPARATUS COLLISIONAL COOLING APPARATUS Buffer Gas Line Pot Pumping Line LN 2 Reservoir Vacuum Jacket LHe Reservoir 50 cm Continuous LHe Fill Line Sample Gas Injector Cell/Pot 4K and 77K Heat Shields 40 cm Pot Pumping Line Millimeter Wave Probe Path Buffer Gas Line Expeimental Cell Sample Gas Injector Liquid Helium Pot Scaling Parameters SCALING PARAMETERS An Intermolecular Potential r ro Comparison of (well depth in K) He H2 Rb He H2 CO CO H2S H2SCH3Cl CHHe 3Cl 18.8 34.7 18.8 57.8 34.7106.5 57.8 61.9 106.5114.1 61.9 10.74 114.1 ( values obtained from Molecular Theory of Gases and Liquids by Hirshfelder, Curtiss, and Bird ) Rb 450 POTENTIAL WELL AND COLLISION Effect of Potential Well on Collision Cross Section CROSS SECTIONS Collisional Cross Section Spectrum 50 250 40 Cross Section (Å2) Intermolecular Potential (cm-1) Potential Energy Surface 30 20 10 0 • • • • • 150 100 50 -10 -20 200 4 6 8 10 12 14 Intermolecular Separation ( bohr) 0 0 10 20 30 40 Collision Energy ( cm -1) 50 High energy collisions sample the repulsive core. Low energy collisions interact with the potential well. Resonances result from the quantum effects. Most resonances correspond to specific rotational energy levels. Well depth & energy level structure determine the height & density of resonances EFFECT OF INCREASED WELL DEPTH EFFECT OF INCREASED WELL DEPTH ON PROPERTIES OF RESONANCES 20 15 -1 Veff (cm ) 10 5 E 0 r E' r' -5 -10 2 3 4 5 6 7 8 9 R (Å) 10 11 12 13 14 15 1. Bound State Energy DecreasedResonance Energy Decreased 2. Classical Turning Point IncreasedCross Section Increased 3. Resonance Energy DecreasedCross Section Narrower H2S - He COLLISION CROSS SECTIONS 110 - 101 Broadening and Shift 220 - 211 Broadening and Shift 110 - 101 Broadening and Inelastic THEORY counterpoise corrected (solid line) counterpoise uncorrected (dashed line)