Experimental and Theoretical Investigations of HBr+He Rotational Energy Transfer M. H. Kabir, I. O. Antonov, J. M. Merritt, and M. C. Heaven Department of Chemistry Emory University 64 th International Symposium on Molecular Spectroscopy June , 2009

Background  The development of high-power lasers using diode pumped solid-state and fiber are currently limited by material damage and thermal problems.  For many applications in the military and industry require higher power (megawatt) than the existing diode and fiber lasers offer.  Poor beam quality, maximum output powers ~ 100 kW.  By combining multiple pump lasers, higher power from the solid-state or fiber lasers can be obtained but in that case phase matching is a problem specially in long distance beam propagation.

Motivation & Concept of an Optically Pumped Gas Laser Specific features and possibilities offered by a gas : large absorption cross sections, gas cycling, large selection of active media, continuous wave output powers, higher quantum efficiency, and excellent optical quality attracts as a superb medium for high-power lasers development. molecular gas Optical pump laser   v =0 v =1 v =2 molecule

Motivation : HBr Laser  Detailed knowledge of collision-induced rotational energy transfer kinetics of HBr : quantum state populations for laser modeling.  HBr has been demonstrated to lase near 4  m. W. Rudolph et al. IEEE J. Quant. Elec. 40, 1471 (2004)  The aim of this work is to obtain both accurate and comprehensive molecular collisional rate coefficients that are needed for laser modeling. Nd:YAG

Pump-probe Double Resonance Scheme Excitation: Stimulated Raman Collision-induced population evolution HBr(v’ =1, J’) + He  HBr (v’ =1, J’+  J’) + He  HBr(v” = 0, J+  J) + He v = 0, J Probe: (2+1) REMPI Ionization level Energy (cm -1 ) X 1  + v” = 0, J” v’ =1, J’ pp ss g 3  - (0 + ) HBr + + e -

Experimental Setup Nd:YAG laser 532 nm Delay Generator Dye laser Nd:YAG laser 355 nm Dye laserSHG HV Pre-amp Oscilloscope Computer HBr REMPI cell Dichroic mirror ~274 nm, ~0.5 mJ 3 mJ 532 nm, 10 mJ ~ 615 nm + - C

CARS & 2+1 REMPI Spectra of HBr Isotopic abundance: H 79 Br (50.5%) and H 81 Br (49.5%) pp ss pp 2  p -  s =  CARS CARS energy scheme v=0 v=1 Q-branch of the g 3  - –X 1  + (0-1) transition Q-branch of the (1-0) transition Isotopomers were not resolved in REMPI spectrum

Total Removal Rate Constants:Typical Depopulation Curve

Total removal rate constants 1. Kabir et al., JCP, 130, (2009) 2. Domanskaya et al., JMS, 243, 155 (2007)

2+1 REMPI spectrum of the g 3  - –X 1  band Population in the  J = ±2 and  J=±3 levels: direct population transfer and/or multiple  J = +1 or –1 steps. Neglecting multiple inelastic collisions Experimental (raw): 50 rate constants

Fitting & Scaling Laws Statistical Power Exponential Gap (SPEG) Law: Modified Exponential Gap (MEG) Law: Rate constants depend on the rotational energy spacing Statistical Fitting Laws Description of energy transfer between the rotational levels of HBr that have significant thermal populations (0-9) requires a matrix of 100 rate constants Fitting and scaling laws are used to reduce the rate constant matrix down to a small number of fixed parameters

Statistical Fitting Law: MEG Fitting parameters:

Statistical Fitting Law: SPEG Fitting parameters:

Dynamical Scaling Laws Energy Corrected Sudden Exponential Power (ECS-EP) law: Rate constants dependence on transferred angular momentum Based on IOS approximation: infinitely short collision duration viewed as pure angular momentum coupling between the states involved in the collision, neglecting the influence of the interaction potentials of the collision partners Collision is not sudden finite collision duration include adiabatic correction

Angular Momentum & Energy Corrected Sudden (AECS) law: Dynamical Scaling Laws Base rates : Adiabatic correction : Existence of an intermediate state. Its finite lifetime limits the amount of possible angular momentum transfer

Dynamical Scaling Law: ECS-EP Fitting parameters:

State-to-State Rate Constants

MOLPRO : C s symmetry RCCSD(T)/Aug-cc-pVQZ + {33211} Br=Aug-cc-pVQZPP {33211} at midpoint between HBr COM and He R =  =0 –180 : 20 degrees Interaction energy: BSSE corrected ab initio PES Calculations HBr He R  r Fit potential to:

Scattering Calculations MOLSCAT codes: solutions of close-coupling equations: compute S matrix Inelastic cross sections: Thermal rare constants:

Comparison of Rate Constants: Expt. vs Calculation

Comparison of State-to-State Rate Constants

SIMULATION Master Equation approach: models the evolution of individual level populations

Kinetic Traces: Experiment & Simulation J i =3, J f =1-5

Time-resolved REMPI Spectra: Experiment & Simulation

SUMMARY  Time-resolved pump-probe measurements were used to examine HBr+He RET within the HBr v =1 rotational manifold for the first time.  State-to-state rate constants matrix for HBr+He collisions generated using fitting and scaling laws.  Largest state-to-state rate constants were found for  J =  1 transitions.  Measured total rate coefficients were found pretty close to the HBr+He collisional pressure broadening coefficients.  Flow of energy in HBr+He collisions is dominated by both the anisotropy of the intermolecular potential and the internal rotational level structure.