# Inelastic Collisions and Chemical Reactions of Molecules at Ultracold Temperatures 

Goulven Qu´ em´ ener, Naduvalath Balakrishnan 

Department of Chemistry, University of Nevada Las Vegas, Las Vegas, NV 89154, USA 

I. Introduction 1 

II. Inelastic atom - molecule collisions 2 

A. Vibrational and rotational relaxation 2 

B. Quasi-resonant transitions 7 

C. Atom - molecular ion collisions 8 

III. Chemical Reactions at ultracold temperatures 9 

A. Tunneling dominated reactions 9 

B. Barrierless reactions 14 

IV. Inelastic molecule - molecule collisions 20 

A. Molecules in the ground vibrational state 20 

B. Vibrationally inelastic transitions 22 

V. Summary and outlook 24 

References 24 

The development of techniques for cooling and trap- ping of a wide variety of atomic and molecular species in recent years has created exciting opportunities for probing and controlling atomic and molecular encoun- ters with unprecedented precision [1]. While many of the initial studies of cold atoms and molecules were centered on the creation of dense samples of cold and ultracold matter, more recent work has focused on the manipulation and control of intermolecular interactions, 

1. Collisions at cold and ultracold temperatures 2 

2. Shape resonances in molecular collisions 6 

3. Feshbach resonances in molecular collisions 6 

1. Reactions at zero temperature 10 

2. Feshbach resonances in reactive scattering 12 

1. Collision systems of three alkali metal atoms 14 

2. Role of PES in determining ultracold reactions 16 

3. Relaxation of vibrationally excited alkali metal dimers 18 

4. Reactions of heteronuclear and isotopically substituted alkali-metal dimer systems 19 

ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA 

## Contents 

## I. INTRODUCTION 

Alexander Dalgarno 

(Dated: October 23, 2018) 

with the ultimate aim of achieving quantum control of atomic and molecular collisions [2]. Though the ideas of quantum control of chemical reactions were proposed many years ago, the ability to create ultracold molecules in specific quantum states has given further stimulus to this field. Its development requires that molecular properties and collisional behavior be well understood at cold and ultracold temperatures where the dynamics of molecules are dramatically different compared to col- lisions at elevated temperatures. Over the last ten years significant progress has been achieved both in theoretical and experimental works. The experimental methods such as photoassociation spectroscopy, magnetic tuning of Feshbach resonances, buffer-gas cooling, and Stark deceleration [3–6] have been developed and applied to a variety of molecular systems. Novel methods to study ultracold chemical reactions involving ion - molecule systems in a linear Paul trap have been proposed [7]. External control of chemical reactions using electric and magnetic fields is another area of active interest [8]. The aim of this chapter is to provide an overview of recent progress in characterizing molecular processes and chemical reactions at cold and ultracold temperatures with particular emphasis on theoretical developments in quantum dynamics simulations of atom - molecule collision systems over the last ten years. 

In contrast to scattering at thermal energies, ultracold collisions offer fascinating and unique opportunities to study molecular encounters in the extreme quantum regime where the entire collision can be dominated by a single partial wave. One of the main motivations of current experimental efforts to create dense samples of ultracold molecules is to study the possibility of chemical reactions at temperatures close to absolute zero. While Wigner’s law [9, 10] predicts that rate coefficients of exothermic processes are finite in the zero-energy limit it does not say if the rate coefficient will be large enough for reactions to be observable in an experiment. Nor does it say anything about how the rate coefficients at zero temperature depend on the interaction potential. Most chemical reactions between neutral atoms and molecules involve an energy barrier and it is not clear if chemical reactions between them generally occur with measurable rates at ultracold temperatures. Calculations for the F + H$_{2}$ reaction which proceeds by tunneling at low energies have shown that the reaction may occur with a significant rate at ultracold temperatures [11]. There is 

