Equilibrium Thermodynamic Properties, Structure and Dynamics of the Lithium Helium (Lihe) Van Der Waals Molecule

University of Nevada, Reno Equilibrium Thermodynamic Properties, Structure and Dynamics of the Lithium Helium (LiHe) van der Waals Molecule A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Physics by Naima Tariq Dr. Jonathan D. Weinstein/Thesis Advisor May 2015 THE GRADUATE SCHOOL We recommend that the thesis prepared under our supervision by NAIMA TARIQ Entitled Equilibrium Thermodynamic Properties, Structure and Dynamics Of the Lithium Helium (LiHe) van der Waals Molecule be accepted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Jonathan D. Weinstein, Advisor Andrew Geraci, Committee Member David M. Leitner, Graduate School Representative David W. Zeh, Ph.D., Dean, Graduate School May, 2015 i Abstract Lithium helium (LiHe) is an interesting van der Waals molecule due to theoretical interest in its molecular structure and properties. We use cryogenic helium buffer gas cooling to produce high densities of atomic lithium at temperatures ranging from 1{5 Kelvin. LiHe molecules are formed by three body recombination: Li + He + He $ LiHe + He: (1) The Li density is continuously monitored via laser absorption spectroscopy. LiHe is detected spectroscopically using both laser induced fluorescence and laser absorption spectroscopy. The LiHe spectrum shows good agreement with a theoretical model of the molecular structure, with only a single bound rovibrational state. In thermal equilibrium, the expected density of LiHe is given by h2 3=2 /kB T nLiHe = nLi · nHe · e ; (2) 2πµkBT where n is the density of the given species and is the binding energy of the single LiHe bound state. Our data shows good agreement with this model, and we use it to determine the binding energy of the LiHe ground state. The measured binding energy is consistent with the calculated value. We also made attempts to measure the rate coefficients for the reactions of Eq.1. ii Dedicated to My loving parents Tariq and Amila, my husband Sheraz, my sisters, Shafaq and Zarmish & my brother Farhan, and my daughter Ajwa and son Hsaan. iii Citations to Previously Published Work Portion of this thesis has appeared previously in the following paper: \Spectroscopic Detection of the LiHe Molecule", Naima Tariq, Nada Al Taisan, Vijay Singh, and Jonathan D. Weinstein, Physical Review Letters 110, 153201 (2013) iv Acknowledgements All appreciation to almighty Allah without His will and consent we cant proceed a single step. Millions of thanks to Prophet Muhammad peace be upon him who is like a beacon in every aspect whether it is the purpose of education or how to work in a group of people. I express my gratitude and obligation to my advisor Prof. Jonathan Weinstein for his valuable discussion, kind supervision and encouragement throughout my research work. He also looked closely at the final version of the thesis and offering suggestions for improvement. This gives me pleasure to thank my lab fellows for their collaboration with me in this thesis. I thank Nada Al Taisan and Vijay Singh for their work on spectroscopic search for LiHe molecule; Nancy Quiros for her work on the measurement of formation rates for LiHe molecule; Andrew Kanagin for his moral support. My sincere regards go to my committee member for serving in my committee and their excellent questions. Furthermore, I would like to thank my friends, teachers and people in the society of physics who have taught and helped me. Last but not least, I wish to express my deeply felt gratitude towards my Ammi and Abbu who are always supportive in whatever I do. It gives me satisfaction to think that they are always praying for my success. I also want to acknowledge my supportive brother and sisters for their prayers and love over the years. Finally, I would like to thank my husband Sheraz Ahmed for his love, cooperation and encouragements. v Contents Abstract.....................................i Dedication.................................... ii Citations to Previously Published Work................... iii Acknowledgements............................... iv Contents.....................................v List of Tables.................................. vii List of Figures.................................. viii 1 Introduction1 1.1 van der Waals molecules.........................1 1.1.1 Nature of van der Waals Forces.................2 1.2 Past work on vdW molecules.......................4 1.3 Helium-containing vdW molecules....................4 1.4 Motivation.................................5 1.5 Three-body recombination........................6 2 Experiment8 2.1 Lithium production and spectroscopy..................8 2.2 Measurements of temperature, pressure and helium density...... 10 2.2.1 Temperature measurements................... 10 2.2.2 Pressure measurements...................... 14 2.2.3 Helium density measurements.................. 14 2.3 Detection setup for LiHe......................... 15 2.4 Improvements in LiHe detection setup................. 17 2.5 Search for 6Li4He molecule....................... 24 2.5.1 Calibrating the transition frequency for 6Li4He......... 25 2.6 LIF calibration.............................. 31 2.6.1 Calibration curve for fluorescence with old optics setup.... 32 vi 2.6.2 Calibration curve for fluorescence with new optics setup... 34 3 Equilibrium Thermodynamics Properties of 7Li4He Molecules 38 3.1 Dependence of nLiHe=nLi on helium density and temperature..... 39 3.2 Measurement of the ground-state binding energy of 7Li4He molecule. 48 4 Dynamics of LiHe 57 4.1 Prior theoretical work for the K3 .................... 57 4.2 Upper limit on three body recombination rate coefficient (K3).... 57 4.3 Techniques used for the measurement of K3 .............. 58 Bibliography 68 vii List of Tables 2.1 Center frequencies, widths and heights of iodine signal from fit func- −5 −3 tion. with y0=0.97±1:8 × 10 (V) , a = 0.02±1 × 10 (V) and −1 x0=14903 (cm )............................. 30 2.2 Center frequencies, widths and heights of 6Li4He spectrum from fit −5 −3 function with y0=0.7±3:4 × 10 (V) , a = -0.12±3 × 10 (V) and x0 = 14903 (cm−1).............................. 30 2.3 Center frequencies and transitions of Li isotopes............. 32 3.1 The fit parameter c obtained from figures 3.5 to 3.9 and its conversion to ODs .................................. 48 3.2 Fit parameters for different helium densities for the measurements of ground state binding energy (B.E.) of 7Li4He molecule......... 56 4.1 The fit parameters obtained from figures 4.3 to 4.6........... 66 viii List of Figures 2.1 The optics setup for the experiment. See the text for a description of the setup..................................9 2.2 6Li spectrum after simulations. The vertical lines in black color are the relative line strengths; plotted against the left axis. The lines, from right to left, are 6Li D1 transition from F = 1=2 to F 0 = 3=2, from F = 1=2 to F 0 = 1=2, from F = 3=2 to F 0 = 3=2 and from F = 3=2 to F 0 = 1=2. The continuous curves, plotted against the right axis, are the relative OD. The curves are colored for different temperature... 12 2.3 The plot of ratio of the height of F = 1/2 peak to the valley formed by F = 3/2 and F = 1/2 peaks of 6Li spectrum versus the temperature of the atoms. The fit in black color is discussed in the text........ 13 2.4 The 6Li spectrum in blue color is recorded as a function of time at a helium density of 9 × 1017 cm−3. The fit (in black) is discussed in the text..................................... 14 2.5 The optics setup for the spectroscopic detection of LiHe molecules. Fluorescence is collected by a lens and steered on photo diode. The PD signal is monitored on the computer (PC) with the help of DAQ. 16 2.6 The LiHe LIF signal (in blue) and the 6Li OD (in green) as a function of time. Both are plotted against the left axis. The red curve, plotted against the right axis, is the synchronized laser scan for both lasers, but scanned over a different frequency range. The Li target is ablated at time t = 0 s. The ablation pulse causes the noise which appear as sharp lines from 0 to ∼ 10 ms. The recorded spectra were taken with the ablation energy of 40 mJ at a helium density of 7 × 1017 cm−3.. 17 ix 2.7 The top view of one of the setup for testing different combinations of lenses with cylindrical lens to get more light on phtodiode (PD). For this face to face lens combination, the lens on the right is LA1002-A and left one is LA1740-B......................... 18 2.8 This is a plot for testing different lenses with cylindrical lens to improve collection efficiency for fluorescence signal on phtodiode (PD). Different colors in the graph are for different lenses and their combinations as labeled................................... 19 2.9 New improved optics setup for the spectroscopic detection of LiHe molecules. Cylindrical lens is introduced in vacuum (between the cell and 4 K window) while the back to back lens combination is at 300 K window. Fluorescence is collected by the combination of lenses and steered on PD. The PD signal is monitored on the computer with the help of DAQ................................ 20 2.10 The bottom view of cryogenic cell before introducing cylindrical lens. 21 2.11 The bottom view of cryogenic cell with cylindrical lens........ 22 2.12 Side view of cryogenic cell with cylindrical lens............. 23 2.13 The 7Li4He LIF (in black) and the 6Li OD (in red) as a function of time after improving detection setup. Both are plotted against the left axis. The blue curve, plotted against the right axis, is the synchronized laser scan for both lasers ,but scanned over a different frequency range. The Li target is ablated at time t = 0 s. The ablation pulse causes the noise which appear as sharp lines from 0 to ∼ 25 ms.

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