Toward Cold Radical Chemistry with Cryogenic Buffer Gas
Beams
byM. I. Fabrikant
B.A., University of Nebraska Lincoln, 2007

A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillmentof the requirements for the degree ofDoctor of Philosophy
Department of Physics
2017This thesis entitled:
Toward Cold Radical Chemistry with Cryogenic Buffer Gas Beams
written by M. I. Fabrikant
has been approved for the Department of Physics

Dr. Heather Lewandowski

Dr. Barney Ellison

Date

The final copy of this thesis has been examined by the signatories, and we find that both thecontent and the form meet acceptable presentation standards of scholarly work in the above
mentioned discipline.

iii
Fabrikant, M. I. (Ph.D., Physics)
Toward Cold Radical Chemistry with Cryogenic Buffer Gas Beams
Thesis directed by Dr. Heather Lewandowski

Creating cold molecular samples allows us to study chemical reactions that happen at temperatures characteristic of the interstellar medium. Additionally, cold environments can stabilize
very reactive molecules like radicals, which can allow us to study difficult-to-observe reactions orintermediate states in the reaction process. Cryogenic buffer-gas beams (CBGB) have gained popularity as bright, low temperature molecular sources for spectroscopy and reaction studies. We
have determined a method for efficiently loading a significant fraction of these new sources into a
traveling-wave Stark decelerator, which uses time-varying inhomogeneous electric fields to decelerate polar molecules. We have also combined a CBGB with the decades-old technology of matrix
isolation to create matrix isolated molecule samples, to help us achieve the goals of characterizing
this new source and of investigating interactions of cold molecules .

Dedication

For my parents

v

Acknowledgements

This thesis could not have been written without the help of a network of scientists, craftsmen,
and friends. I am particularly indebted to Dr. Lewandowski, who helped me devise this experiment,
to Dr. Jonathan Weinstein, whose work kickstarted the theoretical ideas of this thesis, and to Dr.
Gary Douberly, whose collaboration on the experimental side was timely and indispensable. I havealso been extremely privileged to be able to discuss my research with my dad, Dr. Ilya Fabrikant,whenever what I’m doing happens to fall within his wheelhouse, and so I thank him for many
crucially useful conversations over the course of some 25 years. I also thank him for his invaluable
help with editing this thesis. The realization of the experiment should really be credited to the
JILA support staff, namely the shop, whose employees Kyle, Todd, Kim, Tracy, Hans, and Blaine
always figured out how to do the impossible, and who were very understanding about all the broken
taps, drill bits, and saw blades. On the computational side, I have to thank Jim McKean who wassimilarly understanding about the times I crashed the yotta headnode. All of my work of course
also builds and intertwines with that of my former and current labmates Noah, Travis, Yomay,
John, Jason, Phillip, James, Kyle, and Cam, whom I thank for helpful conversations. Finally thecompanionship and support of my wonderful friends always helped me forget that physics existed
at the right times, so particular thanks to Anne, who has always set such a good example for me,
to Jon, who doesn’t think he helped, but did.

viContents

Chapter
1 Cold Molecules
1.1

1.2

1.3

1

Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.1.1

Controlling Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.1.2

Relevance to the Interstellar Medium . . . . . . . . . . . . . . . . . . . . . . .

2

1.1.3

Fundamental Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3Methods of production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.2.1

Laser Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.2.2

Feshbach Resonance Assisted Association . . . . . . . . . . . . . . . . . . . .

4

1.2.3

Supersonic Expansion and Buffer Gas Beams . . . . . . . . . . . . . . . . . .

4

1.2.4

Merged Beam Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

1.2.5

Deceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

1.2.6

Helium Droplets and Matrix Isolation . . . . . . . . . . . . . . . . . . . . . .

9This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92 The CH molecule

11

2.1

Motivations for using CH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2

CH structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3

CH detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4

Making CH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

vii
2.4.1
2.5

Electrical Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Dissociation of Haloforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Simulations of Stark Deceleration of Buffer-Gas Beams

25

3.1

Stark Deceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2

3D Monte Carlo simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.1

Hexapole Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3

Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.4

Comparison of the Model to Simulation Results . . . . . . . . . . . . . . . . . . . . . 46

4 Cell Characterization

54

4.1

Buffer Gas Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.2

Cryogenics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.3

Absorption Spectroscopy of Rb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.4

Scattering of Molecules by Neon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5 Matrix isolation and FTIR spectroscopy

71

5.1

FTIR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.2

Infrared Intensities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.3

Matrix Isolation

5.4

Contaminants and Background Handling . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.5

Matrix FTIR of NH3 Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.6

Isolation of Buffer Gas Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.6.1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Cryogenics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

6 Matrix FTIR of a Buffer-Gas Beam of Carbon Clusters

95

6.1

Peak Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

6.2

Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

6.3

Conclusions and Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

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6.3.1

Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6.3.2

Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

6.3.3

Gas Phase Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Bibliography

107

ix

TablesTable
2.1

A summary of the available experimentally measured diatomic molecule constantsfor the CH electronic levels shown in Fig.2.5. Values from [82] . . . . . . . . . . . . . 17

3.1

Parameters of the buffer-gas beam used in simulations. The expansion out of the cellis assumed to be in the hydrodynamic regime. These parameters would correspondto a cell extraction time of about 2 ms and a cell aperture diameter of roughly 5 mm
for a physical cell [47].

3.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

The fraction of the initial beam that is decelerated to 25 m/s, central well densities, and number of decelerator rings used for various correlation (hexapole) lengths
for both linear and 1/t acceptance functions. The number of rings used to decelerated using the 1/t chirp was set by the final velocity of 25 m/s. The density inthe central well was calculated by assuming 1011 molecules per initial pulse, and a
uniform distribution within each decelerator well (which therefore represents a slightunderestimate of the peak density).

5.1. . . . . . . . . . . . . . . . . . . . . . . . . . . 53

A summary of the vibrational modes of ammonia clusters observed after deposition with a supersonic jet of ammonia seeded in argon into an argon matrix. Lineassignments and modes are from [119]. . . . . . . . . . . . . . . . . . . . . . . . . . . 85

x
6.1

A summary of the vibrational modes of carbon clusters observed after ablation withlaser scanning an deposition onto a cold window. IR intensities are quoted whereavailable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

xiFiguresFigure1.1

A schematic of the supersonic expansion process. Figure from [5]. . . . . . . . . . . .

1.2

A schematic of the buffer gas cooling process. Figure from [47] Molecules are in-5troduced via ablation into a cryogenically cooled cell filled with buffer-gas. The
molecules thermalize and are entrained in the buffer-gas flow to create a cold molecular beam. Other methods of molecule insertion are available but not shown. . . . .
1.3

7

A cartoon of the process of Stark deceleration. The ideas for magnetic and electric
deceleration are the same- inhomogeneous fields acting on the electric or magnetic
dipole moment of a particle create a potential hill that the particle must climb,
thereby losing kinetic energy. Figure from [56]. . . . . . . . . . . . . . . . . . . . . .

8

2.1

The coupling of angular momenta for Hund’s case a). From [77] . . . . . . . . . . . . 13

2.2

The coupling of angular momenta for Hund’s case b). From [77]2.3

The fine structure of CH, from [77], showing the spin-rotation splitting of the lower. . . . . . . . . . . 13

lying N states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4

The Stark manifold of CH showing the stark shift for each of the Λ doublet statesin the J = 1/2 branch of the rotational ground state. . . . . . . . . . . . . . . . . . . 16

2.5

Experimentally measured electronic level structure of CH. Minimum electronic energy values are from [82]. The ionization energy of 10.64(1)eV (85817 cm−1 ) is notshown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

xii
2.6

potential energy surfaces of CH. Note that the equilibrium distance for the X and B
states are extremely close, resulting in a large Franck-Condon overlap. The ionizationenergy of 10.64(1)eV (85817 cm−1 ) is not shown. Figure from [79]. . . . . . . . . . . 18

2.7

Visible spectrum of the discharge of methane. The lines at 431 nm from fluorescenceof CH from the A to X state show that some CH is being produced, but very
inefficiently, as we creating both C2 and electronically excited hydrogen. . . . . . . . 20

2.8

The Visible spectrum of C2 , from [91]. . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.9

Visible spectrum of the discharge of bromoform. 5 mL of bromoform was heatedto 60◦ C creating a vapor pressure of 40 Torr in 4psig of Ar (a 4% mixture). The
duration of the discharge pulse was 100 us, at 1 kV . . . . . . . . . . . . . . . . . . 22

2.10 Spectra of X 2 Π(v 00 = 0, N 00 = 1, J 00 = 1/2) cryogenic CH molecules. The main
figure shows the Q-branch transitions; the frequency offset is 25723.4 cm−1 . The
inset shows the P -branch transition plotted on the same scale; its frequency offset is25698.2 cm−1 . The spectra were obtained from 1 to 2 ms after the ablation pulse.
The experimental measurements are shown as points, the fit to a Gaussian (twoGaussians, in the case of the Q-branch transition) is shown as a solid line. The data
were taken at a cell temperature of 5 K, ablation energy of 0.1 J, and helium buffer
gas density of 1 × 1016 cm−3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.11 A picture of the CHI3 ablation precursor, glued to a copper plate and ready for cell
installation.
3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Proposed experiment for decelerating and trapping buffer gas beams. The use of
these beams creates the opportunity for many detection methods at different stagesof the deceleration process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2

Schematic of the pulsed deceleration process. From [96] . . . . . . . . . . . . . . . . 27

3.3

A travelling wave decelerator uses rings instead of rods to slow molecules. The rings
are grouped into sets of eight such that each set creates a longitudinal potential well. 28

xiii
3.4

Longitudinal potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.5

The bound longitudinal phase-space volume created by the TWD potentials in
Fig.3.4. We see that to be captured a particle must not only be physically inside themoving potential, but that each well supports only a finite range of particle velocities. 30

3.6transverse separatrix of the TWD, from [96]. Because this separatrix is not constantwith longitudinal position Z, we show slices where Z is at the center of a ring (“ringaligned”), halfway in between rings (“gap aligned”) and the average of both. . . . . 31

3.7

Comparison of the longitudinal phase space distribution for a supersonic beam vs a
buffer gas beam. The distributions on the right show what the molecule phase space
looks like after traveling through a field-free region. . . . . . . . . . . . . . . . . . . . 32

3.8

Cartoon schematic of the acceptance method. The vertical line in each panel marks
the position of the TWD. In the first panel the molecule packet exits the source.
At time t1 it has evolved in free-flight such that particle velocity is correlated withparticle position, and the instantaneous velocity width is small. At time t2 the fastpart of the packet has been accepted and decelerated, by which time the entering
molecules have matching velocity. The process repeats until the entire packet enters
the decelerator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.9

Comparison of the TWD potential well for two deceleration magnitudes.

. . . . . . 34

3.10 Comparison of TWD separatrices for two deceleration magnitudes: |a| = 0 (larger
curve), and |a| = 2.1 × 104 m/s2 (smaller curve). . . . . . . . . . . . . . . . . . . . . 35
3.11 Comparison of linear and nonlinear acceptance functions. The linear acceptancefunction is sufficient to decelerate a 210m/s index molecule, which is 3σ above thecenter velocity and therefore puts an upper limit on the acceleration required. The
inset shows the deformation of the potential well experience by the molecules atdifferent times. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.12 TWD decelerator electrodes.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

xiv
3.13 Comparison of time-of-flight signals from molecular dynamics simulations of our decelerator using cylindrically symmetric electrode models and more realistic “hairpin”
shaped models. From [96].

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.14 Results from a small simulation sending a beam of molecules through an analytical
hexapole potential, for several hexapole lengths. The number of molecules increases
until the phase spaces are as well matched as possible, after which the number
oscillates while the maximum number stays flat. The oscillation is a consequenceof defocusing near the end of the hexapole, an its frequency depends on how theaverage radial distance of molecules varies with length. Since molecule trajectories
will undergo more oscillations in a longer hexapole, the surviving molecule number
varies more rapidly with voltage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.15 A snapshot of the final phase space for decelerating molecules from 180m/s to 25m/s
using a hexapole length of 1.5m

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.16 Times of flight for deceleration of buffer gas and supersonic beams. The relative
signal heights of the two simulations should be ignored (although each simulation isinternally consistent)- both simulations were run with the same number of molecules,
whereas in the lab each source produces different numbers of molecules per pulse indifferent densities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.17 The velocity acceptance width shown as a function of acceleration . . . . . . . . . . 44
3.18 Comparison of separatrices used in the simulations (blue) to those model approxiation (red). Both separatrices are superimposed on the PSD of the molecular packet
after it has undergone 1m of free flight. The inset zooms in on the two separatrices showing that the model really is an approximation, since it sweeps continuously
through the entering packet in position, an since the velocity width is averaged velocity width of the simulation separatrix. . . . . . . . . . . . . . . . . . . . . . . . . . 45

xv
3.19 3D simulation results plotted on top of theoretical model calculations, for threedifferent hexapole lengths. The model calculations have been scaled to be the sameheight as the maximum of the simulation results. The good agreement suggests that
1D calculations are suitable for predicting how many molecules will be decelerated,obviating the need for computationally expensive 3D simulations. . . . . . . . . . . . 47
3.20 This figure shows the portion of the initial PSD that has been accepted into thedecelerator for linear and H/t acceptance schemes. The gray regions show the PSDof the molecular beam as it enters the decelerator after traveling through a 1.5 m
hexapole guide. These gray regions are identical in each frame. The black regions
show which molecules will be accepted after the acceptance process is complete. The
top row shows the overlap for linear acceptance schemes, while the bottom row shows
the overlap for H/t acceptance schemes. . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.21 A comparison of the 3D simulation results, 3D separatrices, and 1D model separatrices. One 3D separatrix is superimposed on one filled well from the beginning,
middle, and end of the decelerated molecule PSD. The 1D model approximates the
PSA as a continuous region in the position coordinate, so we show only the velocity
boundaries (horizontal lines). The difference can only be discerned when the scale
is increased to show individual wells. We see that the model separatrix does accept molecules between individual wells, which, although unphysical, results only ina consistent overestimate of how many molecules can be accepted. This accounts
for the excellent agreement between the model and simulations in Fig. 3.19 after aconstant scaling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.22 1D model predictions of the fraction of molecules decelerated using the 1/t chirp forhexapole guide lengths of 0.5 m, 1.5 m, and 4 m. The number of rings required todecelerate the molecular pulse using a particular hexapole guide length are shown
for a index molecule with a velocity of 231 m/s (dashed line), which is 180 m/s
plus three times the longitudinal velocity width.

. . . . . . . . . . . . . . . . . . . . 50

xvi
4.1

Our original cell set up for Rb absorption spectroscopy experiments. . . . . . . . . . 55

4.2

Picture of the absorption spectroscopy setup with old cell. When we eventuallyswitched to a new cell design, the new cell -being almost the same size transverselywas simply swapped in. A cryopump is anchored to the second stage, for reasons
discussed in sec.4.2

4.3

Schematic representation of our new buffer gas cell, based on the design of the Doylegroup.

4.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Realization of the Doyle-style buffer gas cell, looking on the absorption spectroscopy
windows.

4.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

A cartoon of the dependence of cell lifetime on flow rate, meant to show how, forsome cell parameter choices, Tpump can compete with Tdif f at low flow rates. . . . . 57

4.6

The number of collisions required to translationally cool CH (red) and C6 (green)from 5000 K (a typical ablation temperature) to 25 K (the coldest temperature we
can reach with our cell). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.7

A picture of the cryopump at work. Several hours of neon flow are required to build
up this amount of neon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.8

Schematic of the absorption spectroscopy setup. . . . . . . . . . . . . . . . . . . . . . 63

4.9

A typical absorption spectroscopy signal for RbCl, monitoring the AC channel. In
this case the flow rate is 40sccm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.10 Signal lifetimes as a function of flowrate . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.11 Optical depth of Rb as a function of flow rate. . . . . . . . . . . . . . . . . . . . . . 65
4.12 Scattering cross sections of Rb with different noble gases, plotted on a log-log scale.
The scattering cross section of Rb with Ne is about ten times larger than what is
generally estimated to be for a wide range of molecules. At 590 K This calculationis 18% larger than the value measured by [107], who estimated their error at 10%.
The measurement in [107] provides only a lower limit on the Rb-Ne scattering crosssection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

xvii
4.13 Calculation of scattering cross sections using Eq. 4.13, using Van der Waals constantsfrom [112],[113], [114], and [115]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.14 Theoretical dependence of signal lifetime on flow rate for our cell parameters andwith a more realistic Rb-Ne scattering cross section. . . . . . . . . . . . . . . . . . . 69
5.1

A schematic of our interferometer setup . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.2

A spectrum showing wavelength-dependent scattering as a function of deposition
time. The slope and offset seem to grow linearly with time, but this is likely becauseof small dynamic range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.3

A typical background signal from our spectrometer. The IR beam is being aimed
through the vacuum chamber and the deposition window. . . . . . . . . . . . . . . . 78

5.4

A typical background signal from our spectrometer. The IR beam is being aimed
through the vacuum chamber and the deposition window. . . . . . . . . . . . . . . . 79

5.5

Signatures of contaminants on the crystal surface.

Such contamination can be

avoided by evacuating the experiment chamber before cooling with a turbo pump,and not relying solely on the cryopumping ability of the cold head. . . . . . . . . . . 80
5.6

Lines due to glue in the beamsplitter . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.7

apparatus schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.8

A picture of a crystal of ammonia clusters in an argon matrix.

5.9

IR spectrum of NH3 clusters in argon. Line assignments are from [118]. These. . . . . . . . . . . . 83

spectra were gathered after depositing NH3 for 60 min and firing the valve at 10Hz.
Observed lines are tabulated in Tab. 5.1.

. . . . . . . . . . . . . . . . . . . . . . . . 84

5.10 Traces showing IR spectrum of NH3 clusters in argon at two different times. At someconcentration monomers begin to react with each other to form clusters.

. . . . . . 86

5.11 Apparatus schematic for isolating a buffer gas beam. The molecules are introduced
into the cell via 532 nm ablation and are extracted by neon flow through an aperture,
after which they are deposited onto an isolation window. . . . . . . . . . . . . . . . . 87

xviii5.12 A picture of the apparatus modified to deposit buffer gas beams onto a matrix
isolation window. In the figure one can see the strong coupling of the window to thesecond stage and the weaker coupling of the second stage to the cell.

. . . . . . . . 88

5.13 The vapor pressure of neon. Data from [120]. We could conceivably operate ourbuffer gas cell in temperature regimes below the melting point, but in that case theequilibrium pressure is influenced by the competition between neon in and out flow,
and the sticking probability of neon with the walls. In these regimes the pressure
should be measured directly to determine the neon density in the cell . . . . . . . . . 90
5.14 The intercept of the cell temperature vs second stage temperature as a function ofcopper block area. The slope of this dependence should remain constant while theintercept should go like the square of the copper block area. This is not borne out,
likely because the force which compresses the block is not constant. . . . . . . . . . . 91
5.15 Temperature difference sustained by the Cell and cryopump/Deposition window.
This curve is not a constant of the apparatus and fluctuates somewhat depending
on how well all components are tightened after modification and reassembly. . . . . . 92
5.16 Cross section of old housing of the deposition window. A copper holder supports
the window which is secured with a copper face plate and brass screws. Two indium
gaskets actually made the contact between the copper housing and window poorer
and failed to equilibrate the window center and edge. . . . . . . . . . . . . . . . . . . 93
5.17 Cross section of new window housing. This configuration gave the best results forequilibrating the window and copper holder temperatures, even though contact withthe retaining ring surface area has now shrunk to nothing because of the viton o-ring. 93
6.1

A view of the neon crystal through the vacuum chamber and black body radiation
shield. The fast crystallization of the neon on the window creates an opaque neon
matrix (which is nonetheless transmissive enough for us to see absorption signals. . . 96

xix
6.2

FTIR spectrum of carbon clusters embedded in neon. A graphite sample was ablated
at 4 mJ/pulse while neon was flowed through a buffer gas cell at 70 sccm. The celltemperature was 34 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

6.3

The height of the C9 (ν6 ) peak at 2010 cm−1 as a function of deposition time. The
plateau in signal should be caused by a drop in cluster production, since the peakheight is nowhere near 100% transmission.

6.4. . . . . . . . . . . . . . . . . . . . . . . 98

A picture of the surface of the graphite target after undergoing many hours of ablation. The target is 5 mm across, and the laser is focused to about a 50 um spot
size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

6.5

FTIR spectrum of carbon clusters embedded in neon, now with ablation laser scanning across the sample. A graphite sample was ablated at 2 mJ/pulse while neon
was flowed through a buffer-gas cell at 60 sccm. The cell temperature was 34 K.

6.6

. 100

Peak absorption of each cluster scaled by the infrared intensity and normalized to
the largest abundance. It should be noted that calculations of the IR intensity of
the C9 ,ν6 mode have yielded results different by many orders of magnitude. [132]measured the intensity relative to the height of the peak at 2010 cm−1 , which wasused to calculate the abundance of C9 from this mode, although there is clearly someerror. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

6.7

Reactions in a crystal of C clusters in Ne with CO contamination, after annealing to
11 K and re-freezing. The CO peak is completely depleted and new peaks appear,
although we were unable to assign them with certainty. We believe there were also
some reactions involving just clusters, as some cluster peaks are partially depleted
while the C9 peak grows. No deposition or ablation occurred during the annealing/refreezing process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Chapter 1

Cold Molecules

1.1

Motivations
The cooling of molecules to very low temperatures is a frontier of both physics and physicalchemistry whose exploration promises to yield new insights into the physics of exotic environments
and fundamental processes, as well as more practical progress toward study of basic chemical
reactions, or measuring fundamental constants [1]. An entire field dedicated to cold molecules has
sprung up in the past few decades with these goals in mind [2, 3, 4, 5, 6, 7].

1.1.1

Controlling Chemical Reactions

The collisions of cold atoms have long been an active area of study. As the techniques
for cooling and trapping molecules and atoms improved, there has been a growth of interest incontrolling atom-molecule and molecule-molecule interactions, both for the purposes of studying
reactions in which the quantum state of each species was controlled, and to investigate the possibilityof reactions that happen at low interaction energies, which are typically prohibited by an energy
barrier. However, some reactions, like F + H2 → FH + H, are expected to proceed by tunnelingat low energies, and might have large reaction rates at low temperatures [8][9]. Other reactions,such as the CH + C2 H4 system [10] lack a barrier entirely, and have also been observed to havereaction rates that increase with lower temperature [11]. The enhancement of reaction rates in
the former system depends on increased importance of the Van der Waals interaction between
reaction partners, and can be observed only at temperatures of less than 0.2 K. In the latter2
system, the barrier-less nature of the reaction manifests at temperatures of less than 10K, although
there is some disagreement about the dependence of the rate coefficient on temperature[12] due tocompeting reaction pathways[13].
There are other avenues available for controlling the rate or outcome of a chemical reaction.
For some time, there has been interest in using electric or magnetic fields to control products, filter
reactants[14, 15], or directly influence how they interact by tuning parameters such as collision
angle[16, 17]. Unfortunately, this is not possible above temperatures at which thermal motion ofmolecules either scrambles the selected quantum states or averages down the effect of the appliedfields. However, below temperatures of about 1 K, the energy of the field interaction overcomes thetranslational energy of the molecules [18].

1.1.2

Relevance to the Interstellar Medium

The barrierless nature of many reactions relevant to cold chemistry has lead to the proposalthat they dominate the neutral chemistry of dense interstellar clouds, whose temperature has beenmeasured at 10-15 K [19]. Reactions in the interstellar medium of note include the formationof water from OH radicals interacting with hydrogen OH + H → H2 O [20], the creation of cyclichydrocarbons [21], and the synthesis of molecular nitrogen[22].

N + OH → NO + H
N + NO → N2 + O
This last reaction may play an important role in the eventual formation of the ammonia
molecule (NH3 ), which, in addition to being abundant in the ISM, can act as a useful diagnostic
tool for measuring interstellar cloud temperature [23]. The temperatures of these clouds havethe effect of stabilizing otherwise reactive molecules like free radicals and reaction intermediates[10, 24, 25]. The creation of environments on earth cold enough to sustain such intermediates would
be valuable not only for replicating the chemistry of interstellar clouds, but also gaining insight into

3
the exact mechanisms and stages of chemical reactions. What is more, there is significant overlap
between the chemistry of these intermediates and that of earth’s upper atmosphere [26, 27, 28],
so understanding this chemistry can have practical implications for processes like pollution andozonolysis.

1.1.3

Fundamental Tests

In addition to chemistry considerations, molecules offer a convenient medium for the precision
measurement of fundamental constants[29, 1] and values that test fundamental symmetries, mostnotably the electron dipole moment (EDM). Although the value of the EDM is very close tozero, narrowing the uncertainty of this value will give scientists the ability to rule out or confirm
corrections to the standard model[30, 31, 32]. Any EDM measurement involves the applicationof an external field to an electron and measuring the shift of the electron energy eigenstate dueto the interaction of its spin with the applied field. Compared to atoms, measuring the EDM ofelectrons bound to heavy polar molecules exponentially increases the sensitivity of the electron to
the applied field, because of the large polarizability of the molecules[33]. Molecules are also usefulas media for parity violation experiments and investigating Lorenz invariance[18]. For all of theseapplications, molecules must be cooled to increase as much as possible the coherence time of the
prepared states.

1.2

Methods of production
Studying the systems described above presents several challenges to the experimenter. For

any molecule of interest there must exist a detection mechanism, the ability to cool the molecule tothe desired temperatures, and method of synthesis that can create the molecule in densities large
enough to sustain cooling and detection. There are broadly two approaches toward satisfying all
three of these critera- that of synthesizing molecules and cooling the molecules themselves (known as
direct methods) and that of cooling atoms and assembling these atoms into cold molecules (indirect
methods). These two approaches are somewhat complimentary, as the former, while successful in4creating molecules commonly found in nature, tends to reach temperatures of only a few K, whereas
the latter method commonly reaches the ultracold regime of < 1 mK, but cannot be easily adapted
toward the synthesis of chemically important molecules. Direct methods are making steady progress
toward the ultracold regime, and are beginning to show promise for bridging the temperature gap.
A selection of direct and indirect methods are outlined in more detail below.

1.2.1

Laser CoolingLaser cooling has been a workhorse cooling mechanism for atoms for many years, and relies ontranslationally cooling particles by photon scattering. Traditionally, cooling molecules has provenmuch more difficult because of their rich internal structure, which prevents the existence of closed
cycling transitions and necessitates the use of many repump lasers to pump molecules out of darkstates [34]. This technique has been successfully employed for CaF [35], SrF [36], and YO[37],among others. Recently, the use of microwaves to mix dark rotational states with states that canbe repumped has drastically simplified the laser cooling of YO molecules [38]. The temperatures
reached by these methods can be as low as few hundred mK [39], demonstrating that direct methods
can reach the ultracold regime.

1.2.2

Feshbach Resonance Assisted Association

Currently the ultracold regime is dominated by molecules assembled from ultracold atoms.
Instead of cooling molecules directly, atoms are laser cooled and combined by tuning the response toeither an optical or magnetic interaction to coerce the atoms into a bound state[18]. The technique
has been successfully used to create ultracold samples of KRb[40, 41], LiCs[42], and Na2 [43] toname a few. Clearly, the disadvantage of this method is that only alkali and alkaline-earth atoms
may be used as the molecular constituents, producing molecules that have only abstract relevanceto natural chemistry. However, the samples produced are in high density and can be as cold as
100 nk [18, 2, 7].

5
1.2.3

Supersonic Expansion and Buffer Gas Beams

Supersonic expansion relies on forcing molecules to undergo many collisions with a noble gas
atom in order to convert internal rovibrational energy into translational kinetic energy. Typically,
this is accomplished by seeding a reservoir of noble gas with the molecule of interest and forcing
it through a nozzle, usually 1-2 mm in size, into vacuum. The molecules collide inelastically withthe atoms to reach rovibrational temperatures [5] of a few K. This process often happens in pulses,
which reduces the gas load on the vacuum chamber. The parameters of reservoir pressure andtemperature, aperture geometry, and choice of noble gas may all be varied to achieve different
results. A schematic is shown in 1.1.
Figure 1.1: A schematic of the supersonic expansion process. Figure from [5].

The result of this process is a beam of rovibrationally cold molecules with large longitudinalvelocity. This velocity, which changes according to the type of noble gas used, is usually a few
hundred m/s, which can limit interrogation times and make subsequent trapping nearly impossible.

6
The experiment must either stop the molecules while at the same time preserving their density andlow temperature, or must find some other way to interrogate them for long enough times to achieve
good signal to noise.
Buffer-gas beams were developed in part to address the disadvantages of large longitudinalvelocities, and are one of the most intuitive methods of creating a beam of rovibrationally cold
molecules. For this method, a volume is held at approximately the freezing temperature of a noble
gas (a schematic is shown in Fig.1.2). This same noble gas is allowed to flow through the volume
while the molecule of interest is introduced and allowed to thermalize with the noble gas. In thepast, the most popular noble gas used was helium[44], as it reaches the coldest temperatures, butneon has recently emerged as an attractive buffer gas because of the ease with which it can bepumped. If lower temperatures are required, an additional cell stage can further cool the beam[45]. Molecules can be introduced into the cell via ablation, molecular beam insertion, capillary
insertion, or discharge etching [46], although this thesis will focus only on ablation. The buffergas cooling method is suitable for a large variety of molecules, as long as the collision cross section
between the molecule and buffer gas is large enough, and as long as the molecules can be introduced
into the cell efficiently, and such that the method of introduction (such as ablation or injection)
does not heat the molecules (either translationally or internally) so much that they can no longer
be cooled to useful temperatures.

7
Figure 1.2: A schematic of the buffer gas cooling process. Figure from [47] Molecules are introduced
via ablation into a cryogenically cooled cell filled with buffer-gas. The molecules thermalize andare entrained in the buffer-gas flow to create a cold molecular beam. Other methods of molecule
insertion are available but not shown.

The velocity of a molecular beam produced by this source can, in principle, be much slower
than that produced by a supersonic expansion. The range of possible velocities is large, as demonstrated by beams of NH3 created at 130 m/s[48], whereas beams of CaH molecules have beencreated with velocities of just 40 m/s. However, it is often necessary to decelerate even a beamwith this small of a velocity.

1.2.4

Merged Beam Experiments

One way to deal with large molecular velocity is not to reduce it at all. If the interaction
partner of the molecules is set up as a beam of nearly co-propagating molecules, then the collisionenergy can be tuned to very small values by tuning the collision angle[49]. Even though no deceleration occurs, guiding apparatus must still be employed to preserve the molecule phase space. This8
method is exploited by [50, 51, 52] and has successfully been employed to look at interactions ofCH[53],H2 [54] to collision energies as small as 10 mK[55].

1.2.5

Deceleration

If a merged beam experiment is not suitable, molecular beams must be decelerated. Magnetic
or electric fields are constructed in such a way that they create potential hills that reduce the kinetic
energy of molecules riding up them.
Figure 1.3: A cartoon of the process of Stark deceleration. The ideas for magnetic and electric
deceleration are the same- inhomogeneous fields acting on the electric or magnetic dipole moment of
a particle create a potential hill that the particle must climb, thereby losing kinetic energy. Figure
from [56].

There are several options for doing this, depending on what molecule is to be decelerated, andon what “molecular handle” (i.e. magnetic or electric dipole) is to be used [57, 54, 58]. Deceleration
is appropriate for a wide range of molecules, and to date been used for OH[59, 60, 61], NH[62, 63],
ND3 [64, 56], among others. In principle molecules of any dipole moment to mass ratio can be
decelerated given a long enough apparatus, but molecules with ratios of at least 0.08 Debye Amu−1
can be slowed with decelerators on the order of a meter long, (depending on the speed of the source).
A disadvantage of these techniques is that the fields used are conservative and cannot compress
the phase-space of the molecular distribution. This means that no internal cooling takes place,9and any temperature reduction of the translational degrees of freedom of the molecular packet isdue to rejection of translationally hotter molecules. It is therefore necessary for molecules to berovibrationally cold before deceleration, in order to fully reap the benefits of a cold, slow molecularsample.

1.2.6

Helium Droplets and Matrix Isolation

In contrast to methods that create rovibrationally cold molecules in beams to be detectedwith gas phase spectroscopy, there also exist methods which, although not technically gas phase,
can achieve comparably cold samples whose detection signatures are similarly narrow in linewidth.
These methods include capturing molecules in helium droplets [65, 66] and freezing them in solid
matrices [67, 68, 69]. In particular, matrix isolation can completely “freeze” out the rotationalmodes of a molecule at the cost of coupling it to the trapping potential of a noble gas matrix,
and somewhat shifting its electronic and vibrational modes. On the other hand, helium droplets
can lower the temperatures of all the degrees of freedom of a molecule to as low as 0.4 K [65],compared to only a few K for the coldest molecular hydrogen (H2 , D2 , and HD) matrices [70].
Trapping molecules in helium droplets and matrix isolation are uniquely useful for stabilizing reactive molecules that would otherwise be difficult to detect spectroscopically[71]. We choose to makeuse of the matrix isolation method and will discuss it more extensively in Ch.5.

1.3This Thesis
This thesis will present progress along two separate paths toward the ultimate goal of com-bining two of the methods discussed in this chapter- the coupling of a buffer-gas beam into a Stark
decelerator. The buffer-gas beam remains a relatively novel molecular source, and its potential tocreate a variety of species for the purposes of investigating molecule interactions remains largely
unexplored. Our work has shown that the buffer-gas source is promising for creating bright, slow
beams of molecules that could be electrostatically trapped if combined with a decelerator. After
giving an overview of our molecule of interest, this thesis will explain how we use simulations to10determine the best method of adapting this novel source to the inherent limitations of the Stark
decelerator. The following chapters will document the our successful implementation of a buffer-gas
beam in our lab and our construction of an intermediate experiment that can detect the molecularbeam output of the buffer-gas cell, as progress toward decelerating and trapping it.

Chapter 2

The CH molecule

2.1

Motivations for using CH
Because our group creates diffuse beams of cold molecules, any physics/chemistry we investi-

gate will be most relevant in the interstellar medium (ISM). We therefore often focus on moleculesthat are abundant in the ISM, and are especially interested in unstable molecules that are difficult
to study or may not exist under normal (hot, dense) conditions. CH is important as an observed
constituent of the ISM, a free radical, and a simple hydrocarbon. As a radical, CH is difficult to create in the laboratory, but plays an important role in interstellar medium chemistry and combustion
chemistry: CH participates in archetypical reactions such as hydrogen exchange with deuterium[72]

CH(X 2 Π) + D2 → CD(X 2 Π) + HD,(2.1)

the formation of more complex hydrocarbons [73]CH + H2 → CH3 + hν,and simple combustion reactions [53]

CH(X 2 Π) + C2 H2 → C3 H2 + H
CH(X 2 Π) + C2 H2 → C3 H + H2

(2.2)

12
In contrast to chemistry that is more relevant to that which occurs on earth, two-bodybarrierless reactions such as eq.2.1 are expected to be dominant in the ISM[74]. CH reactions havebeen studied in merged beam experiments [10], and at temperatures as low as 23 K [75], but thoseexperiments did not achieve the simultaneous low temperatures and low translational velocities
needed to be able to control the interaction energies and study these reactions.

2.2

CH structure
The structure of CH has been known for some time from astronomical observations [76],and is shown in Fig.2.5. We will focus primarily on the X 2 Π ground state, which has orbital
configuration 1σ 2 2σ 2 3σ 2 1π 1 . The coupling of angular momenta in the CH ground state will have
implications for both our ability to decelerate and detect it. For many polar molecule groundstates, these couplings are well described by Hunds case a), shown in Fig.2.1. Because we are
dealing with a linear polar molecule in a Π state, the total electronic orbital angular momentum
cannot be conserved. However, the linear nature of the molecule means that the axial component of
the orbital angular momentum L is conserved, by symmetry. Therefore, although L is not a goodquantum number, its projection onto the internuclear axis, Λ, is. What is more, if the spin-orbit
interaction is relatively strong, the total spin S will tend to precess about the internuclear axis,
meaning that both S and Σ will be conserved. Finally, the rotation of the molecule about its centerof mass will produce another angular momentum R, which will combine with Ω = Λ + Σ to givethe total angular momentum J.

13
Figure 2.1: The coupling of angular momenta for Hund’s case a). From [77]However, for the CH ground state, the spin-orbit coupling is actually very weak, and is therefore better described by Hunds case b), although it will be useful to consider both representations
when we analyze the effect of electric fields on the molecule.
Figure 2.2: The coupling of angular momenta for Hund’s case b). From [77]In the B case, because of the weak L − S coupling Ω is no longer a good quantum number.
Instead L couples with the rotation R to form N , which couples with S to form J. To summarize
the coupling scheme for Hund’s case B:

14

R + L = N,

N = 1, 2, 3...

N + S = J,

J = N − 1/2, N + 1/2,

J+I=F
The good quantum numbers for CH are then Λ, N, S, J, I, and F . Therefore we can write therotational level splittings (or fine structure) as [77]

F1 (N ) = BνF1 (N ) = Bν!
p
2 + Y (Y − 4))(N + 1))(4N(N + 1)2 −2!
p
2 + Y (Y − 4))N )(4N,(N + 1)2 −2where Bν is the rotational constant, A is the spin-orbit constant, and Y = A/Bν . In many
papers, (including our own [78]) it is common to refer to the fine structure of the CH ground state
as containing, say, 2 Π1/2 or 2 Π3/2 states, and although this is not incorrect, it is a little confusing,since Ω is not defined and it would make more sense to group the fine structure levels by N [77].
A picture of the fine structure, from [77] is show in Fig.2.3 and shows the grouping of levels into
integer N , with each level being split by the spin-rotation coupling.

15
Figure 2.3: The fine structure of CH, from [77], showing the spin-rotation splitting of the lower
lying N states.

Because L can be either aligned or anti-aligned with the internuclear axis, the projection Λ
can have two signs, only one of which we would be able to decelerate. In CH, the coupling of Lwith the rotation R further splits each of the fine structure states in Fig.2.3 into two Λ -doublets.
A Stark manifold is shown in Fig.2.4. It is clear from the figure that only the state whose energy
decreases with higher E is suitable for deceleration and trapping, since the other will simply fly
into the high voltage electrodes and be lost.

16
Figure 2.4: The Stark manifold of CH showing the stark shift for each of the Λ doublet states in
the J = 1/2 branch of the rotational ground state.
0.15

EnergyHcm-1L

0.10
0.05
0.00
-0.05
-0.10
-0.15
0

2.3

5

Electric Field HkV•cmL
10

15

20

CH detection
The electronic potential energy surfaces were measured by [79] and are shown in Fig.2.6. This

structure of CH lends itself to several state-selective detection methods. The first category might
be labeled state-selective absorption, either via direct absorption spectroscopy or cavity ring-down
spectroscopy. Both the A←X and B←X transitions have been used for absorption spectroscopy[78, 80], but if both laser wavelengths are available, the B←X is preferable, because of the superior
Franck-Condon overlap, evident in Fig.2.6. In addition to absorption, a laser induced fluorescence
can also take advantage of these two transitions [81].

17Figure 2.5: Experimentally measured electronic level structure of CH. Minimum electronic energy
values are from [82]. The ionization energy of 10.64(1)eV (85817 cm−1 ) is not shown.

70000

60000

D2 P

Energy Hcm-1 L

50000

40000

C2 S+
30000

B2 SA2 D

20000

10000

a 4 S0

State
X2 Π
a4 Σ−
A2 ∆
B2 Σ −C2 Σ+
D2 Π

Minimum Electronic
Energy Te (cm−1 )05844
23189.826044
31801.5
60394

X2 P

Vibrational
Constant ωe (cm−1 )2858.53145
2930.71794.92840.2

Rotational ConstantBe (cm−1 )14.45715.4
14.93412.64514.603
13.7

Centrifugal Distortion De (cm−1 )0.001450.001540.002220.00156

Table 2.1: A summary of the available experimentally measured diatomic molecule constants for
the CH electronic levels shown in Fig.2.5. Values from [82].

18
Figure 2.6: potential energy surfaces of CH. Note that the equilibrium distance for the X and B
states are extremely close, resulting in a large Franck-Condon overlap. The ionization energy of
10.64(1)eV (85817 cm−1 ) is not shown. Figure from [79].

Another method that exploits electronic transitions is resonance enhanced multiphoton ionization (REMPI). Ionization schemes can be very attractive because of possible large signal to noise
enhancement, since the collection efficiency, once molecules are ionized, approaches 100%. [83, 84]
take advantage of such a method by using both the C and D levels as intermediate states. If theD state is used, the C state is very close to halfway in energy toward the D state, meaning thatthe first photon in a 2+1 REMPI scheme would be near resonant with it, causing an enhancementin the signal [84]. Our group has spent some time developing and improving on a source of 118
nm (10.5eV) light, which has been used to detect other molecules with 1+1’ REMPI [85, 86]. In19this case, a primary excitation to either the A or B states may be used, combined with subsequentionization by the 118nm photon.
As we will see below, a “quick and dirty” method that serves to simply confirm the presenceof CH is to create CH in a highly excited state an observe the fluorescence to the ground state(either from the A or B state) with a visual spectrometer. However, as this method is not state
selective, we use it only as a diagnostic tool.
In addition to exploiting the electronic and rotational structure, CH also has one vibrationalmode at 2861 cm−1 [87]. This will be discussed further in ch.5.

2.4

Making CH
From a naive perspective, it might seem that making CH should not pose too much of achallenge, since hydrocarbons are so ubiquitous. However, because CH is so reactive, the real
challenge comes when one tries to make CH from one of these materials in high enough densities
to detect with the available methods.

2.4.1

Electrical Discharge

Since CH has three lone electron pairs and is extremely reactive, the best way to make it is
one which involves breaking apart a stable precursor, (although other methods, such as formation
as the product of a chemical reaction, have been successful [88]). One of the easiest ways to breakapart molecules is by electrical discharge. Discharge works by placing molecules inside a large
electric field, accelerating many electrons (and in turn, ions), from one discharge plate to the other,bombarding the molecule with energy and breaking it apart[89]. Because the energy distribution is
not narrow or selective in any way, there is no way to predict what molecules are made other thanempirically.
We attempted to make CH this way, using methane (CH4 ) as a precursor, based on the workof [90]. We constructed a small vacuum chamber containing an electrode that could be charged toseveral kV. We tried the DC method first, in which charge builds up on the discharge electrodes

20
until the breakdown voltage is reached, as well as a pulsed discharge, in which voltage is applied
for only a few tens of microseconds. The advantage of the second method is that the breakdown
happens more predictably, and we can trigger our spectrometer off the high voltage pulse in order toreduce noise. This chamber was filled with methane (CH4 ) after which a DC voltage was applied tothe electrodes. The resulting fluorescence was observed with an Ocean Optics visible spectrometer.
Figure 2.7: Visible spectrum of the discharge of methane. The lines at 431 nm from fluorescenceof CH from the A to X state show that some CH is being produced, but very inefficiently, as wecreating both C2 and electronically excited hydrogen.
D is c h a r g e o ff
D is c h a r g e o n
A r lin e s
H y d r o g e n L in e s
C H lin e s

In te n s ity (a rb .)4 0 0 0

D is c h a r g e o ff
D is c h a r g e o n
A r lin e s
H y d r o g e n L in e s
C H lin e s

1 4 0 01 2 0 01 0 0 08 0 0

2 0 0 0
6 0 0
4 0 0
2 0 0
0
4 0 0

5 0 0

6 0 0

7 0 0

8 0 0

9 0 0

1 0 0 0w a v e le n g th (n m )

4 0 0

4 2 0

4 4 0

4 6 0

4 8 0

w a v e le n g th (n m )The peaks at 431 nm clearly show the presence of CH. However, the spectrum is dominatedby the peaks in the 400-600 nm region, which are the “C2 Swan System”, see (Fig.2.8) [91]. Since
we are making C2 , it is clear that this is at best an inefficient method for making CH, since we are
dumping enough energy into the methane to break all of the C-H bonds and allow the C atoms toreact with each other to create excited states of C2 .

21
Figure 2.8: The Visible spectrum of C2 , from [91].

2.5

Dissociation of Haloforms
Most CH sources use haloform molecules as precursors [92, 93, 94]: these are methane

molecules in which three of the four carbon atoms have been replaced with halogens (ie, of theform HCX3 ). The thinking behind using haloforms is that the lone hydrogen atom is strongly
bound to the carbon atom, compared to the relatively weak halogen bonds. For instance, the bondstrength of C-H is 80.86 kcal/mol, whereas for C-Br it is only 67 kcal/mol. The expectation istherefore that the halogen bonds will break preferentially, generating higher densities of CH.
We investigated both the discharge and photolysis of bromoform, which has been used in[93]. For both methods we prepare a mixture of bromoform in argon by heating it to 60◦ C, which
results in a 4% gaseous mixture. This is flowed through a pulsed valve and is either discharged at
1kV, or flows through a quartz capillary upon which is focused a 193 nm excimer laser firing at
10mJ/pulse. In both cases we were able to observe the fluorescence with a visual spectrometer, andboth processes yielded similar results, shown in Fig.2.9. It appears once again that these are very
inefficient processes which dump energy unnecessarily into the creation of C2 , although we again
do make some CH.

22
Figure 2.9: Visible spectrum of the discharge of bromoform. 5 mL of bromoform was heated to60◦ C creating a vapor pressure of 40 Torr in 4psig of Ar (a 4% mixture). The duration of thedischarge pulse was 100 us, at 1 kV
4 5 0 0A r o n ly
B ro m o fo rm
C H lin e s

3 5 0 03 5 0 03 0 0 03 0 0 02 5 0 02 0 0 0
1 5 0 02 0 0 0
1 5 0 01 0 0 0

5 0 0

5 0 0
0

0
4 0 0

5 0 0

6 0 0

7 0 0

8 0 0

w a v e le n g th (n m )9 0 0

1 0 0 01 1 0 0a d d e d

2 5 0 01 0 0 03 0 0

A r o n ly
B ro m o fo rm
C H lin e s

4 0 0 0in te n s ity (A rb .)in te n s ity (A rb .)4 0 0 04 5 0 0a d d e d

4 0 0

5 0 0

6 0 0

w a v e le n g th (n m )Our collaborators in [78] had the most success making CH by ablating the precursor CHI3
(iodoform). The bond strength of C-I is only 50 kcal/mol, so in principle it should yield evenhigher densities of CH when dissociated. Iodoform is usually synthesized as a yellow powder andcan therefore be difficult to form into an ablation target. It is possibly for this reason that they did
not have much success with iodoform in its pure form. However, when our collaborators dissolved
the iodoform in acetone, covered the beaker in aluminum foil, and let the concoction sit on a shelffor several months, the resulting substance (which “had the consistency of day-old chewing gum”),
when ablated with a a 532 nm laser at 100 mJ/pulse in a buffer-gas cell yielded high enoughdensities to detect via absorption spectroscopy of the B←X transition.

23
Figure 2.10:

Spectra of X 2 Π(v 00 = 0, N 00 = 1, J 00 = 1/2) cryogenic CH molecules.

The mainfigure shows the Q-branch transitions; the frequency offset is 25723.4 cm−1 . The inset shows the
P -branch transition plotted on the same scale; its frequency offset is 25698.2 cm−1 . The spectra
were obtained from 1 to 2 ms after the ablation pulse. The experimental measurements are shownas points, the fit to a Gaussian (two Gaussians, in the case of the Q-branch transition) is shown asa solid line. The data were taken at a cell temperature of 5 K, ablation energy of 0.1 J, and helium
buffer gas density of 1 × 1016 cm−3 .
3 .5 x 1 0 -3
3 .0
2 .5

O p tic a l D e n s ity

2 .0
1 .5
1 .0
0 .5
0 .0
-0 .5
-1 .0
-1 .5

-1 .0

-0 .5

0 .0

0 .5

1 .0

1 .5

F re q u e n c y (G H z )We have since managed to recreate this CH precursor “goo” (Fig.2.11, and happily on amuch shorter timescale than months. After dissolving the iodoform in acetone and covering withaluminum foil, the mixture may be heated to increase the reaction of I2 with the aluminum. The
black substance that is created is “gooey” because of remaining moisture, probably water dissolvedin the acetone. If the mixture is heated gently at about 90 C it can be reduced to a hard glassy
substance that is much more vacuum friendly (since it outgasses less).

24
Figure 2.11: A picture of the CHI3 ablation precursor, glued to a copper plate and ready for cell
installation.

From the data in Fig.2.10, we were able to conclude that we created 1011 CH molecules in theupper lambda-doublet state. They created these molecules in a buffer-gas cell (with no extraction
aperture) with volume 10 × 10 × 2.5 cm3 , which works out to N = 4 × 108 mol/cc assuming uniform
cell density.

Chapter 3

Simulations of Stark Deceleration of Buffer-Gas Beams

3.1

Stark Deceleration
Although buffer gas beams show great promise for creating bright beams of cold molecules,

in order for our group to exploit these beams for collision experiments and for us to be able tocompare them directly with their supersonic expansion predecessors, we need to be able to couple
them into a Stark decelerator 1 . We therefore propose the experiment represented in Fig.3.1 whichloads a buffer gas beam source into a Stark decelerator. We use CH as our candidate molecule insimulations, since in addition to the other interesting qualities discussed in this thesis, its dipole
moment of 1.46(6) D[95] is very close to that of the Lewandowski group workhorse deceleration
molecule NH3 (1.42 D).
1Portions of this chapter were previously published in [78]26
Figure 3.1: Proposed experiment for decelerating and trapping buffer gas beams. The use of thesebeams creates the opportunity for many detection methods at different stages of the deceleration
process.

Since the processes by which molecular beams are cooled often cause them to acquire a largetranslational velocity, [5] they must be decelerated to rest before trapping experiments can be
performed. Our group does this with the use of Stark decelerators, which rely on the Stark shift(Eq.3.1) of a molecule to create a longitudinal potential hill, which removes translational energy
from the beam.
s
Ustark = ± (→−∆Uinv 2
M K 2 ∆Uinv−) + (|→µ || E |) ∓2
J(J + 1)
2

(3.1)

Historically, this has been done with pulsed Stark deceleration, whereby pairs of charged rods
create stark potential hills directly in front of the molecular packet, a schematic of which is shownin Fig.3.2[5].

27
Figure 3.2: Schematic of the pulsed deceleration process. From [96]As the packet rides up these hills, the potentials on the rods are switched so that the packet
is always losing energy. The rods have the effect of squeezing the packet in alternate transverse
dimensions, so that the transverse Stark potential averages out to a confining transverse potential.
However, as the molecule packet slows down and spends more and more time between rod pairs, it
has more opportunities to “leak out” through the sides, causing large losses in molecule number,not just from lack of confinement but because of active transverse over-focusing by the electrodes.
For this reason, our group has been working for several years on a “traveling wave” Stark
decelerator (TWD), which uses 8 sets of charged rings (Fig.3.3) to create a longitudinal potential
well Fig.3.4, which slows down continuously, effectively causing molecules to ride up a long potential
hill until they are stopped at the end of the decelerator.

28
Figure 3.3: A travelling wave decelerator uses rings instead of rods to slow molecules. The rings
are grouped into sets of eight such that each set creates a longitudinal potential well.

Our decelerator is designed such that the potential on each electrode will be given by
Un = Ua sin
2πn− ωt ,
8(3.2)

where Un is the potential on electrode i, Ua = 12 kV . This configuration creates the Stark
potential shown in Fig.3.4, and the time dependence ensures that this potential well moves down
the decelerator with a speed that matches the incoming molecule velocity v, so long as the appliedfrequency ω satisfies

ω=
where d is the ring spacing.

2πv
,
8d

(3.3)

29
Figure 3.4: Longitudinal potential
Longitudinal Potential On Z-axis for ±12 kV
0.6

0.5

Energy HKL

0.4

0.3

0.2

0.1

0.0
-10

-5

0

z HmmL

5

10

Because every 8th electrode is connected to the same rod, the potential well is repeated manytimes over the length of the decelerator, meaning that molecules could be trapped in any of thesewells at a time. The wells move in unison down the decelerator as the phases of each sine wave on
the electrodes are varied. A consequence of this is that the decelerator can sustain only a narrow
range of longitudinal velocities. To illustrate this further, I show a picture of the longitudinal phasespace (Fig.3.5) of our decelerator, which shows the “separatrix,” or the phase space trajectory
which separates molecules bound by the potential wells in Fig.3.4 from those that are not trapped.

30
Figure 3.5: The bound longitudinal phase-space volume created by the TWD potentials in Fig.3.4.
We see that to be captured a particle must not only be physically inside the moving potential, butthat each well supports only a finite range of particle velocities.
20

Vz HmsL

10

0

- 10

- 20

- 10

-5

0

z HmmL

5

10

We see that molecules that are exactly matched to the longitudinal movement of the well
will sit in the well center, whereas those within a small range of this velocity will oscillate within
the well. However, if the velocity of the molecule becomes too large or too small, it will ride overthe potential from one well to the next, and will not be effectively decelerated.
Because the electrodes are now rings, the molecules would see a true transverse trapping fieldat all times, so that we would expect transverse losses from such a decelerator to be much smaller.
We illustrate this by showing a transverse separatrix of the TWD in Fig.3.6

31
Figure 3.6: transverse separatrix of the TWD, from [96]. Because this separatrix is not constantwith longitudinal position Z, we show slices where Z is at the center of a ring (“ring-aligned”),
halfway in between rings (“gap aligned”) and the average of both.

As of this writing, the mechanical aspects of this decelerator have all been assembled, but
the electronics have yet to be perfected. Therefore, while this is happening, we have endeavored totest the efficacy of this decelerator with simulations.
The material differences between slowing a supersonic beam and a buffer gas beam arise
from their different phase space distributions. To illustrate this, we show a typical phase space
distribution of a buffer-gas beam compared to the more standard alternative of supersonic beams
in Fig.3.7.

32
Figure 3.7: Comparison of the longitudinal phase space distribution for a supersonic beam vs a
buffer gas beam. The distributions on the right show what the molecule phase space looks like after
traveling through a field-free region.

We see that the buffer-gas beam’s initial phase space is much more extended in space and(relatively) in velocity. The large spatial extent of the beam is a consequence of the large cell
aperture required for good extraction. In addition, to prevent a hydrodynamic boost [5], there
should not be too many collisions near the aperture of the cell. This has the effect that the relative
velocity spread of the beam is large. These large spreads pose a coupling problem, as the TWD
can only accept a narrow range of velocity classes a time.
We choose to solve this problem by noticing that after the beam undergoes free flight, thepacket of molecules deforms in phase space (Fig.3.7), since fast molecules increase their distancewith respect to the average molecule, and the slow ones lag behind. This causes the phase space ofthe packet to rotate and stretch out, with the upshot being that the velocity width of a part of thepacket at any given point tends to 0 with larger freeflight time, (although the total velocity width
stays the same). If the packet were allowed to undergo freeflight for a long time and then enter
the decelerator, molecules entering at any time would be all of a single velocity class. Mitigating
the transverse expansion that the molecules undergo during this free flight requires the addition ofhexapole guiding.

33
As discussed above, the velocity acceptance of the decelerator is a consequence of the movement of the Stark potential wells along the decelerator. This means that as TWD slows molecules
down, the accepted velocity decreases. Since our goal is to accept many different velocity classes
into the decelerator, the cleverest way to do this would be to slow the molecules down such thatthe accepted velocity of the decelerator at any given time was equal to the velocity of the entering
molecules. This is represented schematically in Fig.3.8
Figure 3.8: Cartoon schematic of the acceptance method. The vertical line in each panel marks
the position of the TWD. In the first panel the molecule packet exits the source. At time t1 it
has evolved in free-flight such that particle velocity is correlated with particle position, and theinstantaneous velocity width is small. At time t2 the fast part of the packet has been acceptedand decelerated, by which time the entering molecules have matching velocity. The process repeats
until the entire packet enters the decelerator.

t1

t2

t3

Velocityt0

Position

To aid our mathematical formulation of the acceptance, we define an “acceptance function”
A(t) that determines the central accepted velocity of the decelerator. The acceptance function
which describes the process of Fig.3.8 is that which matches the velocity of the molecules as they
arrive, namely
A(t) = H/t(3.4)

where H is the length of the hexapole (the distance that molecules travel under the influenceof no longitudinal fields). Although this acceptance method is ideal, it poses some problems. For
one, the acceleration that the molecules undergo, given by the time derivative of the acceptance34function, starts out as very large. When the molecules experience large accelerations, the shapeof the potential well in the rest frame of the molecules deforms. The shape of the well acquires alinear offset, shown in Fig.3.9:
Figure 3.9: Comparison of the TWD potential well for two deceleration magnitudes.
n o a c c e le ra tio n|a | = 2 . 1 E 4 m / s 2

S ta rk P o te n tia l (m e V )0 .0 80 .0 60 .0 40 .0 20 .0 0- 0 .0 0 6- 0 .0 0 4- 0 .0 0 2

0 .0 0 0

0 .0 0 2

0 .0 0 4z p o s itio n (m )Intuitively this linear offset may be explained as the same thing that happens when runningwith a cup of coffee. If you manage to run at a constant velocity with the coffee and then try tostop too quickly, the coffee sloshes over the front rim of the cup, and the number of coffee molecules
is diminished, potentially devastating the day’s caffeine intake. The coffee cup can only sustain
small accelerations; the same is true of the TWD potential well. Any constant acceleration applied
to the well is the result of a constant force, which creates a linear potential that deforms the welland causes the effective well depth to decrease.
We also can illustrate the problem of large accelerations by looking at the phase space generated by these potentials. We look specifically at the “separatrix,” or the phase space trajectory thatmarks the boundary between trapped orbits (“phase stable”) and orbits in which the molecules simply travel over the wells and through the decelerator (phase unstable). Fig.3.10 shows separatrices
for the same accelerations as those in fig.3.9:

35
Figure 3.10: Comparison of TWD separatrices for two deceleration magnitudes: |a| = 0 (larger
curve), and |a| = 2.1 × 104 m/s2 (smaller curve).
30

20

Velocity (m/s)

10

0

-10

-20

-30

-0.003-0.002-0.001

0.000
Position(m)

0.001

0.002

0.003

As the acceleration increases, the available phase space volume will decrease, and fewer
molecules will be phase stable. It may therefore be advantageous to use a more standard linear
deceleration scheme that approximates the nonlinear version.
For a deceleration method in which the acceleration experienced by the molecules was constant, we might guess that the best acceleration to use would be the smallest acceleration that is
sufficient to bring the molecule to the desired velocity within the declerator, i.e. one that satisfiesa=Vf2 − Vi2
2S

(3.5)

where Vf and Vi are the final and initial velocities and S is the decelerator length. However,since the molecule packet contains molecules with many initial velocities, the choice of Vi is nottrivial. We now let Vi be the velocity of an “index molecule”, whose velocity becomes the central
accepted velocity of the potential well. The velocity of the wells and the index molecule would thenbe given byH
V (t) = −a t −
+ Vi
Vi

(3.6)

We refer to Eq.3.6 as the linear “acceptance function”, in contrast to the nonlinear acceptance36function V = H/t. We can get an idea of the limiting acceptance functions and their associatedaccelerations by plotting Va for several different index molecules, shown in Fig.3.11:
Figure 3.11: Comparison of linear and nonlinear acceptance functions. The linear acceptancefunction is sufficient to decelerate a 210m/s index molecule, which is 3σ above the center velocity
and therefore puts an upper limit on the acceleration required. The inset shows the deformationof the potential well experience by the molecules at different times.

1 .0

A

2 0 0

S ta rk e n e rg y (K )D e c e le ra to r w e ll v e lo c ity ( V a) (m /s )

3 0 0

D

D
C
B
A

0 .5

B
C

0 .0

-5

0

5

Z p o s itio n (m m )

1 0 0

0
6

8

1 0

1 2

1 4

1 6

1 8

T im e (m s )3.2

3D Monte Carlo simulations
In order to determine which deceleration schemes work best, we generate 3 dimensional

potentials for 24kV sine waves on the decelerator electrodes using a commercial finite element
solver (COMSOL2 ), and use these to evolve trajectories of molecules with randomly generated
initial phase space coordinates.
The decelerator electrodes are modeled in COMSOL as a string of donut-shaped electrodes.
This is actually an approximation- in fact the electrodes are shaped more like hairpins with acircular bulb at the end (Fig.3.12). This is because the electrodes are made by bending and then
2

COMSOL Multiphysics, version 4.3, www.comsol.com

37
electropolishing tantalum wire. The surfaces of these electrodes have to be mirror-smooth to avoid
electron field emission on any protruding points. If we somehow tried to bend the tantalum wire
into more of a tennis racket shape, we would not be able to ensure good surface quality at thejunction. The hairpin shape introduces a defect in the transverse Stark potential.
Figure 3.12: TWD decelerator electrodes.

In the actual decelerator design, the hairpin “pinch” spirals around the longitudinal axis,
which in principle should average out the transverse Stark potential defect. Simulations run by
Nicholas Farrow show that this defect does indeed have almost no consequences for molecular
dynamics simulations of our decelerator. His results are reprinted in Fig 3.13. We can be especiallyconfident that the defect is unimportant because the agreement of the cylindrically symmetric andasymmetric COMSOL models does not get worse with smaller velocity, which we would expect
if it were important, since the average transverse potential would become a poorer and poorer
approximation as the time spent by the molecules withing each electrode increased.

38
Figure 3.13: Comparison of time-of-flight signals from molecular dynamics simulations of our decelerator using cylindrically symmetric electrode models and more realistic “hairpin” shaped models.
From [96].

These initial molecule distributions are 6 dimensional Gaussians. We choose the widths inevery dimension to be characteristic of typical buffer-gas beam parameters. We also run simulations
for supersonic expansion beams for comparison; the parameters for both types of distributions arelisted in Table 3.1.

39
Parameter

Buffer Gas Beam

Supersonic Beam

180 m/s

445 m/sLongitudinal Velocity Spread

17 m/s (1σ)

10 m/s (1σ)

Longitudinal Position Spread

10 cm (1σ)

10 mm (1σ)

Transverse Velocity Spread

21 m/s (1σ)

1 m/s (1σ)

Transverse Position Spread

1.7 mm (1σ)

1.0 mm (1σ)

Average Forward Velocity

Table 3.1: Parameters of the buffer-gas beam used in simulations. The expansion out of the cell isassumed to be in the hydrodynamic regime. These parameters would correspond to a cell extraction
time of about 2 ms and a cell aperture diameter of roughly 5 mm for a physical cell [47].

3.2.1

Hexapole Parameters

In contrast to the decelerator, we use analytical potentials for the hexapole part of thesimulation, where the voltage on the hexapole is set to 400V. The dependence of preserved molecule
number on the hexapole voltage was only briefly investigated and was found to increase at small
voltages but to then quickly plateau. This is because the hexapole can only preserve the distributionof molecules in phase space, but cannot compress it. Because of the large aperture of the buffergas cell, many molecules will simply start outside of the decelerator phase space acceptance, andattempting to fit them inside it, either by collimating or focusing the molecular beam, will merely
trade a large velocity spread for a large position spread or vice versa.
This point can be illustrated with a mini-simulation that includes only the initial Gaussian
distribution being loaded into an analytial hexapole potential. Coupling into the decelerator issimulated with a hard radial cutoff at the end of the hexapole. In Fig.3.14, we show the resultsof such a simulation, which counts the number of surviving molecules at the end of a hexapole
as a function of hexapole voltage. We see that the number increases steadily with voltage as theavailable phase space volume is filled, but then plateaus when the molecules being loaded into thehexapole contain too much energy to exhibit stable trajectories inside the hexapole phase space.
Full simulations which include the decelerator, although too computationally expensive to run at

40
a similar resolution, show a similar leveling-off behavior with hexapole voltage.
Figure 3.14: Results from a small simulation sending a beam of molecules through an analytical
hexapole potential, for several hexapole lengths. The number of molecules increases until the phasespaces are as well matched as possible, after which the number oscillates while the maximum
number stays flat. The oscillation is a consequence of defocusing near the end of the hexapole, an
its frequency depends on how the average radial distance of molecules varies with length. Since
molecule trajectories will undergo more oscillations in a longer hexapole, the surviving molecule
number varies more rapidly with voltage.
H e x a p o le T u n in g

n u m b e r o f s u rv iv in g m o le c u le s

5 0 0 04 0 0 03 0 0 02 0 0 00 .5 m
1 .5 m
2 .5 m

1 0 0 00
-2 0 0

0

2 0 0

4 0 0

6 0 0

8 0 0

1 0 0 01 2 0 0

1 4 0 0H e x a p o le P o te n tia l (V )Armed with the results of Fig.3.14, we set the hexapole voltage to 400V, judging that this is
comfortable above the “shoulder” of the plateau. This parameter was set for all simulations that
included the decelerator. The result of one of these “full” simulations is shown in Fig3.15. As themolecule trajectories are evolved, any given molecule can meet with three different fates: it can
hit an electrode, fly radially outward until it is too far away to ever be recaptured by any of thepotentials, or it survives until the simulation times out. When any of these events happens, thephase-space coordinates of that molecule are frozen for the rest of the simulation.

41
Figure 3.15: A snapshot of the final phase space for decelerating molecules from 180m/s to 25m/s
using a hexapole length of 1.5m
2 5 0
2 . o u ts id e tra n s v e rs e
P S A ( 9 .2 % )L o n g itu d in a l v e lo c ity (m /s )

2 0 0
3 .
o u ts id elo n g itu d in a l
P S A ( 4 .9 % )1 5 0
1 . o u ts id e h e x a p o le
P S A ( 8 1 .3 % )1 0 0

0 .2 %

5 0
4 . s u c c e s s fu lly
s lo w e d ( 4 .4 % )

0
-1

0

1

2

3

4

L o n g itu d in a l p o s itio n (m )Fig.3.15 shows that most molecules are lost at the cell aperture. Because of the large aperturesizes necessary for efficient molecule extraction, most molecules start outside the hexapole phasespace and cannot be compressed into it, so this loss is inevitable and can really only be addressedwith a larger diameter hexapole and decelerator. Another chunk of molecules is lost from out-ofphase loading of molecules into the wells. When this happens, molecules slosh from one well tothe other instead of being decelerated, and to first order exhibit phase-space “rotation” similar toparticles traveling through a field-free region.
We can also use these trajectories to extract simulated time-of-flight (TOF) signals, which iswhat we would measure in the lab. A TOF trace is shown in Fig.3.16, with the TOF of a supersonicbeam simulation shown for comparison.

42
Figure 3.16: Times of flight for deceleration of buffer gas and supersonic beams. The relative
signal heights of the two simulations should be ignored (although each simulation is internallyconsistent)- both simulations were run with the same number of molecules, whereas in the lab eachsource produces different numbers of molecules per pulse in different densities.
B u ffe r G a s B e a m

1 .0

S u p e r s o n ic B e a m

0 .1 00 .0 6d e n s ity (a rb .)d e n s ity (a rb .)0 .0 80 .5

0 .0 40 .0 20 .0 00 .0
5 .0

1 0 .01 5 .0tim e (m s )2 0 .02 5 .0

2 .0 m

4 .0 m

6 .0 m

8 .0 md e te c t tim e (s )At early times, a glut of “unslowed” molecules is detected- these are the green molecules from
Fig.3.15. At later times, the slowed molecules appear. It seems at first glance that the separationof slowed and unslowed molecules is worse for buffer gas beams, but in fact this is because the large
velocity spread of the initial beam is mapped to a large position spread in the decelerator, whichcauses the molecule packets to fill a large time interval upon detection. The width in time for eachindividual well is about the same for both beams; there are just so many filled wells that the entire
space between slowed and unslowed molecules is filled for the buffer gas beam case.

3.3

Theoretical Model
Because of the symmetry of this new type of decelerator, it is natural to question whether,

despite good agreement with results in the past [97], the large computational cost of a three
dimensional simulation is really necessary. For the previous generation of pulsed decelerators,
agreement with 1D simulations has been poor [98] because of strong coupling between the transverseand longitudinal coordinates, and because of the poor suitability of using an averaged transverse

43
potential at slow velocities. The ring decelerator obviates the need to think about these problems,
which suggests the suitability of constructing a theoretical model for acceptance.
We base the 1D model on the overlap between the phase-space distribution of the packet(PSD)
and the phase-space acceptance (PSA) of the decelerator. We model the PDA as a bivariate gaussian
distribution G(z, Vz , t), where z vz are longitudinal position and velocity variables. The number ofmolecules withing the PSA of the decelerator can be approximated by

Z Va +∆v/2
G(H, Vz , t0 ) dVz (t0 ),

n=

(3.7)

Va −∆v/2

where ∆v is the width of the decelerator acceptance in the velocity coordinate. This widthis not constant and changes as a function of the acceleration used, because of the well distortion
discussed above. The acceleration a is the time derivative of Va (t) the accepted velocity at a giventime.
To determine the size of ∆v we compute the separatrix for different accelerations from a = 0(“bunching”) a = −100 km/s2 - the largest acceleration required to decelerate a molecule that was
3σ faster than average in the time allowed by a decelerator that was 624 rings long. To computea separatrix, we use the following reasoning: the separatrix describes the largest closed phasespace trajectory. Because all the fields we are dealing with are conservative, these trajectories areconstants of the hamiltonian, meaning the energy should not change along them. Therefore we canwrite

1
E = mV 2 + U (z)
2

(3.8)

And solving for V gives:r
V (z) = ±2
(E − U (z))
m

(3.9)

These two functions of z, which we will call V (z)+ an V (z)− are defined up to the energy
constant E. If we vary the energy until the two halves of the function become continuous, i.e.

44require thatmin(V (z)+ ) = max(V (z)− )(3.10)

Once E is determined then ∆V /2 is given by
Z zmaxV (z)+
zmin

dz
zmax − zmin

(3.11)

Velocity acceptance width Hm•sL

Figure 3.17: The velocity acceptance width shown as a function of acceleration

20
15
10
5
0
-100

-80

-60
-40
-20
Acceleration Hkm•s2L0

As far as acceptance in the position coordinate z, molecules can be accepted over a rangeof positions, but we approximate it as happening only at the decelerator entrance. To show thisvisually, we compare an actual separatrix (in this case for bunching) to the model separatrix in
Fig.3.18.

45
Figure 3.18: Comparison of separatrices used in the simulations (blue) to those model approxiation(red). Both separatrices are superimposed on the PSD of the molecular packet after it has undergone
1m of free flight. The inset zooms in on the two separatrices showing that the model really is anapproximation, since it sweeps continuously through the entering packet in position, an since thevelocity width is averaged velocity width of the simulation separatrix.

PSD envelope
PSA used in simulations

Velocity

PSA used in model

Position

Finally, since molecules are accepted over a range of times we have to do a further integral
over all later times to get the total number of molecules accepted:

Z t=∞ Z Va (t)+∆v/2
N=

G(H, Vz , t) dVz (t) dt.
t0(3.12)Va (t)−∆v/2

With an infinitely small separatrix width in position and a continuous integration over alltimes, we are essentially approximating the acceptance as a continuous sweep through the PSD.
In fact this acceptance happens in bunches- as mentioned earlier if molecules are not accepted at
the right point of the well movement, they will slosh from well to well and exit the apparatus
undecelerated. Building in a phase-dependent acceptance may be one avenue for improving themodel, although this approximation was not significant for the parameter space we explored.

46
We stop here and do not consider any loss mechanisms inside the decelerator itself. The
validity of this assumption is supported by Fig.3.15, since over 95% of molecules are not lost within
the decelerator itself. Therefore we expect that the results of Eq.3.12 should be proportional to thenumber of molecules decelerated in our simulations.

3.4

Comparison of the Model to Simulation Results
Using this formalism, we compute the number of molecules accepted into the decelerator for

many linear acceptance functions. We can see from Eq.3.6 that each such function is defined once
H and Vi are chosen. We would expect that the choice of a larger H would generally result in
more molecules being accepted, since this would both decrease the instantaneous velocity spread of
the PSD at the decelerator entrance and increase ∆v because of the smaller accelerations needed.
We might also expect that the best index molecule to use would be the molecule at the centerof the initial phase space distribution, i.e. one with initial phase-space coordinates of (z, Vz ) =(0m, 180m/s). This choice is especially tempting, since this choice would suggest that we could ingeneral ignore the “distriubution” part of the PSD and concentrate on just one molecule.
In Fig.3.19, we plot the results of theoretical model on top of simulations that count the
number of decelerated molecules for many different index molecules. Each simulation was run
several times so that we could get an idea of how the size of the distribution maps to the error
in the number of molecules decelerated. We can immediately see that: 1) the agreement of themodel with simulations is startlingly good, which confirms that the cylindrical symmetry of the
TWD allows us to disregard the transverse dimensions of the decelerator. 2) This agreement also
confirms our assumption that molecule losses within the decelerator itself are rare, since we arecomparing molecules accepted (theoretical model) to molecules decelerated (3D simulations). 3)
Both of our naive assumptions seem to be incorrect- increasing the hexapole length does not always
translate to more molecules captured, and the best choice of index velocity is not always the averagevelocity of 180 m/s - in fact, for a 1.5m hexapole we get almost a factor of two improvement byusing an index velocity of 210 m/s.

47
Figure 3.19: 3D simulation results plotted on top of theoretical model calculations, for three different hexapole lengths. The model calculations have been scaled to be the same height as the
maximum of the simulation results. The good agreement suggests that 1D calculations are suitablefor predicting how many molecules will be decelerated, obviating the need for computationally

F ra c tio n o f m o le c u le s d e c e le ra te dexpensive 3D simulations.
0 .0 50 .0 40 .0 30 .0 20 .0 10 .0 0
1 0 0

2 0 0

3 0 0

4 0 0 1 0 0

2 0 0

3 0 0

4 0 0 1 0 0

2 0 0

3 0 0

4 0 0

In d e x m o le c u le v e lo c ity (m /s )We can explain point 3 by considering the turn-on time of the decelerator. In the simulations,the decelerator turns on as soon as the index molecule arrives at the entrance (t0 ). We again
consider the overlap of the PSA of the decelerator and the actual phase-space volume occupied by
the molecular distribution. Qualitatively, this overlap is influenced by three factors: 1)how closely
Va(t) approximates H/t, 2)whether t0 is early enough to capture a majority of molecules at thedecelerator entrance, and 3)how large ∆v is for the acceleration used. The first and third factors
are similar for 180 and 210 m/s index molecules, but since the decelerator turns on when the index
molecule arrives, using a 180 m/s index molecule means that 50% of the molecules have alreadypassed the decelerator entrance. Using a 210 m/s index molecule decreases the number of moleculesthat escape the acceptance region before t0 .

48
Figure 3.20: This figure shows the portion of the initial PSD that has been accepted into thedecelerator for linear and H/t acceptance schemes. The gray regions show the PSD of the molecularbeam as it enters the decelerator after traveling through a 1.5 m hexapole guide. These gray regions
are identical in each frame. The black regions show which molecules will be accepted after theacceptance process is complete. The top row shows the overlap for linear acceptance schemes,
while the bottom row shows the overlap for H/t acceptance schemes.
V i= 1 8 0 m / s

V i= 2 3 0 m / s
L in e a r A c c e p ta n c e

V i= 2 1 0 m / s

2 0 0
1 5 0
2 5 0

H /t A c c e p ta n c e

L o n g itu d in a l v e lo c ity (m /s )

2 5 0

2 0 0
1 5 0
1 0 0

1 .0

1 .5

2 .0

1 .0

1 .5

2 .0

1 .0

1 .5

2 .0

L o n g itu d in a l p o s itio n (m )We show a visualization of the overlap between the PSD and the accepted molecules in Fig.
3.20. We see that for linear acceptance functions, using a 210 m/s molecule more effectively samples
the high-density center of the incoming PSD, resulting in more molecules accepted. Typically,
decelerators are operated such that they turn on when the synchronous molecule, which is analogous
to our index molecule, reaches the entrance of the decelerator. Fig. 3.20 suggests that a better modeof operation could be to turn the decelerator on immediately after the molecular beam exits thesource. However, most molecules that are faster than the index molecule will exit the decelerator
before they reach the final velocity. The number of molecules rejected this way cancels out mostof the benefit of turning the decelerator on earlier.
To illustrate the agreement between the 1D and 3D results in a different way, we compare
separatrices used in the model and the simulations, as well as final phase space positions of thesimulation molecules (Fig. 3.4) in an individual well.

49
Figure 3.21: A comparison of the 3D simulation results, 3D separatrices, and 1D model separatrices.
One 3D separatrix is superimposed on one filled well from the beginning, middle, and end of thedecelerated molecule PSD. The 1D model approximates the PSA as a continuous region in theposition coordinate, so we show only the velocity boundaries (horizontal lines). The difference canonly be discerned when the scale is increased to show individual wells. We see that the model
separatrix does accept molecules between individual wells, which, although unphysical, results only
in a consistent overestimate of how many molecules can be accepted. This accounts for the excellent

L o n g itu d in a l v e lo c ity (m /s )1 0 0

L o n g itu d in a l v e lo c ity (m /s )agreement between the model and simulations in Fig. 3.19 after a constant scaling.

8 0
6 0

5 0
4 0
3 0
2 0
1 0
0

2 .2 42 .2 6

2 .4 3

2 .4 5

2 .6 6

2 .6 8

L o n g itu d in a l p o s itio n (m )

4 0
2 0
0
2 .0

2 .5

3 .0

L o n g itu d in a l p o s itio n (m )We also tested deceleration schemes using a deceleration function that matched the incoming
velocity of the molecular beam (i.e., H/t). The results of that model are shown in Fig. 3.4.

50
Figure 3.22: 1D model predictions of the fraction of molecules decelerated using the 1/t chirp forhexapole guide lengths of 0.5 m, 1.5 m, and 4 m. The number of rings required to decelerate
the molecular pulse using a particular hexapole guide length are shown for a index molecule witha velocity of 231 m/s (dashed line), which is 180 m/s plus three times the longitudinal velocity

F ra c tio n o f m o le c u le s d e c e le ra te dwidth.
4 m h e x a p o le
4 3 7 7 rin g s
1 .5 m h e x a p o le
1 6 4 1 rin g s

0 .0 60 .0 50 .0 40 .0 30 .0 2

0 .5 m h e x a p o le
5 4 7 rin g s

0 .0 10 .0 0
1 0 0

2 0 0

3 0 0

In d e x m o le c u le v e lo c ity (m /s )For the H/t chirp scheme, the index molecule sets only the time the decelerator turns on.
Thus, if it turns on before most of the molecules reach the decelerator entrance, the number ofmolecules decelerated should be independent of the exact index molecule velocity (that is, the decelerator turn on time). This effect can be seen as a plateau in the number of molecules decelerated
for large index molecule velocities (Fig. 3.4). Unlike the results for the linear simulations, thenumber of molecules accepted does reliably increase with hexapole length just as we would expect,since a choice of large index molecule velocity will ensure that the entire packet is accepted. As themolecular beam becomes more correlated in position and velocity with longer hexapole lengths, the
PSA will better match the incoming molecular beam PSD. The increase saturates once the overlapof the PSD of the molecular beam and PSA of the decelerator is a maximum. This occurs at afraction of 6%. (Note: 90% of the molecular beam is outside the transverse PSA regardless of thecorrelation length.)

51
There is one problem we still have not considered associated with using a 1/t chirp, whichcomes to light when we consider the longitudinal phase-space trajectory, V (z), experienced by thesemolecules. If we know that V (t) = Ht , then we can integrate this to obtainz(t) = Hln(t) + C(3.13)We require that at time t0 the index molecule (with velocity V0 ) has traveled the distance ofthe hexapole H, meaning z(t0 ) = z( VH0 ) = H, which givesC = H − Hln

H
V0


.

(3.14)We plug this back into z(t) and invert the function to get t(z):t(z) =

z

H
exp
−1 ,
V0
H

(3.15)

which we can plug into V (t) = H/t to getzV (z) = V0 e1− H .

(3.16)

Immediately evident from these trajectories is that molecules can only be slowed to a stopwith an infinitely long decelerator. The dependence on hexapole length also means that the numberof rings must be considered when implementing 1/t chirp schemes. In contrast, any length may
be chosen for a linear chirp scheme with the caveat that shorter decelerators will require the useof larger accelerations. However, for the 1/t chirp, the number of rings is a fixed value dependingon the hexapole length and the initial and final velocities. The number of rings required for a 1/t
chirp is given by

Nrings =H ln VVf0∆d,(3.17)

where ∆d is the ring spacing. Thus, to realize the large gain in decelerated molecule fraction,
one must build an unreasonably long Stark decelerator of several meters(Fig. 3.4), whose versatility

52
would be severely hampered, since the initial and final velocities cannot be varied.
The naive solution to this would be to simply switch to a linear chirp once all the molecules
were accepted into the decelerator, and then slow them to the desired velocity. If we attempt thissolution several new questions arise: How much decelerator length should we allocate to linear
chirp? The molecules are now spread out over many rings; what should we consider the position of
the index molecule to be now? What acceleration (which depends on the remaining deceleration
distance as in eq.3.5) should be used? If this new can of worms seems familiar, it is because it is
the same as the one we have been dealing with the whole time- we are merely trading the problemof large velocity spread for one of large position spread, and would have to consider different chirps
based on an index molecule position instead of an index molecule velocity.
The linear chirp ends up being a practical compromise, especially since, if the length ofdecelerator is fixed at 600 rings, the linear chirp produces three times more decelerated molecules
than a 1/t chirp.
Until now, we have evaluated the deceleration schemes based on total number of molecules
decelerated. For experiments that use a slow controlled molecular beam, the total number or
integrated flux is the important metric, but for experiments requiring loading molecules into a
trap, density also plays a role. A table of the decelerated fraction, molecular density, and numberof rings used for the different protocols is shown Table 3.2. The densities were calculated from thesimulations by counting the number of molecules in the central well of the decelerator and assuming
the molecules were uniformly distributed in the well volume. We note this underestimates the true
peak well density. We expect that slowing protocols that make use of longer hexapoles would result
in decreased well densities because longitudinal phase-space distribution spreads during the flighttime in the hexapole. This idea is borne out in the case of linear slowing protocols; the peak density
decreased for longest hexapole length, although the decrease is not very significant over the range
explored.

53
Hexapole Length1
t Deceleration

Linear Deceleration
Density (mol./cc)

Fraction

Rings

Fraction

Rings

0.5m

1.7 × 109

0.025

600

0.016

547

1.5m

1.5 × 109

0.045

600

0.049

1641

4.0m

8.2 × 108

0.025

600

0.060

4377

Table 3.2: The fraction of the initial beam that is decelerated to 25 m/s, central well densities, andnumber of decelerator rings used for various correlation (hexapole) lengths for both linear and 1/t
acceptance functions. The number of rings used to decelerated using the 1/t chirp was set by the
final velocity of 25 m/s. The density in the central well was calculated by assuming 1011 molecules
per initial pulse, and a uniform distribution within each decelerator well (which therefore represents
a slight underestimate of the peak density).

Chapter 4

Cell Characterization

4.1

Buffer Gas Apparatus
Our apparatus employs a sumitomo 1 SRDK series two-stage cryocooler, which has thecapability to cool the first stage to 40 K and the second stage to 4 K. All cooled components areanchored to the second stage except or the black body radiation shield, which lowers the heat loadfrom black body radiation from the laboratory incident on 2nd stage components. Temperature
measurements are made with the use of Lake Shore 2 temperature sensitive diodes, and components
may be heated with high power resistors placed on the cell and cryopump. We will discuss cryogenic
requirements later in the chapter, but for now we focus on the design of our buffer gas cell. We
began our experiments using a cell we designed with the help of Jonathan Weinstein. The geometry
we used first was very simple from a machining standpoint, being simply the intersection of threecylinders through a copper cube (Fig.4.1,4.2).
1

Sumitomo RDK-415 pulsed tube cryostat, Sumitomo Corporation, http://www.sumitomocorp.co.jp/english/
Lake Shore Cryotronics uncalibrated cryogenic temperature sensor,
PN DT-670-B1-CU,
http://www.lakeshore.com
2

55

Neon
lines

50 K shield attached to 1st stage

To 1st stage

Cold head 2nd stage

Rb Target

Cu block for improved
conduction to cell

Steel bolts securing
circular plate to 2nd stage

355nm ablation (~5mJ)

Cryopump, attached to 2nd stage

Figure 4.2: Picture of the absorption spectroscopy setup with old cell. When we eventually switched to a new cell design, the new
Figure 4.1: Our original cell set up for Rb

cell -being almost the same size transversely-

absorption spectroscopy experiments.

was simply swapped in. A cryopump is anchored to the second stage, for reasons discussed in sec.4.2

We eventually incorporated a new kind of cell design with a simpler internal geometry andextra features designed to improve signal stability. The new cell (Fig.4.3,4.4) is based on thedesign of the Doyle group, and incorporates parts made by them. This cell supposedly has several
empirically important advantages in that it features a neon inlet and reservoir meant to direct theflow of neon downward in a smooth, vortex-free way, a spacer unit between the neon inlet and theablation region, and a user friendly “mix-and-match” style assembly that allows us to easily tinker
with the geometry. In general, we found that using the Doyle style cell produced less noisy signals
and more predictable lifetimes and extraction efficiencies, which may be partly due to the fact thatthe simpler internal geometry made measurement of the cell parameters easier.

56

Figure 4.3: Schematic representation of our

Figure 4.4: Realization of the Doyle-style

new buffer gas cell, based on the design ofbuffer gas cell, looking on the absorption

the Doyle group.

spectroscopy windows.

The cell stack starts with the neon inlet, below which is mounted the ablation target, withthe ablation laser aligned into the page. Below the ablation target are two widows through which
an absorption spectroscopy laser may be aligned. Finally, there is an aperture at the bottom of
the cell. The dimensions of the cell and aperture must be designed to favor extraction of the buffer
gas from the cell. To this end, we consider two timescales- the time for molecules to diffuse to
the walls of the cell (Tdif f ), and the time for molecules to be “pumped out” through the aperture(Tpump )[99].

Tdif f =L2 nσX−N e 2kb T −1/2
4
mN e

(4.1)

L3 kb T −1/2
4A mN e(4.2)

Tpump =

Here, L is the characteristic length scale of the cell, A is the area of the aperture, n is neon
number density, kb is Boltzmann’s constant, and T and mN e are the temperature and mass of theneon atoms. σX−N e is the scattering cross section of the ablated species with neon.
[100] found that extraction efficiency generally increases with aperture size. Since the persistence time of molecules inside the cell is unimportant for our experiment, we use an aperture size

57
of 5.5mm, which gives pumpout times of < 1 ms. Our cells are not cubic, but for calculations we
use the cube root of the volume as the characteristic length scale. The newer Doyle group cell has
a length scale of L = 27 mm.
For good extraction we require Tpump < Tdif f [101]. If this condition is not met all themolecules will stick to the walls of the cell and will never be extracted from the cell. Since Tpump
depends only on the collision rate between molecules and the aperture area, it has no dependence
on the density of neon, which is assumed to be uniform in the cell. On the other hand, the Tdif f
depends on the mean free path of molecules in the cell, which is a result of collisions between
molecules and neon atoms, and so depends linearly on neon density. At a constant flow rate φthrough the cell density reaches an equilibrium, such that density and flow rate are related by:

φ = nAp
kb T /8m(4.3)

We will often use flow rate as a shorthand for density, since they are proportional to eachother and since flow rate is the experimentally controlled variable.
Figure 4.5: A cartoon of the dependence of cell lifetime on flow rate, meant to show how, for somecell parameter choices, Tpump can compete with Tdif f at low flow rates.

58
At first, the diffusion time grows linearly, as the time for the diffusion to the walls becomes
longer. At some point the Tdif f becomes larger than Tpump and the lifetime in the cell becomes
independent of flow rate.
Tpump < Tdif f ensures that we will extract our molecules from the cell, but is not sufficient toensure good cooling. We must also consider a thermalization time that ensures that the molecules
reach the temperature of the buffer gas. We can get an idea of how long this might take in terms ofthe number collisions a species must undergo in order to thermalize. In each collision, the averagekinetic energy lost by a molecule (assuming hard sphere collisions) is [47]:∆Tm = −(Tm − Tb )/µ(4.4)

where Tb and Tm refer to buffer gas and molecule temperatures and µ is the reduced mass.
After N collisions, the temperature of the molecule will be

Tm (N ) − Tm (N − 1) = −Tm (N − 1) − Tb
κ

(4.5)

This is a discrete difference equation, but if we assume that the change in temperature percollision is much smaller than the molecule temperature (and therefore that the number of collisions
N is large) then Eq.4.5 becomesdTm
Tm (N ) − Tb
=−
dN
κ

(4.6)

where κ = (mm + mb )2 /2mb mm . The solution to this equation is

Tm (N )
=1+
Tb




Tm (0)− 1 e−N/κ
Tb

(4.7)

And since the molecules are originally much hotter than the buffer gas we have

Tm (N )Tm (0) −N/κ
=1+
e
Tb
Tb

(4.8)

59
For CH in neon we have κ ≈ 2, and for temperatures on the order of 1000 K we find that it
takes about 20 collisions for the molecules to reach neon temperatures. Surprisingly, the number ofcollisions does not change much even for heavier species like C6 - here we benefit again from the useof neon, whose large mass compared to helium cools the entrained species much more effectively.
The mean free path of the molecules in the cell is given by [47]

λ=

1
nσm−b

p

1 + mm /mb(4.9)

where σm−b is the collision cross section between the molecule and the buffer gas atom. Thiscross section will be discussed later in the chapter, but for now can be estimated as on the orderof 10−14 cm2 . We show plots of the number of collisions required to cool molecules from typicaltemperatures in Fig.4.6.
Figure 4.6: The number of collisions required to translationally cool CH (red) and C6 (green) from5000 K (a typical ablation temperature) to 25 K (the coldest temperature we can reach with ourcell).

In Fig.4.6 we see that 40 collisions quickly cool the translational temperature of the molecules
to the temperature of the neon buffer-gas. How many collisions actually occur in the cell? We can

60
estimate a lower limit on the collision rate r withr = nσV(4.10)

where n is the neon density, σ is the collision cross section, and V is the relative collisionvelocity. Although this velocity starts out very large, owing to the hot temperature of the molecules,
we can get a lower limit on the collision rate by using the most probable Boltzman velocity of theneon atoms. For typical cross sections and densities we obtain a collision rate of 8 × 106 collisions/s.
For a Tpump of 1 ms, as we designed our cell to have, this gives almost 104 collisions, meaning thatmolecules are certainly thermalized by the time they leave the cell.
This formalism is a good predictor of translational cooling, but for vibrational/rotationalcooling the vibrational/rotational relaxation cross sections should be used- these cross sections are
generally smaller[47] than the collision cross section, which makes internal state quenching lessefficient than translational cooling. However, since the number of collisions inside the cell is solarge, and since vibrational and rotational relaxation cross sections are usually only 1-2 orders ofmagnitude smaller than the elastic collision cross sections, these degrees of freedom are also likely
to be quenched in the cell.

4.2

Cryogenics
The temperature and pressure requirements of our buffer-gas cell are less demanding thanthose of conventional cells because of our choice to use neon instead of helium. However, the gasload is not insignificant. We already require the neon density to be high in order to maintain asmall mean free path, however, in addition to this previous experimenters [99],[102] claim that theablation technique requires even larger densities for good molecule cooling and extraction. The
reasons for this are somewhat nebulous, although it is possible that since the ablation process
is known to heat samples to several thousand K [103][104] the number of collisions required tothermalize the radicals becomes larger, decreasing the required mean free path even further. These61
density restrictions require us to flow neon at flow rates on the order of 50-100 sccm. To handle
this gas load, both for this and future experiments, it is sufficient to add a large piece of metalthat is well anchored to the second stage of the cryocooler, which is as cold as possible to maximize
sticking probability, which we will refer to as the “cryopump.” We can make a rough estimate of
the required cryopump size assuming that the probability of molecules sticking to be close to 1.
This is actually a good approximation for neon, since we are so far below its freezing point. For abeam that is completely in the effusive regime, the angular spread of the beam can be as large as√120◦ [47]. If the cryopump is 2 cm away then we require a diameter of 2 × 2 3 = 6.9 cm, or justunder 3 in. Since our cell and beam parameters cause us to be much closer to the hydrodynamic
regime our angular spread is likely smaller, although with this cryopump size we have the option
to make our beam more effusive (for instance by increasing the size of the extraction aperture).
This illustrates one of the main advantages of using neon over helium- since a helium beam would
be operated much closer to its freezing temperature, the sticking probability is not close to 1, so
a cryopump with a very convoluted surface area (like charcoal sorb) is required to ensure many
collisions of the gas atoms with the cold surface.
Fig.4.7 shows the cryopump in action- neon ice has accumulated on it after several hours ofcell operation. A heater located on the bottom of the cryopump allows us to sublimate the neon
to prevent beam backscatter once the neon mountain gets too high.3
3

Care must be taken when warming up any part of the apparatus after neon deposition- without cryopumping
the pressure in the chamber spikes to a few torr and quickly destroys any ion gauges or auxiliary turbopumps thatare still running.

62
Figure 4.7: A picture of the cryopump at work. Several hours of neon flow are required to build
up this amount of neon.

This is a much simpler way to handle the gas load than would be required by helium buffer
gas beams- helium, being much harder to pump necessitates the use of extremely large surface area
cryopumps, which can only be achieved with charcoal sorb that must be periodically reactivated.

4.3

Absorption Spectroscopy of Rb
We can test the properties of our cell by performing an absorption spectroscopy experiment.

We installed a target of RbCl and ablated it with 532 nm light to produce Rb atoms. We thenaimed a 780 nm diode laser through the cell and detected on the opposite side. A schematic of
the experiment is shown in Fig.4.9

63
Figure 4.8: Schematic of the absorption spectroscopy setup.

With each ablation laser pulse, the number of absorbers inside the cell spikes to a maximum,
after which Rb atoms are pumped out through the aperture, causing the absorption signal to decay
exponentially. A typical ablation pulse signal is shown in Fig.4.9:
Figure 4.9: A typical absorption spectroscopy signal for RbCl, monitoring the AC channel. In thiscase the flow rate is 40sccm.
T y p ic a l R b A b s o r p tio n S p e c tr o s c o p y S ig n a l

0 .2
0 .0

A C s ig n a l (V )- 0 .2- 0 .4- 0 .6- 0 .8- 1 .0- 1 .2- 1 .4
-2

0

2

4

6

8

1 0

tim e (m s )We fit this decay with an exponential to measure the signal lifetime. We can also performthe same experiment immediately outside the cell. If the molecules are being efficiently extracted

64(meaning the cell lifetime is dominated by tpump ), the lifetimes inside and outside the cell should
be similar. If we repeat these experiments at many different flow rates, we can get an idea of whatmechanisms govern cell extraction. The results of these experiments are shown in Fig.4.10
Figure 4.10: Signal lifetimes as a function of flowrate
D o y le C e ll, 4 5 K , a b s o r b tio n a fte r a b la tio n

2 .5 mO u tC e ll
In C e ll

life tim e ( s )2 .0 m

1 .5 m

1 .0 m

5 0 0 .0 µ

0 .0
0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

flo w r a te ( s c c m )It is tempting to explain these data by assuming that the lifetime in the beginning grows
linearly due to increasing diffusion times, and plateaus when the Tpump < Tdif f . The only problem
is that the diffusion time is proportional to the Rb-Neon scattering cross section. The guideline
for designing buffer gas cells has been that the cross sections of most species with neon should be
about 1 × 10−14 cm2 , and has been as small as 3 × 1−15 cm2 [101], but in fact the scattering crosssection is large enough that Tdif f is usually too large to matter.
Measuring signal inside and outside the cell also allows us to see how the beam density changes
upon leaving the cell by comparing the peak optical depth of Rb signals, extracted by combining
the information from the AC channel (fig.4.9) with the DC offset and computing OD = ln(V0 /V ).
When we measure this for the cell, we get the dependence of OD on flow rate (fig. 4.11).

65
Figure 4.11: Optical depth of Rb as a function of flow rate.
E x tr a c tio n E f fic ie n c y

1 .0

in c e ll O D
o u t o f c e ll O D

0 .8

O D a m p litu d e

0 .6

0 .4

0 .2

0 .0
0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

flo w ra te (s c c m )The extraction efficiency approaches 1 at higher flow rates, but in principle should be large
whenever Tdif f is larger than Tpump .

4.4

Scattering of Molecules by NeonWe can gain some insight into the order of magnitude of this collision cross section by con-sidering the type of interaction involved when Rb scatters off of Ne. Qualitatively, because both
species are neutral, the interaction between them is dominated by a strong repulsion at short distances due to the Pauli exclusion principle, and by an attractive Van der Waals interaction at large
distances, which depends heavily on the polarizability of each atom. This interaction is empiricallydescribed by the Lennard-Jones potential [105], which has the form (for two neutral species):"V (R) = 

R0
R

12


−2

R0
R

6 #
(4.11)The Lennard-Jones parameters are known for Rb-Ne collisions, but the calculation is simplified when we consider that the collision energies, given by Kb T , are only in the range of 2 − 6 meV(that is, 25-70 K). At these energies, the atoms do not penetrate to small R, so that only the long

66
range term need be considered, and the potential takes the form

V (R) = −Cw
R6

(4.12)

where Cw is the Van der Waals constant. For a potential of this form [106] uses quasiclassicalscattering theory to show that the cross section σ is given by


σ=A

Cw
~v

a
(4.13)

Where v is the collision velocity, and a and A are dimensionless constants that depend only
on the power of the potential. For a 1/R6 potential A = 8.08278 and a = 25 . This result is valid aslong as many collisional angular momenta contribute to the cross section so that the summation
over partial waves required by the quantal calculation ([106]) and be converted into an integral.
From a classical perspective, this is because the particle cannot penetrate into the center of thepotential, because the impact parameter is too high, meaning the particle only sees the long-range
interaction. This condition can be expressed as l >> 1, where l is [106]µCw k 4>> 1
~2

(4.14)In Eq.4.14, µ is the reduced mass of the colliding particles, and k is the wavenumber of therelative motion. Eq.4.14 is equivalent toE 2 >>~6,
4µ3 Cw(4.15)

and which in our case results in E >> 10−6 eV. Another, more strict, condition requiresthat the particles remain far enough apart that the potential really does have Van der Waals form.
This requirement can be expressed as


d >>

µCw
~2 k

1
5

(4.16)

67
The parameter d is of the same order as R0 in Eq.4.11. For the Rb-Ne interaction this resultsin E < 37meV . The interaction energies for our experiment fall comfortably within these limits.
In Fig.4.12, we show the scattering cross sections for Rb with three different buffer gases- He,
Ne, and Ar, with vertical lines showing typical operating temperatures for that gas. These crosssections are much larger- almost an order of magnitude for Rb- than those generally assumed.
Figure 4.12: Scattering cross sections of Rb with different noble gases, plotted on a log-log scale.
The scattering cross section of Rb with Ne is about ten times larger than what is generally estimatedto be for a wide range of molecules. At 590 K This calculation is 18% larger than the value measuredby [107], who estimated their error at 10%. The measurement in [107] provides only a lower limiton the Rb-Ne scattering cross section.

In this case the large scattering cross section is probably more due to the Rb than the Neon.
Although neon is not very polarizable, being a noble gas, Rb is extremely polarizable because of its
one valence electron[108], which causes the potential to be more attractive than the one we would
expect for a Li-Ne interaction or, as a limiting case, a Ne-Ne interaction. [109] measured the Li-Ne
cross section for thermal energies, from which they extracted a Van der Waals constant, and [110]did the same for Ne-Ne. We are concerned with this mainly so that we can extrapolate what theinteraction might look like for molecule-neon scattering, since we will eventually be dealing with

68
large, rotationally hot, linear carbon chains in later chapters whose scattering cross section withneon we would at least naively expect to be big. As an example of molecule-neon scattering [111]measured Lennard-Jones parameters for acetylene-neon, for which we also plot cross sections in
Fig.4.13 The Cw parameter for C2 H2 (averaged over the approach angles, as would be reasonable
for a rotationally hot molecule) is quite small, again due to the fact that C2 H2 is not very polarizable. However, for a polar molecule it could be possible that the collision cross section becomes
more significant. Lennard-Jones parameters have been measured for HBr, HCl, and H2 O, and thecalculated cross sections are shown in Fig.4.13. We have also plotted the cross sections for large
carbon clusters as a limiting (albeit nonpolar) example.
Figure 4.13: Calculation of scattering cross sections using Eq. 4.13, using Van der Waals constantsfrom [112],[113], [114], and [115].

These cross sections are not significantly larger than that for Rb-Ne scattering. It could
be that averaging over rotation misses some of what is going on, although this should be a good
approximation if the timescale of the collision is fast compared to the molecule rotation, which
is typical. Van der Waals constants can become really huge when dealing with polar molecules,
as in [116], although once again [116] considers scattering with alkali metal atoms. Ultimately,
the common assertion that the scattering cross section can usually be estimated as a few times

69
10−14 cm2 , regardless of molecule seems to be not unreasonable.
The upshot of these large cross sections is that, at least for the parameters of our cell, thediffusion time never gets small enough to compete with the pumpout time and thereby become an
problem for beam extraction. In fact, when measured by [100] it has usually been on the orderof tens of ms. Moreover, because the mean free path becomes so small at only moderate neon
densities the distance that a molecule has to travel in the cell before it thermalizes (translationally)
also becomes small- only a few mm [47], so that we can be somewhat confident that molecules havethermalized by the time they leave the cell.
Unfortunately, the relationship between Tpump and Tdif f no longer describes our data. Below
I show a figure similar to Fig.4.5, but in this case Eqs.4.1and 4.2 have been set to our cell parameters
and with a suitable cross section for Rb-Ne at 45 K - 6 × 10−14 cm2 .
Figure 4.14: Theoretical dependence of signal lifetime on flow rate for our cell parameters and witha more realistic Rb-Ne scattering cross section.
70
60

Time HmsL

50
40
30
20
10
0

0

20

40
60
Flow Rate HsccmL

80

100

The sorts of trends in fig.4.10 for lifetime vs flow are not unprecedented. In [101] the author
reports a signal vs flow rate plateau when looking at Ne beams seeded with ThO. What is more, in[99], very similar behavior is observed for Tdif f vs Tpump when the author switches to a neon beam.

70
The reason for the failure of our data to agree with the Tpump vs Tdif f model could possibly be thatthe assumption of uniform density inside the cell is not valid. The design of our cell (Fig.4.3) issuch that the neon flow is aimed directly at the aperture, which makes this assumption unlikely to
be true. It could be that we are building toward turbulent flow at higher flow rates which increases
extraction time while it homogenizes the density of neon in the cell. Certainly the larger scatteringcross section means that the Reynolds number, given by

Re =

2ra
,
λb−b

(4.17)(where ra is the aperture radius and λb−b is the mean free path) becomes large very quickly,
such that flow is unlikely to be laminar, especially at the high densities we are aiming for in ourcell. For our current cell parameters, R is on the order of 1000, which corresponds to a Knudsen
number K ≈ 2Re−1 = 0.002. This puts us solidly in the hydrodynamic regime, suggesting that we
at least have room to operate at lower flow rates, if achieving a laminar flow in the cell becomes
important.

Chapter 5

Matrix isolation and FTIR spectroscopy

Coupling the output of a buffer-gas beam into a Stark decelerator presents many experimental
and practical challenges, only some of which have been addressed by our simulations. We require amethod of evaluating the quality of a buffer gas beam before investing significant effort in to buildinga hexapole guide, adapting our Stark decelerator to accommodate a cold head, and devising a statespecific detection scheme for our molecule of choice, to name just a few experimental hurdles. One
way to address the detection issue is to use a “broadband” detection method, suitable for manydifferent kinds of molecules. The workhorse detection method of the Lewandowski group has so far
been ionization spectroscopy, but because this method hinges on addressing the electronic statesof a molecule it requires UV laser wavelengths, which can vary by hundreds of nm for different
molecules. For example, the relatively simple operation of switching from a molecular beam of OH
to one of NH3 requires changing the dye of our pulsed dye laser- a tedious process that can eat up
a day of work in the lab and might result in covering the experimenter with carcinogenic laser dye.
A more serious objection to this detection method is that if we are interested in characterizing a
new molecule precursor, we would be blind to any unexpected ablation products because of thehighly specific nature of ionization spectroscopy.
To address these issues, we turn to vibrational spectroscopy. Because molecular vibrational
levels are much more closely spaced [105] than electronic levels, a blackbody infrared source is easily
broad enough to interrogate the vibrational states of many different types of molecules. We havechosen to make use of FTIR spectroscopy, which gives us the additional advantage of being able to72measure absorption in all wavelength channels simultaneously.
It is true that using a high-enough energy ionization laser can ionize a broad range of molecules
which can be sorted out later by time-of-flight mass spectroscopy, but wavelengths longer thanthose in the VUV range do not have enough energy to ionize most diatomic molecules that we areparticularly interested in (NH, CH, OH)[85, 86]. What is more, for larger molecules this method
would lack the ability to distinguish isomers, whereas IR spectroscopy would be sensitive to theshifts of vibrational modes caused by the presence of various isomers in the sample.

5.1

FTIR
Fourier transform infrared spectroscopy (FTIR) works by aligning a broadband source ofinfrared radiation into a Michaelson interferometer with a moving mirror (Fig.5.1). The infraredexits the interferometer and travels to an infrared sensor. The mirror moves and produces a phaseshift, which modulates the intensity of each infrared frequency in a predictable way. Recording thesignal as a function of mirror position produces data called an interferogram that is the Fouriertransform of signal as a function of frequency. A sample may be introduced before the detector
which further modulates the frequencies in the source- the two signals can now be compared todetermine which frequencies are absorbed by the sample.

73
Figure 5.1: A schematic of our interferometer setup

moving flat mirror
changes phasebeamsplittersourceiris

elliptical mirror
focuses through irisparabolic mirror
collimates light into
interferometer

detector

elliptical mirror
focuses on detector

parabolic mirror
focuses through sample

No laser is required to be tuned to the absorbtion frequencies of the sample, which in ourcase are unknown, as we are not certain of the molecules that will be produced by laser ablation.
Scanning a tunable laser can also assure us that no absorption frequencies are missed, but has the
disadvantage that most tunable infrared laser systems such as quantum cascade lasers have only
limited wavelength range, and require much longer data collection times to scan through the entire
region of interest[68].

5.2

Infrared Intensities
Physicists who do spectroscopy who are used to dealing with cross sections and linewidths

may be unfamiliar with the IR spectroscopy concept of infrared intensity and the unit “km/mole”.

74
Infrared intensity A is defined as the integral over the frequency dependent cross section σ(ν):ZA≡

σ(ν)dν

(5.1)

A should not be confused with the intensities I or I0 , which represent signal strengths withand without the presence of absorbers, respectively. It should also not be confused with Absorbance,
which will be discussed later. According to Beer’s lawσ(ν))nl = ln

I(ν)
I0


(5.2)

substituting eq.5.2 into eq.5.1 gives

1
A=
nl



Z
ln

I(ν)
I0


dν

(5.3)

1
−1 ], or [cm]/[mol], which becomes [km]/[mole] in SI units.
which has units of [mol/cm
3 ][cm] [cm

It is worth becoming familiar with these units, as they are the default unit in which IR intensities arereported by databases such as NIST and HITRAN, and by computational software like Gaussian.

5.3

Matrix Isolation
Since we are using this experiment partially as a “buffer-gas source work” setup to test out

new molecule precursors, we are cannot be sure of producing molecules in high density. To accountfor this, we choose to deposit the beam we make in the buffer-gas cell onto a matrix isolation
window. To do this, we place an infrared-transparent window (typically CaF2 , but depending on
which wavelengths we are interested in, these can also be KBr or even NaCl) below the apertureof our cell and cool it to well below the freezing temperature of our buffer gas. The buffer gas
freezes onto the window, trapping the entrained molecules in the lattice sites (or between thelattice sites) of the resulting buffer-gas crystal. The concentration should be tuned such that it ishighly unlikely that molecules will be trapped on adjacent lattice sites, which eliminates the strong
molecular interaction broadening typical of absorption spectroscopy in solids.

75
To determine the limits on our allowed concentration, we consider first the requirement thatmolecules cannot be located on adjacent lattice sites of the neon crystal. Neon has a face centeredcubic crystal structure [117], which means that any molecule deposited on a lattice site will have
12 nearest-neighbor lattice sites. Since we want to eliminate interactions between molecules, wewould like to ensure that the nearest-neighbor lattice sites are NOT also occupied by molecules.
If molecules/atoms are deposited randomly at lattice sites, the probability of all nearest-neighborlattice sites being occupied by neon is

Pnoneighbors = (1 − C)12

(5.4)

where C is the fractional concentration of the molecule in neon. If we set this probability
to be at least 99.99% then the concentration can be at most 8 × 10−5 to prevent interactions. We
typically operate our cell with neon flows of 60 sccm, which works out to 2.7 × 1019 atoms/s. We
have also measured our ablation pulses to produce 1011 CH molecules per shot, and we ablate at 10
shots/s, meaning we produce 1012 mol/s. Therefore our concentrations for CH only work out to≈ 10−7 . The caveats of this calculation include the fact that the concentration of molecules overall
is higher, that we cannot be sure what the entrainment efficiency of the beam is, and that matrix
FTIR experiments often use concentrations as large as 10−2 , and given all these we stress that
this calculation is useful only as giving a rough order-of-magnitude estimate for when interactions
might become significant.
In principle, the entrained molecules can be deposited indefinitely, increasing the amount ofmolecules to the point where we can detect them. However, in practice the molecular beam is
impinging on the crystal at a large velocity (180 m/s), which results in fast crystallization andsmall crystal domains. These small domains can scatter away the infrared light and cause a sloping
background (since shorter wavelengths are scattered more easily), Fig.5.2.

76
Figure 5.2: A spectrum showing wavelength-dependent scattering as a function of deposition time.
The slope and offset seem to grow linearly with time, but this is likely because of small dynamic
range.
A b s o r b a n c e S ig n a l S c a t t e r

S lo p e o f S c a t t e r v s D e p o s it io n T im e

0 .9

O ffs e t o f S c a t t e r v s D e p o s it io n T im e

3 6

0 .5

0 .0 0 0 2 5
3 5

0 .7
3 1
3 0

0 .3

in te rc e p t

3 2

0 .0 0 0 2 0s lo p e

3 3

a b s o rb a n c e (b a s e 1 0 )s in g le b e a ms ig n a l (a rb .)

0 .4
0 .8

3 4

0 .0 0 0 1 5

0 .2

0 .1
0 .0 0 0 1 0
0 .0

0 .6

2 9

0 .0 0 0 0 5

2 8
2 2 0 02 4 0 0

2 6 0 02 8 0 03 0 0 03 2 0 0p h o to n e n e rg y (c m

3 4 0 0-1

3 6 0 0-0 .1
03 8 0 0

5

1 0

1 5

2 0

2 5

3 0

3 5

0

5

d e p o s itio n tim e (m in )
)

1 0

1 5

2 0

2 5

3 0

3 5

d e p o s itio n tim e (m in )This scatter in principle sets a lower detection limit on the concentration of molecules inneon, but is difficult to quantify, as it depends strongly on the temperature of the window, theneon flow rate, and the velocity of the beam.
Although the lower limit on concentration due to scattering is difficult to analyze, we can set
a lower detection limit on our CH production efficiency. For the calculations below, we will assume
a typical linewidth for transitions to be 1 cm −1 , which is typical for matrix isolation experiments[25]. To begin, we can approximate the integral in Eq.5.3 as



Z
ln

I0
I



Z
dν =

ODdν ≈ OD∆ν,∆ν = 1 cm−1

A complication is that our spectrometer measures base-10 optical density, i.e.


OD10 = Log

I0
Iν


(5.5)

We solve Eq.5.3 for n, and include conversion coefficients so we can use A in km/mole and
OD10 . Units are included for clarity.

n[cm−3 ] =Na [mol/mole] ln(10) OD10 1[cm−1 ]105 [cm/km] l[cm] A[km/mole]

(5.6)

77
where n is number density in mol/cm3 , Na is Avogadro’s number, and l is the crystal
thickness.
We assume that we consistently make the same number of CH molecules, which, as previously
mentioned, is 1011 mol/pulse. In this case it is convenient, instead of finding the minimum molecule
density, to find the minimum number of absorbing molecules. The most optimistic estimate assumes that all CH molecules are deposited inside the IR beam detection volume. Multiplying by
2 πl, where ra detection volume Vdetect = rmin
min is the outer diameter of the infrared beam at its

focus, we haveNabsorb =Na ln(10)OD10 1 2
πrmin
105 A

(5.7)

The noise of our spectrometer ∆OD10 is about 2 × 10−4 , the infrared intensity of the CH
ground state vibrational transition of is variously estimated to be ≈ 150 km/mole, and the IR beam
size at the focus is 4 mm ø. Therefore, to achieve a signal-to-noise ratio of 1 we need 2.32 × 1012
CH molecules. Assuming we create 1012 mol/s, the number of absorbers is reached after just a
few seconds.
The most pessimistic estimate would assume that the CH molecules were deposited overthe entire CaF2 surface, which has a radius of 2.54 cm. In this case the required number of
CH molecules becomes 3.74 × 1014 absorbers, which we would deposit after 6 min. The required
deposition time likely lies within these two limits.

5.4

Contaminants and Background Handling
The path of the infrared beam must inevitably pass through some amount of air outside of

the vacuum chamber, which produces a background infrared signal. A characteristic spectrum isshown in Fig.5.3.

78
Figure 5.3: A typical background signal from our spectrometer. The IR beam is being aimed
through the vacuum chamber and the deposition window.
7 0

B a c k g r o u n d I n te n s ity ( A r b .)

6 0

H

5 0

2

O

b e a m s p litte r
ic e
h y d ro c a rb o n s

4 0

C O
3 0

H
2

O

2

2 0
1 0
0
1 0 0 0

1 5 0 02 0 0 02 5 0 03 0 0 0p h o to n e n e rg y (c m-1

3 5 0 04 0 0 0)The strongest lines we see are caused by the vibration-rotation spectrum of CO2 . The lines are
centered about the energy of the antisymmetric stretching mode, and produce two bands governedby the selection rule for transitions between rotational energy levels for linear molecules:∆J = ±1,(5.8)

which holds if there is no change in vibrational state [105]. This rule gives rise to tworotational bands- the P branch (∆J = −1), and the R branch (∆J = +1), and the spacing ofrotational states in each band is given approximately by [68]:EJ − EJ−1 = BJ(J + 1) − BJ(J − 1) = 2BJ(5.9)

Centrifugal distortion caused by coupling of vibration and rotation means that the spacingof both bands is not exactly the same. Because CO2 remains linear in its antisymmetric stretch
mode (i.e. it does not bend) the Q branch (∆J = 0) is forbidden. The CO2 lines we see are shownin fig.5.4

79
Figure 5.4: A typical background signal from our spectrometer. The IR beam is being aimed

B a c k g r o u n d I n te n s ity ( A r b .)through the vacuum chamber and the deposition window.

5 0

4 0

2 2 5 02 3 0 0p h o to n e n e rg y (c m

2 3 5 0-1)

The two other sets of vibration-rotation bands that we see are H-O-H bending modes andO-H stretching modes of water. Because water is nonlinear, its vibration-rotation bands are notnearly as symmetric as those of CO2 , but we can still be confident that this is gaseous H2 O becauseof the line spacing.
In typical FTIR experiments, purging the inside of the spectrometer and the out-of-vacuum
beampath is standard practice. We do purge the inside of our spectrometer with dry nitrogen,but because the vacuum chamber fits very snugly inside the spectrometer sample compartment wecannot purge the rest of the beam path very well. We are not overly concerned with these lines since
they do not overlap with the molecule transitions we will be looking for. In fact the presence of theserotational bands is useful in separating out contributions from gas-phase molecules outside of thevacuum chamber and in-chamber contaminants, such as ice. The broad ice feature is due to once
again to the water O-H stretch mode, but shifted from the effect of hydrogen bonding and broadened
from collisions/interactions. If ice builds up significantly on the crystal, the experiment must be
warmed to room temperature so that the water can be vaporized and pumped out. Ice buildup
tends to happen because the vacuum chamber is continuously roughed, to prevent overpressures80
during crystal cleaning. However, as the cryopumping of the cryocooler is extremely powerfulenough to reach base pressures of 5 × 10−8 Torr- the comparatively weak roughing line tends toact more like a leak for contaminants like water vapor. For our experiment, ice buildup becomessignificant on timescales of about 1 month.
For molecules trapped in the matrix, rotational lines are generally frozen out. We occasionallydetect the presence of contaminants like solid CO, CO2 , and H2 O, which we can assign to condensed
phase contamination because of the presence of only vibrational modes (Fig.5.5).
Figure 5.5: Signatures of contaminants on the crystal surface. Such contamination can be avoided
by evacuating the experiment chamber before cooling with a turbo pump, and not relying solely
on the cryopumping ability of the cold head.
C O

c o n t a m in a tio n

HO

c o n t a m in a t io n0 .0 6a b so rb a n c e (b a se 1 0 )0 .0 2a b so rb a n c e (b a se 1 0 )2

0 .0 10 .0 40 .0 20 .0 00 .0 02 1 0 02 1 5 0p h o to n e n e rg y (c m

2 2 0 0-1)

3 0 0 03 5 0 0p h o to n e n e rg y (c m

4 0 0 0-1)

Another extremely irritating aspect of the background spectrum are the broad lines locatedaround 2900 cm−1 (Fig.5.6). These seem to be a feature of the spectrometer and are, according
to the good people at Thermo-Fisher, “some kind of glue” on the beamsplitter. This part of thespectrum is the C-H stretch region, and most hydrocarbons would show up here. The broadnessof the lines does indicate some kind of condensed-phase material, and they are present even whenthe entire beam path is fully purged and no sample obstructs it.

81
Figure 5.6: Lines due to glue in the beamsplitter
5 5

B a c k g r o u n d I n te n s ity ( A r b .)

5 4
5 3
5 2
5 1
5 0
4 9
4 8
2 8 0 02 8 5 02 9 0 02 9 5 0p h o to n e n e rg y (c m

3 0 0 0-1

3 0 5 0)The last background feature that is important to take into account is the overall intensity
envelope, which is a function of the spectral range of the IR lamp, as well as the size of the aperturein Fig.5.1 (diffraction around the aperture means that small aperture settings begin to cut out the
far infrared).
We do not have a way of moving the deposition window out of the beam of the spectrometer,
which means that we can take only one background every time we grow a crystal. We can movethe spectrometer away from the vacuum chamber, but this is not ideal since we are not properly
imaging the lamp intensity and the way it interacts with the three CaF2 windows. Deposition with
only one background trace works well for us because we have not had to look for lines in the CO2
and water regions.
The background signal itself is measured in arbitrary units and is proportional to the voltage
output of the IR detector. The spectrometer software calculates absorbance Abs and transmittanceT according to

82



S
B



× 100

B
,
Abs = lnS
T =

where S and B are raw and background signals respectively, in arbitrary units.
In addition to this automatic background subtraction performed by the spectrometer, we also
subtract away baselines due to scattering and shoulders of broad features. For all spectra shownin later parts of this thesis we perform this subtraction in order to be able to report just the peakheight of relevant transitions, to isolate the contributions of just the molecules we are interested in.

5.5

Matrix FTIR of NH3 Clusters
As both buffer gas beams and matrix FTIR are new technologies for our lab, we first tested

our matrix isolation setup with a supersonic beam of ammonia (NH3 ). A schematic of the setup is
shown in Fig.5.7.
Figure 5.7:

A schematic of a test setup to image ammonia clusters in a matrix. The source is asupersonic beam of ammonia seeded in argon at a concentration of 0.5%, which impinges onto a
CaF2 window cooled to 14 K. The beam makes use of a skimmer, which is not shown.

The experimental demands of this intermediate measurement are rather lighter than for a83
buffer gas setup. Firstly, we can use argon as the cooling gas instead of neon, which a much higher
melting point (84 K compared to 25 K). Secondly, we only have to cool the window and do nothave to maintain a temperature difference between two cryogenically cooled objects, as we would
for a buffer gas setup (discussed later in this chapter). Finally, the source allows us to prepare
an exact mixture of gases whose concentration is controlled, while the choice of ammonia obviates
the necessity of synthesizing the molecule from a precursor and will give us the opportunity ofobserving molecule clusters with strong vibrational transition strengths.
One other experimental perk of this setup is the fact that we do not have to use a black bodyshield to adequately cool the deposition window. This increases our optical access to the sample,
and allows us to take pictures of the crystal (Fig.5.8).
Figure 5.8: A picture of a crystal of ammonia clusters in an argon matrix.

The vibrational spectrum of NH3 in an argon matrix has been measured [118]. We show oneof our own spectra with line assignments in Fig.5.9.

84
Figure 5.9: IR spectrum of NH3 clusters in argon. Line assignments are from [118]. These spectra
were gathered after depositing NH3 for 60 min and firing the valve at 10Hz. Observed lines aretabulated in Tab. 5.1.
6 1 m in u te s
m o n o m e r
d im e rtrim e r
a g g re g a te s
C o m p le x e s w ith C O

a b so rb a n c e (b a se 1 0 )

0 .1

2

a n d w a te r

0 .0

- 0 .13 1 5 03 2 0 03 2 5 03 3 0 0p h o to n e n e rg y (c m

3 3 5 0-1)

3 4 0 03 4 5 085Line Position (cm−1 )NH3 Cluster

Vibrational mode

3239

monomer2ν43447

monomer

ν3

3310

dimer

ν1

3400

dimer

ν3

3212

trimerν1

3306

trimerν1

3391

trimerν3

3199

aggregate

3207

aggregate

3232

aggregate

3304

aggregate

3391

aggregate

Table 5.1: A summary of the vibrational modes of ammonia clusters observed after deposition witha supersonic jet of ammonia seeded in argon into an argon matrix. Line assignments and modes
are from [119].

The cluster lines exhibit significant broadening- at a concentration of 0.05% we are nowhere
near below the concentration limit given by Eq.5.4, and because of ammonia’s lone electron pairinteractions can happen over a longer range. This also causes ammonia to cluster more easily,and clusters have larger IR intensities because of the ease with which they deform, which causes
large changes in the magnitudes of their dipole moments. All this makes monomer lines difficult toisolate. We do, however, manage to pinpoint one monomer mode far away from the cluster modes
for which IR intensities are known- the NH3 monomer mode at 3447 cm−1 . This mode exibits
a 0.087% shift away from the gas phase value, which is well within the expected bounds for Ar.
The height of this peak is 0.036OD10 , and its IR intensity is given as 7.1 km/mole, meaning that
we have deposited 8.8 × 1015 NH3 monomers within the detection volume. The OD of this peak

86
was shown to decrease for longer deposition times while other peak heights increased, suggestingthat the monomers were forming clusters within the matrix, which is not surprising, given theconcentration.
Figure 5.10: Traces showing IR spectrum of NH3 clusters in argon at two different times. At someconcentration monomers begin to react with each other to form clusters.

0 .1 0a b so rb a n c e (b a se 1 0 )6 1 m in
1 8 6 m inc lu s te rs

0 .0 5m o n o m e r

0 .0 03 4 2 03 4 4 0p h o to n e n e rg y (c m

-1

)

87

5.6

Isolation of Buffer Gas Beams

Figure 5.11: Apparatus schematic for isolating a buffer gas beam. The molecules are introduced
into the cell via 532 nm ablation and are extracted by neon flow through an aperture, after which
they are deposited onto an isolation window.

88
Figure 5.12: A picture of the apparatus modified to deposit buffer gas beams onto a matrix isolation
window. In the figure one can see the strong coupling of the window to the second stage and theweaker coupling of the second stage to the cell.

We show the realization and schematic of a setup that combines the elements required tocreate a buffer-gas beam and isolate it in a matrix. The setup shown in Fig.5.11 is similar tothat of Fig.4.1, except that we have modified the cryopump to be used as a deposition window
for a noble gas matrix seeded with the contents of our molecular beam. For the purposes of IR
transparency, it is made, like the sides of our vacuum chamber, out of CaF2 . Most groups who domatrix FTIR experiments use other materials like CsI or KBr. These materials are too soft andhygroscopic for us to use, since our windows require frequent cleaning and the only way to clean a

89hygroscopic window is by polishing 1 it. What is more, CaF2 has desirable thermal conductivity
properties. However, its cutoff in light transmittance near 6 µm means that we are insensitive tothe “fingerprint region that characterizes the low frequency vibrations of complex molecules.

5.6.1

Cryogenics

The deposition window should be as cold as absolutely possible, which requires the use of a
blackbody shield. The cryocooler is capable of dissipating 15 W of power when the second stage
is held at 10 K, and the power delivered from blackbody radiation at room temperature is 420
W/m2 . This limit theoretically allows us to leave a huge amount of area open to lab radiation, but
in practice poor conductance to all the components mounted on the second stage means that thedifference between full radiation shielding and none can be as large as 10 K. Inside the blackbody
shield, we see the second stage, which houses the cell and window. One complication of thisexperiment is that only one cold head is available for cooling both the cell and the window, whichmust be at very different temperatures. The cell must be hot enough so that there is no dangerof freezing the neon onto the cell walls, whereas the window must be as cold as possible. It is
tempting to think that the temperature of the window need only be below the freezing point ofneon, at 25 K, but in fact the neon vapor pressure is still significant at temperatures below 25 K,
enough that crystals will not immediately begin to grow at 25 K. What is more, at intermediate
temperatures, the crystal is not “rigid,” meaning that the bonds between atoms are not strong
enough to isolate trapped molecules, which migrate through the crystal [69]. Therefore, we must
actually cool the window to at least 1 K below the annealing temperature, which is reported as
10-12 K for neon[67]. We could relax this condition by working with argon, which has an annealing
temperature of just 40K, but argon does not adequately cool the molecular beam. We could also
relax this condition by cooling the cell below the melting point of neon as it still has appreciable
1

Subsequent students take note- do not try to polish CaF2 ! Even though it is much more robust and lesshygroscopic than other salts, the polishing setup- usually an abrasive sandwiched between two lapping plates- uses
water as a lubricant. The abrasive creates a large surface area for the water to attack, and the result will be a cloudy
optic. In a pinch, hand polishing can work using high-grit sandpaper and acetone as the lubricant, but it is better tojust live with the scratches.

90
vapor pressure there (Fig.5.13), but this makes it difficult to estimate the density of neon, andit would be preferable to work above this point. Furthermore, as we will see, controlling the celltemperature in our apparatus is a complicated proposition. The cell and window temperature aremonitored by diodes from Lake Shore Cryotronics and high power resistors are mounted on bothcomponents to allow us heat them and adjust their temperature quasi-independently.
Figure 5.13: The vapor pressure of neon. Data from [120]. We could conceivably operate our buffer
gas cell in temperature regimes below the melting point, but in that case the equilibrium pressure
is influenced by the competition between neon in and out flow, and the sticking probability of neon
with the walls. In these regimes the pressure should be measured directly to determine the neon
density in the cell
V a p o r P re s s u re o f N e o n
1 0 0

P re s s u re (to rr)

1 0

1ExpGro1Model

y = A1*exp(x/t1) + y0

Equation

0 .1

ReducedChi-Sqr3.3565

Adj. R-Square

0.99865
Value

B

Standard Error

y0-6.26527

0.99865A1

0.00206

5.60843E-4

t1

2.03460.04927

0 .0 1
1 6

1 8

2 0

2 2

T e m p e ra tu re (K )We attempted to tune the temperature of the cell by inserting a copper block in between
the cell and the second stage. The laws of heat conduction suggest that the temperature difference
between the second stage and the cell should go like the area of the copper block[121], that is

∆T =

QL
,
−kA

(5.10)

where Q is the heat dissipated, k is the conductivity, and L and A are the length and cross91
sectional area of the copper block. However, as we show in Fig.5.14, changing the size of the block
did almost nothing to change the final ∆T of the cell and second stage.
Figure 5.14: The intercept of the cell temperature vs second stage temperature as a function ofcopper block area. The slope of this dependence should remain constant while the intercept should
go like the square of the copper block area. This is not borne out, likely because the force which
compresses the block is not constant.
5d e lta T in te rc e p t (K )

4

3

2

1

0
0 .0

0 .1

0 .2

0 .3

0 .4

0 .5

2

C u b lo c k a re a (in )This is likely due to the difficulty of controlling the force with which the cell compresses thecopper block. In future incarnations of this experiment, it may be worth it to redesign the cellhousing in such a way that this force can be measured and fine-tuned. Lacking this, we ultimately
had to resort to trial and error to cool the cell to a temperature that was cold enough to properly cool
the entrained molecules and above the melting point. We ultimately ended up with a configurationthat could sustain the temperature differences shown in Fig.5.15

92
Figure 5.15: Temperature difference sustained by the Cell and cryopump/Deposition window. This
curve is not a constant of the apparatus and fluctuates somewhat depending on how well allcomponents are tightened after modification and reassembly.
1 8

C ry o p u m p te m p e ra tu re (K )

1 6
1 4
1 2
1 0
8
6
0

2 0

4 0

6 0

8 0

1 0 0

C e ll te m p e ra tu re (K )We also ran into cryogenics problems with the deposition window. As we mentioned, thetemperature of the window must reach ≈ 10 K for crystal growth. Our deposition window islarger than usually used for matrix isolation (2”) and the temperature sensor is mounted on thecopper housing near its edge. According to this sensor, the copper housing was well within thecorrect temperature range (see Fig.5.15). However, during this time, we consistently failed to growa crystal. After mounting a temperature sensor onto the window center it turned out the centerof the window was not equilibrated with the edge, which pointed to poor contact with the window
housing. At this point, the window was mounted in the copper housing according to Fig. 5.16,
using two indium gaskets.

93
Figure 5.16: Cross section of old housing of the deposition window. A copper holder supports thewindow which is secured with a copper face plate and brass screws. Two indium gaskets actually
made the contact between the copper housing and window poorer and failed to equilibrate thewindow center and edge.

These gaskets had to be compressed with extreme care, as any kind of uneven force would
tend to fracture the CaF2 crystal. Ultimately, we discovered that two gaskets were worse in termsof temperature equilibration than one. The best results were obtained by heating the entire copper
housing, indium gasket, and window to the melting point of indium (157 C), and allowing thewindow to sink down into the melting gasket, and thereby matching the two surfaces perfectly.2
Although the two surfaces now conform, the indium does not actually stick to the copper, so we
add a viton gasket above the window to compress it to the bottom of the holder during installation.
Figure 5.17: Cross section of new window housing. This configuration gave the best results forequilibrating the window and copper holder temperatures, even though contact with the retaining
ring surface area has now shrunk to nothing because of the viton o-ring.

This gasket of course loses elasticity at cryogenic temperatures and is only used to prevent
separation of the window and copper when the window is being mounted. With this procedure the2
The window must be heated along with the copper holder and indium wire, since dropping the window into a
hot copper holder will cause it to shatter from heat shock.

94
edge of the window and the center finally became equilibrated and we were able to grow a crystal.

Chapter 6

Matrix FTIR of a Buffer-Gas Beam of Carbon Clusters

Detecting CH in a matrix FTIR setup can be a difficult proposition because of the reactivity ofthe molecule, the “average” strength of the transition, and the possibility of mixing the vibrationalsignal up with the CH-stretch mode of the precursors. We can learn a lot about our apparatus byattempting a simpler molecule instead. In our case, we chose to make a molecular beam of carbon
clusters, made by ablating a graphite target.
Ablation of graphite will produce many different carbon clusters, some of which may take theform of long chains[122, 123]. Molecules that consist of long chains are likely to have large transition
strengths, since vibrational transition strength is proportional to the change in dipole moment of
the molecule, and since linear molecules can have bending modes in which the dipole momentchanges more than for a compact molecule. Indeed, the transition strength of some molecules
has been measured to be on the order of thousands of km/mole [124, 125]. The structure andvibrations of small [124, 126] and large [127] clusters are known, and have been measured in matrices[123, 128, 129], making for convenient line assignment. This makes carbon clusters a good molecule
to work with for characterizing our apparatus.
Laser ablation has been successfully used to create carbon clusters in the past[122, 130], andwe were able to reproduce the creation of carbon clusters ablating graphite. We mount a graphitetarget into the sample holder and ablate at 532 nm using 4 mJ/pulse power. The spectra weobserve are affected by the scattering background due to crystals of poor optical quality (we showa photo in Fig.6.1, but we subtract it in order to determine relative signal strength. A spectrum is96shown in Fig.6.2.
Figure 6.1: A view of the neon crystal through the vacuum chamber and black body radiation
shield. The fast crystallization of the neon on the window creates an opaque neon matrix (which
is nonetheless transmissive enough for us to see absorption signals.

97
Figure 6.2: FTIR spectrum of carbon clusters embedded in neon. A graphite sample was ablated
at 4 mJ/pulse while neon was flowed through a buffer gas cell at 70 sccm. The cell temperature
was 34 K.

A b s o rb a n c e (b a s e 1 0 )0 .0 0 4

0 .0 0 3

0 .0 0 2

0 .0 0 1

0 .0 0 0

1 9 0 02 0 0 0p h o to n e n e rg y (c m

6.1

2 1 0 0-1)

Peak Growth
We initially expected that peak height would grow linearly, as more and more clusters were

deposited onto the crystal. However, we observed that the peak height would plateau on a timescaleof about 15 min (Fig.6.3

98
Figure 6.3:

The height of the C9 (ν6 ) peak at 2010 cm−1 as a function of deposition time.

The

plateau in signal should be caused by a drop in cluster production, since the peak height is nowhere
near 100% transmission.
0 .0- 0 .22 0 1 0 p e a k a m p l i t u d e ( ∆T )- 0 .4- 0 .6- 0 .8- 1 .0- 1 .2- 1 .4- 1 .6- 1 .8
0

2

4

6

8

1 0

1 2

1 4

1 6

d e p o s itio n tim e (m in )We suspected that the signal plateau was caused by “exhaustion” of the target by the ablation
laser. Most groups who create molecules via ablation address this by rotating or translating theablation target, but working at cryogenic temperatures forbids the use of any kind of moving
target housing. Although we tried to raster the position of the laser spot by hand, it was difficult
to do this consistently, and we eventually began to observe decreased signal sizes after weeks ofoperation. When we disassembled the target the surface appeared to have undergone significant
chemical changes (Fig.6.4)

99
Figure 6.4: A picture of the surface of the graphite target after undergoing many hours of ablation.
The target is 5 mm across, and the laser is focused to about a 50 um spot size.

It is interesting that many of the features on the target surface are much larger than the laser
spot size, pointing to the face that only a little laser fluence is required to “destroy” the target
through heating. Many groups who ablate targets often have to resort to moving either the target
or ablation laser in order to present a fresh portion of precursor to the laser spot. In our case,the low temperature of the cell prohibits easy sample movement, so moving the laser spot is our
only option. We installed stepper motors on the mirror mount just before the lens and caused thelaser spot to move across the sample during deposition. This had the effect of making line intensity
grow, if not linearly, then on a much longer timescale than previously. This seems to have affected
all vibrational modes uniformly, but new lines appear as they emerge above the noise. A spectrumof clusters with scanning is shown in Fig.6.5. We summarize the modes we observe in Tab.6.1.

100
Figure 6.5: FTIR spectrum of carbon clusters embedded in neon, now with ablation laser scanning
across the sample. A graphite sample was ablated at 2 mJ/pulse while neon was flowed througha buffer-gas cell at 60 sccm. The cell temperature was 34 K.
0 .0 5A b so rb a n c e (b a se 1 0 )0 .0 40 .0 30 .0 20 .0 10 .0 0
1 6 0 0

1 8 0 02 0 0 0p h o to n e n e rg y (c m-1

2 2 0 0)As we mentioned in Ch. 5, part of our motivation behind using matrix isolation to detectmolecules is the potential to improve our signal to noise by continuously depositing molecules in
the isolation crystal and waiting for adequate peak growth. It is therefore heartening that, barring“exhaustion” of the ablation sample, the carbon cluster vibrational signals do indeed continue togrow, and that we are not yet limited by scattering of the incident beam, or by other effects likecrystal sublimation.

101Line Position (cm−1 )Molecule

Vibrational mode

IR intensity (km/mole)

1603

C9

ν7

1813

C13

1853

C11

ν8

1897

C7

ν5

1939

C11

ν7

1958.7

C6

ν4

1073[123]

2004

C12

2010

C9

ν6

6520[123]

2036

C3

ν3

772[123],612[131]

2068

C8

ν5

1989[123]

2081

C9

ν5

704[132]

2135

C7

ν4

4652[123]

2166

C5

ν3

1649[131]2539[123]394[123]1307[123]

Table 6.1: A summary of the vibrational modes of carbon clusters observed after ablation withlaser scanning an deposition onto a cold window. IR intensities are quoted where available.

Taking into account the IR intensities reported for carbon clusters in [123] we can extract
the relative abundances of each cluster in each vibrational mode. These are shown in fig.6.6

102
Figure 6.6: Peak absorption of each cluster scaled by the infrared intensity and normalized to thelargest abundance. It should be noted that calculations of the IR intensity of the C9 ,ν6 mode haveyielded results different by many orders of magnitude. [132] measured the intensity relative to theheight of the peak at 2010 cm−1 , which was used to calculate the abundance of C9 from this mode,
although there is clearly some error.
C a rb o n C lu s te r P ro d u c tio n b y A b la tio n
1 .0

C 6 , ν4re la tiv e a b u n d a n c e

0 .8

0 .6

C 9 , ν6

C 9 , ν7

C 3 , ν3

C 9 , ν50 .4

C 7 , ν5

C 8 , ν50 .2

C 5 , ν3
C 7 , ν40 .0
1 6 0 0

1 7 0 0

1 8 0 0

1 9 0 0p h o to n e n e rg y (c m

2 0 0 0-1

2 1 0 02 2 0 0)It seems that ablation produces similar amounts of each type of cluster. Using the resultsof Ch. 5 to extract the number of absorbers we find that we make 2 × 1013 C6 molecules (mostabundant) and 1.6 × 1012 C9 molecules (least abundant). We know from our work in Ch. 2 that we
make large amounts of C2 , but as its vibrational modes are not IR-active, we are not sensitive tothem. Studies of carbon cluster production with laser vaporization have been conducted, but haveachieved very disparate results in the relative abundances of the clusters produced [122], [133] (atfirst glance these sources use much larger ablation energies, but they are unfocused, whereas we
focus 2 mJ/pulse onto a small spot size).

103

6.2

Reactions
Occasionally, if there is a leak in the vacuum chamber or if the neon lines have not sufficiently

been pumped out, there can be contamination of the system with other gases. Early on in our
carbon cluster investigations, we deposited a crystal that had significant CO2 contamination. As
discussed in Ch.5 a crystal is below the annealing temperature will be rigid enough to prevent
molecule migration and reaction, but since we have a heater on the window holder we can control
this to some extent. In this case, after depositing the CO contaminated carbon cluster beam, weheated the crystal to just above the annealing temperature at 10 K, and then re-froze it to takeanother spectrum. The results are shown in Fig.6.7.
Figure 6.7: Reactions in a crystal of C clusters in Ne with CO contamination, after annealing to
11 K and re-freezing. The CO peak is completely depleted and new peaks appear, although wewere unable to assign them with certainty. We believe there were also some reactions involving justclusters, as some cluster peaks are partially depleted while the C9 peak grows. No deposition or
ablation occurred during the annealing/re-freezing process.
0 .0 2A b so rb a n c e (b a se 1 0 )d e p o s ite d c lu s te rs
a fte r a n n e a lin g

C 9
C O

C 11

C 7

C 5

C 7

C 11
C 6

C 3

C 8

0 .0 0
1 8 0 0

1 9 0 02 0 0 02 1 0 0p h o to n e n e rg y (c m-1

2 2 0 0)

Unfortunately, we were unable to assign many of the peaks which participated, but it seems
that at least some of the carbon clusters combined or fragmented to form C9 . This instance was not104really a controlled-enough experiment to be able to characterize any one reaction, but we believe
this is a good proof-of-principle case that reactions can be studied using this source with a matrix
isolated environment. Better candidates for such work might include simpler molecules with fewer
vibrational modes with reaction partners whose abundance in the crystal could be more precisely
controlled. In particular the CH+O2 reactions discussed in Ch.2 would be almost ideal because ofCH’s one vibrational mode, although the amount of O2 would have to be estimated, since O2 is
not IR active.

6.3

Conclusions and Further Work
We have created a buffer-gas beam of molecules, deposited it into a neon matrix, and observed

the vibrational spectra of the constituents. The apparatus is promising for its ability to characterize
the content of molecular beam output, and is therefore an excellent source work experiment, since it
has the capability to identify many beam constituents without the experimenter knowing they would
be present beforehand and testing for the existence of each one with a species-specific protocol.
We have also shown that this is a suitable environment for observing reactions of molecules on thematrix surface.

6.3.1

Characterization

This is of course just the beginning realization of this experiment. Much more work needs
to be done toward stabilizing molecule signals and characterizing the experiment parameters. One
problem that we consistently run into is our lack of knowledge about how radicals are distributed
over the window surface. Knowing the angular distribution is vital for coupling such a beam into a
decelerator, since it sets limits on the hexapole parameters, ultimate molecule density per well, etc.
It certainly looks as though the entire window is covered, but we suspect that much of the neonthat flows out of the cell does not actually stick to the window on its first collision, but instead
diffuses through the vacuum chamber and re-condenses on all the coldest surfaces. Technically the

105
angular distribution of molecular beam density n should be given by [47]n(R, θ) = n(R, 0)cos

2



πθ
2φ


(6.1)

where n(r, 0) is the longitudinal density of the beam and φ is the opening angle of the beam,
usually ≈79◦ . However, we are unable to verify this because we do not have the capability of tuning
the IR beam alignment in a controlled way. Because the beam output is that of a lamp an not alaser, it is difficult to contain all of the beam energy with conventional optics. What is more, once
optics are used to direct the beam out of the spectrometer for alignment control, it becomes much
more difficult to purge the beam path, causing significant problems with background subtraction.
However, all of these difficulties amount only to design challenges which could in principle beovercome to allow us to scan over the window surface and map out the dependence of molecule
density on angle.
Another aspect of this experiment in need of characterization is the efficiency with which we
produce molecules with ablation. Clearly ablation has the potential to make interesting molecules
at rates high enough for us to see them. However, when we attempted to look for CH with thisexperiment, we were unable to detect it. The best way to characterize the ablation and entrainmentof molecules within our beam would be to use a precursor whose ablation products and branchingratios are known. If the ultimate goal is detecting CH, then we need to be able to see how well we
can detect molecules with very small probabilities of being created in the ablation process.

6.3.2

Reactions

The possibility of looking at reactions on the surface should be explored in more detail. The
apparatus can be modified such that the addition of a reaction partner is more controlled- thiscan be accomplished with the addition of a second, room temperature pulsed valve, or simply tube
flowing gas over the window. If a second pulsed valve is used, consideration must be given to howmuch space it will occupy, whether it will reduce the optical access of the beam, and how additional
heat load it will provide in the form of black body radiation. The tube option obviates many of

106these concerns, as it can be made much smaller, and can even be anchored to the first stage toreduce heat load (if the reaction partner does not freeze at 40 K).

6.3.3

Gas Phase Spectroscopy

One of the greatest limitations of this experiment is that it cannot tell us much about theinternal temperature of the beam. Even if we could somehow do this with vibrational spectroscopy,
trapping the molecules in the neon matrix removes information about their temperature in thebeam, and broadens and distorts transition signatures because of (admittedly weak) interactions
with the substrate. The translational and rotational temperatures can only be probed with gas
phase spectroscopy, by looking at Doppler broadening and rotation state-specific detection. Although knowing these beam characteristics is not absolutely essential for our eventual goal of
coupling a buffer-gas beam into a Stark decelerator, they are useful for conducting trapping experiments. In fact, our group is currently working on building a buffer-gas beam experiment in whichmolecules will be detected by IR absorption spectroscopy using a quantum cascade laser. The laser
will be much more sensitive to gas phase molecule densities, which eliminates the need for matrix
isolation.

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