UNIVERSITY OF CALIFORNIA SAN DIEGO
Positron Annihilation on Atoms and Molecules
A dissertation submitted in partial satisfaction of the requirements for
the degree of Do ctor of PhilosophyinPhysics
by
Ko ji Iwata
Committee in charge
Cli ord M Surko Chair
John M Go o dkind
William E Mo erner
Lu J Sham
John D Simon
Copyright
Ko ji Iwata
All rights reserved
The dissertation of Ko ji Iwata is approved and it is acceptable in quality and
form for publication on micro lm
Chairman
University of California San Diego
iii iv
Contents
Signature Page iii
Table of Contents iv
List of Figures ix
List of Tables xi
Acknowledgments xiii
Vita Publications and Fields of Study xv
Abstract xviii
Intro duction
Simple illustration of a p ositron interacting with a molecule
Background in p ositron physics
Prediction and discovery of the p ositron
Positron sources
Physics involved in the interaction of a p ositron with a molecule
Long range p olarization and dip ole charge interactions
Short range interactions r a
Potential from atomic nuclei
Pauli exclusion principle
Positronium atom formation
Annihilation
Interaction of p ositrons with solids liquids and gases
Solids
Positron mo derators
Liquids
Gases
Outline of dissertation
Overview of previous atomic and molecular physics studies us
ing p ositrons
Dense gas and low pressure exp eriments
Dense gas exp eriments
Low pressure exp eriments
Annihilation rates v
Anomalously high annihilation rates
Momentum distribution measurements
Ion mass sp ectrum measurements
Description of the exp eriments
Source and mo derator
Beamline
Positron trap
Gas handling system
Gases
Liquids and solids
Annihilation rate measurements
ray sp ectral measurements
Exp erimental pro cedure
Sp ectral analysis
Calibration and detector resp onse
Annihilation rates
Theoretical considerations
Long lived resonances
Large cross sections from the resonance collision
Results
Noble gases
Inorganic molecules
Alkanes and substituted alkanes
Alkenes
Oxygen containing hydro carb ons
Aromatics and saturated rings
Deuterated hydro carb ons
Deuterated alkanes
Deuterated b enzenes
Partially uorinated hydro carb ons
Discussion
Empirical scaling of annihilation rates
Dep endence of annihilation rates on p ositron temp erature
Recent theoretical work
Semi empirical approach
Large scale calculations for molecules
Other issues
Noble gas atoms
Repro ducibil ity of measurements
Delo calized b onds in b enzene vi
Determination of p ositron annihilation sites in a
molecule
Current state of annihilation rate studies
Concluding remarks on annihilation rate measurements
Annihilation ray sp ectra
Introduction
Momentum distribution measurements
Annihilation ray angular correlation measurements
Doppler broadened ray sp ectral measurements
Results
Noble gases
Helium
Neon argon krypton and xenon
Previous measurements from other exp eriments
Inorganic molecules
Other gases
Alkanes
Alkane alkene and alkyne
Aromatics
Fully halogenated carb ons
Partially uorinated hydro carb ons
Other organic molecules
Annihilation on inner shell electrons
Sp ectral analysis b eyond the Gaussian approximation
Discussion
Concluding Remarks
Positron annihilation with inner shell electrons in noble gas
atoms
Introduction
Exp eriment
Results
Concluding remarks for inner shell electron annihilation
Positron annihilati on in the interstellar media
Introduction
Positrons in the interstellar media
Interstellar molecules
Astrophysical p ositron annihilation simulation
Description of the exp eriment
Exp erimental results vii
Summary of p ositron annihilation in the interstellar media
Conclusion
Summary of this dissertation
Future work
Concluding remarks
App endices
A Ion gauge sensitivity calibration for gases and molecular va
p ors
BTable of physical parameters of atoms and molecules
CTable of annihilation ray sp ectra from atoms and molecules
References viii
List of Figures
Schematic diagram a low energy p ositron interacting with a molecule
Schematic illustration of p ositronium atom formation
Schematic diagram of p ositron trapping in a defect
Apparatus for measuring annihilation time sp ectra in high pressure
exp eriments
Schematic drawing of annihilation time sp ectrum in a high pressure
exp eriment
Annihilation time sp ectrum for helium gas
D ACAR sp ectra of noble gases
Schematic overview of the exp erimental setup
Schematic diagram of the source and cold head assembly
Schematic diagram of a Penning Malmb erg trap
Schematic diagram of the p ositron trap electro de structure
Gas pressure in the third stage of the p ositron trap during a
pump out cycle
Schematic diagram of the p ositron trap
Aschematic diagram of a gas handling system for test substances
that exist in gas form at atmospheric pressure
Aschematic diagram of a gas handling system for test substances
which are in liquid or solid form at atmospheric pressure
Annihilation rate data for b enzene d
ray sp ectrum of the keV line from a Sr source
tal values of Z Z plotted against Z Exp erimen
e
Theoretical and exp erimental values of Z for noble gases
e
Values of Z and structures of alkenes with six carb ons
e
Values of Z and structures of cyclohexane and substituted b ezenes
e
Ratio of Z for deuterated alkanes to those for protonated alkanes
e
Values of Z and structures of deuterated b enzenes studied
e
Empirical scaling of Z for non p olar molecules containing only
e
single b ond ix
Empirical scaling of Z for oxygen containing hydro carb ons and
e
small molecules with a dip ole moment and or double b onds
Empirical scaling of Z for alkenes ring hydro carb ons and sub
e
stituted b enzenes
Dep endence of annihilation rates of noble gases on p ositron tem
p erature
Illustration of the momentum of an annihilating electron p ositron
pair and the resulting raymomenta
Observed sp ectra from H and Ne
Annihilation ray sp ectrum from helium atoms
Exp erimentally measured ray sp ectra from noble gases
ray sp ectrum from p ositron annihilation on molecular hydrogen
ray sp ectra for p ositrons annihilating with CO and CO
The Gaussian linewidth for alkane molecules
ray sp ectrum from p ositron annihilation on uoro ethane
Fraction of p ositrons annihilating on uorine atoms in partially
uorinated hydro carb ons
rayspectrumofH
ray sp ectrum of hexane
The ray sp ectrum resulting from p ositrons annihilating on xenon
atoms
The ray sp ectrum resulting from p ositrons annihilating on kryp
tonatoms
The ray sp ectrum resulting from p ositrons annihilating on ar
gon atoms
Positron annihilation ray sp ectrum from the Galactic center
Positron annihilation ray sp ectrum from the Galactic center
using a Ge detector
Molecular structures and Z of p olycyclic aromatic hydro carb ons
e
ray line for p ositrons annihilating on mixture of hydrogen and
naphthalene molecules x
List of Tables
Parameters of the neon and tungsten mo derators and the p ositron
trap
Values of Z for noble gases
e
Measured values of Z for inorganic molecules
e
Measured values of Z for alkanes and substituted alkanes
e
Measured values of Z for isomers of p entane
e
Measured values of Z for alkenes
e
Measured values of Z for alcohols carb oxylic acids and ketones
e
Measured values of Z for ring molecules and aromatics
e
Measured values of Z for other large organic molecules
e
Measured values of Z for protonated and deuterated alkanes
e
Measured values of Z for deuterated b enzenes
e
Measured values of Z for partially uorinated hydro carb ons
e
The ray linewidths for noble gases
The ray linewidths for H
The ray linewidths for inorganic molecules
The ray linewidths for hydro carb ons
The ray linewidths for fully halogenated carb ons
The ray linewidths for partially uorinated hydro carb ons
The ray linewidths for other organic molecules
Values of from ts to various mo dels
r
The annihilation ray line shap es for argon krypton and xenon
in the static Hartree Fock approximation
Results of astrophysical p ositron annihilation simulation
A Relative sensitivities of ion gauge resp onse
B Physical parameters of molecules studied
C ray line shap e parameters from ts to two Gaussians for all
atoms and molecules xi xii
Acknowledgments
This dissertation could not have b een completed without the help of numer
ous p eople I will mention p eople who help ed me most signi cantly through the
last years of my graduate work
First of all I am very grateful to my thesis adviser Prof Cli Surko Even
though I was not always the b est student he has guided me through the pro cess
of my graduate work patiently helping me realize my p otential to b e a go o d
scientist I have learned greatly from his insight and dedication to the advance
ment of science His high standards for publications and presentation as well
as his active critiquing of his students work has help ed us tremendously My
ability to communicate in a scienti c environment has certainly b ene ted from
his help Since he was so critical in preparation of manuscripts for publications
he sometimes corrected his own mo di cations back to what they were in the
previous version It was an encouraging sign however since his b ehavior indi
cated that the manuscript was nally converging to the nal form after numerous
mo di cations He likes manycommasinmanuscripts and I thank him for all
the commas he has given me
I am indebted to our sup er p ostdo c Ro d Greaves who has b een in the lab
with me for years and patiently guided me through my thesis researchona
daily basis His dedication to our work and his ability to run exp eriments as
well as his general scienti c insight are noteworthy Iwas also impressed with
his ability to sneakily get rid of extra commas inserted in manuscripts by Cli
He will b e leaving the group at the end of the year for a new p osition and I
wish him the very b est for his future
I thank our senior technician in the group Gene Jerzewski for his exp ert
technical supp ort for the exp eriments His mastery of electronics p ersonal com
puters and every asp ect of technical matters has b een an absolutely indisp ensi
ble asset to the lab He has taught me Zen and the art of electronic maintenance
through y shing My pro ductivitywas also greatly enhanced by our daily ritual
of walking to the Grove Ca e for cups of co ee
Others in the research group in last years Chris Kurz Arthur La Porta
Mark Tinkle Steve Gilb ert SteveYamamoto Chris Lund Bill Baxter Keith
Eaton and S Z Tang have also given me supp ort for mywork
Our secretary Judy Winstead is gratefully acknowledged for her assistance
and sp eedy pro of reading of manuscripts including this dissertation
Scienti c interactions outside of our research group to ok place mainly at
conferences b ecause nob o dy else at UCSD works in my sp eci c research eld
Ihave had many delightful exp eriences meeting world class scientists at these
conferences and I appreciate them for treating me with resp ect We had a
pleasure of collab orating with Gleb Gribakin in University of South New Wales
in Sydney Australia and Peter Van Reeth and John Humb erston in University
College London UK I appreciate them for their theoretical input in the pro ject xiii
Personally I thank all my p eers and friends for giving me emotional supp ort
Esp ecially my surfer buddies Alex Burke Bernie Freisler and Neil Dilley have
stuck to the principle of the friends don t let friends surf alone p olicy and in
turn sur ng has enhanced my creativityatwork I thank mymentor in Japan
Kimiaki Nakata for encouraging me to study in the US Toward the end of the
graduate work AmyChua Yew Yew has provided me with sup erb emotional
supp ort and I acknowledge her for pro of reading this dissertation
Finally my parents are acknowledged for their continuing supp ort for my
study and my father for teachingmeawork ethic by an example
Financial supp ort of this thesis work was provided by the O ce of Naval
Research and the National Science Foundation xiv
Vita
January Born Tokyo Japan
B S Astronomy and Physics University of Arizona
Teaching Assistant University of Arizona
Research Assistant National Optical Astronomy Observatories
Research Assistant University of California San Diego
M S Physics University of California San Diego
Ph D Physics University of California San Diego
Publications
JOURNAL ARTICLES
Ko ji Iwata G F Gribakin R G Greaves and C M Surko Positron
annihilation with inner shell electrons in noble gas atoms Physical Review
Letters
Ko ji Iwata R G Greaves and C M Surko ray sp ectra from p ositron
annihilation on atoms and molecules Physical Review A
K Iwata R G Greaves and C M Surko Positron annihilation in a
simulated interstellar medium Canadian Journal of Physics
P Van Reeth J W Humb erston Ko ji Iwata R G Greaves and C M
Surko Annihilation in low energy p ositron helium scattering Journal
of Physics B Letters L
K Iwata R G Greaves T J Murphy M D Tinkle and C M Surko
Measurement of p ositron annihilation rates on organic molecules Phys
ical Review A
K Iwata R G Greaves and C M Surko Annihilation rates of p ositrons
on aromatic molecules Hyper ne Interactions
PAPERS AT CONFERENCES AND WORKSHOPS
C M Surko Ko ji Iwata R G Greaves C Kurz and S J Gilb ert
Atomic and molecular physics using p ositrons in a Penning trap to
b e published in the Pro ceedings of the XX International Conference on
the Physics of Electronic and Atomic Collisions World Scienti c xv
Ko ji Iwata R G Greaves C Kurz S J Gilb ert and C M Surko Stud
ies of p ositron matter interactions using stored p ositrons in an electro
static trap to b e published in Material Science Forum Pro ceedings of
the Eleventh International Conference on Positron Annihilation Kansas
City Missouri May edited by Y C Jean M Eldrup D M Schrader
and R N West
D M Rabin D Jaksha C Plymate J Wagner and K Iwata Plage
magnetic eld strengths from near infrared sp ectra in Solar Polarimetry
Pro ceedings of the Eleventh National Solar Observatory Sacramento Peak
Summer Workshop edited by L J Novemb er pp
INVITED TALKS
Ko ji Iwata A new lo ok at p ositron annihilation in atoms and molecules
Workshop on Low Energy Positron and Positronium Physics a satellite
conference of the International Conference on the Physics of Electronic
and Atomic Collisions Nottingham UK
Ko ji Iwata Lo calization of p ositrons in atoms and molecules the th
International Conference on Positron Annihilation Kansas City MS
K Iwata Chemical trends in p ositron attachment to molecules th
American Chemical So ciety National Meeting New Orleans LA
K Iwata Positron molecule interactions Positron workshop a satellite
conference of the International Conference on the Physics of Electronic
and Atomic Collisions Vancouver Canada
CONFERENCE ABSTRACTS
Ko ji Iwata G F Gribakin R G Greaves and C M Surko Positron
annihilation with inner shell electrons in atoms Bul letin of the American
Physical Society
K Iwata R G Greaves C Kurz and C M Surk o Positron annihilation
studies in a Penning trap partially uorinated hydro carb ons Bul letin of
the American Physical Society
C M Surko K Iwata and R G Greaves Measurements of atomic and
molecular p ositron annihilation rates using trapp ed p ositrons Bul letin of
the American Physical Society
K Iwata R G Greaves and C M Surko Gamma ray sp ectra from
p ositron atom and p ositron molecule interactions Bul letin of the Amer
ican Physical Society xvi
T J Murphy C M Surko and K Iwata Annihilation of p ositrons on
organic molecules Bul letin of the American Physical Society
Fields of Study
Ma jor Field Physics
Studies in Atomic and Molecular Physics
Professor Cli ord M Surko
Studies in Positron Physics
Professor Cli ord M Surko xvii
ABSTRACT OF THE DISSERTATION
Positron Annihilation on Atoms and Molecules
by
Ko ji Iwata
Do ctor of PhilosophyinPhysics
University of California San Diego
Professor Cli ord M Surko Chair
Positron annihilation on a wide variety of atoms and molecules is studied
Ro om temp erature p ositrons con ned in a Penning trap are allowed to inter
act with molecules in the form of low pressure gases so that the interaction is
restricted to binary encounters b etween a p ositron and a molecule Data are
presented for the annihilation rates and ray sp ectra resulting from p ositrons
annihilating in suchinteractions The variety of substances includes noble gases
simple inorganic molecules hydro carb ons substituted hydro carb ons fully and
partially uorinated hydro carb ons deuterated hydro carb ons and aromatics
Anomalously large annihilation rates are observed for large organic molecules
and the annihilation rates scale with the ionization p otentials of molecules To
date these anomalously large annihilation rates and the observed scaling have
not b een understo o d The ray sp ectra are Doppler broadened due to the mo
mentum distribution of the annihilating electron p ositron pairs Consequently
these sp ectra provide information ab out the electron and p ositron wavefunc
tions The measurements are used to determine the probability of p ositrons
annihilating at sp eci c lo cations in the atom or the molecule In the case of
partially uorinated hydro carb ons wehave b een able to determine the relative
probability of annihilation on uorine atoms and on C H b onds For noble gas
atoms the inner shell electron annihilation was identi ed for the rst time in
gaseous media The large annihilation rates for hydro carb ons have astrophysi
cal implications and a study of p ositron annihilation in a simulated interstellar
medium is also presented New insights which these studies provide in under
standing the interaction of low energy p ositrons with atoms and molecules are
discussed xviii
Chapter
Intro duction
A p ositron the anti particle of an electron is the most accessible form of anti
matter Since its discovery the prop erties of the p ositron have b een studied
extensively At a rst glance the studies of a p ositron interacting with an
atom or molecule would seem to b e di cult since the p ositron might b e ex
p ected to annihilate with an electron rapidly However this annihilation time is
much longer than the collisional slowing pro cess in media and so studies of slow
p ositrons in matter are p ossible This dissertation deals with the interactions of
low energy p ositrons with isolated atoms or molecules
In this chapter background information ab out p ositrons and p ositron matter
interactions is presented The pro cesses relevant to the research topic of this
dissertation are illustrated brie y in Sec A history of the prediction and
discovery of p ositrons is given in Sec Then the p ositron atom and p ositron
molecule interactions are describ ed in Sec including the comparison with
the analogous electron atom and electron molecule interactions The physics
of p ositrons interacting with matter in di erent states solid liquid and gas
is discussed in Sec Finally the outline of the dissertation is describ ed in
Sec
Simple illustration of a p ositron interacting with
a molecule
Alow energy p ositron interacting with a molecule is illustrated in Fig By
low energy we mean sp eci cally b elow the p ositronium formation threshold en
ergy The p ositrons used in the exp eriments describ ed here are stored and co oled
to ro om temp erature in a Penning trap A test substance is intro duced into the
Penning trap in vap or form and a p ositron exp eriences collisions with the test
molecules These two particles generally y apart after a collision However a
A molecule here means an atom or a molecule Molecule is used interchangeabl y with
atom and or molecule throughout the dissertation
Chapter
molecule e+
Ee+ ~ 0.04 eV λ time de Broglie ~ 60 A
e+
+* γ-rays
+ +
fragmentation
Figure Schematic diagram a low energy p ositron interacting with a molecule
small fraction of collisions results in the annihilation of the p ositron with one of
the b ound electrons in the molecule emitting two quanta of rays and leaving
Introduction
a p ositive ion in an excited state The excited p ositive ion can fragment For
higher energy p ositrons p ositronium atoms a b ound state of a p ositron and an
electron can b e formed by the collision pro cess However at ro om temp erature
i e the typical p ositron energy discussed here the formation of p ositronium
atoms is energetically prohibited for the typ es of molecules under study
One typ e of measurementwe are capable of making is annihilation rates mea
surements which is describ ed in Ch These measurements provide information
ab out the annihilation cross sections of molecules and as discovered earlier the
annihilation rates for large organic molecules are several orders of magnitude
larger than those exp ected from simple elastic collisions This enhance
mentmay b e explained by the existence of long lived p ositron molecule complex
but the nature of these complexes is still not understo o d
Another typ e of exp eriment is sp ectral measurements of keV annihilation
rays and these are describ ed in Ch The annihilation ray line is gener
ally Doppler broadened due to the momenta of the annihilating pairs These
momenta are dominated by the momenta of the b ound electrons since the zero
p ointmomenta of these electrons are larger than those of thermal p ositrons
Thus we can obtain information ab out the states of the annihilating electrons
We can also measure the ion mass sp ectra resulting from the annihilation us
ing a time of ight TOF mass sp ectroscopytechnique as discussed in Refs
Background in p ositron physics
Since the discovery of a p ositron the eld of p ositron physics has b ecome quite
diverse As the p ositron is the most readily available anti particle on earth
studies of the interaction of p ositrons with matter have attracted a signi cant
interest Current research includes the analysis of surfaces using p ositrons
studies of quantum electro dynamics using p ositronium atoms and the p os
sible pro duction of anti hydrogen Since the eld of p ositron physics is
to o diverse to cover in this dissertation the materials presented here are the sub
jects relating to p ositron molecule interactions In other literature p ositronium
research is reviewed nicely byRich includin g the history of the discovery of
the p ositron Positron interaction in gases is reviewed by Massey while ear
lier exp erimental techniques are discussed in detail by Gri th and Heyland
Research e orts in p ositron interactions with condensed matter whichhavebeen
pursued very actively are reviewed in Refs
Prediction and discovery of the p ositron
The p ositron was rst predicted by Dirac in He applied relativistic
quantum theory to an electron moving in an external magnetic eld and was
successful in predicting the spin prop erties of the electron However his theory
Chapter
involved one serious di culty his theory contained a solution with a negative
energy in addition to the p ositive energy solution that corresp onds to the elec
tron He then argued that if there was a negative energy state the electron
with p ositive energy can decayinto the negative energy state with the emission
of mc radiation and concluded that an electron with negative energy moves
in an external eld as though it carries a p ositivecharge He had predicted
annihilation of an electron p ositron pair However the only p ositively charged
particle known at that time was a proton and he assumed that the particle was
a proton even though the di erence in the mass of an electron and a proton was
puzzling The annihilation rate of an electron and a p ositron or the negative
energy state was calculated by Dirac and Opp enheimer In these cal
culations the p ositron mass was assumed to b e the same as that of an electron
It is interesting to note that in Dirac s work he mentioned regarding the
mass of this other particle This means of course a serious de ciency in our
work and prevents one from attaching muchphysical imp ortance to the result
In fact his assumption of the same mass for an electron and a p ositron was
right and the assumption that the negative energy state b eing the proton was
wrong The annihilation rate for a p ositron in a gas of electrons with density
n of spin opp osite to that of the p ositron in the non relativistic limit is
s
cn r
s s
where r is the classical radius of the electron and c is the sp eed of light For
an uncorrelated electron gas of density n n n so that the spin averaged
e s e
rate of annihilation for free electrons is
r cn
e s
The rst discovery of a p ositron came when Anderson was measuring traces
of cosmic rays in cloud chamb ers He discovered evidence of particles with
p ositivecharge Up to this time the only known p ositive particles were protons
and particles This new particle p enetrated a mm lead plate and made a
path much longer than that exp ected for a proton To explain this observation
Anderson concluded that the particle had to b e less massive than a proton most
likely the mass of an electron Anderson called this new particle the p ositive
electron or a p ositron
The discovery of a p ositron was particularly signi cant inthatitwas the
rst form of an anti matter The unique prop erties of p ositrons can b e exploited
for the study of antimatter matter interactions
Positron sources
A p ositron source with high intensity and known energy distribution is desirable
Currently two di erenttyp es of p ositron sources are employed linear accelerator
Introduction
LINAC based sources and radioactive isotop es that undergo i e p ositron
decay
A LINAC source consists of a high energy electron b eam and a p ositron
converter The high energy electron b eam MeV isslowed down in a
material causing the emission of Bremsstrahlung rays The high energy rays
create electron p ositron pairs and the p ositrons can b e extracted The intensity
of the p ositron b eam pro duced is prop ortional to the intensity of the incoming
high energy electrons The intensity of the p ositrons pro duced also increases
very rapidly with the energy of the electron source in the range of energies
MeV An advantage of LINAC based sources is their high intensity
slow p ositrons s Another advantage is that they can b e op erated in
pulsed mo de so that exp eriments can b e p erformed con ning the detection
time to that of the p ositron pulse thereby improving the signal to noise ratio
A disadvantage is the cost of LINAC s and the facility tends to b e relatively
large
There are several radioactive isotop es commonly used as p ositron sources
High activity and long lifetimes are imp ortant criteria for use in studies of
p ositron matter interactions Commercially available sources that satisfy these
criteria include Na Co and Ge We utilize a Na source whichhasthe
half life of years and is commercially available in sealed sources at
activities up to mCi Advantages of radioisotop e sources are their av ailabil
ity and compactness while a disadvantage is the relatively lowintensitycom
paredtoLINAC sources One waytoovercome this disadvantage of radioisotop e
sources is use of Cu Using Cu an intense high energy p ositron s
short lived hours source has b een generated in a high ux nuclear
reactor However this source also has a similar disadvantage to LINAC
sources namely the need for a large facility in this case a nuclear reactor on
site
Physics involved in the interaction of a p ositron
with a molecule
The basic physics involved in a p ositron interacting with an isolated neutral atom
or molecule is describ ed in this section This discussion fo cuses in particular on
low p ositron energies where the time scale of a p ositron approaching a molecule
is much larger than the electron cloud relaxation time The interaction has
some similarities to the case of an electron interacting with a molecule and
comparisons and contrasts b etween these two di erent systems are given
Chapter
Long range p olarization and dip ole charge interactions
At distance r much larger than the molecular size r a wherea is the Bohr
radius the interaction of a p ositron with a molecule is dominated by the in
duced dip ole charge and p ermanent dip ole charge interactions for nonp olar and
p olar molecules resp ectively Whenacharged particle approaches a nonp olar
molecule the electron cloud in the molecule is p olarized giving the induced
electric dip ole moment E where is the p olarization constant of the
molecule and E is the eld inducing the moment The eld at the origin due
to a p ositron lo cated at r has the form E e r r where e is the electric
charge andr is an unit vector in the direction of r The induced dip ole moment
in the presence of a p ositron therefore is
e
r
r
The force b etween the molecule and the p ositron due to the induced dip ole
charge interaction is
e
F
r
This p olarization induced dip ole moment charge interaction is attractive for ei
ther an electron or a p ositron interacting with a neutral molecule
For the case of molecules with a p ermanent dip ole moment the force on
p
the p ositron exerted by this dip ole is
e
p
F
p
r
One can notice that the r dep endence for nonp olar molecules is r Eq
while that for p olar molecules is r Eq Thus the long range interaction
for p olar molecules is much stronger than that for nonp olar molecules
Short range interactions r a
At shorter distances r a the interactions are more complicated The p olar
ization no longer has the simple multip ole expansion form given in Eq In
addition the p otential of the atomic nuclei the Pauli exclusion principle p ositro
nium atom formation and annihilation of a p ositron with an atomic molecular
electron must b e considered
Potential from atomic nuclei
Once a p ositron approaches a molecule and p enetrates the electron shielding
cloud it will exp erience Coulomb repulsion from the atomic nuclei whichare
p ositively charged while the screening from the molecular electrons continues
to reduce the repulsion of the p ositron This is in contrast to the case of an
electron interacting with a molecule where the Coulombinteraction with the
atomic nuclei is attractive
Introduction
molecule e+
Ee+ > Ei - EPs time
e+
+
e+e-
Figure Schematic illustration of p ositronium atom formation
Pauli exclusion principle
For an electron interacting with a molecule the Pauli exclusion principle needs
to b e considered since the scattering electron is an identical particle with the
b ound electrons in the molecule For a p ositron interacting with a molecule the
scattering p ositron is not in uenced by the Pauli exclusion principle with the
b ound electrons
Positronium atom formation
A p ositron can form a b ound state with an electron which is called a p ositron
ium atom often denoted by the symb ol Ps The pro cess is schematically illus
trated in Fig The p ositronium atom was rst discovered by Deutsch
Studies of p ositronium atoms are an active area of research and have b een re
viewed byRich Even though studies of p ositronium atoms are not a
Chapter
sub ject of this dissertation the formation of p ositronium atoms is imp ortant
in the p ositron trapping scheme used here and p ositronium maywell p ossibly
b e crucial for understanding the annihilation pro cesses since the formation of
psudo p ositronium atoms are susp ected for resp onsible for the anomalously
high annihilation rates observed Ch Therefore the prop erties of p ositron
ium atoms are brie y reviewed here
The binding energy of a p ositronium atom E is eV which is ab out half
Ps
that of the hydrogen atom since the reduced mass of the system is m There
are two di erent total spin states and they di er greatly in mean lifetime The
singlet S state decays by the emission of two rays The ground singlet state so
called para Ps annihilates in the time of s On the other hand
p
for the triplet S state ortho Ps annihilation is forbidden by conservation
of the spin angular momentum and in this case the annihilation o ccurs with
emission of rays with the time scale of s In the center
o
of mass frame b oth and annihilation must carry away mc In the rest
frame of the annihilating particles for annihilation each ray carries
keV energy while in the case of annihilation the energies of these three
rays are continuously distributed up to keV
The ortho Ps annihilation time is orders of magnitude larger than that for
para Ps The spin averaged annihilation time of p ositronium atom is
s
It turns out that this annihilation time is a reasonably go o d estimate of
annihilation times in condensed matter
In order for a p ositron to capture an electron from a gas molecule in the
usual case where E E the incident p ositron must p ossess an initial kinetic
i Ps
energy E of at least
k
E E E
k i Ps
where E is the ionization energy of the molecule
i
Annihilation
A free p ositron annihilates with an electron in a molecule with emission of
quanta of rays This is an unique pro cess in p ositron molecule interactions
The annihilation signal can give information ab out the interaction whichisnot
available in electron molecule interactions and it is the main detection metho d
used in this dissertation
One quantity that can b e measured is the annihilation rates of p ositrons for
molecules which is describ ed in Ch The annihilation rate for a molecule
is prop ortional to the overlap of the wave functions of the p ositron with the
molecular electrons Therefore the measurement of annihilation rates gives
information ab out the close range interaction of the p ositron with the molecular electrons
Introduction
Another quantity that can b e measured is the Doppler broadening of the
keV ray line from p ositron annihilation on a molecule The line is broadened
due to the momentum distribution of the annihilating electron p ositron pairs
For the case of ro om temp erature p ositrons discussed here the momentum of
the pair is dominated by the momentum of the annihilating electron This
ray sp ectral measurementgives information ab out the site of annihilation in the
molecule This typ e of measurement is the topic of Ch and
Interaction of p ositrons with solids liquids and
gases
Positrons interact di erently with solid liquid and gaseous media as do elec
trons and the interactions of p ositrons with these di erent media are brie y
reviewed in this section This dissertation fo cuses on the interaction of p ositrons
with gaseous media Due to their inherent simplicity knowledge of these p ositron
interactions with gases can aid in the understanding of p ositron solid and liquid
interactions
Positrons p ossess high kinetic energies MeV when they are created
either bythe decay of radioactivenuclei or by the pair pro duction from
high energy rays Once the high energy p ositrons encounter matter they
quickly slowdown through inelastic pro cesses such as ionization and electronic
excitation of the media eventually reaching thermal equilibriu m with the matter
since the energy loss cross sections are much larger than the annihilation cross
section For p ositrons with energies ab ove the p ositronium formation threshold
p ositronium formation ionization and electronic excitation are the dominant
e ects This picture of the slowing down of p ositrons is valid for solid liquid
or gas medium However the physics involved after thermalization can b e very
di erent in these three media The in teraction of thermalized p ositrons with
matter is the sub ject of this dissertation
At high energies the main interaction is the ionization of the atoms in the
media and the cross section for this pro cess is similar for electrons and p ositrons
However at low energies p ositrons b ehavevery di erently from electrons since
as discussed ab ove the di erences in the interactions of p ositron and electrons
with molecules play bigger roles
Solids
Studies of p ositrons interacting with solids are an intense eld of research see for
example the review pap ers bySchultz and Lynn by Puska and Nieminen
and by Mills
A brief history of an energetic p ositron is as follows After its intro duction
into the solid the p ositron loses energy by ionization or creation of electron
Chapter + + + + + + e+ + + + + + + + + + + + + + + + + +
+ + + + + +
Figure Schematic diagram of p ositron trapping in a defect
hole pairs and at lower energies by p ositron phonon interactions The p ositron
eventually comes to thermal equilibrium with the environment and then di uses
due to p ositron phonon collisions During this di usion pro cess the p ositron can
interact with defects in the solid resulting in the trapping of the p ositron in
lo calized states Eventually the p ositron annihilates with an electron resulting
in the emission of rays
One imp ortant facet of earlier studies of p ositron solid state interactions was
on the mapping of Fermi surfaces in metals Measurementofmomentum dis
tribution of conducting electrons in metals using p ositrons provided an accurate
measure of the detailed shap e of the Fermi surface
The trapping of p ositrons in defects is also an area in which there has b een
much activity The mechanism of p ositron trapping in a defect is illustrated
schematically in Fig A thermalized p ositron di uses freely in the eld cre
ated by the lattice ion cores The p ositron is attracted to a defect since the ion
is missing at the defect and the repulsive p otential is absent The p ositron forms
a lo calized state at the defect and the annihilation signal provides information ab out the nature of this lo calized state and the defect itself
Introduction
Positron mo derators
One interesting and imp ortant asp ect of p ositron solid interactions is the in
teraction of p ositrons with the solid surface Thermalized p ositrons in solids
can di use to the surface In some materials the work function of a p ositron
on the surface is negative and a fraction of p ositrons can b e re emitted from
the surface with electron Volt energies This p ositron mo deration in fact was
rst discovered by Cherry and con rmed later by Costello et al An
example of applications of this pro cess is the p ositron re emission microscopy
which maps the work function of p ositrons on the surface The e ciency of
p ositron mo deration is a few p ercents at the most with the loss due predomi
nantly to annihilation in the solid However compared with the energy selection
from a continuous sp ectrum of a decay which range up to energies of hun
dreds of kilo electron Volts whichwas mainly used b efore the invention of the
mo derator p ositron mo derators are several orders of magnitude more e cient
in pro ducing slow p ositrons Current p ositron matter interaction research relies
heavily on this p ositron mo deration pro cess to obtain the slow p ositron b eams
and this e ect is crucial to the work describ ed here
The e ciency of mo derators has seen steady increase from the e ciency
value of for Cherry s work where the is de ned as the
ratio of p ositrons extracted in a b eam to the numb er b eing pro duced bythe
radioisotop e Single crystals of various metals such as tungsten nickel
and copp er haveslow p ositron e ciencies as large as It has b een
observed that rare gas solids can mo derate p ositrons with an order of magnitude
more e cien tly than single crystal metals and currently we are using a solid
neon mo derator Pro duction of solid rare gas mo derators
involves making provision for a cold surface where the rare gas can b e dep osited
as a solid
Liquids
The interaction of p ositrons with liquids is complicated by the fact that the
atoms or molecules are not lo cated at the xed p ositions One phenomenon
unique to p ositron liquid interactions is the existence of Ps atoms in self trapp ed
states Because of the strong exchange repulsion b etween the electron in
the Ps and the nearby atoms with tightly b ound electrons of parallel spin it is
energetically favorable for the Ps atom to b e in a region of lower than average
atom density Once in this region in a liquid the Ps can rep el the nearby atoms
thereby creating a cavity or a bubble
Gases
Positron interactions with isolated atoms and molecules are relatively simple
as compared to p ositron condensed matter interactions yet they exhibit rich
Chapter
b ehavior A numb er of the many b o dy e ects that exist in condensed matter
are not present and the b ehavior is describ ed by a p ositron scattering o a
molecule Many exp erimental and theoretical techniques develop ed for studies
of electron molecule interactions have b een adopted for the studies of p ositron
molecule interactions They include measurement of collision cross sections
including di erential cross sections and measurement of p ositronium formation
cross sections for various molecules
One typ e of exp eriment which is unique to p ositron molecule interactions
is the annihilation of the p ositron with a molecular electron In earlier annihila
tion studies on molecules a radioisotop e suchas Na which decays via p ositron
emission was placed directly in a gas cell and the measurements using this con
guration are describ ed in details in Ch For small atoms and molecules the
p ositron interactions are well understo o d by the scattering picture including
p ositron electron correlations However Paul and Pierre rst observed un
usually high annihilation rates for methane ethane propane and butane
and Heyland et al later con rmed these observations Surko et al have
observed even higher annihilation rates for larger alkanes using p ositrons stored
inaPenning trap These anomalously high annihilation rates cannot b e
understo o d with the simple scattering picture and the pro cess resp onsible for
these high rates is still not understo o d
Outline of dissertation
This dissertation is organized in the following manner Previous measurements
on annihilation rates and momentum distributions in gases are summarized
in Ch Our p ositron trap and exp erimental setup are describ ed in Ch
The most complete survey of annihilation rate studies for a varietyofchemical
sp ecies is presented in Ch The test substances includes noble gases inorganic
molecules alkanes substituted alkanes and aromatics The exp erimentally mea
sured annihilation rates are compared with theoretical calculations and previous
measurements The studies of keV annihilation ray sp ectra in gases for a
v arietyofchemical sp ecies are presented in Ch The substances under study
are similar to those of Ch Results from Ch indicate that annihilation is
dominated byvalence electrons However a small fraction of inner shell elec
tron annihilation was detected which is describ ed in Ch An application of
p ositron annihilation rate and ray sp ectrum studies is the p ositron annihilation
in astrophysical media and this asp ect of research is describ ed in Ch Finally
the conclusions are presented in Ch Additional information is presented in
app endices the exp erimentally measured ion gauge sensitivities App endix A
various physical parameters App endix B and ray line shap es App endix C for atoms and molecules studied are tabulated
Chapter
Overview of previous atomic
and molecular physics studies
using p ositrons
Exp erimental con gurations of p ositron molecule interaction studies can b e roughly
divided into high gas pressure and low pressure exp eriments While they have
b oth b een used to obtain useful information on the two b o dy interactions b e
tween p ositrons and molecules they employ di erent detecting metho ds and
involve di erent complexities These issues are discussed in Sec
Twotyp es of physical quantities have b een mainly measured the annihila
tion rates Sec and the momentum distributions of annihilating electron
p ositron pairs Sec Recently mass sp ectra of ions resulting from p ositron
annihilation on molecules have b een measured in low pressure exp eriments Sec
The annihilation rate measurement is sensitive to the over all interaction of
p ositrons with molecules while the momentum distribution measurement is sen
sitive to the quantum states of annihilating electrons Historically the rates of
p ositron annihilation on molecules have b een expressed in terms of nor
malized annihilation rates Z by mo difying the Dirac annihilation rate for
e
free electrons Eq to include the e ectivenumb er of electrons Z in the
e
molecule that contribute to the annihilation pro cess In particular
r cnZ
e
where n is the numb er density of molecules As discussed in Ch this is a crude
parameterization Even though the Z is in the same order of magnitude with
e
the numb er of electrons Z for small atoms and molecules this assumption of ef
fectivenumb er of electrons breaks down for large organic molecules where these
Z values are several orders of magnitude higher than Z due to the formation of
the long lived p ositron molecule states
Chapter
Dense gas and low pressure exp eriments
Dense gas exp eriments
The rst exp eriments on p ositron molecule interactions were p erformed at rel
atively high pressures P atm In this work the exp erimental setup is
relatively simple since the high energy p ositrons from the source are directly
injected into the gas cell They also have the advantage that at high material
densities the annihilation o ccurs in a small volume near the source so that angu
lar correlation of annihilation radiation ACAR metho d discussed in Sec
is applicable However since the mo deration gas is the same as the test gas
the energies of p ositrons at moment of annihilation dep end on mo deration pro
cesses and maynotbewell characterized for some gases The annihilation ray
signals come from the annihilation of p ositronium atoms and from free p ositron
annihilation on molecules These p ositronium signals must b e taken into ac
count resulting in the considerable reduction in the signal to noise ratio of free
p ositron annihilation Another disadvantage is that b ecause of the gas pres
sures required for these exp eriments the numb er of test molecules is limited
to those with high vap or pressures at ro om temp erature e g atmospheric or
higher pressure The results of these exp eriments are reviewed as
are exp erimental techniques involved in these typ es of measurements elsewhere
in detail
Positrons emitted from the source typically have energies of a few hundred
keV They lose energy rapidly through ionization and electronic excitation of
gas molecules until their energy falls b elow the threshold energy for electronic
excitation For example the ionization cross section at eV is ab out
i
cm while the annihilation cross section is
r cZ
e
a
nv v
At eV Z cm For these energies Therefore the
a e a i
p ositrons slowdown without signi cant loss from annihilation at these energy
ranges Further mo deration of p ositrons o ccurs through elastic collisions in
the case of noble gases and mainly through inelastic vibrational and rotational
excitation collisions in the case of p olyatomic molecules In elastic collisions a
p ositron loses at most a fraction m M of its initial energy p er collision where
m and M are the masses of the p ositron and the gas atom resp ectively Asa
result ab out M m large angle elastic collisions are required for thermalization
leading to the de nition of an e ective thermalization cross section for elastic
collisions
m
m
el
t
M
where is the elastic momentum transfer cross section which is on the order of
m
atomic dimensions For p olyatomic molecules vibrational and rotational excita
Overview of previous atomic and molecular
tions provide a more e cient thermalization mechanism and the cross sections
inel
are typically around cm In order to study the interaction of
t
thermalized p ositrons with molecules wemust have
t
a
For noble gases
el
t
MZ
a e
where M is in atomic mass units while for p olyatomic molecules
inel
t
Z
a e
Thus thermalization o ccurs b efore annihilation for small noble gases suchas
helium and neon and for p olyatomic molecules with Z However
e
these estimates indicate that p ositrons can annihilate b efore they reach thermal
equilibrium for large noble gases and for some large organic molecules In par
ticular Z can b e as large as for large noble gases and
e
for large organic molecules A mixed gas technique has b een
develop ed to address this thermalization problem
Low pressure exp eriments
In the last decade p ositron trapping techniques havebeendevelop ed byour
group to overcome some of the disadvantages of the previous high pressure
measurements In these trapping exp eriments the p ositron energies are well
characterized since the mo deration of high energy p ositrons is achieved by me
dia di erent from the test substances In addition the p ositron energy can b e
reduced b elow p ositronium formation threshold so that the signals from p ositro
nium annihilation can b e eliminated
The exp erimental setup is generally more complicated as compared to the
high pressure measurements It involves a Penning trap which is a trap us
ing electrostatic p otentials and a magnetic eld for con ning charged parti
cles High energy p ositrons pro duced by either radioactiveisotopes
or LINAC s are mo derated to a few eV energy by a solid state mo derator suchas
tungsten or solid noble gas lms This slow b eam of p ositrons a few eV energy
is guided through a magnetic b eam tub e into a Penning trap The p ositrons may
b e mo derated further through various energy loss mechanisms such as collisions
with bu er gas For the bu er gas system these p ositrons reach thermal equi
librium These stored p ositrons ha ve desirable characteristics In addition to
their well characterized energy the numb er of p ositrons is large so that
the resulting signal to noise ratio of annihilation measurements is large Since
the p ositrons can b e stored for a long p erio d of time they can b e used very
Chapter
Figure Apparatus for measuring annihilation time sp ectra used in Ref The
copp er pressure vessel contains a Na source and gas at pressure up to atmospheres
The two plastic scintillators provide start and stop pulses from which sp ectra are
obtained with resolution of ns
e ciently One unique feature of the low pressure measurements is that mass
sp ectrometry of ions resulting from p ositron annihilation is p ossible
A detailed description of our p ositron trap is presented in Ch
Annihilation rates
Previous high pressure gas exp eriments were p erformed in an apparatus similar
to that shown in Fig This technique to measure annihilation rates uses a
Na radioactive source which emits a MeV ray with a negligible delay
after the emission of a p ositron The p ositron annihilates in a pressurized gas
chamb er and delayed coincidences are observed b etween signals recorded on
scintillation counters from the MeV ray and the annihilation rays
Thus the time delay is a measure of the annihilation rate and is typically of
the order of s in gases at atmospheric pressure
Figure shows an illustrated annihilation time sp ectrum The prompt p eak
A is due to the fast decay of para p ositronium atoms ns CurveI
is due to free p ositrons annihilating with the molecule while curve I I is due to
Overview of previous atomic and molecular
Figure Schematic drawing of annihilation time sp ectrum taken from Ref The
prompt p eak is lettered A and BC is the gradually changing shoulder region
Curve I is the contribution from free p ositron annihilation curve I I is the contribution
from ortho p ositronium annihilation
the decay of ortho p ositronium atoms ns The gradually changing
shoulder region BC is due to changes in the free p ositron annihilation rates
with energy Generally annihilation rates are smaller at higher energies which
o ccur while p ositrons are slowing down The rate of p ositrons slowing down
dep ends on the mo derating gas and the sp eci c energy distribution during the
slowing down of p ositrons is not well known The straight section of curveI
time after C is due to the thermalized free p ositrons annihilating with the
gas molecules and during this time the annihilation rate can b e measured An
example of data for helium is shown in Fig
This technique was rst employed to con rm the existence of p ositronium
atoms byDeutsch in The rst studies of free p ositron annihilation so on
followed The annihilation rates of most of the simple atoms and molecules
that exist in the gas phase at standard temp erature and pressure havebeen
measured and these measurements were summarized in Ref The varieties
of substances studied were widely extended by measurements p erformed at low
pressure by Surko et al and Murphy and Surko
Chapter
Figure Annihilation sp ectrum observed with the apparatus of Fig for helium
gas at a density of Amagat atm at ro om temp erature taken from Ref
Eachchannel corresp onds to ns Curve a is unpro cessed data curvebhasthe
background subtracted curve c is the free p ositron comp onent and curve d is the
ortho p ositronium comp onent
Anomalously high annihilation rates
One surprising result is the observation of anomalously large annihilation rates
for large organic molecules This phenomenon is still not understo o d Deutsch
Overview of previous atomic and molecular
noticed very fast decayoffreepositronsonCCl F in He susp ected
that it was due to a large p ositron attachment co e cient but the attachment
mechanism was not discussed Paul and Saint Pierre p erformed systematic stud
ies of this rapid annihilation of free p ositrons on some p olyatomic gases includ
ing alkanes that exist in gas form at atmospheric pressure in They
have suggested p ositron binding to molecules to explain the high annihilation
rates In order to explain the anomalously high annihilation rates Heyland et
al later hyp othesized clustering of molecules around the p ositron as well as the
formation of p ositron molecule b ound states to explain this phenomenon but
their data and analysis could not distinguish b etween these two p ossible mech
anisms In the case of xenon Wright et al then ruled out the p ossibilityof
clustering by measuring the annihilation rate for a wide range of pressures
In Surko et al measured even higher annihilation rates for larger organic
molecules using stored p ositrons in a Penning Malmb erg trap where the test
substances were intro duced as low pressure gases They prop osed the for
mation of long lived p ositron molecule comp ounds by the vibrational excitations
of molecules based on the unimolecular reaction theory An empirical scaling of
log Z with E E where E is the ionization energy of the molecule
e i Ps i
was discovered byMurphy and Surko in To date the physical pro
cess resp onsible for this scaling is not understo o d Detailed discussions of these
annihilation rates are presented in Ch
Momentum distribution measurements
In contrast to the large num b er of annihilation rate measurements in gases mo
mentum distribution measurements of annihilating pairs on isolated atoms or
molecules have not b een widely p erformed due to technical di culties There
are two exp erimental techniques for measuring the momentum distribution of
annihilating electron p ositron pairs One metho d of measuring momentum dis
tributions is use of the ACAR technique By measuring the angular correla
tion b etween two keV rays the momentum p erp endicular to the rays
can b e measured In gaseous media an ACAR measurementsu ersfromlow
count rates b ecause of limited ux of p ositrons and the relatively large vol
ume of annihilation region Two dimensional ACAR technique D ACAR was
used recently and was able to increase the count rates considerably as shown
in Fig However the signal to noise ratios of free p ositron annihilation
signals were relatively p o or since the annihilation from p ositronium atoms had
to b e subtracted
The other technique for measuring the momentum distributions is to mea
sure the Doppler broadening of keV annihilation rays This metho d had
previously b een applied to a limited numb er Detailed discussions
of momentum distribution measurements are presented in Ch
Chapter
Figure D ACAR sp ectra of noble gases from Ref a He b Ne c Ar d
Kr e Xe The narrowcomponent is the free p ositronium annihilation signal while
the wider comp onent is the signal from free p ositron annihilation on atoms
Ion mass sp ectrum measurements
Positron and p ositronium chemistry such as the formation of p ositronium hy
dride has b een studied previously A Penning Malmb erg trap can
be a powerful to ol to study this typ e of reaction One typ e of study is the
observation of p ositive ions
Positron annihilation on atoms and molecules results in formation of p ositive
ions The mass sp ectroscopy of the resulting ions are p ossible The techniques for
ion mass sp ectroscopy are generally available only for low pressure exp eriments
Sec such as those p ossible in p ositron traps
Positron annihilation and p ositronium formation are qualitatively di erent
ways of pro ducing p ositive ions and they mayhave applications in chemical
analysis These metho ds may also b e gentler ways of removing an electron
from a fragile molecule than the conventional metho ds such as electron impact
ionization
In Passner et al rst measured the ion mass sp ectrum following
p ositron annihilation in a p ositron trap using a time of ight TOF tech
nique For alkane molecules they observed a high probability of frag
mentation following annihilation with ro om temp erature p ositrons Later these
Overview of previous atomic and molecular
observations were analyzed more carefully
Hulett et al develop ed an improved TOF mass sp ectrometer attached to
aPenning trap and studied di erent asp ects of the fragmentation of organic
molecules A highlight of their studies was the discovery of a
large probability of pro ducing unfragmented ions in the narrow energy range
just ab ove the p ositronium formation threshold Studies of various organic
molecules revealed that the molecules with double and triple b onds tends to
pro duce unfragmented ions The mechanism of fragmentation has b een investi
gated theoretically and the theory is in general agreement with the exp erimental results
Chapter
Chapter
Description of the exp eriments
This chapter describ es the apparatus and metho ds used to p erform exp eriments
on p ositron molecule interactions The schematic overview of the exp erimental
setup is shown in Fig High energy p ositrons emitted from a Na source
are mo derated to a few eV by the solid neon mo derator Sec These slow
p ositrons are magnetically guided through the b eam line Sec into the
p ositron trap Sec The p ositron trap is a Penning Malmb erg trap de
signed to accumulate and store a large numb er of p ositrons The con nement
for these p ositrons is provided by the electrostatic and magnetic elds in axial
Positron trap Detecting Beam line Source/ devices e+ moderator e+
Test gas
Gas handling
system
Figure Schematic overview of the exp erimental setup Positrons from the source
chamb er is guided through the b eam line into the p ositron trap whichisaPenning
Malmb erg trap for p ositron accumulation The accumulated p ositrons designated by
e interact with the test gas intro duced from the gas handling system The annihi
lation signals and remaining p ositrons are recorded by the detecting devices
Chapter
and radial directions resp ectively The stored p ositrons interact with the test
gas intro duced through the gas handling system where the test gas admission
and pressure are regulated Sec The signals from the p ositron annihilation
in the trap are recorded with a Ge detector for ray sp ectral measurements
For annihilation rate measurements the numb er of remaining p ositrons are mea
sured by dumping these p ositrons on a plate at the end of the trap where the
accumulated charges or the rays resulting from p ositron annihilating on the
plate are recorded
Source and mo derator
The p ositrons were obtained from a Na radioactive p ositron emitter purchased
from DuPont Pharma This source has a relatively long lifetime of y and
the strength at the time purchased was mCi It is sealed b ehind a m
tantalum window The sp ectrum of p ositron energies is continuous up to
keV
These high energy p ositrons were mo derated by a single crystal tungsten lm
in the earlier stages of the exp eriments and by solid neon lm in the later stages
The tungsten mo derator assembly was relatively simple and was used in a trans
mission geometry The neon mo derator assembly is more complicated
but the mo deration e ciency is ab out an order of magnitude larger than that
of the tungsten
The schematic diagram of the neon mo derator system is shown in Fig
The source is recessed into a parab olic copp er cup mounted on an Elkonite ro d
which is attached to the second stage of a two stage closed cycle refrigerator
APD mo del DE SLB The Elkonite ro d is electrically isolated from ground
by a sapphire washer to allow electrical biasing of the source Indium gaskets
are inserted b etween all surfaces in contact The entire assembly is enclosed in
a copp er heat shield which is attached to the rst stage of the refrigerator The
heat shield extends cm b eyond the source to minimize the heat load on the
source The interior surface of this extension is coated with a layer of commercial
spra y on colloidal graphite to minimize re ection of incoming infrared radiation
from ro om temp erature surfaces
The temp eratures of the copp er parab oloid and the second stage of the cold
head are monitored by silicon dio des using a Lakeshore temp erature controller
whichcontrols the temp erature over a wide range by means of heater coils at
tached to the second stage The second stage temp erature is typically K
while the source itself is ab out K warmer
The source cold head assembly is installed in an all metal UHV system
pump ed by an ion pump The base pressure of the system is torr
after bakeout at C and rises to ab out torr after neon has b een
frozen onto the source presumably b ecause of neon subliming from the warmer
Description of the experiments
Figure Schematic diagram of the source and cold head assembly
parts of the source cold head assembly
Before a new mo derator is grown the source is slowly heated to K and the
sublimated neon from the previous mo derator is pump ed out of the system using
a turb o pump backed by an oil free molecular drag pump During the pump out
phase the coldhead temp erature is regulated so that the neon pressure do es not
rise ab ove torr
The mo derators are grown at a slightly elevated temp erature K
Neon is admitted at a pressure of torr This pressure is to o high for
op eration of the ion pump which is therefore shut o during this neon admission
phase As so on as the neon gas is switched o the mo derator is annealed by
raising its temp erature to K for a few minutes
The p erformances of our neon and tungsten mo derators are summarized in
Table As can b e seen in the table the neon mo derator signi cantly
increased the mo deration e ciency as compared to the tungsten mo derator
Detailed description of the solid neon mo derator apparatus and op eration is
given in Ref
Chapter
Table Parameters of the neon and tungsten mo derators and the p ositron
trap
Parameter Neon mo derator Tungsten mo derator
Source strength mCi Na mCi Na
Source e ciency
Fast e ux sec sec
Mo derated e ux sec sec
a
E ciency
b
E ciency
Energy spread FWHM eV eV
Trapping rate sec sec
Trapping e ciency
c
Positron lifetime sec sec
d
Positron lifetime hr hr
Total trapp ed p ositrons
a
Relative to source strength
b
Relative to emitted p ositrons
c
With bu er gas p torr
d
At base pressure p torr
Beam line
The b eam line consists of standard UHV comp onents with stainless steel vacuum
tub es The tub es are surrounded by solenoid coil to exert con ning magnetic
eld so that the p ositrons go through the tub es without hitting the wall The
eld is generally ab out G The tub e is b ent so that the MeV and keV
annihilation rays emitted from the Na source do not go into the detectors
which are lo cated on the other side of the p ositron trap
Positron trap
The low energy p ositron b eam is injected into the p ositron trap through the
b eam tub e The p ositron trap is a Penning Malmb erg trap sp eci cally designed
to accumulate and store p ositrons e ciently Malmb erg et al mo di ed a Pen
ning trap to con ne electron plasmas and it was discovered that the device had
avery long con nement time Taking advantage of this long con nement
time Surko et al mo di ed this trap to accumulate p ositrons e ciently
Description of the experiments
+ GND +
e+ electrodes
B 1.0
0.5 e+ 0.0 (arb. units) (arb.
electrostatic potential axial distance
Figure Schematic diagram of a Penning Malmb erg trap A set of three cylindrical
electro des ab ove provides a p otential well b elow for charged particles
resulting in the rst creation in the lab oratory of a p ositron plasma in
The simplest form of a Penning Malmb erg trap is shown in Fig In a
Penning Malmb erg trap charged particles are con ned magnetically and elec
trostatically in radial and axial directions resp ectively Ascanbeseenin
Fig the outside electro des are biased p ositively while the middle electro de
is grounded This creates a p otential well for charged particles In order to trap
charged particles two metho ds have b een commonly used One metho d is a
fast switching of the gate p otential This is e ective when the b eam is sentin
pulses rather than as a continuous b eam such as when the p ositrons come from
LINAC sources The other metho d is to send a b eam of particles with energy
higher than the gate p otential and to arrange for an energy loss mechanism
to reduce the energy of the particles b elow that of the gate p otential so that
they are trapp ed The energy loss mechanism can b e resistive damping or
inelastic collisions with bu er gas molecules Chaotic particle orbits have
also b een used to enhance trapping For p ositron trapping the highest p os
sible e ciency is desirable b ecause of the limited ux of p ositrons We employ
a bu er gas for the energy loss mechanism which has proven to b e very e cient
Chapter
(a) fourth third second first
60 e+ 40 A potential (V) potential 20 B C 0 -20 -1 10 (b)-2.5 -2.0 -1.5 -1.0 -0.5 0.0 fourth third second first 10-2 z (m)
10-3
10-4
10-5
10-6 buffer gas pressure (torr) buffer 10-7 -2.5 -2.0 -1.5 -1.0 -0.5 0.0
z (m)
Figure Schematic diagram of the p ositron trap electro de structure
when used with a continuous p ositron source
Aschematic diagram of our four stage p ositron trap is shown in Fig a
along with the con ning p otential well The geometry of the electro des is such
Description of the experiments
that the bu er gas pressure is high at the rst stage of the trap where the
p ositrons have high probability of making inelastic collisions resulting in a high
trapping e ciency They continue to lose energy by inelastic collisions and
eventually accumulate in the low pressure region where annihilation on the
bu er gas is relatively slow The pressure of the bu er gas in the p ositron trap
is plotted in Fig b
The p otentials are adjusted so that in the rst stage the main inelastic
pro cess is electronic excitation of N shown A in Fig a which results in
the p ositrons b ecoming trapp ed in the p otential well The p ositrons lose further
kinetic energy through subsequent inelastic collisions B and C in the gure
and b ecome con ned in the third stage The fastest pro cess is the electronic
excitation of the N at ab out eV They reach thermal equilibrium with the
bu er gas in the time scale of s through vibrational and rotational excitations
of N The p ositron temp erature in the third stage is measured to b e K
using the magnetic b each energy analyzer The p ositrons stored in the
third stage are shuttled to the fourth stage bylowering the p otential barrier as
shown in the gure since in this stage they are the closest to the detector and
the bu er gas pressure is lower
The p otentials on each stage of the trap were adjusted to obtain optimal
p ositron trapping This optimization was achieved by the computer assisted
optimization software and the e ciency of trapping i e numb er of trapp ed
p ositrons incidentslow b eam p ositrons is typically
Following p ositron loading the nitrogen bu er gas can b e pump ed out The
time scale of bu er gas pump out is ab out s as shown in Fig In this ultra
high vacuum environment torr p ositron lifetime can b e as long
as h when a cold trap is lled with the liquid nitrogen This long lifetime is
esp ecially imp ortant for the ray sp ectrum measurements as it minimizes the
signal due to the annihilation on nitrogen gas
A diagram of the p ositron trap including other hardware is shown Fig
The cryogenic vacuum pumps are placed to provide appropriate di erential
pumping of the bu er gas whichisintro duced at the rst stage as indicated
by the arrow in the gure Originally oil di usion pumps were used for the
p ositron trap but it was discovered that the large oil molecules have extremely
large annihilation rates and so an oil free vacuum system is required
Magnetic eld coils are used to supply approximately G and G in
the rst and third stages of the trap resp ectively The p ositron lling of the
trap is optimized byvarying the currents in these magnetic eld coils
The con ning electro des are made of copp er or aluminum and they are gold
coated to avoid corrosion Test substances are intro duced through a gas handling
Chapter
10-7
10-8 pressure (torr) pressure
10-9
0 20 40 60 80
time (sec)
Figure Gas pressure in the third stage of the p ositron trap during a pump out cycle
The bu er gas feed is switched on at t s and switched o at t s
system with input lo cated at the left end of the trap as indicated in the arrow
This system is describ ed in the next section A cold trap is lled with liquid
nitrogen when the test substance do es not freeze at that temp erature These
substances includes helium neon argon krypton hydrogen nitrogen oxygen
methane and carb on tetra uoride The p ositron lifetime is typically ab out h
with liquid nitrogen in the cold trap When a more condensable test substance
is used the cold trap is lled with a water ethanol mixture chilled to ab out
C The use of chilled water ethanol mixture results in the p ositron lifetimes of
ab out m which is still much longer than the typical annihilation time scale of
s for the ray sp ectrum measurements
The trapp ed p ositrons can b e dump ed onto an annihilation plate and the
charge accumulated on the plate can b e measured using a charge sensitiveam
pli er The numb er of dump ed p ositrons can also b e measured by detecting the
keV annihilation rays We generally use a NaI Tl scintillator crystal in
combination with a photomultiplier tub e for this purp ose For the ray sp ec
trum measurements an intrinsic Ge detector is used to measure the line shap e
of the keV annihilation rays as a result of p ositron annihilation with the test gas in the fourth stage
Description of the experiments
Figure Schematic diagram of the p ositron trap
Chapter
Gas handling system
As previously noted it is imp ortant to study high purity test sub
stances The annihilation rates of large organic substances can b e several orders
of magnitude higher than those of small inorganic atoms and molecules As a
consequence a very small amount of impurities can havevery large e ects on the
exp erimental results Thus the careful handling of test substances and clean
ness of the system are essential We used substances with the highest purity
commercially available
For the annihilation rate measurements stability of the test gas pressure in
the p ositron trap is also imp ortant while fast switching of the test gas is imp or
tant for the ray sp ectral measurements to utilize available p ositrons e ciently
We use di erent gas handling systems for substances that exist as gases
liquids or solids which are describ ed b elow
Gases
Aschematic diagram of a gas handling system for gaseous substances at atmo
spheric pressure and ro om temp erature is shown in Fig Test gas from a
cylinder go es through a regulator the piezo electric valve and a solenoid valve
to the p ositron trap The piezo electric valveiscontrolled to adjust and stabi
lize the test gas pressure using a capacitance manometer pressure gauge reading
For ray sp ectral measurements the solenoid valveisusedtoswitchonando
the test gas into the p ositron trap In order to reduce the impurities in this
gas handling system the entire gas line is baked to C under vacuum after
a new test gas cylinder is installed In addition the gas line is ushed with the
test gas at least three times b efore a measurementistaken
Liquids and solids
The substances that exist as liquid or solid are intro duced as low pressure vap or
gases into the p ositron trap A schematic diagram of a gas handling system for
these substances is shown in Fig To ensure stable vap or pressure of a test
substance a test tub e containing the substance is submerged in a tub e containing
awater ethanol mixture The temp erature of this mixture is regulated with a
thermo electric unit The pressure of the test gas going into the p ositron trap is
regulated with a needle valve which is adjusted to pro duce a suitable p ositron
annihilation rate in all cases larger than the rate on the background gas For
ray sp ectral measurements two solenoid valves are used to switchonando
the test gas While the test gas is not going into the trap it is pump ed bya
Description of the experiments
Piezo- electric Power supply valve controller Switch
Piezo- Vacuum electric gauge valve To the Solenoid positron trap Valve Valve valve
Regulator
Gas cylinder Pumpout
port
Figure A schematic diagram of a gas handling system for test substances that exist
in gas form at atmospheric pressure
vacuum pump to avoid the pressure build up in the line The vacuum pump
is an oil free molecular drag pump backed by a diaphragm pump In order to
minimize the gas dissolved in the liquid substances a pro cess of freezing at liquid
nitrogen temp erature and thawing under vacuum is rep eated three times prior
to measurement Solid test substances were placed under a vacuum for an hour
prior to measurement in order to minimize the absorb ed gases
Annihilati on rate measurements
Positron annihilation rates are presented in Ch These rates are measured
using techniques similar to those describ ed in Refs
As discussed in the previous section various gases and vap ors may b e in
tro duced directly into the fourth stage in order to study the annihilation of
p ositrons on these substances Molecules that exist as liquids or solids at ro om
temp erature are intro duced in vap or form into the trap The use of low pressure
gases helps to insure that one is studying a binary pro cess involving one p ositron
Chapter
Needle Solenoid valve valve To the positron trap Solenoid valve Switch
Vacuum pump
Power supply Test tube
Water bath
Test Thermoelectric substance
unit
Figure A schematic diagram of a gas handling system for test substances which
are in liquid or solid form at atmospheric pressure
and a single molecule This avoids the p otential complications due to the clus
tering of atoms or molecules at the site of the p ositron b efore annihilation takes
place Annihilation rates are determined byaccumulating p ositrons for
a xed amount of time in the third stage lling waiting one second for the
p ositrons to thermalize after they are shuttled to the fourth stage and then
waiting a variable amount of time while the p ositrons annihilate with the test
gas storing After this storage time the remaining p ositrons are dump ed
onto a metal annihilation plate shown in Fig while the characteristic
keV annihilation radiation is measured using a NaI Tl scintillator The light
pulse amplitude from the scintillator is prop ortional to the numb er of p ositrons
detected A typical set of data is shown in Fig a and the annihilation rate
as a function of test gas pressure is shown in Fig b
The linear dep endence of the annihilation rate on test gas pressure shown
in Fig b con rms that the pro cess studied is a binary encounter b etween
the p ositron and a molecule In particular for a binary pro cess the observed
Description of the experiments
(a) 103
102 N (arb. units) N (arb.
101 0 4 8 12 store time (s) 1.0 (b) )
-1 0.8
0.6
0.4
0.2 annihilation rate (s
0.0 0 1 2 3 4 5
pressure (10-7 torr)
Figure Data for the annihilation of p ositrons on b enzene d a Numb er of p ositrons
remaining N as a function of time for various test gas pressures
and torr b Annihilation rate as a function of test gas pressure deduced from the data in a
Chapter
annihilation rate is given by
N X
where and S P are the annihilation rates due to the nitrogen bu er
N X X X
gas and to the molecule under study Here P is the test gas pressure S is a
X X
prop ortionality constant and is the annihilation rate on other large molecules
present in the vacuum system Using Eq r cn Z where n is
X X e X
the numb er density of the test molecule In the regime studied the ideal gas
approximation is valid and this density is related to the test gas pressure by
n P k T where k is the Boltzmann constantandT is the temp erature
X X B B
of the test gas Combining these equations Z of the test molecule can b e
e
expressed as
Z CS
e X
where C k T r c The value of this constantatT C K
B
is C s torr Thus Z can b e obtained from the slop e in the
e
observed annihilation rates versus pressure plot e g Fig b using Eq
The test gas pressure P is measured using a Bayard Alp ert ion gauge The
X
sensitivity ofthistyp e of gauge dep ends on the gas measured and the calibration
of this e ect is describ ed in App endix A
ray sp ectral measurements
Exp erimental pro cedure
The keV ray sp ectra resulting from p ositrons annihilating on a wide variety
of atoms and molecules are presented in Ch The exp erimentisoperatedin
a series of rep eated cycles of p ositron lling and annihilation In each cycle
p ositrons are accumulated for a xed p erio d of time typically s in the presence
of the N bu er gas The bu er gas is then shut o following a p ositron co oling
time of s The bu er gas is then pump ed out for s An intrinsic Ge detector
is then gated on and the test gas is intro duced Typically the sp ectrum is
accumulated on a multichannel analyzer MCA for s in the presence of the
test gas and then the test gas is turned o This cycle is rep eated for ab out h
to accumulate a large numb er of counts The total counts in the p eak is typically
The numb er of p ositrons in the trap and the pressures of the test gases
are carefully adjusted to obtain the highest count rates consistent with avoiding
ra y pileup in the detector which can distort the shap e of the sp ectrum
Description of the experiments
Sp ectral analysis
Wehave found that a Gaussian line shap e is a useful tting function for b oth
the detector calibration lines and the annihilation sp ectra observed from atoms
and molecules The tting function used also contains a complementary error
function comp onent which mo dels Compton scattering in the detector crystal
and a constant background It has the form
E E E E
f E A exp A A erfc
a E a E
t t
where E is the ray energy E is the full width half maximum FWHM of
t
the line a ln A and A are amplitudes A is the background and
erfc x is the complementary error function The t parameters are A A
A E and E Representing the counts in each energy bin E by y the
t j j
quantity minimized is
N
X
y f E
j j
r
N k
j
j
N is the numb er of bins used in the t and k is the number where y
j
j
is used as a measure of go o dness of the of tting parameters The value of
r
t and is exp ected to b e of order unity for a t to a go o d mo del The tting
function given by Eq is a go o d approximation for the calibration ray lines
b ecause the numb er of free electron hole pairs pro duced by a mono energetic
ray in a germanium crystal has a Gaussian distribution For calibration weused
essentially mono energetic rays emitted from a test source
To rst order wehave found that the annihilation lines can also b e analyzed
by tting Eq While this is a convenientwayofcharacterizing and com
paring data there is no a priori reason why the annihilation lines should have
Gaussian line shap es As discussed in Ch our data are now of su ciently high
quality to b e able to resolve departures from Gaussian line shap es The mea
sured annihilation line is the convolution of the intrinsic annihilation line shap e
and the detector resp onse Under the assumption of Gaussian line shap es the
intrinsic FWHM E is given by
E E E
t det
where E is the detector linewidth and E is the tted linewidth from
det t
Eq The linewidths quoted in this dissertation are the values of E
obtained in this way InSec we discuss other attempts i e b eyond the
one Gaussian approximation to t the measured sp ectra
Chapter
Calibration and detector resp onse
The energy scale of the detector resp onse was calibrated using keV and
keV ray lines from Eu and Cs test sources resp ectively The lines
are t with Eq to obtain the centroids and linewidths of the two p eaks
The centroids are used to calibrate the energy scale of the sp ectra while the
widths of these two lines are interp olated to nd the detector energy resolution
at keV The resolution is typically keV
The detector line shap e was also calibrated using a Sr calibration source
which has a ray line at keV conveniently close to the keV line
The sp ectrum measured with a Ci source is shown in Fig a The t
to Eq is shown in the gure as a solid line and yields The
r
linewidth of the Gaussian E istypically keV which agrees with
det
the interp olated value from keV and keV lines where keV is
the drift in the detector linewidth during a measurement The residuals from
the t are shown in Fig b These data deviate slightly from the t on the
lower energy side of the line This low energy tail may b e due to the trapping of
electrons holes in the defects of the Ge crystal Nonetheless the residuals
are generally quite small less than of the p eak counts on the lower energy
side and even smaller on the higher energy side As describ ed in
Ch these residuals are also generally much smaller than the deviations from
the Gaussian shap e of the observed annihilation lines In the follo wing we quote
the linewidth of the Gaussian t typically keV as the width of the detector
resp onse The detector energy resp onse and line shap e vary by a small amount
from daytoday typically keV and a separate calibration sp ectrum was
taken b efore and after each run
Description of the experiments
104 (a) 103
102
101 counts per channel 100
2 (b) 1
0
-1
residual counts (%) -2 505 510 515 520
E (keV)
Figure a ray sp ectrum of the keV line from a Sr source observed
sp ectra and t to the sp ectrum with a combination of a Gaussian and a step
function Eq The linewidth is keV b Residuals of the t
Chapter
Chapter
Annihilation rates
A p ositron can annihilate with one of the b ound electrons in a molecule The
annihilation rate is closely related to the interaction of the p ositron with the
molecule at very short distances since the rate is determined by the overlap of
p ositron and electron wave functions In this chapter exp erimental results of
annihilation rate measurements are presented along with previously measured
and theoretically calculated values Muchofrecent e ort in this area was fo cused
on p ossible explanations for the anomalously large annihilation rates observed
for large molecules and for the empirical scaling of annihilation rates with
ionization and p ositronium binding energies Sec Research on these
issues is also presented The ma jority of material covered in this chapter has
b een published elsewhere and unpublished data are sp eci cally noted
Theoretical considerations
As describ ed in Ch the p ositron annihilation rates on molecules are typ
ically expressed in terms of Z de ned as r cnZ Eq The
e e
annihilation of p ositrons on small atoms can b e understo o d in terms of simple
collisions Empirically it is found that Z for these molecules is of the
e
order of but somewhat larger than Z the numb er of electrons in the molecule
In contrast the annihilation rates for larger organic molecules are observed to b e
much higher than exp ected on the basis of simple mo dels It is
b elieved that this is due to the attachment of p ositrons to the molecule via long
lived p ositron molecule resonances but the detailed mechanism of attachment
and subsequent p ositron annihilation are not understo o d Pre
vious measurements givevarious values of Z Z ranging from
e
order unityto with anomalously high values for large organic molecules
Chapter
105
104
103 / Z eff
Z 102
101
100
0 50 100 150 200
Z
Figure Exp erimental values of Z Z plotted against Z noble gases sim
e
ple molecules alkanes p er uorinated alkanes p erchlorinated alkanes
p erbrominated and p erio dated alkanes solid square alkenes solid triangle up oxygen
containing hydro carb ons op en hexagon ring hydro carb ons solid triangle down sub
stituted b enzenes and solid diamond large organic molecules
Exp erimental values of Z Z for molecules are plotted against Z in Fig
e
showing the strong dep endence of Z Z on the size and chemical comp osition
e
of the molecules
Long lived resonances
The physical pro cess resulting in the observed values of Z might b e under
e
sto o d qualitatively in the following way The long range interaction b etween
Annihilation rates
the p ositron and the molecule is attractive due to the dip ole resulting from the
p ositron p olarizing the electron cloud in the molecule Atlow incident p ositron
energy this interaction will increase the collision cross section abovethe
c
value determined by the size of the molecule The collision rate canbe
c
expressed as n v where v is the velo city of the p ositron The velo city
c c
of the molecule is assumed to b e negligible When the p ositron molecule inter
action is a simple elastic collision the time spentby the p ositron in the
c
molecular electron cloud is approximately d v where d is the molecular di
c
ameter The probability of the p ositron annihilating during the collision maybe
c
where is the annihilation exp ected to have the heuristic form e
rate during the collision A rough estimate for is s whichis
the spin averaged lifetime of a p ositronium atom With these assumptions
el
the annihilation rate for such an elastic collision can b e expressed as
el
c
n v e
c
Because this expression can b e approximated as
c
c
el
n v
c
If on the other hand it is assumed that the p ositron forms a resonance with
the molecule the p ositron sp ends the resonance time in the vicinityof
res
the molecule Electron molecule resonances are known to o ccur with measured
values of as large as s so is not assumed here By
res res
res
analogy with Eq the annihilation rate for resonance collisions can
b e expressed as
res
res
n v e
res
where is the resonance formation cross section Comparing Eq and
res
Eq with the de nition of Z Eq it is found that
e
v
c c
el
Z
e
r c
for annihilation in elastic collisions and
v
res
res
res
e Z
e
r c
for annihilation in resonance collisions For p ositrons at K if we assume that
is of the order of cm and a simple elastic collision is considered where
c
el
from Eq When the collision is of the order of s then Z
c e
Chapter
involves attachment via long lived p ositron molecule resonances Eq can
b e expressed as
res
res
res
e Z
e
cm
res
Thus Z has its maximum value when If of the order of
res res
e
res
cm is assumed then Z from Eq This range of Z from
e
e
to is what have b een observed For Z Z the quantity Z can no
e e
longer b e interpreted as an e ectivenumb er of electrons participating in the
annihilation pro cess In this case Z should then b e regarded as a normalized
e
annihilation rate
For the case of electron molecule resonance collisions values of have
res
b een calculated successfully by applying the Marcus Rice equilibrium
mo di cation of the Rice Ramsp erger Kassel theory RRKM whichwas
develop ed to describ e unimolecular reactions The RRKM theory is a statistical
theory which assumes a rapid statistical redistribution of energy among the
various degrees of freedom of the molecule The theory has b een successfully
applied to describ e resonance collisions of electrons with selected molecules
and could p otentially pro vide quantitative insights into p ositron molecule
resonance lifetimes and annihilation rates
Large cross sections from the resonance collision
Consideration must b e given to the scattering of slow particles kd where
k is the wavenumb er of the scattering particle and d is the size of the target
molecule in a eld when the discrete sp ectrum of energy levels includes an s
state whose energy is small compared with the value of the eld U within its
range of action d This level is denoted by for a b ound state and
for an unb ound virtual state When the energy E of the particle undergoing
e
scattering is close to j j a considerable increase in the scattering cross section is
observed This enhancement of scattering cross sections is considered
in Ref and discussed in Sec
Results
In this section the values of Z measured in low pressure gases using the
e
p ositron trapping techniques describ ed in Ch are compared with those of
A unimolecul ar reaction is a reaction involvin g the isomerization or decomp osition of a
y
single isolated reactant molecule A through an activated complex A whichinvolves no other
y
molecule A A pro ducts
Annihilation rates
other exp eriments where the measurements were made in dense gases The
exp eriments in dense gases were p erformed
at pressures torr while the low pressure exp eriments
were p erformed at pressures torr In general the values of
Z in dense gases and those in low pressure gas exp eriments agree to within
e
Values of Z Z which scale Z by the numb er of electrons in the atom
e e
or molecule are also tabulated and they are summarized in Fig When
plotted in this manner the data show a large scatter Plotting Z as a function
e
of molecular p olarizability do es not appreciably reduce this scatter except for
small molecules where a dep endence on molecular p olarizabilitywas previously
noted Values of molecular p olarizability are tabulated in App endix B
along with other physical parameters In Sec another way of plotting
the data which app ears to provide more insightinto the physical mechanism
underlying the annihilation pro cess is describ ed
The data recently published in Ref and unpublished data mainly in
Tables and were measured using an ion gauge readout system with
a di erent resp onse from the previous measurements and some of the values
are di erent from the previous measurements The values of Z measured
e
with this ion gauge readout can b e larger than the previous measurements by
However the same ion gauge readout system is used for the data sets in
Tables and and the relative error should b e within Ion gauge
sensitivity calibrations were not done for some of the molecules in the new data
sets and they are estimated from the values of similar molecules The error
asso ciated with this estimation is not exp ected to exceed and should not
change the observed trends These p oints are noted in the text and or in the
tables
Noble gases
Exp erimentally measured and theoretically calculated values of Z for noble
e
gases are listed in Table and illustrated in Fig The theoretical calcula
tion based on the Kohn variational mo del for helium is in go o d agreement
with the measurements The p olarized orbital calculation for neon also
agrees reasonably well with the measurement Our values for argon krypton
and xenon are higher than those rep orted by other groups for measurements in
dense gases The ratios of the thermalization to the annihilation cross sections
calculated from Eq for argon krypton and xenon are and
resp ectively These values suggest that p ositrons may not b e thermalized b efore
annihilation in heavier noble gases in the dense gas exp eriments A higher
Chapter
Table Values of Z for noble gases References are given for previous
e
measurements
Molecule Formula Z Z Theory Z Z Z Ref
e e e
a b
Helium He
c
Neon Ne
d y
Argon Ar
e y
Krypton Kr
e y
Xenon Xe
z
y z
Measured in the p ositron trap measured in a dense Xe H gas mixture
a b c d e
Ref Ref Ref Ref Ref
temp erature p opulation of p ositrons would lead to a lower Z according to
e
theoretical calculations and the trend of higher values of Z measured
e
in our p ositron trap is consistent with this
In order to overcome the problem of slow thermalization of p ositrons in
the larger noble gases Wright et al develop ed a technique for measuring
p ositron annihilation in dense gas mixtures In their exp eriments a small admix
ture of H is used to increase the thermalization rate of the p ositrons The Xe H
exp eriments gave Z of which agrees with the value obtained in
e
the p ositron trap For krypton and argon the gas mixture exp eriments
pro duced similar results to the pure gas exp eriments in dense gases Our results
for krypton and argon are not in very go o d agreement with the dense gas results
Wehave no de nitive explanation of this discrepancy In principle systematic
errors in our measurements could account for the di erence and more careful
measurements for krypton and argon in the p ositron trap are planned It is
noted that the values measured in the p ositron trap for argon krypton and
Annihilation rates
100 eff Z
10
0 10 20 30 40 50 60
Z
Figure Theoretical and exp erimental values of Z for noble gases theoretical
e
values exp erimental values measured in the p ositron trap values measured in
exp eriments in dense gases and dense gas exp erimentwithH test gas mixture
The values measured in the p ositron trap are generally higher than those in dense gas
exp eriments
xenon are higher than the theoretical ones Table
Inorganic molecules
Values of Z for simple inorganic molecules are listed in Table Polar and
e
nonp olar molecules are tabulated separately The molecular dip ole moments
are also listed in Table and it can b e seen that p olyatomic p olar
molecules have relatively large values of Z with Z Z The exception
e e
Chapter
Table Measured values of Z for inorganic molecules The values of dip ole
e
moment DM have units of debye D
a
Molecule Formula Z Z Z Z DM D Ref
e e
Diatomic molecules nonp olar
Hydrogen H
Deuterium D
Nitrogen N
y
Oxygen O
Diatomic molecules p olar
Carb on monoxide CO
Nitric oxide NO
Polyatomic molecules nonp olar
Carb on dioxide CO
y
Sulfur hexa uoride SF
Polyatomic molecules p olar
Ammonia NH
y
y
Water H O
Nitrous oxide N O
Nitrogen dioxide NO
Methyl chloride CH Cl
Dichloro di uoromethane CCl F
y a
Measured in the p ositron trap Ref
is nitrous oxide which has a small dip ole moment The diatomic molecules
carb on monoxide and nitric oxide also have relatively small annihilation rates
At separations much larger than molecular dimensions the long range in
teraction b etween a p ositron and a p olar molecule is a dip ole interaction with
force prop ortional to p r where p is the p ermanent molecular dip ole moment
and r is the separation b etween the molecule and the p ositron This interaction
is stronger than that b etween a p ositron and a nonp olar molecule for which
Annihilation rates
the p ositron p olarizes the molecular electron cloud inducing a dip ole moment
and pro ducing a force prop ortional to r where is the p olarizabilityofthe
molecule
In the partial wave expansion the most signi cant comp onentisthes wave
where the p ositron wave function has a nite amplitude at the lo cation of the
molecule since the annihilation rate is the measure of the overlap of p ositron
and electron wave functions The p ermanent dip ole moment should not a ect
the scattering cross section for the s wave considerably However the p ositron
a nitymaybea ectedby the dip ole moment It is not clear how dip ole moments
sp eci cally enhance the annihilation rates
For nonp olar substances a correlation b etween Z and p olarizability for
e
some chemical sp ecies has b een rep orted earlier
Because of the structural complexity of p olyatomic molecules theoretical
values of Z are available only for a limited numb er of substances Positron
e
annihilation on H has b een extensively studied b ecause of the relative simplicity
of its structure A calculation using the Kohn variational metho d yields a Z
e
of which is smaller than the exp erimental values see Table The
calculation for N using p olarization p otentials with a phenomenological cuto
gives Z This value is smaller than the exp erimen tal values Ab
e
initio calculations using the Kohn variational metho d for N are currently b eing
investigated The calculation for NH with the xed nuclei approximation
and without the p olarization of molecular orbitals due to the incoming p ositrons
gives Z while the calculation including the p olarization increases the
e
value to ab out which is still much smaller than the exp erimental value
of or
Alkanes and substituted alkanes
Values of Z for alkanes and substituted alkanes are listed in Table and
e
values of Z Z are plotted against Z in Fig For alkanes Z Z increases
e e
from for methane to for hexadecane These anomalously high
values of Z Z might b e explained by long lived resonances It is noted
e
that Z Z do es not increase b etween do decane and hexadecane
e
Theoretical calculations of Z for CH are available Using the xed
e
nuclei approximation the values are without including the p olarization of
the molecular orbitals and with the p olarization These values are smaller
tal values see Table than the exp erimen
Substitution of hydrogen atoms in the alkanes by other atoms dramatically
changes Z Substitution by uorine decreases Z while substitution by io
e e
Chapter
Table Measured values of Z for alkanes and substituted alkanes
e
Molecule Formula Z Z Z Z Ref
e e
Alkanes
Methane CH
Ethane C H
Propane C H
y
Butane C H
isoButane C H
y
Pentane C H
y
Hexane C H
y
y
Heptane C H
y
Nonane C H
y
Decane C H
y
Do decane C H
y
Hexadecane C H
Deuterated alkanes
y
d Heptane C D
Per uorinated alkanes
y
Carb on tetra uoride CF
y
Per uoropropane C F
y
Per uorohexane C F
y
Per uoro o ctane C F
Perchlorinated alkanes
y
Carb on tetrachloride CCl
y
Hexachloro ethane C Cl
Perbrominated alkanes
y
Carb on tetrabromide CBr
Perio dated alkanes
y
Carb on tetraio dide CI
y Measured in the p ositron trap
Annihilation rates
Table Measured values of Z for isomers of p entane Some of data may
e
b e inconsistent with previous measurements due to the ion gauge readout All
values are measured in the p ositron trap
Molecule Formula Z Z Z Z Ref
e e
Pentane CH CH CH
Methylbutane CH C CH H C H
Dimethylpropane C CH
Ion gauge sensitivities are estimated
Table Measured values of Z for alkenes All values are measured in the
e
p ositron trap
Molecule Formula Z Z Z Z Ref
e e
Ethylene C H
Acetylene C H
Hexene C H
trans Hexene C H
Hexadiene C H
cis trans Hexadiene C H
trans trans Hexadiene C H
Hexatriene C H
dine chlorine or bromine increases Z by di ering amounts
e
Isomeric e ects of alkanes were studied for three di erent isomeric con g
uration of p entane and the measurements are listed in Table We do not
observeany systematic di erences b etween these three isomers even though the
values of Z di er by a factor of
e
Alkenes
The molecular structures and values of Z are illustrated in Fig Table
e
gives values of Z for various alkene molecules Intro ducing one double b ond
e
into the alkanes ethane and hexane to form ethylene and hexene resp ectively
has the e ect of approximately doubling Z In the case of hexene there is
e
no strong dep endence of Z on the lo cation of the double b ond Intro ducing
e
a second double b ond into hexene to form hexadiene further increases Z by
e
approximately another factor of two Once again there is no signi cant iso
meric dep endence Intro duction of a third double b ond do es not change Z e
Chapter
HEXANE HEXENES HEXADIENES HEXATRIENE
1,3-Hexadiene 1-Hexene 389,000 185,000 cis 2, trans 4-Hexadiene 1,3,5-Hexatriene
trans 3-Hexene 120,000 413,000 414,000
196,000 trans 2, trans 4-Hexadiene
388,000
Figure Values of Z and structures of alkenes with six carb ons
e
Table Measured values of Z for alcohols carb oxylic acids and ketones
e
All values are measured in the p ositron trap
a
Molecule Formula Z Z Z Z DM D Ref
e e
Alcohols
Methanol CH OH
Propanol C H CH OH
Carb oxylic acids
Acetic acid CH COOH
Propionic acid C H COOH
Ketones
Acetone CH COCH
a
Ref
appreciably as compared to hexadiene
Oxygen containing hydro carb ons
Values of Z for alcohols carb oxylic acids and ketones are listed in Table
e
These measurements fo cus on chemical trends of Z in molecules containing e
Annihilation rates
oxygen Alcohols carb oxylic acids and ketones eachhavevalues of Z Z ap
e
proximately an order of magnitude higher than do alkanes with the same number
of carb on atoms For the three carb on family of these molecules it is found that
acetone which has a C O group has the highest Z Z and that propionic
e
acid which has b oth O H and C O groups has slightly higher Z Z than
e
propanol which has an O H group The large dip ole moment of acetone Table
may b e resp onsible for its high Z Z value
e
Aromatics and saturated rings
Values of Z for ring hydro carb ons substituted rings aromatics and other
e
organic molecules are given in Table Forming hexane into the cyclic ring
comp ound cyclohexane dramatically reduces the value of Z A similar de
e
crease is noted when the symmetric ring b enzene is compared with hexane
The similar values of Z for b enzene and for cyclohexane compared with the
e
large value for hexane suggest that symmetry plays a more imp ortant role in
determining the value of Z than do es the presence of double b onds or delo cal
e
ized electrons It is noted however that b oth b enzene and cyclohexane lack
methyl groups whichmight b e the reason that Z is lower in these molecules
e
than in hexane As in the case of the alkanes p er uorinating aromatic hydro
carb ons to form such comp ounds as o cta uoronaphthalene hexa uorob enzene
and o cta uorotoluene results in a dramatic decrease in Z
e
Anumb er of substituted b enzene comp ounds were studied and Fig is
a summary of these results Substituting one hydrogen atom in the b enzene
molecule with any other functional group increases Z This is true even for
e
F which usually has the prop erty of reducing Z when substituted for hydro
e
gen atoms This phenomenon p oints to the imp ortance of molecular symmetry
in reducing Z in ring comp ounds The magnitude of the increase shows a wide
e
variation dep ending on the functional group b eing substituted varying from a
factor of two for F to a factor of for NO In the latter case the large
dip ole momentintro duced by the NO substitution mayalsocontribute to the
increase in Z Table Substituting one four or ve additional uorines
e
in C H F decreases Z monotonically which is consistent with the observa
e
tion that p er uoro carb ons havemuchlower values of Z than the analogous
e
hydro carb ons
In order to test the e ect of isomeric symmetry Z of xylene isomers i e
e
b enzene rings with two substituted CH groups in various relative p ositions
were measured The Z for para ortho and meta xylenes are all identical to
e
within the accuracy of the measurements and they are not signi cantly di erent
Chapter
Table Measured values of Z for ring molecules and aromatics All values
e
are measured in the p ositron trap
a
Molecule Formula Z Z Z Z DM D Ref
e e
Ring hydro carb ons
Benzene C H
Cyclohexane C H
Cyclo decane C H
Naphthalene C H
Decahydronaphthalene C H
Anthracene C H
Substituted rings
Octa uoronaphthalene C F
Substituted b enzenes
Toluene C H CH
para Xylene C H CH
ortho Xylene C H CH
meta Xylene C H CH N A
Aniline C H NH
Nitrob enzene C H NO
Chlorob enzene C H Cl
Bromob enzene C H Br
Fluorob enzene C H F
Di uorob enzene C H F
Penta uorob enzene C HF N A
Hexa uorob enzene C F
Octa uorotoluene C F CF N A
Other
Pyridine C H N
a
Ref Ion gauge sensitivity is estimated
from toluene Thus it app ears that once the symmetry of the b enzene ring is
broken by the addition of a methyl group further substitutions do not havea
strong e ect Para ortho and meta xylenes have di erent but small dip ole
moments If the isomeric symmetry is not signi cant in determining Z as the e
Annihilation rates
Benzene Cyclohexane Toluene CH 3
Zeff = 15,000 20,000 190,000
para-Xylene ortho-Xylene meta-Xylene CH 3 CH3 CH3 CH3
CH3 CH3 200,000 180,000 210,000
Fluoro- 1,4-Difluoro- Pentafluoro- Hexafluoro- benzene benzene benzene benzene F F F F H H F F F F
H H F F F F F H F 34,000 10,700 1,800 1,200
Chlorobenzene Bromobenzene Aniline Nitrobenzene
Cl Br NH 2 NO 2
72,300 172,000 400,000 430,000
Figure Values of Z and structures of cyclohexane and substituted b ezenes Sub
e
stitution of one hydrogen atom byany functional group increases Z indicating the
e
imp ortance of molecular symmetry in reducing Z in ring comp ounds
e
xylene data suggest studies of isomeric symmetry using molecules with larger
dip ole moments such as dinitrob enzenes may give us information ab out the
contribution of the molecular dip ole momenttoZ for these molecules without
e
signi cantly changing other prop erties of the molecules
Chapter
Table Measured values of Z for other large organic molecules All values
e
are measured in the p ositron trap
Molecule Formula Z Z Z Z Ref
e e
Tetraethylsilane Si C H
Glycerol C H O
Sebacic acid dimethyl ester C H O
An imp ortant factor in the conventional chemistry of substituted b enzenes is
whether the substituted group donates or withdraws electrons from the ring
Functional groups suchas CH which donate electrons to the ring tend to
activate the ring for electrophilic substitution of a second group and they induce
that substitution to o ccur at the ortho and para p ositions On the other hand
electron withdrawing groups like NO tend to deactivate the ring and to direct
substitution to the meta p osition Our data show no evidence that this e ect
in uences the value of Z For example the meta director NO pro duces a
e
value of Z similar to that resulting from the ortho para director NH while
e
Cl Br F CH and NH whichareallortho para directors havevery
di erentvalues of Z
e
Pyridine has similar electronic structure to b enzene Its Z see Table
e
is several times larger than that of b enzene p ointing to the imp ortance of molec
ular symmetry in determining Z This molecule also has nite dip ole moment
e
As can b e seen in Table the values of Z Z for some large molecules
e
suchasanthracene glycerol and sebacic acid dimethyl ester are higher than
those of large alkanes in which Z values are saturated namely those of do
e
decane and hexadecane In the framework of the mo del describ ed by Eq
this might imply that values of for these molecules are larger than those for
res
large alkanes
Deuterated hydro carb ons
Comparison of a deuterated molecule to a analogous protonated molecule pro
vides unique information ab out the annihilation pro cess Deuteration of molecules
do es not change their electronic structure but signi cantly changes the vibra
tional mo des of the molecules Annihilation rates of deuterated and protonated
hydro carb ons are measured and presented in this subsection The values of Z
e
Deuteration of molecules actually changes the electronic structure of the molecules slightly
Deuterons are heavier than protons and this causes the carb on hydrogen b ond length to change
However this change is much smaller than the change in the vibrational mo des
Annihilation rates
Table Measured values of Z for protonated and deuterated alkanes All
e
values are measured in the p ositron trap and presently unpublished The last
column is the ratio of Z for protonated alkanes to those for deuterated alkanes
e
Some of data may b e inconsistent with previous measurements due to the ion
gauge readout
Molecule n Protonated C H Deuterated C D Ratio
n n n n
Z
e
Methane
Hexane
Heptane
Octane
Nonane
Decane
for deuterated molecules are obtained using the ion gauge sensitivity calibration
of analogous protonated molecules which should b e a reasonable approximation
Deuterated alkanes
Annihilation rates of deuterated and protonated alkanes are measured system
atically and listed in Table Some inconsistency with other tabulated values
may b e noted as discussed earlier due to the ion gauge readout error How
ever the values listed in Table were measured sequentially using the same
ion gauge readout and the relativeerrorbetween deuterated and protonated
alkanes is small
The ratio of Z for deuterated alkanes to those for protonated alkanes is
e
listed in the last column of the table and plotted in Fig for comparison
Contrary to the data of deuterated b enzenes in the previous publication
which is also describ ed in Sec annihilation rates for the deuterated and
protonated alkanes except for decane are identical within the exp erimental er
ror as can b e seen in the gure These data do not supp ort the picture of the
p ositron forming a long lived resonance state with the molecule transferring
its kinetic energy to the vibrational mo des of the molecule The treatmentof
Christophorou et al for electron molecule collisions assumes the electron
transferring its kinetic energy to all vibrational mo des of the molecule statisti
cally The p ositron may only b e interacting with lower frequency mo des involv
ing C C b onds or chain b ending but not the C H or C D b onds whichmay
explain our observation
Chapter
3
(Protonated) 2 eff Z
1 (Deuterated) /
eff 0
Z 0 2 4 6 8 10
Number of carbon atoms
Figure Ratio of Z for deuterated alkanes to those for protonated alkanes plotted
e
against the numberofcarbonatoms n
The reason for the large di erence in the annihilation rates b etween deuter
ated and protonated decanes Table is not known at this moment One
p ossibility is that the deuterated decane sample mayhavebeencontaminated
Deuterated b enzenes
The annihilation rates of protonated partially deuterated and fully deuterated
b enzenes are listed in Table and the structures of these b enzenes are also
illustrated in Fig As can b e seen deuterated b enzenes have higher Z
e
than the fully protonated b enzene Benzene d C H D and b enzene d
C H D have higher Z than b enzene C H and b enzene d C D This
e
maypoint to the imp ortance of molecular symmetry discussed in Sec
Annihilation rates
Table Measured values of Z for deuterated b enzenes All values are
e
measured in the p ositron trap
Molecule Formula Z Ref
e
Benzene C H
Benzene d C H D
Benzene d C H D
Benzene d C D
Partially uorinated hydro carb ons
As can b e seen in Sec alkanes havevery large annihilation rates In
contrast the analogous p er uorinated alkanes have a few orders of magnitude
smaller annihilation rates The transition from the large annihilation rates to the
small rates mayprovide us with insights into determining the physical pro cess
resp onsible for the anomalously large annihilation rates observed for large hydro
carb ons Hydrogen atoms in hydro carb on molecules can b e selectively replaced
with uorine atoms to form partially uorinated hydro carb ons and studies of
these molecules are discussed in this subsection
The exp erimentally measured annihilation rates of partially uorinated hy
dro carb ons are listed in Table Some inconsistency with previously tabu
lated values may also b e noted for this table due to the ion gauge readout error
as discussed earlier
An interesting trend is that the molecules with one uorine atom havethe
highest annihilation rates among the molecules with the same number of carbon
atoms Further uorination reduces the annihilation rates gradually to the lowest
value for p er uorinated molecules It is noted that the molecules with one uo
rine atom are highly dip olar However the e ect of p ermanent dip ole moments
to the annihilation rates is not understo o d as discussed earlier Sec
Gribakin attempted to explain this e ect of increased Z for one substi
e
tuted uorine atom in terms of large scattering cross section as discussed in
Sec He calculated the scattering lengths of partially uorinated methanes
employing the zero range p otential approximation and the trend of annihi
lation rates at ro om temp erature are in reasonable agreement with this mo del
This theory also predicts the dep endence of annihilation rate on p ositron mo
mentum p to b e
e
Z p
e e
p
e
Chapter
Table Measured values of Z for partially uorinated hydro carb ons All
e
measurements are p erformed in the p ositron trap and unpublished Some of data
may b e inconsistent with previous measurements due to the ion gauge readout
Molecule Formula Z Z
e
carb on molecules
Methane CH
a
Methyl uoride CH F
a
Di uoromethane CH F
a
Tri uoromethane CHF
Carb on tetra uoride CF
carb on molecules
Ethane C H
a
Fluoro ethane C H F
a
Tri uoro ethane CF CH
a
Tri uoro ethane CHF CH F
a
Tetra uoro ethane CF CH F
a
Tetra uoro ethane CHF CHF
a
Hexa uoro ethane C F
carb on molecules
Propane C H
a
Di uoropropane CH CF CH
a
Tri uoropropane CF C H
Per uoropropane C F
carb on molecules
Hexane C H
a
Fluorohexane CH FC H
Per uorohexane C F
Benzene based molecules
Benzene C H
Fluorob enzene C H F
a
Di uorob enzene C H F
a
Di uorob enzene C H F
Di uorob enzene C H F
a
Tri uorob enzene C H F
a
Tetra uorob enzene C H F
Penta uorob enzene C HF
Hexa uorob enzene C F
a
Ion gauge sensitivityisapproximated
Annihilation rates
Benzene Benzene-d H D H H H H
H H H H H H
Z eff = 15,000 36,900
Benzene-1,3,5d3 Benzene-d 6 D D H H D D
D D D D H D
43,800 30,500
Figure Values of Z and structures of deuterated b enzenes studied Deuterated
e
b enzenes have higher values of Z as compared to the ordinary b enzene
e
where is the inverse of scattering length If the trend of annihilation rates for
partially uorinated methanes are explained by the mo del describ ed here this
equation indicates a stronger annihilation rate dep endence on p ositron temp er
ature for CH F than for CH However a preliminary measurementby Kurz et
al suggests that the annihilation rates dep end similarly for CH F and CH
which disagree with the prediction Further measurements of the dep endence of
Chapter
Z on p ositron temp erature are warranted Even if Gribakin s theory were to
e
explain the trend of annihilation rates for partially uorinated hydro carb ons it
is not exp ected to explain the anomalously large annihilation rates Even if the
scattering length is very large the annihilation rate is limited by the
thermal momentum of the p ositron as can b e seen from Eq
Discussion
In this section studies closely related to annihilation rate measurements are
discussed The empirical scaling of annihilation rates discovered by Murphy
and Surko is presented in Sec Tinkle et al develop ed a technique
for heating electron or p ositron plasmas This metho d is applied to
measure the dep endence of annihilation rate on p ositron temp erature whichis
presented in Sec The latest theoretical progress in this area is summa
rized in Sec including a recent attempt to explain the anomalously large
annihilation rates for large organic molecules Other issues are discussed in
Sec and a summary is given in Sec
Empirical scaling of annihilation rates
Murphy and Surkodiscovered previously a linear relationship b etween log Z
e
and E E for molecules without double b onds where E is the
i Ps i
ionization p otential of the molecule and E eV is the
Ps
binding energy of a p ositronium atom see App endix B for values of E This
i
relationship holds for alkanes substituted alkanes noble gases and all nonp olar
molecules studied thus far and is illustrated in Fig It should b e noted that
plotting the data as any function of E would also collapse the data on a single
i
curve Cho osing E E results in the curve approximating a straight line
i Ps
on a semi log plot No theory explains this relationship however Murphy and
Surko previously p ointed out that this empirical scaling might suggest a mo del in
which a p ositronium atom moves in the electrostatic eld of a p ositive ion
Murphy and Surko found that the linear relation b etween log Z and E
e i
E do es not hold for molecules with double b onds However some
Ps
of these molecules do come close to the linear relation as shown in Fig
This gure shows data for oxygen containing hydro carb ons and simple molecules
with dip ole moments and or double b onds Oxygen containing hydro carb ons lie
slightly b elow the line Most of the simple molecules lie close to the line with the
exception of O NH NO and NO Any systematic trends for these molecules
have not b een identi ed
Annihilation rates
Ei (eV) 25 15 13 12 11 10
106
104
eff Z
102
100 0.1 0.2 0.3 -1 -1
( Ei - EPs ) (eV )
Figure Values of Z for non p olar molecules containing only single b onds are plot
e
ted against E E where E is ionization p otential of molecule lab eled on top of
i Ps i
graph and E eV is the binding energy of a p ositronium atom noble gases
Ps
simple nonp olar molecules alkanes p er uorinated alkanes perchlo
rinated alkanes p erbrominated alkane and solid diamond tetraethylsilane The
solid line is a linear regression to the data The ionization p otentials of p erchlorinated
alkanes and the largest alkanes are not known accurately which could account for larger
deviations from the line for these molecules
Figure shows the same plot for alkenes ring hydro carb ons and sub
stituted b enzenes The ma jority of these molecules are quite far from the t
ted line to the data in Fig and Z values seem to reach a saturation
e
around Z for alkenes and substituted b enzenes This saturation
e
may b e a result of a p ositron molecule resonance time b eing larger than res
Chapter
Ei (eV) 25 15 12 11 10 9.5 9.1
106
CH3COCH3
C2H5COOH CH3Cl C2H5CH2OH 104 CH3COOH
eff CH3OH Z CCl2F2 NH3 NO2
H2O 102 CO2 N2O NO O N2 2 CO
100 0.1 0.2 0.3 0.4 -1 -1
( Ei - EPs ) (eV )
Figure Values of Z plotted against E E for oxygen containing hydro
e i Ps
carb ons and small molecules with a dip ole moment and or double b onds simple
nonp olar molecules with double b onds solid triangle down simple p olar molecules
and oxygen containing hydro carb ons The solid line is the linear regression from
Fig
the spin averaged annihilation time for a p ositronium atom i e in the notation
of Sec which as discussed in Sec might lead to sucha
res
saturation The value of Z for anthracene is an order of magnitude larger than
e
this saturated value which could p ossibly b e explained as follows Z dep ends e
Annihilation rates
Ei (eV) 10 8.5 8.0 7.7 7.5 107
Anthracene
106 Naphthalene Aniline
5 eff 10 Z
104
103 0.4 0.8 1.2 1.6 -1
( Ei - EPs ) (eV-1)
Figure Values of Z plotted against E E for alkenes ring hydro carb ons
e i Ps
and substituted b enzenes solid square alkenes op en hexagon ring hydro carb ons
toluene and xylenes and other substituted b enzenes The solid line is the linear
regression from Fig Note that the range of E E plotted is much larger
i Ps
than those in Figs and
b oth on the resonance formation cross section and the resonance time
res res
as shown in Eq An order of magnitude increase in is reasonable for
res
a large molecule suchasanthracene as compared with the alkenes substituted
b enzenes and naphthalene which could account for the higher saturation value
of Z e
Chapter
1.0 He Ne 0.8
0.6 Ar
0.4 Kr
normalized anihilation rate anihilation normalized 0.2 Xe
0.1 1
positron temperature, kBT (eV)
Figure Dep endence of annihilation rates of noble gases on p ositron temp erature
taken from Ref Exp erimental data He Ne Ar Kr and
Xe Also shown are theoretical calculations Kohn variational approximation for
He and p olarized orbital approximation
Dep endence of annihilation rates on p ositron temp erature
Tinkle et al develop ed a technique for heating the p ositron gas con ned in the
p ositron trap by applying RF noise to one of the electro des Using this
technique Kurz et al were able to make the rst systematic measurements
of the dep endence of annihilation rates on p ositron temp erature for noble gas
atoms Although I was not directly involved with this work I brie y re
view the results here since they provide an imp ortant part of our understanding
of the p ositron atom interaction The measured values of Z are plotted in
e
Fig where the data are normalized to the ro om temp erature values The
theoretically calculated temp erature dep endences based on the p olarized orbital
approximation except for He are also shown in the gure These
predictions are in excellent agreement with exp eriment This agreement is some
what surprising since the predicted absolute values of Z at ro om temp erature
e
for krypton and xenon do not agree well with the measurements as
Annihilation rates
canbeseeninTable Recently Kurz et al have made preliminary measure
ments of dep endence of annihilation rates on p ositron temp erature for a small
number of hydro carb ons These measurements are exp ected to provide an
additional constraint to theoretical mo dels e g Secs and
Recent theoretical work
Semi empirical approach
The anomalously large annihilation rates observed for large organic molecules
have not b een theoretically understo o d and a mo del for explaining the
large annihilation rates in the constraint of other exp erimental evidences which
are presented in this chapter has b een a challenge Recently Laricchia and
Wilkin have attempted a semi empirical approach to explain this phenomena
Motivated by the empirical scaling describ ed in Sec their mo del
assumes that the incoming p ositron forms a p ositronium atom inside a molecule
in the uncertainty principle time scale of
h
t
jE E E j
e i Ps
They argue that in this time scale the p ositron in the virtual p ositronium atom
annihilates by picking o one of the other b ound electrons in the molecule where
the electron density around the p ositron is enhanced by p olarization This mo del
is consistent with the scaling of annihilation rates with E E for p ositrons
i Ps
with energy E E E and reasonable agreement with observed ro om
e i Ps
temp erature annihilation rates is seen
They interpret their mo del as predicting that the annihilation rates diverges
at E E E with the form
e i Ps
Z
e
jE E E j
e i Ps
Motivated by this mo del Humb erston and Van Reeth have p erformed precise
numerical calculations of p ositron annihilation rate of helium just b elowthe
p ositronium formation threshold and they have observed a divergence in
the annihilation rate The nature of the divergence is however much faster
than that exp ected from the mo del byLaricchia and Wilkin The divergence
observed by Humb erston and Van Reeth can b e understo o d by the divergence
in the scattering length as discussed in Sec not due to the uncertainty
principle An exp eriment using the narrow energy spread p ositron b eam recently
develop ed in our lab oratory to study Z near the p ositronium formation e
Chapter
threshold energy may give us deep er insightinto the nature of the interaction
at the threshold for Ps formation
Large scale calculatio ns for molecules
Annihilation rate measurements for a wide range of molecules havenowbeen
made as can b e seen in Sec However theoretical work on annihilation
rates for molecules had b een limited to the simplest molecules Sec Re
cently daSilva et al have made the rst large scale calculation of a hydro carb on
molecule with an anomalously large annihilation rate namely ethylene C H
using the Schwinger multichannel metho d The scaling of annihilation rates
with E E suggests that the physics involved in the observed anoma
i Ps
lously high annihilation rates may b e dominated by pseudo p ositronium atom
formation in the eld of the molecular ion Their calculation of annihilation rate
including the pseudo p ositronium formation channel brings the annihilation rate
close to the observed value In addition the recent measurement of annihilation
rate dep endence on p ositron temp erature for this molecule by Kurz et al is
also in reasonable agreement with their calculation
Other issues
Noble gas atoms
The relatively simple atomic structure of the noble gases provides a test of
our understanding of low energy p ositron atom interactions Even in this case
there are discrepancies b etween exp erimental values measured in the p ositron
trap and theoretical values based on p olarized orbital calculations see Table
for the case of krypton and xenon The data presented here indicate that
reexamination of the theory mightbewarranted Recently Dzuba et al hav e
theoretically investigated the e ect of the virtual p ositronium formation channel
on the annihilation of noble gas atoms as suggested in the scaling describ ed
in Sec Even though they have not calculated the annihilation rates their
analyses provide useful insights into p ositron atom interactions
Repro ducibility of measurements
For earlier studies only a small numb er of p ositrons were available and con
sequently uncertainties of a factor of two are p ossible in the measured values
of Z Subsequently considerably more p ositrons have b ecome available
e
and the main source of error is now the uncertainty in the pressure of the
Annihilation rates
test gas It is likely that the early measurementofZ of nonane see Table
e
is higher than the recent measurementofZ of decane for this reason
e
Delo calized b onds in b enzene
As a result of earlier studies it was suggested that the reduction of Z in
e
b enzene as compared with hexane might b e due to the presence of delo calized
b onding electrons in the b enzene ring However measurements for cy
clohexane whichcontains no delo calized electrons yield a value for Z similar
e
to b enzene indicating that delo calized electrons may not b e resp onsible for this
e ect
Determination of p ositron annihilati on sites in a molecule
The determination of p ositron annihilation sites in a molecule can give a strin
gent constraint on a theoretical mo del of annihilation pro cesses This kind of
information can b e obtained from studies of the Doppler broadening of the
keV annihilation ray line The earliest study of this typ e concentrated on
hydrogen b ecause of its imp ortance in the pro duction of astrophysical p ositron
annihilation radiation Tang et al b egan more comprehensive studies of the
energy sp ectra of annihilation radiation in a variety of molecules including hy
dro carb ons and p er uoro carb ons These studies havenow b een extended
to include many of the comp ounds rep orted in this chapter Wehave made
signi cant progress in this area recently which is the sub ject of the next
chapter Ch
Current state of annihilation rate studies
The anomalously large annihilation rates have still not b een explained theo
retically even though some attempts have b een made The deuterated alkane
studies describ ed in Sec seem to rule out the p ossibility of p ositron form
ing long lived comp ound with the target molecule b y transferring its kinetic en
ergy to the vibrational mo des The scaling of annihilation rates describ ed in
Sec p oints to a pro cess involving electronic excitation e g highly corre
lated electron p ositron complex in the eld of a p ositive molecular ion b eing
resp onsible for the observed annihilation rates The enhancement in the scat
tering cross section alone is not likely to explain the observation as discussed in
Sec An inelastic channel other than molecular vibration may b e resp on
sible for the formation of long lived p ositron molecule comp ounds but if sucha
channel exists it has not b een identi ed
Chapter
Concluding remarks on annihilation rate mea
surements
In this chapter p ositron annihilation rates on molecules studied in a p ositron
trap have b een presented These measurements are compared with those done
using other techniques Where more than one measurementisavailable for a
particular molecule the data are in general in reasonable agreement The data
exhibit a numberofchemical trends and illustrate the imp ortance of electronic
structure and symmetries Even though theoretical progress has b een made re
cently features of the results such as the anomalously large annihilation rate
observed for large organic molecules have not b een understo o d A systematic
survey of annihilation rates for various molecules presented in this chapter pro
vides stringent constraints for the development of theoretical mo dels to explain
the observed trends including the anomalously large annihilation rates
Chapter
Annihilation ray sp ectra
Intro duction
Extensive measurements of the momentum distributions of annihilating electron
p ositron pairs have b een p erformed in solid and liquid targets and they
provide information ab out the annihilation pro cesses and other prop erties of
materials In this chapter a technique for measuring the momentum distribu
tion is applied to make systematic measurements in gaseous media which are
su ciently tenuous so that the interaction of p ositrons with an individual atom
or molecule can b e isolated and studied
Earlier measurements of this typ e in gases were mainly p erformed in high
density using a di erent technique from the one describ ed here As discussed
in Sec one disadvantage of the earlier metho d is that p ositronium atom
formation can take place during the slowing down of the p ositrons and subse
quent annihilation of the thermalized p ositronium atoms can obscure the free
p ositron annihilation signal Weavoid the annihilation signals from p ositronium
atoms by the use of the p ositron trap The signals from p ositronium atoms dur
ing a measurement are eliminated by co oling the p ositrons b elow the formation
threshold b efore the sample gas is intro duced
Previous exp eriments of Doppler broadened ray sp ectra in Penning traps
demonstrated the feasibility of the use of stored p ositrons for sp ectral
measurements Subsequent improvements in p ositron mo deration and
trapping e ciency aswell as in the gas handling system havenow enhanced
the signal to noise ratio bytwo orders of magnitude This has p ermitted a
range of new exp eriments including detailed comparison of the annihilation line
shap e with theoretical calculations the simulation of astrophysical p ositron
annihilation and the lo calization of the sites of p ositron annihilation in
Chapter
complex molecules
In this chapter a systematic study of p ositrons interacting with a wide va
riety of atoms and molecules is describ ed Data are presented for noble gases
inorganic molecules alkanes alkenes aromatics substituted hydro carb ons as
well as fully and partially uorinated hydro carb ons Imp ortant results include
demonstration of the ability to resolve for the rst time in gaseous media non
Gaussian features in the line shap es and the detection of more than one annihi
lation site in molecules including distinguishing annihilation on the C H b ond
from that on the uorine atom in partially uorinated hydro carb ons The data
presented also indicate that in hydro carb ons annihilation on the C H b ond from
that on the C C b ond can b e distinguished In all molecules studied the data are
consistent with the p ositrons annihilating predominantly with valence electrons
A study of halogenated hydro carb ons is also presented This study shows that
the p ositrons annihilate on the halogen atoms with a linewidth very similar to
that of the related noble gas atom particularly in the case of the larger halogens
The systematic studies presented in this chapter provide useful constraints on
theories of low energy p ositron atom and p ositron molecule interactions
This chapter is organized in the following manner In Sec previous
exp eriments to measure the momentum distributions of annihilating electron
p ositron pairs are reviewed The results of the exp eriments are describ ed in
Sec including the results of an extensive study of partially uorinated hy
dro carb ons The exp erimental setup was describ ed previously in Sec
Detailed analyses of sp ectral line shap es are presented in Sec In Sec
the implications of these results for current theoretical work and for progress in
other areas of p ositron molecule interactions are discussed A brief set of con
cluding remarks is presented in Sec The sub ject discussed in this chapter
is published in Ref
Momentum distribution measurements
An electron p ositron pair annihilates by emitting two quanta of keV rays
at an angle of in the center of mass frame of the two particles However in
the lab oratory frame the rays carry awa y the initial momentum of the center
of mass of the pair Thus as illustrated in Fig the angle of emission of
the two photons relative to one another deviates slightly from due to the
p erp endicular comp onents of the momentum of the electron p ositron pair p and
x
p The rays are Doppler shifted in energy due to the longitudinal momentum
y
comp onentofthepair p When p p m c the angle of deviation can
z x y
Annihilation ray spectra
S\ S /θ\ γ
S ] γ /θ[ S[
/
Figure Illustration of the momentum of an annihilating electron p ositron pair
p and the resulting raymomenta and An annihilation event is observed
with two detectors placed with resp ect to the annihilation site at distance L
The longitudinal comp onentof p p shifts the energies of rays and the tangential
z
comp onents p and p de ect the rays by an angle The angle of
x y
x y
de ection is exaggerated in this gure
b e expressed as
p
j
j
m c
where j x or y m is the rest mass of the electron and c is the sp eed of light
The Doppler shift in the energy E is given by
cp p
z z
E E
m c
where E m c is the rest mass energy of the electron The p erp endicular
comp onents of the momentum of the annihilating pair can b e studied by mea
suring the angular correlation of two rays The longitudinal comp onent can
b e measured by observing the Doppler broadening of the ray sp ectrum using
high resolution solid state detectors such as lithium drifted or intrinsic germa
nium detectors
When annihilation follows thermalization of the p ositrons in the medium
e g with the characteristic energy of kT eV corresp onding to ro om
temp erature the momentum of the annihilating pairs is typically dominated
by the momenta of the electrons Techniques for measuring the momentum
distributions of the annihilation rays were develop ed initially for the studies
Chapter
of p ositron annihilation in condensed media These techniques havebeen
applied to studies of p ositron gas interactions as well When the medium
is a crystalline solid p and p can b e distinct For example the anisotropyin
x y
two dimensions has b een observed and studied in some materials When
the medium under investigation is a liquid or gas the momentum distribution
is rotationally averaged and the three momentum comp onents are equivalent
In this case the angular deviation and the energy spread E are related by
E m c
and angular correlation and Doppler broadening measurements can b e com
pared
Annihilation ray angular correlation measurements
The technique of angular correlation of annihilation radiation ACAR was de
velop ed to determine the p erp endicular comp onents of the momenta of annihi
lating electron p ositron pairs in solids liquids and dense gases Initially
the measurements were p erformed in a one dimensional geometry in which
two ray detectors are lo cated b ehind slit collimators on opp osite sides of the
annihilation region One of the detectors is scanned as a function of the angle
between the two detectors and coincidentevents are recorded One advantage of
the ACAR metho d is its high resolution Typical angular resolutions achievable
are ab out mrad whichisequivalenttothe ray energy resolution of
keV using Eq
In order to obtain high resolution the slits must b e placed as far from the
annihilation cell as p ossible typically tens of meters This results in reduced
count rates due to the small solid angle subtended by the detector at the sam
ple In order to obtain b oth high resolution and a large number of counts in a
reasonable amount of time one would liketohaveasmany p ositrons as p ossi
ble annihilating in a small volume This condition can b e satis ed in solid and
liquid targets but in this case annihilation mayinvolve the interaction
of a p ositron with multiple atoms or molecules In contrast in gaseous media
the two b o dy assumption is more likely to b e met but ACAR measurements
are more di cult b ecause the mean free path of p ositrons in gases is relatively
large and results in a large annihilation region and low count rates The rst
ACAR measurements in gaseous media w ere rep orted byHeinb erg and Page in
However their study was fo cused on p ositronium atoms in which the
information content of the signal is less sensitive to the details of the sp ectra
The intro duction of the D ACAR detector has enabled measurements
Annihilation ray spectra
in the gas phase with signi cantly increased count rates For D ACAR two
relatively large NaI crystals with p osition sensitive detectors attached replace
the detector slit combinations The p osition sensitive detectors can accurately
identify the lo cation of scintillations pro duced by rays without muchlossof
count rate The rst quantitativeACAR results of free p ositrons annihilating
on atoms in gaseous media were done by Coleman et al using a D ACAR
detector
Doppler broadened ray sp ectral measurements
For the exp eriments describ ed in this chapter an alternative metho d of ob
taining the momenta of the annihilating electron p ositron pairs was used The
Doppler broadening of the annihilation line was directly measured using a high
energy resolution solid state ray detector an intrinsic germanium detector
in conjunction with a multi channel analyzer MCA This yields the longitudi
nal comp onent p of the annihilating pair s momentum which is equivalentto
z
either of the other two comp onents in an isotropic medium such as a gaseous
target One advantage of the Doppler broadening technique is that a high count
rate can b e obtained since the detector can b e placed close to the annihilation
region and this results in a large collection solid angle This p ermits mea
surements in di use media suchaslow pressure gases Another
advantage of this technique is the compactness of the equipment and the ease of
installation As describ ed in Ch this technique can also b e applied to studies
of p ositron annihilation in the interstellar medium where ACAR techniques are
inapplicable However one disadv antage of the Doppler broadening technique
is its relatively p o or resolution For example an intrinsic Ge detector typically
has an energy resolution of keV at keV as compared with the equivalent
ACAR resolution of keV In the exp eriments describ ed here an intrinsic Ge
detector is used to takeadvantage of the high count rate in di use media where
p ositrons are interacting with low pressure gas atoms or molecules
Lynn et al employed an improved implementation of the Doppler broadening
approach which utilizes two high resolution Ge detectors placed with re
sp ect to the annihilation region This technique can dramatically increase
the signal to noise ratio of the data Use of this technique allowed them to detect
p ositron annihilation on inner shell electrons in condensed media This metho d
can in principle also b e used for studies of p ositron annihilation in gaseous
media which are discussed in Sec
Chapter
Results
In this section the results of the Doppler broadening of the ray sp ectra from
p ositrons annihilating on a variety of atoms and molecules in the Penning trap
are rep orted The results from previous studies of momentum distributions and
theoretical calculations are also tabulated and compared
Typical sp ectra from our exp eriment are shown in Fig along with the
detector resp onse The annihilation lines shown are the sp ectra from H and Ne
which are the narrowest and widest lines observed resp ectively The observed
linewidths corresp ond to the p ositrons annihilating predominantly with the va
lence electrons of the atoms and molecules However we also have evidence of
annihilation on inner shell electrons and this will b e discussed in Sec and
in Ch As can b e seen in Fig the detector width is substantially narrower
than the observed annihilation lines The high precision of the measurements is
evident from the small scatter in the data The total number of ray counts in
a sp ectrum is ab out unless otherwise stated For the exp erimentally mea
sured sp ectra presented in gures the error bars shown represent the exp ected
statistical uncertainties in sp ectral amplitude due to the nite number of ray
counts Sp ectra were recorded in hour time segments and the linewidth
was calculated from each segment The tabulated linewidths were obtained by
averaging these linewidths The variations were typically to keV Mea
surements of some substances were rep eated in separate runs on di erentdays
and those linewidths generally agree within keV The uncertainty in the de
tector resp onse is at most keV The exp erimental precision of the linewidths
is estimated to b e typically k eV
In the remainder of this section annihilation line data for a variety of sub
stances are presented Some of the tables also list the annihilation rates in
terms of Z where they are relevant in the discussion The sources of the
e
values are listed in Ref and in Ch unless otherwise noted The values
of the previously measured linewidths from ACAR measurements are quoted in
keV as converted from the ACAR linewidths using Eq
Noble gases
The simple electronic structure of noble gas atoms has made them attractive
candidates for studies of p ositron atom interactions Comparison b etween ex
p eriments and theories are available for all of these atoms Previ
ous theoretical calculations were based on the p olarized orbital approximation
with the exception of the helium studies
Annihilation ray spectra
1.0
0.8
0.6
0.4 normalized counts
0.2
0.0
506 508 510 512 514 516
E (keV)
Figure Observed sp ectra from H and Ne plotted on a linear scale Solid lines
are drawn to guide the eye For the purp ose of comparison the keV line from
Sr is shifted to keV which represents the detector resp onse The sp ectra are
normalized to unity at the p eak
A qualitative understanding of the linewidths of the noble gases can b e ob
tained by considering the simple approximation of the p ositron in the static
p otential of the atom in its Hartree Fock ground state While this theory gives
Chapter
Table The ray linewidths for noble gases obtained from Gaussian ts to
the data in keV For comparison exp erimental values from other metho ds as
well as theoretical values are listed
a b c d
Gas This Shizuma Coleman Stewart Theory Theory
study static
e
Helium
f
g
h
i
Neon
j
Argon
k
Krypton N A
k
Xenon
a b c d e f g
Ref Ref Ref Ref Ref Ref Ref
h i j k
Ref Ref Ref and Ref
a signi cant underestimate of Z the ray linewidths are in reasonable agree
e
ment with exp eriment Table This indicates that the momentum dis
tribution of the electrons in the atomic ground state is the most signi cant
factor in determining the linewidths The exp erimentally measured linewidths
are consistently smaller than the predictions of this simple theory
In Table we compare our ray sp ectra for noble gases with the previous
measurements as well as with theoretical calculations The theoretical calcula
tions predict the general trend of the exp erimental linewidths even though the
calculated values di er from our measurements
Helium
Helium is the simplest stable atomic gas and it has b een studied extensively
Rigorous calculations are p ossible for p ositron helium interactions Measure
ments for helium in our system are restricted by the limited capacity of our
cryogenic pumps for this gas so that the data quality is not as go o d as those
for other gases The exp erimentally measured sp ectrum is shown in Fig
together with a very recent calculation using the Kohn variational metho d
Excellent agreement can b e seen b etween exp eriment and theory extending over
three orders of magnitude in sp ectral amplitude These data provide the rst
exp erimental evidence for deviations from the empirical Gaussian line shap e de
scrib ed ab ove and shown by the dashed line in Fig While such deviations
Annihilation ray spectra
104 (a) 103
102
101
100 400 (b)(b)506 508 510 512 514 516 200
0 counts per channel per counts -200 400 (c)506 508 510 512 514 516 200 Energy (keV)
0
-200 506 508 510 512 514 516
E (keV)
Figure a Annihilation ray sp ectrum for p ositrons interacting with helium atoms
exp erimental measurements theoretical prediction of Ref convolved with
the resp onse of the Ge detector Gaussian function t to the exp erimental data
b Residuals from the Gaussian t c Residuals from the theoretical calculation
are exp ected previous exp eriments were not su ciently precise to discern them
Neon argon krypton and xenon
Sp ectra for neon argon krypton and xenon are shown in Fig and the values
of the linewidths are listed in Table The linewidth for neon is the largest
Chapter
100
10-1
normalized counts 10-2
10-3 512 514 516 518 520 522
E (keV)
Figure Exp erimentally measured ray sp ectra from noble gases neon
argon solid square krypton and xenon The p eak heights are normalized to
unity The sp ectra shown are for the higher energy side of the ray line since the step
function in the detector resp onse is absent in this region and consequently the data
qualityisbetter
In fact it is the widest line observed for anyatomormolecule For atoms
larger than neon the linewidths decrease as the sizes of the atoms increase
Calculations using the p olarized orbital approximation are listed in Table
Annihilation ray spectra
The higher momentum comp onents in Kr as compared to Ar can b e
seen by the crossing of the data around keV This crossing was predicted
by the static Hartree Fock approximation and the theory indicates that the
crossing is due to a larger fraction of p ositrons annihilating with inner shell
electrons in Kr Inner shell electron annihilations will b e discussed in more
detail in Sec and in Ch The agreementbetween the exp erimental
and theoretical values for these noble gases is not as go o d as that for helium
probably re ecting the di culty in p erforming accurate calculations for all but
the simplest atoms
Previous measurements from other exp eriments
Selected values of the linewidths measured for the noble gases are listed in Ta
ble Stewart et al p erformed ACAR measurements in condensed media
while Coleman et al obtained D ACAR measurements from gaseous tar
gets at a pressure of atm High energy p ositrons were directly injected into the
gas cells in these exp eriments Thus these ACAR sp ectra include a contribution
from the annihilation of thermalized p ositronium atoms This app ears as a nar
row p eak in the sp ectrum sup erimp osed on the annihilation of free p ositrons on
atoms which app ears as a wide comp onent in the sp ectrum The free p ositron
comp onentwas subtracted assuming Gaussian line shap es for b oth contribu
tions The linewidths from these measurements are qualitatively similar to our
measured values although the absolute values are larger This discrepancy may
come from the high sample gas pressures in the ACAR exp eriments which can
intro duce three b o dy interactions Also the p ositronium contributions in the
ACAR exp eriments were relatively large esp ecially for the larger noble gases
which makes the extraction of the free p ositron comp onent more di cult The
only previous Doppler broadening studies in the gas phase were rep orted by
Shizuma et al Although they did not tabulate linewidths wehave es
timated numerical values from their graphical data Table Their values
are signi can tly narrower than other measurements and theoretical predictions
The reason for the discrepancy is not clear
Inorganic molecules
Molecules are signi cantly more complicated than atoms and consequently theo
retical calculations exist for only a limited numb er of molecules Exp erimentally
measured linewidths are listed in Tables and for the inorganic molecules
that wehave studied
Chapter
Table The ray linewidths from a Gaussian t to the data for H along
with other measurements and calculations The value of Z is
e
Reference E keV
This study
a
Brisco e
b
Brown
c
Darewych
d
Ghosh
a b
ACAR measurementinliquidH mrad Doppler broadening ray
c
sp ectrum measurement in gas theoretical calculation mrad and
d
theoretical calculation mrad
Table The ray linewidths for inorganic molecules using Gaussian ts
See Ref for the sources of Z values
e
Molecule Formula E keV Z
e
Nitrogen N
Oxygen O
Carb on monoxide CO
Carb on dioxide CO
Water H O
Sulfur hexa uoride SF
a
Ammonia NH
a
Ref
Hydrogen
H is the simplest molecule and its signi cance in astrophysical p ositron annihi
lation has attracted interest from b oth exp erimentalists and theorists
The astrophysical asp ects of our measurements are discussed in Ch Our mea
sured sp ectrum for hydrogen is shown in Fig along with theoretical predic
tions for the line shap e The measured value of the linewidth of
keV is compared with other measurements and with theoretical predictions
in Table All of the exp erimental measurements and the value calculated by
Darewych are similar while the prediction byGhoshet al is much larger
Annihilation ray spectra
100
10-1
normalized counts 10-2
10-3 508 510 512 514
E (keV)
Figure ray sp ectrum from p ositron annihilation on molecular hydrogen ob
served sp ectrum from our measurement theoretical calculation of Ref and
theoretical calculation of Ref
Other gases
Nitrogen An ACAR measurement in liquid N gave E keV
mrad which is in reasonable agreement with our measured value of
keV The only theoretical calculation available gives a linewidth of keV
Chapter
mrad whichismuchnarrower than the exp erimental values
Carb on monoxide and carb on dioxide Carb on monoxide stands out in
that the line shap e exhibits the largest departure from a Gaussian of any molecule
that wehave studied as shown in Fig This is due to a small fraction of
p ositrons annihilating with electrons having high momenta Since this molecule
is relatively simple it maybeaninteresting sub ject for theoretical calculations
In contrast to carb on monoxide as shown in Fig carb on dioxide has only a
weakly non Gaussian line shap e
Sulfur hexa uoride Sulfur hexa uoride has very high electron a nity and
it is well known as an electron scavenger In contrast with regard to the
interaction with p ositrons it has a very low annihilation rate for a molecule
of this size Z The annihilation line is almost as wide as neon
e
We note that the electronic structure of the uorine atoms in many molecules
including SF is similar to the closed shell structure of neon For example
sulfur hexa uoride has a linewidth very similar to the p er uorinated alkanes
This suggests that annihilation in all of these cases o ccurs predominantly on the
uorine atoms which are exp ected to have a close shell structure similar to neon
atoms
Ammonia Ammonia has an anomalously large annihilation rate Z Z
e
It has a linewidth comparable to that of the alkanes Ammonia has a
signi cant dip ole moment but it is not known at present how this would a ect
the linewidth
Alkanes
The linewidths for the alkanes are listed in Table Methane has the narrowest
linewidth keV The linewidth increases to a v alue around keV for the
larger alkanes While cyclohexane has a value of Z ab out an order of magnitude
e
smaller than hexane Table the linewidth of the ray sp ectrum is only
slightly larger than that of hexane Considering saturated hydro carb ons with
ve carb on atoms there are three di erent isomeric con gurations and data
for them are shown in Table While their ray sp ectra are identical to
within the exp erimental error the values of annihilation rates Z di er by
e
approximately a factor of two In general wehave not b een able to detect any
systematic relationship b etween Z and linewidth for the hydro carb ons or for
e
any of the other molecules studied
Annihilation ray spectra
0 10 (a)
10-1
10-2 normalized counts
6 (b)
4
2
0
-2 residual counts (%)
-4 504 506 508 510 512 514 516 518
E (keV)
Figure a ray sp ectra for p ositrons annihilating with CO and CO b
Residuals from the Gaussian ts The data and residuals are normalized to the p eak
height of the sp ectra
Chapter
Table The ray linewidths for hydro carb ons using Gaussian ts See
Ref for the sources of Z values
e
Molecule Formula E keV Z
e
Alkanes
Methane CH
a
Ethane C H
Propane C H
Butane C H
a
Pentane C H
Hexane C H
Nonane C H
Do decane C H
Cyclohexane C H
carb on alkanes
a
Pentane CH CH CH
a
Methylbutane CH C CH H C H
a
Dimethylpropane C CH
carb on molecules with di erent saturation level
a
Ethane C H
Ethylene C H
a
Acetylene C H
Aromatic hydro carb ons
Benzene C H
Naphthalene C H
Anthracene C H
Toluene C H CH
a
Ref
In earlier work based on measurements of linewidths for four hydro carb ons
Tang et al concluded that it was likely that the p ositrons interact primarily
with C H b ond electrons in these molecules In order to test the p ossibil
ity of p ositrons annihilating with C C b ond electrons using our improved data
we plot in Fig the linewidths E as a function of the fraction of valence
electrons in C C b onds for the alkanes includin g cyclohexane The fact that
E increases approximately linearly with the number of valence electrons in C
C b onds suggests that p ositrons are annihilating with C C b ond electrons In principle annihilation on C H b ond electrons can b e separated from annihila
Annihilation ray spectra
2.35
2.30
2.25 (keV) E
Δ 2.20
2.15 Linewidth,
2.10
2.05 0.0 0.1 0.2 0.3
Fraction of valence electrons in C-C bonds
Figure The Gaussian linewidth E plotted against the fraction of valence electrons
in C C b onds for alkane molecules assuming two electrons each in the C C and C H
b onds The solid line is a t to the data
tion on C C b ond electrons assuming that each b ond has its own characteristic
linewidth Then the linear combination of these linewidths weighted bythe
numb er of b ond electrons should yield the observed linewidths From a linear
regression of the data in Fig we estimate the linewidths asso ciated with the
C H b ond and C C b ond electrons to b e keV and keV resp ectively
The momentum distributions for the C C b ond and C H b ond electrons have
b een calculated previously Using the graphs of the calculated momentum
distributions in Ref we estimate the predicted linewidths of C H b ond and
C C b ond to b e keV and keV resp ectively The predicted linewidth
Chapter
for C H b ond electrons agrees reasonably well with our exp erimentally mea
sured value of keV However the linewidth extrap olated for the C C b ond
electrons is in greater disagreement These linewidths were calculated using the
static approximation in which the e ect of the p ositron was not included As
can b e seen in the case for noble gases wave functions without including the
e ect of the p ositron can give the qualitative estimates but not the quantitative
comparisons Therefore it is di cult to distinguish whether this discrepancy in
the linewidth asso ciated with the C C b ond is caused by the inadequacy of the
approximation used in the calculations or by the validity of the assumption that
p ositrons annihilate equally with anyvalence electron and the assumption that
each b ond has a characteristic linewidth
This conclusion is in agreement with p ositron annihilation momentum distri
butions for liquid hexane and decane measured by using ACAR techniques
Calculated momentum distributions for C H and C C b ond electrons were com
pared with the observed ACAR sp ectra and it was concluded that p ositrons
annihilate with b oth C H and C C b ond electrons
Alkane alkene and alkyne
Alkenes and alkynes are generally more reactive than alkanes b ecause the b ond
is weaker than the b ond The smallest memb ers of the alkane alkene and
alkyne families are ethane ethylene and acetylene resp ectively The values of
the linewidths for these molecules are listed in Table They show that as the
b ond saturation level is reduced the linewidths decrease One p ossible expla
nation of this trend is that for the alkenes and alkynes p ositrons can annihilate
with b ond electrons which are less tightly b ound and consequently havea
smaller momentum distribution than that of the b ond electrons Assuming
that eachchemical b ond has its own c haracteristic linewidth and that the linear
combination of these linewidths weighted with the numb er of b ond electrons
yields the observed linewidths we estimate the linewidth of the C C b onds
to b e and keV for ethylene and acetylene resp ectively using the C H
b ond and C C b ond values of and keV Wewould hop e that these
results would stimulate further theoretical work in this area
Aromatics
Aromatic comp ounds havevery di erent electronic and geometrical structures
compared to alkanes The values of the linewidths from our measurements are
listed in Table for the smaller aromatic molecules b enzene naphthalene and
anthracene and for some of the substituted b enzenes
Annihilation ray spectra
Table The ray linewidths for fully halogenated carb ons using Gaussian
ts See Ref for the sources of Z values
e
Molecule Formula E keV Z
e
Carb on tetra uoride CF
Carb on tetrachloride CCl
Carb on tetrabromide CBr
The existence of p olycyclic aromatic hydro carb ons PAH in the interstellar
media has b een deduced from infrared measurements It was found that the
PAH s havevery large annihilation cross sections and it has b een conjectured
that these molecules maycontribute signi cantly to astrophysical p ositron an
nihilation This facet of the research is discussed in Ch Measurements
of larger PAH s suchaspyrene were attempted but were not successful due to
the low vap or pressure of these substances
Fully halogenated carb ons
The linewidths for fully halogenated carb ons are listed in Table where we
have ordered these molecules by the size of the halogen The linewidths de
crease from CF CCl toCBr This trend is very similar to that of the noble
gas atoms neon argon and krypton Table In addition the linewidths
are almost identical to those of analogous noble gas atoms particularly for the
larger halogens as one would exp ect if the valence electrons of the carb on atoms
were completely transferred to the halogen atoms In particular comparing the
halo carb ons and noble gas atoms the linewidths are for CF Ne
for CCl Ar and for CBr Kr These data provide
evidence that in halo carb on molecules the p ositron annihilates with the valence
electrons of the halogen atoms
The di erence in the linewidths for hydro carb ons and p er uoro carb ons are
signi cant hydro carb ons have large annihilation rates and relatively narrow
linewidths while p er uoro carb ons havelow annihilation rates and wide linewidths
It was concluded byTang et al that p ositrons annihilate predominantly
with C H b onds in hydro carb ons and with uorine atoms in p er uorinated
molecules In order to examine further the lo calization of p ositron annihila
tion in a molecule exploiting the easily distinguishable annihilation linewidths
for uorine atoms and the C H b onds wehave studied a series of partially
uorinated hydro carb ons These results are discussed in the next subsection
Chapter
Table The ray linewidths for partially uorinated hydro carb ons using
Gaussian ts
Molecule Formula E keV
Methane CH
Methyl uoride CH F
Di uoromethane CH F
Tri uoromethane CHF
Carb on tetra uoride CF
Ethane C H
Fluoro ethane C H F
Tri uoro ethane CF CH
Tri uoro ethane CHF CH F
Tetra uoro ethane CF CH F
Tetra uoro ethane CHF CHF
Hexa uoro ethane C F
Propane C H
Di uoropropane CH CF CH
Tri uoropropane CF C H
Per uoropropane C F
Hexane C H
Fluorohexane CH FC H
Per uorohexane C F
Benzene C H
Fluorob enzene C H F
Di uorob enzene C H F
Di uorob enzene C H F
Di uorob enzene C H F
Tri uorob enzene C H F
Tetra uorob enzene C H F
Penta uorob enzene C HF
Hexa uorob enzene C F
Partially uorinated hydro carb ons
The exp erimentally measured ray linewidths of a series of partially uorinated
hydro carb ons are summarized in Table and a typical ray sp ectrum is
shown in Fig a As p ointed out earlier the hydro carb ons have signi cantly
Annihilation ray spectra
105 (a)
104
103 counts per channel per counts 102
2 (b)
0
-2
2 (c) χ2 = 1.42
residual counts (%) 0
-2
505 510 515 520
E (keV)
Figure ray sp ectrum from p ositron annihilation on uoro ethane a observed
sp ectrum and t to the sp ectrum using a combination of the exp erimentally mea
sured ethane and hexa uoro ethane sp ectra The two comp onents in the t are also
shown the ethane sp ectrum and the hexa uoro ethane sp ectrum The
fraction of the area in the ethane comp onent is while that in hexa uoro ethane
plotted as a p ercentage of the is b Residuals from a Gaussian t
r
p eak height of the sp ectrum c Residuals from the twospectrum t r
Chapter
narrower linewidths than the p er uoro carb ons This substantial di erence
between the two annihilation linewidths has now made it p ossible for us to
distinguish multiple annihilation sites in a single molecule
For the purp ose of this analysis the annihilation line shap e cannot b e mo d
eled adequately with a Gaussian as is evident from the residuals in Fig b
and the corresp onding values of which are of the order of to However
r
at present we do not know of an appropriate general functional form for the
annihilation ray line shap e Consequently in order to separate the line shap es
for the partially uorinated hydro carb ons into two comp onents we tted the
sp ectra with a linear combination of the exp erimentally observed sp ectra for
the analogous hydro carb on and p er uoro carb on molecules This t has the am
plitudes of the hydro carb on and p er uoro carb on comp onents as only twofree
parameters A typical t and residual are shown in Figs a and c The t
pro duces of order of unity indicating that the mo del of tting with the two
r
exp erimentally measured sp ectra is an excellent one
The area under the p er uoro carb on sp ectral comp onent can yield the rela
tive fraction of p ositrons annihilating on the uorine atoms This fraction is then
normalized by the fraction of valence electrons on uorine atoms in the p er u
orinated molecule to takeinto account the annihilation on C C b ond electrons
The normalized fraction is plotted in Fig as a function of the fraction of the
total number of valence electrons on the uorine atoms The go o d correlation
between these two quantities as seen in Fig suggests that the p ositrons
annihilate with equal probabilityonanyvalence electrons In this analysis we
have assigned eightvalence electrons to eac h uorine atom assuming the forma
tion of a closed shell neon like structure and two electrons each to a C H b ond
and to a C C b ond For a delo calized C C b onds in b enzene a total of six
electrons is assumed in a b enzene ring Wehave assumed for simplicity that
the line shap e of annihilation from C C b ond electrons are the same as that
from C H b ond electrons As indicated in Sec this is probably not strictly
correct but it is likely to b e a reasonable approximation since the number of
C C b ond electrons is small compared to the total number of valence electrons
and the C C b ond linewidth is not as wide as that from uorine atoms
The only theoretical prediction we are aware of regarding p ositron lo caliza
tion in molecules is the study of p ositron attachment using approximate molecu
lar orbital theory bySchrader and Wang A study of ethylene and its uoro
derivatives predicts that the p ositron is likely to b e found preferentially in the
vicinity of the hydrogen atoms e g for C H F of the p ositron densityis
in the vicinity of the twohydrogen atoms attached to one carb on atom Our
exp erimental results do not con rm this prediction
Annihilation ray spectra
1.0
0.8
0.6
0.4
Fractionof annihilation on F 0.2
0.0
0.0 0.2 0.4 0.6 0.8 1.0
fraction of valence e- on F
Figure Normalized fraction of p ositrons annihilating on uorine atoms plotted
against the fraction of the valence electrons on uorine atoms The fraction of an
nihilation on p er uoro carb ons is obtained with the two sp ectrum tting pro cedure
This fraction is normalized with the fraction of valence electrons in uorine atoms in
the p er uoro carb ons one carb on i e methane based molecules two carb on
ethane based molecules three carb on propane based molecules six carb on
hexane based molecules Filled symb ols are for six carb on b enzene based molecules
with solid square di uorob enzene solid triangle up di uorob enzene solid
triangle down di uorob enzene and other six carb on b enzene based molecules
Wehave measured three di erent isomeric con gurations of di uorob enzenes
The di uorob enzene has a higher fraction of p ositron annihilation on the
uorine atoms than do es the or di uorob enzene This may b e due to
Chapter
Table The ray linewidths for other organic molecules using Gaussian
ts See Ref for the sources of Z values
e
Molecule Formula E keV Z
e
Methanol CH OH
Tetraethylsilane Si C H
Nitrob enzene C H NO
a
Pyridine C H N
a
Ref
the dip ole moment which is the largest for the isomer
Other organic molecules
The linewidths of four other molecules are listed in Table Methanol
has a Z value an order of magnitude larger than methane The O H group
e
also increases the annihilation ray linewidth Pyridine has a similar electronic
structure to b enzene It has a higher Z value and a somewhat larger linewidth
e
Annihilation on inner shell electrons
Our data show that p ositrons annihilate predominantly with the valence elec
trons in atoms or molecules The p otential exerted by the atomic nucleus on
a p ositron is repulsive so that the amplitude of the p ositron wave function is
small near the inner shell electrons However a small fraction of p ositrons can
tunnel through this repulsivepotential and annihilate with inner shell electrons
The typical linewidth from inner shell electron annihilation is exp ected to b e
E keV and a study of inner shell electron annihilation requires a
detailed study of this region of ray sp ectra Evidence of inner shell electron
annihilation can b e seen in our data for Ar and Kr Fig Using the am
plitude of sp ectra around keV where we exp ect that the contribution from
valence electron annihilation is small we estimate the upp er b ound of inner
shell electron annihilation contribution to b e and for Ar and Kr resp ec
tively A similar analysis of carb on monoxide data indicates the upp er b ound on
inner shell annihilation to b e in this molecule whichmay explain the large
deviation from a Gaussian line shap e discussed in Sec This b ound on
inner shell annihilation in hexane is which is smaller than those for Ar and
Kr As a consistency check we estimate the upp er b ound for H which do es not
have inner shell electrons to b e whichismuch smaller than those of the
Annihilation ray spectra
Table Values of from ts to various mo dels
r
Molecule Gauss Non interacting H Gauss convolved to Eq Gauss
Eq Eq Eq Eq C
Hydrogen
Krypton
Hexane
substances with inner shell electrons A more detailed description of inner shell
electron annihilation is presented in Ch
Sp ectral analysis b eyond the Gaussian approx
imation
The analyses of the measured sp ectra discussed thus far were done using either
a single Gaussian approximation or using a combination of the exp erimentally
measured line shap es e g in the case of the partially uorinated hydro carb ons
As discussed in Sec wehave observed departures from Gaussian line shap es
and examples are shown in Figs and Wehave also attempted to
use other functional forms for tting the observed sp ectra Values of from
r
various ts are summarized in Table for hydrogen krypton and hexane as
examples For the hydrogen atom in the approximation that the p ositron
do es not p erturb the electron wave function the line shap e is predicted to b e
C E E where C a hc eV a is the Bohr radius
and h is the Planck constant Motivated by this prediction weconvolved
the function
g E b E E
with the detector resp onse whichwe parameterize by
E E E E
B erfc B r E B exp
a E a E
det det
We tried to t the resulting function
Z
g E r E E dE G E
to some of the observed sp ectra using E keV and E B B B
det
and b as the tting parameters Examples of the ts and the residuals using
Eq are shown in Figs and As indicated in Table these
Chapter
105 (a)
104
103 counts
102
(b) 505 510 515 520 2 X Axis
0
-2
1.0 (c) 505 510 515 520 X Axis 0.5
0.0
-0.5 normalized residual counts (%)
-1.0 505 510 515 520
E (keV)
Figure a ray sp ectrum of H observed sp ectrum Gaussian t
Eq t with non interacting atomic hydrogen functional form Eq
and t with Gaussian convolved non interacting H form Eq b resid
uals from the Gaussian t and residuals from the non interacting hydrogen t c
residuals from the Gaussian convolved non interacting hydrogen t and residuals
from the Gaussian t Eq C
ts pro duced generally larger values of than the Gaussian ts Eq
r
esp ecially for the hydro carb ons Fits to the hydrogen helium and xenon sp ectra
values than those from the with this functional form created slightly smaller
r
Gaussian ts but these values are still much greater than unity
It is interesting to note that the residuals from the Gaussian ts Eq
Annihilation ray spectra
105 (a)
104
counts 103
102
6 (b) 3 0 -3 -6
2 (c) 1 0 -1 normalized residual counts (%) -2 505 510 515 520
E (keV)
Figure a ray sp ectrum of hexane C H observed sp ectrum
Gaussian t Eq t with non interacting atomic hydrogen functional form
Eq twithGaussianconvolved non interacting H form Eq and
t with Gaussian t Eq C b residuals from the Gaussian t and
residuals from the non interacting hydrogen t c residuals from the Gaussian
convolved non interacting hydrogen t and residuals from the Gaussian t
are p ositive at the p eak while the residuals from ts with Eq are nega
tive A Gaussian line shap e is exp ected from p ositrons annihilating with free
electrons having a thermal momentum distribution The p otential exerted by
the nuclei in the atoms or molecules will tend to increase the p opulation of high
momentum comp onents of the electrons There are two di erentinteractions
that can account for the di erence b etween the observed sp ectra and the func
Chapter
tional form Eq which is derived in the approximation that the p ositron
do es not disturb the electronic con guration of a hydrogen atom One is the
presence of the other electrons in the atom or molecule The other is the e ect
of the p ositron on the atom or molecule The fact that the distribution lies
between the form of Eq and the Gaussian shap e indicates that the distri
bution is more relaxed compared to Eq in other words the distribution
is more free electron like The e ect of other electrons seems to b e strong as
can b e seen by the p o or t to Eq for the case of hydro carb ons In princi
ple measurementof ray sp ectra from atomic hydrogen is p ossible and
it would indicate the magnitude of the e ect of the p ositron on the momentum
distribution
Since the actual line shap e lies somewhere b etween the Gaussian shap e and
Eq we attempted tting another function which is the line shap e from
Eq g E convolved with a Gaussian having a variable width E
Z
E E E
h E g E exp dE
a E
This was an attempt to takeinto account the degree to which electrons relax
from the p otential exerted by the nuclei due to the e ect of the nearby p ositron
This function h E was then convolved with the detector resp onse given by
Eq and used for the actual t This function has free parameters As
can b e seen in Figs a and c it ts sp ectra of some atoms and molecules
reasonably well but do es not t others such as argon and krypton
Wehave also tried to t two Gaussians to the data This tting function
around unity and the residuals are generally within the pro duces values of
r
error bars as can b e seen in Figs c and c However the widths of
two Gaussians and the relative amplitude of the second Gaussian are highly cor
related and weknowofnophysical meaning for such a line shap e Nonetheless
the two Gaussian t is a convenientway of representing the data more accurately
with an analytic form The tting pro cedure using two Gaussians is discussed
in App endix C along with a compilation of the tting parameters for various
atoms and molecules resulting from this analysis
Discussion
Previous theoretical studies of p ositron annihilation in gases have fo cused on un
derstanding annihilation rates This is likely due at least in part to the fact that
exp erimental data for annihilation rates are available for a variety of substances
while previous to our p ositron trap exp eriments there have b een relatively few
Annihilation ray spectra
ACAR and ray Doppler broadening studies of atoms and molecules except
for media su ciently dense that multiple atom and molecule e ects maynotbe
neglected Consequently we exp ect that the data presented here will b e useful
for comparison with the predictions of theoretical mo dels of low energy p ositron
molecule interactions As describ ed ab ove wehaverecently carried out sucha
comparison for the case of helium resulting in excellent agreement
In order to calculate either annihilation rates or ray line shap es the com
bined wave function for the p ositron and electrons must b e calculated Once
the wave function is known calculation of either the annihilation rate or the
Doppler broadened annihilation line shap e is straightforward Sp eci c calcula
tions that would b e useful include prediction of the ray sp ectra for annihilation
on noble gases where theory and exp eriment are not in go o d agreement except
for helium inorganic molecules such as nitrogen and carb on monoxide which
showed strong non Gaussian features the C H and C C b onds in alkanes the
and b onds in aromatics such as b enzene and calculations for halo carb ons
We describ ed an unsuccessful attempt to nd a physically meaningful uni
versal line shap e b eyond the single Gaussian applicable to a variety of atoms
and molecules Theoretical insights on this sub ject would b e of value Do es such
a general function exist and if so what is its physical interpretation
Regarding p ossible improvements in exp erimental capabilities wenowhave
the abilitytovary the temp erature of the trapp ed p ositrons in a systematic way
and a study of annihilation rates in noble gases has b een recently carried out
v arying the temp erature of the p ositron gas from ro om temp erature to ab out
eV Thus in the near future we should b e able to provide data on the
e ect of p ositron temp erature on ray linewidths The increased temp erature
of the p ositrons may for example change the fraction of annihilations at sp eci c
sites in molecules and we will b e able to search for this e ect
It is interesting to note that our measurements of the temp erature dep en
dence of annihilation rates on noble gas atoms agree well with calculations
using the p olarized orbital approximation However the absolute values
of the annihilation rates are underestimated in these calculations and the
predicted ray linewidths describ ed in Sec are larger than those that are
observed Thus calculations in this approximation are capable of capturing the
temp erature dep endences but not the absolute annihilation rates or the ray
sp ectra
Our ray sp ectral measurements on partially uorinated hydro carb ons in
dicate that p ositrons annihilate with equal probability with any of the valance
electrons In addition the data from the alkanes are also consistent with an
nihilation with equal probabilityonanyvalence electron At present wedo
Chapter
not see howthe ray sp ectral measurements give direct information ab out the
physical pro cess resp onsible for the anomalously large annihilation rates It is
interesting to note that as discussed in Sec the static approximation
gives reasonably go o d estimates for the ray linewidths but not for the an
nihilation rates This may p oint to the imp ortance of short range correlation
between the p ositron and electrons in calculating annihilation rates whichis
reasonable since the overlap in the p ositron and electron wave functions deter
mines the annihilation rate This correlation do es not seem to b e critical for the
calculation of the ray sp ectra
Concluding Remarks
In this chapter wehave presented measurements of the Doppler broadening of
the annihilation ray line which complement other studies of p ositron molecule
interactions Measurements were p erformed on a wide variety of substances
including noble gases inorganic molecules alkanes aromatics and substituted
alkanes The precision of the measurements is su ciently high that for the rst
time in gaseous media one can distinguish non Gaussian features in the line
shap es In the case of helium the measurements are in excellent agreementwith
new state of the art theoretical calculations
Wehave also shown that we are able to distinguish annihilation on sp eci c
sites in molecules such as on uorines and on C H b onds in partially uori
nated hydro carb ons These partially uorinated hydro carb on data indicate that
p ositrons annihilate with equal probability on the valence electrons Interpreta
tion of our data for alkanes is also consistent with this statistical mo del where
the valance electrons are those in the C H and C C b onds in this case The
results presented in this chapter for the ray sp ectra from p ositron annihilation
will provide useful tests of theoretical mo dels of p ositron atom and p ositron
molecule interactions
Chapter
Positron annihilation with
inner shell electrons in noble
gas atoms
The inner shell electron annihilation whichwas describ ed brie y in Sec
is discussed here This work is published in Ref
Intro duction
Positrons annihilate predominantly with valence electrons in insulators or with
conduction electrons in metals b ecause of the repulsive p otential exerted on the
p ositron by the nuclei However a small fraction of the p ositrons can tunnel
through this repulsive p otential and annihilate with inner shell electrons In the
work presented here we detect inner shell annihilation by measuring the mo
mentum distribution of the annihilating electron p ositron pairs by the Doppler
broadening of the annihilation rays Inner shell annihilation has b een studied
previously for p ositrons interacting with condensed matter targets using a clever
coincidence technique with two detectors This technique improves the
signal to noise ratio which in turn enables one to explore the high momentum
region of the sp ectra The interactions in condensed matter however are very
di erent from the isolated interaction of a p ositron with a single atom discussed
here For example in metals the p ositron forms a Blo chwave under the p erio dic
p otential generated by the ions while p ositron annihilation in a single atom is a
scattering pro cess We con ne p ositrons for a long time in the p ositron trap so
that they can b e used e ciently as discussed in Ch Using this p ositron trap
wehave b een able to obtain su ciently go o d statistics to identify inner shell
Chapter
annihilation using a single detector
In this chapter we present precise measurements of the annihilation ray
sp ectra for argon krypton and xenon The measured sp ectra are compared
with calculations based on the Hartree Fock HF approximation The high
momentum comp onents in the sp ectra provide a quantitative measure of the
fraction of p ositrons that annihilate with inner shell electrons This is the rst
exp erimental study of p ositrons annihilating with inner shell electrons in isolated
two b o dy p ositron atom interactions
Exp eriment
Measurements of the ray sp ectra are p erformed using a technique similar to
previous measurements as discussed in Sec The data were taken
for h for argon and krypton and for h for xenon The sp ectra were taken
in h time segments and the drift in the detector less than keV in h
was carefully monitored The numb er of p ositrons in each llwas adjusted to
minimize ray pile up
Results
The observed sp ectra were rst tted with the Gaussian function similarly to
that discussed in Ch The step function and the baseline were then subtracted
after convolution of the step function with the tted Gaussian width The am
plitudes of the step function and the baseline were determined by requiring that
the sp ectrum b e zero at energies far e g keV from the centroid of the p eak
keV
The corrected sp ectra for xenon krypton and argon are shown in Figs
and resp ectively The error bars represent the exp ected statistical vari
ation in sp ectral amplitude due to counting statistics The sp ectra can b e re
solved over four orders of magnitude in sp ectral amplitude and this is crucial
in separating the contribution to the annihilation signal due to inner shell elec
trons from that due to electrons in the outermost shell In Figs and
only the high energy side of the symmetric ray line is shown since this
region has greater statistical signi cance due to absence of the Compton scat
tering comp onent The measured and calculated sp ectra are normalized so that
R
f E dE where f E is the amplitude of the sp ectrum at ray energy
E The theoretically predicted sp ectra shown in Figs and havebeen
convolved with the Gaussian detector resp onse which has a full width at half
maximum FWHM of keV
Positron annihilation with inner shell electrons
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8 5
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Figure The Doppler broadened ray sp ectrum resulting from p ositrons annihilating
on xenon atoms at p Torr Shown are the exp erimental data the
static Hartree Fock calculation the b est t to the data which includes a
con tribution from the states with principle quantum number n the
contribution from the outer shell states with n and that from the inner
shell states with n
In order to identify the contributions of inner shell electrons to the annihila
tion ray sp ectra the line shap es were calculated using the static HF approxi
mation In this approximation the wave function of the p ositron at thermal
energies is calculated from the Schro dinger equation using the p otential of the
HF atomic ground state and annihilation ray sp ectra are determined for elec
trons in each atomic subshell The annihilation fractions and the asso ciated
Chapter
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6WDWLF +)
QRUPDOL]HG FRXQWV
8 5 /
8 5
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Figure The Doppler broadened ray sp ectrum resulting from p ositrons annihilating
on krypton atoms at p Torr The notation is similar to that in Fig
line shap es FWHM E for electrons from the two outer shells with principal
quantum numbers n and n are summarized in Table for argon krypton
and xenon n resp ectively The sum of the annihilation fractions for
the two outer subshells and those from the three or two for argon inner
nl
subshells is normalized to unity There is go o d agreementbetween the
n l
widths and shap es of the ray sp ectra obtained in the static HF approximation
and the exp erimental data see Table and Figs and
As exp ected the main contribution to the annihilation probability comes from the outer shell electrons The linewidths from inner shell annihilation
Positron annihilation with inner shell electrons
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6WDWLF +)
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Figure The Doppler broadened ray sp ectrum resulting from p ositrons annihilating
on argon atoms at p Torr The notation is similar to that in Fig
keV are much larger than those from outer shells keV due to the
higher momenta of the former The values of are roughly prop ortional
n l
to the numb er of electrons in the s p and d subshells namely and
resp ectively The lack of an inner d subshell for argon only electrons in the
inner shell as compared to for krypton and xenon results in a lower total
annihilation fraction from inner shell electrons relative to krypton and xenon
Table The reason for in xenon b eing greater than in krypton
n d n d
is the more di use character of the d orbital in xenon the radial densityofthe
n d orbital in xenon p eaks at a u as compared to a u for n d
Chapter
Table The FWHM of annihilation ray sp ectra E in keV and par
tial contributions to the annihilation probability from the subshells of noble gas
atoms calculated in the static Hartree Fock approximation
Shell Argon Krypton Xenon
E E E
np
ns
n d
n p
n s
total
exp eriment
n tot th
n t
in krypton and the value of E is smaller for the d orbital in xenon
As can b e seen from Figs and a contribution from the shell with
principal quantum number n is essential to account for the shap e of the
high energy tail in the sp ectra of xenon and krypton However it app ears that
the static HF approximation overestimates the values of by ab out a factor
n
of two There are p ositron electron correlation e ects not treated by the static
approximation which preferentially enhance the annihilation rate for the most
weakly b ound electrons i e the outer shell electrons On the other hand they
do not a ect much of the shap e of the ray sp ectra as suggested by the agree
ment observed in Figs and This enables us to treat the fraction
of annihilations with the inner shell electrons as a tted parameter to
n
obtain a more precise estimate of this e ect Thus we are able to achievegood
agreement shown as the solid line in Fig over four orders of magnitude
in sp ectral amplitude with compared with the static HF value of
n
for xenon Table Figure shows the results of this analysis
n
for krypton with similarly go o d agreement for the sp ectral line shap e In this
case the tted value which is appro ximately of that pre
n
dicted by the static HF calculation For argon Fig the comparison b etween
the measurement and the theory cannot accurately determine the contribution
of inner shell annihilation events We estimate which is less than
n
of the value predicted by the static theory
We note that in the analysis presented in Asoka Kumar et al Ref the
Positron annihilation with inner shell electrons
high momenta shoulder of the ray sp ectrum was tted by the inner shell
annihilation contribution alone It is clear from our work that the outer shell
annihilation sp ectra also p ossess this shoulder like feature due to oscillations
in the structure of the outer shell electron wave functions Neglect of this would
result in an overestimate of the fraction of inner shell annihilation
While go o d agreement for the annihilation ray sp ectra is achieved using
simple static HF theory there is considerable evidence that the p ositron wave
function obtained in this approximation is not correct For example the HF
approximation fails to repro duce p ositron atom scattering and seriously under
estimates the total annihilation rate There is a strong attractive p otential
between the p ositron and the atom due to p olarization of the atom by the electric
eld of the p ositron and virtual p ositronium formation As a result the
actual p ositron wave function near the atom is much larger than that predicted
by the static approximation There are also short range correlation e ects due
to the electron p ositron interaction These interactions enhance the total wave
function at small electron p ositron separations and further increase the annihila
tion rate However as seen from Figs and these e ects seem to have
little in uence on the shap es of the ray sp ectra In particular the ray sp ec
tra are exp ected to b e insensitive to short range electron p ositron correlation
e ects since the sp ectra dep end only on the momentum of the electron p ositron
pairs and their center of mass momenta are weakly a ected by this correlation
This means that the annihilation sp ectra are basically determined by the mo
mentum distribution of the atomic electrons which are describ ed well bythe
HF approximation
There are correlational corrections which can account for the discrepancy
between the theoretical and exp erimental E Table As discussed ab o ve
correlations also lead to a large enhancement of the annihilation rates whichis
greater for the weakly b ound outer shell electrons Accordingly the tted
n
values are smaller than from the static HF calculation
n
The robust nature of the shap es of the ray sp ectra in atoms should b e of
help in analyzing the details of p ositron interactions in more complicated systems
such as molecules and solids For example the annihilation ray sp ectra can
provide quantitative information ab out preferential sites of p ositron annihilation
in molecules
An imp ortant implication of the inner shell annihilation is the emission of
Auger electrons and the consequent formation of doubly ionized atoms The
p ositron induced Auger electron emission has b een observed in condensed matter
The work describ ed here op ens up a p ossibility of the Auger sp ectroscopy
in gaseous media Our work suggests that the doubly ionized atoms asso ciated
Chapter
with Auger electron emission should b e observable e g using time of ight
mass sp ectrometry We exp ect the highest pro duction of doubly ionized
atoms for heavier atoms such as krypton and xenon since they have large inner
shell annihilation fractions
Concluding remarks for inner shell electron an
nihilation
In summary our exp erimental results demonstrate that p ositron annihilation
with inner shell electrons can b e studied in a quantitative manner in isolated
atomic systems While a simple static HF calculation was used successfully to
identify the inner shell electron contribution the relative fraction of annihila
tions with inner shell electrons is not predicted accurately by this theory We
hop e that these results will motivate further theoretical work in this area
Chapter
Positron annihilation in the
interstellar media
Simulations of p ositron annihilation in the interstellar media ISM have pre
viously b een studied Since these publications new information has
emerged from observations with various instruments on the Compton Gamma
Ray Observatory GRO In this chapter p ositron annihilation in the ISM is
discussed After an intro duction Sec a brief summary of current under
standing of p ositron annihilation is describ ed in Sec The observational
evidence of the existence of interstellar p olycyclic aromatic molecules PAH s
is discussed in Sec followed by our p ositron annihilation study in a sim
ulated ISM namely hydrogen PAH mixture in Sec and this chapter is
summarized in Sec
Intro duction
The keV p ositron annihilation line is the strongest ray line of astrophysi
cal origin and it has b een studied extensively b oth observationally and
theoretically The narrow energy spread of the observed annihila
tion line is interpreted as coming from p ositrons that have b een slowed down to
a few eV b efore annihilating on either free electrons or on electrons in molecules
of the ISM The physics of p ositron slowing and annihilation in the ISM has b een
the sub ject of many analytical mo dels and numerical simulations One
scenario p ostulates that the p ositrons thermalize with the ISM and then anni
hilate on neutral gas atoms and molecules In this case the line shap e of
the ray sp ectrum would b e determined entirely by the temp erature and chem
ical comp osition of the ISM In this kind of interstellar environment PAH s
Chapter
maycontribute signi cantly to the p ositron annihilation since these molecules
have anomalously high annihilation rates as discussed earlier even though their
abundance is muchlower than that of hydrogen atoms
Another scenario for the fate of astrophysical p ositrons involves annihilation
following in ight p ositronium atom formation byinteraction with neutral gas
atoms and molecules In this scenario the ray line shap e would b e qualitatively
di erent from that of annihilation on neutral atoms and molecules and would
dep end on the dynamics of the slowing down pro cess The e ects of the tem
p erature of annihilating media have also b een studied theoretically Other
scenarios include the e ects of interstellar dust and molecular clusters
The technique wehave develop ed for accumulating and storing cold p ositrons
in a vacuum of less than torr provides a to ol for studying low energy
p ositron molecule interactions in an environmentrelevant to that of the ISM
Wehave previously measured annihilation rates and anni
hilation ray sp ectra and discovered that large organic molecules
suchasPAH s have anomalously high annihilation rates attributed to reso
nance binding of the p ositron to the molecule with measurably di erent
ray sp ectra from that of hydrogen as describ ed in Ch
Positrons in the interstellar media
Recently the Gamma Ray Observatory has increased our knowledge of as
trophysical p ositron annihilation dramatically The strongest
sources of p ositron annihilation rays are those asso ciated with our Galaxy The
spatial distribution of the radiation has observed to show three distinct features
a central bulge the galactic plane and an enhancement or extension of emission
at p ositive latitudes ab ove the galactic center The time variation of
radiation intensity previously noted in ballo on exp eriments was not observed
by the GRO
An observed ray sp ectrum from these Galactic regions is shown in Fig
This sp ectrum is taken using a NaI Tl CsI Na detector and the energy reso
lution at keV is The data were tted over the energy range
MeV with a function consisting of a single p owerlaw a photop eak line xed
in energy and width at keV and keV resp ectively and a p ositronium
continuum comp onent The tted photop eak and p ositronium comp onents cor
resp onds to a p ositronium fraction of which indicates that
almost all of Galactic p ositrons form p ositronium atoms This sp ectral analysis
of annihilation radiation makes the scenario of direct p ositron annihilation on
atoms and molecules less likely for the p ositrons asso ciated with our Galaxy
Positron annihilation in the interstellar media
Figure Positron annihilation ray sp ectrum from the Galactic center The data
were tted with a mo del function consisting of a single p owerlaw a photop eak line and
a p ositronium continuum comp onent The dashed lines show the contribution of each
of these comp oments Taken from Ref
Higher energy resolution sp ectra are shown in Fig They were measured
using a Ge detector on a ballo on and the energy resolution is keV The
linewidth from the April observation is keV while that from the
May is keV
The p ositronium fraction of nearly unity and the narrow annihilation line
Chapter
Figure Positron annihilation ray sp ectrum from the Galactic center Taken from
Ref
suggest that the p ositrons annihilate in a warm K and either neutral or partially ionized medium
Positron annihilation in the interstellar media
Benzene Naphthalene Anthracene
Z eff =15,000 494,000 4,330,000
Chrysene Pyrene
7 7
>10 >10
Figure Molecular structures and Z of p olycyclic aromatic hydro carb ons Mea
e
sured values of Z are shown for b enzene naphthalene and anthracene and estimated
e
values of Z are also indicated for chrysene and pyrene As discussed in the text
e
these latter molecules may b e signi cant sources of astrophysical ray radiation from
p ositron annihilation
Interstellar molecules
The anomalously high values of Z observed for many molecules haveim
e
plications for astrophysical pro cesses There exist extensive sets of in
frared sp ectral measurements indicating that hydro carb ons are presentinthe
ISM The molecules have b een identi ed as p olycyclic
aromatic hydro carb ons PAH and their molecular concentration is of
that of hydrogen Stability analyses of these molecules indicate that PAH s
with to aromatic rings examples of which are shown in Fig dominate
the interstellar PAH p opulation Chrysene and pyrene are the smallest of
the PAH molecules known to b e present in the ISM At present we are only
able to study the two and three ring PAH s naphthalene and anthracene in
the p ositron trap b ecause the larger PAH s havevery lowvap or pressure How
ever we b elieve that these tw oPAH s are representative of the family in that
all hydro carb ons studied previously includin g the single ring b enzene the two
Chapter
ring naphthalene and three ring anthracene have larger ray linewidths than
that of hydrogen and we exp ect this to extrap olate to the larger PAH s
Moreover wehave noted a systematic increase in the annihilation rates for the
PAH s as one adds more rings This trend should continue up to some saturation
level where the resonance binding time b ecomes comparable to the annihilation
time scale The saturated value could b e as high as or greater than that of
atomic hydrogen which is so that the interstellar PAH molecules may
contribute signi cantly to the annihilation of slow p ositrons in the ISM due
to their anomalously high annihilation rates even though the PAH molecules
are present in only small concentrations as p ointed out earlier This p ositron
annihilation on PAH s would then b e re ected in the keV annihilation ray
line shap e from the ISM These measurements have led us to simulate
p ositron annihilation in a cold medium similar to the cold cloud phase of the
ISM
Astrophysical p ositron annihilation simulation
In this section we describ e an exp eriment to measure the annihilation ray
sp ectrum from a simulated ISM consisting of molecular hydrogen and a PAH
namely naphthalene at ro om temp erature To our knowledge this is the rst
exp erimental simulation of astrophysical p ositron annihilation in a mixed gas
medium Section describ es the exp eriment in more detail In Sec
we present the annihilation data and describ e the analysis while Sec sum
marizes the chapter and discusses the implications of the exp eriment for the
analysis of astrophysical data
Description of the exp eriment
This exp erimentwas p erformed using the same technique to the ra y study
describ ed in Ch The pressures of molecular hydrogen and naphthalene were
adjusted so that approximately equal number of rays originate from annihila
tion on each of the sample gases The numerical values are listed in Table
Note that although the naphthalene has four orders of magnitude lower pressure
than that of hydrogen it nonetheless contributes signi cantly to the annihila
tion owing to its anomalously large annihilation cross section
Exp erimental results
The observed sp ectrum from p ositrons annihilating on the mixture of molecular
hydrogen and naphthalene molecules is shown in Fig The Gaussian func
Positron annihilation in the interstellar media
Table The fraction of annihilations on each comp onent F calculated
from t to data F calculated from pressure and Z
p e
Molecule Pressure torr Z Width keV F F
e p
a
Hydrogen
b
Naphthalene
a b
Ref Ref
100
10-1
10-2 normalized intensity
10-3
504 506 508 510 512 514 516 518
E (keV)
Figure ray line for p ositrons annihilating on mixture of hydrogen and naphthalene
molecules annihilation sp ectrum from molecular hydrogen annihilation
sp ectrum from naphthalene combined t to annihilation sp ectrum from the mixed medium
Chapter
tion Eq was t to the data pro ducing a linewidth of keV However
the t parameter was which indicates that a single Gaussian do es not
n
mo del the data adequately
In order to nd a b etter tting function the sp ectra from annihilation on
H and naphthalene were measured separately Then a sup erp osition of these
two sp ectra was t to the mixed gas data by adjusting the relativeweights
of the two comp onents as describ ed in Sec The thasonlytwofree
parameters namely the weights of the H and of the naphthalene sp ectra The
resulting t and the separate comp onents from H and naphthalene are plotted
on Fig The t pro duced indicating that the choice of the
n
individuall y measured comp onent sp ectra as tting functions is a very go o d
mo del By integrating the area under each comp onent the fractions of p ositrons
annihilating on H and on naphthalene can b e calculated see Table
Annihilation fractions were also calculated indep endently using the pressures
and annihilation rates listed in Table The annihilation rates are expressed
in terms of the normalized rates Z The total annihilation rate of each
e
comp onent is prop ortional to the Z and partial pressure of the molecule The
e
annihilation fractions are calculated comparing the data for H and naphthalene
These fractions di er by a factor of four from the fractions calculated with the
two sp ectrum tting pro cedure Uncertainties in measuring the low naphthalene
pressure torr using an ionization v acuum gauge could b e in error by
as much as whichwould account for a large part of this discrepancy
Summary of p ositron annihilati on in the inter
stellar media
Wehave demonstrated a metho d for analyzing ray sp ectra from p ositrons an
nihilating on gas mixtures These data intro duce the p ossibility of identifying
the minority constituents of the ISM from the ray sp ectra assuming a sce
nario in which p ositrons thermalize and then annihilate on neutral atoms and
molecules in the ISM In practice such an analysis would involve building up a
library of annihilation line shap es for candidate molecules in the ISM and us
ing them to t the astrophysical measurements At present the signal to noise
ratio of astrophysical data is to o low to attempt such ts but these kinds of
analyses may b e p ossible in the future using high resolution data from orbital
missions
For the exp eriment describ ed here molecular hydrogen was used for conve
nience but in principle exp eriments with atomic hydrogen are also p ossible
Positron annihilation in the interstellar media
At present annihilation studies of PAH s larger than naphthalene are di cult
b ecause of the lowvap or pressures of these molecules To eliminate this restric
tion a hot cell could b e used in order to p erform studies of these molecules
In the future exp eriments to test other scenarios for p ositron annihilation in the
ISM could b e carried out in the p ositron trap suchasinteraction with dust and
clusters as well as the annihilation by in ight p ositronium formation
Recent observation makes the scenario of low energy p ositrons annihilating
with neutral atoms and molecules unlikely to account for the intense annihilation
radiation from the Galaxy However annihilation radiation from the cold cloud
of the ISM may b e used to p erform chemical analysis simulated in this chapter
Chapter
Chapter
Conclusion
Summary of this dissertation
Atomic and molecular physics studies using p ositrons has gained renewed in
terests since the intro duction of studies in p ositron traps as discussed in this
dissertation The range of molecules studied has increased dramatically due to
the ability to conduct studies at low test gas pressures where two b o dy interac
tions can b e isolated and studied The p ositrons used in these exp eriments have
awell de ned energy distribution and the numb er of p ositrons available is much
larger than in previous exp eriments This results in a considerable increase in
the signal to noise ratio of the measurements
Using these trapp ed p ositrons annihilation rates of various molecules were
studied systematically Ch Anomalously large annihilation rates havebeen
observed previously for large organic molecules The annihilation
rate data exhibit a number of chemical trends and highlight the imp ortance
of the electronic structure of the molecule The empirical scaling of the rates
with molecular ionization p otentials and the p ositronium binding energy
suggests that a highly correlated p ositron electron pair moving in the eld of
molecular p ositive ion dominates the physics involved Even though attempts
havenow b een made the anomalously high annihilation rates and this empirical
scaling havenotyet b een understo o d theoretically
The sp ectra of the keV annihilation line for various molecules were sys
tematically studied Ch The observed sp ectra are Doppler broadened mainly
due to the momenta of annihilating electrons which are b ound to the molecule
These sp ectra give information ab out the quantum states of the electrons The
observed sp ectrum for helium was compared to a recent theoretical calculation
resulting in an excellent agreement The data from alkanes and partially uori
Chapter
nated hydro carb ons indicated that p ositrons annihilate with an equal probability
with anyvalence electron in these molecules Inner shell electron annihilation
was detected in gaseous media for the rst time and a study of this e ect on
noble gases was presentedinCh
The anomalously large annihilation rates measured for p olycyclic aromatic
hydro carb ons have implications for p ositron annihilation in the ISM These
molecules are exp ected to havevery high annihilation rates which leads us to
conjecture that the annihilation rays from the ISM may contain information
ab out these molecules A lab oratory exp eriment in a simulated ISM is presented
in Ch
Future work
As shown in this dissertation a broad survey of annihilation rates and ray
sp ectral measurements using ro om temp erature p ositrons is more or less com
pleted Wehavedevelop ed two techniques to change the energy distribution of
p ositrons in the p ositron trap The rst technique is to heat p ositron plasmas
by applying a RF noise to one of the electro des and as discussed in Sec
it has b een successfully applied to measure the dep endence of annihilation rates
on p ositron temp erature for noble gases Extending this typ e of measurement
to hydro carb ons where the anomalously high annihilation rates are observed
will b e fruitful In particular a large scale calculation of p ositron annihilation
on ethylene C H isavailable and a comparison with exp erimental data
will help to verify the validity of the calculation
The second technique is the generation of p ositron b eams with very narrow
energy spread eV The rst technique is limited in the useful range
of p ositron energies eV since application of large RF noise kicks p ositrons
out of the trapping p otential well The mono energetic b eam is exp ected to b e
apowerful to ol for atomic and molecular physics studies since p ositrons with
well de ned energies can prob e the molecules under study in a precise way The
empirical scaling indicates that the parameter E E isimportant for ro om
i Ps
temp erature p ositrons For higher energy p ositrons the parameter E E
e i
E is the energy di erence from the p ositronium formation threshold and
Ps
it may play an imp ortant role Recent theories predict resonance b ehavior in
annihilation rates at E E E and this can p otentially b e observed
e i Ps
exp erimentally using the mono energetic p ositron b eam
The ray sp ectral studies suggest that p ositrons annihilate equally with
anyvalence electron in molecules while the empirical scaling suggests that the
physics involved may b e dominated by highly correlated electron p ositron pairs
Conclusion
Near the p ositronium formation threshold this picture of equal probabilityof
annihilation may break down and wemay b e able to study this e ect using the
technique describ ed ab ove
Positron annihilation is a qualitatively di erentway of ionizing molecules
from conventional metho ds and studies of the ions formed after p ositron annihi
lation are p otentially useful in mass sp ectroscopy applications Previously mass
sp ectroscopyofpositive molecular ions in our p ositron trap has b een attempted
and these studies showed that there was a large probabilityoffragmentation for
alkanes Hulett et al have discovered that the resulting molecu
lar ions were predominantly unfragmented when the incident p ositron energy is
tuned near the p ositronium formation threshold This e ect can b e studied
more systematically using the mono energetic p ositron b eam describ ed ab ove
Our p ositron trap is not optimized for time of ight mass sp ectrometry and
the application of ion cyclotron mass sp ectrometry may prove useful for these
exp eriments
Currently the substances we can study are limited to those whichhave suf
ciently high vap or pressures at ro om temp erature Installation of a hot cell
would enable us to study other substances which could give us useful physical
insights Metal vap ors suchasCd ZnandHg have relatively low ionization
energies and we could test the validity of the empirical scaling for these atoms
If the empirical scaling holds for atoms then these metal are exp ected to have
Z These atoms are simple enough that the theoretical calculation can
e
b e p erformed and compared with exp eriments At elevated temp eratures w e
may also b e able to p erform more realistic simulations of p ositron annihilation
in the ISM
Concluding remarks
In the past several years wehave systematically studied annihilation on a variety
of atoms and molecules using p ositron trapping techniques As a result of these
studies wehave gained signi cantphysical insights into the interaction of low
energy p ositrons with molecules Wenowhave a considerable b o dy of data
which can b e compared with theoretical mo dels A numb er of outstanding issues
still remain to b e addressed The work presented here demonstrates the utility
of the p ositron trap as a to ol for atomic and molecular physics Presently
new exp erimental techniques are b eing develop ed that can increase the range
of p ositron energies and the varietyofchemical sp ecies that can b e studied
and these developments are exp ected to further enhance our understanding of
physics involved in this area
Chapter
App endix A
Ion gauge sensitivity
calibration for gases and
molecular vap ors
As describ ed in Sec the ion gauge sensitivities for the test gases are necessary
to measure the pressure precisely and in turn to obtain the annihilation rate
Z Where available published pressure gauge sensitivities were used For
e
those substances for whichdatawere not available we measured the sensitivities
using a technique similar to that describ ed in Ref The sensitivities for the
molecules discussed in this dissertation are listed in Table A As can b e seen
from the table for the molecules where b oth our measurements and previously
published data are available the values are in go o d agreement in most cases
agreeing to b etter than
Appendix A
Table A Sensitivities of ion gauge resp onse R relative to that of nitrogen
gas
Molecule Formula Measured R R from Ref
Noble gases
Helium He
Neon Ne n a
Argon Ar
Krypton Kr
Xenon Xe
Inorganic molecules
Hydrogen H n a
Nitrogen N
Oxygen O n a
Carb on dioxide CO n a
Water H O
Sulfur hexa uoride SF n a
Ammonia NH n a
Alkanes
Methane CH n a
Ethane C H n a
Propane C H n a
Butane C H n a
Pentane C H n a
Hexane C H
Heptane C H n a
Decane C H n a
Cyclohexane C H
Cyclo decane C H n a
Alkenes
Ethylene C H n a
Hexene C H n a
Aromatic hydro carb ons
Benzene C H
Naphthalene C H n a
Anthracene C H n a
Toluene C H CH n a
o Xylene C H CH
m Xylene C H CH n a
p Xylene C H CH n a
Ion gauge sensitivity calibration for gases
Table A Continued
Molecule Formula Measured R R from Ref
Substituted alkanes
Carb on tetra uoride CF n a
Per uoropropane C F n a
Per uorohexane C F n a
Per uoro o ctane C F n a
Carb on tetrachloride CCl
Substituted b enzenes
Fluorob enzene C H F n a
Di uorob enzene C H F n a
Penta uorob enzene C HF n a
Hexa uorob enzene C F n a
Chlorob enzene C H Cl n a
Bromob enzene C H Br n a
Nitrob enzene C H NO n a
Aniline C H NH n a
Oxygen containing molecules
Methanol CH OH n a
Propanol C H OH n a
Acetone CH COCH n a
Acetic acid CH COOH n a
Propionic acid C H COOH n a
Other molecule
Tetraethylsilane Si C H n a
Appendix A
App endix B
Table of physical parameters
of atoms and molecules
Physical parameters of atoms and molecules studied are listed in Table B for a
reference purp ose The parameters include numb er of electrons Z annihilation
rate Z ray linewidth E p olarizability dip ole moment and ionization
e p
p otential E The sources of Z can b e found in Ch ray linewidths are
i e
taken from Ref which is also the sub ject of Ch Atomic p olarizabilitie s
are taken from Ref while molecular p olarizabili ties are calculated using
the empirical metho d describ ed by Miller and Savchik Dip ole moments
are taken from Refs and expressed in the units of debye D Ionization
p otentials are taken from Refs
Appendix B
Table B Physical parameters of molecules studied
Molecule Formula Z Z E E
e p i
keV A D eV
Noble gases
Helium He
Neon Ne
Argon Ar
Krypton Kr
Xenon Xe
Diatomic molecules non p olar
Hydrogen H
Deuterium D n a
Nitrogen N
Oxygen O
Diatomic molecules p olar
Carb on monoxide CO
Nitric oxide NO n a
Polyatomic molecules non p olar
Carb on dioxide CO
Sulfur hexa uoride SF
Polyatomic molecules p olar
Water H O
Nitrous oxide N O n a
Nitrogen dioxide NO n a
Ammonia NH
Alkanes
Methane CH
Ethane C H
Propane C H
Butane C H
Pentane C H
Hexane C H
Heptane C H n a
Octane C H n a
Nonane C H
Decane C H n a
Do decane C H
Table of physical parameters of atoms and molecules
Table B Continued
Molecule Formula Z Z E E
e p i
keV A D eV
Hexadecane C H n a
Alkane Isomers
Isobutane C H n a
Isop entane C H
Neop entane C H
Ring alkanes
Cyclohexane C H
Cyclo decane C H n a
Alkenes and alkyne
Ethylene C H
Acetylene C H
Hexene C H n a
trans Hexene C H n a
Hexadiene C H n a n a
cis trans
Hexadiene C H n a
trans trans
Hexadiene C H n a
Hexatriene C H n a
Aromatic hydro carb ons
Benzene C H
Naphthalene C H
Decahydronaphthalene C H n a
Anthracene C H
Toluene C H
o Xylene C H n a
m Xylene C H n a
p Xylene C H n a
Deuterated alkanes
d Methane CD n a n a
d Hexane C D n a n a
d Heptane C D n a n a
d Octane C D n a n a
d Nonane C D n a n a
d Decane C D n a n a
Appendix B
Table B Continued
Molecule Formula Z Z E E
e p i
keV A D eV
Deuterated b enzenes
Benzene d C H D n a
Benzene d C H D n a n a
Benzene d C D n a
Per uorinated alkanes
Carb on tetra uoride CF
Hexa uoro ethane C F
Per uoropropane C F n a n a
Per uorohexane C F
Per uoro o ctane C F n a
Perchlorinated alkanes
Carb on tetrachloride CCl
Hexachloro ethane C Cl n a
Perbrominated alkane
Carb on tetrabromide CBr
Perio dited alkane
Carb on tetraio dide CI n a n a
Methyl chloride CH Cl n a
Dichloro
di uoromethane CCl F n a
Oxygen containing molecules
Methanol CH O
Propanol C H O n a
Acetone C H O n a
Acetic acid C H O n a
Propionic acid C H O n a
Per uorinated aromatics
Hexa uorob enzene C F
Octa uorotoluene C F CF n a n a
Octa uoronaphthalene C F n a
Substituted b enzenes
Chlorob enzene C H Cl n a
Bromob enzene C H Br n a
Nitrob enzene C H NO
Aniline C H NH n a
Table of physical parameters of atoms and molecules
Table B Continued
Molecule Formula Z Z E E
e p i
keV A D eV
Partially uorinated hydro carb ons
Methyl uoride CH F
Di uoromethane CH F
Tri uoromethane CHF
Fluoro ethane C H F
Tri uoro ethane C H F
Tri uoro ethane C H F n a
Tetra
uoro ethane C H F n a n a
Tetra
uoro ethane C H F n a n a
Di uoropropane C H F n a
Tri uoropropane C H F n a
Fluorohexane C H F n a n a
Fluorob enzene C H F
Di uorob enzene C H F
Di uorob enzene C H F
Di uorob enzene C H F
Tri uorob enzene C H F n a
Tetra
uorob enzene C H F
Penta uorob enzene C HF n a
Other molecules
Tetraethylsilane Si C H n a
Glycerol C H O n a n a n a
Sebacic acid
dimethyl ester C H O n a n a n a
Pyridine C H N
Appendix B
App endix C
Table of annihilation ray
sp ectra from atoms and
molecules
As discussed in Sec our measurements are precise enough to b e able to
study the line shap es of the sp ectra and not just their widths While Gaussian
line shap es are reasonable rst approximations to the data departures from a
Gaussian line shap e can b e clearly distinguished This can b e seen from the
values of from tting the Gaussian function Eq e g see Table C
r
The values of which are exp ected to b e an order of unity for a go o d mo del are
r
typically around or higher for the Gaussian t Wehave attempted to nd a
general functional form to describ e the measured line shap es However wewere
unsuccessful in obtaining a functional form that is unambiguous and has physical
signi cance Thus in order to present our exp erimental data analytically in
a quantitativeway wehave tted the observed sp ectra with a two Gaussian
function which is describ ed by
E E E E
A exp C q E exp
r
a E a E
convolved with the detector resp onse as given in Eq The numb er of free
parameters is E E E A B B and B This tting function has
r
no physical signi cance of whichwe are aware In addition the Gaussian line
widths E and E and the relative amplitude of the second Gaussian A
r
are highly correlated However this tting pro cedure yields go o d values of
r
e g except for carb on monoxide and carb on tetrachloride and this
r
functional form serves the purp ose of representing the exp erimentally measured
Appendix C
line shap es analytically with reasonable accuracy The tting parameters E
E andA are listed along with the values of in Table C
r r
Table of annihilation ray spectra from
Table C ray line shap e parameters from ts to two Gaussians Eq C
for all atoms and molecules that wehave studied A is the relative amplitude
r
of the second Gaussian
Molecule Formula Gaussian t Gaussian t
E E E A
r
r r
Noble gases
Helium He
Neon Ne
Argon Ar
Krypton Kr
Xenon Xe
Inorganic molecules
Hydrogen H
Nitrogen N
Oxygen O
Carb on monoxide CO
Carb on dioxide CO
Water H O
Sulfur hexa uoride SF
Ammonia NH
Alkanes
Methane CH
Ethane C H
Propane C H
Butane C H
Pentane C H
Hexane C H
Nonane C H
Do decane C H
Cyclohexane C H
carb on alkane isomers
Methylbutane C H
Dimethylpropane C CH
carb on alkene and alkyne
Ethylene C H
Acetylene C H
Aromatic hydro carb ons
Benzene C H
Naphthalene C H
Anthracene C H
Toluene C H CH
References
Table C Continued
Molecule Formula Gaussian t Gaussian t
E E E A
r
r r
Halo carb ons
Carb on tetra uoride CF
Carb on tetrachloride CCl
Carb on tetrabromide CBr
Partially and fully uorinated hydro carb ons
Methyl uoride CH F
Di uoromethane CH F
Tri uoromethane CHF
Fluoro ethane C H F
Tri uoro ethane CF CH
Tri uoro ethane CHF CH F
Tetra uoro ethane CF CH F
Tetra uoro ethane CHF CHF
Hexa uoro ethane C F
Di uoropropane CH CF CH
Tri uoropropane CF C H
Per uoropropane C F
Fluorohexane CH FC H
Per uorohexane C F
Fluorob enzene C H F
Di uorob enzene C H F
Di uorob enzene C H F
Di uorob enzene C H F
Tri uorob enzene C H F
Tetra uorob enzene C H F
Penta uorob enzene C HF
Hexa uorob enzene C F
Other organic molecules
Methanol CH OH
Tetraethylsilane Si C H
Nitrob enzene C H NO
Pyridine C H N
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