ray spectra from positron annihilation on atoms and molecules

19 Pages·1997·0.39 MB·English

PHYSICALREVIEWA VOLUME55,NUMBER5 MAY1997
(cid:103)-ray spectra from positron annihilation on atoms and molecules
Koji Iwata, R. G. Greaves, and C. M. Surko
PhysicsDepartment,UniversityofCalifornia,SanDiego,LaJolla,California92093-0319
(cid:126)Received23October1996(cid:33)
Positron annihilation on a wide variety of atoms and molecules is studied. Room-temperature positrons
confinedinaPenningtrapareallowedtointeractwithmoleculesintheformoflow-pressuregasessothatthe
interaction is restricted to binary encounters between a positron and a molecule. Data are presented for the
(cid:103)-ray spectra resulting from positrons annihilating in such interactions. The Doppler broadening of these
spectra is a measure of the momentum distribution of the annihilating electron-positron pairs. Consequently,
thesespectraprovideinformationabouttheelectronandpositronwavefunctions.Systematicstudiesofanni-
hilationlineshapesarediscussedfornoblegases,avarietyofinorganicmolecules,alkanes,alkenes,aromatics,
andperfluorinatedandpartiallyfluorinatedhydrocarbons.Inthecaseofmolecules,themeasurementsareused
todeterminetheprobabilityofpositronsannihilatingatspecificlocationsinthemolecule.Forexample,inthe
case of partially fluorinated hydrocarbons, we have been able to determine the relative probability of annihi-
lation on the fluorine atoms and on the C-H bonds. Insights that these studies provide in understanding the
interactionoflow-energypositronswithatomsandmoleculesarediscussed.(cid:64)S1050-2947(cid:126)97(cid:33)05405-X(cid:35)
PACSnumber(cid:126)s(cid:33): 34.50.(cid:50)s,78.70.Bj,71.60.(cid:49)z,36.10.(cid:50)k
I.INTRODUCTION annihilating electron-positron pairs have been performed in
solid and liquid targets (cid:64)4(cid:35), and they provide information
Theinteractionsoflow-energypositronswithmatterhave about the annihilation processes and other properties of ma-
been studied extensively (cid:64)1,2(cid:35). In some respects, positrons terials. In this paper, this technique is applied to make sys-
interactwithmatterinwaysthataresimilartothoseofelec- tematic measurements in gaseous media, which are suffi-
trons because of the identical masses of an electron and a ciently tenuous so that the interaction of positrons with an
positron.However,inotherrespectstheybehaveverydiffer- individual atom or molecule can be isolated and studied.
ently because the electron and positron have opposite signs Earliermeasurementsofthistypeweremainlyperformed
of electric charge and are distinguishable particles. This is in dense or high pressure gases using a different technique
generallymostnoticeableforlow-energyinteractionssinceit fromtheonedescribedhere.Inthoseexperimentsapositron
is in this regime that differences related to the Coulomb in- source(cid:126)usuallyaradioactiveisotopesuchas 22Naor 66Co(cid:33)is
teraction and the Pauli exclusion principle play larger roles. placed in a gas cell so that high-energy ((cid:59)10–500 keV(cid:33)
In addition, positrons can also exhibit unique processes, positrons are emitted directly into the annihilation medium.
namely, positronium atom formation (cid:64)3(cid:35) and annihilation Thepositronsexperienceenergylossthroughcollisionswith
withanelectron.Centraltotheworkdiscussedhere,positron theatomsormolecules,eventuallyreachingthermalequilib-
annihilation can provide information not available from riumwiththemedium.Theannihilation(cid:103)raysaremeasured
electron-matter interactions. For example, much information using either high-resolution Ge detectors or the angular cor-
about defects near the surfaces of solids can be obtained by relation technique, described in Sec. II. In general, the ther-
studying positron annihilation (cid:64)4(cid:35). malization time is shorter than the annihilation time scale so
The interaction of low-energy positrons with atoms and that studies of free positron annihilation on molecules at the
molecules has been the subject of numerous studies and is temperatureofthemediumarepossible.Onedisadvantageof
currentlyafieldofactiveresearch(cid:64)5–9(cid:35).Studiesofthiskind this method is that positronium atom formation can take
havemanypotentialapplications,forexample,inmassspec- place during the slowing down of the positrons, and subse-
trometry, where positron annihilation is a qualitatively dif- quent annihilation of the thermalized positronium atoms can
ferent way of ionizing molecules (cid:64)10–12(cid:35). Positrons also obscure the free positron annihilation signal. Another poten-
provide stringent tests of scattering theories. In recent work, tialcomplicationisthat,incondensedgasesorhighpressure
three types of positron-molecule measurements have been gases, it is difficult to isolate and study the interaction of a
performed using positrons stored in Penning traps. One type positron with a single atom or molecule. For studies of sub-
of experiment is measurement of the lifetime of positrons stancesinthegasphase,compoundsarelimitedtothosethat
annihilatinginasamplegas(cid:64)7(cid:35).Suchmeasurementsprovide exist in gaseous form at the operating temperature and pres-
information about annihilation cross sections. Another type sure.Inpractice,theoperatingpressuremustbesuitablyhigh
of experiment involves measurement of the spectra of posi- sothatthepositronsstopinthetestmedia.Forthoseexperi-
tive ions produced as a result of positron annihilation ments, the sample temperatures are typically room tempera-
(cid:64)10,12–14(cid:35). In the experiments discussed in this paper, we ture or lower, while the pressure is typically atmospheric
study the momentum distribution of the annihilating pressure or larger.
electron-positronpairsbymeasuringtheDopplerbroadening Wehavebeenabletoavoidtheseshortcomingsbytheuse
of the (cid:103)-ray annihilation spectrum (cid:64)15,16(cid:35). of positrons accumulated and cooled in a Penning trap (cid:64)17(cid:35),
Extensive measurements of momentum distributions of where they are confined by a combination of magnetic and
1050-2947/97/55(cid:126)5(cid:33)/3586(cid:126)19(cid:33)/$10.00 55 3586 ©1997TheAmericanPhysicalSociety
55 (cid:103)-RAYSPECTRAFROMPOSITRONANNIHILATIONON ... 3587
electrostatic fields. Positronium atom formation is avoided
sincethepositronscanbecooledbelowtheformationthresh-
old before the sample gas is introduced. This technique can
be used at low sample gas pressure ((cid:44)10(cid:50)6 torr(cid:33) so that
substancesthatexistasliquidsorsolidsatroomtemperature
can be introduced into the trap as low-pressure vapors.
In addition to their application for studies of positron-
molecule interactions, stored positrons have also been used
for a variety of other experiments, including studies of
electron-positron plasmas (cid:64)18(cid:35). They also have the potential
for supplying positrons for antihydrogen formation (cid:64)19–21(cid:35).
PreviousexperimentsofDoppler-broadened(cid:103)-rayspectra
in Penning traps (cid:64)15,16(cid:35) demonstrated the feasibility of the
FIG. 1. Illustration of the momentum of an annihilating
use of stored positrons for spectral measurements. Subse- electron-positron pair p(cid:87) and the resulting (cid:103)-ray momenta, (cid:103)(cid:87) and
quentimprovementsinpositronmoderation(cid:64)22,23(cid:35)andtrap- (cid:103)(cid:87). An annihilation event is observed with two detectors p1laced
ping efficiency as well as in the gas handling system have 2
180° with respect to the annihilation site at distance L. The longi-
now enhanced the signal-to-noise ratio by 2 orders of mag-
tudinal component of p(cid:87), p , shifts the energies of (cid:103)rays, and the
nitude. This has permitted a range of new experiments, in- z
tangential components, p and p , deflect the (cid:103)rays by an angle
cluding detailed comparison of the annihilation line shape x y
with theoretical calculations (cid:64)24(cid:35), the simulation of astro- (cid:117)(cid:53)((cid:117)x2(cid:49)(cid:117)2y)1/2. (cid:126)The angle of deflection is exaggerated in this fig-
ure.(cid:33)
physical positron annihilation (cid:64)25(cid:35), and the localization of
the sites of positron annihilation in complex molecules. tory frame, the (cid:103)rays carry away the initial momentum of
In this paper, we describe a systematic study of positrons
the center of mass of the pair. Thus, as illustrated in Fig. 1,
interactingwithawidevarietyofatomsandmolecules.Data
the angle of emission of the two photons relative to one
are presented for noble gases, inorganic molecules, alkanes,
another deviates slightly from 180° due to the perpendicular
alkenes,aromatics,substitutedhydrocarbons,aswellasfully
components of the momentum of the electron-positron pair,
and partially fluorinated hydrocarbons. Important results in-
p and p . The (cid:103)rays are Doppler shifted in energy due to
clude demonstration of the ability to resolve, for the first x y
the longitudinal momentum component of the pair, p .
time in gaseous media, non-Gaussian features in the line z
When p ,p (cid:33)m c, the angle of deviation (cid:117) can be ex-
shapes and detection of more than one annihilation site in x y 0
pressed as
molecules, including distinguishing annihilation on the C-H
bond from that on the fluorine atom in partially fluorinated
p
hydrocarbons.Wealsopresentdataindicatingthat,inhydro- (cid:117)(cid:46) j , (cid:126)1(cid:33)
j m c
carbons, we can distinguish annihilation on the C-H bond 0
fromthatontheC-Cbond.Inallmoleculesstudied,thedata where j(cid:53)x ory,m istherestmassoftheelectron,andc is
are consistent with the positrons annihilating predominantly the speed of light.0The Doppler shift in the energy, (cid:68)E, is
withvalenceelectrons.Astudyofhalogenatedhydrocarbons
given by
isalsopresented.Itshowsthatthepositronsannihilateonthe
halogen atoms with a linewidth very similar to that of the p cp
related noble gas atom, particularly in the case of the larger (cid:68)E(cid:53) z E (cid:53) z, (cid:126)2(cid:33)
2m c 0 2
halogens. We expect that the systematic studies presented in 0
this paper will provide useful constraints on theories of low- whereE (cid:53)m c2 istherestmassenergyoftheelectron.The
0 0
energy positron-atom and positron-molecule interactions.
perpendicular components of the momentum of the annihi-
This paper is organized in the following manner. In Sec.
lating pair can be studied by measuring the angular correla-
II, we review previous experiments to measure the momen- tionoftwo(cid:103)rays.Thelongitudinalcomponentcanbemea-
tum distributions of annihilating electron-positron pairs. The sured by observing the Doppler broadening of the (cid:103)-ray
experimentalsetupisdescribedinSec.III.Theresultsofthe
spectrum using high-resolution solid-state detectors such as
experimentsaredescribedinSec.IV,includingtheresultsof
lithium-drifted or intrinsic germanium detectors.
an extensive study of partially fluorinated hydrocarbons and
Whenannihilationfollowsthermalizationofthepositrons
a simulation of astrophysical positron annihilation. Detailed
in the medium, e.g., with the characteristic energy of
analysesofspectrallineshapesarethenpresentedinSec.V. (3/2)kT(cid:53)0.04 eV (cid:126)corresponding to room temperature(cid:33), the
In Sec. VI, we discuss the implications of the results pre-
momentum of the annihilating pairs is typically dominated
sented in this paper for current theoretical work and for
by the momenta of the electrons. Techniques for measuring
progress in other areas of positron-molecule interactions. A
these momentum distributions were developed initially for
brief set of concluding remarks is presented in Sec. VII. the studies of positron annihilation in condensed media (cid:64)4(cid:35).
They have been applied to studies of positron-gas interac-
tions as well (cid:64)9(cid:35). When the medium is a crystalline solid,
II.MOMENTUMDISTRIBUTIONMEASUREMENTS
p andp canbedistinct.Forexample,theanisotropyintwo
x y
An electron-positron pair annihilates by emitting two dimensionshasbeenobservedandstudiedinsomematerials
quanta of 511-keV (cid:103)rays at an angle of 180° in the center- (cid:64)26(cid:35). When the medium under investigation is a liquid or
of-mass frame of the two particles. However, in the labora- gas,themomentumdistributionisrotationallyaveraged,and
3588 KOJIIWATA,R.G.GREAVES,ANDC.M.SURKO 55
thethreemomentumcomponentsareequivalent.Inthiscase,
theangulardeviation(cid:117)andtheenergyspread(cid:68)E arerelated
by
(cid:117)
(cid:68)E(cid:53)m c2 , (cid:126)3(cid:33)
0 2
and angular correlation and Doppler-broadening measure-
ments can be compared.
A.Annihilation(cid:103)-rayangularcorrelationmeasurements
Thetechniqueofangularcorrelationofannihilationradia-
tion (cid:126)ACAR(cid:33) was developed to determine the perpendicular
componentsofthemomentaofannihilatingelectron-positron
pairs in solids, liquids, and dense gases (cid:64)4(cid:35). Initially, the
measurements were performed in a one-dimensional geom-
FIG.2. Schematicdiagramofthelasttwostagesofthepositron
etry(cid:64)27(cid:35)inwhichtwo(cid:103)-raydetectorsarelocatedbehindslit
trapandthedetector.
collimators on opposite sides of the annihilation region. One
ofthedetectorsisscannedasafunctionoftheanglebetween
manium detector(cid:33) in conjunction with a multichannel ana-
the two detectors, and coincident events are recorded. One
lyzer(cid:126)MCA(cid:33).Thisyieldsthelongitudinalcomponent, p , of
advantage of the ACAR method is its high resolution. Typi- z
the annihilating pair’s momentum, which is equivalent to
cal angular resolutions achievable are about 0.65 mrad (cid:64)28(cid:35),
either of the other two components in an isotropic medium
whichisequivalenttothe(cid:103)-rayenergyresolutionof0.2keV
such as a gaseous target. An advantage of the Doppler-
using Eq. (cid:126)3(cid:33).
broadening technique is that a high count rate can be ob-
Inordertoobtainhighresolution,theslitsmustbeplaced
tained since the detector can be placed close to the annihila-
asfarfromtheannihilationcellaspossible,typicallytensof
tion region, and this results in a large collection solid angle.
meters. This results in reduced count rates due to the small
This permits measurements in diffuse media, such as low-
solid angle subtended by the detector at the sample. In order
pressure gases (cid:64)15,16,32(cid:35). Another advantage of this tech-
to obtain both a large number of counts and high resolution
nique is the compactness of the equipment and the ease of
in a reasonable amount of time, one would like to have as
installation.AsdescribedinSec.IVJ,thistechniquecanalso
many positrons as possible annihilating in a small volume.
be applied to studies of positron annihilation in the interstel-
This condition can be satisfied in solid and liquid targets
larmedium,whereACARtechniquesareinapplicable.How-
(cid:64)29,30(cid:35), but in this case, annihilation may involve the inter-
ever, a disadvantage of the Doppler-broadening measure-
action of a positron with multiple atoms or molecules. In
ments is their relatively poor resolution. For example, an
contrast, in gaseous media the two-body assumption is more
intrinsic Ge detector typically has the energy resolution of
likelytobemet,butACARmeasurementsaremoredifficult
(cid:59)1 keVat511keVascomparedwiththeequivalentACAR
becausethemeanfreepathofpositronsingasesisrelatively
resolution of 0.2 keV discussed above. In the experiments
largeandresultsinalargeannihilationregionandlowcount
described here, an intrinsic Ge detector is used to take ad-
rates. The first ACAR measurements in gaseous media were
vantage of the high count rate in diffuse media where posi-
reported by Heinberg and Page in 1957 (cid:64)31(cid:35). However, their
trons are interacting with low-pressure gas atoms or mol-
study was focused on positronium atoms in which the infor-
ecules.
mation content of the signal is less sensitive to the details of
Lynn etal. employed an improved implementation of the
the spectra. The introduction of the two-dimensional (cid:126)2D(cid:33)
Doppler-broadening approach, which utilizes two high-
ACAR detector (cid:64)28(cid:35) has enabled measurements in the gas
resolution Ge detectors placed 180° with respect to the an-
phase with significantly increased count rates. For 2D
nihilation region (cid:64)33(cid:35). This technique can dramatically in-
ACAR, two relatively large NaI crystals with position-
crease the signal-to-noise ratio of the data. Use of this
sensitive detectors attached replace the detector-slit combi-
technique allowed them to detect positron annihilation on
nations.Theposition-sensitivedetectorscanaccuratelyiden-
inner-shell electrons in condensed media. This method can,
tify the location of scintillations produced by (cid:103)rays without
in principle, be used for studies of positron annihilation in
muchlossofcountrate.Themeasurementsingaseousmedia
gaseous media, which is discussed in Sec. VI.
using a 2D ACAR detector were reported by Coleman etal.
(cid:64)9(cid:35), and their study showed the first quantitative ACAR re-
III.DESCRIPTIONOFTHEEXPERIMENT
sults of free positrons annihilating on atoms.
A.Thepositrontrapandgashandlingprocedures
B.Doppler-broadened(cid:103)-rayspectralmeasurements
The experiments were performed using a technique simi-
Fortheexperimentsdescribedinthispaper,analternative lartothatdiscussedpreviously(cid:64)16(cid:35).Theschematiclayoutof
method of obtaining the momenta of the annihilating the experiment is shown in Fig. 2. Positrons emitted from a
electron-positron pairs was used. We measure directly the 60-mCi 22Naradioactivesourceataspectrumofenergiesup
Doppler broadening of the annihilation line using a high- to 540 keV are moderated to a few electron volts by a solid
energy resolution solid-state (cid:103)-ray detector (cid:126)an intrinsic ger- neon moderator (cid:64)22,23(cid:35). They are then accelerated to about
55 (cid:103)-RAYSPECTRAFROMPOSITRONANNIHILATIONON ... 3589
30 eV and guided by a magnetic field into the four-stage merciallyavailableacethylenecontainsacetone.Weplaceda
Penning trap. The trap consists of a vacuum chamber sur- cold trap in the gas line to remove this impurity.
rounded by a solenoid that provides positron confinement in
the radial direction and an electrode structure that provides B.Spectralanalysis
electrostaticconfinementintheaxialdirection.Thepositrons
WehavefoundaGaussianlineshapetobeausefulfitting
experience inelastic collisions with nitrogen buffer gas mol-
function for both the detector calibration lines and the anni-
ecules introduced into the first stage of the trap. These colli-
hilationspectraobservedfromatomsandmolecules.Inprac-
sions result in the positrons being trapped in the potential tice, the fitting function also contains a complementary error
well created by the electrodes. More detailed descriptions of function component, which models Compton scattering in
the operation of the positron trap are presented elsewhere the detector crystal (cid:64)37(cid:35), and a constant background. This
(cid:64)34,35(cid:35). fitting function has the form
Positronsaccumulatedinthethirdstageofthetrapcoolto (cid:70) (cid:83) (cid:68) (cid:71) (cid:83) (cid:68)
room temperature in approximately 1 s by electronic, vibra- f(cid:126)E(cid:33)(cid:53)A exp (cid:50) E(cid:50)E0 2 (cid:49)A erfc E(cid:50)E0 (cid:49)A , (cid:126)4(cid:33)
tional, and rotational excitation of nitrogen molecules. The 1 a(cid:68)E 2 a(cid:68)E 3
fit fit
positrons are then shuttled to the fourth stage, where the
N pressure is the lowest and where the positrons are closer where E is the (cid:103)-ray energy, (cid:68)E is the full width at half
2 fit
to the (cid:103)-ray detector. The trap protocol is designed to accu- maximum (cid:126)FWHM(cid:33) of the line, a(cid:53)1/(4 ln2)1/2, A and
1
mulate an optimal number of positrons with minimal losses A2 are amplitudes, A3 is the background, and erfc(x) is the
from annihilation on buffer gas molecules. A cold trap, complementary error function. The fit parameters are A1,
showninFig.2,isfilledeitherwithliquidnitrogenorwitha A2, A3, E0, and (cid:68)Efit. Representing the counts in each en-
water-ethanol mixture chilled to (cid:50)7°C in order to reduce ergy bin Ej by yj, the quantity minimized is
impurities in the vacuum system. The base pressure of our (cid:70) (cid:71)
system is typically 5(cid:51)10(cid:50)10 torr, and the positron lifetime (cid:120)2(cid:53) 1 (cid:40)N yj(cid:50)f(cid:126)Ej(cid:33) 2, (cid:126)5(cid:33)
with the buffer gas turned off is typically 1 h with liquid r N(cid:50)kj(cid:53)1 (cid:115)j
nitrogen in the cold trap and a few minutes with the chilled
water-ethanol mixture. Liquid nitrogen in the cold trap can where (cid:115)(cid:53)y1/2, N is the number of bins used in the fit, and
j j
be used only for gases that do not condense at 77 K. Mea- k isthenumberoffittingparameters.Thevalueof(cid:120)2 isused
r
surements of some of the substances, obtained with liquid as a measure of goodness of the fit and is expected to be of
nitrogen in the cold trap, were repeated with the chilled order unity for a fit with a good model. The fitting function
water-ethanol mixture. No difference in the spectra was de- given by Eq. (cid:126)4(cid:33) is a good approximation for the calibration
tected except that higher count rates were observed when (cid:103)-ray lines because the number of free electron-hole pairs
liquid nitrogen was used. produced by a monoenergetic (cid:103)ray in a germanium crystal
The experiment is operated in a series of repeated cycles has a Gaussian distribution. For calibration we used essen-
of positron filling and annihilation. In each cycle positrons tially monoenergetic (cid:103)rays emitted from test sources.
are accumulated for a fixed period of time (cid:126)typically 5 s(cid:33) in To first order, we have found that the annihilation lines
thepresenceoftheN buffergas.Thebuffergasisthenshut can also be analyzed by fitting Eq. (cid:126)4(cid:33). While this is a con-
2
off, following a positron cooling time of 1 s. The buffer gas venient way of characterizing and comparing data, there is
pressureisthenallowedtodropforanother8s.Theintrinsic no a priori reason that the annihilation lines should have
Ge detector is gated on, and the test gas is introduced. Typi- Gaussian line shapes. As discussed in Sec. IV, our data are
cally,thespectrumisaccumulatedontheMCAfor5sinthe now of sufficiently high quality to be able to resolve depar-
presence of the test gas, and then the test gas is turned off. tures from Gaussian line shapes. The measured annihilation
This cycle is continued for about 12 h to accumulate a large lineistheconvolutionoftheintrinsicannihilationlineshape
number of counts, with the total counts in the peak typically andthedetectorresponse.UndertheassumptionofGaussian
(cid:59)106.Thenumberofpositronsinthetrapandthepressures line shapes, the intrinsic FWHM, (cid:68)E, is given by
of the test gases are carefully adjusted to obtain the highest
countratesconsistentwithavoiding(cid:103)-raypileup,whichcan (cid:68)E(cid:53)(cid:126)(cid:68)E2(cid:50)(cid:68)E2 (cid:33)1/2, (cid:126)6(cid:33)
fit det
distort the shape of the spectrum.
The positron temperature is measured separately. The where (cid:68)E is the detector linewidth and (cid:68)E is the fitted
det fit
depth of the confining potential well is lowered slowly, and linewidth from Eq. (cid:126)4(cid:33). The linewidths quoted in this paper
thenumberofpositronsescapingfromthetrapisanalyzedto are the values of (cid:68)E obtained in this way. In Sec. V, we
measure the positron temperature. This technique is de- discuss other attempts (cid:126)i.e., beyond the one-Gaussian ap-
scribed in detail elsewhere (cid:64)36(cid:35). We find that the positrons proximation(cid:33) to fit the measured spectra.
are at room temperature (cid:126)i.e., (cid:59)300 K(cid:33).
Small amounts of impurities with high annihilation rates
C.Calibrationanddetectorresponse
in test substances can greatly affect the experimental results
(cid:64)7(cid:35). We have used substances with highest purity commer- The energy scale of the detector response was calibrated
cially available (cid:126)generally (cid:46)99.9%(cid:33), and the annihilation using 344.3- and 661.6-keV (cid:103)-ray lines from 152Eu and
contribution from impurities is less than 1%. Some of the 137Cstestsources,respectively.ThelinesarefitwithEq.(cid:126)4(cid:33)
substances have additives for various reasons, and appropri- to obtain the centroids and linewidths of the two peaks. The
atetreatmentswereusedtoremovethem.Forexample,com- centroidsareusedtocalibratetheenergyscaleofthespectra,
3590 KOJIIWATA,R.G.GREAVES,ANDC.M.SURKO 55
FIG.4. ObservedspectrafromH ((cid:115)) andNe((cid:100)) plottedon
2
a linear scale. Solid lines are drawn to guide the eye. For the pur-
poseofcomparison,the514.02-keVlinefrom 85Sr(cid:126)dottedline(cid:33)is
FIG. 3. (cid:126)a(cid:33) (cid:103)-ray spectrum of the 514.0-keV line from a 85Sr shifted to 511 keV, which represents the detector response. The
source: ((cid:115)) observed spectra and (cid:126)—(cid:33) fit to the spectrum with a spectraarenormalizedtounityatthepeak.
combination of a Gaussian and a step function (cid:64)Eq. (cid:126)4(cid:33)(cid:35). The line-
widthis1.16keV.(cid:126)b(cid:33)Residualsofthefit.
resultsfrompreviousstudiesofmomentumdistributionsand
theoretical calculations are also tabulated and compared.
while the widths of these two lines are interpolated to find
thedetectorenergyresolutionatthe511-keVline.Thereso- Typical spectra from our experiment are shown in Fig. 4
lution is typically 1.16 keV. along with the detector response. The annihilation lines
The detector line shape was also calibrated using a 85Sr shown are the spectra from H2 and Ne, which are the nar-
source, which has a (cid:103)-ray line at 514.02 keV, conveniently rowest and widest lines we have observed, respectively. The
close to the 511-keV line. The spectrum measured with a 3- observed linewidths correspond to the positrons annihilating
(cid:109)CisourceisshowninFig.3(cid:126)a(cid:33).ThefittoEq.(cid:126)4(cid:33)isshown predominantly with the valence electrons of the atoms and
in the figure as a solid line and yields (cid:120)2 (cid:53) 1.3. The line- molecules. However, we also have evidence of annihilation
r
width of the Gaussian, (cid:68)E , is typically 1.16(cid:54)0.01 keV, on inner-shell electrons, and this will be discussed in Sec.
det
which agrees with the interpolated value from 344.4- and IVI. As can be seen in Fig. 4, the detector width is substan-
661.6-keV lines, where 0.01 keV refers to the drift in the tiallynarrowerthantheobservedannihilationlines.Thehigh
detectorlinewidthduringameasurement.Theresidualsfrom precisionofthemeasurementsisevidentfromthesmallscat-
the fit are shown in Fig. 3(cid:126)b(cid:33). These data deviate slightly ter in the data. The total number of (cid:103)-ray counts in a spec-
from the fit on the lower-energy side of the line. This low- trum is about 106 unless otherwise stated. For the experi-
energy tail may be due to the trapping of electrons and/or mentallymeasuredspectrapresentedinfigures,theerrorbars
holes in the defects of the Ge crystal (cid:64)37(cid:35). Nonetheless, the
shownrepresenttheexpectedstatisticaluncertaintiesinspec-
residuals are generally quite small: less than 0.5% of the tralamplitudeduetothefinitenumberof(cid:103)-raycounts.Spec-
peak counts on the lower-energy side and even smaller
trawererecordedin121-htimesegments,andthelinewidth
((cid:59)0.1%(cid:33)onthehigher-energyside.AsdescribedinSec.IV,
was calculated from each segment. The tabulated linewidths
these residuals are also generally much smaller than the de-
were obtained by averaging these linewidths. The variations
viations from the Gaussian shape of the observed annihila-
were typically 0.01–0.02 keV. Measurements of some sub-
tion lines. In the following, we quote the linewidth of the
stanceswererepeatedinseparaterunsondifferentdays,and
Gaussianfit(cid:126)typically1.16keV(cid:33)asthewidthofthedetector
thoselinewidthsgenerallyagreewithin0.01keV.Theuncer-
response. The detector energy response and line shape vary
by a small amount from day to day (cid:126)typically (cid:44)0.02 keV(cid:33), tainty in the detector response is at most 0.01 keV. We esti-
mate the experimental precision of the linewidths to be typi-
and a separate calibration spectrum was taken before and
cally 0.02 keV.
after each run.
In the remainder of this section, we present annihilation
line data for a variety of substances. The tables also list the
IV.RESULTS
annihilation rates. For some of these molecules, the annihi-
Inthissection,wereporttheresultsoftheDopplerbroad- lationrateshadnotbeenmeasuredpreviouslyintheposition
ening of the (cid:103)-ray spectra from positrons annihilating on a trap and our measurements of them are also listed. The rates
variety of atoms and molecules in the Penning trap. The are expressed in terms of a normalized annihilation rate (cid:64)7(cid:35),
55 (cid:103)-RAYSPECTRAFROMPOSITRONANNIHILATIONON ... 3591
TABLE I. The (cid:103)-ray linewidths for noble gases obtained from Gaussian fits to the data (cid:126)in keV(cid:33). For
comparison, experimental values from other methods as well as theoretical values are listed. The values of
Z arealsoquoted.(cid:126)SeeRef.(cid:64)7(cid:35)forthesourcesofZ values.(cid:33)
eff eff
Gas Thisstudy Shizumaa Colemanb Stewartc Theory(cid:126)static(cid:33)d Theory Z
eff
Helium 2.50 2.01 2.63 2.4 2.53 2.50e 3.94
2.20f
2.45g
2.50h
Neon 3.36 2.04 3.19 3.32 3.82 3.73i 5.99
Argon 2.30 1.96 2.86 2.61 2.64 2.81j 33.8
Krypton 2.09 N/A 2.65 2.63 2.36 2.50k 90.1
Xenon 1.92 1.69 2.58 2.43 2.06 2.22k 401
aReference(cid:64)32(cid:35). gReference(cid:64)38(cid:35).
bReference(cid:64)9(cid:35). hReference(cid:64)44(cid:35).
cReference(cid:64)30(cid:35). iReference(cid:64)39(cid:35).
dReference(cid:64)45(cid:35). jReference(cid:64)40(cid:35).
eReference(cid:64)24(cid:35). kReference(cid:64)41(cid:35).
fReference(cid:64)43(cid:35).
(cid:71) 1.Helium
Z (cid:91) , (cid:126)7(cid:33)
eff (cid:112)r2cn Helium is the simplest stable atomic gas, and it has been
0
studied extensively. Rigorous calculations are possible for
where (cid:71) is the observed annihilation rate, r is the classical positron-helium interactions. Measurements for helium in
0
radius of the electron, and n is the number density of the oursystemarerestrictedbythelimitedcapacityofourcryo-
molecules. The experimental error of these annihilation rate genic pumps for this gas so that the data quality is not as
measurements is limited by the difficulties in the test gas good as those for other gases. The experimentally measured
pressuremeasurementsandestimatedtobetypically20%for spectrum is shown in Fig. 5 together with a very recent cal-
most substances. Detailed accounts of this type of measure- culation (cid:64)24(cid:35) using the Kohn variational method. Excellent
ment are summarized elsewhere (cid:64)7(cid:35). The sources of the val- agreement can be seen between experiment and theory, ex-
ues are listed in Ref. (cid:64)7(cid:35) unless otherwise noted. tendingoverthreeordersofmagnitudeinspectralamplitude.
The values of the previously measured linewidths from These data provide experimental evidence for deviations
ACAR measurements are quoted in keV as converted from from the empirical Gaussian line shape described above and
the ACAR linewidths using Eq. (cid:126)3(cid:33). shownbythedashedlineinFig.5.Whilesuchdeviationsare
expected, previous experiments were not sufficiently precise
to discern them.
A.Noblegases
The simple electronic structure of noble gas atoms has 2.Neon,argon,krypton,andxenon
made them attractive candidates for studies of positron-atom
interactions. Comparison between experiments (cid:64)9(cid:35) and theo- Spectraforneon,argon,krypton,andxenonareshownin
ries (cid:64)38–42(cid:35) are available for all of these atoms. Previous Fig. 6, and the values of the linewidths are listed in Table I.
The linewidth for neon is the largest. In fact, it is the widest
theoretical calculations were based on the polarized orbital
line we have observed for any atom or molecule. For atoms
approximation, with the exception of the helium studies
(cid:64)24,43,44(cid:35). larger than neon, the linewidths decrease as the sizes of the
atoms increase. Calculations using the polarized-orbital ap-
Aqualitativeunderstandingofthelinewidthsofthenoble
proximation are listed in Table I (cid:64)39–41(cid:35). The higher mo-
gases can be obtained by considering the simple approxima-
mentumcomponentsinKrascomparedtoArcanbeseenby
tion of the positron in the static potential of the atom in its
the crossing of the data around 515 keV. This crossing was
Hartree-Fock ground state. While this theory gives a signifi-
cant underestimate of Z , the (cid:103)-ray linewidths are in rea- predicted by the static Hartree-Fock approximation, and the
sonable agreement witheeffxperiment (cid:126)Table I(cid:33) (cid:64)45(cid:35). This in- theoryindicatesthatthecrossingisduetoalargerfractionof
positrons annihilating with inner-shell electrons in Kr (cid:64)45(cid:35).
dicatesthatthemomentumdistributionoftheelectronsinthe
(cid:126)Inner-shell electron annihilations will be discussed more in
atomic ground state is the most significant factor in deter-
Sec.IVI.(cid:33)Theagreementbetweentheexperimentalandthe-
mining the linewidths. The experimentally measured line-
oreticalvaluesforthesenoblegasesisnotasgoodasthatfor
widths are consistently smaller than the predictions of this
helium,probablyreflectingthedifficultyinperformingaccu-
simple theory.
In Table I, we compare our (cid:103)-ray spectra for noble gases rate calculations for all but the simplest atoms.
with the previous measurements as well as with theoretical
3.Previousmeasurementsfromotherexperiments
calculations.Wenotethatthetheoreticalcalculationspredict
thegeneraltrendoftheexperimentallinewidthseventhough Selected values of the linewidths measured for the noble
the calculated values differ from our measurements. gases are listed in Table I. Stewart etal. (cid:64)30(cid:35) performed
3592 KOJIIWATA,R.G.GREAVES,ANDC.M.SURKO 55
FIG. 6. Experimentally measured (cid:103)-ray spectra from noble
gases: neon ((cid:100)), argon ((cid:115)), krypton ((cid:106)), and xenon ((cid:104)). The
FIG.5. (cid:126)a(cid:33)Annihilation(cid:103)-rayspectrumforpositronsinteracting
peakheightsarenormalizedtounity.Thespectrashownareforthe
with helium atoms: experimental measurements (cid:126)(cid:115)(cid:33); theoretical higher-energy side of the (cid:103)-ray line since the step function in the
predictionofRef.(cid:64)24(cid:35)(cid:126)—(cid:33);convolvedwiththeresponseoftheGe
detectorresponseisabsentinthisregion,andconsequentlythedata
detector; Gaussian function fit to fit the experimental data (cid:126)- - -(cid:33).
qualityisbetter.
Gaussian function fit to the experimental data. (cid:126)b(cid:33) Residuals from
theGaussianfit.(cid:126)c(cid:33)Residualsfromthetheoreticalcalculation.
limitednumberofmolecules.Experimentallymeasuredline-
widthsarelistedinTablesIIandIIIforthevariousinorganic
ACAR measurements in condensed media, while Coleman
molecules we have studied.
etal. (cid:64)9(cid:35) obtained 2D ACAR measurements from gaseous
targets at a pressure of 1 atm. High-energy positrons were
1.Hydrogen
directly injected into the gas cells in these experiments.
H is the simplest molecule, and its significance in astro-
Thus, these ACAR spectra include a contribution from the 2
physicalpositronannihilationhasattractedinterestfromboth
annihilation of thermalized positronium atoms. This appears
experimentalists(cid:64)15(cid:35)andtheorists(cid:64)46,47(cid:35).Theastrophysical
as a narrow peak in the spectra, superimposed on the anni-
aspects of our measurements are discussed in Sec. IVJ. Our
hilation of free positrons on atoms, which appears as a wide
measured spectrum for hydrogen is shown in Fig. 7 along
component in the spectrum. The free-positron components
with theoretical predictions for the line shape (cid:64)46,47(cid:35). The
were extracted assuming Gaussian line shapes for both con-
measuredvalueofthelinewidthof1.72(cid:54) 0.02keViscom-
tributions. The linewidths from these measurements are
pared with other measurements and with theoretical predic-
qualitativelysimilartoourmeasuredvaluesalthoughtheab-
tions in Table II. All experimental values and the calculated
solutevaluesarelarger.Thediscrepancymaycomefromthe
high sample gas pressures in the ACAR experiments, which
can introduce three-body interactions. Also, the positronium TABLEII. The(cid:103)-raylinewidthsfromaGaussianfittothedata
contributions in the ACAR experiments were relatively forH2,alongwithothermeasurementsandcalculations.Thevalue
large, especially for the larger noble gases, which makes the ofZeffis14.6(cid:64)70(cid:35).
extractionofthefreepositroncomponentmoredifficult.The
Reference (cid:68)E (cid:126)keV(cid:33)
only previous Doppler-broadening studies in the gas phase
were reported by Shizuma etal. (cid:64)32(cid:35). Although they did not Thisstudy 1.71(cid:54) 0.02
tabulate linewidths, we have estimated numerical values Briscoea 1.66
from their graphical data (cid:126)Table I(cid:33). Their values are signifi- Brownb 1.56(cid:54) 0.09
cantlynarrowerthanothermeasurementsandtheoreticalpre-
Darewychc 1.70
dictions. The reason for the discrepancy is not clear.
Ghoshd 1.93
aACARmeasurementinliquidH (cid:126)6.5mrad(cid:33)(cid:64)29(cid:35).
B.Inorganicmolecules 2
bDoppler-broadening(cid:103)-rayspectrummeasurementingas(cid:64)15(cid:35).
Moleculesaresignificantlymorecomplicatedthanatoms, cTheoreticalcalculation(cid:126)6.65mrad(cid:33)(cid:64)46(cid:35).
and consequently theoretical calculations exist for only a dTheoreticalcalculation(cid:126)7.54mrad(cid:33)(cid:64)47(cid:35).
55 (cid:103)-RAYSPECTRAFROMPOSITRONANNIHILATIONON ... 3593
TABLE III. The (cid:103)-ray linewidths for inorganic molecules (cid:126)us-
ingGaussianfits(cid:33).(cid:126)SeeRef.(cid:64)7(cid:35)forthesourcesofZ values.(cid:33)
eff
Molecule Formula (cid:68)E (cid:126)keV(cid:33) Z
eff
Nitrogen N 2.32 30.5
2
Oxygen O 2.73 36.7
2
Carbonmonoxide CO 2.23 38.5
Carbondioxide CO 2.63 54.7
2
Water H O 2.59 319
2
Sulfurhexafluoride SF 3.07 86.2
6
Ammonia NH 2.27 1600a
3
aThisstudy.
value by Darewych are similar, while the prediction by
Ghosh etal. is much larger than the experimental values.
2.Othergases
(a) Nitrogen. Nitrogen is the second simplest molecule.
An ACAR measurement in liquid N gave (cid:68)E(cid:53)2.25 keV
2
(cid:126)8.8 mrad(cid:33) (cid:64)30(cid:35), which is in reasonable agreement with our
measuredvalueof2.32keV.Theonlytheoreticalcalculation
available gives a linewidth of 1.34 keV (cid:126)5.28 mrad(cid:33) (cid:64)47(cid:35), FIG. 8. (cid:126)a(cid:33) (cid:103)-ray spectra for positrons annihilating with CO
which is much narrower than the experimental values. ((cid:100)) and CO ((cid:115)). (cid:126)b(cid:33) Residuals from the Gaussian fits. The data
2
(b) Carbon monoxide and carbon dioxide. Carbon mon- andresidualsarenormalizedtothepeakheightofthespectra.
oxide is unique in that the line shape exhibits the largest
departure from a Gaussian for any molecule, as shown in (c) Sulfur hexaflouride. Sulfur hexafluoride has very high
Fig. 8. This is due to a small fraction of positrons annihilat- electron affinity, and it is well known as an electron scaven-
ingwithelectronshavinghighmomenta.Sincethismolecule ger (cid:64)48(cid:35). In contrast, with regard to the interaction with pos-
is relatively simple, it may be an interesting subject for the- itrons, it has a very low annihilation rate for a molecule of
oretical calculations. In contrast to carbon monoxide, carbon thissize(Z (cid:53)86.2).Theannihilationlineisalmostaswide
eff
dioxide has only a weakly non-Gaussian line shape (cid:126)Fig. 8(cid:33). as neon. We note that the electronic structure of the fluorine
atoms in many molecules, including SF , is similar to the
6
closed-shellstructureofneon.Sulfurhexafluoridehasaline-
width very similar to the perfluorinated alkanes. This sug-
gests that annihilation in all of these cases occurs predomi-
nantly on the fluorine atoms, which in these molecules are
electronically similar in structure to neon atoms.
(d) Ammonia. Ammonia has an anomalously large anni-
hilationrate(Z /Z(cid:59)100) (cid:64)8(cid:35).Ithasalinewidthcomparable
eff
to that of the alkanes. Ammonia has a considerable dipole
moment, but we do not know, at present, how this would
affect the linewidth. However, for more complicated mol-
ecules such as partially fluorinated hydrocarbons, we have
someindicationthatapermanentdipolemomentcanhavean
effect on positron annihilation, as discussed in Sec. IVG.
C.Alkanes
The linewidths for the alkanes are listed in Table IV.
Methanehasthenarrowestlinewidth,2.09keV,andtheline-
width increases to a value around 2.3 keV for large alkanes.
While cyclohexane has a value of Z about an order of
eff
magnitude smaller than hexane, the linewidth of the (cid:103)-ray
spectrum is only slightly larger than that of hexane. Consid-
ering saturated hydrocarbons with five carbon atoms, there
arethreedifferentisomericconfigurations,anddataforthese
FIG.7. (cid:103)-rayspectrumfrompositronannihilationonmolecular molecules are shown in Table IV. While their (cid:103)-ray spectra
hydrogen: observed spectrum ((cid:115)), theoretical calculation of Ref. are identical to within the experimental error, the values of
(cid:64)46(cid:35)(cid:126)—(cid:33),andtheoreticalcalculationofRef.(cid:64)47(cid:35)((cid:149)(cid:149)(cid:149)). annihilationrates,Zeff, differbyapproximatelyafactorof2.
3594 KOJIIWATA,R.G.GREAVES,ANDC.M.SURKO 55
TABLE IV. The (cid:103)-ray linewidths for hydrocarbons (cid:126)using
Gaussianfits(cid:33).(cid:126)SeeRef.(cid:64)7(cid:35)forthesourcesofZ values.(cid:33)
eff
(cid:68)E
Molecule Formula (cid:126)keV(cid:33) Z
eff
Alkanes
Methane CH 2.09 142
4
Ethane C H 2.18 1780a
2 6
Propane C H 2.21 3500
3 8
Butane C H 2.28 11300
4 10
Pentane C H 2.24 40200a
5 12
Hexane C H 2.25 120000
6 14
Nonane C H 2.32 643000
9 20
Dodecane C H 2.29 1780000
12 26
Cyclohexane C H 2.31 20000
6 12
5-carbonalkanes FIG.9. TheGaussianlinewidth(cid:68)E plottedagainstthefraction
Pentane CH3(cid:126)CH2)3CH3 2.24 40200a of valence electrons in C-C bonds for alkane molecules, assuming
2-Methylbutane CH3C(cid:126)CH3)H2C2H5 2.23 50500a twoelectronseachintheC-CandC-Hbonds.
2,2-Dimethylpropane C(cid:126)CH ) 2.23 21400a
3 4 estimate the predicted linewidths of the C-H bond and the
C-C bond to be 2.06 and 2.42 keV, respectively. The pre-
2-carbonmoleculeswithdifferentsaturationlevel
dicted linewidth for C-H bond electrons agrees reasonably
Ethane C H 2.18 1780a
2 6 well with our experimentally measured value of 2.09 keV.
Ethylene C2H4 2.10 1200 However, the linewidth extrapolated for the C-C bond elec-
Acetylene C2H2 2.08 3160a trons is in greater disagreement. These linewidths were cal-
culatedusingthe‘‘static’’approximationinwhichtheeffect
Aromatichydrocarbons of the positron was not included. As can be seen in the case
Benzene C H 2.23 15000 for noble gases, wave functions without including the effect
6 6
Naphthalene C H 2.29 494000 ofthepositroncangivethequalitativeestimates,butnotthe
10 8
quantitative comparisons. Therefore, it is difficult to distin-
Anthracene C H 2.45 4330000
14 10
guish whether this discrepancy in the linewidth associated
Toluene C H CH 2.28 190000
6 5 3 with the C-C bond is caused by the inadequacy in the ap-
aThisstudy. proximationusedinthecalculationsorbythevalidityofthe
assumption that positrons annihilate equally with any va-
lenceelectronandtheassumptionthateachbondhasachar-
In general, we have not been able to detect any systematic
acteristic linewidth.
relationship between Z and the linewidth for the hydrocar-
eff Tang etal. measured the linewidths of benzene, toluene,
bons studied or for any other molecules.
hexane, and dodecane to be 2.16, 2.15, 2.29, and 2.19 keV,
In earlier work based on measurements of linewidths for
respectively.Ourcurrentmeasurementsgivethelinewidthof
four hydrocarbons, Tang etal. concluded that it was likely
these molecules to be 2.23, 2.28, 2.25, and 2.29. The uncer-
thatthepositronsinteractprimarilywithC-Hbondelectrons
tainty of their measurements was 0.05 keV or larger so that
in these molecules (cid:64)16(cid:35). In order to test the possibility of
the variation in the linewidths they measured were within
positronsannihilatingwithC-Cbondelectronsusingourim- their uncertainty. In addition, the numbers of valence elec-
proved data, we plot in Fig. 9 the linewidths (cid:68)E as a func- tronsinC-Cbondsarerelativelysmallcomparedtothenum-
tionofthefractionofvalenceelectronsinC-Cbondsforthe bersofvalenceelectronsinC-Hbonds,whichledTangetal.
alkanes including cyclohexane. The fact that (cid:68)E increases to conclude that all hydrocarbons have the same linewidth.
approximately linearly with the number of valence electrons Giventhemoreprecisemeasurementspresentedhere,itnow
in C-C bonds suggests that positrons are also annihilating appearsthatannihilationinthehydrocarbonsisequallyprob-
with C-C bond electrons. In principle, annihilation on C-H ablewithanyofthevalenceelectronsincludingthoseinC-C
bond electrons can be separated from annihilation on C-C bonds.
bond electrons assuming that each bond has its own charac- This is in agreement with positron annihilation momen-
teristic linewidth. Then the linear combination of these line- tum distributions for liquid hexane and decane measured by
widths weighted by the number of bond electrons should using ACAR techniques (cid:64)49(cid:35). Calculated momentum distri-
yieldtheobservedlinewidths.Fromalinearregressionofthe butionsforC-HandC-Cbondelectronswerecomparedwith
datainFig.9,weestimatethelinewidthsassociatedwiththe the observed ACAR spectra, and it was concluded that pos-
C-H bond and C-C bond electrons to be 2.09 and 2.76 keV, itrons annihilate with both C-H and C-C bond electrons.
respectively.
D.Alkane,alkene,andalkyne
The momentum distributions for the C-C bond and C-H
bond electrons have been calculated (cid:64)49(cid:35). Using the graphs Alkenes and alkynes are generally more reactive than al-
of the calculated momentum distributions in Ref. (cid:64)49(cid:35), we kanes because the (cid:112)bond is weaker than the (cid:115)bond. The
55 (cid:103)-RAYSPECTRAFROMPOSITRONANNIHILATIONON ... 3595
TABLE V. The (cid:103)-ray linewidths for fully halogenated carbons TABLE VI. The (cid:103)-ray linewidths for partially fluorinated hy-
(cid:126)usingGaussianfits(cid:33).(cid:126)SeeRef.(cid:64)7(cid:35)forthesourcesofZ values.(cid:33) drocarbons(cid:126)usingGaussianfits(cid:33).
eff
Molecule Formula (cid:68)E (cid:126)keV(cid:33) Z Molecule Formula (cid:68)E (cid:126)keV(cid:33)
eff
Carbontetrafluoride CF 3.04 54.4 Methane CH 2.09
4 4
Carbontetrachloride CCl 2.29 9530 Methylfluoride CH F 2.77
4 3
Carbontetrabromide CBr 2.09 39800 Difluoromethane CH F 2.86
4 2 2
Trifluoromethane CHF 2.85
3
Carbontetrafluoride CF 3.04
4
smallest members of the alkane, alkene, and alkyne families
are ethane, ethylene, and acetylene, respectively. The values Ethane C2H6 2.18
of the linewidths for these molecules are listed in Table IV. Fluoroethane C2H5F 2.62
They show that, as the bond saturation level is reduced, the 1,1,1-trifluoroethane CF3CH3 2.95
linewidthsdecrease.Onepossibleexplanationofthistrendis 1,1,2-trifluoroethane CHF2CH2F 2.91
that for the alkenes and alkynes, positrons can annihilate 1,1,1,2-tetrafluoroethane CF3CH2F 3.00
with(cid:112)-bondelectrons,whicharelesstightlyboundandcon- 1,1,2,2-tetrafluoroethane CHF2CHF2 2.97
sequentlyhaveasmallermomentumdistributionthanthatof Hexafluoroethane C2F6 3.04
the(cid:115)-bondelectrons.Iftheassumptionsarecorrectthateach
chemical bond has its own characteristic linewidth and that Propane C3H8 2.21
thelinearcombinationoftheselinewidthsweightedwiththe 2,2-difluoropropane CH3CF2CH3 2.78
numberofbondelectronsyieldstheobservedlinewidths,the 1,1,1-trifluoropropane CF C H 2.86
3 2 5
linewidthoftheC-C(cid:112)bondcanbeestimatedtobe1.48and Perfluoropropane C F 3.05
3 8
1.73 keV for ethylene and acetylene, respectively, using the
C-H bond and C-C (cid:115)-bond values of 2.09 and 2.76 keV. Hexane C H 2.25
6 14
1-fluorohexane CH FC H 2.46
2 5 11
E.Aromatics Perfluorohexane C F 3.09
6 14
Aromatic compounds have very different electronic and
Benzene C H 2.23
geometrical structures compared to alkanes. The values of 6 6
Fluorobenzene C H F 2.43
the linewidths from our measurements are listed in Table IV 6 5
for the smaller aromatic molecules benzene, naphthalene, 1,2-difluorobenzene C6H4F2 2.66
and anthracene and for some of the substituted benzenes. 1,3-difluorobenzene C6H4F2 2.52
Theexistenceofpolycyclicaromatichydrocarbons(cid:126)PAH(cid:33) 1,4-difluorobenzene C6H4F2 2.53
in the interstellar media has been deduced from infrared 1,2,4-trifluorobenzene C6H3F3 2.71
measurements (cid:64)50,51(cid:35). We have found that the PAH’s have 1,2,4,5-tetrafluorobenzene C H F 2.77
6 2 4
very large annihilation cross sections and speculated that Pentafluorobenzene C HF 2.89
6 5
thesemoleculesmaycontributesignificantlytoastrophysical Hexafluorobenzene C F 2.95
6 6
positron annihilation (cid:64)52(cid:35). This facet of the research is dis-
cussed in Sec. IVJ. Measurements of larger PAH’s, such as
pyrene, were attempted, but were not successful due to the The differences in the linewidths for hydrocarbons and
low-vapor pressure of these substances. We are planning to fluorocarbons are significant; hydrocarbons have large anni-
installahigh-temperaturecellinthevacuumchamber,which hilation rates and relatively narrow linewidths, while per-
shouldmakemeasurementsoftheselow-vaporpressuresub- fluorocarbons have low annihilation rates and large line-
stances possible. widths. It was concluded by Tang etal. (cid:64)16(cid:35) that positrons
annihilate predominantly with C-H bonds in hydrocarbons
F.Fullyhalogenatedcarbons andwithfluorineatomsinperfluorinatedmolecules.Inorder
tofurtherexaminethelocalizationofpositronannihilationin
The linewidths for fully halogenated carbons are listed in
amolecule,exploitingtheeasilydistinguishableannihilation
Table V where we have ordered these molecules by the size
linewidths for fluorine atoms and the C-H bonds, we have
of the halogen. The linewidths decrease from CF , to
4 studied a series of partially fluorinated hydrocarbons. These
CCl ,toCBr .Thistrendisverysimilartothatofthenoble
4 4 are discussed in the next section.
gas atoms; neon, argon, and krypton (cid:126)Table I(cid:33). In addition,
the linewidths are almost identical to those of analogous
G.Partiallyfluorinatedhydrocarbons
noble gas atoms, particularly for the larger halogens, as one
would expect if the valence electrons of the carbon atoms Theexperimentallymeasured(cid:103)-raylinewidthsofaseries
werecompletelytransferredtothehalogenatoms.Inparticu- of partially fluorinated hydrocarbons are summarized in
lar,comparingthehalocarbonsandnoblegasatoms,theline- Table VI, and a typical (cid:103)-ray spectrum is shown in Fig.
widths are 3.04 (cid:126)3.36(cid:33) for CF (cid:126)Ne(cid:33), 2.29 (cid:126)2.30(cid:33) for CCl 10(cid:126)a(cid:33). (cid:126)We have also measured the values of Z for these
4 4 eff
(cid:126)Ar(cid:33), and 2.09 (cid:126)2.09(cid:33) for CBr (cid:126)Kr(cid:33). These data provide evi- molecules and will present and discuss the implication of
4
dence that, in halocarbon molecules, the positron annihilates these measurements in a separate publication (cid:64)53(cid:35).(cid:33) As
with the valence electrons of the halogen atoms. pointed out earlier, the hydrocarbons have significantly nar-