Charge Exchange and Chemical Reactions with Trapped Th$^{3+}$

0.28 MB·English

by  L. R. Churchill

Charge Exchange and Chemical Reactions with Trapped Th3+
∗
L. R. Churchill, M. V. DePalatis, and M. S. Chapman
School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430
(Dated: January 4, 2011)
We have measured the reaction rates of trapped, buffer gas cooled Th3+ and various gases and
have analyzed the reaction products using trapped ion mass spectrometry techniques. Ion trap
lifetimes are usually limited by reactions with background molecules, and thehigh electron affinity
ofmultiplychargedionssuchasTh3+makethemmorepronetoloss. Ourresultsshowthatreactions
ofTh3+ withcarbondioxide,methane,andoxygenalloccurneartheclassical Langevinrate,while
1 reaction rates with argon, hydrogen, and nitrogen are orders of magnitude lower. Reactions of
1 Th3+ with oxygen and methane proceed primarily via charge exchange, while simultaneous charge
0 exchange and chemical reaction occurs between Th3+ and carbon dioxide. Loss rates of Th3+ in
2 heliumareconsistentwithreactionwithimpuritiesinthegas. ReactionratesofTh3+ withnitrogen
n and argon depend on theinternal electronic configuration of the Th3+.
a
J PACSnumbers: 34.70.+e,82.30.Fi

3

I. INTRODUCTION ion trap. The primary modes of Th3+ loss are charge
]
h exchangeand chemical reactionswith backgroundgases.
p Byimprovingthebackgroundvacuumandincreasingthe
- Unlike most atomic nuclei, which have excitation en-
m ergies in the range of keV to MeV, the nucleus of the purity of the buffer gas used for initia3l+cooling, we were
able to extend the trap lifetime of Th to minutes. By
o thorium isotope, 229Th, has an excited state just several
removingthebuffergasimmediatelyaftertheinitialtrap
t eV above the nuclear ground state [1]. The transition
a loading and laser cooling the ions, a lifetime of > 10
. between the nuclear ground state and this unique iso-
s minutes was obtained [8].
meric state lies within the UV optical spectrum, where
c 3+
The limited Th trap lifetime presents a significant
i it can be addressed using coherent light sources. The
s challenge in time-intensive experiments like measuring
coherent control of the electronic states of atoms with
y thehyperfinestatesof229Th3+ andsearchingforthe nu-
h tunable lasers has been a major focal point of modern
clear isomer transition. Furthermore, the short lifetime
p atomic physics. Extending this paradigm to the control
[ of nuclear states of atoms would represent a significant represents a tremendous cost in performing experiments
achievement. The transition between the 229Th nuclear with229Th3+ giventheextraordinarypriceoftheisotope
2
(> $100k/mg).
v states could potentially be used as a frequency reference
8 withafractionaluncertaintyapproaching10−20 [2]. Fur- To better understand the charge exchange and chem-
7 thermore, the transition may be especially sensitive to ical reaction processes and quantify their rates, we con-
5 changes in the value of the fine structure constant, al- ducted a series of experiments to determine the reaction
2 lowing up to 5–6 orders of magnitude enhancement in ratecoefficientsbetweenTh3+ andvariousgases. Asum-
2. measurements of its time variation [3]. However, this maryoftheexperimentalresultscanbefoundinTableI.
1 latter point requires further study [4–7]. Theremainderofthispaperisdevotedtodescribingthese
0 experiments in greater detail.
Inordertodemonstratecoherentcontrolofthenuclear
1 A schematic of the ion trap used in these experiments
state,thoriumatomsmustbeconfinedinsuchawaythat
:
v theycanbecontinuouslyinterrogatedandobserved. Un- is shown in Fig. 1. The trap is outfitted with a chan-
i nel electron multiplier (CEM) for electronic detection of
X likethelowerionizationstates,triplyionizedthoriumhas
trapped ions. When used in combination with the well
aconvenientlevelstructureforfluorescencedetectionand
r
a laser cooling [2]. The low-lying electronic states of Th3+ understood mass selection characteristics of a linear ion
trap, the CEM can be used to determine if a specific
and the optical transitions between them are shown in
Fig. 1. Using the more common thorium isotope, 232Th, species of ion is present in the trap.
our group has demonstrated the creation, trapping, and The ion trap is loaded with Th3+ via laser ablation
laser cooling of Th3+ [8]. of a thorium metal target with the third harmonic of
Inourearliestobservationsof232Th3+,the ionswould a pulsed Nd:YAG laser (λ = 355 nm). The target is lo-
catednearthetrapaxisandorientedperpendiculartoit.
remain in the trap for only a few seconds. In general,
The voltage on the dc endcap nearest the ablation tar-
elasticcollisionswithbackgroundmoleculesarenotlikely
get is gated with the ablation pulse, dropping to ground
to result in ejection of ions due to the large depth of an
when the pulse is fired, and increasing to 100 V for ion
confinement.
Helium buffer gas is present in the system throughout
∗Permanent address: Applied Physics Laboratory, Johns Hopkins the loading process. The ablated Th3+ ions are initially
University,Laurel,Maryland20723 moving at speeds of 10 km/s as they approach the ion
2
Reactant k k (ε) k ×10−9
ε L
NHee <<34..41××1100−−1155 <<61..02××1100−−1165 ((00..138)) 11..60 a.u.] 106
Ar(∗) 1.3×10−14 1.7×10−14 (1.3) 1.5 ce [
N(2∗) 1.6×10−13 1.6×10−13 (1.0) 1.8 scen
H2 4.6×10−13 2.1×10−13 (0.46) 4.4 ore
COH24 23..67××1100−−99 33..67××1100−−99 ((11..40)) 21..87 otal flu
CO 2.8×10−9 4.0×10−9 (1.4) 1.8 T
2
5
10
0 50 100 150 200
TABLE I: Charge exchange and chemical reaction rate coef- Time [s]
ficientsforTh3+. Reactionratecoefficientsaregiveninunits
of cm3s−1. Here, kL is the calculated Langevin rate, and k FIG. 2: (Color online) Accumulated fluorescence signal for
is the experimental reaction rate coefficient. The corrected determination of Th3+ loss rate. This data was taken with
reaction ratecoefficient iskε =ε·k,whereεistheion gauge 5×10−5 torrofheliuminthevacuumchamber. Thelossrate
correction factor for the gas in question. Experimental reac- was determined to beτ−1=0.0100(2) s−1.
tion rate coefficients for helium and neon are upper bounds.
The accuracy of the coefficients given here is limited by the
accuracyoftheiongaugeusedtomeasurethepressureofthe Theheliumpressureiscommonlyheldbetween10−5and
reactants. (*) The reaction rate for Ar and N depends on
the electronic configuration of Th3+. The expe2rimental rate 10−4 torr in these experiments. Generally, the number
refers to reaction from the5F ground state. of ions loaded increases with higher buffer gas pressure,
5/2
while the final equilibrium temperature of the trapped
ions decreases.
(a)
II. HELIUM
The loss of Th3+ from the ion trap in 5 10−5 torr
(b) of helium buffer gas is shown in Fig. 2. Her×e, the Th3+
decayrateismeasuredbyobservingthereductioninflu-
orescence over a series of images. This method can be
used only when the lifetime of the ions is sufficient to
allowenoughfluorescencemeasurementsforaproperex-
ponential fit.
3+
When the Th trap lifetime is too short for observa-
tion of fluorescence, mass selective electronic detection
with the CEM is employed to measure the decay rate.
Weloadionsintothetrapviaablationandwaitforsome
amount of time. The rf and dc voltages applied to the
FIG. 1: (Color online) (a) Th3+ energy levels and optical 3+
trapare then tuned suchthat only Th remainsstable.
transitions. (b) Schematic drawing of ion trap system. A
The contents of the trap are then delivered to the CEM
target outsideof theion trap (left) is ablated usingthethird
by lowering the voltage of the trap endcap nearest it.
harmonic of a pulsed Nd:YAG laser (diagonal line). Lasers
Thetimeintervalbeforethemassselectionisvaried,and
used for optical excitation of the trapped ions are aligned
along thetrap axis(horizontal line). A CEM located outside the data is accumulated over several iterations for each
of thetrap (right) is used for electronic detection. TheCEM time interval. Many iterations are required to suppress
is mounted off-axis to allow clear optical access. the variation due to fluctuations in the number of ions
3+
loaded. This method is typically used when the Th
lifetime is a few seconds or less.
trap. As the hot Th3+ ions collide with room tempera- The decay rate through any given reaction channel is
ture helium atoms, they lose some of their thermal en- proportionaltothedensityofthereactantinthesystem.
ergy. This process serves two critical purposes. First, This relationcan be written as τ−1 =kn, where n is the
it reduces the energy of some ablated Th3+ ions as they density ofthe reactant,andk= σv is the reactionrate
h i
traversethelengthoftheiontrap,therebyincreasingthe coefficient for the given channel. Here, σ is the reaction
likelihood they will be trapped. Secondly, it damps the cross-section and v is the relative velocity between the
motion of trapped Th3+ ions, allowing them to come to reactants. For a given reaction, the rate coefficient can
3+
thermal equilibrium at some fraction of the trap depth. be determined by measuring the Th decay rate as a
3
spiralingorbitoftheionandmoleculeabouttheirshared
16
centerofmass. Ifareactionbetweentheionandmolecule
14
1] isexothermic,itisassumedtooccurwithunitprobability
3- s 12 when a spiraling orbit occurs. The so-called Langevin
-10 10 cross-sectionfor reaction is then [10]
e [
at 8 Ze α
R
ss 6 σL =2π v µ, (1)
o r
L 4
wherev isthe relativevelocitybetweenthe particlesand
2
µ is the reduced mass. The corresponding reaction rate
0 2 4 6 8 10
coefficient is
-5
Helium Pressure [10 torr]
k =2πZe√αµ (2)
L
FIG. 3: (Color online) Th3+ loss rate as a function of BIP
The preceding equations are given in Gaussian (cgs)
helium buffergas pressure. Theslopeof thelinearfitimplies
a reaction rate coefficient of k = 3.4×10−15cm3s−1 (k = units, which is how they are most commonly found in
ǫ
6.0×10−16cm3s−1 withaniongaugecorrection factorofǫ= the literature.
0.18), while the intercept implies a background loss rate of TheLangevinmodelisnotacomprehensivetheoretical
τ−1 = 3.3×10−3s−1. It is likely that the Th3+ reacts with formulation, and therefore, it only suffices to provide an
an impurity in thehelium ratherthan with thehelium itself; estimate of the reactionrate betweena givenion andre-
therefore,thevaluefork setsanupperboundonthereaction actantmolecule. The model does notapply to molecules
rate coefficient for helium. that possess a permanent dipole moment. In that case,
the leading term in the interaction potential scales as
r−2 rather than r−4 [11]. Furthermore, several experi-
functionofthepressureofthe reactivegas. The reaction ments [12–14] have shown a departure from the inverse
rate coefficient is extracted from the slope of a linear fit velocitydependence oftheclassicalcross-sectioninsome
of this data. The intercept of the linear fit gives the loss reactions. Ultimately,theprobabilityofareactionoccur-
rateduetobackgroundgasesinthevacuum. Forhelium, ring in the event of a classical interaction is dependent
the data and correspondinglinear fit are shownin Fig. 3 on the combined energy state of the reactants,the avail-
Helium is a noble gas, and a charge exchange reaction able energy states in the final products, andthe possible
3+
betweenitandTh isendothermicby4.6eV.Thissug- reaction pathways between them [15]. Several experi-
gests that such a reaction is strongly inhibited for low ments [16–20], including our own, have found that some
energy reactants. Therefore, the loss shown in Fig. 2 is reaction rates can differ significantly depending on the
mostlikely due to animpurity in the helium ratherthan internal energy state of a reactant.
to the helium itself. Nevertheless, the Langevin rate is useful in setting an
Theheliumgasweuseinourexperimentcomesfroma upper bound onthe reactionrate between ions and non-
cylinderwithabuilt-inpurifier(BIP).TheBIPheliumis polar molecules [21]. Many ion-molecule reactions do
supplied by Airgas, Inc. According to the specifications, occur at or near the Langevin rate [17, 22–26]. The
the BIP helium gas has an impurity level <1 ppm. The Langevinratesforthereactionsweinvestigatedaregiven
data of Fig. 3 implies a reaction rate coefficient between in Table I with the experimental results.
theBIPheliumandTh3+ ontheorderof10−16 to10−15
cm3s−1. Thus, the reaction between Th3+ and the con-
taminant within the BIP helium responsible for its loss III. GASES WITH LOW REACTION RATES
proceeds with a reaction rate coefficient on the order of
10−10 to 10−9 cm3s−1. Loss rates of Th3+ in the presence of neon and ar-
Areactionratecoefficientof10−9 cm3s−1 isconsistent gon are shown in Fig. 4, while loss rates in the presence
with the value predicted by a classical collision model of nitrogen and hydrogen are shown in Fig. 5. For all
introduced by Langevin [9] and refined by Gioumousis of these decay measurements, a partial pressure of 10−5
and Stevenson [10]. This model is helpful in estimating torr of helium was added to the system to cool the ions
the reaction cross-sections between ions and molecules. for fluorescence imaging. As can be seen from Fig. 3,
We assume the ion is a point particle with charge Ze, this quantity of helium does not add significantly to the
and that the molecule is spherically symmetric with po- backgroundlossrateofTh3+. The reactionswithargon,
larizability α. The primary interaction between the ion nitrogen,andhydrogenallproceedrelativelyslowly,with
and molecule is due to the electric field of the ion and reaction rate coefficient orders of magnitude below the
the field-induced diploe moment of the molecule. The corresponding Langevin rates. Since our interest was in
interaction potential scales as r−4. gases that react with Th3+ near the Langevin rate, we
Below thresholdvalues of the relative velocityand the did not attempt to identify the products of these reac-
impact parameter, the interaction potential leads to a tions.
4
to rf micromotion could conceivably contribute to over-
7 come anotherwise endothermic energygap[27–29], such
1] 6.5 as with helium and neon. However, such micromotion-
3- s 6 enhanced reactions would require micromotion ampli-
-0 5.5 tudes much larger than is likely. While some contri-
1
e [ 5 bution of the micromotion to the loss rates is possible
Rat 4.5 forendothermicreactions,ourresultsareconsistentwith
ss 4 quoted impurities [30].
Lo 3.5 Neon Argonis also a noble gas,but a charge exchange reac-
3 Argon
3+
tion between it and Th is exothermic by 4.2 eV. The
2.5
3+
0 1 2 3 4 5 Th reactionrates with argonand nitrogen were found
3+
-6 to depend on the electronic configuration of the Th .
Test Gas Partial Pressure [10 torr]
The data in Fig. 4 represent loss rates from the 5F
5/2
3+
ground state of Th . The 5F state was isolated for
5/2
FIG. 4: (Color online) Th3+ loss rate in the presence of study by shuttering the 690 nm laser between fluores-
neon and argon. A partial pressure of 10−5torr of he- cencemeasurements. ThisallowsTh3+intheΛ-manifold
lium was added to the test gas to cool the ions for fluores-
(see Fig. 1) to be pumped back into the ground state by
cence observation. The reaction rate coefficient for neon is
k = 4.1×10−15cm3s−1 (k = 1.2×10−15cm3s−1 with an the984nmlaser. Bykeepingthe timebetweenmeasure-
ǫ ment sufficiently long, the systematic effect introduced
ion gauge correction factor of ǫ = 0.30). The decay rates
shown for argon represent Th3+ loss from the 5F ground during measurement was held below 10%.
5/2
state. Thereaction ratecoefficient isk=1.3×10−14cm3s−1
(k =1.7×10−14cm3s−1 with an ion gauge correction factor
ǫ
of ǫ=1.3). IV. Th3+ EXCITATION EFFECTS ON
REACTION RATES
100 State dependent effects on electron capture in colli-
Hydrogen sions between neutral atoms and multiply charged ions
1] 80 Nitrogen have been studied extensively (see, e.g., [31–34]). The
3- s effectofTh3+ opticalexcitationonits reactionratewith
-0 60
1 argon can be seen clearly in Fig. 6. In one set of mea-
ate [ 40 surements,the 690nm laserwas shuttered between fluo-
R rescencemeasurements. This is the samedata setshown
s
os 20 inFig.4. Inthe othertwosetsofmeasurements,the 690
L
nm laser was left on continuously. Increasing the power
0 ofthe984nmlaserincreasesthepopulationofthe6D
5/2
0 1 2 3 4 5 excited state, and hence the reaction rate, until the ex-
Partial Pressure [10-6 torr] citedstateis saturated. The correspondingsaturationof
theargonandnitrogenreactionratesareshowninFig.7.
Ifthe5F –6D manifoldisapproximatedasatwo-
FIG. 5: (Color online) Th3+ loss rate in the presence of hy- 7/2 5/2
level system, the excited state population obeys the re-
drogen and nitrogen. A partial pressure of 10−5torr of he-
lation
lium was added to the test gas to cool the ions for fluores-
cence observation. The reaction rate coefficient for hydrogen I/Isat,eff
isk=4.6×10−13cm3s−1(k =2.1×10−13cm3s−1withanion σ . (3)
ǫ ∝ 1+I/Isat,eff
gauge correction factor of ǫ = 0.46). The decay rates shown
fornitrogenrepresentTh3+ lossfromthe5F5/2 groundstate. whereIsat,eff istheeffectivesaturationintensity. Thera-
The reaction rate coefficient is k=1.6×10−13cm3s−1. tiooftheeffectivesaturationintensitytothenaturalsat-
uration intensity, Isat = 2π2hcΓ/3λ3, is approximately
equal to the ratio of the Doppler-broadened linewidth,
Like helium, neon is a noble gas with a high ioniza- Γ , to the natural linewidth, Γ. Therefore,
D
tion energy that inhibits charge exchange reactions with
3+ 2π2hc
eTVh.A.sScaunchbreesaecetnioinnsFairge.i4n,tThhis3+calsoessenradtoetshienrmneiconbyw1er.6e Isat,eff ≈ 3λ3 ΓD. (4)
never significantly larger than what could be attributed By fitting the data in Fig. 7 to a function in the form
tothe presenceofthe heliumbuffergas. Inaddition,the of Eq. (3), we find an effective saturation intensity of
rceoancstisiotnenrtawteithcoreeffiacctieionntowcecudrertienrgmbientewdefernomthethTehd3+ataanids sIpsaot,nedffs∼to40amDWop/pclmer2-b.rAoacdcoenrdeidnglintoewEidqt.h(4o)f, Γthis cor3r0e0-
D
0.5 ppm impurity in the gas. MHz, which is consistent with an independent me∼asure-
3+
It is worthnoting that the kinetic energy of Th due ment of the transition linewidth.
5
30
40 P = 20 µW, P = 0 mW
-3-110 s] 30 PP999888444 == 2400 µµWW,, PP666999000 == 11..2255 mmWW 3-1 s] 2205
e [ 20 -10
Rat e [ 15
Loss 10 ss Rat 10
o
L
0 5
0 1 2 3 4 5
-6 0
Argon Partial Pressure [10 torr]
0 50 100 150 200 250 300 350 400
FIG. 6: (Color online) Effect of atomic excitation on Th3+
90
loss rate in the presence of argon. The data that was taken
without 690 nm light represents loss from the Th3+ 5F5/2 -1s] 75
ground state. Increasing the power of the 984 nm laser in- -30 60
creases the reaction rate by increasing the number of ions in 1
the6D5/2 excited state, from which reaction is more likely. ate [ 45
R
s 30
s
o P = 1.25 mW
The reaction rate from the 5F7/2 electronic state was L 15 P669900 = 300 µW
found to be equal to within experimental error to the 0
0 50 100 150 200 250 300 350 400
reactionratefromthe 5F stateforbothargonandni-
trogen. The5F7/2 statew5a/s2isolatedformeasurementby P984 [µW]
shutteringthe984nmlaserbetweenmeasurements,while
continuously applying the 690 nm laser. In this way, the
FIG. 7: (Color online) Saturation of Th3+ reaction rate in
long-lived 5F7/2 state was continuosly repopulated. To the presence of (top) 3×10−6 torr argon and (bottom) 3×
further demonstrate that optical excitation to the 6D5/2 10−6 torrnitrogen. Ineach case, 1×10−5 torrhelium is also
state wasresponsible forthe increasedreactionrates,we present.
verified that detuning the lasers far from resonance had
the same effect as shuttering them.
Byopticallyexcitingwiththe1087nmlaser,wefound selective CEM detection. For these measurements, 2
that reactions with nitrogen were also faster from the 10−8 torr of the test gas and 10−4 torr of helium buffe×r
6D state than from the 5F state. No quantitative gas was introduced into the system. The ion trap was
3/2 5/2
comparisons were made between the reaction rates from loadedanumberoftimes. Eachtimethetrapwasloaded,
the 6D state and the 6D state. The reaction rate we waited a short period ( 1 s) for reactions to occur,
3/2 5/2 ∼
betweenTh3+ andargonwith1087nmopticalexcitation performedamassselection,andcheckedforthepresence
was not measured. of ions. Since the rf power supply for our trap could not
provide high enough voltage to perform rigorous mass
selection on singly ionized molecules, we were able to
identify only doubly ionized molecules.
V. GASES WITH HIGH REACTION RATES
When either carbon dioxide or oxygen was present in
the system, Th2+ and ThO2+ were found in the trap.
Loss rates of Th3+ in the presence of carbon dioxide, Althoughthoriumdioxideischemicallystable,noThO2+
2
methane, and oxygen are shown in Fig. 8. All of these was detected with either gas. In a previous work with
gases react relatively quickly with Th3+ at rates com- singly-ionized thorium, Johnsen et al. [22] found that
parable to the Langevin rate. Even at partial pressures oxidation occurs via the sequential reactions
below10−8torr,reactionsoccurringinthespacebetween
the ablation target and the trapping region significantly Th++O2 ThO++O (5)
reducedthenumberofTh3+ ionsloaded. Toensuresuffi- + → +
ThO +O2 ThO2 +O (6)
cientloadingandanadequateSNRforfluorescencemea- →
surement, 10−4 torr of helium was added to the system Theyfoundthatthefirstreactionproceededquickly,with
foreachmeasurement. Thelossratesmeasuredherewere a rate coefficient of 6 10−10 cm3s−1, while the rate of
×
in all cases significantly higher than the loss rate with thesecondreactionwasmorethananorderofmagnitude
only 10−4 torr of helium present. lower, with a coefficient of 2 10−11 cm3s−1.
The products of reaction between Th3+ and carbon Reactions between Th3+ a×nd methane, CH4, resulted
dioxide,methane, and oxygenwereidentified using mass in Th2+ and ThCH2+. Special care was taken to prop-
2
6
5 100
208 ThCH22+ (a)
-1oss Rate [s] 234 (a) U [V]dc 220004 TThhOO222++ 468000 M Counts [a.u.]
L 1 E
20 C
0
196 0
0 0.5 1 1.5 2 2.5 3 3.5 4 1200 1215 1230 1245 1260
CO Partial Pressure [10-8 torr] V [V]
2 rf
4 100
208 ThCH22+ (b)
-1oss Rate [s] 123 (b) U [V]dc 220004 TThhOO222++, ThCH42+ 468000 M Counts [a.u.]
L E
20 C
0
196 0
0 0.5 1 1.5 2 2.5 3 3.5 4 1200 1215 1230 1245 1260
CH Partial Pressure [10-8 torr] V [V]
4 rf
6 100
5 208 ThCH22+ (c)
-1oss Rate [s] 234 (c) U [V]dc 220004 TThhOO222++ 468000 M Counts [a.u.]
L E
1 20 C
0
196 0
0 0.5 1 1.5 2 2.5 3 3.5 4 1200 1215 1230 1245 1260
O Partial Pressure [10-8 torr] V [V]
2 rf
FIG. 8: (Color online) Th3+ loss rate in the presence of (a) FIG. 9: (Color online) Doubly-ionized thorium molecules.
carbon dioxide, (b) methane, and (c) oxygen. Measurements Ions are identified by comparing the voltage space in which
weremadewith10−4torrofheliumbuffergas. Thedatapoint they are stable to the theoretical stability region. (a) The
atzeropressureisthelossratewhenonlyheliumat10−4torr reaction between Th3+ andcarbon dioxideproducesThO2+.
is present. Reaction rate coefficients for each case are listed (b)ThereactionbetweenTh3+ andmethaneproducesTh2+,
in Table I. which in turn reacts with methane to produce ThCH2+. (c)
2
ThereactionbetweenTh3+andoxygenproducesTh2+,which
in turn reacts with oxygen to produceThO2+.
erly identify ThCH2+. Andrews and Cho [26] were able
2
to create ThCH4 by ablating thorium in a methane en-
vironment. However, Marc¸alo et al. [35] found that the
were stable, we were able to achieve the resolution nec-
onlyreactionchannelbetweensingly-ionizedthoriumand
essary to correctly determine the product (see Fig. 9).
methane is
Once the reaction products were identified, we were
Th++CH4 ThCH+2 +H2. (7) abletomeasurehowTh3+ evolvedovertime inthe pres-
→
ence of each of these gases. The results are shown in
Only 1 amu/e separates the mass-to-charge ratio of Fig. 10 for carbon dioxide, methane, and oxygen. Each
ThCH2+ from ThCH2+ and ThO2+. By carefully map- data point in these graphs represents the average and
2 4
ping the voltage space in which ThO2+ and ThCH2+ standard deviation of six measurements. For each mea-
2
7
However, by ramping the rf to its maximum voltage, we
1
couldisolateionswithmass-to-chargeratiosgreaterthan
0.8 156amu/e. Theonlyionsinthetrapabovethatmass-to-
n
o charge ratio would be singly-ionized thorium molecules.
ulati 0.6 Th23++ These are represented as ThX+ in Fig. 10.
p Th
o (a) Direct comparison of the CEM signals of the various
P ThO2+
ative 0.4 ThX+ iforonms iisoonftloimiointe.dIovnasluweisthinhceigthheergchaianrgoefsataCteEsMexcpaenrivenarcye
el 0.2
R a greater acceleration in the field created by the high
negative bias at the entrance of the dynode. These ions
0
strikethedynodesurfacewithgreaterenergy,resultingin
0 20 40 60 80 100 120 140 160 180 ahigherinitialemissionofelectrons. TheCEMgainalso
Time [s] depends on mass, as lighter ions tend to cause a larger
response than more massive ones. The chemical nature
1
of the ion can also play a role.
0.8 We verified several times that the Th3+ CEM signal
n
o was linear with measurements of total fluorescence over
ati Th3+
ul 0.6 2+ the dynamic range of both instruments. However, the
p Th
Po (b) ThCH2+ specific slope of the relationship at any given time was
ative 0.4 ThX+2 hsyigsthelmy.senCsuitritvaeintsowtheerebaecmkpglrooyuenddtloigshttalbeivliezleaaronudnmditnhie-
Rel 0.2 mize background light; however, small shifts in the cur-
tains incurred while the system was prepared for data
0
collection still had a noticeable effect.
0 20 40 60 80 100 120 140 160 180 In order to compare the relative populations of the
Time [s] various ions in the trap over time, we adopted a simple
method for scaling the CEM data. The method is based
1
on two assumptions. We assume first that ions are not
lost from the trap over the period of investigation. This
0.8
n
o is reasonablegiventhatthe trapdepth is onthe orderof
ulati 0.6 Th23++ 100eVfortheionsinquestion,whiletheexothermicityof
op (c) Th thereactionsisonlyontheorderofafeweV.Wefurther
P ThO2+
ative 0.4 ThX+ aidsesnutmifieedthiantotuhreeoanrllyieriosnesarpcrhesfeonrtthinetrheaecttrioanpparroedtuhcotsse.
el 0.2 Since our method of searching for reaction products fo-
R
cusedonlyonproductsresultingfromfastreactions,this
0 assumption could lead to error when considering longer
0 20 40 60 80 100 120 140 160 180 time scales. However,here we focus our attentiononthe
Time [s] rapid chemical kinetics that occur on short time scales.
To scale the data we consider the sum
FIG.10: (Coloronline)232Th3+ inthepresenceof(a)carbon
dioxide, (b) methane, and (c) oxygen. The data is scaled N(t)= α n (t), (8)
i i
according to the values given in Table II. The data sets are
i
fit to thesystem of equations given in Eqs. (15)–(18). X
where N is the total trap population, and n and α are
i i
the fluorescence normalized CEM signal and the CEM
surement, the trap was loaded, and Th3+ was mass se- scaling factor for ion i, respectively. The sum is over all
lected. A fluorescence measurement would be taken im- ion species present in the trap. The scaling factors are
mediately after the mass selection. After the specified determined via a least-squares algorithm that attempts
waittime, the ionofinterestwouldbe massselectedand to make N(t) = 1 for all t. The data shown in Fig. 10
thecontentsofthetrapdeliveredtotheCEM.Theresult- was scaled using this method. The scaling factors are
ing CEM signal was normalized according to the initial given in Table II.
fluorescence measurement. By normalizing the signal in It is clear from Fig. 10 that the dynamics responsi-
this way, the impact of loading fluctuations on the data ble for the appearance of ThO2+ in the presence of car-
was minimized. bon dioxide are different from the dynamics that cause
As was mentioned previously, the rf power supply for ThO2+ toariseinoxygenandthatbringaboutThCH2+
2
our trap could not provide high enough voltage to per- inthepresenceofmethane. Basedontheidentifiedprod-
formrigorousmassselectiononsinglyionizedmolecules. ucts,thepossiblereactionsbetweenTh3+andthesegases
8
Species Carbon Dioxide Methane Oxygen Branching Ratio Carbon Dioxide Methane Oxygen
Th3+ 9.0 4.6 3.6 [α,β,γ] 0.36 0.89 1.0
1
Th2+ 23.4 26.2 14.7 [α,β,γ] 0.78 0.0 0.09
2
ThO2+ 36.8 – 12.7 [α,β,γ] 0.10 0.0 0.08
3
ThCH2+ – 53.9 – [α,β,γ] 0.44 0.94 0.83
2 4
ThX+ 20.5 30.0 39.3
TABLE III:Branching ratios for thorium reactions.
TABLE II:CEM scaling factors for Th3+ reaction data.
Gas Minimum Purity CO2 O2 Hydrocarbons
can be written generally as Argon 99.9997% <0.5 <0.2 <0.2
Hydrogen 99.999% <0.5 <1 <0.5
Th3++CO2 ( −αα→21 TThhO2+2+++COC+2O+ (9) Neon 99.999% <0.5 <0.5 <0.5
−→
TABLE IV: Purity specifications for research grade argon,
Th3++CH4 ( −ββ→21 TThh2C+H+2+C+H+4H+ (10) ureltarcathioinghexppuerirtiymehnytdsr.ogVena,luaensdlisrteesdearacrhe ginradpepmn.eonAlulsegdaseins
−→ 2 2 werepurchasedfromAirgas,Inc. andspecificationsarelisted
Th3++O2 ( −γγ→21 TThhO2+2+++O+2O+ (11) in the Airgas 2009 Product Catalog [30].
−→
enforced on subsequent fits. The branching ratios that
Here,α , β ,andγ representtherelativeprobabilitiesof
i i i
were determined in this fashion are given in Table III.
the reactionchannels. Thepossiblesubsequentreactions
2+ The values given in Table III can only be considered
with Th can be summarized as
roughestimatesoftheactualbranchingratiosbecauseof
2+ α3 ThX++ theuncertaintiesinherentintheCEMscalingprocedure.
Th +CO2 ( −α→4 ThO2++·C··O (12) They are given only to illustrate3+the general reaction
−→ dynamics. While reactions of Th with methane and
2+ β3 ThX++ oxygen proceed predominantly via charge exchange, si-
Th +CH4 ( −−β→→4 ThCH22++···H2 (13) mdoumltiannaenotubsrcahnacrhgeinexrcehacatnigoensanbdetcwheeemnicTahl3r+eaacntidoncaisrbtohne
2+ γ3 ThX++ dioxide. Sincemethanehasthehighestionizationenergy
Th +O2 ( −γ→4 ThO2++·O·· (14) and lowest polarizability among hydrocarbons [36], the
−→ charge exchange reaction rates between other hydrocar-
3+
No decay in the quantity of ThO2+ or ThCH2+ is seen bons and Th are likely as high as those of methane.
2 Itisworthconsideringwhetherimpuritiesofthesefast
overthe time scalesinvestigated,so these canbe treated 3+
reacting gases could explain the Th losses in the pres-
as stable final products. Thus, from the above reaction
equations,wecanwriteasystemofdifferentialequations ence of argon, nitrogen, and hydr3o+gen. CO2, O2, and
describingthechemicalkineticsineachgas. Forexample, CH4 each react strongly with Th at rates very close
to the calculated Langevin rates. In order for these
in carbon dioxide,
molecules to account for the observed loss rates in the
d other gases, they would have to be present as impurities
n Th3+ = k1n Th3+ (15) atthe10−4 levelreactingattheLangevinrate,consider-
dt −
ably higher than the levels specified by the gas supplier
d (cid:0) 2+(cid:1) (cid:0) 2+(cid:1) 3+
n Th = k2n Th +α1k1n Th (16) (see Table V). Furthermore, none of these molecules ex-
dt −
hibited different reaction rates due to optical excitation
dn T(cid:0)hO2+(cid:1) = α2k1n(cid:0)Th3+(cid:1) +α4k2n(cid:0) Th2+(cid:1)(17) ofTh3+,sotheirpresenceasimpuritiescouldnotexplain
dt
the reaction rates observed for argon and nitrogen. For
dn(cid:0)ThX+(cid:1) = α3k2n(cid:0)Th2+(cid:1) (cid:0) (cid:1)(18) these reasons, it is unlikely that impurities of the type
dt measured to react at the Langevin rate are responsible
(cid:0) (cid:1) (cid:0) (cid:1) for the losses observed for the slowly reacting gases.
Similar systems of equations can be written to describe
the reaction dynamics in methane and oxygen.
To estimate the relative probabilities of the various
reactionchannels,the dataofFig.10wasnumericallyfit VI. CONCLUSION
todynamicequationsoftheformshownabove. Fitswere
performed in the order of the above equations. Once a We have determined the effect of various gases on the
3+
valuewasobtainedforafittingparameter,thatvaluewas trap lifetime of Th . Reactions involving carbon diox-
9
ide,oxygen,andmethaneproceedatarateneartheclas- Acknowledgments
sicalLangevinlimit. Althoughchargeexchangereactions
with them are exothermic, the reaction rate coefficients
for nitrogen, hydrogen, and argon are orders of magni-
tude less than the Langevin rate. The reaction rate co- WegratefullyacknowledgeAdamSteele,CoreyCamp-
3+
efficient between Th and helium provides a measure bell, Alex Radnaev, and Alex Kuzmich for their assis-
of the impurities in the buffer gas. The measurement of tance with this work,andwe thank KenBrownfor valu-
thecoefficienthereprovidesastandardagainstwhichthe able discussions. This work was supported by the Of-
vacuum and buffer gas quality of future systems can be ficeofNavalResearch(N000140911024)andtheNational
measured. Science Foundation (PHYS-1002550).
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