Separated Oscillatory Fields for High-Precision Penning Trap Mass Spectrometry

0.31 MB·English

by  S. George

Separated Oscillatory Fields for High-Precision Penning Trap Mass Spectrometry
S. George1,2,∗ S. Baruah3, B. Blank4, K. Blaum1,2, M. Breitenfeldt3, U. Hager5,
F. Herfurth1, A. Herlert6, A. Kellerbauer7, H.–J. Kluge1,8, M. Kretzschmar2,
D. Lunney9, R. Savreux1, S. Schwarz10, L. Schweikhard3, and C. Yazidjian1
1GSI, Planckstraße 1, 64291 Darmstadt, Germany
2Johannes Gutenberg-Universit¨at, Institut fu¨r Physik, 55099 Mainz, Germany
3Ernst-Moritz-Arndt-Universit¨at, Institut fu¨r Physik, 17487 Greifswald, Germany
4Centre d’Etudes Nucl´eaires de Bordeaux-Gradignan, 33175 Gradignan Cedex, France
5University of Jyv¨askyl¨a, Department of Physics, P.O. Box 35 (YFL), 40014 Jyv¨askyl¨a, Finland
6CERN, Division EP, 1211 Geneva 23, Switzerland
7Max-Planck Institut fu¨r Kernphysik, 69117 Heidelberg, Germany
8Ruprecht-Karls-Universit¨at, Physikalisches Institut, 69120 Heidelberg, Germany
9CSNSM-IN2P3-CNRS, 91405 Orsay-Campus, France and
7 10NSCL, Michigan State University, East Lansing, MI 48824-1321, USA
0 (Dated: February 5, 2008)
0
2 Ramsey’s method of separated oscillatory fields is applied to the excitation of the cyclotron
motion of short-lived ions in a Penning trap to improve the precision of their measured mass. The
n
theoretical description of the extracted ion-cyclotron-resonance line shape is derived out and its
a correctness demonstrated experimentally by measuring the mass of the short-lived 38Ca nuclide
J with an uncertainty of 1.6·10−8 using theISOLTRAPPenning trap mass spectrometer at CERN.
9 The mass value of the superallowed beta-emitter 38Ca is an important contribution for testing the
1
conserved-vector-current hypothesis of the electroweak interaction. It is shown that the Ramsey

method applied to mass measurements yields a statistical uncertainty similar to that obtained by
1
theconventional techniqueten times faster.
v
7
PACSnumbers: 07.75.+h,21.10.Dr,32.10.Bi
2
Keywords:
0
1
0
In1989theNobelprizeinphysicswasawardedtoN.F. tions,whichpostulatesa vector-currentpartofthe weak
7
Ramsey [1] in recognition of his molecular beam reso- interaction unaffected by the strong interaction. Thus,
0
nance method with spatially separated oscillatory fields thedecaystrengthofallsuperallowed0+ →0+ β-decays
/
x proposed 40 years earlier [2, 3]. In 1992 G. Bollen et isindependentofthenucleiexceptfortheoreticalcorrec-
e al. [4] demonstrated the use of time-separated oscilla- tions [6, 7]. Here, a relative mass precision of 10−8 is
-
l tory fields for the excitation of the cyclotron motion of required.
c
u an ion confined in the Penning trap mass spectrome- Comparisons with the conventional excitation
n ter ISOLTRAP. This and experiments performed later scheme [8, 9] show that the line width of the resonance
: at SMILETRAP [5] showed that the method may im- is reduced by almost a factor of two and the statistical
v
i prove the precision of mass measurements with Penning uncertaintyofthe extractedresonancefrequencyismore
X traps - on the condition that the shape of the detected than a factor of three smaller. It is shown that the
r ion-cyclotron-resonancecouldbeputonasoundtheoret- Ramsey method allows a measurement with the same
a
ical basis. In the case of exotic nuclides, the extremely statistical uncertainty, but ten times faster. This is an
low productionrates make precisionmeasurements chal- enormous improvementin the very active field of on-line
lenging because of the time required to accumulate the high-precision mass measurements with Penning traps
necessary statistics. The Ramsey method would there- at radioactive beam facilities [10].
fore allow accumulation of sufficient statistics in a much The prerequisite for the successful implementation of
shorter time, which is of prime importance for on-line the Ramsey method to stored ions is the detailed un-
measurements. derstanding of the observed time-of-flight cyclotron res-
In this Letter, we introduce the correcttheoreticalde- onance curves using time separated oscillatory fields.
scriptionoftheapplicationoftheRamseymethodtoions While here only the most important parts of the the-
stored in a Penning trap. We also demonstrate its valid- oryanditsexperimentalconfirmationisgiven,adetailed
ity for the first time with an on-line mass measurement presentation will be published elsewhere.
of 38Ca (T = 440(8) ms). This short-lived nuclide is In a Penning trap an ion with a charge-to-mass ratio
1/2
used for testing the conserved-vector-currenthypothesis q/misstoredinastronghomogeneousmagneticfieldB0
(CVC) of the Standard Model of fundamental interac- combinedwithaweakelectrostaticquadrupolefield. The
mass measurement is performed via the determination
of the cyclotron frequency ν = qB /(2πm). For the
c 0
basic theory of the ion motion in Penning traps we refer
∗Correspondenceto: [email protected] to the review article of Brown and Gabrielse [11]. Our
2
(a) expressed in terms of T
1
rb. units2/9 τ trf/ ms H(t) = +~ω~1·(T2g0(+co21s)φ+d(~t)ω·cTT13((tt))+sinφd(t)·T2(t))(5)
a 0 900 governs the time development of the Bloch vector oper-
e / τ τ τ (b) ator. Compare this result to the Hamiltonian Hmag that
ud 1 1 0 1 describestheprecessionofthenuclearspinIinmagnetic
plit resonance experiments, I=I1e1+I2e2+I3e3,
m
A
H = −~µ·B (6)
mag
t / ms
rf = −~ω I −~γB (cosωt·I −sinωt·I ),
0 100 800 900 L 3 1 1 2
where ~µ = γI is the nuclear magnetic moment, γ the
FIG.1: Excitation schemes: (a)conventionalexcitation with
a continuous rf pulse (here τ=900 ms), (b) excitation with gyromagnetic ratio, and ωL the Larmor frequency. Both
two100-msRamseypulsesτ1interruptedbya700mswaiting Hamiltonians govern the time development of a vector
period τ0. operator,thus exhibitingadynamicalsimilaritybetween
nuclearmagneticresonanceontheonehandandionmo-
tioninaPenningtrapwithquadrupoleexcitationonthe
considerations here focus on the process of conversionof other hand. This structural analogy provides deeper in-
the magnetron mode into the cyclotron mode under the sight why Ramsey’s idea of using separated oscillating
influence of the quadrupolarrf-field in the Penning trap, fields can be successfully applied also to Penning trap
extendingpreviousstudiesbyoneofus[12]ofthisprocess physics.
in a quantum mechanical framework. In this work the Initially (t = 0) the ions are prepared in a pure mag-
effective interaction of a quadrupolar field with driving netron mode (Ntot = N−(0) = −2hT3(0)i), with the ob-
frequency ν ≈ ν with a trapped ion is described in jective to convert the magnetron motion as completely
d c
terms ofthe annihilation (a) and creation(a†) operators as possible into cyclotron motion and thus to bring the
of the magnetron (-) and cyclotron (+) oscillators, the radialenergytoitsmaximum. Fortheconventionalexci-
phaseofthe quadrupolefieldφ (t)=ω t+χ withω = tationschemewithasinglepulse(seeFig.1a)ofduration
d d d d
2πν , and a coupling constant g that is proportional to τ and constant amplitude the expectation value for the
d
the amplitude of the quadrupolar field: percentage of converted quanta is obtained as
N (τ) 4g2
H (t)=~g e−iφd(t)a†(t)a (t)+h.c. , (1) F (ω ,τ,g)= + = ·sin2(ω τ/2) , (7)
1 + − 1 R N ω2 R
(cid:16) (cid:17) tot R
“h.c.” denotes the Hermitian conjugate of the firstterm. where ω = (2g)2+δ2 is the analog of the Rabi fre-
R
Addition ofthis interactionto the Hamiltonianofanion quency andδp=ωd−ωc the detuning ofthe quadrupolar
inanidealPenningtrapyieldsamodelsystemforwhich field. The “conversion time”, i.e. the time required for
Heisenberg’s equations of motion can be solved rigor- complete conversion exactly on resonance, is seen to be
ously. The interaction (1) has the important property τ =π/(2g).
c
thatthetotalnumberofquantainthemagnetronandcy- Iftwopulsesofquadrupolarradiation,eachofduration
clotron oscillators is conserved,Ntot =N+(t)+N−(t)= τ1, and separated by a waiting period τ0 (see Fig. 1b),
a†+(t)a+(t)+a†−(t)a−(t) = 2T0. The conversion process are used for the excitation, the expectation value for the
can be studied in terms of the “Bloch vector operator” percentage of converted quanta becomes
T=T e +T e +T e , introduced in [12], with
1 1 2 2 3 3
16g2 ω τ
F (δ,τ ,τ ,g)= ·sin2 R 1 (8)
T1(t) = 21 a†+(t)a−(t)+a†−(t)a+(t) , (2) 2 0 1 ωR2 (cid:16) 2 (cid:17)
(cid:16) (cid:17) 2
δτ ω τ δ δτ ω τ
T (t) = 1 a†(t)a (t)−a† (t)a (t) , (3) · cos 0 ·cos R 1 − ·sin 0 ·sin R 1 .
2 2i + − − + (cid:20) 2 2 ω 2 2 (cid:21)
(cid:16) (cid:17) R
T (t) = 1 a†(t)a (t)−a† (t)a (t) . (4)
3 2 + + − − In order to compare experimentally the different exci-
(cid:16) (cid:17)
tationmethods the total durationofthe excitation cycle
Thecomponentsobeythe samecommutationrulesasan was chosen equal for both, namely 900 ms. The calcu-
angular momentum, [T ,T ] = iǫ T (j,k,l = 1,2,3) latedenergyconversionisshowninFig.2asafunctionof
j k jkl l
and T2+T2+T2 = T (T +1). The expectation value the frequencydetuning δ′ =δ/(2π)andthe waitingtime
1 2 3 0 0
hTiisareal3-dimensionalvectorofconstantlengththat τ . Theconventionalsinglepulseexcitationappearshere
0
describesaprecessionalmotionona“Blochsphere”dur- as the limiting case with waiting period τ =0. The ex-
0
ing the quadrupolar excitation. The model Hamiltonian perimental resonance spectra for a conventional scheme
3
0.7
s
m
τe / 0 0.5 (a)320
m
Waiting ti0.3 ght / s 300
0.1 of fli 280
e
a 1 m
fo egatnectnreauq detrevn0.50 Mean ti 224600 38 19 +
Poc -4 -2 0 2 4 Ca F
Frequency detuning δ´ / Hz
-4 -2 0 2 4
FIG. 2: Percentage of converted quantaversusthefrequency ( C-159436 6 Hz) / Hz
detuning δ′ = δ/(2π) and versus the waiting time τ0 of the (b)320
38 19 +
two-pulse Ramsey scheme of Fig. 1b. Each pulse has a dura- Ca F
tionofτ1 =τc/2toobtaincompleteconversionatresonance, s 300
thetotal duration of theexcitation cycle is fixed to 900 ms. ht /
g
of fli 280
as well as for a scheme with two excitation periods of e
m 260
τ = 100 ms and τ = 700 ms are shown in Fig. 3. In
th1elattercasethesi0debandsareverypronouncedandthe n ti
a
full-width-at-half-maximum(FWHM)isconsiderablyre- Me 240
duced. The solid line represents the fit of the theoretical
line shape to the data points. 220
The mass measurements on the short-lived nu- -4 -2 0 2 4
clide 38Ca using the Ramsey method were per- ( C-1594366 Hz) / Hz
formed using the Penning trap mass spectrometer
ISOLTRAP [13] installed at the on-line mass separa-
tor facility ISOLDE/CERN. The calcium isotope was
FIG. 3: Time-of-flight ion-cyclotron-resonance spectra of
produced by bombarding a heated titanium metal foil 38Ca19F+ with the conventional quadrupolar excitation (a)
target with 1.4-GeV protons from the CERN proton- and with a two-pulse Ramsey scheme with two 100 ms dura-
synchrotron-booster accelerator. A hot tungsten sur- tionexcitationperiodsinterruptedbya700mswaitingperiod
face was used to ionize the released atoms. In order (b). Thesolid curvesare fitsof thetheoretical line shapes to
to suppress isobaric contaminations by 38K+ ions, a thedata. Thecenterfrequency,wherethedetuningis0,isat
CF leak was added and the ions of interest were de- 1594365.92 Hz.
4
livered to ISOLTRAP in form of the molecular sideband
38Ca19F+. Ions extracted from the source were accel-
erated to 30 keV, mass separated in ISOLDE’s high- cyclotron resonance of 38Ca19F+ ions using the conven-
resolutionmassseparator,andinjectedintothefirstpart tional excitation technique with one continuous rf pulse
of the ISOLTRAP apparatus,a gas-filledlinear radiofre- (Fig. 1a) is shown in Fig. 3a. The mass of the ion of in-
quency quadrupole ion trap for accumulation, cooling terest is obtained froma comparisonof its cyclotronfre-
and bunching of the ion beam [14]. From here the ions quency with the one of a reference ion with well-known
were transferred at lower energy as short bunches to a mass, here 39K+.
cylindrical Penning trap for further buffer-gas cooling The uncertainty of the center frequency depends
and isobaric purification [15]. The actual mass measure- mainly on three parameters. First, the relative uncer-
ment was performed in a second, hyperboloidal Penning tainty is inversely proportional to the square root of the
trap [16] via the cyclotron frequency determination. numberofrecordedions. Second,itisproportionaltothe
The time-of-flight ion cyclotron resonance detection linewidth of the resonance and third it depends on the
technique [8] relies on the coupling of the ion’s orbital shape of the resonance and its sidebands. The stronger
magnetic moment to the magnetic field gradient after thesidebandsare,themorepreciselythecenterfrequency
excitation of the ion motion with rf-fields and axial ejec- can be determined. For the latter two aspects Ramsey’s
tion from the trapinto a time-of-flight section. The sum excitationmethod with separatedoscillatoryfields is su-
frequency of the modified cyclotron mode and the mag- perior to the conventional method.
netron mode ν = ν +ν is probed by the measure- Altogether eight resonances of 38Ca19F+, each with a
c + −
mentoftheradialenergy[17,18]. Atypicaltime-of-flight scan width of ±4 Hz around the expected cyclotron fre-
4
facility at MSU and being a factor of two more precise.
The 12 best known superallowed Fermi-type beta de-
cays rangingfrom 10C to 74Rb yield an averageFt value
40 ofFt=3072.7(0.8)s[7],whichconfirmstheCVChypoth-
pb esisat alevelof3·10−4. Further massmeasurementson
p 20
n superallowedβ-emittersfor anevenmorestringentCVC
iave 0 test have been performed recently [21, 22, 23], demon-
R -20 strating the continuous interest in this weak interaction
-
R
and Standard Model test. 38Ca is a new candidate for
-40
testing the CVC hypothesis. Its largeisospin symmetry-
1 2 3 4 5 6 7 8 breaking correction of 0.73(5)% makes it a proper can-
Measurement number didate for testing the validity of the calculations. Until
recentlytheFtvaluehadarelativeuncertaintyof4·10−3,
limited by the uncertainty of the ground-state mass, the
FIG. 4: Difference of the measured cyclotron frequency ra- uncertainty of the 0+ → 0+ branching ratio, and the
tios R and their average value Rave between 38Ca19F+ and accuracy of the half-life (T1/2 = 440(8)ms), which was
39K+. The error bars are the statistical uncertainties. Each measured and improved in parallel to our experiment at
data point contains the same numberof recorded ions in the ISOLDE.Here, the data analysisis presently under way.
resonance.
Obviously, our accuracy is not limited by the statisti-
caluncertainty,butbythesystematicerror,whichcomes
from magnetic field fluctuations and mass dependent er-
quency weremeasuredwiththe Penningtrapmass spec-
ror of the experimental setup. In the future these sys-
trometer ISOLTRAP. The first two employed the con-
tematic errors can be reduced by a stabilization of the
ventionalexcitationschemewith900ms,theothersused
magnetic field and a local determination of mass depen-
the Ramsey-typeschemeoftwo100-msexcitationpulses
dent deviations with carbon clusters [19].
and one 700-ms waiting period ( Fig 1). Thus, the total
excitation period of both schemes was 900 ms and they In conclusion, the method of separated oscillatory
can be easily compared. Taking only into account the fields has been for the first time theoretically derived
statistical error, the mass excess can be determined to and applied to the mass measurement of radioactive
withina1.03keVuncertaintyforthetworesonanceswith ions confined in a Penning trap. It allows a consider-
conventional excitation. The uncertainty of the mass able reduction in data-taking time by its improvement
excess obtained from two Ramsey type measurements of precision with much less statistics. Thus, it is ide-
under identical experimental conditions is here drasti- ally suited for radionuclides, especially of half-lives be-
cally reduced to 0.25keV. All six measurements lead to low100ms andproductionratesofonly afew 100ions/s
an overall statistical uncertainty of the mass excess of where the uncertainty is often limited by the statistical
only 0.12keV. After consideration of systematic uncer- error,asinthecaseof32Ar(T1/2 =98ms)[24]and74Rb
tainties of ISOLTRAP [19] we obtain finally a frequency (T1/2 =65ms) [25].
ratio R between the ion of interest and the reference ion This work was supported by the German Ministry
ν /ν =1.4622576087(50)(229),where the first error for Education and Research (BMBF) under contracts
ref ion
derives from the statistics and the second one denotes 06GF151 and 06MZ215, by the European Commission
the systematic error of the measurement. Together with undercontractsHPMT-CT-2000-00197(MarieCurieFel-
the mass excess of 19F ME(19F)=-1487.39(07)keV [20] lowship) and RII3-CT-2004-506065 (TRAPSPEC), and
we obtain a mass excess ME(38Ca)=-22058.01(65)keV, bytheHelmholtzassociationofnationalresearchcenters
which is in agreement with the previously accepted (HGF) under contract VH-NG-037. We also thank the
value [20] as well as with the recent value ME(38Ca)=- ISOLDE Collaboration as well as the ISOLDE technical
22058.53(28)keV[21],measuredbythenewPenningtrap group for their assistance.
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