Table Of ContentVolume105,Number1,January–February2000
Journal of Research of the National Institute of Standards and Technology
[J.Res.Natl.Inst.Stand.Technol.105,89(2000)]
Neutrino Induced Doppler
Broadening
Volume 105 Number 1 January–February 2000
J. Jolie and N. Stritt Whenanucleusundergoesbetadecayvia theatomduringthefirsthundredsof
theelectroncapturereaction,itemitsan femtosecondscanbereconstructed.The
Institut de Physique, electronneutrino.Theneutrinoemission relevanceofthisknowledgeforanew
Universite´ de Fribourg, givesasmallrecoiltotheatom,which neutrinohelicityexperimentisdiscussed.
canbeexperimentallyobservedasa
Pe´rolles, CH-1700 Fribourg,
Dopplerbroadeningonsubsequently Keywords: crystalspectrometer;
Switzerland emittedgammarays.Usingthetwo-axis gamma-rayspectroscopy;interatomic
flat-crystalspectrometerGAMS4andthe potentials;neutrinohelicity;phonon
electroncapturereactionin152Eu,the creation.
motionofatomshavinganexcesskinetic
Accepted: July22,1999
energyof3eVinthesolidstatewas
studied.Itisshownhowthemotionof Availableonline:http://www.nist.gov/jres
1. Introduction
During the last decade ultra-high resolution gamma- Besides the (n, (cid:2)) reaction, atomic electron capture
ray spectroscopy with the two-axis flat crystal spec- providesboththeexcitationandtheextrakineticenergy
trometer GAMS4 [1,2], installed at the high flux beam leading to Doppler broadened energy profiles of sub-
reactor of the Institut Laue-Langevin (ILL), Grenoble, sequently emitted gamma rays. Electron capture is a
France, in a ILL/NIST collaboration, has allowed the beta-decay process in which a nucleus captures an
observation of very small Doppler broadening of atomic electron and emits a neutrino which, in first
gamma-raytransitions[3].Themeasuredbroadeningis approximation, is the only particle to leave the atom.
of the order of (cid:1)E/E=10–4to10–6 and is induced by Because the neutrino has a well defined energy, it
preceding high-energy gamma-ray emissions following induces a well-defined recoil velocity in contrast to
neutron capture. The resolving power of the GAMS4 normalbetadecaywhichleadstoacontinuousrangeof
spectrometer, which is of the order of 10–6 even allows initial recoil energies. Note that pure electron capture
the measurement of the Doppler broadening caused by occurs only if the mass difference between the initial
the thermal motion of the atoms in a solid state target andfinalatomdoesnotexceed1022keV,becausethen
[4]. The observation of such small broadenings led to the competing (cid:3)+ decay is forbidden.
the development of the GRID (Gamma Ray Induced The initial motivation to study Neutrino Induced
Dopplerbroadening)method[4],whichisusedeitherto Dopplerbroadening(NID)wasthemeasurementofthe
determineshortlifetimesofnuclearexcitedstates,orto neutrino helicity as proposed 10 years ago by H.G.
studytheslowing-downprocessoflow-energyrecoiling Bo¨rneretal.[7].Thebasicideaofthisproposalwasto
atoms in the bulk of the target. The latter permits the redo the classical experiment of Goldhaber, Grodzins
extractionofinformationontheformoftheinteratomic and Sunyar [8] in which the helicity of the neutrino
potential [5,6]. is transferred to a Doppler-shift dependent circular
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Volume105,Number1,January–February2000
Journal of Research of the National Institute of Standards and Technology
polarisation of 963keV gamma rays. In contrast to the In Eqs. (2) and (3) M(AX)c2 and M(AY)c2 denote the
earlierexperimenttheDopplershiftwouldbemeasured atomic rest masses in the initial and final states and B
e
directlybyGAMS4withouttheneedtorelyonnuclear is the binding energy of the captured electron. After
resonance fluorescence. An additional motivation was electron capture a hole is created in an inner electron
thattheNIDexperimentsallowthestudyoftheslowing shell and the filling of this hole leads to secondary
downprocessatverylowkineticenergies[9].Atthese effectssuchasx-rayemissionortheemissionofAuger
energies the recoiling atom is not able to definitively electrons. In the former case the recoil energy equals:
leave its lattice site but instead performs vibrations
around its equilibrium position.
(cid:4) E
r (cid:2)
= . (4)
2. Neutrino Induced Recoil c M(AY)c2
Beta decay associated with electron capture takes with E the photon energy. When an Auger electron
(cid:2)
place via the following nuclear reaction: with energy E is emitted one has:
e
AX +e→ AY +v. (1)
N N+1 (cid:1)
which (as discussed above) results in a well defined (cid:4) Ee(Ee+2mec2)
r
valuefortheinitialrecoilenergyiftheQvalueislower = . (5)
c M(AY)c2
than 1.022MeV. Because of this upper limit on the
Q-valuetherecoilenergiesthatcanbeobtainedareonly
of the order of a few eV for heavy nuclei. The recoil Figure 1 compares the recoil velocities obtained by
velocity of the newly formed atom is given from gamma-ray,neutrinoorelectronemissionasafunction
the conservation of momentum (for zero-rest mass ofAwithtwoothertypicalvelocities:thethermalveloc-
neutrinos and using nonrelativistic kinematics) by: ity (cid:4) associated with a maxwellian distribution:
T
(cid:4)cr=MQ(ecAY–)Bce2 . (2) D((cid:4))=4(cid:5)(2(cid:5)3(cid:4)T2)3/2(cid:4)2e–1.5((cid:4)(cid:4)T)2, (6)
The Q value for the reaction is defined as: and the typical Bohr velocity of an electron.
ec
Qec=[M(AX)–M(AY)]c2. (3)
Fig. 1. Comparison as a function A of the recoil velocities obtained after gamma-ray,
neutrinoandelectronemissiontotheBohrandthermalvelocities.
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Journal of Research of the National Institute of Standards and Technology
ForNIDtheinducedrecoilisverylow(3eVintheEu transition.Thistransitiondecaysfromalong-livedstate
case)andsotherecoilingatomisnotabletodefinitively such that the broadening is solely due to the thermal
leave its equilibrium position. In order to analyse the motion.
measured line shapes different approaches can be fol-
lowed. The first, analytic, approach is based on a 4. Description of the Slowing Down
phonon creation model, and was used to analyse the Process and Results
NIDdatainRef.[9].Thesecond,numerical,approach
reliesonMolecularDynamics(MD)simulationsofthe Before discussing the two different ways that were
slowing-down process at ultra-low recoil energies, and used to analyse the neutrino induced Doppler broaden-
is presented in [10–12]. Both approaches allow one to ing line shapes, we note the main differences to those
obtain information on either the lifetime of the nuclear observed using gamma-ray induced Doppler broaden-
statefedbytheelectroncaptureprocess,ortostudythe ing. The recoils induced in medium-heavy nuclei by
effectofultra-lowrecoilenergiesonatomslocatedina electron capture are too small to create significant
lattice of bulk matter. dammageoftheregularlattice.Instead,aftertheinitial
recoil, the atom moves a small distance away from its
3. Performed Experiments equilibrium position, due to the extra kinetic energy.
Because of this, it pulls the neighbouring atoms away
All NID experiments have relied on electron capture from their positions, loses energy and slows down.
intheisomeric0–stateof152Eu.Inordertopopulatethis When the recoiling atom has lost all of its kinetic en-
state,whichhasahalflifeof9.3h,naturaleuropiumis ergy, because of the forces exerted by the other atoms,
used. Placed at the GAMS4 in-pile target position, the it stops and starts to move back to its initial position.
isotope151Eu,whichhasa48%naturalabundance,cap- Now, regaining energy, the velocity will increase and
turesathermalneutronandforms152Eu.Thecrosssec- reach a maximum near the equilibrium position. This
tion for this reaction is 9204barns, making the targets time the velocity will be smaller than the initial one,
black for thermal neutrons. Thus the neutron capture sinceenergyisdissipatedinthecrystalbypullingmore
rate per cm2 of target area is limited to 2.5(cid:6)1014s–1. and more atoms away from their equilibrium positions.
Following the electron capture a 1– level at 963keV in Thusalatticevibration,orphonon,iscreated.Since,as
152Sm is populated. This 1– state decays to the nuclear thenamesuggests,thisisacollectiveprocess,itissen-
ground state by emitting either a single 963.4keV sibletotestcollectivedescriptionsoftheslowingdown
gamma ray, or a 841.4keVto121.8keV gamma-ray process. In contrast, in standard GRID measurements
cascade via the long-lived 2+ state. These three gamma the recoil energies are about 400 eV and the velocity
rays were measured with the GAMS4 spectrometer. functionoftherecoilingatomis,toagoodapproxima-
Two different kinds of targets have been used for the tion, deduced from binary collisions until the atom
experiments. In the first measurements powder targets movesatvelocitiesintheorderofthethermalmotionof
ofdifferentchemicalcompositionwereused[9].These the target atoms [4]. In this respect the slowing down
polycrystaline targets consisted out of Eu O , EuF , processcanbedescribedbyconsideringindividualtwo-
2 3 3
EuF and EuCl powders. In the more recent experi- body collisions. Another difference is the influence of
2 3
mentsorientedsinglecrystalsofEuOwereobservedfor the thermal motion itself which is important even for
differentorientationstowardsthespectrometer[11,12]. shortlifetimes,becauseitisinthesameorderofmagni-
EuO crystal has a fcc cubic structure and the NID tude as the recoil velocity.
measurements were performed once with the [100] di- Tounderstandthisprocessalldatahavebeenanalyzed
rection towards the GAMS4 spectrometer and once using two different approaches: the analytical phonon
withthe[110]direction.Detailsonthisexperimentare creation model and the semi-microscopic Molecular
given in ref [12]. Table 1 lists the thermal velocities (cid:4) Dynamics simulations.
T
(cf.Eq.(6))whichweremeasuredusingthe121.8keV
4.1 Analytic Description of the Slowing
Table1. Fittedvaluesofthethermalvelocity(cid:4) Down Process
T
Fortheslowingdownofatomswithverylowkinetic
EuO,EuF EuF,EuCl EuO
2 3 3 2 3 energies in solids the Phonon Creation Model (PCM)
(cid:4)
T[m/s] 515(51) 414(57) 537(24) givesananalyticandsimpledescriptionofthevelocity.
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Journal of Research of the National Institute of Standards and Technology
Assuming the Debye approximation and neglecting linewidth of the deexciting state I (E,v) is approxi-
D
phonon-phonon interactions and incoherent thermal mately given by:
oscillationsoftheatomsinthelattice,thevelocityofthe
recoilingatomforaisotropicmediumoramonoatomic c (cid:4) (cid:4)
I (E,(cid:4))= for E (1– )<E<E (1+ ) (9)
cubic Bravais lattice, is given by [13]: D E (cid:4) 0 c 0 c
0
The integration of Eq. (8) is done numerically.
2 1 2
(cid:4)(t,(cid:7))=3(cid:4)[ cos((cid:7)t)+( – )sin((cid:7)t)]. Because the initial recoil velocity, (cid:4)/c=6.54(cid:6)10–6,
D 0 (cid:7)2t2 D (cid:7)t (cid:7)3t3 D r
D D D is very close to the thermal velocity, one has to take
(7) account of the velocity spread due to the thermal mo-
tion. This is done by folding the theoretical line shape
Equation[7]givesthevelocityoftherecoilingatomas with a thermal width as explained in detail in Ref. [9].
afunctionofthetimetandtheDebyefrequency(cid:7).In Table 2 lists the deduced frequencies (cid:7) for all five
D D
the Debye approximation the direction of the recoil is targetsusingthelifetimevalueof(cid:8)=29fsobtainedby
ignored because of the assumed isotropy and the ne- Jungclaus et al. [14]. Note that all crystal effects con-
glection of temperature. nectedtotheEuOtargetwereneglected.Inthisanalysis
Employing the Debye approximation, the Doppler alsotheeffectsofx-rayandAugerelectronemissionare
broadened line shape is described by: neglected. Figure 2 shows the corresponding time-de-
pendentvelocities.Oneclearlynoticesthequickslowing
(cid:2) down in Eu2O3 and EuCl3 compared with the other
I(E,(cid:8))= +(cid:9)I (E,(cid:4)(t,(cid:7)))N0 e–(cid:8)tdt, (8) targets.Forahelicityexperimentitisclearthattheideal
D D (cid:8) target would be EuF . We have also tried to find an
0 2
effectofafinitelifetimeofthecreatedphonons,butthe
fitofanexponentiallydampedEq.(7)convergedalways
withv(t,(cid:7))givenbyEq.(7)and(cid:8)thelifetimeofthe to an infinite lifetime for the phonons. This shows that
D
deexciting nuclear state. When neglecting the natural this effect is negligible when dealing with a nuclear
lifetime of a few tens of fs while typical phonon life-
times are about 1ps.
Table2. Adoptedvaluesfor(cid:7) forthedifferenttargetcompositionsusingtheproceduredescribedinthetextand(cid:8)=29fs.
D
EuO EuF EuCl EuF EuO
2 3 3 3 2
(cid:7) [1013s–1] 5.9(cid:10)1.06 3.6(cid:10)0.7 6.1(cid:10)1.0 2.8(cid:10)0.4 3.16(cid:10)0.15
D
Fig. 2. Time dependence of the recoil velocity obtained with the Phonon Creation
Modelforthedifferenttargets.
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Journal of Research of the National Institute of Standards and Technology
4.2 Molecular Dynamics Description of the Table3. ValuesoftheparametersfortheBuckinghampairpotential
Slowing Down Process
i–j A (eV) (cid:12) (Å) C (eV Å6) q (e)
ij ij ij j
Using Molecular Dynamics (MD) simulations and
Eu–Eu 1715 0.317 0.0 +2,+3
MonteCarlosimulationsthedescriptionoftheslowing
Eu–F 3429 0.280 14.0 –1
downcanbedoneinamuchmoredetailedway[10].By
F–F 369 0.280 12.5 –1
solving the Newtonian equations for atoms recoiling in Eu–Cl 3886 0.349 169.6 –1
random directions it is possible to study the spread in Cl–Cl 7911 0.383 2027.0 –1
velocitiesandtotreatindetailtheeffectofthethermal Eu–O 5045 0.290 34.0 –2
O–O 22764 0.149 27.9 –2
motion,x-rayandAuger-electronemissionontheslow-
ingdown.FortheMDsimulationsthemaininputisthe
interatomic potential which is treated as a set of pair ture.Theexperimentallineshapeswereanalysedusing
potentials dependent on the distance r in between the thecomputercodeGRIDDLE[15],andFig.3illustrates
ij
atomihavingchargeq andtheatomjhavingchargeq . theverygoodqualityofthefitofthelineshapeforthe
i j
InthecaseofNIDenergiesitwasfoundthataBucking- EuOmeasurement[11].Thefittedlifetimesaregivenin
ham-type of potential describes best the data [10–12]. Table4andagoodagreementisobtainedincomparison
This potential has the form: with the (n,n’(cid:2)) experiment, justifying the use of
(cid:8)=29fs in the phonon creation model. In the study
e2 1 –rij Cij usingtheorientedEuOcrystalsasmall,butobservable,
V(r )=q q +A exp – (10)
ij i j4(cid:5)(cid:11)0 rij ij (cid:12)ij ri6j dependence of the Doppler broadening on the crystal
orientation was found [12]. In contrast to the analytic
Table 3 lists the parameters used for the analysis of the descriptiontheMDsimulationstreatthethermalveloc-
data.Knowingtheinteratomicpotentialthelifetimecan ity and the emission of xrays and Auger electrons
be fitted and compared to those available in the litera- exactly.
Fig. 3. Comparison between fitted and measured line shape for the
841.6keV transition in 152Sm. The dashed line gives the instrumental re-
sponse[11].
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Journal of Research of the National Institute of Standards and Technology
Table4. Lifetimevaluesforthe963keVlevel.Columns1-5areobtainedfrom[10]andcolumn6from[12].Theyarecomparedtothelifetimes
obtainedusingthe(n,n'(cid:2))reaction[14],nuclearresonancefluorescence[16]andtheGRIDtechnique[17].
EuO EuF EuCl EuF average EuO (n,n'(cid:2)) ((cid:2),(cid:2)') GRID
2 3 3 3 2
(cid:8)[fs] 27.8(cid:10)2.8 22.4(cid:10)2.9 36.8(cid:10)2.8 24.2(cid:10)2.7 28(cid:10)6 28.7(cid:10)1.0 29(cid:10)4 41(cid:10)3 28(cid:10)12
Aparticularbutalbeitmarginalproblemencountered individual trajectories in EuO. While the oscillatory
inthesimulations,isCoulombimplosionofthesimula- character of this motion is clear by the turning point at
tion cell. In rare cases the atom reaches a very high 70fs one notices a large velocity spread at any time.
chargestateafteranAugercascadewhichleadsbythe Thisspreadisduetothethermalmotionatthemoment
attractiveCoulombforcetothedestructionofthelattice. oftheinitialrecoil.Becauseofthislargeeffectwehave
Whether such an effect really takes place in nature is, studied the time dependence of the angle(cid:13)(t), defined
however, not clear. as the angle between the recoil velocity (cid:1)(t) at time t
and the direction opposite to the neutrino momentum.
5. Discussion Thisangleisdirectlyrelatedtothemeasurementofthe
neutrino helicity. This because the helicity:
FromtheMDsimulationsdiscussedaboveadetailed
description of the slowing down is obtained which we
analysehereinthecontextofthehelicitymeasurement. p (cid:14)S
v v
Although EuF is the ideal target we will rely on the H= (11)
2 (cid:3)p (cid:3)(cid:14)(cid:3)S (cid:3)
EuO data for our study, because the experimental data v v
set was the best defined for EuO due to the use of
oriented single crystals and the good statistics. The ismeasuredviatheDopplershiftrelatedto(cid:1)(t)andany
slowing down in EuO and EuF is also similar as was deviationfromthe p directionisgivenby (cid:13)(t).Figure
2 v
illustrated in Fig. 2. 5showsthevaluesfor(cid:13)(t)for25individualrecoils.At
Beforeproceedingwerecallthreepositivepoints:the time t=0 the averaged value for (cid:13)(0) equals already
dependence on crystal structure is small, the Auger 12.5(cid:15).Thebehaviorofthisvalueasafunctionoftemper-
cascades are rare and the lifetime of the 963keV level ature can be approximated by:
in 152Sm is very short. However, a major problem (cid:4)
remains.Figure4showsthevelocitiesobtainedfor100 (cid:13)(0)=arctan( T) , (12)
(cid:4)
r
Fig.4. IndividualrecoilvelocitiesofEurecoilinginEuOasafunctionoftime.
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Volume105,Number1,January–February2000
Journal of Research of the National Institute of Standards and Technology
Fig.5. Timedependenceof(cid:13)for25individualrecoilsinEuO.
yielding in our case 14(cid:15). The individual thermal veloc- 6. Conclusions
itiesfollowthebroadMaxwelldistributionand(cid:4) isonly
T
therootmeansquarevelocityofthisdistribution,there- Over the last years we have analysed the different
forindividualatomscanhaveveryloworhighthermal Neutrino Induced Doppler broadening experiments
velocities.ThiscanbeobservedinFig.5.Insomecases usingEucompoundsastargets.Exceptfortheproblems
one finds atoms that perform either linear oscillations associated with Auger cascades, a good understanding
while other perform quasi-circular orbits around their of the slowing down process at kinetic energies around
equilibriumpositions.Inordertoreducethisdisturbing 3eVwasobtainedwiththeMolecularDynamicssimu-
effect, which obscures the helicity measurement, the lations. Moreover, the lifetime of the 963keV state in
temperature should be reduced drastically. A spread of 152Sm could be determined to be (28.7(cid:10)1.0)fs. This
(cid:13)(0) of 1(cid:15) corresponds for instance to a (cid:4) of 34m/s knowledgewasthenusedtostudytheroˆleoftheslowing
T
occuring at 7(cid:15)K. This is clearly not attainable at an down and the temperature on the measurement of the
in-pile source. neutrino helicity. We found important effects which
AtthisstageonemightwonderhowGoldhaberetal. needtobeconsideredindetailifonewantstoobtaina
[8]wereabletoreachdefiniteconclusionsintheirwork. precise measurement of the helicity. We consider that
Besidesthefactthattheyhadonlytoshowaneffect,it nowalldataneededforafullMonteCarlosimulationof
should be remembered that they relied on difference the experiment proposed in [7] are available.
measurementsandvariedthecompositionofthetarget.
The slowing down only affects the information on the
Acknowledgments
neutrino momentum independent from the one on the
neutrino spin. The measurement of the difference in ThisworkwassupportedbytheSwissNationalScience
circular polarisation allowed than the elimination of Foundation. The experimental part of this work was
grosseffectsconnectedtotheslowingdownortemper- doneincollaborationwithH.G.Bo¨rner,S.J.Robinson,
ature. Nevertheless, for a very precise measurement P. Schillebeeckx, Ch. Doll, R. D. Deslattes, G. L.
these effect become dominant. Greene, M. S. Dewey, A. Williams and the theoretical
part with M. Jentschel, A. Kuronen, and J. Keinonen.
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Volume105,Number1,January–February2000
Journal of Research of the National Institute of Standards and Technology
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