High‐resolution wavelength‐dispersive spectroscopy of K‐shell transitions in hydrogen‐like gold

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High-resolution wavelength-dispersive spectroscopy of K-shell transitions in hydrogen-like gold

T. Gassner, A. Gumberidze, M. Trassinelli, R. Heß, U. Spillmann, D. Banaś, K.-h. Blumenhagen, F. Bosch, C. Brandau, W. Chen, et al.

To cite this version:

T. Gassner, A. Gumberidze, M. Trassinelli, R. Heß, U. Spillmann, et al.. High-resolution wavelength- dispersive spectroscopy of K-shell transitions in hydrogen-like gold. X-Ray Spectrometry, Wiley, 2019,

�10.1002/xrs.3098�. �hal-02362557�

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DOI:xxx/xxxx

ARTICLE TYPE

High-resolution Wavelength-dispersive Spetrosopy of

K-shell Transitions in Hydrogen-like Gold

T. Gassner 1,2

| A. Gumberidze*

2

| M. Trassinelli 3

| R.Heÿ 2

| U. Spillmann 1,2

| D.

Bana±

4

| K.-H. Blumenhagen 1

| F. Bosh‡² ^| ^C. ^Brandau^2,5 ^| ^W. ^Chen² ^| ^Chr.

Dimopoulou 2

| E.Förster 1,6

| R.E. Grisenti 2,7

| S. Hagmann 2,7

| P.-M. Hillenbrand 2

| P.

Indeliato 8

| P.Jagodzinski 9

| T. Kämpfer 1

| M. Lestinsky 2

| D. Liesen 2,10

| Yu.A.

Litvinov 2

| R.Loetzsh 1,6

| B. Manil 11

| R. Märtin 1

| F. Nolden 2

| N. Petridis 2,7

| M. S.

Sanjari 2

| K.S. Shulze 1,6

| M. Shwemlein 1

| A.Simionovii 12

| M. Stek 2

| Th.

Stöhlker 1,2,6

| C. I. Szabo 8,13

| S.Trotsenko 1,2

| I. Ushmann 1,6

| G.Weber 1

| O.

Wehrhan 1

| N. Winkler 2

| D.F.A. Winters 2

| N. Winters 2

| E.Ziegler 14

| H.F. Beyer 2

1

Helmholtz-InstitutJena,Jena,

Germany

2

GSIHelmholtzzentrumfür

Shwerionenforshung,Darmstadt,

Germany

3

INSP,CNRSandSU,Paris,Frane

4

InstituteofPhysis,JanKohanowski

University,Kiele,Poland

5

PhysikalishesInstitut,

Justus-Liebig-Universität,Gieÿen,

Germany

6

IOQ,FSU,Jena,Germany

7

IKF,Goethe-Universität,Frankfurt

amMain,Germany

8

LKB,CNRS-UMR8552,Collègede

Frane,ENS-PSLResearh

University,SU,UPMC,Paris,Frane

9

DepartmentofMathematisand

Physis,KieleUniversityof

Tehnology,Kiele,Poland

10

FakultätfürPhysikundAstronomie,

Rupreht-Karls-Universität,

Heidelberg,Germany

11

LPL,UMR7538CNRS-Université

Paris13,Villetaneuse,Frane

12

ISTerre,UGA,CNRS,CS40700,

Grenoble,Frane

13

TheissResearh,LaJolla,CA

92037,UnitedStates

14

ESRF,Grenoble,Frane

Correspondene

Email:a.gumberidzegsi.de

Abstrat

We present a measurement of K-shell transitions in H-like gold (Au

78+

)

usingspeiallydevelopedtransmission typerystalspetrometersombined

with Ge(i) miro-strip detetors. The experiment has been arried out at

theExperimental Storage Ring (ESR) at GSI in Darmstadt.This isa rst

high-resolutionwavelength-dispersivemeasurementofaK-shelltransitionin

ahigh-Z H-like ion, thus representing an importantmilestone in this eld.

Ideasonpossiblefuture improvementsaredisussedaswell.

KEYWORDS:

Storagerings,X-rayspetrosopy,Highly-hargedions,QED

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1 INTRODUCTION

Preise measurementsofatomi strutureand transitionshaveprovidedthroughout manyyearsadrivingfore for

developingthefundamentaltheoriesinphysis.Inpartiular,thedisoveryoftheLambshiftinhydrogenhasplayed

amajorroleinthedevelopmentofthequantumeletrodynamis(QED).Nowadays,themeasurementsonhydrogen

and lightatoms ahieveanextraordinarypreisionof upto 10

−15

whih isoftenmathedby theQEDalulations

emphasizingitsimpressivepreditingpower[13,28,18,24,12,23℄.

Thesituationisquitedierentintherealmofheavyhydrogen-likesystems,i.e.heavyionswithonlyoneeletron.

Here,bothexperimental andtheoretial preisionare still orders ofmagnitude lowerthan thoseavailable forlight

atoms. On thetheoretial side, themain hallenge isrelated to thefat that sinetheparameter αZ ∼1 ^one ^an

not use perturbative methods (as for light atoms) and one has to perform all-order numerialalulations in the

relativistiframework.Ontheexperimentside,thehallengesare:rstly,theprodutionoftheheavyH-likeionsin

suientquantities andthen storingthemwith properqualityfor preisemeasurements. Furthermore,thebinding

energies of suh heavyH-like ions are of the order of several 10s of keV up to 100keV. Therefore, instead of the

laserspetrosopytehniquesusedforthelightsystems,herex-rayspetrosopyhasbeenusedthroughouttheyears

[11,10, 9,25,4,6℄,exeptforhypernetransitions [20,21,27℄.

Heavy-ion aelerators and storage rings as well asnew generation ion traps have been the failities where H-,

He- andLi-likeions withhighestnulear hargesupto Z=92 havebeenmadeavailable forpreisionexperiments

[8,22,2,7,26,16, 1℄.

For the ase of the ground state Lamb shift in high-Z H-like systems, where the strongest Coulomb elds an

be obtained and thus QED eets are strongest, the spetrosopy was until reently onduted with solid state

Ge(i) detetorsensuringahighdetetioneieny.Therst-orderQED ontributions(the selfenergyandvauum

polarization) havebeentested at the level of 1%. However,theurrentexperimental preision is still notenough

to testthehigher-orderQEDeets, whoseevaluationshavebeenreentlyompletedafter manyyearsofextensive

theoretialwork(see[29℄andreferenestherein).Inordertogainthesensitivitytothehigher-orderQEDeets,the

experimentalunertaintyofthe1sLambshifthastobereduedbelow1eV.Oneofthemainlimitationshereisdue

to theenergyresolution oftheonventional semiondutordetetorsused in theseexperiments.Toirumventthis

problem, dediated rystalspetrometers togetherwithmiro-stripGe(i) detetorshavebeendeveloped, optimized

forhardx-rayspetrosopyatstoragerings.Inthiswork,wepresentthersthigh-statistismeasurementusingthis

instrument at the Experimental Storage Ring (ESR) at GSI in Darmstadt. The measurement was arried out for

H-likegold(Au

78+

).

2 THE EXPERIMENT

Thedetaileddesriptionoftheexperimentanbefoundin[5,14℄.Briey,upto10

8

offullyionizedgoldions(Au

79+

)

with aninitial kinetienergyof about300MeV/uwereinjeted into theESR. Here,theywerestored, ooled, and

deeleratedto nalveloityofβ =vion/c= 0.47136(10)^.^Theôoledîon^beam^was^thenôlliding^withâ^supersoni

gasjetofKrypton atomshavinganarealdensityof∼10¹²âtoms/m²^.^Someôf^theôllisions^lead^to ^theâpture ôf

thetargeteletronintoanexitedstateoftheprojetileion,thusformingtheH-likegold.Theseexitedstatesthen

deay to theground-stateleading (amongothers) to theemission of the Lyman-α^radiation ^whih ^is ^measured^by

ourspetrometers.

Forthe measurementofthe Ly-α1 ^transition wavelength, twotwin spetrometersoperatedinthe foussingom- pensated Laue(FOCAL)geometry havebeenused [5℄. Theshematisof theFOCAL setupat thegasjettarget of

theESRisshowninFig.1.

One of the main hallenges for preision spetrosopy of relativisti ions is the Doppler eet. In the urrent

experiment, thetwoidential rystalspetrometer armsarealignedperpendiular withrespet to theionbeamat

‡^Deeased^16.12.2016

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Motivation

Lamb shift in H-like Gold

FIGURE 1ShemativiewoftheFOCALsetupatthegasjettargetoftheESR. Thetwospetrometerarmswith

leadshieldingareshowninblueaswellasthereetedx-raypathinredimpingingontheGe(i)miro-stripdetetor.

both sides of the interation hamberon one ommon line of sight. In this speial geometry rest-frame transition

wavelengthλ0 ^an^be^derived^via

λ1+λ2= 2γ λ0, ⁽¹⁾

where λ1,2 âre^the wavelengths measuredbythe tworystalspetrometerarms andγ îs^Lorentz ^fator^. În ^this

way,theunertaintyduetotheobservationanglestemmingfromthepossiblemisalignmentofthebeamisanelled.

The wavelengths λ1,2 âre ^measured ^with ^respet ^to â ^well ^known 63120.44(4) eV γ ^transition ^from ân îsotope

enrihed

169

Ybsoure.Theion-beamveloityhasbeenhosensuh(β= 0.47136(10)^),^that^theDoppler-shiftedlab- frame energyoftheLy-α1 ^transition approximatelyoinideswith this alibrationenergythusavoidingsystemati unertaintiesduetolargeextrapolations.

3 RESULTS

Our experimental value for the Lyman-α1 ^transition ênergy ⁱⁿ ^H-like ^gold îs E_Lyêxp_α₁ = 71531.5(15.0)êV ^[14℄. ^The

unertaintyof15eVinludesallthestatistialandsystematiunertainties(addedquadratially).Theexperimental

value for the 1s Lamb shift is obtained by subtrating our value for the Lyman-α1 ^transition ^energy ^from ^the

theoretialvalueforthe2p3/2^bindingênergy,^whihîs^suiently^well^known^[29℄.În^Table^1,ôurexperimentalresult for the ground-state Lamb shift in H-like gold is presented together with the experimental value obtained with a

Ge(i)detetorinanearlyexperimentattheESReletronooler[3℄andtheresultobtainedwithamiroalorimeter

detetorinthesamebeamtime[19℄.Inthelastentryofthetable,thetheoretialvalueofYerokhinandShabaev[29℄

isgiven.OurpresentvalueoftheLambshiftishigherthanthetheoretialvalueandtheotherexperimentalresults

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TABLE 1The1s^Lamb^shiftôfÂu⁷⁸⁺ ⁱⁿêV.

Ourresult 244.1(15.0)

Beyeretal.1995[3℄ 202.3(7.9)

Kraft-Bermuthetal.2017[19℄ 211(42)

Theory,YerokhinandShabaev2015[29℄ 205.2(2)

TABLE 2DierentontributionstothetotaluertaintyoftheLyman-α1^transition^energy.

Soure Value(eV)

Statistis 2.2

TemporalDrift 2.8

Gas-TargetPosition 13.0

Ion-BeamVeloity 4.3

Detetor-CrystalPosition 5.1

Total 15.0

4 EXPERIMENTALUNCERTAINTIESAND POSSIBLE FUTUREIMPROVEMENTS

Intable2,varioussouresofunertaintiesforourmeasuredvalueofthetransitionenergyarepresented.Theahieved

statistialunertaintyof2.2eVisalreadyquiteimpressive,espeiallyforarystalspetrometeroperatedintheregion

of hard xraysof H-likehigh-Z ions. However,it is still at leastfator of 2higher thanwhat is needed to test the

higher-orderQEDeets.Furthermore,thesystematiunertaintiesduetothetargetanddetetorrystalpositions

aswellasthosedue tobeamveloityandthetemporaldriftofthewholesetupareunaeptablyhigh.

Inthefollowing,webrieypresentfewideasonhowto reduetheseunertainties.

Statistis: here, a further inrease of the stored beam intensity in the ESR ould be possible. In addition, four

detetors, instead of the two used in the present measurement and with bigger areas overing fully all the

reexesoftheFOCALspetrometerwouldleadtosigniantinreaseinthestatistis.

Temporal drift: here,by using arigidsupport struture (withsteel and granite)mounted severalmonths before

themeasurementalongwithtemperatureontrols, weouldexpetasigniantimprovement.

Beam veloity: theion-beamveloityanalreadybedeterminedwithamuhhigheraurayusingahigh-voltage

dividerfromthePhysikalish-TehnisheBundesanstalt(PTB)intheeletron-oolerterminal,whihwillestab-

lishanabsolutelyalibratedveloitystandard[17℄.Here,weexpetarelativeunertaintyinthemeasurement

oftheoolervoltagewellbelow10

−4

andthustheresultingontributiontotheerrorbudgetoflessthan1eV.

Targetand rystal positions: theserepresenturrentlythebiggestontributiontothesystematiunertaintyand

probablymosthallengingtoredue totheneededlevel.Intheurrentexperiment,thosepositionshavebeen

measuredseparately withatelesopeandspeialalignmentdevies [15,14℄. Here,oneof theideasis tousea

modiedassemblymakingitpossibletomeasurethegastargetpositionrelativetothedetetorrystalinsitu,

whihwouldeliminatetheneedof usingthetelesopeandthuswould reduetheunertaintytoloseto1eV.

Anotherpossibilitywouldbetousethetwospetrometerstiltedby90degreeswithrespettoeahother,thus

resultingintheperpendiulardispersionplanesofthetwospetrometerarms.Thisarrangementtogetherwith

usingfour detetorsinsteadof twohasapotentialof reduingthissystematiunertaintyto thelevelof 0.1

eV.However,heremorestudiesandsimulationsareneededwhihareurrentlyongoing.Here,wewouldliketo

addthat thistopihasalsobeenintensivelydisussedreentlybyinternationalexpertsattheso-alledEMMI

RapidReationTask Forewhih took plae in September2018(https://indio.gsi.de/event/7662/overview).

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ACKNOWLEDGEMENTS

Laboratoire Kastler Brossel (LKB) is Unité Mixte de Reherhe de Sorbonne University-UPMC, de ENS-PSL

ResearhUniversity,duColl¨gedeFraneetduCNRSn

◦

8552.InstitutdesNanoSienesdeParis(INSP)isUnité

Mixte deReherhedeSorbonneUniversity-UPMCet duCNRS n

◦

7588. This work hasbeen partiallysupported

by:theEuropeanCommunityFP7- Capaities,ontratENSARn

◦

262010,theAllianzProgramoftheHelmholtz

Assoiationontratn

◦

EMMIHA-216ExtremesofDensityandTemperature:CosmiMatterintheLaboratory,the

Helmholtz-CASJointResearhGroupHCJRG-108andbytheGermanMinistryofEduationandResearh(BMBF)

under ontrat05P15RGFAA.

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