Exp eriments on exotic

sp ectroscopy

D Gotta

Institut fur Kernphysik Forschungszentrum Julic h D Julic h

Germany

Abstract Results are reviewed from recent exotic atom exp eriments

using a fo cussing Bragg sp ectrometer The measured energies of the

L Xrays from antiprotonic and deuterium and the K

transition from pionic deuterium are compared to the transition ener

gies as calculated from quantum electro dynamics in order to determine

the and nucleon scattering

parameters at threshold A high precision exp eriment to determine

the mass of the charged pion to ppm has b een started by investigat

ing the transitions in pionic nitrogen where the o ccurance of Coulomb

explosion has b een seen now directly from the Doppler broadening In

a forthcoming high precision exp eriment of the pionnucleon scatter

ing length new calibration metho ds using an ECR source will b e used

to connect energy standards b oth from exotic and electronic

Such techniques oer the p ossibility of high precision studies in few

systems

Intro duction

Atoms in which the electron shell is replaced partly or in total by other

elementary of negative charge are called exotic atoms Up to now

the systems with and sigma hyp erons

have b een established Muonic and pionic atoms are b eing investigated

since years at the factories of the PaulScherrerInstitut PSI TRI

UMF or earlier at LAMPF At CERN in the years until the

LowEnergyAntiprotonRing LEAR provided highquality lowenergy an

tiproton b eams which were esp ecially suited for stop exp eriments and thus

for the formation of antiprotonic atoms

Normally the observables in the Xray sp ectroscopy of exotic atoms are

the energies and the intensities of the radiation which is emitted during the

deexcitation of the atomic system From the line intensities conclusions are

drawn b oth for the capture pro cess and the interaction with the remaining

part of the electron cloud and pro cesses originating from the interaction

with neighb ouring target atoms during the rst steps of the atomic cas

cade In the lower part of the cascade the exotic atom can b e prepared as

a hydrogenlike system when suitable exp erimental conditions are chosen

Such hydrogenlike atoms may then serve as a testing ground for the calcula

tions of transition energies and to investigate the prop erties of the captured

itself At smaller distances ie for the lowlying states the in

uence of the nite nuclear size on the binding energy increases and for

strongly interacting particles the eects of the nuclear forces b ecome more

and more visible Of sp ecial interest are the elementary systems formed with

the hydrogen isotop es to study the strong pion and antiprotonnucleon in

teraction at threshold Thus the Xray sp ectroscopy of exotic atoms oers

access to a large variety of problems

The precise calculation of the binding energies has to use the relativistic

description as given by the Dirac or the KleinGordon formula and in addi

tion has to include the contributions of quantum electro dynamics QED

relativistic recoil corrections and p olarisation eects Due to the large mass

of the orbiting particle the predominant QED contribution in exotic atoms

is vacuum p olarisation in contrast to self energy as in the case of electronic

atoms

Highest energy resolution for Xrays in the few keV range is achievable

only with crystal sp ectrometers which however on principle are devices of

low eciency Although high uxes are reached in the b eam lines of the

meson factories the exp erimental challenge is to achieve a high resolution

together with sucient count rates as well as to achieve stable conditions

for the nevertheless unavoidable long measuring p erio ds It is essential to

use the particle ux provided by the accelerator in an optimal way and to

maximize b oth the line yields of the Xray transitions and the detection

ecieny up to the theoretical limits

In particular for the atoms formed with the hydrogen isotop es high

line yields can b e obtained only with gas targets A crystal sp ectrometer

however requires a small and bright Xray source which cannot b e achieved

with the usual linear setup to stop the b eam Sucient stop densities are

available if for degrading and stopping of the b eam the cyclotron trap is

used For such exp eriments with low counting rates an ecient background

suppression is essential It is achieved by the use of ChargeCoupledDevices

CCDs as Xray detectors Figure

Formation and atomic cascade of exotic atoms

After slowing down to a kinetic energy of a few eV negatively charged par

ticles are captured in the Coulomb eld of atoms into highly excited atomic

levels by the emission of The depletion of the electron cloud pro

ceeds shell by shell by continued emission of Auger electrons as so on as

the energy dierence b etween two exotic atom levels exceeds the ionisation

energy Thus the lighter exotic atoms in the end b ecome hydrogenlike

systems provided no electron relling o ccurs as is the case for dense or solid

targets In the lower part of the atomic cascade the deexcitation by

emission of Xray quanta dominates even in the presence of electrons

The dimensions of exotic atoms are obtained by replacing the electrons

mass in the expression for the Rydb erg energy by the reduced mass m of

r ed

the particlenucleus system During the last steps of the atomic cascade the

extensions of exotic atoms are already closer to nuclear dimensions than to

the atomic scale There in the case of the electromagnetic deexci

tation then has to comp ete with channels op ened by the strong interaction

A detailed discussion of the atomic cascade may b e found in

Exotic hydrogen o ccupies a sp ecial p osition regarding the interaction

with the target material It is electrically neutral and therefore can easily

p enetrate the Coulomb eld of neighb ouring atoms This leads to a drastic

reduction of the Xray yields in pionic and antiprotonic hydrogen Day

SnowSuchereect b ecause in the high angular momentum states

now s and pwave contributions are induced and in hadronic atoms an

admixture of s or pwaves leads with high probability to annihilation For

atomic levels with large n the Stark mixing prevails all other internal and

external deexcitation pro cesses Hence for hydrogen the use of low pressure

gas targets is indisp ensible to achieve high Xray yields

Exp eriment

Cyclotron trap and Xray source

A fo cussing Bragg crystal sp ectrometer requires a small and bright Xray

source having an extension matched as go o d as p ossible to the extension

of the line pattern to b e observed Such conditions are achieved when the

cyclotron trap is used a device which was designed to obtain high stop

densities with pion and antiproton b eams The range

curve of the b eam is wound up in a magnetic eld with fo cussing prop erties

which is pro duced by two sup erconducting coils Between the coils the

target chamb er is installed containing a suitable degrader arrangement and

the target gas The particles lo ose kinetic energy rst in the degraders and

in the target gas itself thus approaching the center of the magnet on spiral

3

orbits and nally are stopp ed in a volume of a few cm even at low gas

pressures

Crystal sp ectrometer

For Xradiation with energies b elow keV b ecause of the absorption losses

reection typ e crystal sp ectrometers are used The Xrays are scattered at

the electrons of atoms arranged regularly in lattice planes having the dis

tance d According to Braggs law n dsin a coherent sup erp osition

B

for one wave length o ccurs only at the Bragg angles where n is the

B

order of reection The width of the angular distribution of a parallel b eam

ro cking curve width reected from a plane crystal yields consequently the

theoretical limit for the energy resolution It is given only by the intrinsic

prop erties of the material and the wave length Usually quartz or silicon

crystals are used which b ehave like ideal crystals The intrinsic prop er

ties can b e calculated from the dynamical theory to one p er cent or b etter

except in the close vicinity of absorption edges

For the investigation of broad Xray lines or multiplets horizontally b ent

crystals are of great advantage Johann geometry b ecause here an energy

interval according to the width of the source can b e recorded simultaneously

with twodimensional p ositionsensitive detectors Thus an acceptable

duration of measuring p erio ds of a few days p er transition b ecomes p ossible

To achieve in addition partial vertical fo cussing spherically b ent crystals

were used The reduced height of the image then allows the ecient

use of the rather small pixel detectors like CCDs

6

An accuracy of up to is aimed at for the energy measurement in the

describ ed exp eriments which requires an energy resolution of the order of

4

Such values are reached in the few keV range with quartz and silicon

crystals having b ending radii of ab out m and Bragg angles larger than

4

degrees where the geometrical abb eration accounts at maximum to

and hence do es not ab olish the intrinsic resolution of the crystal lattice

6

The overall eciency of such a sp ectrometer is ab out for crystal areas

2

of cm

CCDs are the optimal detectors for recording Xrays in a high back

ground environment b ecause of their distinguished twodimensional p osi

tion resolution together with an excellent energy resolution E eV

at keV Because the charge pro duced by one Xray is dep osited

in one or two pixels only and particle or Comptoninduced events pro duce

larger clusters the pixel structure allows by analysing the hit pattern an

almost complete separation of Xray and background events Thus for the

long measuring p erio ds an ecient background suppression is obtained

Figure Setup of cyclotron trap crystal sp ectrometer and CCD detector

for the pion mass exp eriment at PSI from The massive concrete

shielding is essential to suppress the induced background

Absolute calibration

The precision envisaged requires an energy calibration and a determination

of the sp ectrometer resolution function at a high level In practise b oth

uorescence Xrays Table and exotic Xray transitions Tables and

must b e used up to now Narrow nuclear rays with sucient yields are

not available in the few keV range for practical cases

Fluorescence Xrays excited by means of an Xray tub e are always at

disp osal The precise adjustment of the Bragg angle and the accumula

tion of sp ectra with high statistics can b e p erformed within a short time

and tests of stability are p ossible without signicant losses of b eam time

From those elements where the line shap es have b een determined precisely

energy calibrations can b e obtained The large natural line width how

ever do es not allow the determination of the resolution of the sp ectrometer

with sucient accuracy An even more severe problem is to asso ciate with

the p osition of a uorescence line a wave length b ecause of the presence of

satellite transitions originating from multiple ionisation

Though b eam time consuming transitions of completely ionised exotic

atoms are ideal calibration lines The atomic levels must not b e aected

by the strong interaction or the presence of remaining electrons in order to

make use of the precise results from the QED calculations The natural line

Table Energies E and natural line widths of K uorescence Xrays

X X

in eV

K K

2 1

E E

X X X X

Si    

S    

Cl    

Sc 

Cu  

Si S and Cl Sc Cu

widths are of the order of a few meV only and therefore can b e neglected

compared to the typical resolution of a few meV of the sp ectrometer

The resolution functions are obtained from such narrow transitions having

energies as close as p ossible to the measured transitions Unfortunately

not in all cases a calibration line from an exotic atom with an energy close

enough is available to serve also as an energy calibration

The absolute energy is determined from the Bragg angle dierence to an

Xray line of known energy The angle dierence according to the rotation

of the crystals is measured with a precision absolute angular enco der having

an accuracy of  seconds of arc or ppm for small angle dierences

The total dierence of the Bragg angle for two lines is given by the values

obtained from the angular enco der and the p ositions of transitions as mea

sured at the CCD detectors In general some small corrections for the

index of refraction the b ending and the p enetration depth in the crystal

have to b e applied in order to obtain the nal value for the Bragg angle and

from that for the transition energy see also

Antiprotonic hydrogen and deuterium

The hadronic part of the antinucleonnucleus p otential causes an energy

shift of the atomic levels as determined by the pure Coulomb interaction

Furthermore the o ccurance of annihilation reduces the life time of low

lying atomic states leading to an additional level broadening Shift and

broadening are related to the complex scattering lengths of the nucleus

particle system The sp ectroscopy of hadronic atoms therefore

is equivalent to a scattering exp eriment directly at threshold The strong

interaction shift and broadening of the p levels in antiprotonic hydrogen

and deuterium was directly measured by LEAR exp eriment PS

Electromagnetic level energies and hyp erne structure

The mean L transition energy without the inuence of the strong interac

tion has b een calculated by Barmo Pilkuhn and Schlaile Borie

and recently by Boucard and Indelicato yielding slightly dierent values

Table For the hyp erne splittings however the results deviate signi

cantly Table The origin of these discrepancies is supp osed to stem from

the treatment of the g corrections

Table Calculated electromagnetic transition energies of the antiprotonic

lines in eV The values corresp ond to the center of of the corre

sp onding ne or hyp erne structure multiplets

3 20

p Hegf pHdp pDdp p Neon ref

In light antiprotonic atoms the masses of the nucleus and the orbiting

particle are almost equal and therefore also are the magnetic moments

Hence for the hydrogen isotop es b oth the ne and the hyp erne structure

2

splitting is of the order E  E  B Owing to the large mass

FS HFS 1

the recoil corrections due to the anomalous magnetic moment of the

and antiproton are signicant Therefore for example the level ordering

in is no longer the same as in the analogue system p ositronium

Because of the complex multiplet structure the extraction of hadronic

parameters demands the precise knowledge of the electromagnetic hyp erne

splitting The L line consists altogether of transitions in the case of

hydrogen and of transitions for deuterium Because of the rather small

splitting of the d levels as compared to the p levels the line shap e of the

dp transition yields already the p level structure in go o d approximation

Nuclear p olarisation

The electric force induces a dip ole in the extended charge distributions

b oth in the orbiting particle and in the nucleus In light atoms the en

ergy shifts of the p and higher levels caused by the p olarisation of pions

and antiprotons usually are meV or less and hence far b elow the exp eri

mental accuracy Only for deuterium due to its large quadrup ole moment

the p olarisation shift E in the p level reaches already sizeable values

pol

3

Following the approach of and using D fm for the p olar

pol

Table Predictions for the electromagnetic hyp erne splittings of the p

2S +1

und d levels notation n L in hydrogen and deuterium in meV The

F

spin factor w FF corresp onds to a statistical p opulation of

the sublevels A p ositive sign of the electromagnetic shift B stands

QE D

for a more strongly b ound atomic level

HFS w B B HFS w B B

QE D QE D QE D QE D

pH

3 3

P D

2 3

3 3

D P

2 1

1 1

P D

1 2

3 3

P D

0 1

pD

4 4

P D

52 72

2 4

D P

52 32

2 4

P D

32 52

4 2

P D

12 32

2 4

P D

12 32

4

D

12

isibility of the deuterons a change of E meV is calculated

pol

for the dp transition energy

Interaction with the external magnetic eld

The static magnetic interaction energy B of a nuclear magneton in

N cy c

the external eld of the cyclotron trap of ab out T amounts to neV

which is ppm of the p hyp erne splitting Also the movement of the

antiprotonic atom induces only a negligibly small electric eld E v B

cy c

motional Stark eect when compared to the strength of the internal eld

6

Assuming a velo city of v cms corresp onding to a kinetic energy of

6

eV for the antiprotonic atom an electric eld strength of E  

Vm results The strength of the internal Coulomb eld however reaches

11

values of Vm already at radii corresp onding to n

Results for the p multiplet in antiprotonic hydrogen

The measurement of the hadronic parameters of the p state tests explicitely

the long range part of the antinucleonnucleon interaction Using the

L transition antiprotonic hydrogen oers the unique p ossibility to prepare

the antiprotonproton system in a pure pwave state Almost of the

antiprotons reaching the p level annihilate there as seen from the large

spinaveraged p level broadening of  meV which has b een de

termined earlier from the intensity balance of the total Balmer series to

the Lyman transition In gaseous targets annihilation at rest o c

curs mainly from the atomic p states b ecause of the reduced Stark mixing

The fraction of absorption from the d level is predicted to b e

only This is in agreement with the nonobservation of hadronic eects

which should show up in the line yields of the Balmer series for hydrogen

or deuterium Therefore the p hyp erne levels are assumed to b e

p opulated according to their statistical weight

The line prole of the dp transition in antiprotonic hydrogen exhibits

3

a shoulder at the high energy side Figure It is interpreted as the P

0

hyp erne state b ecause its relative intensity obtained to  in a

free t to the line prole is in go o d agreement with the statistical p opula

3

tion of for the P level Table The main part of the line consists

0

3 3 1

of the not resolved comp onents P P P

2 1 1

3

The P state plays a particular role Its shift and broadening is

0

predicted to ab out meV which is veried by the exp eriment yielding

 meV when the result from the recent QED calculation is

3

used Such large hadronic eects in the P state are mandatory for

0

the mesonexchange mo del from which the real part of the antinucleon

nucleon p otential is derived The value obtained for the spin

3 3 1

averaged shift of the group P P P is compatible with zero and the

2 1 1

spinaveraged broadening is of the order of the spinaveraged width as pre

dicted Obviously the level structure originating from the real part

of the hadronic p otential is not destroyed by the very fast annihilation

The exp erimental results are considered as strong supp ort for the validity

of the mesonexchange mo dels to describ e the longrange real part of the

lowenergy antinucleonnucleon interaction

Results for the p multiplet in antiprotonic deuterium

In antiprotonic deuterium at present the only p ossibility to determine any

hadronic eects is a direct measurement of the the plevel width and broad

ening Because of the more frequent annihilation from p levels as compared

to antiprotonic hydrogen the observation of the transitions to the atomic

remains doubtful b ecause of the smaller line yields of the Ly

man series and the increased hadronic broadening of the s level

The two results for the QED hyp erne splitting dier considerably Ta

ble Barmo et al predict that the hyp erne splitting in the p level

is dominated by the electromagnetic interaction Therefore the dp

Figure Line shap es of the L transitions in antiprotonic hydrogen and

deuterium and corresp onding antiprotonic calibration transitions

line shap e should form approximately a doublet structure from the groups

4 4 4 4 2

P P P and P P showing a small tail to the high en

32 12 12 52 32

2

ergy side stemming from the P state

12

The measured line shap e do es not show any evidence for such a dou

blet structure Figure The calculation of Boucard and Indelicato yields

a much smaller hyp erne splitting which allows to treat the whole

multiplet as a single line only in comparison with the exp erimental res

olution The numerical results from the single line t are indistinguish

able within the exp erimental errors from the results from a t forcing

the hyp erne pattern as given by Boucard and Indelicato With that

for the spinaveraged hadronic shift and broadening  meV

2p

and  meV is obtained The annihilation width is found

2p

ab out smaller than in the previous analysis The shift is negative

ie the interaction is repulsive as predicted For the spinaveraged broad

ening the multiple scattering ansatz of Wycech Green and Niskanen yields

ab out meV in go o d agreement with the exp erimental result whereas

the magnitude of the shift is underestimated by a factor of

Mass of the charged pion

The motivation for an improved pion mass measurement reaching an ac

curacy of at least ppm arises from several asp ects Future muon neu

trino mass measurements should b e able to improve their sensitivity from

2 2

keVc to b elow keVc Theoretical considerations using the Stan

dard Mo del as well as all p opular classes of theories which go b eyond the

Standard Mo del and take into account cosmological b ounds reduce con

siderably the range of p ossible mass values It was shown eg that the

2

mass of the muon is either  keVc for unstable or

2

 eVc for stable neutrinos contributing to the density of the

universe within the cosmological b ound

The recent highly sensitive search for Antimuonium M M

conversion aiming at an improvement in sensitivity by an order of

3

magnitude to ab out for G G would together with a factor of



F

M M

almost two for a reduced upp er limit of the mass exclude a

certain typ e of theories extending the Standard Mo del

The exp erimental accuracy for the hadronic s level shift in pionic hy

drogen obtained in an earlier crystal sp ectrometer measurement was meV

for the statistical and meV for the systematical error The error orig

inating from the uncertainty of the pion mass already accounts for meV

The systematical error stems mainly from the limited precision of the cali

bration line and the lattice constant of the Bragg crystal Such systematical

errors could b e reduced signicantly in future indep endent measurements

In order to avoid the problems inherent to energy calibrations using

uorescence Xrays or screening eects from the remaining electrons it

is prop osed to obtain the absolute calibration from a muonic transition of

almost equal energy as a pionic one The exp eriment uses the fact that

the p ositive muon mass is known to an accuracy of ppm and assumes

CPT invariance The requirement to measure the same transition in terms

of quantum numb ers and the request to use gas targets at pressures of

ab out bar led to the pair pionic nitrogen and muonic oxygen and the

transitions Table The natural line widths of meV are negligible

as compared to the exp erimental resolution of ab out meV Because of

the small energy dierence the crystal sp ectrometer can b e set up without

movable parts b etween crystal and detector which excludes any systematic

errors from the adjustment of the Bragg angle

A feasibility study was p erformed with the Ngf transition using

the cyclotron trap I and the Cu K uorescence line as the energy calibra

1

tion Figure The ambiguity of ppm of a previous measurement

with the Mggf transition could b e removed There a solid state tar

get was used The ambiguity was due to the numb er of K electrons

Table Calculated electromagnetic transition energies in eV of muonic

and pionic Xray lines from

20 16 14 20

Dps Neih Og f Ngf Nehg

92 72

present at the time of emission of the Xray The result of Lenz et al

2

for the mass of the charged pion is m  MeVc b eing

ppm larger than the result B K electrons of Jeckelmann et al

The ab ovementioned value is also consistent with the limits extracted

from the muon neutrino mass measurements

Figure Measured line shap es of the Ngf transition and the Cu K

uorescence line The parameters for the line shap e of the Cu K

transition have b een taken from

Cascade calculations based on the co de of Akylas and Vogel predict

for nitrogen a probability of less than at a pressure of bar for one

remaining K electron when the pion or muon reaches the n level which

could b e veried as an upp er limit by the feasibility study

In the forthcoming nal measurement the source of Xrays emitted by

the exotic atoms will b e formed by stopping the pion b eam in the new

cyclotron trap ZF I I The muons originate from pion decay inside the

target chamb er With the new trap a sucently high stop density also for

the decay muons has b een achieved recently

Test of the KleinGordon equation

14

The energy dierence b etween the circular transition Ngf and the

14

next inner parallel transition Nfd Figure was measured by Lenz

et al to Egf fd  meV The precision achieved

exceeds the one of earlier tests of the KleinGordon equation by Delker et

al by a factor of ab out A recent QED calculation of Boucard and

Indelicato yielded in go o d agreement meV

Direct observation of Coulomb explosion

The observed line width of ab out meV FWHM of the N Figure or

the O g f transition is a factor larger than exp ected from the resolution

of the sp ectrometer First checks assumed distorted crystal material

which however is not sucient to explain such a broadening On the other

hand for diatomic like N or O a signicant Doppler broadening

2 2

originating from Coulomb explosion cannot b e excluded Here the N

system gains kinetic energy when after Auger emission of several electrons

the binding of the molecular system N breaks and the two fragments of

2

almost equal mass are accelerated by the Coulomb force Evidence for such

an eect has b een deduced earlier from the dierent pressure dep endence

of the K Xray line yields of pionic nitrogen and neon

A measurement of the Nehg transition Table has b een p er

formed in order to test such a hyp othesis b ecause the width of that re

ection is only due to the exp erimental resp onse function The Ne line

of meV is signicantly narrower than the N and O transitions and

therefore the large widths of the latter are assumed to originate from

Coulomb explosion The measured additional width of the pionic g

f transition amounts to meV dep ending on the details for the

assumptions of the line shap e of the resolution function It corresp onds

to a kinetic energy of the N system of eV Assuming that the

decomp oses at distances comparable to the molecular b ond length

8

of  cm at the time of separation for the pro duct of the charges

q q  is obtained Consequently the range of charge states at the

1 2

time of explosion is to which corresp onds to the removal of

electrons from the N molecule Separation distances of ab out molecular

2

b ond length as observed in the slow laser induced Coulomb explosion

can b e excluded b ecause a value of q q cannot b e reached for

1 2

nitrogen and oxygen

Pionic hydrogen

The description of the pionnucleon interaction in the connement region is

considered as a fundamental problem in QCD The progress achieved on the

theoretical side in describing low energy phenomena from basic principles

in the framework of the chiral p erturbation theory allows the prediction

of the pionnucleon scattering lengths with an accuracy at the p er cent

level Consequently the exp erimental information stemming from

the hadronic shift and broadening of the ground state in pionic hydrogen

should at least reach a precision at that level

The last generation of exp eriments on pionic hydrogen and deuterium

achieved already an accuracy of ab out for the isospin separated N

scattering lengths Recently new developments in the exp erimental

techniques see pion mass exp eriment and in the atomic cascade of pionic

and muonic hydrogen b ecame available For a precision exp eriment

a detailed study of the cascade is essential in order to reach a precision of

b etter than Below that level Coulomb deexcitation which com

p etes with external Auger and Xray emission during the atomic cascade

hinders the precise determination of the line width The deexcitation energy

is used to accelerate the H system during the encounter with another atom

in the target and thus the measured line shap e is comp osed of a sup erp o

sition of many discrete Doppler proles convoluted with the sp ectrometer

resp onse function It is prop osed to quantify such a complex line shap e

using the Hps transition where the eects of Coulomb deexcitation

can b e studied in a system without strong interaction Inserting the

knowledge from the cascade studies an accuracy of b ecomes feasible for

the strong interaction broadening of the s level in pionic hydrogen

Feasibility study with pionic deuterium

To demonstrate the count rate and background conditions for such mea

surements in pionic and muonic hydrogen the p s transition in pionic

deuterium has b een studied Figure The cyclotron trap II was used to

stop the high intensity E b eam in a gas target at bar pressure The

Xrays were measured with the fo cussing crystal sp ectrometer setup for the

pion mass measurement As energy calibration the K uorescence Xrays

from chlorine have b een used and the resolution function has b een obtained

20

from the narrow Neih transition

New improved values for the strong interaction shift and broadening of

the atomic ground state have b een extracted from the p osition and line

shap e b eing  eV and  eV

1s 1s

The result is in agreement with the previous measurement where the Dp

s transition and the argon K radiation as energy calibration was used

In the calculation of the electromagnetic ps transition energy Ta

ble for the deuteron a value of fm was used The

minus sign of the shift indicates a repulsive interaction The rst error of

could b e easily reduced by a high statistics measurement The second

1s

error of stems only from the accuracy of the energy determination of the

1s

Figure Left Dps line shap e obtained from the feasibility study

for the H exp eriment Right reection of the Ne transition

K transition in chlorine Table and can only b e improved when a new

1

calibration standard will b e available

New calibration standards

In the few keV range a ma jor problem b oth for the energy calibration and

the determination of the crystal sp ectrometer resp onse function stems from

the fact that no narrow lines are available from easily accessible sources

like Xray tub es The Xray line widths of low Z multiple electron systems

are dominated by the Auger widths and then quickly increase with the

nuclear charge The natural width usually exceeds the typical values for

the sp ectrometer resolution by at least a factor of

In addition the line shap e exhibits a complex structure due to satellite

transitions originating from multiple ionisation Although light elements

like silicon and sulfur do not show pronounced satellite structures when the

ionisation o ccurs from weakly ionising radiation like Xrays or electrons

due to the large natural widths a precise determination of the p osition of

the diagram line stemming from atoms with one Kshell vacancy only to

b etter than ppm is problematic in most cases

Systematic measurements of all elements using up to date exp erimental

techniques are in preparation But the problem of the large natural line

width and the satellite structure of the uorescence Xrays could b e over

come by using the narrow transitions of light exotic atoms and hydrogenlike

electronic atoms

Exotic atoms

The transition energies of completely stripp ed exotic atoms now are able to

serve as a calibration standard for Xray energies For count rate reasons

14

pionic atoms are the most promising ones As an example the Ngf

transition has b een used to obtain a value for the Sc K transition energy

1

which is a factor more accurate than the value given in the published tables

Table The energy of the Ti K transition has b een redetermined

20

by the same metho d using the Nehg transition A precise

determination of the p ositions of diagram lines requires always a detailed

study of the line shap e

ECR source

Transition energies and widths of hydrogenlike electronic systems can b e

calculated with the metho ds of QED to an accuracy of b etter than ppm

Because only radiative transitions o ccur the line widths are of the order of

to meV in the range from phosphorus to argon Such transitions

would b e much b etter suited to calibrate energies and to study the resp onse

functions of crystal sp ectrometers

Low Z electronic atoms with few electrons can b e pro duced with high in

tensity in ElectronCyclotronResonance ECR devices as used as sources

for atomic b eams It is prop osed to build up such a device in using the

cyclotron trap mirror eld Then it will b e p ossible to measure uo

rescence Xrays and few electron systems with a crystal sp ectrometer in a

xed exp erimental setup A small Doppler broadening of a few meV is

exp ected from the Maxwellian velo city distribution inside the ECR source

For hydrogenlike electronic atoms energy measurements on the sub ppm

level for the ps diagram lines will b ecome feasible which can b e related

to transitions from exotic atoms The variety of transitions yields a dense

net of transitions to b e used as calibration standards

Further applications of such a setup would b e the measurement of

heliumlike or few electron atoms in order to study various theoretical ap

proaches of the electronelectron interaction strong interaction eects

in pionic atoms or nuclear size eects in muonic atoms In a rst step

such an apparatus will b e used to measure accurately the resp onse function

of the crystal sp ectrometer for the determination of the strong interaction

broadening in pionic hydrogen

Summary and outlo ok

A series of precision exp eriments is b eing p erformed of the characteristic

Xradiation from exotic atoms Main goals of the exp eriments are the de

termination of the hadronic level shifts and broadenings of the atomic s

and p states in hydrogen isotop es a new value for the mass of the charged

pion and the pionnucleon scattering length from pionic hydrogen The ac

curate knowledge of values for the pure electromagnetic part of the atomic

energy levels is mandatory for the interpretation of those measurements

Results from the exp eriments with antiprotons at LEAR are

3

 The P hyp erne state was resolved from the antiprotonic hydrogen

0

L transition The results for the strong interaction shift and broad

ening of the p hyp erne strongly supp ort the prediction for the real

part of the antinucleonnucleon p otential derived in the framework of

the meson exchange mo del from the nucleonnucleon interaction

 The plevel stronginteraction eects in antiprotonic deuterium were

observed by measuring the L transition b eing in reasonable agreement

with the prediction of the multiple scattering approach

 The line shap e of the L transition in antiprotonic deuterium discards

an earlier calculation of the electromagnetic hyp erne splitting in favor

of a recent one

The studies with pionic and muonic atoms at PSI yielded

 The ambiguity of ppm for the mass of the charged pion from a

previous high resolution exp eriment could b e removed Taking the

weighted average of the results of and the presently reached

accuracy for the pion mass is already less than ppm

3

 The b est test up to now of the KleinGordon equation to  has

b een achieved from the Ngf transitions

 The Coulomb explosion in diatomic symmetric molecules has b een di

rectly observed from the line broadening of N and the O transi

tions

 The energies of uorescence Xrays have b een redetermined using tran

sitions from hydrogenlike pionic atoms as calibration lines

At PSI in the near future

 a high precision exp eriment of the charged pion mass to ppm will b e

p erformed by calibrating the N transition energy with the O

transition

 The determination of the pionnucleon scattering length and the pion

nucleon coupling constant to has b een started

 For that calibration measurements will b e necessary using an ECR

source implemented into the cyclotron trap which allows in addition

the investigation of few electron systems

Acknowledgements I am very grateful to the organizers of the workshop

on Frontier tests of QED and physics of the vacuum for the gener

ous supp ort which enabled me to participate in that meeting at Sandansky

Bulgaria

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