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Nuclear Instruments and Methods in Physics Research A 618 (2010) 160–167

Contents lists available at ScienceDirect

Nuclear Instruments and Methods inPhysics Research A

0168-90

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/nima

New experimental method for investigation of the nucleon polarizabilities

O. Yevetska a, S. Watzlawik a, J. Ahrens b, G.D. Alkhazov c, V.P. Chizhov c, E.M. Maev c,P. von Neumann-Cosel a,�, E.M. Orischin c, G.E. Petrov c, J.-M. Porte a, A. Richter a,d,V.V. Sarantsev c, G. Schrieder a, Yu.V. Smirenin c

a Institut fur Kernphysik, Technische Universitat Darmstadt, D–64289 Darmstadt, Germanyb Institut fur Kernphysik, Johannes Gutenberg–Universitat Mainz, D–55099 Mainz, Germanyc Petersburg Nuclear Physics Institute, 188300 Gatchina, Russiad ECT*, Villa Tambosi, I–38123 Villazzano, Trento, Italy

a r t i c l e i n f o

Article history:

Received 16 November 2009

Received in revised form

8 February 2010

Accepted 11 February 2010Available online 17 February 2010

Keywords:

Bremsstrahlung production

High-pressure ionization chamber

Active target

Compton scattering

Nucleon polarizability

02/$ - see front matter & 2010 Elsevier B.V. A

016/j.nima.2010.02.091

esponding author.

ail address: vnc@ikp.tu-darmstadt.de (P. von

a b s t r a c t

At the continuous wave (cw) Superconducting Darmstadt Electron Linear Accelerator S-DALINAC, a new

method has been developed for the determination of the electric (a) and magnetic (b) polarizabilities of

the proton and the deuteron. For that purpose the energy and angular dependence of the differential

cross-section for elastic gp and gd scattering of bremsstrahlung photons in the energy range between

20 and 100 MeV is measured by detecting the recoiling proton (deuteron) in coincidence with the

scattered bremsstrahlung photon. a and b are then found by means of a best fit to a theoretical

description of the scattering cross-section with these quantities as open parameters. The experimental

setup consists of a bremsstrahlung photon facility, two specially designed high pressure hydrogen

(deuterium) ionization chambers which serve as targets and detectors of the recoil proton (deuteron),

NaI gamma spectrometers and several additional detectors for beam diagnostics and normalization. The

whole setup was tested using bremsstrahlung photon beams with endpoint energies of 60 and

79.3 MeV. The results of the test experiments show that future high-statistics measurements are

feasible.

& 2010 Elsevier B.V. All rights reserved.

1. Introduction

The electric (a) and magnetic (b) polarizabilities are basicstructure constants of the nucleon, which characterize theresponse of the nucleon to the action of external electric andmagnetic fields. The knowledge of a and b provides a stringenttest of models describing the quark-meson structure of thenucleon, e.g. in Chiral Perturbation Theory [1]. These polarizabil-ities are found by measuring Compton scattering cross-sections asa function of photon energy and scattering angle and by a best fitusing a theoretical description with the quantities of interest asopen parameters. Reviews of the current status of experiment andtheory can be found in Refs. [2–4].

Experiments focus on photon energies below the pion massbecause the Compton scattering cross-sections can be relatedmodel-independently to the polarizabilities through a Low EnergyTheorem, or LET [5–7], which takes into account the protonstructure in lowest order and shows that the scattering amplitudeof Compton scattering off a system with spin 1/2 can be expanded

ll rights reserved.

Neumann-Cosel).

in powers of Eg. The LET reads as

dsðEg;ygÞdO

� �LET

¼dsðEg;ygÞ

dO

� �point

�rþOðE4g Þ ð1Þ

with the structure term

r¼ e2

4pm

Eg0

Eg

� �2

ðEgEg0 Þaþb

2ð1þcosygÞ2þ

a�b2ð1�cosygÞ2

" #: ð2Þ

Here, ½dsðEg; ygÞ=dO�point is the differential cross-section forscattering of photons on a point-like proton (deuteron), Eg and Eg0

are the energies of the incident and scattered photons, respec-tively, and yg is the photon scattering angle in the laboratorysystem. The energy Eg0 of the elastically scattered photon on aparticle with mass m is connected to the energy Eg of the incidentphoton by

Eg0 ¼Eg

1þEgmð1�cosygÞ

: ð3Þ

Eq. (2) indicates that ½dsðEg; ygÞ=dO�LET is sensitive to the sum ofthe polarizabilities in forward scattering, to their difference inbackward scattering and to a at yg ¼ 903.

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O. Yevetska et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 160–167 161

There exists a sum rule for the polarizabilities (called Baldin’ssum rule) which follows from a dispersion relation. It connectsthe sum of the polarizabilities with the total absorption cross-section stotðEgÞ as

aþb ¼Z 1

mp

stotðEgÞ

E2g

dEg: ð4Þ

It can be utilized as an additional constraint in the extraction ofpolarizabilities from the data.

Recent experiments using Compton scattering to measure thepolarizability of the proton and the deuteron were mostlyperformed using quasi-monoenergetic photons from bremsstrah-lung tagging [8–14]. The photons were scattered off liquidhydrogen or deuterium, and the scattered photons were detectedunder one or several scattering angles with NaI or BaF2 spectro-meters. These experiments then provided the four vectors of theincoming and the scattered photon and the number of incomingphotons. A disadvantage of this method is the limited photon fluxa tagger system can provide. To increase the luminosity, thickliquid targets were used.

The most precise values for the polarizabilities of the protonwere derived in Ref. [8] from a global fit to the data of fourexperiments [8–10,15]

a ¼ 12:170:380:4 b ¼ 1:670:470:4

The values are given in units of 10�4 fm3, and the uncertaintiesdenote statistical and systematic errors, respectively.

In contrast to the above experiments, where tagged photonbeams were used and the scattered photons were registered, inthe method proposed here and sketched in Fig. 1 bremsstrahlungphotons produced by a cw electron beam are used, and not onlythe angle and energy of the scattered photons but also the angleand energy of the recoiling protons (deuterons) are measured. Wenote that the use of untagged bremsstrahlung spectra forCompton scattering experiments is not uncommon [9,16–19]but no coincidence experiments have been reported for cases atlow photon energies (Ego100 MeV). Coincident neutrons fromdeuteron breakup were measured in quasifree kinematics [18].However, in the new method one can separate elastic Comptonscattering from the breakup channel. In general, the approachsketched in Fig. 1 increases the luminosity and lowers thebackground considerably, especially below 50 MeV.

The scattered photons are detected under two angles, 901 and1301, by means of 10 in:� 14 in: NaI(Tl) detectors. The energyspectrum of the incoming photons is continuous up to the

Fig. 1. Experimental method (schematic). A photon beam with a full bremsstrah-

lung spectrum is scattered from a gaseous hydrogen/deuterium target inside a

high pressure ionization chamber, the energy of the scattered photons is

determined in a g-detector under a certain angle. By detecting the scattered

bremsstrahlung photon in coincidence with the recoiling proton (deuteron) in the

ionization chamber the incoming photon energy is determined.

endpoint energy. The measured spectrum of the scatteredphotons contains, however, a noticeable low-energy tail (due tothe response functions of the NaI(Tl) spectrometers), which doesnot allow a precise determination of the energy. But the energy ofthe recoiling protons (deuterons) is measured as well. This isachieved with a special hydrogen/deuterium ionization chamber(IC), which acts as target as well as detector [20]. In order toincrease the statistics in the spectra requiring a coincidencebetween the recoiling particle and the scattered photons, twochambers are used simultaneously under two angles. In thefollowing we shall discuss the option when the IC’s are filled withhydrogen. To detect the small number of scattered protons in aregime of many Compton-scattered electrons, the anodes of theIC’s are segmented into strips, as will be described later in Section4. These strips are oriented in the direction of the recoilingprotons. One should notice that the directions of the scatteredprotons are defined mainly by the scattering angles of thephotons, whereas the dependence of the proton recoil angles onthe energy of the incident photons is negligible.

2. Bremsstrahlung photon facility

Fig. 2 shows a schematic view of the high-energybremsstrahlung photon facility built at the S-DALINAC [21]. Theaim has been to generate a high-intensity, nearly background-freephoton beam. To reach this goal, at first beam optics calculationsfor the electron beam as well as GEANT4 [22] simulations for thewhole gamma production process were performed. For optimalfocusing and position corrections of the electron beam impingingthe radiation target, a triplet of quadrupole lenses and two pairs ofvertical and horizontal correction magnets are used. To controlthe electron beam position, different diagnostics tools areinstalled. With targets inserted into the electron beam, the sizeand the position of the beam can be determined. Scintillatingberyllium oxide targets are used for low intensity beams and thinaluminum foil targets, emitting optical transition radiation whenhit by electrons, for high intensity beams.

The fully controlled cw electron beam is transformed into aphoton beam by passing through a 0.3 mm (corresponding to0.1 radiation lengths) thick bremsstrahlung-radiator made of gold.Directly behind the radiator, the electrons are deflected out of theforward direction into a beam dump by means of a dipole magnet.This beam dump was specially constructed to stop most of theelectrons without creating considerable background from brems-strahlung photons and neutrons. It consists of three radiationlengths of aluminum plates and additional 200 mm of lead, both

Fig. 2. Setup of the bremsstrahlung facility: The electron beam from the S-

DALINAC passes dipole magnets for electron beam corrections, a wire

scanner for beam diagnostics, beam position targets, a beam intensity and

position rf monitor before it hits a bremsstrahlung converter target. A dipole

cleaning magnet bends the electrons into an electron beam dump (Faraday

cup). The produced photon beam passes a collimation system. The whole setup

is embedded in heavy concrete shielding.

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9

7

4

6

84

76

51

2

3

e-

Fig. 3. General view of the experimental setup: bremsstrahlung converter and dipole magnet; collimation system; beam dump for electron beam; concrete

shielding; high pressure target ionization chambers; large g-spectrometer (10 in� 14 in NaI(Tl) detectors); collimation system for a small g-spectrometer

(10 in� 10 in NaI(Tl) detectors); position sensitive ionization chamber, Gaussian quantameter (beam dump for g-beam); small g-spectrometer. The wavy line shows

the photon beam. The dashed lines indicate photons from Compton scattering off the atomic electrons in the beryllium exit window of the high pressure ionization

chamber.

Fig. 4. Bremsstrahlung spectrum and a part of a color-inverted polaroid picture of

the collimated bremsstrahlung approximately 3 m behind the bremsstrahlung

target: Areas with high beam intensity are dark, those with low intensity are gray.

Circles correspond to the measured bremsstrahlung spectrum taken at an electron

energy E0 = 70 MeV. The line shows a spectrum simulated with GEANT4.

O. Yevetska et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 160–167162

placed electrically insulated within a concrete wall. The alumi-num plates are air cooled. This electron beam dump is also used asa Faraday cup for the measurement of the electron beam current.Behind the cleaning magnet the photon beam is collimated first ina three-stage lead collimator, consisting of several layers withdifferent slit size parameters, and some additional layers ofpolyethylene as shielding against neutrons produced in thecollimator. After the passage through a 3 m concrete wall and asecond lead collimation system the photon beam enters theexperimental hall, where the Compton scattering setup (Fig. 3) isinstalled.

The position and intensity of the photon beam is measureddownstream from the experiment by means of two specialionization chambers placed inside a hole in a concrete walldirectly in front of the g beam stop (position in Fig. 3) forbackground minimization. The first chamber has segmentedanode and cathode plates and allows an online determination ofthe photon beam position. In future experiments the position ofthe electron beam on the radiator target, and therefore theposition of the photon beam will be steered with the help of theoutput signals of this detector. The second ionization chamber is aso called Gaussian quantameter. It allows to measure the gammaintegrated beam power in a wide energy range from 10 MeV up toseveral GeV [23].

In order to determine the absolute cross-sections for theCompton scattering off the proton (deuteron) with the reportedtechnique, it is essential to know not only the integral intensity ofthe photon beam measured with the above-mentioned quanta-meter, but also the shape of the energy spectrum of the beam. Theshape of this spectrum is extracted with two additional 10 in:�10 in: NaI-spectrometers, which detect Compton scatteredphotons from the atomic electrons in the exit beryllium windowof the ionization chambers (i.e. in Fig. 3). They are placedapproximately 10 m downstream from this window under anglesof 1.891 and 2.421, respectively. As follows from Eq. (3), photonsCompton scattered from electrons under these angles have thesame energies as photons Compton scattered off the proton in theionization chambers at 901 and 1301. The 10 in:� 10 in: spectro-meters are equipped with the same active and passive shieldingas the main gamma spectrometers to be described below. With aknowledge of the response functions of the NaI(Tl) crystals it ispossible to evaluate the intensity as well as the shape of theenergy spectrum of the incoming bremsstrahlung beam.

Fig. 4 shows the energy spectrum of the bremsstrahlung beammeasured with the above-mentioned g-spectrometer incomparison with the results of GEANT4 calculations. Excellent

agreement is observed. A color-inverted polaroid picture of thecollimated gamma beam cross-section obtained 3 m behind thebremsstrahlung target is also shown as insert in this figure. Thebeam spot size at this position corresponds to a size of 20�10 mm2 inside the ICs.

3. Gamma ray spectrometers

All NaI(Tl) photon spectrometers (see Fig. 5) for detecting thescattered photons are items on loan from the Institute of NuclearPhysics of the Johannes Gutenberg-Universitat Mainz. Those usedto detect the photons scattered from protons (deuterons) are10 in� 14 in in size. Compton scattered photons from theionization chambers enter these g spectrometers throughcollimation systems, which determine a solid angle of about10 msr. With this collimator system only the inner part of the gdetectors is hit, which reduces the low-energy tails in theresponse functions.

An energy calibration was achieved up to Eg ¼ 4:44 MeV withthe help of standard g sources. At higher energies the energy

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Fig. 5. Layout of the large volume g-spectrometer with a 10 in� 14 in NaI(Tl)

crystal, active and passive shielding and the collimation system.

Fig. 6. High pressure hydrogen/deuterium double ionization chamber:

Beryllium window for the incoming photon beam; permanent magnet to

remove electrons from the photon beam; chamber with multi-strip anode for

proton detection from Compton scattering events under yg ¼ 903; beryllium

windows for scattered photons; chamber with multi-strip anode for proton

detection from Compton scattering events under yg ¼ 1303; beryllium window

for outgoing photon beam.

Fig. 7. Top view on a multi-strip anode: The 2 cm broad photon beam enters the

volume of the IC from the left side. In case of a Compton scattering process under

yg ¼ 1303 the backscattered proton gets a momentum along an anode strip

(j¼ 223).

Table 1Main parameters of the ionization chambers.

Cathode-grid distance (mm) 17

Grid-anode distance (mm) 1

Grid wire pitch (mm) 0.4

Wire diameter (m) 55

Anode strips width (mm) 2.5

Gaps between the strips (mm) 0.3

Direction of strips (j) in the 1st IC (deg) 44

Number of strips in the 1st IC 17

Length of strips in the 1st IC (mm) 65

Direction of strips (j) in the 2nd IC (deg) 22

Number of strips in the 2nd IC 9

Length of strips in the 2nd IC (mm) 96

Number of additional strips (j=0) in each chamber 2

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calibration was determined by using an electron beam withknown energy scattered from an aluminum target replacing thehydrogen ionization chamber. According to GEANT4 simulations,the response functions of the detectors for photons and electronsare practically identical. An extrapolation with the energycalibration parameters to the low-energy region shows goodagreement with the results of the g-source measurements.

Since these detectors work as trigger detectors and the deadtime of the ionization chamber is rather long (about 4ms), it isessential to minimize their background counting rate. Therefore,the NaI(Tl) crystals are well shielded. Plastic scintillators of100 mm thickness act in anticoincidence as active shieldingagainst cosmic muons. Cosmic muons produce signals in NaI(Tl)crystals, with sizes almost evenly distributed in the energyinterval of interest from 15 to 100 MeV. The integrated countingrate of these signals was about 2 s�1 without the active shielding.When the active shielding was switched on, the background wasreduced by a factor of about 7.

Beam-related sources of background in the NaI(Tl) detectorsare associated with the beam collimation system and the electronbeam dump. To suppress these contributions, the scintillators aresurrounded by 100 mm lead and by 50 mm of borated poly-ethylene, the latter acting against a possible neutron background,which may cause (n, g) reactions in the NaI(Tl) detectors.Nevertheless, the test experiments showed a total backgroundcounting rate of signals from the NaI(Tl) crystals amounting toabout 5 s�1 with ‘‘beam on’’. Thus, the trigger rate wassignificantly larger than the counting rate of useful events, whichwas of the order of 10�2 s�1 only. It is planned to further enforcethe shielding to reduce the background for future experiments.

4. High pressure ionization chambers

Fig. 6 shows a scheme of two ionization chambers (IC). Theincident photons scattered on the filling gas of the first/secondchamber are detected under the angles of yg ¼ 903=1303. Bothchambers have a cathode, a grid and an anode divided in strips(Fig. 7). The main parameters of the chambers are summarized inTable 1.

The body of the chamber is made of stainless steel with a wallthickness of 14 mm. The photon beam enters (leaves) thechambers through 6 mm (7 mm) beryllium windows. This

material was chosen in order to minimize the absorption ofphotons and production of e+e�-pairs. The Compton scatteredphotons on hydrogen at the selected angles (yg ¼ 903743 andyg ¼ 1303733) leave the IC’s through 9 mm beryllium windows tothe g spectrometers described above. The ICs are operated in theelectron collection mode, i.e. the signal results from the electronscollected after ionization produced by protons. The applied highvoltages are �40 kV on the cathode and �3.5 kV on the grid, theanode being at zero potential (see Fig. 8). The electron drift timesare 3.5 and 0:12ms for the cathode-grid and grid-anode distances,respectively.

To measure the angle of the recoiling proton, a specialgeometry of the IC anode is used (Fig. 7). It is designed to detect

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Fig. 8. (a) Side view of the chamber electrodes. The upper part shows the track of a

proton, parallel to the anode. The lower part demonstrates the proton under a

finite angle. Dimensions are in mm. (b) Simulated pulse form for different

azimuthal angles and for different proton energies: 1 MeV (solid line), 4 MeV

(dotted line) and 8 MeV (dashed line).

Fig. 9. Example of a signal in IC from a 4 MeV recoil proton, registered by a FADC,

compared to a GEANT4 simulation.

O. Yevetska et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 160–167164

tracks of recoiling protons in a background of tracks of Comptonscattered electrons and secondary electron–positron pairs. Theanode of the IC consists of several strips aligned along thedirection of the recoil protons. In particular, in the case ofCompton scattering under yg ¼ 1303, the proton recoil anglej¼ 223.

Along its path, the proton ionizes hydrogen molecules. Asschematically shown in Fig. 8(a), the ionization electrons movetowards the anode and are collected there on one or two anodestrips. When Compton scattered electrons and electron–positronpairs are formed, they have angles different from the recoilprotons. The charges released by them are collected by severalstrips and produce only small signals on a single strip. In Fig. 8(b)different simulated proton pulse forms are shown. At anazimuthal angle 01 (proton path is parallel to the anode) pulselengths have a minimal value and are equal for all energies. Forprotons with higher energies and at larger azimuthal angles thepulse shape becomes wider and asymmetric.

Due to the high hydrogen pressure in the ICs (75 bar), the effectof recombination of the electrons and positive ions formed by anionizing particle becomes significant. The effect of recombinationfor a particles was studied with a 237Pu source (Ea ¼ 5:15 MeV)mounted on the IC cathodes. It was found to be rather large,reducing the registered signals by about 30%. The effect ofrecombination in case of ionizing protons is expected to benoticeably smaller. According to Ref. [24], the collected chargeproduced by protons with energies Ep40:5 MeV in hydrogen at

the conditions of our experiment can be estimated by thefollowing empirical formula:

Q ¼ eKðEp�E0Þ=W ð5Þ

where E0

=0.15 MeV, K = 0.9, e is the electron charge, and W =36.3 eV is the energy per electron–ion pair production inhydrogen. The proton recoil energy is thus

Ep ¼ E0 þQW

eK: ð6Þ

Another process that might cause a reduction of the registeredsignals is the attachment of electrons to electronegative impu-rities (such as O2 and H2O) in the working gas of the chambers. Toreduce the amount of gas impurities, the chambers were heattrained under vacuum pumping. The hydrogen used for experi-ments contains less than 1 ppm impurities. Signals from a 237Pualpha source are used for checking the gas quality. During the testexperiments, the position of the energy peak of the 5.15 MeV aparticles decreased by � 5% per week, indicating slow evapora-tion of contaminants from the chamber walls.

To remove any admixture of electrons to the photon beam,permanent magnets were installed in the photon beam line (seeFig. 6). However, as simulations have shown, a noticeable amountof electrons (on the level of 0.1%) appears in the photon beam inthe active regions of the ionization chambers due to interaction ofphotons with the working gas of the chambers. To excluderegistration of scattered electrons in the gamma-ray spectrometers,anticoincidence scintillation counters (not shown in the figures),so-called veto detectors, are placed in front of the NaI detectors.

5. Electronics

The electronics used in the data acquisition consists mostly ofstandard NIM, CAMAC and VME components. The signals on theanodes of the ICs are registered by special low-noise preampli-fiers, amplifier-discriminators and 14-bit 100 MHz Flash ADCs(FADC). The FADCs digitize the analog signal in 10 ns stepscontinuously and hold the values for 4:5ms in a ring buffermemory. This is necessary, since the signals from ICs are delayedrelative to the trigger pulse of the NaI(Tl) detectors by the drifttime of electrons produced by recoil protons in the Comptonscattering event. The trigger signals define a time window of4:5ms, in which the proton pulse is expected to take place. Thecurrent on the IC anodes is always recorded within this window

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O. Yevetska et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 160–167 165

by the FADCs when a trigger signal is generated. Fig. 9 shows anexample of a recoil proton signal, registered by an FADC, incomparison with a GEANT4 simulation. The results of themeasurement and the simulation are in good agreement.

The channels of the FADC have to be read out for each IC,which takes quite a long time (about several ms) making itnecessary to minimize the trigger rate. In order to improve thesignal-to-noise ratio, the registered signals can be treated off-linewith digital filters. A preliminary energy calibration of theamplifier channels was performed by inserting calibrated chargesthrough a small capacitance to the anodes of the ICs.

The NaI(Tl) detectors, which act as trigger detectors, areoperated in anticoincidence mode with the surrounding plasticdetectors. The signal is split in two: one signal starts the wholereadout from the trigger module, the second signal is delayed by4:5ms and stops the recording of the FADCs, which are then readout. This trigger unit also starts the readout of the ADCs, whichdigitize the NaI(Tl) energy pulses. In addition to the energy signalsfrom the main g detectors (for registering gp scattering) and thepulses on the anode strips of the ICs, data of other detectors likethe quantameter, the position detectors, the Faraday cup and thesignals from the g detectors for the beam monitoring arecontinuously read out and written onto tape or disk using theMBS data acquisition system [25].

Fig. 11. Measured energy correlation of the scattered photons (Eg420 MeV) and

recoil protons (Ep 41 MeV) in comparison with the expected kinematic relation for

Eg and Ep from Eq. (3) (solid curve) for the data taken at E0 = 60 MeV and Y¼ 1303 .

The proton recoil energies are determined from the measured charges, collected

on the IC anodes, with the help of Eq. (6).

6. Test experiments

Test experiments were performed at the S-DALINAC usingbremsstrahlung photon beams with endpoint energies of 60 and79.3 MeV. Electron beam currents ranged from 1 to 5mA. The ICswere filled with hydrogen gas of high purity (99.9999%) at apressure of 75 bar. The gas pressure was measured with aprecision of about 0.5%. In these test experiments about 5000Compton scattered events in total were collected in coincidencewith recoil protons. Fig. 10 shows a typical drift-time distributionof signals which appeared at the IC anodes. This distributionreflects the gp interaction points in the vertical direction. Thewidth of this distribution corresponds to a vertical photon beamsize of about 1 cm. It is seen that the position of the photon beamwas not in the middle of the gap between the IC grid and the

Fig. 10. Drift-time distribution of proton signals in an IC. The dashed line denotes

the center of the active volume between electrodes. The actual location of the

photon beam is indicated by the arrow.

cathode, but closer to the grid. The number of events in the drift-time interval from 2.5 to 3:5ms is small demonstrating that thecoincidence between the signals from the g spectrometers and theionization chambers suppresses the background very efficiently.At the same time, one can see some events in the drift-timeinterval of 020:5ms and 222:5ms. Presumably, these eventsappear due to some halo of the photon beam.

The measured energy correlation between the scatteredphotons and recoiled protons is shown in Fig. 11 for the datataken at E0 = 60 MeV, Yg ¼ 1303 and energies Eg0420 MeV,Ep41 MeV. The experimental data are in good agreement with

Fig. 12. Differential cross-sections of Compton scattering on the proton obtained

in the experiments at the S-DALINAC at E0=60 MeV (full diamonds) and

E0=79.3 MeV (full circles) at an angle yg ¼ 1303 . Data from [10] in the same

energy region and at an angle of 1351 are given as squares. The lines correspond to

calculations for different values of a and b in [7]: a ¼ 13:8, b ¼ 0 (solid line),

a ¼ 11:8, b ¼ 2 (dashed line), a ¼ 9:8, b ¼ 4 (dotted line), a ¼ 7:8, b ¼ 6 (dashed-

dotted line). The error bars include statistical contributions only. The data from the

S-DALINAC are normalized with the theoretical curve shown as dashed line.

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O. Yevetska et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 160–167166

the expected kinematical relation following from Eq. (3). Thisfigure also demonstrates that the background is rather small.Events on the left side of the (Eg,Ep) correlation curve are partlydue to the tails of the g response function and partly due to thebackground, which may be reduced in the future by buildingadditional shielding for the g spectrometers.

The cross-sections resulting from the experiments at E0=60and 79.3 MeV are shown in Fig. 12. The overall normalization ofthe (g, p) cross-sections measured as a function of the photonenergy was performed with the help of the theoretical curve witha ¼ 11:8, b ¼ 2 (dashed line). The resulting cross-sections are ingood agreement with a previous measurement [10] at comparablephoton energies. Of course, the low statistics collected in the testexperiment is not sufficient to extract meaningful results on theproton polarizabilities. From those measured values and the rangeof results from theoretical calculations [7] it has been estimatedthat in order to determine the values of a and b for the protonwith a precision of Da ¼ 0:3 and Db ¼ 0:4 with this technique it isnecessary to perform measurements at a 100 MeV electron beam(to increase the photon flux per incident electron) with anintegrated beam current of 2:5� 104 mA� h. The proposed newexperimental method and the results of two test runs have shownthat future high-statistics experiments to determine a and b areindeed feasible.

In order to evaluate the potential of the new method, it may beinstructive to compare its properties with those of the latest andmost precise tagged-photon experiment [8]. As an example, let usestimate expected count rates at Eg ¼ 60 MeV. These depend onthree parameters, viz. the photon flux, the target thickness andthe solid angle of the g spectrometers. The correspondinginformation from the tagged-photon experiment is taken from[26]. In the latter work, the electron beam of 20 nA produces 2�104 MeV�1 s�1 photons at 60 MeV. Including the tagger efficiencyof about 20% leads to a photon flux on the target of4� 103 MeV�1 s�1. Assuming an electron energy of 100 MeV anda beam current of 5mA, the present setup provides about 7�107 MeV�1 s�1 photons. The number of atoms for 20 cm effectivetarget length of liquid hydrogen [26] is 8:7� 1023 cm�2 ascompared to 5:3� 1022 cm�2 for the present setup (75 barpressure and an effective target length of 13 cm). Thus, theluminosity L¼ 3:7� 1030 MeV�1 s�1 cm�2 obtained with the newmethod is about a factor of 1000 larger. On the other hand, thesetup described in [26] gains up to two orders of magnitude fromthe large effective solid angle of the TAPS spectrometer, whichamounts to about 0.5�1 sr (note that the value is energydependent [26]) when summed over the analyzed angular range,while it is 10 msr in the present setup. In total, expected yieldsfrom an experiment based on the technique described here are atleast an order of magnitude larger than in the experiment ofRef. [26]. As a final remark,presently a new IC with a larger activearea is under fabrication. Also, the solid angle of g detection canbe increased by moving the NaI detectors closer to the target.These improvements promise another increase of count rates by afactor of 5–10.

7. Conclusion

A new method for measurements of the electric and magneticpolarizabilities (a and b) of the proton and deuteron has beenproposed and tested at the S-DALINAC. The new approach for thedetermination of a and b is based on Compton scattering ofuntagged bremsstrahlung photons and registration of the recoilprotons (deuterons) with special high-pressure hydrogen ioniza-tion chambers, which serve as targets and detectors. Thescattered photons are registered with NaI(Tl) spectrometers.

Test experiments showed that the whole setup functions in theexpected way.

Acknowledgments

This work was supported by the Deutsche Forschungsge-meinschaft (DFG) under Contracts FOR 727/2-2, 436 RUS 113/794/0-1 and SFB 634, and by the Russian Ministry of Science andEducation. One of us (O.Y.) thanks for the support through theHessisches Gesetz zur Forderung von Nachwuchswissenschaf-tlern.

References

[1] V. Bernard, N. Kaiser, U.-G. Meissner, Int. J. Mod. Phys. E 4 (1995) 193.[2] D. Drechsel, B. Pasquini, M. Vanderhaegen, Phys. Rep. 378 (2003) 99.[3] F. Wissmann, Springer Tracts Modern Phys. 200 (2004) 1.[4] M. Schumacher, Prog. Part. Nucl. Phys. 55 (2005) 567.[5] V.A. Petrun’kin, Sov. J. Part. Nucl. 12 (1981) 278.[6] A.I. L’vov, V.A. Petrun’kin, JETP Lett. 37 (1983) 63.[7] A.I. L’vov, V.A. Petrun’kin, M. Schumacher, Phys. Rev. C 55 (1997) 359.[8] V. Olmos de Leon, F. Wissmann, P. Achenbach, J. Ahrens, H.-J. Arends, R. Beck,

P.D. Harty, V. Hejny, P. Jennewein, M. Kotulla, B. Krusche, V. Kuhr, R. Leukel,J.C. McGeorge, V. Metag, R. Novotny, A. Polonski, F. Rambo, A. Schmidt, M.Schumacher, U. Siodlaczek, H. Stro her, A. Thomas, J. Weiß, M. Wolf, Eur. Phys.J. A 10 (2001) 207.

[9] B.E. MacGibbon, G. Garino, M.A. Lucas, A.M. Nathan, G. Feldman, B. Dolbilkin,Phys. Rev. C 52 (1995) 2097.

[10] F.J. Federspiel, R.A. Eisenstein, M.A. Lucas, B.E. MacGibbon, K. Mellendorf,A.M. Nathan, A. O’Neill, D.P. Wells, Phys. Rev. Lett. 67 (1991) 1511.

[11] F. Wissmann, V. Kuhr, O. Jahn, H. Vorwerk, P. Achenbach, J. Ahrens, H.-J.Arends, R. Beck, M. Camen, G. Caselotti, E. Heid, V. Hejny, P. Jennewein, R.Kondratjev, K. Kossert, M. Kotulla, B. Krusche, M. Lang, R. Leukel, M.I.Levchuk, V. Lisin, V. Metag, R. Novotny, V. Olmos de Leo n, A. Polonski, I.Preobrashenskij, F. Rambo, D. Rosenkranz, E. Schilling, A. Schmidt, M.Schumacher, B. Seitz, U. Siodlaczek, H. Stroher, A. Thomas, T. Walcher, J.Weiss, M. Wolf, F. Zapadtka, Nucl. Phys. A 660 (1999) 232.

[12] N.R. Kolb, A.W. Rauf, R. Igarashi, D.L. Hornidge, R.E. Pywell, B.J. Warkentin, E.Korkmaz, G. Feldman, G.V. O’Rielly, Phys. Rev. Lett. 85 (2000) 1388.

[13] G. Galler, V. Lisin, R. Kondratiev, A.M. Massone, S. Wolf, J. Ahrens, H.-J. Arends,R. Beck, M. Camen, G.P. Capitani, P. Grabmayr, S.J. Hall, F. Harter, T. Hehl, P.Jennewein, K. Kossert, A.I. L’vov, C. Molinari, P. Ottonello, J. Peise, I.Preobrajenski, S. Proff, A. Robbiano, M. Sanzone, M. Schumacher, M. Schmitz,F. Wissmann, Phys. Lett. B 503 (2001) 245.

[14] M. Lundin, J.-O. Adler, M. Boland, K. Fissum, T. Glebe, K. Hansen, L. Isaksson,O. Kaltschmidt, M. Karlsson, K. Kossert, M.I. Levchuk, P. Lilja, B. Lindner, A.I.L’vov, B. Nilsson, D.E. Oner, C. Poech, S. Proff, A. Sandell, B. Schroder, M.Schumacher, D.A. Sims, Phys. Rev. Lett. 90 (2003) 192501.

[15] A. Zieger, R. Van de Vyver, D. Christmann, A. De Graeve, C. Van den Abeele, B.Ziegler, Phys. Lett. B 278 (1992) 34.

[16] V.I. Goldansky, O.A. Karpukhin, A.V. Kutzenko, V.V. Pavlovskaya, JETP 38(1960) 1695.

[17] P. Baranov, G. Buinov, V. Godin, V. Kuznetzova, V. Petrunkin, L. Tatarinskaya, V.Shirtenko, L. Shtarkov, V. Yurtchenko, Yu. Yanulis, Phys. Lett. B 52 (1974) 122.

[18] K.W. Rose, B. Zurmuhl, P. Rullhusen, M. Ludwig, A. Baumann, M. Schumacher,Nucl. Phys. A 514 (1990) 621.

[19] E.L. Hallin, D. Amendt, J.C. Bergstrom, H.S. Caplan, R. Igarashi, D.M. Scopik,E.C. Booth, D. Delli Carpini, J.P. Miller, F.J. Federspiel, B.E. MacGibbon, A.M.Nathan, Phys. Rev. C 48 (1993) 1497.

[20] D.V. Balin, M.J. Borkowski, V.P. Chizhov, G.A. Kolomensky, E.M. Maev, D.M.Seliverstov, G.G. Semenchuk, Yu.V. Smirenin, A.A. Vasiliev, A.A. Vorobyov,N.Yu. Zaitsev, Russian Academy of Science, in: Petersburg Nuclear PhysicsInstitute, Preprint 2104, Gatchina, Russia, 1996.

[21] A. Richter, in: S. Myers et al. (Ed.), in: Proceedings of Fifth European ParticleAccelerator Conference, Barcelona, IOP Publ., Bristol, Philadelphia, 1996, p. 110.

[22] S. Agostinelli, J. Allison, K. Amako, J. Apostolakis, H. Araujo, P. Arce, M. Asai, D.Axen, S. Banerjee, G. Barrand, F. Behner, L. Bellagamba, J. Boudreau, L. Broglia,A. Brunengo, H. Burkhardt, S. Chauvie, J. Chuma, R. Chytracek, G. Cooperman,G. Cosmo, P. Degtyarenko, A. Dell’Acqua, G. Depaola, D. Dietrich, R. Enami, A.Feliciello, C. Ferguson, H. Fesefeldt, G. Folger, F. Foppiano, A. Forti, S. Garelli, S.Giani, R. Giannitrapani, D. Gibin, J.J. Gomez Cadenas, I. Gonzalez, G. GraciaAbril, G. Greeniaus, W. Greiner, V. Grichine, A. Grossheim, S. Guatelli, P.Gumplinger, R. Hamatsu, K. Hashimoto, H. Hasui, A. Heikkinen, A. Howard, V.Ivanchenko, A. Johnson, F.W. Jones, J. Kallenbach, N. Kanaya, M. Kawabata, Y.Kawabata, M. Kawaguti, S. Kelner, P. Kent, A. Kimura, T. Kodama, R. Kokoulin,M. Kossov, H. Kurashige, E. Lamanna, T. Lampen, V. Lara, V. Lefebure, F. Lei, M.Liendl, W. Lockman, F. Longo, S. Magni, M. Maire, E. Medernach, K.Minamimoto, P. Mora de Freitas, Y. Morita, K. Murakami, M. Nagamatu, R.Nartallo, P. Nieminen, T. Nishimura, K. Ohtsubo, M. Okamura, S. O’Neale, Y.Oohata, K. Paech, J. Perl, A. Pfeiffer, M.G. Pia, F. Ranjard, A. Rybin, S. Sadilov, E.

ARTICLE IN PRESS

O. Yevetska et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 160–167 167

Di Salvo, G. Santin, T. Sasaki, N. Savvas, Y. Sawada, S. Scherer, S. Sei, V.Sirotenko, D. Smith, N. Starkov, H. Stoecker, J. Sulkimo, M. Takahata, S.Tanaka, �E. Tcherniaev, E. Safai Tehrani, M. Tropeano, P. Truscott, H. Uno, L.Urban, P. Urban, M. Verderi, A. Walkden, W. Wander, H. Weber, J.P. Wellisch,T. Wenaus, D.C. Williams, D. Wright, T. Yamada, H. Yoshida, D. Zschiesche,Nucl. Instr. and Meth. A 506 (2003) 250.

[23] A.P. Komar, S.P. Kruglov, I.V. Lopatin, Nucl. Instr. and Meth. 82 (1970) 125.[24] V.A. Volchenkov, E. Maev, V.P. Maleev, G.A. Ryabov, G.G. Semenchuk,

Petersburg Nuclear Physics Institute, Preprint N 1368, Gatchina, Russia, 1988.[25] /http://daq.gsi.deS.[26] V. Olmos de Leon, Doctoral Thesis, Johannes Gutenberg-Universitat Mainz,

2000.