Exp.-Nr. A2-01/13Eingang: 21.10.2013an PAC:

Mainz Microtron MAMI

A2 Collaboration at MAMI

Spokespersons: P.Pedroni, A. Thomas

Proposal for an Experiment

�Compton Scattering on the He Isotopes with an Active Target�

Spokespersons for the Experiment:

J.R.M. Annand (University of Glasgow)

D. Hornidge (Mount Allison University)

A. Thomas (University of Mainz)

E. J. Downie (The George Washington University)

Abstract of Physics:

We propose to measure the double di�erential cross section σ(ω, θγ) for γ +3 He→ γ +3 He and γ +4 He→γ +4 He, with su�cient statistics to bin the data in intervals ∆ω ∼ 10 MeV and ∆(cos θγ′) = 0.2. A ChiralE�ective Field Theory (χEFT ) �t will be employed to extract the isospin averaged polarisabilites from thedi�erential cross section. These in turn will yield values for the neutron scalar polarizabilities. Comparedto 2H as an e�ective neutron target, 3He o�ers a Compton cross section which is larger and has greatersensitivity to the polarisabilities. 4He will present an alternative means to obtain the neutron polarisabilitiesand provide an exacting test of the χEFT calculation.

Abstract of Equipment:

A high pressure He gas scintillator will act both as the target and as the detector of low energy recoilingHe ions. The ∼ 4π Crystal-Ball and TAPS electromagnetic calorimeter will detect photons with good angleand energy resolution. The Glasgow/Mainz Tagger will give a tagged-photon intensity of 2.5× 105 Hz/MeV.We estimate that a total of 400 hr of beam time will be su�cient to achieve good precision in energy(∆ω = 10 MeV) and angle bins ∆(cos θγ) = 0.2 for 3He and 4He targets. A further 50 hr is requested fortagging e�ciency measurement.

MAMI-Speci�cations:beam energy 855 MeVbeam polarisation unpolarisedPhoton Beam Speci�cations:tagged energy range 80 - 795 MeVphoton beam polarisation unpolarisedEquipment Speci�cations:detectors Crystal Ball, TAPS, Gas Scintillator Active Targettarget 2MPa Gas Scintillator Active Target 3He,4He.Beam Time Request:set-up without beam 75 hrdata taking 450 hr total

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List of Participating Authors

Physics Department, University of Massachusetts, Amherst, Massachusetts, U.S.A.R. Miskimen, A. Mushkarenkov, A. Rajabi

Institut für Physik, University of Basel, SwitzerlandS. Garni, M. Dieterle, A. Kaeser, I. Keshelashvili, B. Krusche, M. Oberle, T. Rostomyan, Th. Strub, D.Werthmüller, L. Witthauer

Institut für Experimentalphysik, University of Bochum, GermanyW. Meyer, G. Reicherz

Helmholtz-Institut für Strahlen und Kernphysik, University of Bonn, GermanyF. Afzal, R. Beck, K. Spieker, A .Thiel,

Massachusetts Institute of Technology, Cambridge USA.A. Bernstein, P. Martel

Joint Institute for Nuclear Research, Dubna, RussiaN. Borisov, S.S. Kamalov, A. Lazarev, A. Neganov, Yu.A. Usov

School of Physics and Astronomy, University of Edinburgh, Edinburgh, Scotland UK.D. Glowa, D.P. Watts, L. Zana

School of Physics and Astronomy, University of Glasgow, Glasgow, Scotland UK.J.R.M. Annand, D.J. Hamilton, K.Livingston, D.G.Ireland, I.J.D. MacGregor, B. McKinnon, D. O'Donnell,B.Seitz and D.Sokhan

Department of Astronomy and Physics, St. Mary's University, Halifax, CanadaC. Collicott, A.J. Sarty

Racah Institute of Physics, Hebrew University of Jerusalem, IsraelG. Ron

Department of Physics, Kent State University, Kent, Ohio, USAC.S. Akondi, D.M. Manley

Department of Physics and Astronomy, University of California at Los Angeles, California,U.S.A.B.M.K. Nefkens, S. Prakhov

MAX-lab, University of Lund, SwedenL. Isaksson

Institut für Kernphysik, University of Mainz, GermanyH.J. Arends, A. Denig, M.I. Ferretti Bony, W. Gradl, M. Hillenbrand, V.L. Kashevarov, J. Linturi, D.G.Middleton, H. Ortega, M. Ostrick, A. Neiser, P.B. Otte, B. Oussena, C. S�enti, O. Ste�en, A. Thomas, L.Tiator, M. Unverzagt, J. Wettig, S. Wagner, M. Wolfes

Institute for Nuclear Research, Moscow, RussiaG. Gurevich, R. Kondratiev, V. Lisin, A. Polonski

P.N. Lebedev Physical Institute, Moscow, RussiaS.N. Cherepnya, L.V. Fil'kov, V.L. Kashevarov, V.V. Polyansky

INFN - Sezione di Pavia, Pavia, ItalyA. Braghieri, S. Constanza, P. Pedroni

Department of Physics, University of Regina, CanadaG. Huber, D. Paudyal

Physics Department, Mount Allison University, Sackville, CanadaD. Hornidge, P. Martel, D. Middleton

Laboratory of Mathematical Physics, Tomsk Polytechnic University, Tomsk, RussiaA. Fix

Institute of Nuclear Studies, The George Washington University, Washington DC 20052, USAW.J. Briscoe, E.J. Downie, A.E. Krutenkva, A.E. Kudryavtsev, V.V. Kulikov, M.A. Martemyanov, T.W.Morrison, B. Oussena, S. Prakhov, D.M. Schott, I.I. Strakovsky, M.F. Taragin, M.F. Tarasov, V. Sokhoyan,R.L. Workman

Rudjer Boskovic Institut, Zagreb, CroatiaM. Korolija, I. Supek

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Contents

1 Introduction 4

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Previous Experiments 7

2.0.1 Compton Scattering on the proton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.0.2 Neutron Compton Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Experimental Method 9

3.1 Tagged Photon Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.2 The Active Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.3 Crystal Ball, TAPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.4 Experimental Trigger and DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Extraction of the Compton Signal 11

4.1 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.2 Compton Scattering on 3He . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.3 Compton Scattering on 4He . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.4 Threshold Meson Photoproduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5 Count Rate Estimate Uncertainties and Beam Time Request 16

5.1 3He Counting Rate and Statistical Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 16

5.2 4He Counting Rate and Statistical Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 17

5.3 Beam Time Request . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

6 Summary 18

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1 Introduction

Determination of the nucleon polarisabilities is a major component of the physics program in the tagged-photon hall of MAMI. Recently there have been major advances at Mainz in obtaining both the scalarand spin polarisabilities of the proton. A current high precision measurement of Σ3 will provide importantconstraints on the magnetic polarisability βpM1 (as well as constraints on the spin polarisabilities) and the�rst double polarised measurement of Σ2x has yielded the �rst direct means to estimate γE1E1. Howeverinformation on neutron polarisabilities remains extremely fragmentary. The scalar polarisabilities are poorlyknown compared to the proton and the spin polarisabilities are almost entirely unknown. Recently theγ +2 H → γ +2 H reaction has been measured at MAX-lab and the di�erential cross section will shortlybe submitted for publication. A Chiral E�ective Field Theory (χEFT ) analysis of these data is expectedto reduce the uncertainties in αnM1 and βnM1 signi�cantly, but it will be important to check these resultsusing an alternative experimental technique. Glasgow have developed a He gas scintillator active target forphoto-reaction measurements at MAX-lab. Here we propose to bring this target to the tagged photon facilityat Mainz to measure γ +3 He→ γ +3 He and γ +4 He→ γ +4 He, in conjunction with the Crystal Ball andTAPS detectors.

In the following we present:

� the motivation for this proposal (Sec.1.1),

� a review of related experiments (Sec.2),

� a description of the experimental apparatus (Sec.3),

� a description of the data analysis procedures and the separation of competing reaction channels (Sec.4),

� a counting rate estimate and a request beam time at MAMI (Sec.5).

1.1 Motivation

Compton scattering γN → γN , [1, 2] is an extremely �clean� probe of the response of low-energy nucleondegrees-of-freedom, since both initial- and �nal-state interactions are electromagnetic and can be calculatedperturbatively. Its importance is recognised in the 2007 NSAC/DOE and 2010 NuPECC Long-Range Plans [3,4] which emphasise the need to improve the proton, deuteron and 3He data-base. At Mainz there is alreadya highly successful programme of Compton scattering experiments on the proton [5, 6, 7] with both polarisedand unpolarised beams and targets.

Polarisabilities arise because the electric and magnetic �elds of the photon displace the charged constituentsand thus induce many charge and current multipoles, which radiate with characteristic angular distributions.The polarisabilities are the energy-dependent factors between each photon �eld and the corresponding in-duced radiation multipole moment. Each parametrises the response of the internal degrees-of-freedom (withparticular quantum numbers) with respect to deformations of a given electric or magnetic multipolarity atenergy ω. Each interaction of the hadronic constituents is characterised by a speci�c energy- and angle-dependence of the emitted radiation, which can be disentangled in the di�erential Compton scattering crosssection σ(ω, θ). Polarisabilities are the microscopic response functions which give rise to the dielectric ε(ω)and magnetic permeability functions µ(ω) of a macroscopic system. Since the permeabilities characteriseoptical properties, nucleon polarisabilities are related to the refractive index and absorption coe�cient ofbulk systems of nucleons. Thus they have an important bearing on the structure of bodies such as neutronstars.

Multipole analysis produces coe�cients which are the energy-dependent nucleon polarisabilities. They mea-sure the sti�ness of the low-energy degrees of freedom of a nucleon (spin ~σ

2 ) against transitions Xl → Y l′

(l′ = l ± {0; 1}; X,Y = E,M) of de�nite multipolarity, in the electromagnetic �eld of a real photon offrequency ω. The e�ective interaction Hamiltonian up to third order may be written as:

Heff = 2π{αE1(ω) ~E2 + βM1(ω) ~B2 + γE1E1(ω)~σ · ( ~E × ~̇E) (1)

+γM1M1(ω)~σ · ( ~B × ~̇B)− 2γM1E2(ω)σiBjEij + 2γE1M2(ω)σiEjBij}.

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Figure 1: Energy-dependence of the unpolarised di�erential proton Compton cross section, compared withaχEFT �t [2]to extract the polarisabilities. The data points include those of Ref.[13](blue triangle), Ref.[16](black diamond) , Ref. ([14](black square) , Ref. [15](red square) , Ref. [17](red diamond).

The response of the nucleon in the dipole approximation, valid for ω . 300 MeV, is characterised by six linearlyindependent polarisabilities. Two spin-independent (scalar) polarisabilities, αE1(ω) and βM1(ω), parametriseelectric and magnetic dipole transitions and for the proton they are relatively well determined. The 2013values given by PDG are αpE1(0) ≈ 11.2±0.4, βpM1(0) ≈ 2.5±0.4, in units of 10−4 fm3, the small magnitudesof αpE1 and βpM1

1 being indicative of a rigid proton with respect to electromagnetic deformation. However aBaryon Chiral Perturbation Theory (BχPT ) analysis [8] has produced αpE1 ≈ 10.8± 0.7, βpM1 ≈ 4.0± 0.7, sothat there is signi�cant disagreement about the size of βpM1, and a new experiment [7] is in progress at Mainzto improve constraints on βpM1 by measurement of Σ3(ω, θγ′). For the neutron, αnE1 and β

nM1 are known much

less precisely.

The largely unknown spin polarisabilities, which parametrise the response of the nucleon spin, have receivedmuch theoretical attention recently. γE1E1(ω) and γM1M1(ω) describe how the electromagnetic �eld associ-ated with the spin degrees-of-freedom produces a birefringence e�ect in the nucleon. An incoming photoncauses a dipole deformation in the nucleon spin, which in turn leads to dipole radiation, related to its axis.The two mixed spin polarisabilities, γE1M2(ω) and γM1E2(ω), relate to scattering where the angular momentaof the incident and outgoing photons di�er by one unit.

Until recently only the linear combinations γp0 = −(γpE1E1 + γpM1M1 + γpE1M2 + γpM1E2) and γpπ = −γpE1E1 +γpM1M1 − γpE1M2+γ

pM1M1, had been obtained from helicity-dependent total cross section data and proton

1αE1 ≡ αE1(0); βM1 ≡ βM1(0) in the following discussion

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Compton scattering (see Sec.2.0.1). Signi�cant di�erences in measured cross sections have produced somedisagreement in γpπ results for the proton. Again the neutron values are very poorly known [1].

Each interaction of the photon with low-energy hadronic constituents produces a unique signal in dispersivee�ects. Since the polarisabilities are the parameters of a multipole decomposition, the underlying mechanismsmay be identi�ed by characteristic signatures in speci�c channels. The polarisabilities are dominated by thelowest nucleonic states, the πN (αE1) and ∆(1232) (βM1), so that Compton scattering at low energies,ω . 300 MeV, (Fig.1) probes the long-distance properties of the nucleon.

χEFT predicts that small proton�neutron di�erences stem from chiral-symmetry breaking interactions ofthe pion cloud around the nucleon and therefore probe the symmetries of QCD directly. However neutroninformation to date is extremely fragmentary. Experimentally the target neutron must be bound in a lightnucleus, which complicates the polarisability analysis. On the other hand, this provides the opportunity tocouple to the charged meson-exchange currents which bind the nucleus together. Around pion-productionthreshold, one can also study the transition to a dynamical ∆, to understand better its role not only fornucleons, but also for the few-body nuclei.

New experiments on light nuclei are needed to determine speci�c polarisabilities and test our understandingof strong and photonuclear interactions on the hadronic scale. A recent review [2] has emphasised the degreeof scatter in the unpolarised proton database (Fig.1) and the poor quality of (sometimes contradictory) databetween 190 MeV and 250 MeV. For the deuteron (Sec.2.0.2), only 29 points are published, with limitedangular and energy coverage (49 to 95 MeV) and typical uncertainties of around ±7 − 10%. No data existfor 3He or 4He, although 6Li measurements have recently been made at HIγS (Sec.2.0.2). Our currentunderstanding of the nucleon polarisabilities is limited by experimental, rather than theoretical uncertainties.

The past twenty years have seen signi�cant developments in theory using a variety of techniques, which includeχEFT , dispersion relations, quark models and lattice QCD. χEFT predictions exist for a variety of polarisedand unpolarised observables for protons, deuterons and 3He . An energy-dependent multipole analysis ofCompton scattering provides important information on the scales, symmetries and mechanisms which governthe interactions between the low-energy constituents of the nucleon. With improved experimental data onecan explore topics such as the chiral symmetry of the pion cloud and its isospin-symmetry breaking e�ects,the properties of the ∆(1232) resonance, nuclear-binding e�ects, and the e�ect of various degrees-of-freedomon the response of the nucleon spin to electromagnetic �elds.

Fig.2 displays the calculation made by Shukla et al. [9] for γ + 3He → γ +3 He, using Heavy-BχPT(HBχPT ) to order O(e2Q). The authors of Ref.[9] emphasised that these calculations are a �rst exploratorye�ort and highlighted possible improvement by extension to O(e3Q2) and explicit inclusion of the ∆. Theyalso advocated further exploration of the dependence on choice of nuclear wavefunction (and techniques toreduce this) and of e�ects due to the use of a �static approximation� for nucleons in HBχPT. Calculationsof this type were a major point of discussion at the recent ECT workshop in Trento. There is con�dence [10]that 3He calculations, can be made su�ciently accurate to extract meaningful neutron polarisabilities. Agroup of theorists who specialise in this �eld have expressed strong support [11] for the current experimentalprogramme of Compton scattering.

He isotopes (Z=2) have a signi�cantly larger Compton scattering cross section than the deuteron (Z=1)and at 120 MeV the cross section scales as ∼ Z. In He, interference of the proton Thomson terms withthe neutron polarisability amplitudes produces a greater sensitivity of the di�erential cross section to thepolarisabilities. Experiments at lower energies are easier to interpret theoretically although the sensitivityto the polarisabilities increases with energy. Theoretical interpretation of Compton data in terms of theproperties of the individual nucleons is well developed [2] for the proton and deuteron around the pion-production threshold, has been started for 3He [9] and is under investigation for 6Li [12]. 4He is both ascalar and isoscalar target, o�ering the potential for complementary polarisability information, and it willalso provide important checks on the accuracy of the theoretical treatment of nuclear binding and meson-exchange currents. Ultimately a polarised 3He (e�ectively a polarised neutron target) experiment wouldprovide access to the neutron spin polarisabilities. However, before this stage is reached, it is importantto test χEFT predictions of the 3He di�erential cross section which are relatively undeveloped due to acomplete lack of data. New data on 4He will provide a more exacting test of χEFT predictions and also analternative proton-neutron �mix� of the isospin averaged polarisabilities.

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Figure 2: Calculation of the γ +3 He → γ +3 He di�erential cross section [9] showing the dependence onαnE1 (top 4 plots) and βnM1(bottom 4 plots). Each set of 4: top-left 60 MeV, top-right: 80 MeV, bottom-left:100 MeV, bottom-right: 120 MeV. Curves top: full ∆αnE1 =0, long-dash =-4; dot-dash =-2; dot =+2; dash=+4. Curves bottom: full ∆βnM1=0; long-dash =-2; dot-dash =+2; dotted = +4; dash = +6. All in units10−4 fm3.

2 Previous Experiments

Previous experiments to obtain the nucleon polarisabilities are summarised in this section. In general,experiments on the neutron are more di�cult so that there is much less neutron data compared to the

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proton and generally it has relatively large uncertainties.

2.0.1 Compton Scattering on the proton

Fig.1 displays proton Compton data up to ω = 300 MeV. Pioneering e�orts to measure proton Comptonscattering were made as early as the 1950's, but the �eld was reinvigorated when high-duty-factor electronaccelerators appeared, allowing experimental techniques such as photon tagging to be used. The �rst taggedphoton measurement was made at Illinois [13], followed by measurements at SAL [14, 15] and Mainz [16, 17].Experiments have also been made at somewhat higher energies at Mainz [22] as a test of dispersion theorypredictions into the second resonance region. The �rst polarised-beam measurements (Σ3 asymmetry) havebeen made at LEGS [18] in the ∆ resonance region. This data produced the �rst value for γpπ but this wasrevised signi�cantly after subsequent Mainz measurements [19, 17]. Note that a value γp0 has been obtainedfrom data taken to evaluate the Gerasimov-Drell-Hearn integral [20].

Probably the biggest in�uence on proton polarisabilities up to now has been the Mainz measurement madewith TAPS, covering an incident energy range ω = 60 − 160 MeV and scattering angles θγ = 59 − 155◦

[17]. Recent uncertainty about the extraction of βM1(ω) have motivated a new measurement of σ(ω, θγ′) andΣ3(ω, θγ′) at Mainz [7] using the CB and TAPS. Double polarised measurements at Mainz [6] are providingthe �rst direct evidence on the spin polarisabilities.

2.0.2 Neutron Compton Scattering

Figure 3: The di�erential cross section for Compton scattering on the deuteron. Data points: circle [30],triangle [31], diamonds [32]. The curves are from a χEFT �t to these data [2].

For the proton, the electric and magnetic polarisabilities have a relatively pronounced e�ect on the crosssection, due to interference with the Thomson amplitude. For a free neutron, there is no Thomson term, sothe e�ect of the polarisabilities on the cross section is smaller and consequently neutron Compton scatteringwas for many years not considered to be feasible experimentally. An alternative technique to extract polar-isabilities from electromagnetic scattering of ∼ 600 keV neutrons in the Coulomb �eld of enriched 208Pb [24]

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has been used. However there are sizeable systematic uncertainties in this procedure and the actual size ofthe uncertainties is disputed.

Lacking a free neutron target, almost all of the information on the neutron polarisabilities, αnE1 and βnM1,comes from Compton scattering on the deuteron. Quasi free γ +2 H → γ + n + p, where the proton is aspectator, has been used to approximate free scattering and pioneering work [25] was performed at Mainz.However there was considerable model dependence in the extraction of αnE1, β

nM1 from sub-pion-threshold

data and further experiments were performed at somewhat higher energies at SAL [26] and Mainz [27]. TheMainz experiment covered the incident energy range ω = 200 − 400 MeV and measured γ′ − n coincidencesusing the CATS NaI gamma spectrometer and a neutron time-of-�ight array. Dispersion theory analyses[28] of these data produced the scalar polarisabilities αnE1 = 12.5 ± 1.8(stat)+1.1

−0.6(sys) ± 1.1(theory), βnM1 =2.7 ∓ 1.8(stat)+0.6

−1.1(sys) ∓ 1.1(theory) with the condition [29] αnE1 + βnM1 = 15.2 (all units 10−4 fm3). Todate the only value of γnπ (= 58.6± 4.0) was obtained from a �t to these data, where αnE1, β

nM1 and γnπ were

treated as free parameters.

Given a knowledge of the proton polarisabilites, the neutron polarisabilities can be extracted from the isospin-averaged nucleon polarisabilities obtained from elastic Compton scattering on the deuteron. The dependenceof the isospin-averaged polarizabilities on cross section is enhanced strongly, compared with Compton scat-tering by free neutrons, due to interference with the Thomson amplitude. On the other hand, bound nucleonsrequire consideration of coupling to meson exchange currents and the n − p interaction in the intermediatestate. Experimentally the technique requires very good γ′ energy resolution to separate elastic scatteringfrom breakup channels (2.225 MeV separation).

Following a pioneering Illinois experiment [30], di�erential cross sections for Compton scattering from thedeuteron were measured at MAX-Lab [31] and SAL [32]

An analysis [2] of these data in terms of χEFT (Fig.3) has produced the isoscalar polarisabilities αsE1 =10.5± 2.0(stat)± 0.8(theory), βsM1 = 3.6± 1.0(stat)± 0.8(theory) from which neutron values αnE1 = 10.5±4.0(stat)± 0.8(theory), βnM1 = 4.4± 2.1(stat)± 0.8(theory) were obtained.Most recently, a new MAX-lab experiment [33] has been performed at incident energies ω = 67 − 116 MeVand scattering angles θγ′ = 60, 90, 120, 150◦, using three very large NaI spectrometers. It is expected thatthese data will be published shortly.

No Compton scattering data exists for the He isotopes, but there has been a measurement on 6Li [34] at theHIγs facility at relatively low energy. A theoretical framework to interpret these data is under investigation[12].

3 Experimental Method

We propose to measure the double di�erential cross section σ(ω, θγ) for Compton scattering on 3He and 4He,with su�cient precision to extract values of the isospin averaged polarisabilities αsE1, β

sM1 . Extraction will be

preformed using a χEFT �t to the angular distributions, which will be binned in 10 MeV intervals of ω andin 0.2 intervals of cos θγ . With 10 angles per energy, the angular de�nition of the present experiment will besuperior to previous experiments on the deuteron (Fig. 3), placing better constraints on �tting procedures.The energy dependence of the cross section is expected to be smooth and averaging over 10 MeV wide binsis not expected to be problematic. The experiment will take place at the Mainz tagged-photon facility, usingthe main Glasgow-Mainz tagger. The ∼ 4π Crystal-Ball and TAPS electromagnetic calorimeters will detectthe γ′ with good angle and energy resolution, while a high-pressure He gas-scintillator Active Target (AT)will detect the recoiling He nucleus.

A coincidence between the AT and CB/TAPS will be e�ective in suppressing background processes.

3.1 Tagged Photon Facility

The experiment will employ an unpolarised photon beam produced by bremsstrahlung on a 10µm Cu radiator.The bremsstrahlung is momentum tagged in the Glasgow-Mainz tagged-photon spectrometer [35], which is abroad-band dipole covering ∼ 5−95% of E0, the energy of the primary electron beam. At E0 = 855 MeV, theminimum tagged-photon energy is . 50 MeV, extending up to∼ 795 MeV and the average energy width perchannel of the focal-plane detector is ∼ 2 MeV. This detector consists of 352 overlapping plastic scintillators

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and, to avoid excessive counting rates in the low-ω detector elements, only those corresponding to ω > 80 MeVwill be turned on. We will aim for a channel rate of ∼ 1 MHz at ω ∼ 120 MeV. If one factors in the expectedtagging e�ciency εtagg ∼ 50% (obtained with a photon collimator diameter of 4 mm), then the di�erentialtagged-photon rate will be ∼ 2.5× 105 Hz/MeV.

3.2 The Active Target

Figure 4: AT geometry rendered by the Geant-4 simulation (Sec.4.1). The left panel shows the internalvolume �lled with He gas (cyan), while the right panel shows the outer Al body of the AT.

This experiment will use a high-pressure gas-scintillator AT (Fig.4), developed originally for photonuclearexperiments at MAX-lab [36]. The target operates at a pressure of 2 MPa and an active length of 288 mmproduces an overall thickness of 0.105 g.cm−2 for 4He. It consist of four main cells, each read out by fourphotomultipliers (PMT), and two auxiliary, end-cap cells, each read by a single PMT. The end-cap cells isolatethe main cells from particles produced in the Be windows, which hold the pressure and are not included inthe target thickness. Individual cells are isolated optically by 5 µm aluminised Mylar foil and a small-borepipe running between the cells allows the pressure to equalise.

Scintillations in pure He fall mainly in the vacuum UV region which is di�cult to detect e�ciently, so thatthey are shifted to ∼ 420 nm by addition of ∼ 500 ppm N2. This also produces a sharp signal which isbene�cial in terms of timing precision and freedom from pile up. The observed rise and fall times are ∼ 5 nsand timing resolution, measured in tagged photon experiments at MAX-lab, is ∼ 1 ns (σ). The target ishighly insensitive to electrons and can be operated in bremsstrahlung beams of integrated intensity ∼ 108 Hz.At MAX-lab the AT was placed in a maximum-intensity, tagged-photon beam, where greater than MHz rateson the focal-plane detectors produced a few kHz on the AT. Thus we expect that the counting rate in thefocal-plane detector of the Glasgow-Mainz tagger will reach its upper limit well before the AT. Scintillationsin He are approximately linear (i.e. there is little dependence of signal amplitude on ion velocity) and so theAT counts low energy He ions e�ciently. H ions (p, d, 3H) are also detected, but they tend to deposit lessenergy in the target than He ions.

3.3 Crystal Ball, TAPS

The combination of the CB and TAPS provides an electromagnetic calorimeter with excellent energy reso-lution and almost 4π coverage. The CB is the main detector, consisting of 672 NaI(Tl) crystals, which �ttogether into a spherical shape. The polar angle coverage (lab) is 20 − 160◦ with full azimuthal coverage.The energy resolution for photons is σ/E = 0.027/E1/4 (E in GeV) and angular resolution 2− 3◦. The holein forward angle coverage is �lled by TAPS, an array of 384 BaF2 crystals arranged as a hexagonal wall. Itcovers lab angles up to 20◦ over the full 360◦ azimuth. Recently the inner two �rings� (about the photon beamaxis) of BaF2 crystals have been replaced by PbWO4. These have ¼ the cross section of the BaF2 crystalsand also a much shorter pulse length. They are thus much less susceptible to rate-dependent losses at verysmall angles, where the atomic background is maximum. TAPS also has a forward layer of thin plastic �veto�

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tiles to distinguish charged and neutral particles and the BaF2 crystals can distinguish nucleons from lighterparticles by pulse-shape analysis (as well as time of �ight).

For this experiment the particle ID and tracking detectors located at the centre of the CB will be removedto make space for the AT (Fig. 5). The AT itself will provide identi�cation of He ions, recoiling after photonscattering. As space is quite restricted, the PMTs on the end-cap cells may be removed as they have provedto be of marginal utility in analyses of MAX-lab data. The PMT currently attached to the main AT cellsare too long to �t comfortably and will be replaced by shorter alternatives.

Figure 5: Side view of the Crystal Ball and TAPS calorimeters, generated by the A2 Monte Carlo simulation.The active target is located at the centre of the CB and the right panel shows this in more detail.

3.4 Experimental Trigger and DAQ

Recently the trigger and DAQ systems in the Mainz Tagger Hall have been upgraded. The DAQ system isnow based around 23 parallel readout streams which will potentially quadruple the interrupt rate capabilityfrom ∼ 1 kHz to ∼ 4 kHz. The primary trigger will be based on a signal from the active target with therequirement that there is at least one hit cluster detected in the CB or TAPS. This will also allow thedetection of coherent π0 or η production, where two or more photons are produced in coincidence. Based onMAX-lab experience, we would expect the AT to run at rates of several kHz and the application of a CB orTAPS coincidence to bring this down to well below the kHz level. This can be handled comfortably by theDAQ system.

4 Extraction of the Compton Signal

4.1 Monte Carlo Simulation

A Monte Carlo simulation which tracks the reaction products through a realistic model of the detectorsystems is being employed to calculate the response to various reaction channels. The software to simulatethe experiment has three components:

1. An event generator (�AcquMC� [37]) generates a series of kinematic events and stores them in a ROOTtree �le. The photon beam energy and angle are sampled randomly from user speci�ed distributions.The interaction position of the photon with a target nucleon or nucleus is sampled along the length ofthe target. For quasi-free γ−N interactions nucleons inside a nucleus were given a �Fermi momentum�,modelled according to F (p) = p2 exp(−p2/2σ2). Reaction-product particle momenta were sampledfrom available kinematic phase space.

2. Final-state particle interactions in the detector system are simulated using a Geant-4 based modelwhich incorporates the AT, CB and TAPS. The CB and TAPS components have been taken from the�A2� simulation [38] which is a standard software tool of the A2 collaboration. The AT simulation

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[36] was developed for MAX-lab experiments and grafted into the A2 simulation. It uses a realisticmodel of the detector geometry which includes all of the metal and glass incorporated in the highpressure gas container and incorporates the latest low-energy �physics lists� to model electromagneticand hadronic interactions. The variation of scintillation light collection e�ciency with interactionposition is predetermined in a separate calculation and folded with deposited energy as particles aretracked through the detector. The scintillation photon yield has been adjusted to match the observedsmearing of measured energy distributions at MAX-lab.

3. The format of the Monte Carlo generated data is similar to actual data produced in the Mainz TaggerHall. Thus it can be analysed in an almost identical manner, employing same code (�AcquRoot� [37])as used for analysis of real experimental data, with the same techniques and algorithms to reconstructthe reaction kinematics from energies, times and positions in detector elements.

4.2 Compton Scattering on 3He

Simulations have been made for incident photon energies ω = 100 − 150 MeV and, for the purpose ofacceptance calculations, the Compton di�erential cross section has been assumed isotropic. The correlationbetween the pulse height signal in the AT and the scattered photon angle in the CB or TAPS is displayed inFig.6. The Compton signal is obtained from:

Pmiss = (P γ + P T − P γ′); Tmiss = Pmiss : T ; ωmiss = Tmiss − TAT (2)

where Pmiss is the missing four-momentum obtained if only the γ′ is detected, Tmiss is the missing kineticenergy derived from Pmiss, and TAT is the target kinetic energy obtained from the measured pulse height.Calculations have been made for coherent Compton scattering γ+3He→ γ+3He, and background processeswhich produce a neutral particle in the �nal state: quasi-free γ +3 He→ γ + p+ d and breakup γ +3 He→n+ p+ p. Coherent γ +3 He→ π0 +He3, where Eγ exceeds π0 threshold and a single decay photon only isdetected, was also simulated.

Fig.7 compares the missing-energy balance ωmiss for coherent Compton scattering and the background pro-cesses. The coherent Compton signal has been selected by making cuts −2.0 < ωmiss < 1.0 MeV andTAT > 1.0 MeV, before calculating the acceptance (Fig.8) for the channels listed above. The small Comptonacceptance at forward angles results from the low energy of the recoiling 3He (Fig.6), while at backwardangles it is due to the lack of CB coverage at θlab > 160◦. The present calculation suggests that there will besome contamination of the coherent signal by quasi-free Compton scattering, which will require a quantitativeestimation.

4.3 Compton Scattering on 4He

Similar calculations have been made for the signal from γ +4 He→ γ +4 He. With 4He more permutationsof background processes which produce neutral particle(s) are possible: quasi-free Compton γ +4 He →γ+n+3He, γ+4He→ γ+p+3H; breakup γ+4He→ n+3He, γ+4He→ n+p+d, γ+4He→ n+n+p+p.Coherent γ +4 He → π0 +He4, where Eγ exceeds π0 threshold and a single decay photon only is detected,was also simulated. Plots of TAT vs. ωmiss are given in Fig.9. Again for Compton scattering the ωmissdistribution peaks at values around zero. The calculated acceptance is broadly similar to the 3He case,except that the forward-angle drop is more pronounced due to lower recoiling 4He energies.

4.4 Threshold Meson Photoproduction

While the present experiment is motivated to investigate Compton scattering, it will also collect data oncoherent π0 photoproduction on He isotopes. Close to threshold the recoiling He ion will have su�cientlylow energy to stop and produce a large-amplitude signal in the target. Similar to the Compton scatteringcase, a kinetic-energy balance parameter ωmiss (eq.3) can be used to select the coherent π0 signal.

Pmiss = (P γ + P T − P π0); Tmiss = Pmiss : T ; ωmiss = Tmiss − TAT (3)

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Figure 6: Correlation of the AT energy TAT (from pulse height) with the γ′ scattering angle, measured inCB or TAPS for the γ +3 He→ γ +3 He reaction at incident energies Eγ = 100− 150 MeV.

Fig.11 displays TAT vs. ωmiss for coherent π0 production on 3He and 4He and the acceptance for detection

of the recoiling He ion and the two photons from π0 decay. As in the Compton scattering case, the ωmissdistribution shows a peak at values close to zero. Selecting ωmiss in this peak region and requiring thatTAT > 1.0 MeV, produces the acceptances. These are on average lower than for Compton scattering since

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Figure 7: Kinetic-energy balance ωmiss (eq.2) for γ+3He→ γ+3He (black line); γ+3He→ γ+p+d (blueline); γ +3 He→ n+ p+ p (red line); γ +3 He→ π0 +3 He (magenta line).

Figure 8: Acceptance for for γ+3He→ γ+3He (black line); γ+3He→ γ+p+d (blue line); γ+3He→ n+p+p(red line); γ +3 He→ π0 +3 He (green line).

two photons must be detected. However the dependence on θπlab, reconstructed from the two decay photons,is less strong at forward and backward angles.

While the major focus of the present Compton experiment will be on energies just below π0 threshold, thedata will include numerous π0 events at tagged-photon energies from π0 threshold up to almost 800 MeV.

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Figure 9: Distributions of TAT vs. ωmiss for various γ +4 He reaction channels

Figure 10: Simulated acceptance for γ+4He reaction channels: γ+4He→ γ+4He (black line); γ+4He→γ+n+3He (blue line); γ+4He→ γ+p+3H (magenta line);γ+3He→ n+p+d (red line); γ+3He→ 2n+2p(brown line); γ +4 He→ π0 +4 He (green line).

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Figure 11: Near threshold, coherent π0 photoproduction. The incident photon energy range ω = 135 −200 MeV

Preliminary calculations shown here suggest that this data could be analysed e�ectively to produce di�erentialcross sections for coherent meson photoproduction on 3He and 4He at energies relatively close to threshold.The relative merits of an AT with respect to a conventional 3He target will be investigated for coherent π0

production. An LOI [40] proposing to use this channel to extract the Eπ0n

0+ amplitude will be submitted tothe 2013 MAMI PAC.

5 Count Rate Estimate Uncertainties and Beam Time Request

Estimates of the counting rate are based on experience of related experiments at Mainz and on acceptancescalculated using the Monte Carlo simulation (Sec.4.1).

5.1 3He Counting Rate and Statistical Uncertainties

The precision which can be attained for the γ+3He→ γ+3He di�erential cross section has been estimatedusing the following assumptions:

1. The tagger electron detector rate in a 2 MeV wide channel is 1 MHz. Employing a 4 mm diameterphoton collimator, a tagging e�ciency of ∼ 50% will be obtained, giving a tagged-photon rate of2.5 MHz in a 10 MeV wide bin.

2. The target thickness is 0.075 g/cm2, producing a reaction rate of 143/hr per 10 MeV bin of Eγ , per µbof cross section.

3. The cross section calculated by Shukla et al. [9] (Fig.2) is employed. At 120 MeV the angle-integratedcross section is ∼ 200 nb.

4. The calculated acceptance (Fig. 8) is employed.

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5. With 10 bins of cosϑlab, 200 hr of beam time produces statistical uncertainties varying from 4 - 7%.

The calculated statistical uncertainties at Eγ = 120 ± 5 MeV for a di�erential cross section falling on thecurve of Ref. [9] are displayed in Fig.12.

Figure 12: The projected precision for the γ +3 He → γ +3 He di�erential cross section at incident energyEγ = 115 − 125 MeV. The full curve is the χEFT calculation of Ref.[9]. The projected error bars showstatistical uncertainties.

5.2 4He Counting Rate and Statistical Uncertainties

The 4He counting rate estimate has been made assuming that the 3He and 4He cross sections are the same.The target thickness (0.105 g/cm2), is very similar in terms of the number of target nuclei per cm2 and sothe same reaction rate has been taken as for 3He. The counting rate estimate uses the acceptance calculationof Fig.10. Since the recoiling 4He has very low energy after forward angle scattering, the acceptance is lowand thus the statistical uncertainty is large in the forward-angle bin of cos θlab.

5.3 Beam Time Request

Task Target Time with beam (hr) Time without beam (hr)

Initial Setup 75Tagging E�ciency 4He 25Production Running 4He 200

Total 4He 225 75Target re�ll 25

Production Running 3He 200Tagging E�ciency 3He 25

Total 3He 225 25

Table 1: Break down of the beam time request.

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Figure 13: The projected precision for the γ +4 He → γ +4 He di�erential cross section at incident energyω = 115−125 MeV. The full curve is the χEFT calculation of Ref.[9] for 3He. The projected error bars showstatistical uncertainties.

A break down of the requested time for this experiment is given in Table 1. A total of 450 hr beam time isrequested for 3He and 4He Compton measurements, which includes time for tagging e�ciency measurement.The setup, requiring 75 hr, would be performed when the tagger hall is free and would not interfere withbeam operation. A change of target gas requires 25 hr. However the measurement could also be in twoseparate runs.

Although the AT is well tried at MAX-lab, it is new to Mainz. From the practical point of view it would bebene�cial to run 4He �rst, in order to test and debug the mode of operation inside the Crystal Ball. Thiswould avoid any waste of 3He gas, which is currently a precious commodity.

6 Summary

We propose to measure Compton scattering on 3He and 4He nuclei at Mainz using tagged photons of energyω > 80 MeV. The scattered photons will be detected in the CB-TAPS segmented electromagnetic calorimeter,and the recoiling He nuclei in a high-pressure He-gas scintillator, which also acts as the experimental target.The motivation is to extract the isospin-averaged, scalar nucleon polarisabilities and these in turn will yieldvalues for the neutron scalar polarisabilities. He (Z=2) has the advantage over deuterium (Z=1) as an e�ectiveneutron target in that the Compton cross section is higher and the di�erential cross section of more sensitiveto the values of the polarisabilities.

The extraction will depend on a Chiral Perturbation Theory �t to the di�erential cross section and we expectthat the imminent prospect of new data will spur the theoretical e�ort to re�ne the current description of 3HeCompton scattering and extend the calculations to 4He. The latter treatment will be is signi�cantly morecomplicated, and will serve as a rigorous test of several aspects of the calculation. Ultimately if consistentvalues of the polarisabilities can be obtained from 3He and 4He then con�dence in the accuracy of theprocedure is increased.

We request 200 hr of beam time to measure γ+3He→ γ+3He, which will yield the di�erential cross sectionσ(ω, θγ′). Binned in energy intervals of ∆ω = 10_MeV and angle intervals of ∆ cos θγ′ = 0.2 , 200 hr willallow several hundred counts to be accumulated per bin, yielding statistical uncertainties from 4-7% per bin.

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200 hr is also requested to measure γ +4 He → γ +4 He. This will give similar statistical uncertainties to3He apart from the forward angle bin (cos θγ′ = 0.8 − 1.0) where the experimental acceptance is low. Inaddition to production running time, 50 hr total is request for tagging e�ciency measurements, and 75 hr isrequested for setting up the apparatus without beam.

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