Compton Scattering from Nucleon and Nuclear Targets

M.W. Ahmed1, C.W. Arnold2, T. Averett3, M. Blackston1, X.Z. Cai4, J.R. Calarco5,J.G. Chen4, T. Clegg2, D. Crabb6, D. Dutta1, G. Feldman7, H. Gao1, A. Gasparian8,

W. Guo4, C. Howell1, H. Karwowski2, M. Kovash9, K. Kramer1, Y.G. Ma4, R.Miskimen10, A.M. Nathan11, B. Norum6, R. Pedroni8, C.B. Wang4, H.W. Wang4,

H.R. Weller1, S. Whisnant12 Y. Wu13, W. Xu4, Y. Xu4, A. Young14, X. Zong11TUNL & Duke University

2 TUNL & University of North Carolina, Chapel Hill3College of William & Mary

4 Institute of Applied Physics,

Shanghai, Chinese Academy of Science5 University of New Hampshire

6 University of Virginia7George Washington University

8 North Carolina A&T State University9 University of Kentucky, Lexington

10University of Massachusetts, Amherst11 University of Illinois,

Urbana-Champaign12 James Madison University13 DFELL & Duke University

14 TUNL & North Carolina State University, Raleigh

AbstractThe High Intensity Gamma Source (HIγS) at Duke Free Electron Laboratory opens a new

window to the study of fundamental quantities related to the structure of the nucleon through

Compton scattering from both polarized and unpolarized nucleon and nuclear targets. These

studies allow for the extraction of the neutron electromagnetic polarizabilities with unprecedented

accuracy, and will provide data for the first time on currently unknown quantities such as the

spin polarizabilities of the neutron. Compton scattering from the helium isotopes will allow for a

precision determination of the 3He and 4He polarizabilities. These studies will comprise precision

tests of effective field theories, lattice QCD calculations and predictions from the standard model of

nuclear physics. In order to carry out this important and extensive Compton Scattering program

at HIγS, a collaboration involving physicists from 13 Universities has made a detailed study of

the requirements of an experimental program to achieve these goals. They have concluded that a

large acceptance photon detection system is required. We request the support of such a detection

system (HINDA) from the NSF through the agency’s MRI program.

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INTRODUCTION

Understanding the structure of the nucleon from the underlying theory of strong interac-tion in terms of quark and gluon degrees of freedom is a fundamental and challenging taskin physics. The experimental and theoretical investigation of the structure of the nucleonhas been more intense than ever in the last two decades or so, largely due to progress andbreakthroughs achieved both in experiments and theories. With the development in polar-ized beam, recoil polarimetry, and polarized target technologies, polarization experimentshave provided more precise data on quantities ranging from electromagnetic form factors ofthe nucleon from elastic electron-nucleon scattering to spin structure functions probed indeep inelastic lepton-nucleon scattering. At the same time, significant theoretical progresshas been made in describing these data and in providing new insight in understanding thestructure of the nucleon in areas ranging from effective field theories to lattice QCD. Thenewly discovered Generalized Parton Distributions (GPDs)[1, 2], which can be accessedthrough deeply virtual Compton scattering and deeply virtual meson production, connectthe nucleon form factors and the nucleon structure functions probed in the deep-inelasticscattering experiments. The GPDs provide new insights into the structure of the nucleon,and possibly provide a complete map of the nucleon wave-function.

Nucleon polarizabilities comprise another set of fundamental quantities related to thestructure of the nucleon, describing the response of the nucleon to external electromagneticfields. These quantities can be accessed through low energy Compton scattering experi-ments. Compton scattering from nucleons at low energy is specified by low-energy theoremsup to and including terms linear in photon energy. These terms are completely determinedby the static properties of the nucleon, i.e. the nucleon charge, mass and its anomalousmagnetic moment. At next to leading order in photon energy there appear new structureconstants which are related to the dynamic response of the nucleon’s internal degrees offreedom. The electric (α) and magnetic (β) scalar polarizabilities, which describe the re-sponse of the nucleon to external electric and magnetic field, respectively, enter in termswhich are second order in photon energy. At the third order four new parameters, γ1 toγ4, the spin polarizabilities, appear. While spin polarizabilities do not have as intuitive aphysical interpretation as the electric and magnetic polarizabilities, they are neverthelessjust as fundamental. The closest analogy in classical physics that one can make to spinpolarizabilities is the Faraday rotation in which the linear polarization of incoming light isrotated going through a spin polarized medium.

In the last two decades or so significant efforts have been devoted to Compton scatteringmeasurements from the proton in order to extract the proton electric (α) and magnetic(β) polarizabilities. The most precise information on these two quantities are from therecent Mainz experiment [3]: α = [11.9 ± 0.5(stat.) ∓ 1.3(syst.) ± 0.3(mod.)] · 10−4 fm3,β = [1.2±0.7(stat.)±0.3(syst.)±0.4(mod.)]·10−4 fm3. While the proton electric and magneticpolarizabilities are known relatively well, our knowledge of the neutron polarizabilities ismuch poorer than that of the proton due to the lack of free neutron targets in nature. Theneutron electric and magnetic polarizabilities have been extracted from experiments usingdeuterium targets. The first experiment with a deuterium target was low-energy neutronscattering from heavy nuclei [4]. In recent years, coherent elastic Compton scattering bythe deuteron, and the quasi-free Compton scattering from the deuteron are commonly used.The most precise information on the neutron’s electric (αn) and magnetic polarizabilities(βn) is from the quasifree Compton scattering experiment carried out at Mainz [5]: αn =

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12.5±1.8(stat)+1.1−0.6(syst)±1.1(model), βn = 2.7∓1.8(stat)+0.6−1.1(model)∓1.1(model), in units

of 10−4 fm3.Compared to the nucleon electric and magnetic polarizabilities, very little is known about

nucleon spin polarizabilities (γi, i = 1 − 4). The only quantities which have been extractedso far are the forward and backward spin polarizabilities, γ0 and γπ. The forward andbackward spin polarizabilities are two independent linear combinations of γ1, γ2 and γ4.In order to determine all four spin polarizabilities separately, two additional measurementswhich are sensitive to the nucleon’s spin polarizabilities are needed. Unpolarized Comptonscattering differential cross-section measurements are not sensitive to the nucleon spin po-larizabilities. Double-polarization asymmetries from circularly polarized photons Comptonscattering off a polarized nucleon target have been shown to be sensitive to the nucleonspin polarizabilities [6, 7]. Single spin observables and double-polarization observables fromCompton scattering on nucleon and nuclear targets are being proposed with the upgradedHIγS photon energy and high-intensity photon flux. These new experiments will advanceour knowledge of the nucleon polarizabilities greatly, therefore providing stringent tests oftheories.

COMPTON SCATTERING AT LOW ENERGIES

The general amplitude for Compton scattering based on parity, charge conjugation, andtime reversal symmetry can be written [9] in terms of six structure dependent functionsAi(ω, θ), i = 1, ...6 as:

T = A1(ω, θ)~�∗′· ~� + A2(ω, θ)~�∗

′· k̂~� · k̂′ (1)

+iA3(ω, θ)~σ · (~�∗′× ~�) + iA4(ω, θ)~σ · (k̂′ × k̂)~�∗

′· ~� +

iA5(ω, θ)~σ ·[

(~�∗′× k̂)~� · k̂′ − (~� × k̂′)~�∗

′· k̂]

iA6(ω, θ)~σ ·[

(~�∗′× k̂′)~� · k̂′ − (~� × k̂)~�∗

′· k̂]

,

where ω(= ω′) denotes the photon energy in the center-of-mass frame, θ is the center-of-

mass scattering angle of the photon, ~�, k̂ (~�′, k̂′) are the polarization vector and direction ofthe incident (final) photon, and σ represents the spin (polarization) vector of the nucleon.Following the general conventions, the six structure dependent functions, Ai(ω, θ) (i =1, ..., 6) are separated into the pion-pole (“anomalous”) contributions and the remaining(“regular”) terms:

Ai(ω, θ) = Ai(ω, θ)π0−pole + Ai(ω, θ)

reg (2)

One can now carry out a low energy expansion of the six “regular” structure functionsin powers of photon energy:

A1(ω, θ)regc.m. = −Q

e2

MN+ 4π(αE + cos θβM)ω

2 (3)

+4π

MN(αE + βM)(1 + cos θ)ω

3 + O(ω4,1

MN3 ),

3

A2(ω, θ)regc.m. = Q

e2

M2Nω − 4πβMω

2 −4π

MN(αE + βM)ω

3 + O(ω4,1

MN3 ), (4)

A3(ω, θ)regc.m. =

[

Q(Q + 2κ) − (Q + κ)2 cos θ] e2

2M2Nω (5)

+4π[γ1 − (γ2 + 2γ4) cos θ]ω3 + O(ω4,

1

MN3 ),

A4(ω, θ)regc.m. = −

(Q + κ)2e2

2M2Nω + 4πγ2ω

3 + O(ω4,1

MN3 ), (6)

A5(ω, θ)regc.m. =

(Q + κ)2e2

2M2Nω + 4πγ4ω

3 + O(ω4,1

MN3 ), (7)

A6(ω, θ)regc.m. = −

Q(Q + κ)e2

2M2Nω + 4πγ3ω

3 + O(ω4,1

MN3 ). (8)

Where the charge of the nucleon is Q = (1 + τ3)/2, its anomalous magnetic momentis κ = (κs + κvτ3)/2, and the mass of the nucleon is MN . For each structure function theleading order terms in the ω expansion are given by model-independent Born contributions forscattering from a spin 1/2 point particle with an anomalous magnetic moment and are fixedby low energy theorems of current algebra. The higher order terms in ω are model dependentquantities and the comparison between data and theoretical predictions provides sensitivetests of the validity of the theoretical approaches. The more familiar electric (αE) andmagnetic (βM) polarizabilities enter the amplitude at the O(ω

2) and measure the responseor deformation of the system to quasi-static electric and magnetic fields. The γi(i = 1, .., 4),which enter the amplitude at the ω3 order are the so-called spin polarizabilities. Theydetermine independently the response of a microscopic target with spin 1/2 to a quasi-staticelectromagnetic field when the spin degree of freedom is involved. For example, an induceddipole ~ps can be constructed by ~ps = γ3∇(~S · ~B), where ~S denotes the spin of the target.

The forward and backward spin polarizabilities (γ0 and γπ) are linear combination of theγi:

γ0 = γ1 − γ2 − 2γ4 (9)

γπ = γ1 + γ2 + 2γ4

Both γ0 and γπ can be obtained in a model dependent way by relying on a multipole analysisof single-pion-photoproduction data.

Recently, the backward spin polarizability γπ = γ1 + γ2 + 2γ4 has been extracted bythe LEGS group for the first time from unpolarized Compton scattering data from theproton [10]. However, the extracted value γπ = (−27.1 ± 2.2) × 10

−4 fm4 contradicts thepredictions of standard dispersion theory [11–13] as well as those of chiral perturbationtheory [9, 14, 15]. The theoretical prediction for γπ from chiral effective field theory is−36.7 × 10−4 fm4 [9]. The LEGS result is also in disagreement with the TAPS result γπ =(−36.1±2.2)×10−4 fm4 [3]. The most recent Mainz experiment [16] using the LARA detectorextracted a backward polarizability value ranging from (-35.9 to -40.9)×10−4 fm4 dependingon the parameterization used for the photomeson amplitudes, which is in agreement with

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the earlier result from Mainz [3]. The new data confirm the previous observation that thereis a systematic discrepancy between Mainz results and LEGS’ results. The clarification ofthe situation will benefit from double polarization Compton scattering experiments [17] inwhich circularly polarized photons are scattered off a polarized proton target. The neutronbackward spin polarizability was determined to be γnπ = (58.6 ± 4.0) × 10

−4 fm4 [18].A sum rule exists for γ0, which was originally discovered by Gell-Mann, Goldberger and

Thirring (GGT) [19]:

γ0 =1

4π2

∫ ∞

ν0

dω

ω3[σ−(ω) − σ+(ω)]. (10)

Where ν0 is the pion production threshold, and σ−(ω), σ+(ω) are the total photoabsorp-tion cross-sections when the total helicity of the photon-nucleon system is 1/2 and 3/2 alongthe photon momentum direction, respectively. The GGT sum rule is closely related to theDrell-Hearn-Gerasimov (DHG) sum rule [20], which has gained enormous renewed interestin recent years both experimentally and theoretically [21], and which is given by:

πe2κ2

2M2N= −

∫ ∞

ν0

dω

ω[σ−(ω) − σ+(ω)]. (11)

The following results on γ0 were reported [22] based on the multipole analysis of thephotopion production data:

γ0 ∼ −1.34 × 10−4 fm4 (proton) (12)

γ0 ∼ −0.38 × 10−4 fm4 (neutron)

The most recent extraction of the proton forward spin polarizability is from the MainzGDH experiment [23], and the extracted value of γ0 based on the Mainz data and thedispersion analysis is γ0 = [−1.01 ± 0.08(stat) ± 0.10(syst)] × 10

−4 fm4 [24].

COMPTON SCATTERING FROM DEUTERIUM AND NUCLEON POLARIZ-

ABILITIES

In the past ten years, great progress has been made in studies of the proton polarizabilitiesthrough Compton scattering [3, 26], facilitated largely by the advent of high duty-cycletagged photon facilities. Investigations of the neutron polarizabilities, however, have laggedbehind, primarily due to the lack of free neutron targets. Typically these measurementsare performed on deuterium, using either the quasi-free D(γ, γ ′n)p reaction or the elasticscattering D(γ, γ)D reaction.

In the case of the proton, the electric (αp) and magnetic (βp) polarizabilities enter at orderω2 (where ω is the photon energy) in the Compton cross section, due to an interference withthe leading Thomson amplitude. For a “free” neutron (as in the quasi-free reaction), thereis no Thomson term (the neutron is uncharged), so the polarizabilities enter at order ω4

and are much harder to determine. Moreover, strong model dependences in the analysiscan hinder the extraction of αn and βn. In elastic Compton scattering on deuterium, theThomson term is recovered, so the polarizability extraction is similar (in principle) to theproton case, except for the fact that only the sum of the proton and neutron polarizabilities(αN =

αp+αn2

and βN =βp+βn

2) can be unambiguously deduced from the data. But with the

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improved knowledge of the proton values available today, extracting the values of αn and βnis mostly limited by the quality of the deuteron Compton scattering data.

Only three measurements of the differential cross section for the D(γ, γ)D reaction havebeen performed to date. Lucas et al. at Illinois [27] measured 4 angles at 49 MeV and 2angles at 69 MeV. Lundin et al. at Lund [28] covered only a limited range of forward andbackward angles at 55 and 66 MeV. Hornidge et al. at Saskatoon [29] extended the energyrange up to 95 MeV and obtained a five-point angular distribution. Typical statisticaluncertainties in the differential cross sections were around 10% for the 49-69 MeV data and∼ 7% for the 95 MeV data.

The sensitivity to αN and βN (which we refer to as the “isoscalar” nucleon polarizabilities)increases with incident photon energy, but this poses a daunting experimental problem.The loosely bound deuteron has a two-body breakup threshold only 2.23 MeV below theelastic peak, so that the beam and the γ ray detector (usually NaI) must have sufficientlygood resolution to separate the elastic and inelastic contributions in the scattered photonspectrum. The largest existing anti-coincidence shielded NaI detectors have about 2% energyresolution, so Eγ = 100 MeV is effectively a practical upper limit for performing theseexperiments by detecting the scattered photon. More common anti-coincidence shielded 10”by 10” NaI detectors with ∼ 3% resolution are adequate for incident energies Eγ ≤ 70 MeV.Thus, the lower-energy experiments are easier to do, but at the cost of sacrificing somesensitivity to the polarizabilities.

On the theoretical side, a new “industry” of effective field theory (EFT) has arisen inthe past ten years (starting with the development of chiral perturbation theory) and greatattention has been focused on Compton scattering calculations for the proton and deuteron.Using this formalism, it is possible to make predictions for the D(γ, γ)D cross section whichare in fair agreement with the data at 49-55 MeV [30]. At 66-69 MeV, the data are moresparse and somewhat scattered, so it is difficult to make a meaningful statement about thecomparison. However, at 95 MeV, the agreement between data and theory is not very good,especially at the backward angles [31]. A fit to these data [29], in which the polarizabilitiesare free parameters, yields a result in which βN actually equals or exceeds αN , which is instriking contrast with the proton polarizability values (αp = 12 and βp = 2 in units of 10

−4

fm3). Thus far, the back-angle points in the 95 MeV data set have eluded a theoreticalexplanation, and so it will be particularly important to reproduce these experimental pointsin an independent measurement. Clearly, improved data are required in order to make bettercomparisons with the increasingly precise results coming from modern EFT calculationsbeing carried out by various theoretical groups.

Recently, there have been a series of EFT calculations ( [32–35]) which collectively sug-gest three experimental approaches to the problem of determining the isoscalar nucleonpolarizabilities. These calculations have been performed using EFTs where the pions havebeen integrated out. Such pionless theories have been shown to be highly successful for sys-tems whose characteristic momenta are below the pion mass. We are proposing to performall three measurements in order to obtain a precise, reliable and consistent value of thesequantities and therefore of the neutron polarizabilities.

One of the recent papers [34] recommends that “future high-precision deuteron Comp-ton scattering experiments be performed at 25-35 MeV photon energy where the nucleonpolarizability effects are appreciable and the pionless effective field theory is most reliable.”These authors, in fact, state that a measurement (of the absolute value of the cross section)with a 3% error will constrain the isoscalar electric polarizability to an error 3 × 10−4 fm3,

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or about 25% of the expected value of 12 × 10−4 fm3.There are, in fact, two separate considerations here. One is the absolute value of the

cross section. As pointed out in Ref. [34], there is a 12% effect on this quantity at 30 MeVwhen using αN=10βN=12 as opposed to setting αN and βN equal to zero. If the resultsof Chiral Perturbation Theory (namely, αN=10βN) are accepted, then a 3% measurementof the absolute value of the cross section will indeed determine both αN and βN to within25%. The second consideration comes from examining the shape of the angular distributionof the differential cross section. Rupak has performed some preliminary calculations [33] ofthe differential cross section σ(θ) at 50 MeV, as shown in Fig. 1. Using a model-independentsum rule to constrain αN + βN essentially fixes the forward-angle cross section. The back-angle cross section is sensitive to αN − βN , and clearly there is sensitivity to three differentcombinations of this difference, as seen in Fig. 1. Even so, the data from [27] shown in thefigure are not sufficiently precise (with ∼ 10% error bars) to make a significant determinationof the polarizabilities. However, a 3% statistical uncertainty measurement will determineboth αN and βN to an accuracy of 1 × 10

−4 fm3. We are therefore proposing to perform aprecision measurement of the absolute differential cross section (∼ 5%) and of the angulardistribution (five angles with 3% statistics) at an incident γ-ray energy of 50 MeV. At thisenergy, the effect in the absolute cross section is about 25%, so that a 5% measurement willdetermine αN = 10βN to an accuracy of 2.0 × 10

−4 fm3, which is significantly better thanthe theoretical error [34].

To perform these experiments, elastically scattered photons will be detected simultane-ously in four NaI detectors (which will be upgraded to 16 when this proposal is funded)mounted at azimuthal angles φ = 0◦, 90◦, 180◦, 270◦ (left, up, right, down). A frame to holdthe NaI detectors has been constructed at HIγS and has aptly been dubbed the “eggbeater”due to its appearance. The eggbeater has already been utilized in a Compton-scatteringcommissioning run on oxygen. [36] The eggbeater frame can be rotated in the azimuthalangle φ so that detector locations (horizontal and vertical) can be interchanged in order toreduce systematic errors. The “arms” of the eggbeater allow variation of the polar angleθ between 90◦ and 150◦ in the backward hemisphere (or between 90◦ and 30◦ in the for-ward hemisphere). Thus, a complete set of θ and φ angles can be investigated in a mannerconsistent with reducing systematic effects in the polarized photon asymmetry as much aspossible. The unpolarized cross sections will be obtained from the yields of the four detectorsat different azimuthal angles by summing them.

The very low cross section (∼ 10-15 nb/sr) for this reaction below 100 MeV has beenthe principal hindrance in all of the previous experiments. With the presently anticipatedHIγS photon flux of 5 × 107 Hz in a beam having 3-to-5% energy spread and a liquiddeuterium target of 20.0 cm length, counting rates of ∼ 50-70 counts/hour (per detector)can be achieved. Assuming a background contribution from target cell walls of 25% of theyield, it would require collecting empty-target data for about a quarter of the time of thefull-target running in order to collect reasonable statistics for background subtraction. Evenwith this time allocated for background subtraction, a measurement of the cross section with∼2% accuracy (at one angle) would require a foreground yield of about 2600 counts in twodetectors, which can be achieved in ∼33 hours. The upgraded array will allow us to measurefour angles simultaneously, and to have four detectors at each angle in the up, down, leftand right orientations, as required for linear polarization asymmetry measurements.

Since the HIγS beams are 100% polarized (linear at present, linear and circular fol-lowing the upgrade), the measurements of the cross section discussed above will simul-

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taneously produce measured values of the linear analyzing power, Σ(θ). [Note that

Σ = Y (φ=0+180)−Y (φ=90+270)Y (φ=0+180)+Y (φ=90+270)

. In this case, Rupak and Griesshammer [32] have performed

pionless EFT calculation. Their results, as a function of energy at an angle of θ=120◦ areshown in Fig. 2. In this case we are proposing to measure Σ(120◦) in 10 MeV steps from30 to 70 MeV. As can be seen in Fig. 2, a measurement of Σ(120◦) at the 1% level willdetermine αN to an accuracy of 10% of its value which is about 1 × 10

−4 fm3. Althoughthere is some question about the accuracy of the pionless EFT calculations at and above50 MeV, new EFT calculations are underway which include pion degrees of freedom, andwhich are expected to be valid at energies up to pion-threshold [37]. Preliminary reportsof the results of these calculations indicate that the present predictions are, in fact, quiteaccurate up to 70-80 MeV. [37]

These measurements will require running for 120 hours in order to obtain 1% statistics ateach energy if a flux of 5 × 107 Hz is used. Four energy points (in addition to the one at 50MeV above) can be obtained in about 500 hours of beam time. The detector system beingrequested in this proposal will allow us to make measurements at five angles simultaneously,which will improve the accuracy of our result by more than a factor of 2, significantly reducesystematic errors in measurements of the angular dependence of cross sections and analyzingpowers, and reduce the beam time needed by a factor of five.

The third experiment we are proposing is based on a recent study of the spin-dependentcross sections and asymmetries in deuteron Compton scattering performed using EFT [35].In this work, Compton scattering amplitudes were calculated up to order (Q/Λ)2 in low-energy power counting. The authors considered numerous single and double polarization

asymmetries [35]. They found that the single-spin asymmetry Σy =σJy=+1−σJy=−1σJy=+1+σJy=−1

, where

the photon beam is unpolarized and the deuteron target is polarized in the Jy = ±1 statesexhibited a large sensitivity to the values of αN and βN . For example, the value of Σy at 90

◦

and Eγ = 50 MeV changed by ∼ 26% when αN and βN were changed from being equal tozero to their nominal CHPT values (αN=10βN=12). This implies that a ∼ 2% measurementof Σy will determine αN at the ∼ 7% level of accuracy. This work will utilize the frozen-spinpolarized deuterium target which is presently being constructed for the measurement of theGDH sum-rule integrand of the deuteron at HIγS. [38] The same authors [35] also foundthat the double polarization asymmetry ∆ = σA−σp

σA+σpvaried by ∼ 30% at back angles for a

beam energy of 70 MeV. Therefore, a 3% measurement of ∆ will determine αN at the 10%level of accuracy. Since the HIγS beam is “naturally” polarized, our plan is to measure ∆ aswell as Σy - which will be formed by averaging over the two polarization states of the beam.

The frozen-spin polarized deuterium target construction project is being led by Drs.Blaine Norum and Don Crabb of the University of Virginia in collaboration with researchersat TUNL. This target will be about 10 cm long and will provide about 5 × 1023 nuclei/cm2.A beam of 5 × 107 γ/s will produce ∼ 25 counts per hour per detector. A 2% analyzingpower measurement can be obtained in about 70-100 hours using two detectors, includingbackground measurements. An array of 16 detectors will make it possible to measure eightangles at the 2% level in less than 100 hours of beam time.

The uncertainties being demanded in these measurements require detailed attention tosources of systematic error, as well as to obtaining adequate counting statistics to achievethe desired statistical accuracy. In the case of the absolute cross section measurements, theprimary contributions to the systematic errors are the beam intensity measurements, thedetector efficiencies and solid angle, and the target thickness.

Beam intensities at HIγS have so far been measured using low intensity beams and zero-

8

degree detection in order to calibrate secondary devices which could be used with the fullintensity. In addition, atomic Compton scattering from Cu targets has been used to measurethe beam intensities by placing well collimated detectors at angles where the scattered fluxhad an intensity which could be measured directly. Simulations (EGS4) have been usedto compare to the measurements, which were also checked against the zero-degree resultsabove. Overall, the results of these studies indicated that the beam intensities could bemeasured to an accuracy of ∼ 3%.

A new technique has been developed which will allow us to measure the beam intensities toan accuracy of ∼ 1%. This method will employ a system of precision times 10 attenuatorslocated inside the storage ring area where the beam first emerges. This location of theattenuators will assure that there is no unwanted background in the target room area. Asmany as six attenuators can be inserted, thereby reducing the flux by six orders of magnitude,making zero-degree measurements possible. Our ability to make precise measurements of theattenuation values of these blocks has already been demonstrated by work done on severalmaterials in collaboration with researchers from LANL [40]. Furthermore, we are planningto use the same detector(s) to measure the beam intensity at zero degrees as we will use tomeasure the Compton scattered γ rays. That way, the detector efficiency only enters oncein the determination of the absolute cross section.

The efficiency of large NaI detectors is a quantity which has been studied in great detailat TUNL for several decades. The reference point for these measurements is the 15.07 MeVresonance in 13N observed via the 12C(p,γ) reaction, since the number of photons per protonis well-known [41] for a thick-target yield. We will use the TUNL FN-tandem accelerator tomeasure these efficiencies, and duplicate the geometry including the extended target (whichwe will simulate by moving the 12C foil to duplicate the length of our deuterium target).This will provide us with a direct measure of the product of the efficiency and the solidangle of these detectors. The efficiencies at other energies will be obtained using a GEANTsimulation, being certain to reproduce the measured values at 15.1 MeV. Overall, we areconfident that we can achieve an accuracy of 2% or better for this quantity.

The thickness of our liquid deuterium target will be determined by careful measurementsof the cell geometry and the monitoring of the target cell pressure and temperature duringthe experiment. Following the method of [42] we expect to be able to determine our targetthickness to an accuracy of 1%. The combination of uncertainty in beam intensity (1%),detector efficiency and solid angle (2%), target thickness (1%), and peak fitting/backgroundsubtraction uncertainties (2%) should allow us to make an absolute cross section measure-ment at the ∼ 5 − 6% level of accuracy.

Measurements of the shape of the differential cross section will be dominated by thestatistical accuracy (∼ 3% for our measurements). The use of 20 identical detectors in awell defined geometry will essentially eliminate instrumental asymmetries. This will, in anearly stage of the program, be verified directly by measuring one 5 point angular distributionwith a single detector, rotated to five different positions, and comparing the results to thatobtained when 5 different detectors are used. Detectors will also be interchanged to measuretheir relative efficiencies and to remove instrumental asymmetries.

Systematic errors in analyzing power measurements are much easier to deal with thanare those in cross section measurements. In the case of Σ(θ), the use of four detectors ateach scattering angle (located at φ = 0◦, 90◦, 180◦, 270◦) makes it possible to cancel mostsystematic errors, especially since these detectors will be rotated into and out of each other’sposition. Our pilot experiment on 16O [36] achieved a 5% uncertainty, which was entirely

9

due to counting statistics. We are confident that we can obtain 1% uncertainties, givenadequate statistics.

For the double polarization measurements of ∆(θ), we will also cancel systematic errorsby frequent reversals of the direction of polarization of the beam (on the order of every fewminutes). Again, obtaining 3% uncertainties should not be a problem as long as we are ableto obtain the necessary counting statistics.

In summary, we are proposing a comprehensive experimental program which will de-termine the isoscalar electric and magnetic polarizabilities of the nucleon. There will beseveral experimental approaches to this program, which are designed to be complementaryand which will provide consistency checks on our results. We are proposing to:

• Perform a careful measurement of the differential cross section and the analyzing powerat an incident energy of 50 MeV. EFT calculations and a model independent sum rulewill be used to determine the separate values of αN and βN from the differential crosssection to an accuracy of ∼ 10%. At the same time, an accurate (∼5%) measurementof the absolute cross section will determine the polarizability to an accuracy of ∼ 20%.This result depends upon the theoretical result that αN = 10βN , and, especially whencombined with the above result, will test this theoretical relationship.

• The 100% linearly polarized HIγS beam will be used with unpolarized targets tomeasure the analyzing power as a function of energy to a precision of ∼1%. This willbe done at 4 angles, simultaneously, using the upgraded detector system requested inthis proposal. EFT calculations indicate that these data will enable us to determineαN and βN to an accuracy of ∼10%.

• A frozen-spin polarized deuterium target to measure the target analyzing power to anaccuracy of 3%. This should give an independent measure of the isoscalar polarizabilityto an accuracy of ∼7%.

Together, these measurements are expected to provide neutron polarizability measure-ments for both αn and βn to an accuracy of better than ∼5%. Presently, the best valueshave considerably larger errors with, for example, a 14% statistical uncertainty, a 7% sys-tematic uncertainty and a 9% model uncertainty in αn. In the case of βn the statisticaluncertainty alone is presently 65% [39]. Consistency between the three proposed measure-ments will add confidence to our results, while testing some of the fundamental results ofChiral Perturbation Theory and Effective Field Theory.

NUCLEON SPIN POLARIZABILITIES FROM DOUBLE-POLARIZATION COMP-

TON SCATTERING

Spin polarizabilities of the nucleon can be probed directly via circularly polarized photonsCompton scattered from a polarized nucleon target. Because the Thompson amplitude is realand the spin-dependent amplitudes are complex, it is necessary to use circularly polarizedincident photons to obtain a cross section asymmetry linear in γi at O(ω

3). Therefore,we propose the use of circularly polarized photons incident on the target, where the spinpolarization of the target is either along the beam direction, or in the scattering planetransverse to the beam direction.

10

Hildebrandt et al. [7] studied the sensitivity of the spin-dependent Compton scatteringcross section to the spin-polarizabilities of the proton in an O(p3) calculation. The resultsfrom their calculations are reproduced here in Figs. 3- 7. Here we briefly summarize ourconclusions from an examination of these calculations.

For longitudinal target polarization, the effect of the pion-pole term (chiral anomaly) inthe cross section asymmetry is dominant, and the spin-polarizability effect from nucleonstructure is distinctly weaker. Nevertheless, at photon energies of approximately 100 MeVand lab angles near 110◦ there is significant sensitivity to the polarizabilities. For thetransverse target polarization, the spin-polarizability effect is significant and comparable tothe pion-pole term. This sensitivity is appreciable at lab angles greater than 70◦, and photonenergies of approximately 100 MeV.

Spin-Dependent Compton Scattering Experiment on the Proton

Based on the theoretical considerations presented previously, the proposed experimentalsetup at HIγS is as follows:

• Photon detection over a range in lab angles from 60◦ up to approximately 180◦. Be-cause the largest physics asymmetry is seen with transverse target polarization, thedetector elements should be in the plane of the target polarization.

• Incident photon energies ranging from approximately 30 MeV (almost no spin polar-izability effect) up to 140 MeV. The photon polarization should be circular.

• Data taking with longitudinal and transverse target polarizations.

Polarized proton targets

The UVa group is currently building a frozen-spin (butanol) polarized target for the GDHexperiment at HIγS. This target will be similar to one under construction for JLab Hall B.The Hall B target has a length of 2.5 cm, density of 1.5 g/cm3, and a dilution factor of7.4, which gives 3× 1023 polarized protons per cm2. The polarization is 90%. Although theGDH experiment doesn’t require transverse polarization, this feature has been engineeredinto the GDH target design.

It is a great advantage to use a polarized scintillating target. Having a signal from thetarget that would tag a Compton (or π0) event is a great advantage for reducing backgroundsin these experiments. This possibility was seriously considered for the Spin-Compton [43]and the polarized pion threshold photoproduction experiments at Mainz [44] several yearsago. However, the huge flux of low energy photons in the Mainz bremsstrahlung beam madeuse of the scintillating target problematic. Even with low-Z beam hardeners to reduce thelow energy photon flux, the anticipated minimum ionizing background load in the scintillatorwas over 1 MHz. Fortunately, because of the nearly monochromatic character of the HIγSbeam, the low energy backgrounds will be greatly reduced, making the HIγS beam ideal forthe use of a polarized scintillating target. Presently, the UVa group and the JMU group areplanning to build a Phase 2 target, which will be a scintillating-frozen-spin target.

Here we briefly describe some of the properties of these targets as constructed by PSI,and how data analysis with the target might proceed. The PSI polarized scintillating target

11

is described in detail in Ref. [45]. The PSI group has constructed targets with polarizationsof 84%, with scintillator block sizes up to 5 mm by 18 mm by 18 mm. If the beam entersthe target along the 18 mm axis, this gives target protons 9.4×1022 per cm2. The minimumproton energy that can be detected in these targets is approximately 1.5 MeV. Recently,progress has been made in improving the transparency of the polarized scintillator, whichhas been relatively poor up till now.

To use the scintillating target effectively it will be important to reject quasi-free Comptonscattering events 12C(γ, γp) from Compton events on hydrogen. A Fermi gas model programwas developed to study how these events might be separated. Quasi-free Compton scatteringon 12C was modeled by Compton scattering from an initial state nucleon with momentum

k randomly selected from within a Fermi sphere, with energy given by E =√

k2 + m20 − V0.

The Fermi momentum kf = 221 MeV/c was taken from analysis of quasi-elastic electronscattering on 12C, and the binding potential V0 was adjusted to fit the proton binding energyfor 12C , giving V0 = −41.7 MeV. This potential depth is in good agreement with quasi-elastic electron scattering data. The effects of Pauli blocking in the scattering process weremodeled by requiring that the proton scatter above the Fermi sea in the nuclear potentialframe. Light output in the scintillator is estimated at ∼ 3000 photons per MeV of electronionization energy loss. This light output is 30% of the photon yield usually quoted, to accountfor attenuation in the scintillator. The light collection efficiency and the quantum efficiencyof the photodetector are estimated at 10% and 15%, respectively. Low energy protons areless efficient at producing scintillation light than electrons, and equivalent electron energies,calculated using Madey’s empirical expressions, were used to calculate light production inthe scintillator. PSI has reported energy resolutions approximately 25% worse than normalplastic scintillators in the identical configuration. Although it is unclear if this effect isbecause of reduced light output which has already been taken into account, or because ofsome other effect, to be conservative a multiplying factor of 1.25 is applied to the calculatedenergy resolutions in the scintillating target. The target size was taken as 18 mm in thez (beamline) direction, 18 mm in the x (horizontal direction) and 5 mm in the y (verticaldirection), and proton stopping distances were calculated using energy-range tables fromNIST. Energy resolution in the NaI detector was taken as 3% (FWHM). The NaI detectorhas a size of 10” x 12”, and is positioned 1 m from the target.

Figure 8 shows a scatter plot of measured binding energy in the scintillating target,defined as BE = Ei − Ef − Tp, versus measured proton kinetic energy Tp for 100 MeVCompton scattering at 90◦ in the x (horizontal) plane. In the 2-dimensional plot the freeCompton events at BEy0 MeV and Tpy 9 MeV can be easily identified and separated fromthe quasi-free events.

There will be an appreciable background rate in the scintillating target from pair pro-duction, approximately 400 kHz at an incident photon flux of 107 Hz. However, it shouldbe possible to limit the trigger rate from these events by running a discriminator thresholdsufficiently high that many of the minimum ionizing events fall below threshold, but not sohigh that proton events are lost. For example, at backward Compton scattering angles theproton kinetic energy is 7 times the minimum ionizing signal, and at angles as far forwardas 55◦ degrees the proton kinetic energy is still twice minimum ionizing.

In summary, our Monte-carlo studies indicate that the scintillating target should performvery well in a spin-dependent Compton scattering experiment. In a scatter plot of bindingenergy versus proton kinetic energy the Compton scattering events from the proton areclearly separated from those on 12C, giving a target dilution factor of 1. We plan to construct

12

a prototype target and test it in the actual beam at HIγS. It has been proposed that lightcollection in the PSI target can be improved over the old design by using semiconductordevices directly coupled to the polarized scintillator operating at 100 mK. The detectorthat seems most promising in this application is the silicon photomultiplier (SiPM). Thesedetectors have active areas of 1 mm2, and 1000 pixels. An array of ten of these devicesmounted along the 18 mm by 5 mm side of the scintillating target should give light collectionefficiencies at the 10% level. We have obtained samples of the SiPMs from the Russian groupat DESY, and plan to construct a room temperature, non-polarized prototype of a targetthat can be used in beam tests at HIγS. Optimal use of the scintillating target will alsorequire use of a GHz flash ADC for timing and pulse-height information. When used at PSIin a pion-proton experiment, the ADC and TDC resolution could be greatly increased onceappropriate software algorithms were developed. For example, ADC gates can be optimized,double-pulsing detected and removed, baselines subtracted, and constant-fraction softwareutilized to optimize timing. CODA support is now available for commercial PCI fast ADCcards running on Linux PCs.

Rate calculations and Projections

Cross section estimates are presented using the scintillating target. For these estimateswe assume 9.4 × 1022 protons per cm2 in the target, with a polarization of 84%, and 100%detection efficiency for recoil protons. For the photon flux we assume 2×107 photon/s, with100% circular polarization. The proposed detector geometry consists of ten NaI detectorelements, each 10” in diameter by 12” thick, arrayed in two arcs, five on beam left and fiveon beam right, at angles of approximately 30, 60, 90, 120, and 150 degrees. The efficiencyof the NaI’s is taken as 60%, and they are positioned 80 cm from the target. With 16 NaIdetectors as requested in this proposal, larger angular coverage is feasible or less beam timeis needed for the same angular coverage in order to achieve the same statistical uncertainties.Our studies indicate that sensitivity to the polarizabilities is maximized by measuring thehelicity-dependent cross sections, not just the asymmetry. Also, the most effective testof the model-dependent calculations used to extract the polarizabilities is by measuringhelicity-dependent cross sections. For these reasons we plan to measure cross sections in theexperiment. The HIγS group expects that it will be possible to measure the photon flux atthe 3% level. In addition to taking production data at beam energies just below and abovepion production threshold, we also plan to take data at a beam energy of 30 MeV as a wayto test the systematic errors in the experiment. At 30 MeV theoretical uncertainties in theCompton cross sections are expected to be very small.

Figure 9 and Fig. 10 show the helicity-dependent cross sections for a longitudinal polarizedtarget at C.M. photon energies of 120 and 140 MeV, respectively. These beam energies,which correspond to lab energies of 136 MeV and 162 MeV, are approximately 7 MeV belowand 15 MeV above pion production threshold. Also shown are the projected error barsfor a measurement at HIγS assuming 100 hours of beam time at each energy. Fig. 11 andFig. 12 show the cross sections for a transverse polarized target at C.M. photon energiesof 120 and 140 MeV, respectively. The projected error bars shown in the figure are alsofor a 100 hour measurement. Fig. 9 and Fig. 11 demonstrate that there is considerablesensitivity to the spin polarizabilities in the helicity-dependent cross sections below pionthreshold, particularly at backward angles with the longitudinal polarization, and at mid tobackward angles with transverse polarization. Above pion threshold the sensitivity to the

13

spin polarizabilities greatly increases. Fig. 10 and Fig. 12 demonstrate a sensitivity to theS.P.’s in both the longitudinal and transverse cross sections over the entire angular rangecovered by the detector array.

To estimate how accurately the individual spin polarizabilities might be measured in anexperiment at HIγS, we utilize the property that at forward angles the longitudinal crosssection difference is sensitive to γπ = γ1 + γ2 + 2γ4. Furthermore, at 90

o in the C.M. thelongitudinal polarization cross section difference is sensitive to γ1 + γ3, and at 90

o in theC.M. the transverse polarization cross section difference is sensitive to γ4. For this analysiswe will assume that γ0 is fixed from the Mainz GDH experiment with an error of ±13%and neglect uncertainties in α and β. Values for γ1, γ2, γ3, and γ4 are taken from Gellaset al. [14]. With these assumptions, the mid- to backward angle helicity-dependent crosssections at 120 and 140 MeV CM were used to estimate the errors inγ1, γ2, γ3, and γ4. Theresults show that we can anticipate errors at the level of ±12%, 10%, 45%, and 5% forγ1,γ2, γ3, and γ4, respectively. Given that this analysis only uses statistics from 4 of the 16detectors, we believe that the error estimates presented here are conservative.

In summary, we propose data taking at beam energies of approximately 30 MeV, 130MeV and 160 MeV. The two highest energies have a strong sensitivity to the four spinpolarizabilities, which can be extracted from the data with an accuracy at the level of ±10%.The 30 MeV data will provide an important test of systematic errors in the experiment whencompared against theoretical calculations of Compton scattering. Approximately 100 hoursper target polarization are required at 130 MeV and 160 MeV. Approximately 50 hoursare needed at 30 MeV, giving a total beam time of 450 hours. We believe that this is aconservative estimate of the beam time required, and that by using additional detectorsand/or moving the detectors somewhat closer to the target, a refined error analysis willindicate that comparable errors can be obtained with reduced beam time.

Spin-Dependent Compton Scattering on the “Neutron”

The static-spin polarizabilities of the nucleons have been calculated by several groups[8, 9, 14, 15]. The earlier calculations were performed at order p3 and ω3, and were onlysensitive to the isoscalar spin polarizabilities, so the calculated values were the same forthe neutron and the proton. More recently [14, 15], the first nonvanishing contributionsto the isovector part of the spin polarizabilities were calculated in a p4 order calculationusing heavy baryon chiral perturbation theory (HBCHPT). The results indicate that overallthese corrections are almost an order of magnitude smaller than the isoscalar values with theexception of γ1. The values of the neutron and proton spin polarizabilities obtained in Ref.[14] are presented in Table I. Note that the values given here correspond to the structurepart only, since the non-structure pole term contributions have been removed. Finally, wenote that there are some differences between the values of the neutron and proton spinpolarizabiliites presented in Refs. [14] and [15]. However, the authors of Ref. [15] statethat these difference are due to the fact that the authors of Ref. [14] chose not to include aparticular one-particle-reducible diagram in their definition of the polarizabilities. They goon to say that if this term is included, then the two calculations are in agreement-which isreassuring.

Note that we are proposing to extract the values of the static spin polarizabilities for theproton and the neutron. Future experiments will attempt to meaure the dynamic (energydependent) spin polarizabilities. As discussed in Ref. [7], the energy dependence of the

14

Proton HIγS uncertainty Neutron HIγS uncertainty

γP1 = 1.1+−0.25 γ

n1 = 3.7

+−0.4

γP2 = −1.5+−0.36 γ

n2 = −0.1

+−0.5

γP3 = 0.2+−0.24 γ

n3 = 0.4

+−0.5

γP4 = 3.3+−0.11 γ

n4 = 2.3

+−0.35

TABLE I: The calculated spin polarizabilities (Ref.15) along with the anticipated statistical uncer-

tainties expected from these measurements. All quantities are in units of 10−4 fm4. The “neutron”

projection is based on the quasifree Compton scattering events from 3He only.

four leading spin polarizabilities of the proton and neutron should provide profound insightinto the dispersive behavior of the internal degrees of freedom of the nucleon, caused byrelaxation effects, baryonic resonances and mesonic production thresholds.

Since there is no free neutron target in nature, effective neutron targets, i.e. nucleartargets, deuteron and 3He are commonly used for the study of the neutron. A polarized 3Henucleus is very useful in probing the neutron electromagnetic and spin structure because ofthe unique spin structure of the 3He ground state. It is dominated by a spatially symmetricS wave in which the proton spins pair off and the spin of the 3He nucleus is carried by theunpaired neutron [46, 47].

The experiment that we are proposing is a Compton scattering experiment from a polar-ized 3He target at the quasifree kinematics, i.e. the kinematics corresponding to circularlypolarized photons scattering off the nucleons inside 3He. Coincidence measurements of thescattered photons and recoil neutrons will be carried out. The advantages for detecting boththe neutron and the photon in coincidence are background suppression, maximum sensitivi-ties to the neutron spin polarizabilities, and the suppression of the proton contribution. Thedisadvantage is the small Compton scattering cross-section due to the suppression of theThompson amplitude to the process and the relatively low neutron detection efficiency.

Fig. 13 shows the sensitivity of the double polarization asymmetry to the neutron spinpolarizability γ1 as a function of incident photon energy for various photon scattering anglesin the lab. The photon is always circularly polarized, and A⊥ (A‖) corresponds to thetarget spin being perpendicular (parallel) to the incident photon momentum direction inthe reaction plane. The black curve is the asymmetry predicted from a fourth-order chiralperturbation theory [6, 15], and the red (blue) curve corresponds to varying γ1 by −5×10

−4

fm4 (red) (+5 × 10−4 fm4 (blue)), leaving all other polarizability values fixed. The blackdotted curve is the Born term which only includes the pion pole contribution. Fig. 14 is thecorresponding asymmetry result showing sensitivity to neutron γ2, and Fig. 15 and Fig. 16are similar results showing sensitivity to neutron γ3 and γ4, respectively. All calculations arecarried out [6] for a free polarized “neutron” target, and the neutron electric and magneticpolarizability values of α = 12, β = 2 are used in all these calculations. These results showthat the perpendicular asymmetry A⊥ is most sensitive to the neutron spin polarizabilitiesγ1 and γ3 at a photon scattering angle of 90

◦ in the lab frame. The parallel asymmetry A‖is most sensitive to the neutron spin polarizability γ4 at a photon scattering angle of 10

◦

when the incident photon energy is relatively large, ≥ 100 MeV.One can also extract the neutron spin polarizabilities from elastic polarized Compton

scattering off a polarized 3He target. The advantage is a much larger Compton scatteringcross-section and a relatively straightforward theoretical calculation of the Compton scatter-

15

ing process. The complication is that the extraction of the neutron spin polarizabilities willbe sensitive to our knowledge of the proton spin polarizabilities, which will be determinedexperimentally at HIγS (see previous section). Since there is no free neutron target, oneshould carry out both measurements: polarized elastic Compton scattering and polarizedquasielastic Compton scattering from a polarized 3He target. These measurements will al-low the extraction of the neutron spin polarizabilities in two different ways. This will helpreduce theoretical uncertainties in extracting the neutron properties using an effective po-larized neutron target, i.e. a polarized 3He nuclear target. Ideally, one should also carry outthe same measurements (quasifree and elastic) from a polarized deuteron target. We planto carry out the polarized elastic 3He Compton scattering experiment at HIγS using a 140MeV γ-ray beam.

We propose a double polarization Compton scattering experiment of circularly polarizedphotons from a polarized 3He nuclear target at the quasifree and elastic kinematics using theHigh Intensity Gamma Source (HIγS) at the Duke Free Electron Laser Lab. The scatteredphotons and the knockout neutrons will be detected in coincidence for the proposed coinci-dence quasifree measurements. Only the scattering photons will be detected for the elasticmeasurements. We plan to use the upgraded 16 NaI detectors (requested in this proposal)for photon detection, and the Blow Fish detector for detecting the neutrons. The polarized3He target is a high-pressure target based on the spin-exchange optical pumping technique.The double polarization asymmetry will be formed by flipping the circular polarization ofthe incident photon beam. The target spin direction will be reversed from time to timeto minimize effects due to systematic false asymmetries. In this experiment, we will alignthe target spin parallel and perpendicular to the incident photon momentum direction inthe scattering plane to measure both the parallel asymmetry (A‖) and the perpendicularasymmetry (A⊥).

A High-Pressure Polarized 3He Gas Target

The polarized 3He target is based on the principle of spin exchange between opticallypumped alkali-metal vapor and noble-gas nuclei[48]. The design is similar to that usedin electron scattering experiments in Hall A at Jefferson Lab (JLab) [49]. Traditionally,Helmholz coil systems have provided magnetic holding field for the target. But, a mu-metal-shielded sine-theta coil (STC) has potential advantages over the Helmholtz coils, pri-marily from its compact geometry and from the improved B-field uniformity. Preliminarystudies [50] have shown that such a STC could improve the planned experiment to studyCompton scattering from polarized 3He at HIγS. The projected results shown later are basedon a STC for providing the target holding field. A central feature of the target will be sealedglass target cells, which will contain a 3He pressure of about 10 atmospheres. The target cellswill have two chambers, an upper chamber in which the optical pumping and spin-exchangecollision take place, and a lower chamber, through which the photon beam will pass. Inorder to maintain the appropriate number density of alkali-metal (Rb) the upper chamberwill be kept at a temperature of 170-200◦C using an oven constructed of high temperatureresistant plastic, for example Torlon. With a density of 2.75× 1020 atoms/cm3, and a lowercell length of 40 cm, the target thickness will be 1 = 1.0× 1022 atoms/cm2. Due to the factthat the HIγS photon beam spot size is significantly larger than the electron beam size, thediameter of the HIγS target cell will be much larger than that of the 3He target at JLab.Fig. 17 shows the schematics of the polarized 3He target setup. Fig. 18 shows a picture

16

of the first HIγS polarized 3He target “Kansas” on the test stand in our polarized targetlab. The initial measurement from “Kansas” shows a target relaxation time of 18 hours.“Kansas” has an overall volume which is a factor of 2.5 of a typical polarized 3He targetused in Hall A experiments at Jefferson Lab.

The time evolution of the 3He polarization can be calculated from a simple analysis ofspin-exchange and 3He nuclear relaxation rates [51]. Assuming the 3He polarization P3He = 0at t = 0,

P3He(t) =< PRb >

(

γSEγSE + ΓR

)

(

1 − e−(γSE+ΓR)t)

, (13)

where γSE is the spin-exchange rate per3He atom between the Rb and 3He, ΓR is the

relaxation rate of the 3He nuclear polarization through all channels other than spin exchangewith Rb, and PRb is the average polarization of a Rb atom. Our target will be designed tooperate with 1/γSE = 8 hours.

From Eq. (1) it is clear that there are two things we can do to get the best possible 3Hepolarization — maximize γSE and minimize ΓR. Maximizing γSE means increasing the Rbnumber density, which in turn means more laser power. The number of photons needed persecond must compensate for the spin relaxation of Rb spins. In order to achieve 1/γSE = 8hours, about 50 Watts of usable laser light at a wavelength of 795 nm are needed. By“usable,” we essentially mean light that can be readily absorbed by the Rb. It should benoted that the absorption line of the Rb will have a full width of several hundred GHz atthe high pressures of 3He at which we will operate. Furthermore, since we will operate withvery high Rb number densities that are optically quite thick, quite a bit of light that is notwithin the absorption linewidth is still absorbed. Currently, a new technique is being testedto improve the rubidium polarization. Normally, the diode lasers of this wavelength emita light spectrum that is 1-2 nm wide. Since the rubidium can only absorb a very narrowportion of that spectrum, most of the power of the laser is wasted. A series of gratings arebeing used to narrow the line width of the diode laser output. While some laser power islost, the line width is narrow enough so that almost all of the light is absorbed by the Rbatoms and the overall laser absorption efficiency is 2-3 times higher.

The rate at which polarization is lost, which is characterized by ΓR, will have two prin-ciple contributions under the photon beam environment. From experience, target cells withan intrinsic rate of Γcell = 1/50 hours can be produced. This has two contributions: re-laxation that occurs during collisions of 3He atoms due to dipole-dipole interactions [52],and relaxation that is presumably due largely to the interaction of the 3He atoms with thewalls. Finally, relaxation due to magnetic field inhomogeneities are held to better thanΓ∆B = 1/100 hours [53]. Collectively, under operating conditions, we would thus expect

ΓR = Γcell + Γ∆B = 1/50 hours + 1/100 hours = 1/33 hours. (14)

Thus, according to Eq. 1, the target polarization cannot be expected to exceed

Pmax =γSE

γSE + ΓR= 0.80. (15)

Realistically, Rb polarization is less than 100% in the pumping chamber, which will reducethe polarization to about 50-55%.

17

The construction and filling of the target cells have been accomplished with great careto achieve 1/Γcell equal to 40-50 hours. Cells are constructed from aluminosilicate glass, GE180. The cells will be filled to a high density of about 10 amg 3He. The length of the cellis 40 cm, and the diameter is 2.5 cm. The end windows are approximately 150 µ thick andthe side wall is approximately 1 mm thick.

A beam of laser light coming out of the diode laser is essentially unpolarized. A polarizingbeam splitter can be used to make it linearly polarized and then, by passing it through aquarter wave plate, the laser light can be made to be circularly polarized. The circularlypolarized laser light optically pumps the Rb vapor in the pumping chamber to polarize theRb atoms, which then spin-exchanges with 3He gas to polarize the 3He nuclei. Polarizationwill be monitored using the NMR technique of adiabatic fast passage (AFP) [54]. Thesignals are calibrated by comparing the 3He NMR signals with those of water. Further, thepolarization will also be monitored during the experiment by EPR.

The Detectors

For the photon detection, we plan to use a photon detection array which consists of 16NaI detectors (requested in this proposal). Each NaI detector is a cylinder with 10” diameterand 12” length. The energy resolution for a NaI detector is 2%. We propose to use such aphoton detection array for the proposed Compton experiment.

For the proposed coincidence measurements, the kinetic energy of the neutron is from2.7 MeV to 22.0 MeV. The “Blowfish” array with BC-505 liquid scintillators will allow thedetection of these neutrons. The “Blowfish” setup needs to be reconfigured in order to becompatible with a high-pressure polarized 3He target and to match the acceptance of thephoton detectors. The neutron detection efficiency is expected to be between 20% and 35%.The experimental setup for the proposed longitudinal asymmetry measurement is shown inFig. 19.

Projected Measurements from elastic Compton scattering process

In projecting the asymmetry results, we assumed a photon flux of 2×107 /sec for a photonenergy spread of 10 MeV at an incident photon energy of 140 MeV and a target thicknessof 1.1 × 1022 atoms/cm2 with a target polarization of 45%. The circular polarization of thephoton beam is taken to be 100%. A solid angle acceptance of 0.2 sr was assumed for eachscattering angle bin. A total beam time of 350 hours was assumed in the projection with 100and 250 hours for the perpendicular and longitudinal target spin orientation, respectively.The projected results for the elastic Compton scattering are shown in Fig. 20 and Fig. 21.The projected results show clearly the high precision that HIγS measurements will achieveeven with a modest photon flux (2×107 /sec), therefore providing the much needed sensitivityin probing the neutron spin polarizabilities.

Projected Measurements from Quasifree Compton Scattering Process

In projecting the asymmetry results, we assumed a photon flux of 6 × 107 /sec for anincident photon energy of 140 MeV with an energy bin size of 10 MeV and a target thickness

18

of 1.1 × 1022 atoms/cm2 with a target polarization of 45%. The circular polarization of thephoton beam is taken to be 100%. A neutron detection efficiency of 25% was used. Atotal beam time of 1500 hours was used in projecting the results with 500 (1000) hours forthe perpendicular (longitudinal) target spin orientation. The projected results are shown inFig. 22 and Fig. 23.

Anticipated results on Neutron Spin Polarizabilities

The nucleon spin polarizabilities have been calculated by several groups [14, 15, 55]at the next-to-leading order (NLO) in chiral perturbation theory. Predictions on all fourneutron spin polarizabilities at NLO in heavy-baryon chiral perturbation theory by Kumar,McGovern and Birse [15] are:

γ1 = [−21.3]τ3 + 4.5 − (2.1 + 1.3τ3) (16)

γ2 = 2.3 − (3.1 + 0.7τ3)

γ3 = [10.7]τ3 + 1.1 − (0.8 + 0.1τ3)

γ4 = [−10.7]τ3 − 1.1 + (3.9 + 0.5τ3)

γ0 = 4.5 − (6.9 + 1.5τ3)

γπ = [−42.7]τ3 + 4.5 + (2.7 − 1.1τ3),

where τ3 = −1 for neutron, and the term in brackets are the third-order anomalouscontribution. The values of the neutron spin polarizability are γ1 = 25.0, γ2 = −0.1 γ3 =−10.3, γ4 = 13.0, γ0 = −0.9, and γπ = 51.0. One can see that the rather large absolutepolarizability values for γ1, γ3, γ4 and γπ are due to the anomalous contribution. Severalauthors [9, 24] define the nucleon spin polarizabilities differently from those of Kumar,McGovern and Birse [15] and Ji et al. [55] by removing the pion pole contribution. Thecorresponding neutron spin polarizabilities values obtained at the NLO in heavy-baryonchiral perturbation theory [15] using the definition of Refs. [9, 24] are therefore: γ1 =3.7, γ2 = −0.1 γ3 = 0.4, γ4 = 2.3, γ0 = −0.9, and γπ = 8.3. The only experimentalinformation on neutron forward spin polarizability γ0 was estimated using the VPI-FA93multipole analysis [22]:

γ0 ∼ −0.38 × 10−4 fm4 (17)

The predicted neutron forward spin polarizability range between -0.7 and 2.0 [24]. Thepredicted γπ (neutron) value from hyperbolic Dispersion Relation is 9.2 [24], which is veryclose to the aforementioned value of 8.3. The predicted values of γπ (neutron) range between6.3 and 13.7 (see review by Drechsel, Pasquini and Vanderhaeghen [24]). The only availableinformation on γπ (neutron) was γ

nπ = (58.6 ± 4.0) × 10

−4 fm4 [18] obtained from thequasifree Compton scattering on deuteron, which includes the pion pole contribution. L’vovand Nathan [25] derived a sum rule for γπ from a backward angle dispersion relation. Theirpredicted values for γpπ and γ

nπ is −39.5 ± 2.4, and 52.5 ± 2.4, respectively.

The proposed measurements from coincidence quasielastic scattering have the followingstatistical sensitivity to the individual neutron spin polarizability γ1, γ2, γ3, and γ4: 0.42,0.49, 0.53, and 0.35, respectively, in the unit of 10−4 fm4. The proposed experiment willprovide a statistical error of 1.0 in the unit of 10−4 fm4 in the determination of both the

19

neutron γπ and the neutron γ0. Recently, calculations [34, 35, 56] of double polarizedelastic Compton scattering of circularly polarized photons from a polarized deuteron targethave been carried out. In the incident photon energy regime relevant to the proposedmeasurements, the perpendicular double polarization asymmetry is shown [56] to be sensitiveto the neutron spin polarizability, γ1. Currently, calculations [57] of double polarized elasticCompton scattering from a polarized 3He target is underway. More sensitivity to the neutronspin polarizabilties are anticipated by employing a polarized 3He target because of its uniqueground state spin structure.

Theoretical uncertainties in extracting the neutron spin polarizabilities from elastic andquasifree Compton measurements are different. Therefore, two independent extractionsof neutron spin polarizabilities can be carried out. These measurements will allow theextraction of the individual neutron spin polarizabilities for the first time. These projectedresults show clearly the high impact of the projected HIγS measurements in probing theneutron spin polarizabilities. Achieving the desired intensity of the photon flux is essentialto the success of the proposed quasifree Compton scattering program.

COMPTON SCATTERING FROM THE HE ISOTOPES: A MEASUREMENT OF

THE ELECTRIC POLARIZABILITY OF 3HE AND 4HE

Introduction

We propose to make a measurement of the electric polarizability αE of the helium isotopes3He and 4He using elastic Compton scattering of linearly polarized monochromatic photonswith energies between Eγ = 3 and 12.5 MeV. We see this as part of a program to systemati-cally measure the polarizabilities, both electric and magnetic, of the free and bound nucleonand the light nuclei through mass 4. We propose to start with 3He since the polarizabilitiesare two orders of magnitude larger than for nucleons, making a measurement feasible withthe present HIγS beam flux. This will be followed by a similar measurement on 4He. Ourmeasurements will provide early experience with Compton scattering experiments, allowingus to better plan for future Compton scattering experiments on the nucleon at HIγS.

The situation in the light nuclei has been reviewed by Friar in 2002[58]. The 3He polariz-ability has been experimentally investigated by two independent methods: scattering of 3Heby high Z nuclei and from the energy weighted sum rule for total photonuclear absorption(see references 54 and 55 in Friar’s review; reference 55 uses the world’s photonuclear dataprior to 1974). The relation between σ−2 and the electric polarizability αE is:

σ−2 =∫

σabsdEγE2γ

=2π2

h̄c(αE + βM)

where βM is the magnetic polarizability. In the analysis of the data βM is generally neglectedrelative to αE. These two very different methods give results differing by a factor of 2.

Calculations using the Lorentz integral transform method[59] coupled with an expan-sion of the wave functions in correlated hyperspherical harmonics[60] and an effectiveinteraction[61] have resulted in predictions of the electric polarizabilities for both 3He and4He. In 3He, Leidemann and Orlandini[62] have calculated a value of αE = 0.145 fm

3 forthe electric polarizability. This value is in crude agreement with the experimental value of

20

0.130 fm3 compiled by Rinker[63] (and quoted by Friar[58]) from the world’s photonucleardata. It is a factor of almost 2 below the value of 0.250 fm3 obtained from the scattering of3He by lead[64].

Although the compiled photonuclear data are in reasonable agreement with theory, westress two points. The data used by reference [63] show a considerable spread in crosssection. Hence the agreement is fortuitous. Second, as pointed out earlier, it is really thecase from the photonuclear analysis that αE +βM = 0.130 fm

3. Thus if βM is not negligible,the apparent agreement with theory is not as good. There are no direct measurements todate of αE for

3He.

The electric polarizability αE of4He has also been calculated by Orlandini [65] and

Leidemann [62] as part of their work on the mass 4 system. They have found a value ofαE = 0.075 fm

3 for the electric polarizability of 4He.

As in the case of 3He, experimental values for this quantity have been inferred from mea-surements of total photon absorption using the known relation between the energy weightedsum rule σ−2 of the photoabsorption and the polarizability given above. In the case of

4Hethere are considerably more data than for 3He, probably because of the obvious difficultieswith obtaining an adequate 3He target, However, the history of measurements of the pho-todisintegration of 4He is marked by serious discrepancies between different measurementsof the same channels. Factor of 2 discrepancies abound in the literature.[66] More recentmeasurements have not resolved this.

In the case of both 3He and 4He, published data on σ−2 rely on measurements of thevarious disintegration channels 3,4He(γ, p), 3,4He(γ, n), 4He(γ, pn), etc. in order to sum themto form σabs, the total absorption cross section. This method clearly limits the measurementof αE + βM to values of Eγ in excess of 6 MeV for

3He and 20 MeV for 4He. Inference of αErequires that one neglects βM , a reasonable assumption unless an accuracy of better than 5%- 10% is required. The larger uncertainty comes from the discrepancies in published valuesfor the individual cross sections for the various channels. The status of the (γ, p) and (γ, n)cross section measurements on 4He up to 1980 was reviewed by Calarco et al..[66] This papershowed that values published prior to 1980 disagreed with each other by up to factors oforder 2. Subsequent measurements have continued to be plagued by similar disagreements.

For example, if one uses the total photodisintegration data from Erdas et al.[67] or Arka-tov et al.[68], who measured σ−2 of 73±4 × 10

−4 and 72±4 × 10−4 fm2/MeV respectively,then, neglecting βM yields αE equal to 0.072±0.004 and 0.073±0.004 fm

3, in agreement withthe calculations cited earlier. However, their individual values of the (γ, p) and (γ, n) crosssections are not in agreement with more recent measurements nor with the best averageddata cited by Calarco et al..[66] Other published data (see ref [66]) would lead to seriousdisagreement with Orlandini’s and Leidemann’s calculations.

Thus we propose to do a direct measurement of αE by measuring the cross section forelastic photon scattering at 90◦ as a function of Eγ using linearly polarized photons. Wewill show that the energy dependence of the cross section can give a direct measurement ofαE.

21

Compton Scattering with Polarized Photons

The static polarizability, αE, of a nucleus describes the response of a nucleus to a staticelectric field, whereas the dynamic polarizability, αEν, describes the response of a nucleusto a time varying electric field[69]. Both polarizabilities should be accessible by means of aCompton scattering experiment. Our measurement will be done at sufficiently low energiessuch that an expansion of the Compton scattering amplitude is valid (low energy is alsodesirable for the current HIγS beam). The amplitude for Compton scattering, up to O(ω4),is:[69]

�̂1 · �̂2

(

−Z2e2

M+ 4πω2(αE + ω

2αEν)

)

+ 4πω2βM �̂1 × k̂1 · �̂2 × k̂2

where e is the quantum of electric charge, �̂1 is a unit vector along the polarized electricfield of the incident photon, k̂1 is a unit vector along its momentum and �̂2 and k̂2 are thecorresponding unit vectors for the scattered photon. M is the mass of the target and ω isthe energy of the incident photon. In the absence of αE, αEν and βM , this reduces to theleading term proportional to Z2e2/M , the amplitude for Thomson scattering.

The cross section for Compton scattering of linearly polarized photons on a nuclear ornucleon target is then given by, after summing over the polarization of the scattered photonbut not averaging over the incident polarization:[70]

dσ

dΩ=

1

2

(

Z2α

M

)2

(

1 −Mω2α′E

Z2α

)2(

1 − (�̂1 · k̂2)2)

−2Mω2βM

Z2αk̂1 · k̂2

where α is the fine structure constant and α′E = αE +ω2αEν, containing both the static and

dynamic contributions

If k̂1 is taken to be along ẑ and �̂1 is taken to be along x̂, that defines a coordinate systemsuch that k̂2 is at the polar angle ϑ with respect to k̂1 and azimuthal angle ϕ with respectto the plane defined by k̂1 and �̂1. In this coordinate system the cross section can be writtenas:

dσ

dΩ=

1

2

(

Z2α

M

)2

(

1 −Mω2α′E

Z2α

)2

(1 − sin2ϑcos2ϕ) −2Mω2βM

Z2αcosϑ

Now, if we restrict our detectors to a scattering angle of ϑ = 90◦, the term in βM vanishes(except for finite acceptance effects). Furthermore, the cross section vanishes (again, exceptfor finite acceptance effects) for detectors placed at ϑ = 90◦ colinearly with the direction ofincident linear polarization �̂1, left and right in our case since the linear polarization vectorat HIγS is oriented in the horizontal plane.

The Compton scattering cross section in the low energy limit for the horizontally polarizedHIγS beam with detectors oriented at 90◦ in both ϑ and ϕ can thus be shown to be[70]

dσ

dΩ=

1

2

(

Z2α

M

)2 [

1 −(

2MαEZ2α

)

ω2 +

(

M2α2EZ4α2

−2MαEν

Z2α

)

ω4]

(18)

This expression is plotted as a function of energy in Figure 24 for various values of αE.

22

Currently, the dynamic polarizability of 3He has not been measured (nor for any othernucleus). Following the formalism of reference[69] using a simple harmonic oscillator model,we calculate an estimate for αEν , the dynamic electric polarizability, of 0.0005 fm

3/MeV2 for3He. This is small compared to the static polarizability of 0.145 fm3. However, the dynamicpolarizability is multiplied by ω2, making it important for higher energies.

Thus, at low energies, the cross section for Compton scattering can be approximated asa polynomial function that varies with even powers of the γ-ray energy, with coefficientsthat depend on the static and dynamic electric polarizabilities. Thus a measurement of thecross section at ϑ = 90◦ up and down relative to a horizontally polarized incident photonflux at several points in the relevant energy range as a function of ω2 will give us thepolynomial shape of the cross section, allowing the electric polarizabilities of 3He (and 4He)to be extracted.

Proposed Experiment

As mentioned previously, the first measurements will be carried out on 3He. We planto do our measurement at several beam energies between 3 and 12.5 MeV. There will bethree experimental setups with three 4500 psi gas bottles placed successively in the γ-raybeam. 10” x 10” NaI detectors will be placed directly above and directly below each bottleto measure the Compton scattered γ-rays. Shielding will be used to keep γ-rays scatteredfrom the ends of the bottles from entering the detectors. A Monte Carlo code is currentlybeing used to determine the best choice of energies for the extraction of αE and αEν.

In order to make a 3% cross section measurement, we will need about 103 counts at eachenergy point. This corresponds to about 50 hours of beam time per point at higher energiesand about 25 hours per point at lower energies. These estimates assume a beam intensityof 2 x 107 with an energy resolution of ∼5-10%, a 15 cm long effective length for our gascells, detector efficiencies of 0.57, and solid angle of 50 msr, corresponding to the back faceof the NaI being 1 m away. Overall, about 200 hours of beam time will be needed for themeasurement.

For 4He, we are considering gas cells identical to those just described for 3He as well asa 40 cm long liquid He cell of sufficient diameter to accept the collimated flux.

Spectra from the NaI detectors will be accumulated in singles mode and the counts willbe extracted using line shape fits to these spectra. The polarizability will be obtained by apolynomial fit the the cross section as a function of ω2.

Error Analysis

The statistical contribution to the overall uncertainty is about 3%. The principle con-tributions to the overall uncertainty come from two sources: NaI efficiency and integratedbeam flux. Since the overall scale of the cross section, as determined by the intercept atEγ = 0, is independent of the polarizability which determines the slope, this need not beknown absolutely to better than, say, a few percent, assuming we would like to know the ab-solute cross section to that level. However, what is critical is the relative efficiency and fluxintegration as a function of photon energy. Any systematic variation with energy translates

23

directly as a systematic change of the slope, hence of the polarizability. If there is a system-atic change and it can be measured, then a correction can be applied. The uncertainty onthat correction then becomes the systematic error in the measurement.

THE HIγS NAI DETECTOR ARRAY (HINDA)

Large NaI detectors have been used at TUNL for several decades, primarily in the study ofradiative capture reactions. TUNL researchers have a great deal of experience with operatingthese detectors in order to maximize their resolution and performance, while minimizingthe background and pulse-pile up problems in very hostile environments encountered, forexample, in studies of the capture of fast neutrons [71].

More recently, four large NaI detectors have been utilized in the first Compton scatteringexperiment at HIγS. This four-detector system, called the Eggbeater (see Fig. 25), was usedto measure the analyzing powers in the case of Compton scattering from 16O. In this casethe time structure of the HIγS beam along with the so-called Giant Peak Power Pulse modeof operating the HIγS [72] made it possible to reduce beam uncorrelated backgrounds by afactor of 1700. A paper reporting these results has been accepted for publication in PhysicalReview C [73].

The present proposal is requesting the creation of a 16 detector array of 10” by 12”NaI detectors. Even with the intense beams of HIγS, the small cross sections in Comptonscattering reactions along with the demands for high precision data, makes it essential to havea detector array which offers high efficiency, reasonably good energy resolution, and largeacceptance. The essential requirements of a detector system for the proposed experimentsare:

• High efficiency

• Good (2-3%) energy resolution for gamma-rays between ∼ 40 and 100 MeV.

• Large acceptance

• Flexibility in the geometrical configuration of the individual detectors. The arrange-ment, for example, will be entirely different for the longitudinal asymmetry configura-

tion in the ~3He(~γ, γ)3He experiment with circularly polarized beams for which we wantto cover all azimuthal angles at forward scattering angles where the effects to neutronspin polarizabilities are largest (see Fig. 19), compared to linearly polarized beamswhere it is essential to have left, right, up and down detectors at each scattering angle(similar to the Eggbeater arrangement, but at four scattering angles simultaneously).

TUNL presently possesses four high-quality 10” and one 10” or 10” by 12” NaI detectors.If the gamma-ray peak is summed from one width above the centroid to two widths below,it is found that the efficiency is 57% for photon energies between 20 and 100 MeV. Theresolution of these detectors, has been measured to be 3% at 20 MeV [71], and is expectedto be close to 2% at higher energies [71]. Two additional detectors became available fromcollaborators recently. We are therefore requesting funds to purchase nine (9) 10” by 12”NaI detectors in order to construct the HIγS NaI Detector Array (HINDA). The HINDAwill provide counting rates which will allow us to perform the measurements described inthis proposal in the number of hours anticipated for this program. In addition to more

24

than doubling the statistics of our measurements, the ability to make measurements attwice as many angles simultaneously will greatly reduce the systematic errors in the angulardistributions of cross sections and analyzing powers. This is extremely important for thesuccess of this program, since most of the sensitivity to several important physical parameterswe are measuring is contained in the angular dependence of the observables.

ACKNOWLEDGMENT

We thank D. Choudhury, H.W. Griesshammer, T.R. Hemmert, R. Hildebrandt, J.A.McGovern, D.R. Phillips for stimulating discussions. We also thank J. McGovern and R.Hildebrandt for carrying out various calculations at the proposed kinematic settings of thisproposal.

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