Coherent photoproduction of eta-mesons off 3He - search for eta-mesic nuclei

0.38 MB·English

by  F. Pheron

Coherent photoproductionof η-mesons off3He-search forη-mesicnuclei
2
1
F. Pherona, J. Ahrensb, J.R.M. Annandc, H.J. Arendsb, K. Bantawad, P.A. Bartolomeb, R. Becke,
0
2 V. Bekrenevf, H. Bergh¨auserg, B. Boillata, A. Braghierih, D. Branfordi, W.J. Briscoej, J. Brudvikk,
n S. Cherepnyaℓ, B. Demissiej, M. Dieterlea, E.J. Downieb,c,j, P. Drexlerg, D.I. Glazieri, E. Heidb,
a L.V. Fil’kovℓ, D.Hornidgem, D.Howdlec, O.Jahnb, I. Jaeglea, T.C. Judei, V.L. Kashevarovℓ,b,
J
I. Keshelashvilia, R. Kondratievn, M. Korolijao, M. Kotullaa,g, A. Kulbardisf, S.P. Kruglovf,
1
3B. Kruschea,V. Lisinn, K. Livingstonc, I.J.D. MacGregorc, Y. Maghrbia, J. Mancellc, D.M. Manleyd,
Z.Marinidesj, M. Martinezb, J.C. McGeorgec, E. McNicollc, D. Mekterovico, V. Metagg,
]
x S. Micanovico, D.G.Middletonm, A. Mushkarenkovh, B.M.K. Nefkensk, A. Nikolaeve, R.Novotnyg,
e M. Oberlea, M. Ostrickb, B. Oussenab,j, P. Pedronih, A. Polonskin, S.N. Prakhovk, J. Robinsonc,
-
l G. Rosnerc, T. Rostomyana,h, S. Schumannb, M.H. Sikorai, D.I. Soberp, A. Starostink, I. Supeko,
c
u M. Thielg, A. Thomasb, M. Unverzagtb, D.P. Wattsi, D.Werthmu¨llera, L. Witthauera, F.Zehra
n
aDepartment of Physics, Universityof Basel, Ch-4056 Basel, Switzerland
[
bInstitut fu¨rKernphysik, Universityof Mainz, D-55099 Mainz, Germany

1 cSUPA,School of Physicsand Astronomy, Universityof Glasgow, G12 8QQ, UnitedKingdom
v dKentState University,Kent,Ohio 44242, USA
7 eHelmholtz-Institut fu¨r Strahlen- und Kernphysik,UniversityBonn, D-53115 Bonn, Germany
1 fPetersburgNuclear PhysicsInstitute, RU-188300 Gatchina, Russia
5 gII. Physikalisches Institut,Universityof Giessen, D-35392 Giessen,Germany
6 hINFN Sezione di Pavia, I-27100 Pavia, Pavia, Italy
. iSchool of Physics, Universityof Edinburgh, Edinburgh EH93JZ, United Kingdom
1
jCenterforNuclear Studies, The George Washington University,Washington, DC20052, USA
0
kUniversityof California LosAngeles, LosAngeles, California 90095-1547, USA
2
ℓLebedev Physical Institute,RU-119991 Moscow, Russia
1
mMount Allison University,Sackville,NewBrunswick E4L1E6, Canada
:
v nInstitutefor NuclearResearch, RU-125047 Moscow, Russia
i oRudjerBoskovic Institute, HR-10000 Zagreb, Croatia
X pThe Catholic Universityof America, Washington, DC20064, USA
r
a
Abstract
Coherentphotoproductionofη-mesonsoff3He,i.e.thereaction γ3He→η3He,hasbeeninvestigatedinthenear-thresholdregion.
Theexperimentwasperformed at theGlasgow tagged photonfacility oftheMainz MAMIaccelerator with thecombinedCrystal
Ball-TAPSdetector.Angulardistributionsandthetotalcrosssectionweremeasuredusingtheη→γγ andη→3π0 →6γ decay
channels. The observed extremely sharp rise of the cross section at threshold and the behavior of the angular distributions are
evidencefora strongη3Hefinalstateinteraction, pointingtotheexistenceof aresonant state. Thesearch for furtherevidenceof
thisstateintheexcitationfunctionofπ0-protonback-to-backemissionintheγ3He→π0pX reactionrevealedaverycomplicated
structureof thebackgroundand could not support previousconclusions.
1. Introduction can be used for detailed studies of elastic and inelastic re-
actions, revealing the relevant potentials. However, most
The interactionof mesons with nuclei is a major source mesons are short-lived so that their interaction with nu-
for our understanding of the strong interaction. For long- cleons canonly be studied in indirect ways,making use of
livedmesons,likechargedpionsorkaons,secondarybeams final-state interactions (FSI). The general idea is to pro-
ducethemesonswithsomeinitialreactioninanucleusand
thenstudy their interactionwiththe same nucleus.
Email address: [email protected] (B. Krusche).
Preprintsubmitted toPhysics Letters B 1February 2012
It is much discussed whether the strong interaction al- clusterbetween0.2fmand0.3fm.Therealpart,whichde-
lows the formation of quasi-bound meson-nucleus states. termines the existence of quasi-bound states, is much less
So far, all known meson-nucleus bound states involve at constrained. It runs all the way from a negative value of
least partly the electromagnetic interaction. Pionic atoms −0.15fmtonumbersclosetoandevenabove+1fm.How-
are well established. More recently deeply bound pionic ever, most of the more recent analyses prefer large values
stateshavealsobeenreported[1],butinthiscasethebind- above 0.5 fm, which has raised controversial discussions
ing results from the superposition of the repulsive s-wave aboutthe possible existence ofverylight mesic nucleiand
π−-nucleus interactionwith the attractiveCoulombforce. promptedtheoreticalstudies ofthe η-interactionwith 2H,
Neutralmesonsontheotherhandcouldformquasi-bound 3H, 3He, and4He systems[20–29]
states only via the strong interaction. The meson-nucleus Experimentalevidenceforlightη-mesicnucleihasmostly
interaction for slow pions is much too weak to produce beensearchedforinthethresholdbehaviorofη-production
quasi-bound states, but the situation may be different for reactions.Theideaisthatquasi-boundstatesinthevicinity
′
η, η ,andω-mesons. oftheproductionthresholdwillgiverisetoanenhancement
Thecaseofη-mesonsisspecialbecausethethresholdre- of the cross section relative to the expectation for phase-
gionofη-productionisdominatedby ans-waveresonance space dependence. Many different hadron induced reac-
[2,3], the S (1535), which couples very strongly to Nη tions have been studied in view of such threshold effects.
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(branchingratio≈50%[4]).AsaconsequenceFSIinnuclei Alreadythemeasurementofpioninducedη-productionoff
areimportant;η-mesonsareabsorbedinnucleiwithtypical 3He in the reaction π− +3He → η+t at LAMPF [30,31]
crosssectionsaround30mb,basicallyindependentoftheir revealedproductioncrosssectionssignificantlylargerthan
kineticenergyT overawiderangeofT fromafewMeVto DWIApredictions.Subsequently,differentnucleon-nucleon
1GeV[5,6].Firsthintsforthepossibleexistenceofbound and nucleon-deuteron reactions, in particular pp → ppη
η-nucleusstatescamefromthe analysisoftheηN scatter- [32–34],np→dη [35,36],pd→η3He [37], dp→η3He [38–
ing length that characterizes the potential at low kinetic 40],dd→η4He[41],d~d→η4He[42,43],andpd→pdη[44]
energies. Already in 1985 Bhalerao and Liu [7] reported have been studied. Interesting threshold effects have been
an attractive s-wave ηN interaction from a coupled chan- found in most of them, but in particular the pd → η3He
nel analysis of pion-induced reactions, yielding scattering [37] and dp → η3He reactions [38–40] show an extremely
lengths αηN with real parts between 0.27 fm and 0.28 fm steep rise at threshold, implying a very large η3He scat-
andimaginarypartsbetween0.19fmand0.22fm.Shortly tering length. Wilkin and collaborators [45] have argued
afterwards,LiuandHaider[8]pointedoutthatthisinterac- fromananalysisoftheangulardistributionsthat,notonly
tionmightleadto the formationofquasi-boundη-nucleus themagnitude ofthes-waveamplitudefallsrapidlyinthe
states for A > 10. Experimental evidence for such ‘heavy’ threshold region, but that its phase also varies strongly,
η-mesic nuclei has been searchedfor in pion-induced reac- which supports the idea of a quasi-bound or virtual 3He
η
tionsonnucleiintheoxygenregion[9,10],butthoseexper- stateverycloseto the threshold.
imentsdidnotproduceconclusiveevidence.Morerecently, If such states do exist, they should show up as thresh-
Sokol and co-workers [11,12] claimed evidence for the for- old enhancements independently of the initial state of the
mation of η-mesic nuclei from bremsstrahlung-inducedre- reaction.Photoproductionofη-mesonsfromlightnucleiis
actionson12C a very cleantool for the preparationofthe η-nucleus final
γ+12C→p(n)+11B(11C)→π++n+X , (1) state with small relative momenta but, due to the much
η η smaller electromagnetic cross sections, sensitive threshold
where the nπ+ pairs were detected in the final state. In measurements have been sparse until now. A particular
thistype ofexperiment,theη-mesonisproducedinquasi- problem is that the η-mesons have to be produced coher-
free kinematics on a nucleon (p,n), which takes away the ently off the targetnuclei. As a consequence of the results
largestpartofthemomentumandtheηisalmostatrestin fromphotoproductionofη-mesonsofflightnuclei,itisnow
the residualA=11nucleus. Ifa quasi-boundstate is pro- wellunderstoodthatthethresholdproductionisdominated
duced, the η-meson has a large chance to be re-captured by an isovector spin-flip amplitude exciting the S (1535)
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by a nucleon into the S11 excitation, which may then de- resonance(see[46]forasummary).Therefore,thecoherent
cayintoapion-nucleonback-to-backpair.Suchpairswere cross section is very small for the isoscalar deuteron and
searchedforintheexperiment,however,backgroundfrom practically forbidden for the isoscalar-scalar 4He nucleus,
quasi-free pion production must be considered. Sokol and where only higher partial waves could contribute. Among
Pavlyuchenko[12]claimanenhancementabovethis back- the light targets only the (I = 1/2,J = 1/2) 3H and 3He
groundforcertainkinematic conditions. nucleihavereasonablylargecrosssectionsfortheγA→Aη
The topic gained much new interest after precise low- reaction.
energy data for the photoproduction of η-mesons off the The3Hesystemwaspreviouslyinvestigatedwithphoton-
proton [2], deuteron [13–16] and helium nuclei [17,18] be- induced reactions by Pfeiffer et al. [47]. Possible evidence
cameavailableandrefinedmodelanalysesofthescattering fortheformationofaquasi-boundstatewasreportedfrom
lengthweredonebymanygroups(see[19]forasummary). the behavior of two different reactions. The coherent η-
The results for the imaginary part are rather stable, most
2
photoproduction γ3He → η3He showed a strong thresh- detectorhadindividualplasticscintillatorsinfrontforthe
old enhancement with angular distributions much more same purpose. The PID, in combination with the Crystal
isotropic in the threshold region than expected from the Ball,andtheTAPS-TAPS-Vetosystemcouldbeusedfor
nuclearformfactor.TheseareindicationsforstrongFSIef- a E −∆E analysis for the separation of different charged
fects.Furthermore,inanapproachsimilartotheSokolex- particles.TheCrystalBallcoveredthefullazimuthalrange
periment[12],theexcitationfunctionforπ0−ppairsemit- for polar angles from 20◦ to 160◦, corresponding to 93%
ted back-to-back in the γ3He center-of-momentum (c.m.) ofthe full solidangle.The TAPSdetector,mounted 1.457
system was investigated. The difference between the ex- m downstreamfrom the target, coveredpolar angles from
citation functions for opening angles between 170◦ - 180◦ ≈5◦to21◦.Thissetupissimilartotheonedescribedinde-
◦ ◦
(almost back-to-back) and 150 - 170 (background from tailin[59].Theonlydifferenceisthat,intheearliersetup,
quasi-free pion production) showeda narrowpeak around the TAPS forward wall consisted of 510 modules and was
theη-productionthreshold.Suchapeakisexpectedtoarise placed1.75mfromthe target.
whenquasi-boundη-mesonsarere-capturedintoanuclear For the present experiment the main trigger condition
S excitationwithsubsequentdecayintothepion-nucleon was a multiplicity of two separated hits in the combined
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channel. However, the statistical quality of the measure- CB/TAPS system and an integrated energy deposition of
ments was limited and it was pointed out by several au- at least300 MeV in the CrystalBall.Details for the basis
thors [48,49]that the data do not prove the existence of a ofthedataanalysisincludingcalibrationprocedures,iden-
quasi-boundstate. tification of photons and recoil nucleons and the absolute
The present experiment aimed at a measurement with normalizationof crosssections are discussed in [59].Here,
significantlyimprovedstatisticalqualityandbettercontrol wewillonlyoutline the specificstepsforthe identification
ofsystematiceffects.Thiswasachievedbyusingadetector ofcoherentη-production.Resultsforquasi-freeproduction
system with much larger solid-anglecoverage.Apart from ofη-mesonsoffnucleonsboundin3Heinviewofthestruc-
counting statistics this is important for two aspects. It al- ture recently observed for η-photoproduction off the neu-
lowsameasurementofnotonlytheη →2γdecaysbutalso tron[60,61]willbe reportedelsewhere.
the η →3π0 →6γ decaychain.Comparisonofthe twore- The analysis was based on the η → γγ and η → 3π0 →
sultshelpstoestimatesystematiceffectsfromthedetection 6γ decay channels. The measurement of both channels al-
efficiency. Even more important, the coincident detection lowed an additional control of systematic uncertainties.
of recoil nucleons from non-coherentproduction processes Eventswereanalyzedwitheither twoorsixphotoncandi-
becomes much more efficient and can be used to suppress datesandnofurtherhitinthedetectorsystem.Thelatter
this mostimportantbackground. condition reduces the incoherent background since events
with recoil nucleons were suppressed. For the two-photon
decay,η-mesonswereidentifiedwitha standardinvariant-
2. Experimentand analysis mass analysis.Residualbackgroundunder the η-peak was
subtractedbyfittingthespectrawithsimulatedlineshapes
The experiment was performed at the tagged photon andabackgroundpolynomial.Thisprocedurewasapplied
beamoftheMainzMAMIaccelerator[50,51].Theelectron individually for each combination of incident photon en-
beam of 1508 MeV was used to produce bremsstrahlung ergy and meson c.m.-polar angle. For the six photon de-
photonsinacopperradiatorof10µmthickness,whichwere cay,the photonswerefirstcombinedviaaχ2-testtothree
taggedwiththeupgradedGlasgowmagneticspectrometer pairs, which were the best solution for three π0 invariant
[52–54]forphotonenergiesfrom0.45GeVto1.4GeV.The masses. A cut between 110 MeV - 150 MeV was made on
typical bin width for the photon beam energy (4 MeV) is theseinvariantmasses.Subsequently,thesix-photoninvari-
definedbythegeometricalsizeoftheplasticscintillatorsin antmasswasconstructed.Thecorrespondingspectrawere
thefocalplanedetectorofthetagger.Theintrinsicresolu- basically background free under the η-peak (direct triple-
tion of the magnetic spectrometer is better by more than π0 productionhas a verysmallcrosssectionin the energy
anorderofmagnitude.Thesizeofthetaggedphotonbeam rangeofinterest).
spot on the targetwas restrictedby a 3 mm diameter col- Themostimportantstepintheanalysisistheseparation
limatorplaceddownstreamfromtheradiatorfoil.Thetar- of the coherent reaction from breakup where nucleons are
get was a mylar cylinder of 3.0 cm diameter and 5.08 cm removedfromthenucleus.Sincethe 3He recoilnucleican-
lengthfilledwithliquid3Heatatemperatureof2.6K.The notbedetected(theyaremostlystoppedinthetarget)only
correspondingtargetdensity was0.073nuclei/barn. the overdetermined reaction kinematics can be used. The
The reaction products were detected with an electro- kineticenergyoftheη-mesonsinthe γ-3Hec.m.-systemis
magnetic calorimeter combining the Crystal Ball detector fixednotonlybytheincidentphotonenergybutalsofrom
(CB)[55]madeof672NaIcrystalswith384BaF crystals themeasuredlaboratoryenergyandpolarangleoftheme-
2
from the TAPS detector [56,57], configured as a forward son. The difference, the missing energy ∆E, is shown for
wall. The Crystal Ball was equipped with an additional bothdatasamplesinFig.1andcomparedtothesimulated
Particle Identification Detector (PID) [58] for the identi- lineshapesofthecoherentandbreakupreactions.Thesim-
fication of charged particles and all modules of the TAPS ulationsweredonewiththeGeant4programpackage[62],
3
h→ 2g h→ 6g
The relative contributions of these processes have been
40 20
604 MeV determinedbyfittingthedatawithasuperpositionoftheir
line shapes (cf Fig. 1). Since in principle the detection ef-
20 10 ficiency for the different components can be different for
theη →2γ andη →6γ decays,noconstraintsrelatingthe
two channels were imposed on the fits. As a consequence,
0 0
forsomeenergybinsthefittedrelativecontributionsofthe
30 15 612 MeV breakupprocessesaredifferentforthetwodecaychannels,
butthefitofthecoherentcontributionisquitestable.This
20 10
issobecausethebreakupbackgroundmakesalmostnocon-
10 5 tributionatpositivemissingenergies,sothatthecoherent
contributionisonlyweaklydependentontheexactshapeof
0 0
the background.The lowestrangeof photon energies(600
621 MeV
V 40 20 MeV<Eγ <608MeV)liesbetweenthekinematicthresh-
e oldsofcoherentandbreakupreactions.Consequently,only
M 20 10 thecoherentreactioncancontribute.Infact,acleansignal
atzeromissingenergyisseen,whichagreeswiththesimu-
4
0 0 latedcoherentsignalshape.Atevenlowerphotonenergies,
/
s 638 MeV the spectrashowno signalabovestatisticalnoise.
40 20
t
n The count rates are roughly a factor of 2.75 larger
u for the η → γγ data than for the η → 3π0 → 6γ data
20 10
o (note the different scales for the left and right parts of
c
Fig.1),whichisduetotherespectivedetectionefficiencies
0 0
(≈80% for 2γ, ≈35% for 6γ) and decay branching ratios
60 30 655 MeV (b =(39.31±0.20)%, b =(32.57±0.23)%[4]). Absolutely
2γ 6γ
40 20 normalized total and differential cross sections for both
decay channels have been extracted from the yields, the
20 10
target density, the decay branching ratios [4], the simu-
0 0 lateddetectionefficiency,theelectronbeamfluxmeasured
60 30 672 MeV in the focal-plane detector of the tagging spectrometer,
and the tagging efficiency ǫ , i.e. the number of corre-
40 20 tag
latedphotonsthatpassthroughthecollimator.Thelatter
20 10 was measured in special low-intensity runs with a lead-
glassdetectorinthephotonbeam(see[59]fordetails)and
0 0
rangedfrom60%to 75%.Forthe systematicuncertainties
-40 -20 0 20 -40 -20 0 20 40
we estimate 10% for the overall normalization including
D [ ]
E MeV
target density (measurement of target temperature and
possibledeformationofthe coldtargetcell, ≈7-8%),pho-
Fig. 1. Missing energy spectra for the γ3He → η3He reaction for ton flux (measurement of tagging efficiency and electron
the two-photon and 3π0 decay modes for different ranges of inci- flux, <5%) and decay branching ratios (almost negligible
dent photon energy. Black dots: experiment. Curves: Monte Carlo
<1 %). For the reaction dependent simulations of the de-
simulations.Solid(red):coherentcontribution,dashed(blue):recoil
tection efficiency, 5% uncertainties are estimated. Finally,
taken by quasi-free nucleon, dotted (green): recoil taken by di-nu-
cleon, solid(black) sum of all. theenergydependentuncertaintyforthereactionidentifi-
cation (in particular the separation in the missing energy
taking into account all details of the target and detector spectra)rangesfrom2%atthresholdto20%atthehighest
setup. The simulation of the coherent part is straightfor- incidentphotonenergies.
wardduetothetwo-bodyfinal-statekinematics.Incaseof Forthe analysisof the excitationfunction ofπ0-pback-
thebreakuppart,themomentumdistributionofthebound to-back pairs in the γ-3He c.m.-system, Monte Carlo sim-
nucleonshastobeconsidered,andthiswastakenfromthe ulationsweredoneforthesignalandthebackgroundcom-
work of McCarthy, Sick, and Whitney [63]. Several final ingfromquasi-freeproductionofπ0mesons.Forthesignal,
states, such as pd, npp with different participant - spec- the decay of bound S resonances into Nπ was modelled
11
tator combinations, contribute. Good agreement between with a momentum distribution corresponding to the nu-
dataandsimulationswasachieved,atalltheincidentpho- clear Fermi-motion. These simulations were used to select
tonenergiesinvestigated,withthreedifferentreactioncom- thekinematicalconditionsbestsuitedforthesignal.Inthe
ponents: the coherent process, the breakup process with spectraofthepion-protonopeningangle,signaleventsap-
◦ ◦
a quasi-free participant nucleon, and the breakup process pearroughlybetween150 -180 ,whilethebackgroundis
◦ ◦
wherethe recoilis takenby a‘participant’deuteron. distributedbetween100 and180 .
4
3. Results cross section underestimates the data by roughly a factor
oftwo.
3.1. Coherent photoproduction of η-mesons off 3He Shevchenko and collaborators [66] have also calculated
coherentη-productionoffthethree-nucleonsysteminami-
croscopicfew-body description.They finda strongdepen-
The total cross section data for coherent η-production
dence of the result on the elastic ηN rescattering, which
from the two η decay branches is compared to model pre-
is not sufficiently constrained by experiment. Two exam-
dictions [64–66]inFig. 2.The agreementbetweenthe two
ples for different FSI modelling are shown in Fig. 2. They
datasetsisquitegood,butnoneoftheexistingmodelsre-
exhibit strong threshold effects, but do not reproduce the
producethedata,evenwhentheirsystematicuncertainties
measurementsabovethe breakupthreshold.
(shown as shaded band in the figure) are considered. The
mostprominentfeature ofthe datais the extremelysharp
rise at threshold. Here one should note that the binning ]
b
of the data (4 MeV for the 2γ-channel, 8 MeV for the 6γ-
channel)isverylargecomparedtotheenergyresolutionof [m
s
the magnetic taggingspectrometer(roughly200keV).
0.2
0.3
h→ 2g h→ 6g
10
0.1 A
0.2 WI
P
]
b s/
s
[m
s
1
0.1
Tiator et al. 0 600 650 700
Fix et al. 600 620 640 660 680 700 720
Shevchenko et al. E [MeV]
g
0
Fig. 3. Total cross section for γ3He→η3He (averaged over 2γ and
600 620 640 660 680 700 3π0 decays) (reddots)comparedtopreviousdata [47](greentrian-
E [MeV] gles).Solid(dashed)curves:PWIAwithrealistic(isotropic)angular
g
distribution for γn → nη (see text). The present data are binned
in the same way as the angular distributions in Fig. 4 (bin width
Fig.2.Totalcrosssectionfortheγ3He→η3Hereactionfromη→2γ ≈8MeV). Insert: ratioof measuredand PWIA cross sections.
and η → 6γ decays. The shaded band at the bottom indicates the
systematicuncertainty. Thetwoverticallinesindicatecoherent and
breakup threshold. Theory curves: (blue) dotted and dashed from Theaverageofthetwodatasetsiscomparedtothepre-
Shevchenko et al. [66] for two different versions of elastic ηN scat-
viousresultfromPfeifferetal.[47]inFig.3.Thetwodata
tering, (red) solid (dash-dotted): Fix and Arenh¨ovel [65] full model
setsareinreasonableagreement(withinuncertainties)ex-
(plane wave), (black) longdash-dotted: Tiator et al. [64].
ceptfortwopointsaround620MeV.Here,oneshouldnote
TheworkbyTiator,BennholdandKamalov[64]isbased that, in this range, the systematic uncertainty in the pre-
onacoupled-channelanalysisofpion-andphoton-induced viousdatawaslargebecausethecoherentsignalhadtobe
pion-andeta-productionoffthenucleon,whichparameter- extracted by fitting a small coherent contribution in the
izes the resonancecontributionswithanisobarmodeland missingenergyspectra,whichweredominatedbythequasi-
the background terms with effective Lagrangians.For the freereaction.Thequasi-freecontributionislessimportant
coherent production off 3He, realistic nuclear wave func- at lower incident photon energies, and is better separated
tionswereused,butthemodelwasbasedontheplane-wave fromthecoherentcomponentathigherincidentphotonen-
impulse approximation (PWIA). The result strongly un- ergies.The presentexperimentprofitedin this rangefrom
derestimates the magnitude of the measured cross section thealmost4πcoverageofthedetector,whichallowedsome
anddoesnotreproducethe energydependence. suppression of the quasi-free backgroundby the detection
Fix and Arenh¨ovel [65] have modelled coherent η- ofassociatedrecoilnucleons.
photoproduction off 3He and 3H in PWIA, in a distorted- Also shown in this figure are the results from a sim-
wave impulse approximation (DWIA), using an optical ple PWIA model. It uses the effective photon energy
eff
potential, and in a full four-body scattering model. They Eγ (Eγ,x) givenby
find strong FSI effects, which amplify the threshold cross
sectionforthefullfour-bodymodelwithrespecttoPWIA s −m2
Eeff = eff N, s =(P +P )2, (2)
andDWIA (whichgivesimilar results).Neverthelesstheir γ 2m eff γ N
N
5
40
where E is the laboratory energy of the incident photon
γ 600.0 - 608.4 608.4 - 616.9
and Θ⋆ is the polar angle of the η meson in the photon-
η
nucleus c.m. system with x = cos(Θ⋆). The effective pho-
η
ton energy corresponds to the s of the incident photon 20
eff
(four-momentumP )andanucleon(four-momentumP )
γ N
withthree-momentump fromthe nucleonmotioninside
N
the nucleus. The nucleon momentum is related in the fac- 0
torization approximation to the momentum q transferred
616.9 - 625.4 625.4 - 633.9
to the nucleus by[67]: 40
A−1 1
p =− q=− q, (3)
N 2A 3 20
whereallmomentaareinthe laboratorysystem.
The coherent cross section is then composed of three 0
]
factors: r
s 60 633.9 - 642.3 642.3 - 650.8
/
dσPdWΩIA(Eγ,x)= kqηγ((AA)) · kqηγ((NN))!· dσdeΩlem · FFAp22((qq22)) (4) nb 40
[
Wd 20
theelementarycrosssectiondσ /dΩ,akinematicalfac-
elem /
tor,andthenuclearformfactorforpoint-likenucleons.The
sd 0
kinematical factor accounts for the change of phase-space
betweenthedifferentc.m.systemsandisderivedfromthe 75 650.8 - 659.2 659.2 - 667.6
photonandηthree-momentainthephoton-nucleon(k(N),
γ
50
q(N)), and photon-nucleus (k(A), q(A)) c.m. systems. The
η γ η
nuclearform-factorFA2(q2)wastakenfrom[63].Itincludes 25
the spatial distribution of the charge (respectively mag-
netic moment) of the nucleon, while here the distribution 0
of point-like nucleons is relevant. We have therefore used
theratioofthenuclearformfactorF (q2)andthenucleon 75 667.6 - 676.1 676.1 - 684.5
A
dipole form factor F (q2) to approximate the distribution
p 50
ofpoint-likenucleonsinthe 3He nucleus.
Since η-photoproduction in this energy range is almost 25
only due to the S excitation, the dominant electromag-
11
netic multipole is the E spin-flip. Neglecting small con- 0
0+
tributions from other multipoles and higher components -1 -0.5 0 0.5 -1 -0.5 0 0.5 1
in the 3He wave function, only the unpaired neutron con- ccooss((QQ *)
h
tributestocoherentproductionbecauseaspin-flipofapro-
ton is Pauli-blocked.Therefore,we use for the elementary
cross sectionthe experimental results for the γn →nη re- Fig. 4. Angular distributions of γ3He→η3He in the photon-nucleon
c.m. system for different energy bins (range of incident photon en-
actionfrom[60,61].Sincetheangulardependenceuptothe
ergy in MeV indicated by the labels). (Red) dots: η → 2γ decay,
S11 peakisalmostisotropic,onecanapproximatethec.m. (blue) open squares: η→6γ decay, dashed curves: resultsof PWIA
differentialcrosssectionby: modelwithisotropicangulardistributionsforγn→nη,solidcurves
with realistic angular distributions, dotted curves: folded with ex-
dσ
elem eff eff perimental resolution. (see text).
(E ,x)=σ (E )/4π, (5)
dΩ γ n γ
where the total neutron cross section σn is parameter- angulardistributions takenfrom[61].The difference is, as
ized as a Breit-Wigner curve with an energy dependent expected, negligible. Despite the simplicity of the model,
widthusingthenumericalvaluesfrom[61](W=1546MeV, the predicted cross section agrees with experiment within
Γ=176 MeV, An1/2=90×10−3 GeV−1/2, bη=0.5, bπ=0.4, statistical and systematic uncertainties for the highest in-
b =0.1). Variation of the parameters within their un- cident photon energies.In the threshold region it is in ex-
ππ
certainties changes the predictions for the coherent cross cellent agreement with the PWIA calculation by Fix and
sectiontypicallyonthe 10%level. Arenh¨ovel. However, in this region it underestimates the
The results from the PWIA model are comparedto the data by nearly one order of magnitude, which is evidence
data in Figs. 3 and 4. They are shown for the approxima- forstrongFSI effects atthreshold.
tion of Eq. 5 assuming isotropic angular distributions for The behavior of the angular distributions of the PWIA
the elementary γn → nη reaction, and also for realistic isdominatedbythenuclearformfactor,whichisresponsi-
6
bleforthestrongforwardpeaking.Athighincidentphoton ]u.
energiesthe datashowthe sametendency,thoughthe rise a.
[6
to forwardangles is not as steep as in the model. This in- 20 s*Eg 0.8
dicatessignificantFSIeffectsevenforthoseenergies,since nt
u
themoretrivialapproximationsinthePWIAmodelcannot o
c
explain this discrepancy. The use of realistic angular dis- 0.6
]
tributionsfortheelementarycrosssectioninsteadofEq.5 u.
(dashedcurvesinFig.4)hasbasicallyno impact.The use [sa. hold 0.4
optiflvimfieleyodrsesmcraeaallallirscthfioacrnmnguecfsalec[6at5ro]rw.iaFnvienEafqul.lny4,cttliheoaendsesxinopsnetlreyiamdteoonfctoatmhleapnsaigrmua--- count10 thres 0.2 YY pp pp==116550oo--118605oo
lar resolution is only responsible for minor effects. This is Y p p=140o-150o
demonstrated by the dotted curves in Fig. 4, which have Y p p=130o-140o
0
beenfoldedwith the detectorresponse. 400 600 800 1000
E[MeV]
g
Towards the threshold, the measured angular distri-
0
butions become almost isotropic. Between coherent and
breakupthreshold,theydeveloparisetobackwardangles, 600 800 1000 1200
whileinPWIAtheformfactorstillcausesaforwardpeak- E [MeV]
g
ing. Together with the disagreement in the absolute scale
ofthecrosssectioninthethresholdregion,thiscomparison Fig.5.Mainplot:differenceofexcitations functions ofπ0−pback-
clearlydemonstratesthe largeinfluence ofFSI effects. -to-back pairs with opening angles between 165◦ - 180◦ and 150◦ -
165◦.Insertexcitations functionsfordifferentrangesoftheopening
angle Ψπp after removal of the overall energy dependence ∝ Eγ−6.
3.2. Excitation function of π0−p back-to-back pairs Vertical dotted lines:coherent η-production threshold.
The excitation function of π0-proton pairs for different
rangesoftheiropeningangleintheγ-3Hec.m.systemwas photonenergiesforsmalleropeningangles.Thisisapurely
analyzedin a manner similar to that ofPfeiffer et al. [47]. kinematical effect; small opening angles correspondto de-
Theideawas,thatwhenη-mesonsareproducedintoanη- caysof nucleon resonancesmoving forwardin the photon-
3He resonantstate,overlappingwiththe coherentproduc- nucleusc.m.system.Therefore,foragivenmassM =W
R
tionthreshold,thoseproducedatphotonenergiesbelowthe ofthe resonance,smallopeninganglescorrespondtolarge
thresholdare off-shelland cannotbe emitted without vio- incidentphotonenergies(andnucleonFermimomentapar-
latingenergyconservation.Theycan,however,becaptured allel to the photon momentum). Unfortunately, subtrac-
◦
by a nucleon which is then excited to the S -resonance. tion of the normalized excitation functions for the 165 -
11
Sincethisresonancehasa≈50%decaybranchingratiointo 180◦ and150◦ -165◦ opening-anglerangesproducesanar-
Nπ,theexpectedsignalwouldbepion-nucleonpairsemit- rowpeakexactlyattheη-productionthreshold.Thispeak
tedback-to-backintheγ-3Hec.m.system.Theresultsare does,however,notoriginatefromaspecialstructureinthe
showninFig.5.Thefigureshowsthedifferenceoftheexci- back-to-back data, but it is due to the subtraction of the
◦ ◦
tationfunctionsforopeninganglesfrom165 -180 (back- shifted low energy tails of the second resonance region in
to-backrangetakingintoaccounteffectsofFermimotion) singlepionproduction.
◦ ◦
andthedatafrom150 -165 .Theserangeswereoptimized Here,wehaveonlypresentedtheresultsfromananalysis
withMonteCarlosimulationsofsignalandbackgroundand similar to the previous work by Pfeiffer et al. [47]. The
◦
areslightlydifferentfromthoseusedbyPfeifferetal.(170 - much better statistical quality of the present data allows
◦ ◦ ◦
180 and160 -170 ), but this is a minor effect. The result alsomorerefinedanalyseswithadditionalcuts toenhance
shows the peak at the coherentη thresholdthat had been the signal-to-background ratio. For this purpose we have
observedpreviously, but now with much higher statistical donedetailedMonteCarlcosimulationsofthekinematical
significance.However,thedataalsoshowsomestructureat correlationsforthe signalandthe backgroundfromquasi-
higher incident photon energies which was not previously freepionproductionandanalyzedtheexcitationfunctions
seen because the earlier experiment covered only incident with optimizedcuts. However,alsowith these analysesno
photonenergiesupto800MeV.Themuchhigherstatisti- structures that could be uniquely related to the decay of
cal quality of the new data allowed a detailed analysis of an η-mesic state into Nπ could be identified. The π0 −p
thesestructures.ThisissummarizedintheinsertofFig.5. backgroundbeforeveryspecificcutsisatleastthreeorders
It shows the excitation functions for different ranges of of magnitude larger than any expected signal from an η-
opening angle, when the overallenergy dependence of the mesic state. In consequence, it seems to be impossible to
data (∝E−6) is removed.The broad,peak-like structures identify in this reaction channel a small signal from the
γ
areduetothesecondandthirdresonanceregionsofthenu- decayofboundS resonancesontopofthesecomplicated
11
cleon.Thepositionofthesesignalsshiftstohigherincident backgroundstructures,evenwhenthe signalexists.
7
4. Summaryand conclusions [12]G.A.Sokol andL.N.Pavlyuchenko, Phys.of.AtomicNuclei71
(2008) 509.
[13]B. Kruscheat al.,Phys. Lett. B 358 (1995) 40.
Coherentphotoproductionofη-mesonsoff3Hehasbeen
[14]P. Hoffmann-Rothe et al.,Phys. Rev. Lett. 78(1997) 4697.
measuredwithmuchimprovedstatisticalqualitycompared [15]J. Weiss et al.,Eur.Phys. J. A 11(2001) 371.
tothepilotexperimentofPfeifferetal.[47].Thetotalcross [16]J. Weiss et al.,Eur.Phys. J. A 16(2003) 275.
section rises sharply between the coherent and breakup [17]V. Hejnyet al.,Eur.Phys. J.A 6(1999) 83.
[18]V. Hejnyet al.,Eur.Phys. J.A 13 (2002) 493.
thresholds. Compared to a PWIA, which is in fair agree-
[19]R.A.Arndtet al.,Phys. Rev. C 72(2005) 045202.
mentwiththedataintheS peak,thethresholdvaluesare
11 [20]T.Ueda, Phys. Rev. Lett. 66(1991) 297.
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[25]A.M.Green andS. Wycech, Phys.Rev. C 54 (1996) 1970.
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[26]N.N.Scoccola, D.O.Riska, Phys. Lett. B 444 (1998) 21.
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Pfeiffer et al. [47]. This signal was reproduced with much
[41]A. Wronska etal.,Eur. Phys.J A26 (2005) 421.
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[42]N. Williset al.,Phys. Lett. B 406(1997) 14.
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Acknowledgments 399.
We wishto acknowledgethe outstanding supportofthe [47]M. Pfeifferet al.,Phys. Rev. Lett. 92 (2004) 252001.
accelerator group and operators of MAMI. We gratefully [48]A. Sibirtsevetal.,Phys. Rev. C 70 (2004) 047001.
[49]C. Hanhart, Phys. Rev. Lett. 94(2005) 049101.
thankC.Wilkinformanystimulatingdiscussions,instruc-
[50]H.Herminghausetal.,IEEETrans.onNucl.Science.30(1983)
tivesuggestions,andforcarefulandcriticalreadingofthe
3274.
manuscript.We thank A. Fix and L. Tiatorfor veryhelp- [51]K.-H.Kaiseret al.,Nucl.Instr. Meth. A 593 (2008) 159.
ful discussions about the PWIA calculations. This work [52]I. Anthony etal.,Nucl. Instr. Meth. A 301 (1991) 230.
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A 368 (1996) 698.
Forschungsgemeinschaft (SFB 443, SFB/TR 16), DFG-
[54]J.C. McGeorge etal.,Eur. Phys. J.A 37(2008) 129.
RFBR (Grant No. 05-02-04014), UK Science and Tech-
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