EPJ manus ript No.(will be inserted by the editor)Coherent and In oherent 0 Photoprodu tion from the Deuteron?U. Siodla zek1, P. A henba h2, J. Ahrens3, J.R.M. Annand8, H.-J. Arends3, R. Be k3, R. Bilger1, H. Clement1,V. Hejny4, M. Kotulla2, B. Krus he7, V. Kuhr5, R. Leukel3, J.C. M George8, V. Metag2, R. Novotny2, V. Olmosde Leon3, F. Rambo5, M. S hepkin6, A. S hmidt3, I. Seluzhenkov6;9, H. Stroher4, G.J. Wagner1, Th. Wal her3, J.Wei2, F. Wissmann5, and M. Wolf21 Physikalis hes Institut, Universitat Tubingen, Auf der Morgenstelle 14, D-72076 Tubingen, Germany2 II. Physikalis hes Institut, Universitat Gieen, D-35392 Gieen, Germany3 Institut fur Kernphysik, Universitat Mainz, D-55099 Mainz, Germany4 Institut fur Kernphysik, Fors hungszentrum Juli h, D-52425 Juli h, Germany5 II. Physikalis hes Institut, Universitat Gottingen, D-37073 Gottingen, Germany6 Institute for Theoreti al and Experimental Physi s, Mos ow 117218, Russia7 Institut fur Physik und Astronomie, Universitat Basel, Klingelbergstr. 82, CH-4056 Basel, Switzerland8 Department of Physi s and Astronomy, University of Glasgow, Glasgow G128 QQ, UK9 Mos ow State Engineering Physi s Institute, Mos ow 115409, RussiaRe eived: date / Revised version: dateAbstra t. Dierential ross se tions for the rea tions d( ; 0)d and d( ; 0)pn have been measured atMAMI with the TAPS dete tor setup in the energy range 140 MeV< E < 306 MeV. By use of the Glasgowtagging spe trometer an 0.8 MeV energy resolution for photons in ident on the target was a hieved. The0 missing energy resolution was suÆ ient for a reliable separation of oherent and in oherent hannels.The data for the breakup- hannel exhibit very strong nal state intera tion ee ts, whereas the observedangular dependen e of the in lusive pro ess d( ; 0)X is in quantitative agreement with predi tions fora quasi-free pro ess. The observed absolute d( ; 0)X ross se tions on the other hand are signi antlysmaller than predi ted by the quasi-free pro ess for E > 250 MeV. Asso iating this failure with the 0photoprodu tion on the neutron would suggest that its ross se tion is up to 25% below the presentlybelieved value.PACS. 13.60.Le, 25.20.Lj

2 U. Siodla zek et al.: Coherent and In oherent 0 Photoprodu tion from the Deuteron1 Introdu tionNear threshold harged pion photoprodu tion from thenu leon is governed by the s-waveE0+ amplitude originat-ing from non-resonant Born terms. This pro ess is stronglysuppressed in 0 produ tion whi h is already dominatedby the ex itation of the -resonan e at threshold.The pion photoprodu tion ross se tions are very wellestablished for the proton, however, there are no orre-sponding data from dire t measurements on the neutronfor obvious reasons. The only sour e of information stemsfrommeasurements on nu lei, in parti ular on the deuteron,for whi h nu lear stru ture and medium ee ts are thoughtto be best under ontrol.Unlike the harged pion ase there are two rea tion hannels for 0 produ tion on the deuteron, the oherent hannel d( ; 0)d, where the deuteron stays in its ground-state (g. 1a), and the so- alled in oherent or break-up hannel d( ; 0)pn, where the deuteron breaks up. Thelatter is thought to be dominated by the quasi-free pro- ess on the onstituent nu leons (g. 1b). However, as wewill show below, the nu leon-nu leon nal state intera -tion (NN-FSI) following the quasi-free pro ess (g. 1 )strongly in uen es the energy and angular dependen e ofthe break-up hannel. As we will also show, the modi- ations there turn out to be just ounterbalan ed by the oherent hannel, su h that the quasi-free ross se tion isre overed in the sum of both, whi h is the in lusive 0? supported by the BMBF under ontra t 06 TU 886, theDFG (Mu 705/3, Graduiertenkolleg and SFB 201) and DAAD(Euler program)

produ tion ross se tion. On this basis we will suggest aninteresting modi ation of the n( ; 0) ross se tion.2 ExperimentThe measurements were arried out at MAMI using taggedphotons in the energy range E = 140 306 MeV withan energy resolution of E 0:8 MeV. The 0 mesonsemitted from the LD2 target were dete ted via their 2 de ay using the TAPS dete tor as shown s hemati ally ing. 2. It omprises 6 blo ks, ea h ontaining 64 hexago-nal BaF2 modules with individual plasti veto dete tors,together with a forward wall ontaining 120 BaF2-plasti phoswi h teles opes. Compared to a previous investigation[1 of the same rea tion whi h utilized 5 TAPS blo ks butno forward wall the solid angle overed is in reased on-siderably to about 1/3 of 4. Also the number of eventsa umulated in the measured energy range was higher byan order of magnitude. Neutral parti les were identied bytime-of- ight and pulse-shape analyses. Details are givenelsewhere [13.In the photon energy range of this measurement theenergies of deuterons and nu leons emitted from the rea -tion were too low for a signi ant dete tion (instrumentalthresholds Ed = 55 MeV, Ep = 40 MeV, En 30 MeV)in oin iden e with the gammas from 0 de ay. For neu-trons, in addition the dete tion eÆ ien y is not known wellenough. Due to this and also due to an appre iable lossof a eptan e by the onstraint of parti le oin iden esthe oherent ( d ! 0d) and in oherent ( d ! 0np) hannels ould not be separated dire tly by an additional

U. Siodla zek et al.: Coherent and In oherent 0 Photoprodu tion from the Deuteron 3dete tion of d; p or n. However, they ould be identiedby tting the missing energy spe tra (g. 3) with MonteCarlo (MC)-generated line shapes, provided the statisti ala ura y in ea h 20Æ wide angular bin was suÆ ient. Thisrequired a tagged photon bin width E = 10 MeV nearthreshold [3 but E = 1 MeV was suÆ ient for highphoton energies.The obtained experimental results are shown in gs.4-9 together with their statisti al un ertainties. The sys-temati un ertainties in the absolute normalization of the ross se tion are less than 7% [3. Sin e for the separa-tion of oherent and in oherent 0 produ tion hannelsMC-generated line shapes had to be used, this separationis not ompletely model-independent. From using variousrea tion models (see dis ussion in se tion 4) we nd thismodel-dependen e in the separation to be very small, inthe order of 5% [3.3 Experimental ResultsFigs. 4 9 show the experimental results for angular andenergy dependen e of the oherent, in oherent and in- lusive ross se tions for 0 photo produ tion from thedeuteron in the energy range E 306 MeV. Angulardistributions are shown only for a sele tion of in ident en-ergies. The full data are given in Ref. [3.For the oherent produ tion there are just the pre-vious TAPS data [1 plus a few fragmentary data fromearlier experiments [4,5 to ompare with. They were ob-tained primarily at large 0 angles and are shown in g.4 by open symbols. Whereas the oherent produ tion is

strongly forward peaked in its angular dependen e, thein oherent produ tion appears to be peaked at ba kwardangles (g. 6). For the latter there are only the previousTAPS data [1 to ompare with and within statisti s theyare in good agreement.The in lusive ross se tion, i.e. the sum of oherent andin oherent ross se tions, exhibits an angular dependen e(g. 8), whi h essentially is symmetri about 90Æ ex ept atthe lowest energies. This is onsistent with the dominant ontribution originating from a single partial wave, theresonant M1+ amplitude, and resembles very mu h thesituation for 0 produ tion on the nu leon [6.For E < 160 MeV, i.e. near the pion threshold, thereexist data of high statisti al a ura y for the in lusive ross se tion from measurements [7 at SAL. They are ompared in g. 9 to the results of this experiment. Withinthe statisti s of the individual energy bins the data agreewell with ea h other. However, over the full overlap rangethere is a lear trend that the SAL results lie high by about10% ompared to our results, i.e. we nd here a similardis repan y between the data sets of both installations asobserved for p! 0p [8. For E 207 MeV there existprevious TAPS measurements [1 with poorer statisti s inthe overlap region. The ross se tions obtained there arein good agreement with the present results both for theangular dependen e and the integral values (g. 9).Finally we note that the statisti s in the present mea-surement of the total 0 produ tion ross se tion are goodenough to allow a sensitive sear h for narrow dibaryons. A

4 U. Siodla zek et al.: Coherent and In oherent 0 Photoprodu tion from the Deuterondetailed investigation of the data on this matter has beenpublished previously [9.4 Dis ussion of the data(i) Coherent produ tion hannel d( ; 0)dThe data for oherent produ tion are ompared in Figs. 4and 5 to theoreti al al ulations of Arenhovel et al. [10,Laget [11 and Kamalov et al. [12. The experimental en-ergy dependen e is reprodu ed best by the latter al u-lations, whi h also give a near quantitative des ription ofthe experimental angular distributions, in parti ular forE 260 MeV.Also shown in Figs. 4 and 5 are Monte-Carlo (MC)simulations, whi h we arried out in the oales en e model[1315. In its simplest form it assumes that following aquasi-free pro ess on one of the target nu leons the twonu leons re ombine into the deuteron, if q < q0 (withq = q1 q2 being the relative momentum of the outgo-ing nu leons), whereas for q q0 the deuteron breaks upand populates the in oherent exit hannel. Utilizing theHulthen wave fun tion for the deuteron 'd and SAID [16amplitude f N for the elementary pro ess N ! 0Nthese MC-simulations provide an surprisingly good de-s ription of the experimentally observed energy and an-gular dependen es both for the oherent and the in oher-ent hannel. This al ulation has only a single parame-ter, q0, whi h has been adjusted to q0 300 MeV/ fora reasonable des ription of the data. We note that thisvalue is lose to the one obtained for high energy proton-nu leus ollisions [13. For the angle integrated ross se -

tions displayed in gs. 5 and 7 the oales en e model al- ulations are shown without any renormalization.For theangular distributions displayed in gs. 4 and 6 the oales- en e model al ulations have been slightly renormalizedenergy-by-energy to the angle integrated data for the total0 produ tion ross se tion (g. 9), whi h is just the sumof oherent and in oherent produ tion ross se tions. Wealso note that simple PWIA al ulations [3, where theSAID amplitudes for N ! 0N are multiplied with theexperimental deuteron form fa tor, give angular distribu-tions for the oherent hannel whi h, too, are very lose tothose of the oales en e model and those also of Kamalovet al.. From this we on lude that the bulk properties ofthe oherent hannel are well understood.(ii) In oherent produ tion hannel d( ; 0)pnThe situation is somewhat more ompli ated for the in- oherent or break-up hannel. In the absen e of any nalstate intera tion the hannel would be asso iated with thequasi-free 0 produ tion on the nu leons. However, quasi-free al ulations fail badly. For the angular distributionssu h al ulations predi t a shape symmetri about 90Æ(dashed urves in g. 6 and dashed and full urves in g.8), whi h is not observed experimentally. Also for the en-ergy ex itation fun tion they predi t mu h too large a ross se tion (dashed and dashed-dotted urves in g. 7).As already pointed out by Laget [11 the break-up hannelis strongly in uen ed by NN -FSI, whi h greatly redu ethe break-up ross se tion by about 30% and ause its an-gular distributions to be ba kward peaked (solid urvesin Figs. 6 and 7). These ndings are also orroborated by

U. Siodla zek et al.: Coherent and In oherent 0 Photoprodu tion from the Deuteron 5the results of the oales en e model dis ussed above. Inorder to improve this sharp ut-o model towards a morerealisti smooth transition, we have arried out MC sim-ulations, where instead of the sharp ut-o parameter q0the parameter-free NN-FSI of Kolybasov and Ksenzov [17has been used.In ref. [17 the onne tion between oherent and breakuppro esses on the deuteron has been evaluated. By use ofthe ompleteness relation it has been shown therein thatthe sum of the oherent ross se tion and the ross se -tion for the quasi-free pro ess in luding FSI gives the purequasi-free ross se tion, (i.e. without FSI). This meansthat the ee t of the FSI in the break-up pro ess just ounterbalan es the oherent pro ess. Following ref. [17we may write the expression for the res attering graphshown in g. 1 as:MR = f p + f n2 Z dq0 fNN(q;q0) 'd(q0 Q)q02 q2 i" ; (1)where f N stands for the amplitude N ! N and fNNis swave elasti NN amplitude, whi h takes into a ountthat the two nu leons before res attering are o-mass-shell; q0 and q are relative nu leons momenta before andafter res attering, respe tively; Q is momentum transfer;q = jqj, q0 = jq0j, Q = jQj.The amplitudeMR is normalized in the same way as inref. [17, and fNN is normalized so that for two nu leonson mass shell dNN=d = jf (on)NN j2. The pure quasi-freeamplitude d! 0np is given by:MQF = f p'd (qQ) + f n'd (q+Q) : (2)

The summary ontribution of the diagrams shown ing. 1b and g. 1 an then be written as:MFSI =MQF +MR =MQF[1 +R1f (on)NN ; (3)where R1(q;Q) = f p + f nMQF Z dq02 4q2 + 24q02 + 2 'd(q0 Q)q02 q2 i" :Integration over q0 with the Hulthen wave fun tion gives:R1(q;Q) = 4q f p + f nMQF [I() I() ; (4)where 2 = mEd with Ed being the deuteron bindingenergy and m the nu leon mass; = 5:2; is the nor-malization fa tor of the Hulthen wave fun tion: = 4 (+ )2( )2 12 ; (5)and fun tion I(x) equals to:I(x) = i2 lnq +Q+ 2ixq Q+ 2ix ln i +Q+ 2ixi Q+ 2ix : (6)Our MC simulations in luding this FSI are shown ing. 6 by the dashed-dotted urves. In shape these resultsare quite similar to the ones of Laget in luding FSI. In ab-solute magnitude they are below the latter (and in betteragreement with the data), sin e the MC simulations havebeen renormalized energy-by-energy to reprodu e the an-gle integrated total ross se tions (see dis ussion below).(iii) In lusive 0 produ tion d( ; 0)XThe angular distributions of the in lusive ross se tionare ompared in g. 8 to quasi-free al ulations by Laget[11 and our MC simulations assuming a quasi-free pro- ess utilizing just the Hulthen wave fun tion and SAID

6 U. Siodla zek et al.: Coherent and In oherent 0 Photoprodu tion from the Deuteronamplitudes. After renormalizing these simulations energy-by-energy to the angle integrated ross se tions, i.e. thetotal 0 produ tion ross se tions, the agreement to thedata in g. 8 is very good, ex ept for the lowest energy bin.This ex ellent agreement in the angular dependen e of thequasi-free pro ess with the data is in full a ord with thestatement of ref. [17 dis ussed above, that oherent andin oherent ross se tions add up to the quasi-free rossse tion, whi h is therefore seen in the in lusive ross se -tion. The same on lusion has been rea hed by Laget [11.In turn, if this on lusion is orre t, then the energydependen e of the total 0 produ tion ross se tion shouldalso be represented quantitatively by the quasi-free pro- ess. However, this is not the ase for E > 250 MeV,as an be seen in g. 9 by omparing the dashed-dotted urve with the data. In g. 10 the TAPS data [1 obtainedre ently over the full -resonan e region are omparedto the MC simulations of the quasi-free pro ess. As anbe seen, this pro ess overshoots the data for E > 250MeV by up to 15% at the maximum of the -resonan eex itation. Sin e the p ! 0p ross se tions are wellestablished, the only possible un ertainties in the al u-lation of the quasi-free pro ess are the n ! 0n rossse tions. The latter have been taken from the SAID andMAID [18 phase shift analyses, respe tively. Whereas inthe SAID analysis proton and neutron ross se tions arenearly identi al in the region of the -resonan e, the neu-tron ross se tions are smaller by about 3% near the topof the ex itation in the MAID analysis.

In order to reprodu e the data by the quasi-free al u-lation, the MAID neutron ross se tions had to be redu edby up to 25% between E > 250 and 450 MeV (g. 10, bot-tom). This is surprising, sin e no large isospin asymmetryis known for the ex itation of the -resonan e. Hen e thisredu tion would need to be asso iated with ba kgroundterms in the 0 photoprodu tion on the nu leon. Isos alar ontributions, whi h enter the n ! 0n and p ! 0pamplitudes with dierent signs, ould possibly be the ori-gin for the observed dieren es. As dis ussed above thede rease of the break-up ross se tion due to NN FSIought to be ompensated just by the oherent hannel ross se tion, so that their sum, the total 0 produ tion ross se tion, is represented by the pure quasi-free pro ess.This ompensation, however, is exa t only if the full NN phase spa e is available, so that the ompleteness relation is satised. This ondition is wellfullled at high energies. It is still nearly fullled at ourenergies, sin e the range of momenta of the outgoingnu leons is already large ompared to the Fermi mo-mentum of the nu leons inside the deuteron. in the isos alar np hannel, not in the isove tor han-nel. However, if the 0 is produ ed via the me h-anism | as is the ase preferentially in the region then isospin sele tion allows only isos alar np pairs.This again points to the ba kground terms in the 0produ tion as a possible origin for the observed dis- repan y in the region. Though only a full oupled hannel treatment an give a quantitative estimate ofthese ee ts, they are not expe ted to ae t the to-

U. Siodla zek et al.: Coherent and In oherent 0 Photoprodu tion from the Deuteron 7tal 0 produ tion ross se tion by more than a fewper ent and hen e are unlikely to fully explain the ob-served dis repan y.An alternative explanation ould prin ipally be thatthe total 0 produ tion pro ess gets redu ed by strong oupling to the deuteron photo disintegration hannel.However, it is not obvious why this should happen justfor E > 250 MeV and why this should have no in u-en e on the angular dependen e. Above pion threshold thephoto-disintegration pro ess ross se tion is largest (70b)near E 280 MeV and de reases quite rapidly towardshigher energies. At E 330 MeV, where we nd thelargest dis repan ies, the photo-disintegration ross se -tion has already dropped by nearly a fa tor of two. Alsothe al ulations of Laget, whi h in lude this hannel, donot show su h a strong oupling ee t. Finally, the nal-state N res attering with its possibility of pioni hargeex hange would have the potential of lowering the total ross se tion. Again, it is not obvious why this shouldonly happen in the -resonan e region. Furthermore eventhere the N s attering amplitude is an order of magni-tude smaller than the s-wave NN s attering amplitude.Hen e it is not surprising that the N res attering ontri-butions are mu h smaller than the NN ones as borne outagain quantitatively by Laget's al ulations.As seen from g. 10, for 450 MeV< 550MeV the quasi-free al ulations based on SAID/MAID amplitudes omeagain lose to the data. We note, however, that for 550MeV E 800 MeV these al ulations again ex eedthe TAPS data by up to 40% [19.

5 SummaryThe new data on oherent, in oherent and in lusive 0photoprodu tion from the deuteron ll the gap betweenthe pion threshold and the-resonan e region, where dataare available from previous measurements. For E < 160MeV our data are in reasonable agreement with the high-statisti s measurements [7 of the in lusive ross se tionat SAL, though the latter lie systemati ally somewhathigher. At the high-energy end the new data are in goodagreement with the previous poorer statisti s TAPS data[1. The oherent produ tion is strongly peaked towardsforward angles. This may be easily understood be ause ofthe small relative momenta between the nu leons in deu-terium. For larger momenta the deuteron breaks up andfeeds the in oherent hannel, where therefore the angu-lar distributions are ba kward peaked. These features areborne out by the MC simulations using the simple oales- en e model or more realisti ally by using the FSI ansatzof ref. [17 as well as by the theoreti al al ulations ofLaget [11.The angular dependen e of the in lusive d( ; 0)X re-a tion is quantitatively reprodu ed by the pure quasi-freepro ess as predi ted by Laget [11 and Kolybasov [17.However, for E > 250 MeV, the observed absolute rossse tions are lower than the predi tions for the quasi-freepro ess. If this dis repan y is asso iated with the n !0n pro ess, then its ross se tion would need to be re-du ed by up to 25%.

8 U. Siodla zek et al.: Coherent and In oherent 0 Photoprodu tion from the DeuteronReferen es1. B. Krus he et al., Eur. Phys. J. A6, 309 (1999)2. A.R. Gabler et al., Nu l. Instr. and Meth. A346, 168(1994)3. U. Siodla zek, do toral thesis, University of Tubingen,2000http://www.w210.ub.uni-tuebingen.de/dbt/volltexte/2001/2134. G. Holtey et al. Z. Phys. 259, 51 (1973)5. B. Bouquet et al., Nu l. Phys. B79, 45 (1974)6. M. Fu hs et al., Phys. Lett. B368, 20 (1996)7. J.C. Bergstrom et al., Phys. Rev. C57, 3203 (1998)8. A.M. Bernstein et al., Phys. Rev. C55 (1997) 15099. U. Siodla zek et al., Eur. Phys. J. A, a epted for publi- ation10. H. Arenhovel and P. Wilhelm, Nu l. Phys. A593, 435(1995)11. J.P. Laget, Phys. Rep. 69, 1 (1981)12. S.S. Kamalov, L. Tiator and C. Bennhold, Phys. Rev.C55,98 (1997)13. A. S hwarzs hild and C. Zupan i , Phys. Rev. 129, 854(1963)14. S.T. Butler and C.A. Pearson, Phys. Rev. Lett. 7, 69 (1961;Phys. Lett. 1, 77 (1962); Phys. Rev. 129, 836 (1963)15. H. Ma hner, Phys. Rep. 127, 309 (1985)16. Program pa kage SAID, R.A. Arndt et al.,http://www.vtinte.phys.vt.edusee also R.A. Arndt, Phys. Rev. D28, 97 (1983)17. V.M. Kolybasov and V.G. Ksenzov, Sov. J. Nu l. Phys.22, 372 (1976)18. Program pa kage MAID, L. Tiator, http://www.kph.uni-mainz.de/MAIDsee also D. Dre hsel et al., Nu l. Phys. A645, 145 (1999)

a b Fig. 1. Graphs representing the me hanisms for the 0 produ -tion on the deuteron: (a) oherent pro ess, (b) pure quasi-freepro ess, ( ) quasi-free pro ess followed by NN -FSI.2

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Fig. 2. TAPS dete tor setup at MAMI. Six TAPS blo ks ontaining 8 8 BaF2 modules ea h (AF) and the forwardwall ontaining 120 BaF2-plasti phoswi h modules (FW) arepla ed in plane around the target hamber ontaining the liq-uid deuterium target.19. B. Krus he, Pro . V. TAPS workshop, Rez 1999, Cze h. J.Phys., in press

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10 U. Siodla zek et al.: Coherent and In oherent 0 Photoprodu tion from the DeuteronArenhoevelLagetKamalov

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U. Siodla zek et al.: Coherent and In oherent 0 Photoprodu tion from the Deuteron 11Laget without FSILaget with NN-FSI

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0 50 100 1500

10

20

30

0 50 100 1500

10

20

30

40

172 MeV 187 MeV 207 MeV

223 MeVdσ/

dΩ

[µb

/sr]

235 MeV 259 MeV

282 MeV 297 MeV

ΘπγN [deg]

305 MeV

0 50 100 1500

20

40

Fig. 8. Dierential ross se tions for the in lusive 0 photo-produ tion pro ess d ! 0X for a sele tion of in ident pho-ton energies. Solid and dashed lines show the pure quasi-free ross se tions from our MC simulations and from al ulationsby Laget [11, respe tively. The latter are identi al to thoseshown as dashed urves in g. 6. Our MC simulations havebeen renormalized energy-by-energy to the angle integrateddata.

12 U. Siodla zek et al.: Coherent and In oherent 0 Photoprodu tion from the DeuteronTAPS 92

Laget without FSIArenhoevel

MC quasifree

Eγ [MeV]

σ

[µb

]

0

100

200

300

400

500

150 200 250 300

Bergstrom 98

Eγ [MeV]

σ [µ

b]

0

2

4

6

8

140 145 150 155 160 165

Fig. 9. Angle integrated ross se tions for the in lusive 0photoprodu tion pro ess d ! 0X in the measured energyrange E 306 MeV. Solid ir les show the measurements ofthis work. They are ompared to data from Bergstrom et al.[7 (solid squares, bottom) and to previous TAPS results [1(open squares, top). The data are also ompared to theoreti al al ulations of Arenhovel [10 (dotted), Laget [11 without FSI,i.e. purely quasi-free (dashed, identi al to the dashed urve ing. 7) and to MC simulations of the pure quasi-free pro essusing SAID amplitudes with renormalization (dot-dashed).

TAPS 92

Eγ [MeV]σ

[µb

]

quasi-freequasi-free, fit σn

0

100

200

300

400

500

200 300 400 500

MAID, σn

Fit, σn

Eγ [MeV]

σ

[µb

]

0

50

100

150

200

250

300

200 300 400 500Fig. 10. Top: Angle integrated ross se tions for the in lusive0 photoprodu tion pro ess d ! 0X in the energy rangeE < 600 MeV. The data (solid ir les) are from the previousTAPS experiment [1. They are ompared to the MC simula-tions of the pure quasi-free pro ess. The dashed urve showsthe result when the MAID [18 ross se tions for both p! 0pand n ! 0n (bottom, dotted) are used. The solid urve isthe result, when the n! 0n ross se tions in the MC simu-lations are redu ed as shown in the bottom gure by the solid urve.Bottom: Comparison between the n! 0n ross se tion fromMAID (dotted) and that needed for a reasonable des riptionof the data (solid line).