Study of coherentπ 0 photoproduction on the deuteron

Transcription

1 J. At. Mol. Sci. oi:.428/jams.8.22a Vol. 2, o. 3, pp August 2 Stuy of coherent photoprouction on the euteron E. M. Darwish a,b,,. Akopov c, an M. A. El-Zohry a Applie Physics Department, Faculty of Applie Science, Taibah University, P. O. Box 343, Al-Mainah Al-Munawarah, Saui Arabia b Physics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt c Yerevan Physics Institute, Br. Alikhanian 2, 36 Yerevan, Armenia Yerevan State University, A. Manoogian, 25 Yerevan, Armenia Receive 8 January 2; Accepte (in revise version) 2 Feburary 2 Publishe Online 28 March 2 Abstract. We consier the coherent photoprouction reaction on the euteron,, in the energy region from-threshol up to GeV using an enhance elementary pion photoprouction amplitue on the free nucleon an a realistic high-precision potential moel for the euteron wave function. umerical results for total an ifferential cross sections are presente for which the sensitivity to various moels for the elementary pion photoprouction operator is investigate. Consierable epenence of the results on the elementary amplitue is foun at photon lab-energies close to -threshol an above 6 MeV. In aition, the results for ifferential an total cross sections are compare with the available experimental ata an a satisfactory agreement was foun. PACS: 3.6.Le, 25.2.Lj, 4.2.Gk Key wors: Meson prouction, photoprouction reactions, Baryon resonances Introuction The stuy of pion prouction processes on the euteron are of funamental interest in nuclear physics. The photoprouction of mesons is an excellent tool for the stuy of nucleon resonances[] an in consequence of the structure of the nucleon. In this context, meson prouction on the euteron is of specific importance ue to the lack of free neutron targets. With respect to pion prouction, both possible reactions, the coherent an the incoherent one, are worth to be stuie. Coherent pion photoprouction on the euteron may be use as an isospin filter an is especially sensitive to the coherent sum of thep p ann n amplitue. On the other han, incoherent pion photoprouction on the euteron may be use Corresponing author. aress: ÖÛ ÝÓÓºÓÑ (E. M. Darwish) 87 c 2 Global-Science Press

2 88 E. M. Darwish,. Akopov, an M. A. El-Zohry/J. At. Mol. Sci. 2 (2) to obtain information about neutron cross section in quasi-free kinematics. Due to its relative simplicity, the euteron is the ieal target for such stuies. Most recently, an improve calculation of the incoherent pion photoprouction on the euteron has been performe in Ref.[2] in which final-state interactions (FSI) are inclue completely in the - an -subsystems an an enhance elementary pion photoprouction operator taken from Ref.[3] has been use. The influence of the elementary operator on cross sections an spin observables for both the neutral an the charge pion prouction channels has been investigate an was foun to be very important. In many cases the eviation among results obtaine using ifferent operators is very large. For a long time, coherent -photoprouction on the euteron has been stuie as a source of information on the elementary -photoprouction off the neutron. This reaction has been first stuie by Koch an Woloshyn[4] by incluing the contribution from pion rescattering with charge exchange contributions. This effect was then verifie by Boste an Laget[5] in stuies of coherent -photoprouction from the euteron in the threshol region. In Ref.[6] an approach of couple channels for escribing coherent -photoprouction from the euteron in the (232)-resonance region was use. In another approach, evelope in Ref.[7], relativistic Feynman iagrams have been evaluate. Blaazer et al.[8] stuie rescattering corrections to all orers by solving Faeev equations of the -system. They have conclue that the contributions of the neutron an the proton cannot be separate because of the charge-exchange rescattering of the pion. Using a microscopic approach base on the Kerman-McManus-Thaler (KMT) multiple scattering theory[9] in momentum space, Kamalov et al.[] have stuie coherent -photoprouction from the euteron in the (232)-resonance region in a couple channel approach. The coherent -photoprouction from the euteron was stuie by Kuryavtsev et al. []. In particular, it was emonstrate that at large c.m. angles an photon lab-energies between 6 an 8 MeV, the two-step process with the excitation of an intermeiate η-meson ominates over single-step process photoprouction an pion rescattering. The main conclusion of Ref.[] were reprouce in another paper[2], where it was shown that in aition to this two-step process, the full ynamics in the intermeiate η system coul be important as well. Unfortunately, none of these theoretical stuies consiers the energy region above the (232)-resonance region an/or investigates the sensitivity to the elementary pion photoprouction operator on the free nucleon. Therefore, the coherent -photoprouction reaction on the euteron has been investigate in the (232)-resonance region Ref.[3] with special emphasize on the oubly polarize cross sections. The sensitivity of the results to the elementary pion photoprouction amplitue was investigate, an consierable epenence has been foun. Our purpose in the present paper is, therefore, to exten the moel, recently presente in [3], to make theoretical preictions for unpolarize total an ifferential cross sections of the process in the energy range from-threshol up to GeV. For the elementary amplitue, an enhance elementary pion photoprouction operator taken from Ref.[3] is use. This moel isplays chiral symmetry, gauge invariance, an crossing symmetry, as well as a consistent treatment of the interaction with spin-3/2 particles. It also provies a reliable

3 E. M. Darwish,. Akopov, an M. A. El-Zohry/J. At. Mol. Sci. 2 (2) escription of the threshol region. For the euteron wave function, we use the realistic high-precision CD-Bonn potential moel[4]. The calculation of this work is of theoretical interest because it provies an important test of our unerstaning of the elementary neutron amplitue in the absence of a neutron target. This paper is organize as follows. In Section 2, a brief review of the formalism for the reaction, in which the transition matrix elements are calculate, is given. Results for unpolarize total an ifferential cross sections are presente an iscusse in Section 3, focusing on the sensitivity of results to the elementary pion photoprouction operator. Finally, we provie conclusions in Section 4. Throughout the paper we use natural units h=c=. 2 Formalism As a starting point, we will first consier the formalism for coherent -photoprouction on the euteron which contains only two particles in the initial an in the final states. The general form of the two-boy reaction is a(p a )+ b(p b ) c(p c )+(p ), () where p i =(E i, p i ) enotes the four-momentum of particle i with i {a,b,c,}. Following the conventions of Bjorken an Drell[5], the general form for the ifferential cross section of a two-particle reaction in the center-of-mass (c.m.) system is given by σ = Ω c p c E a E b E c E (2W) 2 p a F a F b F c F s µ µ c µ b µ a Tµ µ c µ b µ a ( p, p c, p b, p a ) 2 (2) with T µ µ c µ b µ a as reaction matrix,µ i enoting the spin projection of particle i on some quantization axis, an F i is a factor arising from the covariant normalization of the states an its form epens on whether the particle is a boson (F i =2E i ) or a fermion (F i = E i /m i ), where E i an m i are its energy an mass, respectively. The factor s=(2s a +)(2s b +) takes into account the averaging over the initial spin states, where s a an s b enote the spins of the incoming particles a an b, respectively. All momenta are functions of the invariant mass of the two-boy system W, i.e. p i = p i (W), where W= E a +E b = E c +E. Focusing on coherent -photoprouction from the euteron an choosing the photoneuteron c.m. frame with the z-axis along the photon momentum k, the y-axis parallel to k q an the x-axis such as to form a right-hane system. Thus the outgoing pion is escribe by the spherical anglesφ anθ with cosθ =ˆq ˆk. The reaction () then becomes (E, k,λ)+(e, k) (E, q)+(e, q), (3) where energy an momenta of the participating particles are given in the parentheses, anλ stans for the circular photon polarization. Diagrammatic representation of this reaction is shown in Fig.. The F i factor is given by F a =2E, F b =2E, F c =2E, F =2E, (4)

4 9 E. M. Darwish,. Akopov, an M. A. El-Zohry/J. At. Mol. Sci. 2 (2) k q p k t p q = k p = q ÙÖ ½ ÖÑÑØ ÖÔÖ ÒØØÓÒ Ó Ø ÖØÓÒ Ò Ø ÑÔÙÐ ÔÔÖÓÜÑØÓÒ ÛØ ÒØÓÒ Ó ÑÓÑÒØ Ò Ø ºÑº Ý ØѺ an therefore one fins s=6 taking into account the averaging of the cross section over the initial two possible polarizations of the real photon an the three spin projections of the euteron. Using stanar normalization of particle states, the unpolarize ifferential cross section of the reaction in the c.m. system is then given by σ Ω = E E q (4W ) 2 k 6 T m m λ ( k, q) 2, (5) m m λ where m (m ) is the spin projection of the outgoing (incoming) euteron an q an k are the c.m. momenta of the pion an photon, respectively. Moreover, the invariant energy of the system is given as W =E + k 2 +M 2, E = k, =E + q 2 +M 2, E = q 2 +m 2, (6) where M an m are the euteron an neutral-pion masses, respectively. The scattering amplitue of coherent -photoprouction on the euteron is given in the impulse approximation by T m m λ ( 3 p k, q)=2 (2) 3φ ( p )t λ m ( k, p i, q, p f )φ m ( p) (7) with t λ staning for the corresponing elementary amplitue. Furthermore, the vectors p i an p f enote initial an final momenta of the active nucleon in the euteron, for which we have p i = p k/2 an p f = p q+ k/2, an p = p+( k q)/2 enotes the relative momentum in the final euteron state. The time-orere iagrams taken into account in the

5 E. M. Darwish,. Akopov, an M. A. El-Zohry/J. At. Mol. Sci. 2 (2) present work for the scattering amplitue of coherent -photoprouction on the euteron are epicte in Fig. 2. As the neutral pion has neither charge nor spin, the photon cannot couple to its charge an magnetic moment. So, the mechanisms emboie in iagrams (c), (), an (e) in Fig. 2 an the corresponing ones in Fig. 3 for charge pions o contribute to neutral-pion prouction, but only in the intermeiate state, where first a charge particle is prouce, that turns into a neutral one upon rescattering. Introucing a partial wave ecomposition, one fins for the scattering matrix the relation T m m λ ( k, q)=e i(m +λ)φ t m m λ (W,θ ), (8) where the reuce t-matrix elements are the basic quantities that etermine cross sections an polarization observables. If parity is conserve, the reuce t-matrix obeys the symmetry relation t m m λ =( ) +m +m +λ t m m λ. (9) For the euteron wave function we use the familiar ansatz φ m ( p)= (Lm L m S m )u L (p)y LmL ( ˆp)χ ms ζ, () m L m S L=,2 t = (a) (c) (b) () + ρ,ω (e) Ν * + + (f) Ν * (g) ÙÖ ¾ Ì ÓÒ Ö ÖÑ Ò ÓÖÒØ ÔÓÒ ÔÓØÓÔÖÓÙØÓÒ ÓÒ Ø ÙØÖÓÒº ÓÖÒ ØÖÑ µ ÖØ ÒÙÐÓÒ ÔÓÐ µ ÖÓ ÒÙÐÓÒ ÔÓÐ µ ÔÓÒ ÔÓÐ Ò µ ÃÖÓÐйÊÙÖÑÒÒ ÓÒØØ ØÖÑ µ ÚØÓÖ¹Ñ ÓÒ ÜÒ ρ Òωµ Ö ÓÒÒ ÜØØÓÒ ÓÒØÖÙØÓÒ µ ÖØ Ò µ ÖÓ º

6 92 E. M. Darwish,. Akopov, an M. A. El-Zohry/J. At. Mol. Sci. 2 (2) T = (A) (B) (C) ρ,ω (D) (E) * (F) * (G) ÙÖ ÝÒÑÒ ÖÑ ÓÖ ÔÓÒ ÔÓØÓÔÖÓÙØÓÒ ÖÓÑ ÒÐ ÒÙÐÓÒº ÓÖÒ ØÖÑ µ ÖØ ÒÙÐÓÒ ÔÓÐ µ ÖÓ ÒÙÐÓÒ ÔÓÐ µ ÔÓÒ Ò Ø Ò µ ÃÖÓÐйÊÙÖÑÒÒ ÓÒØØ ØÖÑ µ ÚØÓÖ¹Ñ ÓÒ ÜÒ ρ Òωµ Ö ÓÒÒ ÜØØÓÒ ÓÒØÖÙØÓÒ µ ÖØ Ò µ ÖÓ º where the last two terms enote spin an isospin wave functions, respectively. In the present work, the raial euteron wave functions of the initial an final euteron state are chosen to be ientical for consistency, i.e., both from the realistic high-precision CD-Bonn potential moel[4]. For the elementary pion photoprouction operator on the free nucleon,, we use in this work the effective Lagrangian approach (ELA) elaborate in Ref.[3], which has been applie successfully from threshol up to GeV of photon energy in the laboratory reference system an succees to reconcile[6] pion photoprouction experiments in the (232) region[7,8] with the latest Lattice QCD calculations of the quarupole eformation of the (232)[9]. Recently, the moel has also been applie successfully to eta photoprouction from the proton[2]. This moel is base upon an effective Lagrangian approach which from a theoretical point of view is a very appealing, reliable, an formally well-establishe approach in the energy region of the mass of the nucleon. It isplays chiral symmetry, gauge invariance, an crossing symmetry as well as a consistent treatment of the spin-3/2 interaction. The moel inclues Born terms (iagrams (A)-(D) in Fig. 3), vector-meson exchanges (ρ an ω, iagram (E) in Fig. 3), an all the four star resonances in Particle Data Group (PDG)[7] up to.7 GeV an up to spin-3/2: (232), (44), (52), (62), (65), an (7) (iagrams (F) an (G) in Fig. 3). Born terms are calculate using the Lagrangian Born = ief V Âα ε jk3 j ( α k ) eâ α F V α ief V F S/V +τ 3 2 f  α α 5 m 2 [τ j,τ 3 ] j ie F V 4M 2 2 F S/V 2 +τ 3 αβ F αβ + f m α 5 τ j α j, () where e is the absolute value of the electron charge, m the mass of the pion, M the mass of the nucleon, f the pion nucleon coupling constant, F V j = F p j F n j an F S j = F p j +F n j are the

7 E. M. Darwish,. Akopov, an M. A. El-Zohry/J. At. Mol. Sci. 2 (2) isovector an isoscalar nucleon form factors, F µν = µ Â ν ν Â µ is the electromagnetic fiel (Â µ stans for the photon fiel), the nucleon fiel, an j the pion fiel. The coupling to the pion has been chosen pseuovector in orer to ensure the correct parity an low energy behavior. The main contribution of mesons to pion photoprouction is given by ρ (isospin- spin-) an ω (isospin- spin-) exchange. The phenomenological Lagrangians which escribe vector mesons are: α i K ω αβ β 2M ω = F ω K ρ ρ = F ρ α i αβ β 2M ω α + eg ω 2m ε µναβ F αβ µ j δj3 ω ν, τ j ρ α j + eg ρ 2m ε µναβ F αβ µ j ρ ν j. (2) As alreay mentione above, these terms are absent in the case of irect neutral-pion prouction. The moel isplays chiral symmetry, gauge invariance, an crossing symmetry as well as a consistent treatment of the spin-3/2 interaction which overcomes pathologies present in former analysis[2]. Uner this approach for spin-3/2 interactions the (spin-3/2 resonance)- nucleon-pion an the (spin 3/2 resonance)-nucleon-photon vertices have to fulfill the conition q α α... = where q is the four-momentum of the spin-3/2 particle,α the vertex inex which couples to the spin-3/2 fiel, an the ots stan for other possible inices. In particular, for the (232), the simplest interacting-- (232) Lagrangian is[2] = h ε µνλβ β 5 µ ν j λ j +H.c., (3) f M where H.c. stans for hermitian conjugate, h is the strong coupling constant, f =92.3 MeV is the leptonic ecay constant of the pion, M the mass of the (232), an ν j the (232) fiel. The-- (232) interaction can be written[22] = 3e ig 2M M + 2 F µν + g 2 5 F µν µ ν 3 +H.c., (4) where g an g 2 are the electromagnetic coupling constants, M + = M +M, an F µν = ε µναβ F αβ. The ressing of the resonances is consiere by means of a phenomenological with which contributes to both s an u channels an takes into account ecays into one, oneη, an two. The energy epenence of the with is chosen phenomenologically as Γ(s,u)= Γ j X j (s,u), (5) j=,,η where s an u are the Manelstam variables an X j (s,u) X j (s)+x j (u) X j (s)x j (u), (6)

8 94 E. M. Darwish,. Akopov, an M. A. El-Zohry/J. At. Mol. Sci. 2 (2) with X j (l) given by X j (l)=2 + 2L+ kj k j kj k j 2L+3 Θ l 2 M +m j, (7) where L is the angular momentum of the resonance, Θ is the Heavisie step function, an 2 4m k j = l M 2 m2 2 j j M2 2 l, (8) with m 2m an k j = k j when l= M 2 (M stans for the mass of the resonance). This parameterization has been built in orer to fulfill the following conitions (i) Γ=Γ at s= M ; (ii) Γ when k j ; (iii) a correct angular momentum barrier at threshol k j 2L+ ; (iv) crossing symmetry. For the resonance-pion-nucleon vertex, the form factor X (s,u) has to be use for consistency with the with employe. In orer to regularize the high energy behavior of the moel a crossing symmetric an gauge invariant form factor is inclue for Born an vector meson exchange terms, ˆF B (s,u,t)= F(s)+F(u)+G(t) F(s)F(u) F(s)G(t) F(u)G(t)+F(s)F(u)G(t), (9) where F(l)= + 2/Λ l M 2 4, l=s,u, (2) G(t)= + 2/Λ t m 2 4. (2) For vector mesons ˆF V (t)=g(t) is aopte with the change m m V. The cut-off Λ=.5 GeV in the case of resse pion prouction amplitues, whereas Λ=.95 GeV in the case of bare ones. In the pion photoprouction moel from free nucleons[3] it was assume that FSI factorize an can be inclue through the istortion of the final state wave function (pionnucleon rescattering). -FSI was inclue by aing a phaseδ FSI to the electromagnetic multipoles. This phase is set so that the total phase of the multipole matches the total phase of the energy epenent solution of SAID[23]. In this way it was possible to isolate the contribution of the bare iagrams to the physical observables. The parameters of the resonances

9 E. M. Darwish,. Akopov, an M. A. El-Zohry/J. At. Mol. Sci. 2 (2) were extracte fitting the ata to the electromagnetic multipoles from the energy inepenent solution of SAID[23] applying moern optimization techniques base upon a genetic algorithm combine with graient base routines[24] which provies reliable values for the parameters of the nucleon resonances. Once the parameters, incluing phase shifts, are fitte to ata we can istinguish between bare an resse photo-pion prouction amplitues on the nucleon. In what follows we call bare amplitues to the ones provie by our moel using the fitte values for all the parameters except those of the phase shifts which are set to zero. In orer to examine the various observables for pion photoprouction on the free nucleon we provie in Fig. 4 results for the polarize nucleon-target asymmetry T as a function of pion angle at photon lab-energy of E =3 MeV. Results for the various pion photoprouction channels from the free nucleon are given using the ELA moel[3]. We see that the agreement of the results using the ELA moel (soli curves) in comparison with the ata from SAID[23] is goo an give a clear inication that the ELA moel[3] can be applie irectly to calculate the electromagnetic photoprouction of pions from the euteron T. T p n T. T p n θ (egrees) θ (egrees) ÙÖ ÈÓÐÖÞ ÒÙÐÓÒ¹ØÖØ ÝÑÑØÖÝ T ÙÒØÓÒ Ó ÔÓÒ ÒÐ ÓÖ Ø ÓÙÖ ÖÒØ ÒÒÐ Ó ÔÓÒ ÔÓØÓÔÖÓÙØÓÒ ÖÓÑ Ö ÒÙÐÓÒ ÐÙÐØ Ø E = 3 Åκ ËÓÐ ÙÖÚ ØÒ ÓÖ Ø ÐÙÐØÓÒ Ù Ò Ø ØÚ ÄÖÒÒ ÔÔÖÓ Äµ º Ø Ö ØÒ ÖÓÑ ËÁ ¾ º

10 96 E. M. Darwish,. Akopov, an M. A. El-Zohry/J. At. Mol. Sci. 2 (2) Results an iscussion In this section we explore the epenence of the results for the observables in the reaction on the input elementary pion photoprouction operator. We show results for the unpolarize total an ifferential cross sections in the energy region from -threshol up to GeV in comparison with the available experimental ata, using as elementary reaction amplitues the ones provie by the ELA moel from Ref.[3] an those obtaine using MAID moel[25]. For the euteron wave function, we use for both the initial an final euteron states the realistic high-precision CD-Bonn potential moel[4]. We woul like to explain carefully what we call IA an how we compute it. Our IA calculation oes not employ irectly the amplitues that fit the ata on electromagnetic multipoles for the process. This is ue to the fact that-rescattering is unavoiably inclue in the amplitue in these fits to ata. We call IA to the bare contribution to the observables. Therefore, if we wish to calculate the contribution coming from the pure IA, the bare IA contribution to the amplitue has to be extracte from the analysis of the, where the final state interaction has to be remove. This was one in Ref.[3]. We name IA to the calculations where the -rescattering is inclue in the elementary pion photoprouction reaction on the free nucleon. σ (µb) E (MeV) ÙÖ ÌÓØÐ ÖÓ ØÓÒ ÓÖ ÓÖÒØ ÔÓÒ ÔÓØÓÔÖÓÙØÓÒ ÓÒ Ø ÙØÖÓÒ ÙÒØÓÒ Ó ÔÓØÓÒ Ð¹ÒÖݺ Ì ÓÐ ÙÖÚ ÓÛ Ø Ö ÙÐØ Ó Á Ù Ò Ø ÅÁ ÑÓÐ ¾ º Ì ÓØص ÙÖÚ ÓÛ Ø Ö ÙÐØ Ó Á Áµ Ù Ò Ø Ö Öµ ÐØÖÓÑÒØ ÑÙÐØÔÓÐ Ó Ä ÑÓÐ º

11 E. M. Darwish,. Akopov, an M. A. El-Zohry/J. At. Mol. Sci. 2 (2) σ/ω (µb/sr) θ (egree) ÙÖ ÖÒØÐ ÖÓ ØÓÒ ÓÖ ÓÖÒØ ¹ÔÓØÓÔÖÓÙØÓÒ ÓÒ Ø ÙØÖÓÒ ÙÒØÓÒ Ó ÔÓÒ ÒÐ Ò Ø ºÑº ÖÑ Ø ÒÒ ÖÒØ ÚÐÙ Ó ÔÓØÓÒ ÒÖÝ Ò Ø Ðº ÖѺ Ì ÑÒÒ Ó ÙÖÚ ÜÔÐÒ Ò Ø ÔØÓÒ Ó º º The first comparison (Fig. 5) shows the sensitivity of the results for total cross section on the elementary pion photoprouction operator using the CD-Bonn potential[4] for the euteron wave function in the energy region from-threshol up to GeV. The soli curve shows the results of IA using the MAID moel[25], whereas the ashe (otte) curve shows the results of IA (IA) using the resse (bare) electromagnetic multipoles of ELA moel [3]. As alreay mentione, IA enotes the euteron calculation when the-rescattering is inclue in the elementary reaction. We fin that the total cross section presents qualitative a similar behavior for ifferent elementary operators. One sees that the total cross section has a peak at photon lab-energy of about 35 MeV ue to the ominant excitation of the M + multipole on the free nucleon. The maximum of this peak is greater in IA than in IA an therefore careful must be taken when one uses elementary reactions in nuclear applications. It is also clear that the computations with ifferent elementary amplitues are quite ifferent. For example, at the peak position we obtain larger values using MAID an ELA with-fsi than using ELA without-fsi. Similarly, a bump-like structure is observe at photon lab-energy of about 75 MeV using

12 98 E. M. Darwish,. Akopov, an M. A. El-Zohry/J. At. Mol. Sci. 2 (2) the MAID moel, whereas it is observe at higher energies when one uses the ELA moel. These iscrepancies show up the ifferences among elementary operators which are obvious at photon lab-energies above 5 MeV. This means that the total cross section is sensitive to the choice of the elementary amplitue, especially at high photon lab-energies. The ifference between the ashe (resse ELA) an otte (bare ELA) curves shows the effect ofrescattering in the elementary amplitue, which is also foun to be important. Fig. 6 shows our results for ifferential cross section as a function of pion angle in the c.m. frame at various values of photon lab-energy. We show the sensitivity of the results for ifferential cross section on the elementary pion photoprouction operator using the CD-Bonn potential[4] for the euteron wave function. We fin that the ifferential cross section presents qualitative similar behavior for ifferent elementary operators. It is clear that the computations with ifferent elementary amplitues are quite ifferent, in particular at forwar pion angles an at high photon energies. At backwar angles, one sees that the ifferential cross section is small in comparison to the results at forwar angles. It is seen that the ifferential cross section vanishes at energies above 5 MeV at backwar angles. As in the case of total cross section, obvious ifferences are shown when one uses the MAID moel[25] (soli curve) an ELA moel[3] (otte an ashe curves). These iscrepancies show up the ifferences among elementary operators which are very clear at forwar pion angles for σ (µb) E (MeV) ÙÖ ÌÓØÐ ÖÓ ØÓÒ ÓÖ ÓÖÒØ ¹ÔÓØÓÔÖÓÙØÓÒ ÓÒ Ø ÙØÖÓÒ Ù Ò Ø ÐÓÖØÑ Ð ÙÒØÓÒ Ó ÔÓØÓÒ Ð¹ÒÖÝ Ò ÓÑÔÖ ÓÒ ÛØ ÜÔÖÑÒØРغ Ì ÑÒÒ Ó ÙÖÚ ÜÔÐÒ Ò Ø ÔØÓÒ Ó º º Ì Ø ÔÓÒØ Ö ØÒ ÖÓÑ ÌÈË ¾ º

13 E. M. Darwish,. Akopov, an M. A. El-Zohry/J. At. Mol. Sci. 2 (2) photon lab-energies above 5 MeV. ow, we compare our preictions for unpolarize total an ifferential cross sections of the reaction with the available experimental ata. Fig. 7 shows the results for the total cross section as a function of photon energy in the laboratory frame in comparison with the experimental ata from TAPS[26]. We compare results using as elementary reaction amplitues, the ones provie by the ELA moel of Ref.[3] an those obtaine using MAID moel[25]. For the euteron wave function we use the realistic high-precision CD-Bonn potential moel[4]. The soli curve in Fig. 7 shows the results using the MAID moel [25], the ashe (otte) curve shows the results using the resse (bare) electromagnetic multipoles of the ELA moel[3]. One reaily observe, that the otte curve which represents the results using the bare electromagnetic multipoles of the ELA moel[3] is the nearest one to the experimental ata, especially after the peak position. However, the agreement between the results using the MAID moel[25] an the experimental ata from TAPS[26] is quantitatively not goo. One also sees, that none of the moels is able to escribe the right position of the peak, as well as the behavior of the ata points after the peak. In principle, one can speculate that our results using the bare electromagnetic multipoles of the ELA moel[3] agrees with the slope at high photon lab-energy, but the results using the MAID moel are not. This means in particular that the results are strongly epenent on the pion prouction on the free nucleon an, therefore, one must look more in eep for the reasons in the ifferent results. As next, we compare our results for the unpolarize ifferential cross section of the reaction as a function of the emission pion angle at four various values of photon labenergy with the experimental ata from TAPS[27] as shown in Fig. 8. As in the case of total cross section, we compare results using as elementary reaction amplitue, the ones provie by the ELA moel of Ref.[3] an those obtaine using MAID moel[25]. For the euteron wave function we also use the realistic high-precision CD-Bonn potential moel[4]. At energies less than the (232)-resonance region, one notes that the agreement between our results using ifferent elementary operator is not satisfactory. The reason for this may be ue to the neglecting-rescattering in the intermeiate state which is foun to be important[2]. On the contrary, we obtaine a qualitatively reasonable agreement between our results an the experimental ata from TAPS[27] at energies aroun the -region. At forwar pion angles an high energy, an overestimation of our results using various elementary amplitues is foun. The soli curve which represents the results using the MAID moel[25] is the nearest one to the experimental ata even at forwar pion angle an small energy. Discrepancies between the results using ifferent elementary amplitues are foun at extreme forwar pion angles, whereas at backwar pion angles iscrepancies are observe at small energies. An experimental check of these preictions at extreme forwar pion angles is neee. From the preceing iscussion it is apparent that the choice of the elementary operator has a visible effect on cross sections. Summarizing, we can say that the MAID moel[25] provies ifferent preictions for cross sections than the ELA moel[3] an that these cross sections provie excellent observables to test ifferent pion prouction operators.

14 E. M. Darwish,. Akopov, an M. A. El-Zohry/J. At. Mol. Sci. 2 (2) σ/ω (µb/sr) θ (egree) ÙÖ ÖÒØÐ ÖÓ ØÓÒ ÓÖ ÓÖÒØ ¹ÔÓØÓÔÖÓÙØÓÒ ÓÒ Ø ÙØÖÓÒ Ù Ò Ø ÐÓÖØÑ Ð ÙÒØÓÒ Ó ÔÓÒ ÒÐ Ò Ø ÒØÖ¹Ó¹Ñ ÖÑ Ø ÓÙÖ ÖÒØ ÚÐÙ Ó ÔÓØÓÒ Ð¹ÒÖݺ Ì ÑÒÒ Ó ÙÖÚ ÜÔÐÒ Ò Ø ÔØÓÒ Ó º º Ì Ø ÔÓÒØ Ö ØÒ ÖÓÑ ÌÈË ¾ º 4 Conclusions The main topic of this paper was the investigation of the coherent -photoprouction reaction on the euteron. Results for total an ifferential cross sections are presente, in the energy region from -threshol up to photon lab-energy of GeV, an compare with the available experimental ata. For the elementary pion photoprouction operator, a realistic effective Lagrangian approach has been use which isplays chiral symmetry, gauge invariance, an crossing symmetry, as well as a consistent treatment of the spin-3/2 interaction. For the euteron wave function, the realistic high-precision CD-Bonn potential moel[4] was use. The sensitivity of the results to the elementary pion photoprouction operator on the free nucleon has also been investigate. Within our moel, we have foun that the total an ifferential cross sections are sensitive to the choice of the elementary operator. In many cases, the eviation among results obtaine using ifferent elementary operators is very large. In view of these results, we conclue that the process (, ) can serve as a filter for ifferent elementary operators since their

15 E. M. Darwish,. Akopov, an M. A. El-Zohry/J. At. Mol. Sci. 2 (2) preictions provie very ifferent values for observables. Finally, we woul like to point out that future improvements of the present moel can be achieve by incluing pion rescattering an two-boy effects. In aition, polarization observables constitute more stringent tests for theoretical moels ue to their sensitivity to small amplitues. At this point, measurements on the euteron spin asymmetries will certainly provie us with an important observable to test our knowlege of the pion photoprouction on the free neutron process. Acknowlegments. The work of E.M. Darwish was supporte by the Deanship of Scientific Research of the Taibah University, Saui Arabia uner project o. 43/43. The work of. Akopov was supporte by the ISTC grant uner project A-66. M. El-Zohry woul like to thank Prof. V. Tsakanov for many useful iscussion an support. References [] B. Krusche an S. Schaman, Prog. Part. ucl. Phys. 5, (23) 399. [2] E. M. Darwish, C. Fernánez-Ramírez, E. Moya e Guerra, an J. M. Uías, Phys. Rev. C 76 (27) 445; E. M. Darwish, C. Fernánez-Ramírez, E. Moya e Guerra, an J. M. Uías, AIP Conf. Proc. 6 (28) 65. [3] C. Fernánez-Ramírez, E. Moya e Guerra, an J.M. Uías, Ann. Phys. (.Y.) 32 (26) 48; C. Fernánez-Ramírez, Ph. D. Dissertation(Universia Complutense e Mari, Spain, 26); C. Fernánez-Ramírez, E. Moya e Guerra, an J. M. Uías, Phys. Lett. B 66 (28) 88. [4] J. H. Koch an R. M. Woloshyn, Phys. Rev. C 6 (977) 968. [5] P. Boste an J. M. Laget, ucl. Phys. A 296 (978) 43; J.M. Laget, Phys. Rep. 69 (98). [6] P. Wilhelm an H. Arenhövel, Few-Boy Syst. Suppl. 7 (994) 235; P. Wilhelm an H. Arenhövel, ucl. Phys. A 593 (995) 435. [7] H. Garcilazo an E. M. e Guerra, Phys. Rev. C 52 (995) 49. [8] F. Blaazer, B. L. G. Bakker, an H. J. Boersma, ucl. Phys. A 59 (995) 75; F. Blaazer, Ph. D. Dissertation (Free University of Amsteram, Amsteram, 995). [9] A. K. Kerman, H. McManus, an R. M. Thaler, Ann. Phys. (.Y.) 8 (959) 55. [] S. S. Kamalov, L. Tiator, an C. Bennhol, ucl. Phys. A 547 (992) 559; S. S. Kamalov, L. Tiator, an C. Bennhol, Few-Boy Syst. (99) 43; S. S. Kamalov, L. Tiator, an C. Bennhol, Phys. Rev. C 55 (997) 98. [] A. E. Kuryavtsev, V. E. Tarasov, I. I. Strakovsky, et al., Phys. Rev. C 7 (25) [2] A. Fix, Eur. Phys. J. A 26 (25) 293. [3] E. M. Darwish an M. Y. Hussein, Proceeings of the 4th Annual Meeting of the Saui Physical Society (King Abulaziz City for Science an Technology, Riyah, 28); Appl. Math. & Inf. Sci. 3 (29) 32. [4] R. Machleit, F. Sammarruca, an Y. Song, Phys. Rev. C 53 (996) R483; R. Machleit, Phys. Rev. C 63 (2) 24. [5] J. D. Bjorken an S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, ew York, 964). [6] C. Fernánez-Ramírez, E. Moya e Guerra, an J. M. Uías, Phys. Rev. C 73 (26) 422(R); C. Fernánez-Ramírez, E. Moya e Guerra, an J. M. Uías, Eur. Phys. J. A 3 (27) 572. [7] Review of Particle Physics, W. M. Yao, et al., J. Phys. G 33 (26). [8] G. Blanpie et al., Phys. Rev. C 64 (2) 2523; J. Ahrens et al., Eur. Phys. J. A bf 2 (24) 323; S. Stave et al., Eur. Phys. J. A 3, (26), 47.

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