Incoherent pion photoproduction on 12 C
C.M. Tarbert, D.P. Watts, P. Aguar, J. Ahrens, J.R.M. Annand, H.J. Arends, R. Beck, V. Bekrenev, B. Boillat, A. Braghieri, D. Branford, W.J. Briscoe, J. Brudvik, S. Cherepnya, R. Codling, E.J. Downie, K. Foehl, D.I. Glazier, P. Grabmayr, R. Gregor, E. Heid, D. Hornidge, O. Jahn, V.L. Kashevarov, A. Knezevic, R. Kondratiev, M. Korolija, M. Kotulla, D. Krambrich, B. Krusche, M. Lang, V. Lisin, K. Livingston, S. Lugert, I.J.D. MacGregor, D.M. Manley, M. Martinez, J.C. McGeorge, D. Mekterovic, V. Metag, B.M.K. Nefkens, A. Nikolaev, R. Novotny, R.O. Owens, P. Pedroni, A. Polonski, S.N. Prakhov, J.W. Price, G. Rosner, M. Rost, T. Rostomyan, S. Schadmand, S. Schumann, D. Sober, A. Starostin, I. Supek, A. Thomas, M. Unverzagt, Th. Walcher, F. Zehr
aa r X i v : . [ nu c l - e x ] N ov APS/123-QED
Incoherent neutral pion photoproduction on C C.M. Tarbert, D.P. Watts, ∗ P. Aguar, J. Ahrens, J.R.M. Annand, H.J. Arends, R. Beck,
2, 4
V. Bekrenev, B. Boillat, A. Braghieri, D. Branford, W.J. Briscoe, J. Brudvik, S. Cherepnya, R. Codling, E.J. Downie, K. Foehl, D.I. Glazier, P. Grabmayr, R. Gregor, E. Heid, D. Hornidge, O. Jahn, V.L. Kashevarov, A. Knezevic, R. Kondratiev, M. Korolija, M. Kotulla, D. Krambrich,
2, 4
B. Krusche, M. Lang,
2, 4
V. Lisin, K. Livingston, S. Lugert, I.J.D. MacGregor, D.M. Manley, M. Martinez, J.C. McGeorge, D. Mekterovic, V. Metag, B.M.K. Nefkens, A. Nikolaev,
2, 4
R. Novotny, R.O. Owens, P. Pedroni, A. Polonski, S.N. Prakhov, J.W. Price, G. Rosner, M. Rost, T. Rostomyan, S. Schadmand, S. Schumann,
2, 4
D. Sober, A. Starostin, I. Supek, A. Thomas, M. Unverzagt, Th. Walcher, and F. Zehr (The Crystal Ball at MAMI and A2 Collaboration) School of Physics, University of Edinburgh, Edinburgh, UK Institut f¨ur Kernphysik, University of Mainz, Germany Department of Physics and Astronomy, University of Glasgow, Glasgow, UK Helmholtz-Institut f¨ur Strahlen- und Kernphysik, University Bonn, Germany Petersburg Nuclear Physics Institute, Gatchina, Russia Institut f¨ur Physik, University of Basel, Basel, Ch INFN Sezione di Pavia, Pavia, Italy Center for Nuclear Studies, The George Washington University, Washington, DC, USA University of California at Los Angeles, Los Angeles, CA, USA Lebedev Physical Institute, Moscow, Russia Physikalisches Institut Universit¨at T¨ubingen, T¨ubingen, Germany II. Physikalisches Institut, University of Giessen, Germany Mount Allison University, Sackville, NB, Canada Rudjer Boskovic Institute, Zagreb, Croatia Institute for Nuclear Research, Moscow, Russia Kent State University, Kent, OH, USA The Catholic University of America, Washington, DC, USA (Dated: November 25, 2018)We present the first detailed measurement of incoherent photoproduction of neutral pions to adiscrete state of a residual nucleus. The C( γ, π ) C ∗ . MeV reaction has been studied with theGlasgow photon tagger at MAMI employing a new technique which uses the large solid angle Crys-tal Ball detector both as a π spectrometer and to detect decay photons from the excited residualnucleus. The technique has potential applications to a broad range of future nuclear measurementswith the Crystal Ball and similar detector systems elsewhere. The data are sensitive to the prop-agation of the ∆ in the nuclear medium and will give the first information on matter transitionform factors from measurements with an electromagnetic probe. The incoherent cross sections arecompared to two theoretical predictions including a ∆-hole model. PACS numbers: 25.20.-x
This Letter reports the first detailed measurement ofnuclear π photoproduction populating a specific excitedstate in the residual nucleus. The photoproduction of π sfrom nuclei at intermediate photon energies is of great in-terest for a number of reasons. The dominance of the ∆resonance in the π photoproduction amplitude and theability of the electromagnetic probe to sample the full nu-clear volume makes the reaction one of the cleanest testsof our understanding of the interaction of the ∆ in thenuclear environment. This dominance of the ∆ in theproduction amplitude has a further useful consequencein that it leads to an approximately equal probability for π photoproduction from both protons and neutrons inthe nucleus. Potentially this allows access to accurate ∗ Electronic address: [email protected] information on the transition form factor for reactions inwhich the dominant change takes place in the neutronwave function, while circumventing many of the difficul-ties present in traditional methods using strongly inter-acting probes. Measurement of this incoherent process todiscrete nuclear states also offers opportunities to use thespin-isospin selection rules to study specific componentsof the basic pion photoproduction amplitude.The importance of the incoherent ( γ, π ) process fromnuclear targets has been appreciated for some time[1, 2, 3]. However, although nuclear π photoproductionhas been studied at various facilities for over 30 years,no results for the population of discrete residual nuclearstates have been obtained because the accuracy of theangle and the energy determination of the photons fromthe π → γ decay needed to resolve states in the residualnucleus has not been achieved. The only published infor-mation on the incoherent ( γ, π ) reaction was extractedfrom measurements with an untagged photon beam [4]which obtained the integrated yield of decay photonsfrom the 3.56-MeV state in Li and the 4.4-MeV stateof C. The 3.56-MeV, 0 + , T=1 state in Li is reachedonly via the weak isoscalar single nucleon amplitude anda low cross section is observed illustrating the value ofthe incoherent π reaction for isolating the smaller am-plitude terms. An unpublished study of the 4.4-MeVyield in a restricted π angle range obtained at MAMIis presented in Ref. [5]. There is also some informa-tion on the summed “non-coherent” strength, presentedin Refs [6, 7] for C and Ca. However, it is difficultto extract detailed information from the “non-coherent”strength as it includes both the incoherent processes andthe quasi-free process in which nucleons are also ejected.The general features of these data were described by aFermi gas model of the quasi-free process [7].There are at present only two available calculations ofincoherent π photoproduction to discrete residual nu-clear states, both for the C nucleus. The most detailedtreatment [1] is based on the ∆-hole model and includesa study of the contributions of various π and ∆-nucleusinteraction processes to the incoherent cross section. Thepredictions highlight the sensitivity of the incoherent re-action to the character of the nuclear transition involvedand to specific ∆-nucleus processes such as ∆ N interac-tions, which have a much smaller effect on other observ-ables such as the coherent cross section. The other cal-culation [2] is less sophisticated. It uses the plane waveimpulse approximation and makes a rough estimate ofthe effect of the π -nucleus final-state interaction. Veryimportantly, however, this treatment does derive formu-lae for the angular correlation between the emitted π and the subsequent nuclear decay photon. This correla-tion turns out to be strong and its use is essential in thisdata analysis. Theoretical work, now in progress [8], willgive additional predictions of the incoherent cross sectionbased on the Mainz unitary isobar model [9] with a com-plex pion optical potential and ∆ medium modificationsincorporated using a ∆ self-energy.The data presented here were obtained as part of a se-ries of experiments on neutral pion photoproduction from C, O, Ca and
Pb targets, carried out with theCrystal Ball (CB) detector [10] and the Glasgow photontagger [11, 12] at MAMI [13]. The CB (Figure 1) is a672 element NaI detector covering 94% of 4 π . Photonsincident on the ball produce an electromagnetic showerthat typically deposits 98% of its energy in a cluster of 13crystals. Analysis of the center of gravity of the showerallows angular resolutions for the photon of 2-3 ◦ . Thehigh light output of NaI also permits a good determina-tion of the photon energy ( σE γ ∼ . E γ ( GeV ) . ). Since itsmove to Mainz there has been a complete overhaul of theelectronics for the CB [14] and it has been instrumentedwith additional detectors. A central detector providingcharged particle identification [15] was provided by theEdinburgh and Glasgow groups and two cylindrical Multi FIG. 1: Diagram showing the Crystal Ball detector, the Ctarget (red) and the the PID detector (blue). The MWPC isomitted for clarity ] [MeV/c gg M60 80 100 120 140 160 180 200 220 C o un t s [ a r b . un i t s ] · FIG. 2: The spectrum of invariant mass reconstructed fromthe 2 γ events in the CB for E γ ≤
400 MeV. Events in themass range 117-149 MeV were selected for the analysis.
Wire Proportional Counters (MWPC) were transferredfrom Daphne [16]. The forward hole of the CB was in-strumented with the TAPS detector array [17], but thiswas not used in the present analysis.The tagged photon beam covered the energy range 120to 819 MeV with a tagging resolution of ∼ ∼ × γ s − MeV − . Thetagged photons were incident on a 1.5 cm thick C tar-get. Emitted photons were detected in coincidence inthe CB, with additional information on charged particlesgiven by the central detectors. The reconstructed ver-tex position from multiple charged track events in theMWPC allows accurate reconstruction (to ∼ mm) ofthe target position relative to the CB.Neutral pions were identified in the CB from their 2 γ decay. The invariant mass spectrum reconstructed fromthe detected 2 γ events in the CB is presented in Fig. 2.The contribution of pions not originating from the C Energy [MeV]0 2 4 6 8 10 12 ] (cid:176) [ pq C o un t s [ a r b . un i t s ] FIG. 3:
Upper plot: θ π versus the energy of the low-energyclusters detected in the CB. Lower plot: projection of theenergy distribution for θ π bin of 78 ± ◦ . The gray dotted linesshow the result of an exponential plus Gaussian fit to the data.Both plots for E γ =235 ±
10 MeV and for E diffπ below 20 MeV. target was found to be only ∼
3% in additional runs withthe target removed.The energy difference ( E diffπ ) between the recon-structed π energy and its calculated energy (using thetagged photon energy, measured θ π and assuming coher-ent π photoproduction) was restricted to less than 20MeV to suppress the contribution of quasi-free π pro-duction. Figure 3 (upper) shows a plot of the π polarangle versus the energy of the time-correlated low energyphoton clusters in the CB for these data. Figure 3 (lower)shows the projection of the photon energy distributionfor the angular range θ π =78 ± ◦ . Nuclear decay photonsfrom the 4.4-MeV state in C are clear in both plots.There is no evidence of significant nuclear decay radia-tion from higher-lying residual states. A smoothly fallingbackground of low-energy photons is also evident, whosedistribution of strength with π angle appears stronglycorrelated with the coherent cross section (which is max-imum at θ π ∼ ◦ [18, 19] for the chosen incident E γ bin).GEANT3 (G3) simulations (not shown) confirm the dom-inant cause of this background to be low energy photons,which split off from the π decay photon clusters. A re-duction in the contribution of split off photons is achievedin the present analysis by requiring that low energy pho- ] (cid:176) [ a C o un t s [ a r b . un i t s ] · FIG. 4: Comparison of the distribution of the α , the polarangle of the nuclear decay photon with respect to the recoildirection, for incident E γ =235 ±
10 MeV (black points) withthe distribution suggested in Ref. [2], passed through the G3simulation of the experimental acceptance (red line). tons have angular separation of greater than 35 ◦ fromeither of the π ◦ decay photons.To extract the incoherent cross section to the 4.4-MeVstate, the low-energy photon spectrum for each θ π binwas fitted with a Gaussian centered at 4.4 MeV plusan exponential background. The fitted components areshown in Fig. 3 (lower). The shape of the backgroundwas consistent with the energy distribution predicted byG3. The fitted background also accounts for the smallfraction ( ∼ ∼ π – γ coincidence peak. In principle the strength of the ob-served 4.4-MeV peak may contain contributions fromhigher-lying states cascading through this state. Thecontribution from such cascades was quantified from theratio of double to single low-energy photon detectionrates in the CB and found to be less than 5% of the4.4-MeV yield. This is expected as the strongest branch-ing ratio to the 4.4-MeV state is 2.1% for the 15.1 MeV(1 + , T = 1) state, which is not produced via ∆ excitation[1], and the γ branch for other states is at least a factorof 10 smaller.To convert the incoherent yield to the 4.4-MeV stateat a particular pion angle into a cross section, the ef-ficiency of the CB for simultaneous detection of boththe π and the 4.4 MeV decay γ averaged over the an-gular distribution between them is required. This wasobtained from the G3 simulation. The required π – γ angular correlation was taken from Ref. [2] where it isgiven in terms of the angle α between the decay photonand the C recoil direction which has the distribution sin (2 α ). The combined π – γ detection efficiency soobtained varies from ∼
20 to 30% over the π angularrange 30-160 ◦ but is smaller outside this range due toholes in the CB at forward and backward angles. It wasused to extract the differential π production cross sec- ] (cid:176) [ p q b / s r ] m [ W / d s d = (225-245)MeV g E ] (cid:176) [ p q b / s r ] m [ W / d s d = (240-260)MeV g E ] (cid:176) [ p q b / s r ] m [ W / d s d = (285-305)MeV g E FIG. 5: The C( γ, π ) C . MeV cross section presented as afunction of θ π for E γ bins indicated in the figure. The predic-tions by Takaki et al. [1, 20] are shown by blue lines: modifiedDWIA (dot-dash); many body effects added (dot-dot-dash);multistep mechanisms also added (dash); ∆-N interaction alsoadded (solid). Pink long dashed line shows predictions of Ref.[2] tions for the 4.4-MeV state shown in fig. 5.The validity of the π – γ angular correlation obtainedin Ref. [2], which was used to calculate the overall CBefficiency, was checked by plotting the experimental dis-tribution of the angle α . Figure 4 shows the data for in-cident energies E γ =235 ±
10 MeV. This is compared witha G3 simulation, which uses as its input the predicted α -distribution, sin (2 α ), and a π angular distribution which has the same shape as the data shown in fig. 5.The agreement between the data and the simulated α -distribution of the decay photons clearly establishes thedominance of the sin (2 α ) term in their angular distri-bution. The polarization state of the recoil C nuclei,which leads to the simple predicted distribution shape,results from the dominance of the spin independent termsin the ( γ, π ) amplitude on a single nucleon. In fact thecalculation of Ref. [2] suggests that the spin-dependentterms will also provide a contribution to the incoherentexcitation of the 4.4-MeV state at the few percent leveland that this contribution will have a cos (2 α ) distribu-tion. Such a contribution may account for some of theremaining discrepancy between the data and the predic-tion in Fig. 4. It is clear that angular correlation data ofthis type will be valuable in separating the componentsof the basic photoproduction amplitude.Differential cross sections for incoherent π photopro-duction from C populating the 2 + state at 4.4 MeV areshown in Fig. 5 where they are compared with the twoavailable calculations. The main sources of systematicuncertainty in the present measurement arise from thethe detection efficiency calculations and the yield extrac-tion technique with smaller uncertainties arising from thephoton flux determination and the measurement of thetarget thickness. The total systematic uncertainty in thecross sections is estimated to be ∼ ± π – and ∆ – in-teractions in the nucleus as can be achieved in the ∆-holemodel. It is reassuring, therefore, to see that the angulardistribution shape is very well described. The magnitudeof the theoretical cross sections is mainly affected by thedetails of the pion and ∆ interactions in the nucleus. Thefour E γ =295 MeV curves from Ref [1] in Fig. 5 chartthe reduction in the cross section as many body effects,multistep mechanisms and the ∆-N interaction are suc-cessively introduced. Given the large combined changeproduced by these factors, the full calculation gives afairly good explanation of the results. Additional experi-mental data covering a wider photon energy range wouldprobably help identify which parts of the calculation arenot yet adequate. The calculation of Ref. [2], which isbasically a plane-wave treatment and uses wave functionsfrom an L-S coupling model does significantly less well inexplaining the shape, magnitude and photon energy de-pendence of the measured cross sections.In summary, the present experiment is the first detailedmeasurement of incoherent π photoproduction from anucleus and employs a novel nuclear decay photon tech-nique that will have application to further nuclear mea-surements at the CB and other experimental facilities.The incoherent cross sections are in general agreementwith the available ∆-hole model calculation, but the com-parison indicates refinements in the calculation may benecessary. The extracted incoherent cross sections willalso be important in improving the suppression of inco-herent background in the extraction of the coherent π production process [21, 22], the poor determination ofwhich has previously limited attempts to obtain accu-rate measurements of the matter form factors of nuclei[23]. Acknowledgments
The authors wish to thank T. Takaki for calculationalresults and valuable comments and to acknowledge the excellent support of the accelerator group of MAMI. Thiswork was supported by the UK EPSRC, the DeutscheForschungsgemeinschaft (SFB 443, SFB/Transregio16and the European Community-Research InfrastructureActivity under the FP6 ”Structuring the European Re-search Area” programme (HadronPhysics, contract num-ber RII3-CT-2004-506078), the USDOE, USNSF andNSERC (Canada). We thank the undergraduates stu-dents of Mount Allison and George Washington Univer-sities for their assistance. [1] T. Takaki, T. Suzuki, and J. H. Koch, Nucl. Phys.
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