Photoproduction of ${\pi }^0$ mesons off protons and neutrons in the second and third nucleon resonance regions

Background: Photoproduction of mesons off quasifree nucleons bound in the deuteron allows us to study the electromagnetic excitation spectrum of the neutron and the isospin structure of the excitation of nucleon resonances. The database for such reactions is much more sparse than for free proton targets.

Purpose: Study experimentally single ${\pi }^0$ photoproduction off quasifree nucleons from the deuteron. Investigate nuclear effects by a comparison of the results for free protons and quasifree protons. Use the quasifree neutron data (corrected for nuclear effects) to test the predictions of reaction models and partial wave analysis (PWA) for $\gamma n\to n{\pi }^0$ derived from the analysis of the other isospin channels.

Methods: High statistics angular distributions and total cross sections for the photoproduction of ${\pi }^0$ mesons off the deuteron with coincident detection of recoil nucleons have been measured for the first time. The experiment was performed at the tagged photon beam of the Mainz Microtron (MAMI) accelerator for photon energies between 0.45 and 1.4 GeV, using an almost $4\pi$ electromagnetic calorimeter composed of the Crystal Ball and TAPS detectors. A complete kinematic reconstruction of the final state removed the effects of Fermi motion.

Results: Significant effects from final-state interactions (FSI) were observed for participant protons in comparison to free proton targets (between 30% and almost 40%). The data in coincidence with recoil neutrons were corrected for such effects under the assumption that they are identical for participant protons and neutrons. Reaction model predictions and PWA for $\gamma n\to n{\pi }^0$, based on fits to data for the other isospin channels, disagreed between themselves and no model provided a good description of the new data.

Conclusions: The results demonstrate clearly the importance of a measurement of the fully neutral final state for the isospin decomposition of the cross section. Model refits, for example from the Bonn-Gatchina analysis, show that the new and the previous data for the other three isospin channels can be simultaneously described when the contributions of several partial waves are modified. The results are also relevant for the suppression of the higher resonance bumps in total photoabsorption on nuclei, which are not well understood.

Figure 1

Data coverage for angular distributions and total cross sections [green stars at $\cos ({\theta }_{\pi }^{★}$) = 1.1] for the photoproduction of pions off the nucleon as a function of invariant mass $W$ and of pion momentum polar angle ${\theta }_{\pi }^{★}$. Black circles, previous data; red stars, $n{\pi }^0$ final-state results from this work.

Figure 2

Pion production in the $\mathrm{\Delta }$-resonance region. Measured cross sections: $p{\pi }^0$ final state [38, 39], $n{\pi }^{+}$ final state [40], and $p{\pi }^{-}$ final state [41]. Curves, MAID model [3]; solid, full model; and dashed, only ${\mathrm{P}}_{33}$(1232) resonance.

Figure 3

Single ${\pi }^0$ photoproduction off the free proton and the deuteron in the second resonance region [note that $d(\gamma ,{\pi }^0)X$ includes the $np{\pi }^0$ and $d{\pi }^0$ final states] [39]. Left-hand side: total cross sections. Curves: results from the SAID analysis [1] (solid) and MAID model [3] (dashed). For the deuteron from both models, the sum of proton and neutron cross sections folded with nuclear Fermi motion is plotted. Right-hand side: angular distributions. Solid curves, SAID proton, and dashed curves, Fermi smeared average of SAID proton and neutron.

Figure 4

Setup of the electromagnetic calorimeter combining the Crystal Ball and TAPS (left-hand-side) detectors. Only three quarters of the Crystal Ball are shown. Detectors for charged particle identification were mounted in the Crystal Ball (PID and MWPC) and in front of the TAPS forward wall (TAPS Veto-detector, CPV). The beam enters from the bottom right corner of the figure.

Figure 5

PSA spectra for hits in TAPS. Top row: raw spectra selected with information from CPV detector and ${\chi }^2$ analysis (where applicable). From left to right: photon candidates for inclusive analysis (no condition for recoil nucleons), photons with coincident proton candidates, photons with coincident neutron candidates, candidates for recoil protons, and candidates for recoil neutrons. Bottom row: same after application of all kinematic cuts. The black lines show the cuts applied to the spectra.

Figure 6

Proton identification by the CB-PID detector system. Shown is the energy loss $\mathrm{\Delta }{E}_p$ in the PID vs the total deposited energy $E_p$ in the CB for hits identified as protons, after all other analysis cuts. No background from electrons or charged pions is visible.

Figure 7

Nucleon identification with the TAPS detector showing the deposited energy of the nucleon $E_N$ vs its ToF (normalized to 1 m flight distance). Left column, proton; right column, neutron; top row, $cos\left({\theta }_{{\pi }^0}^{*}\right)<-0.6$; bottom row, $cos\left({\theta }_{{\pi }^0}^{*}\right)>-0.6$. The white line in the upper right histogram indicates background events from misidentified punch-through protons.

Figure 8

Kinetic energy distribution of the recoil proton for exclusive single ${\pi }^0$ photoproduction off quasifree protons for two different regions of $cos\left({\theta }_{{\pi }^0}^{*}\right)$. Black dots with error bars: Measured data, red line: MC signal.

Figure 9

PSA analysis of hits in the TAPS detector for nucleon candidates for events with forward and backward pion angles. Plotted is the PSA radius ($r_{\mathrm{PSA}}$) vs the PSA angle (${\varphi }_{\mathrm{PSA}}$). Left column, proton; center column, neutron without ToF-versus-energy cut; right column, neutron with ToF-versus-energy cut. Top row, $cos\left({\theta }_{{\pi }^0}^{*}\right)<-0.6$; bottom row, $cos\left({\theta }_{{\pi }^0}^{*}\right)>-0.6$.

Figure 10

Coplanarity angle distributions for several incident photon energies for exclusive single ${\pi }^0$ photoproduction off the quasifree proton (top, open upward blue triangles) and the quasifree neutron (bottom, open downward red triangles) integrated over the full angular range. Dashed green line, MC signal; dotted magenta line, sum of MC background contributions; solid black line, sum of MC signal and MC background; and dotted vertical lines, $\pm 1.5\sigma$ cut positions. Spectra shown have cuts on PSA, a rough invariant mass cut, and a ${\chi }^2$ analysis for identification of recoil neutrons in CB.

Figure 11

Missing mass distributions for several incident photon energies for exclusive single ${\pi }^0$ photoproduction off the quasifree proton (top, open upward blue triangles) and the quasifree neutron (bottom, open downward red triangles) integrated over the full angular range. Dashed green line, MC signal; dotted magenta line, sum of MC background contributions; solid black line, sum of MC signal and MC background; and dotted vertical lines, $\pm 1.5\sigma$ cut positions. Spectra with cuts as indicated in Fig. 10 and additionally cuts on coplanarity as indicated in Fig. 10.

Figure 12

Invariant mass distributions for several incident photon energies for exclusive single ${\pi }^0$ photoproduction off the quasifree proton (top, open upward blue triangles) and the quasifree neutron (bottom, open downward red triangles) integrated over the full angular range. Dashed green line, MC signal; dotted magenta line, sum of MC background contributions; solid black line, sum of MC signal and MC background; and dotted vertical lines, $\pm 3\sigma$ cut positions. PSA, ${\chi }^2$ analysis for recoil neutrons, coplanarity, and missing mass cuts (as indicated in Figs. 10 and 11) were applied to the spectra.

Figure 13

Resolution for the final-state invariant mass $W$. The results of full MC simulations of the instrumental response are shown for given values of $W$ (vertical lines).

Figure 14

Measured photon flux for the measurement with the 3 cm target. The left-hand side shows the flux measured as a function of photon energy. The structures in the spectrum are due to tagger channels with reduced efficiency. The right-hand side shows the flux as a function of reconstructed $W$ after folding with the Fermi momentum distribution.

Figure 15

Total detection efficiency based on MC simulations and including all corrections for the exclusive reactions $\gamma d\to p\left(n\right){\pi }^0$ (solid, blue histograms) and $\gamma d\to n\left(p\right){\pi }^0$ (dashed, red histograms) as a function of cm angle for the same bins of incident photon energy as in Figs. 10, 11, 12.

Figure 16

Integrated detection efficiency as a function of incident photon energy $E_{\gamma }$ for the inclusive reaction (dotted, black) and the exclusive reactions with detection of recoil protons (solid, blue) and recoil neutrons (dashed, red).

Figure 17

Determination of the CB energy sum threshold. Upper row: raw count rates. Dashed (blue), experimental data; solid (green), MC simulation. Lower row: ratio of experimental data and simulation (black histogram). Smooth (red) curves: fit to data (see text). Vertical lines: preset hardware threshold. Both rows for inclusive data and data in coincidence with recoil protons and neutrons.

Figure 18

Selected differential cross sections as function of the incident photon energy for quasifree inclusive single ${\pi }^0$ photoproduction compared to former results [39]. Full black circles, present results; open green circles, results from Ref. [39]. Cross sections normalized by $A=2$, the number of nucleons (i.e., average nucleon cross section). Shaded bands: systematic uncertainty excluding 7% overall normalization uncertainty.

Figure 19

Differential cross sections as a function of the cm polar angle for different bins of incident photon energy $E_{\gamma }$ (central values of the bins are labeled in the figures). Black, filled dots correspond to the inclusive cross section $d{\sigma }_{\mathrm{incl}}/d\mathrm{\Omega }$, including all single ${\pi }^0$ production reactions with a ($np$) or $d$ final nucleon state. Magenta circles show the sum $d{\sigma }_p/d\mathrm{\Omega }+d{\sigma }_n/d\mathrm{\Omega }$ of the exclusive cross sections in coincidence with recoil protons and neutrons. The black histograms indicate the systematic uncertainty of the inclusive cross section (without the 7% overall normalization uncertainty).

Figure 20

Differential cross sections for the inclusive reaction $\gamma d\to {\pi }^{0}X$ (black dots) and sum of exclusive cross sections (open magenta circles) as a function of the incident photon energy for different cm-polar angle bins. Notation as in Fig. 19.

Figure 21

Differential cross sections for exclusive single ${\pi }^0$ photoproduction off the quasifree proton. Open blue circles, experimental data; histograms, systematic uncertainty; and solid blue lines, Legendre fit to measured cross sections. Model results: dashed cyan line, SAID; dotted orange line, MAID; and dash-dotted magenta line, BnGa.

Figure 22

Differential cross sections for exclusive single ${\pi }^0$ photoproduction off the quasifree neutron. Open red triangles, experimental data; histograms, systematic uncertainties; and solid red lines, Legendre fit to measured cross sections. Model results: dashed cyan line, SAID; dotted orange line, MAID; and dash-dotted magenta line, BnGa.

Figure 23

Differential cross sections for exclusive single ${\pi }^0$ photoproduction off the free neutron (full red triangles). These are quasifree data corrected for FSI effects. Histograms, systematic uncertainties; and red solid lines, Legendre fit to measured data. Model results: dashed cyan lines, SAID; dotted orange lines, MAID; and dash-dotted magenta lines, BnGa.

Figure 24

Differential cross sections as a function of the final-state invariant mass for exclusive single ${\pi }^0$ photoproduction off the quasifree proton (blue, open circles) and the quasifree neutron (red, open triangles). Histograms: systematic uncertainties. Lines: model results for the free proton with notation as in Fig. 21.

Figure 25

Differential cross sections as a function of the final-state invariant mass for exclusive single ${\pi }^0$ photoproduction off the free neutron (i.e., quasifree neutron data with correction of FSI effects). Red triangles, experimental data; and histograms, systematic uncertainties. Notation for model results as indicated in Fig. 23.

Figure 26

Total cross section as a function of the incident photon energy for quasifree inclusive single ${\pi }^0$ photoproduction. Full (black) circles, quasifree inclusive data; open (magenta) circles, sum of quasifree proton and quasifree neutron total cross section; open (green) diamonds, MAMI 99 quasifree inclusive data [39]; and hatched histograms, systematic errors. Insert: ratio of the inclusive cross section and sum of the two exclusive cross sections.

Figure 27

Total cross section as a function of the final-state invariant mass for exclusive single ${\pi }^0$ photoproduction off the quasifree proton (open blue circles) and the quasifree neutron (open red triangles). Dashed cyan line, SAID; dotted orange line, MAID; and dash-dotted magenta line, BnGa. The insert shows the ratio of the quasifree neutron to the quasifree proton (open black circles).

Figure 28

Full red triangles: Total cross section as a function of the final-state invariant mass for the free neutron (quasifree neutron data corrected for FSI effects). Dashed cyan line, SAID; dotted orange line, MAID; and dash-dotted magenta line, BnGa. The black dashed and dash-dotted lines show the results of the SAID and BnGa analysis previous to the results from the present work and Ref. [35]. The insert shows the ratio of the free neutron to the SAID proton (full black triangles).

Figure 29

Normalized Legendre coefficients as a function of the final-state invariant mass for exclusive single ${\pi }^0$ photoproduction off the quasifree proton (open blue circles) and the quasifree neutron (open red triangles). Hatched histograms: systematic uncertainties of the quasifree proton. Dashed cyan curve, SAID; dotted orange curve, MAID; and dash-dotted magenta curve, BnGa.

Figure 30

Full red triangles: normalized Legendre coefficients as a function of the final-state invariant mass for exclusive single ${\pi }^0$ photoproduction off the free neutron (quasifree data corrected for FSI effects). Solid histograms, systematic uncertainties; dashed cyan curve, SAID; dotted orange curve, MAID; and dash-dotted magenta curve, BnGa.