PHOTOPRODUCTION OF $\pi^0$ MESONS ON HYDROGEN AT ENERGIES UP TO 450 MeV

Beginning in 1950, a number of studies were carried out devoted to the photoproduction of $\pi^0$ mesons on hydrogen under the action of bremsstrahlung $\gamma$ quanta with energies up to 330 MeV. The first studies were reviewed in a survey by A. M. Baldin and V. V. Mikhailov,^1 containing a number of theoretical considerations on the photoproduction of mesons. Experimental registration of $\pi^0$ mesons arising in the reaction $\gamma + p \to \pi^0 + p$ was based on counting coincidences either between two $\gamma$ quanta from the decay of $\pi^0$,^2,3 or between one (or both) of these quanta and the recoil proton.^4,5 Six papers published a total of one of the two $\gamma$ quanta from the decay of $\pi^0$. The results obtained by three methods proved to be in satisfactory agreement. Below is a summary of the principal data for the photoproduction of $\pi^0$ mesons on hydrogen at energies up to 330 MeV.

The total cross section for photoproduction of \(\pi^0\)-mesons on hydrogen at
\((E_\gamma)_{\max}=330\ \text{MeV}\)

\[ \sigma = 0.55\text{--}0.6\times 10^{-28}\ \text{cm}^2/\text{effective quantum}.^3 \]

The differential cross section for an angle of \(90^\circ\) in the laboratory coordinate system:

\[ \left(\frac{d\sigma}{d\Omega}\right)_{90^\circ\ \text{lab}} =2.7^4\ \text{or}\ 3.5\times 10^{-30}\ \text{cm}^2/\text{steradian}\cdot\text{effective quantum}.^3 \]

Differential cross sections for other angles and the angular distribution:

\[ \left(\frac{d\sigma}{d\Omega}\right)_{45^\circ\ \text{lab}} =8.2\cdot 10^{-30}\ \text{cm}^2/\text{steradian}\cdot\text{effective quantum}.^3, \]

\[ \frac{ \left(\dfrac{d\sigma}{d\Omega}\right)_{60^\circ\ \text{lab}} }{ \left(\dfrac{d\sigma}{d\Omega}\right)_{90^\circ\ \text{lab}} } =1.45\pm 0.25^5, \]
which corresponds, in the center-of-gravity system, for the interval of \(\gamma\)-quantum energies from 250 to 310 MeV, to

\[ \frac{ \left(\dfrac{d\sigma}{d\Omega}\right)_{75^\circ\ \text{c.g.s.}} }{ \left(\dfrac{d\sigma}{d\Omega}\right)_{110^\circ\ \text{c.g.s.}} } =1.0\pm 0.2^5. \]

Angular distribution in the c.g.s.:

\[ \frac{d\sigma}{d\Omega}\sim 2+3\sin^2\theta.^6 \]

The energy dependence of the differential cross section for \(90^\circ\) in the laboratory system is

\[ \left(\frac{d\sigma}{d\Omega}\right)_{90^\circ\ \text{lab}} =\text{const}\times (E_\gamma-145\ \text{MeV})^{1.9\pm 0.4}.^5 \]

This dependence is considerably stronger than for the photoproduction of \(\pi^+\) on hydrogen, where the cross sections already become constant at an energy \(E_\gamma\simeq 250\ \text{MeV}\). Although the entire set of experimental data on the photoproduction of \(\pi^0\)- and \(\pi^+\)-mesons on hydrogen had not been fully explained by theory, nevertheless a number of successes had been achieved. In the work of A. M. Baldin and V. V. Mikhailov\(^7\), even before the corresponding experiments were carried out, it was shown that the photoproduction cross section of \(\pi^0\)-mesons should increase with energy more rapidly than the photoproduction cross section of \(\pi^+\)-mesons. This conclusion was obtained by taking into account the electromagnetic interaction of photons with meson “currents,” as a result of calculations for a pseudoscalar meson with pseudovector coupling. The rapid increase of the photoproduction cross section of \(\pi^0\) and the correct ratio of the cross sections for \(\pi^+\) and \(\pi^0\) were also obtained in the work of Brueckner and Watson\(^8\), who assumed the formation of an intermediate excited state of the nucleon with total angular momentum \(\frac{3}{2}\) and isotopic spin \(\frac{3}{2}\). Theory\(^8\) also gave the correct angular distribution of \(\pi^0\)-mesons: \(2+3\sin^2\theta\).

However, a more rigorous test of all theoretical predictions was to be the study of photoproduction of \(\pi^0\)-mesons at higher energies. In 1953 a paper\(^9\) appeared in which the production of \(\pi^0\)-mesons on hydrogen by bremsstrahlung photons with ener-

energies up to 450 MeV. In this work the differential angular cross section for photoproduction of \(\pi^0\) at an angle of \(90^\circ\) in the laboratory system was determined; coincidences of the \(\gamma\)-quanta from \(\pi^0\) decay with the recoil proton were recorded. The apparatus scheme is shown in Fig. 1. The recoil protons were recorded by a telescope of three stilbene scintillation counters, the first two counters being connected in coincidence and the third in anticoincidence. Aluminum filters were placed between the counters. In this way it was possible to determine the specific ionization (from the pulse amplitude in the first counter) and the range of the protons. The photons from \(\pi^0\) decay were recorded by a telescope of three liquid scintillation counters. Between the first and second counters there was a lead converter. The background of charged particles was greatly cut down by connecting the first counter in the telescope in anticoincidence and by the presence of a graphite filter in front of this counter. The calculated efficiency of the entire counting system, depending on the photon energy, was from 0.15 to 0.28. The data for photoproduction of \(\pi^0\) on hydrogen were obtained from the difference of the results with polyethylene and graphite targets. The background from carbon nuclei amounted, depending on \((E_\gamma)_{\max}\), to 15–40%. The spectrum of bremsstrahlung was normalized to the value of the total energy released in an ionization chamber with 2.5 cm copper walls, calibrated for measurements of the absolute beam intensity.

Figure labels: stilbene; \(p\)-counter; Al absorber; target; \(\theta_p\); \(\theta_p \simeq 32^\circ\); \(\gamma\)-counter; Pb; graphite; liquid scintillators; \(\gamma\); 1 2 3 4 5 6 inches.

Fig. 1

In Fig. 2 the circles show the results obtained in \({}^{9}\). For comparison with these data, at lower energies the crosses indicate the results of work \({}^{5}\). The error intervals shown in Fig. 2 correspond to the errors in determining the relative values of the cross sections and therefore do not include errors in determining the beam intensity. Since those results of \({}^{9}\) which pertain to high energies are of special interest, i.e., precisely to the region where the errors associated with the form of the spectrum are greatest, the authors of \({}^{9}\) undertook a special analysis of errors at high energies.

For this purpose experiments were carried out at three nominal values \((E_\gamma)_{\max}\)—480, 420, and 370 MeV; in each case the ratio was recorded of the observed counting rate to the rate that would have been obtained at

in the absence of a sharp drop in the photon spectrum near the maximum energy, and with the cross-section values shown in Fig. 2 being correct. This ratio, denoted by the letter \(R\), is shown in Fig. 3. Three curves plotted in Fig. 3 for different values of \((E_\gamma)_{\max}\) were drawn in such a way that the points \(R=0.5\) fell at \((E_\gamma)_{\max}\), and so that the curves for 420 and

Fig. 2

370 MeV agreed as well as possible with experiment over the entire range. Thus the best internal consistency of the experiments at different energies was achieved. As a result of the analysis described,

correction factors \(\dfrac{1}{R}\) were introduced for determining \(\sigma(E_\gamma)\) at a given \((E_\gamma)_{\max}\). For example, to determine \(\sigma(445\ \text{MeV})\) at \((E_\gamma)_{\max}=480\ \text{MeV}\), the factor \(\dfrac{1}{0.85}\) was introduced.

Fig. 3.

The authors \({}^{9}\) believe that the uncertainty in the form of the photon spectrum in the region of high energies gives an error of no more than \(10\%\) for \(\sigma(400\ \text{MeV})\) and no more than \(25\%\) for \(\sigma(445\ \text{MeV})\).

As regards the position of the maximum of the photoproduction cross section for \(\pi^0\) on hydrogen (at \(E_\gamma = 320\ \text{MeV}\)), the results \({}^{9}\) agree excellently with the calculations of the theory \({}^{8}\) for the isobaric state of the nucleon. However, the decrease of the cross section at high energies occurs, as the authors \({}^{9}\) point out, faster than \({}^{8}\) predicts: in Fig. 2 the dashed line denotes the theoretical curve \((E_\gamma)\), superposed on the experimental one at \(310\ \text{MeV}\). The theory \({}^{8}\) has three parameters for explaining the sum of the experimental data on the photoproduction of charged and neutral mesons and on meson–nucleon scattering: the interaction constant \(g\),

with the interaction radius and the “resonance” energy of formation of the excited state of the nucleon. These parameters prove insufficient for a satisfactory description of all the experiments mentioned. It should be noted, however, that in the calculations of Ref. 8, in the absence of any data on the dynamic magnetic moments of nucleons, the values of the static moments were adopted. It would therefore be premature to draw conclusions about the unsuitability of this theory before experiments are carried out that would make it possible to determine the dynamic magnetic moments of nucleons.

G. I.

CITED LITERATURE

1. A. M. Baldin and V. V. Mikhailov, UPhN 44, 220, 1951.
2. T. Steinberger, W. Panofsky, T. Steller, Phys. Rev. 78, 802 (1950).
3. W. Panofsky, T. Steinberger, T. Steller, Phys. Rev. 86, 180 (1952).
4. A. Silverman and M. Stearns, Phys. Rev. 83, 853 (1951).
5. A. Silverman and M. Stearns, Phys. Rev. 88, 1225 (1952).
6. G. Cocconi and A. Silverman, Phys. Rev. 88, 1230 (1952).
7. A. M. Baldin and V. V. Mikhailov, ZhETF 21, 562 (1951).
8. K. Brueckner and K. Watson, Phys. Rev. 86, 923 (1952).
9. R. Walker, D. Oakley, A. Tollestrup, Phys. Rev. 89, 1301 (1953).