The data clearly show the presence of a pole in the production amplitude due to the one pion exchange. The second and third pion-nucleon resonances are visible as peaks in the total cross-section and axis. In particular, this experiment provides 516 data points at forward angles in the region of the second and third resonances, with improved energy resolution.
In the absence of a dynamical theory Qf photopr::iduction at high energies, a gen:d phenomenological analysis of the angular distributions is considered.
METHOD AND APPARATUS
Contaminants from other photoproduced mesons (p, K, Tl) were similarly eliminated by kinematic constraints and the maximum energy of the bremsstrahlung beam. Two auxiliary monitors, a thin ionization chamber upstream of the hydrogen target and a two-counter telescope below the hydrogen target, were also used to monitor the beam. Fan counters, mounted on each pole face, were used to veto particles scattering from the magnet face.
5 inches of lead and the last counter, S3, shed electrons below the FC threshold that could have come from conversion of gamma rci.ys to Al or elsewhere when the spectrometer was at a small angle to the ph:iton beam.
PROCEDURE
At each setting, measurements were obtained at four energies corresponding to the four sp2ctrom:;ter channels.
RESULTS
Moravcsik-equivalent fits were repeated with a variable scale factor for data from one experiment relative to another. The average scale factor differed from unity by 3 ± 3%, the cross sections obtained by this experiment were larger. This difference was not considered significant and no scale factor was included in any of the examples presented in this thesis.
05 degrees for each point~ Laboratory photon energy calibration is considered consistent between points better than 0.
CHI DI STR IBUT IO N
DATA FITTING
However, it has the disadvantage of clashing the effects of a given angular momentum state among the m8_ny of coefficients. The cross section due to the interference of a TT exchange with states of total angular momentum less than or equal to j has the form For states with total angular momentum less than or equal to j, the cross section is in general a polynomial of order 2j.
The integrated cross section can be obtained from the coefficient P (X) in the table or from. Therefore, choosing M = 4 or even M = 5 is an approximation that neglects the presence of higher angular momentum states. Owing to foe statistical errors of the present ctat, no clear decision can be made ab~:mt.
The importance of choosing the order of fitting is seen in the determination of the coupling constant. An oversized M is less serious, but still undesirable, as some available information covers G2. Unfortunately, this mean is sensitive to choices of M, so the given error is an underestimate due to statistical errors in the cross section alone.
This eliminates the fluctuations of the C(J) with energy due to errors correlated with C(0). 5/2 is eliminated because no bump of the same size is found in C (8) and the 0° cross section, as we will see, implies that the production arises almost entirely from an initial helicity ± 3/2.
0 AND 180 DEGREE CROSS SECTION
CONCLUSIONS
This experiment has provided a large number of measurements, which, when combined with H. Thiessen's data, give a consistent picture of the cross section of the n + photo production in the region of the second and third resonances. The angular and energy resolution, and the spacing of the data points are good enough to clearly see the effects of resonances and a n exchange.
The presence of a small photoproductioncl D 5/2 resonance (or at least an imaginary amplitude) was discovered by its interference with the F 5/2 third resonance. It was seen that useful information about ratios of electrical to magnetic production of the resonances is easily eh.i: realized from the data, providing a useful check of a sum rule calculation. It should be noted that the effects of resonances could be extracted from the large nonresonant background only because of the detailed energy dependence.
Coupling constant measurements given by fits to angular distributions were consistent with the accepted value. Unfortunately, while the statistical error of the obtained value is small, the dependence on the order of fitting and the uncertainty in the choice of orderJ: increases the error considerably. A fit in which the resonant multipoles are given by the Breit-V/igner formula and the coupling constant is varied to fit all the data at once is possible.
BEAM AND TARGET
As a check on the quantum meter itself, it was compared five times with an identical one used in the west beam. It will thus be sufficient to indicate the properties of the spectrometer for the apertures used. Measurements of the edge magnetic field (2'"/) in the central bending plane of the magnet were used to deriv.
The magnetic field of the magnet was set by a nuclear magnetic resonance (NMTI) system. The tension in the wire at the origin, where it is measured, differs from that at the entrance of the magnet by ii T. A correction (a.) for the weight of the wire inside the magnet is calculated assuming that the path is a segment of a circle.
185 inches above the top edge of the lead marker when lowered into the hydrogen target. The calculation of the ratio was cloned by running the cross section program (Appendix VI) for several conditions and finding the ratio for which x2 for the individual runs measuring the same cross section:)n is a minimum. Also shown in Figure 18 is the result of an electronic calibration (3.0) of the energy meter.
There, they reduced the aperture to improve the angular resolution of the spectrometer. This degree of coincidence provided relative beam intensity monitoring that was stable to within 1% at short times.
APPENDIX IV
At small angles to the photon beam, a large number of electrons are produced, so it is necessary to detect them with good efficiency to separate the pion yield. The efficiency of the FC for counting electrons (or p:::>citrons) was measured many times during the experiment and was always found to be better than 99. The spectrometer was then set to zero degrees receiving an electron beam analyzed almost clean of the moment.
To measure its efficiency for protons and pions, protons and pions must be determined independently. The second method'Jd is to choose pi:::ms 'Jr pr'.)ton with time 'Jf flight and scintillator pulse heights (dE/cL'{).
ELEC T RON RATES
The "proton" rate gauges (LCV) with respect to the LC pion velocity are shown in Fig. 24 plotted vs . The LCV rate drops significantly below 750 MeV/c due to the fast time requirements (Tof, Al · Sl). When the sum of the counts (S2 SUM) in all four channels was compared to the actual number of events (S2 OR) an excess was found.
An examination of the many cha1mel events showed that they were not accidents, but were two particles traversing the system at the same time. The 1 fraction of events resulting from scattering in the pole face of the magnet and therefore vetoed by the Fan counters was monitored throughout the experiment. However, at laboratory angles less than 10, the Fan veto was not used due to 0.
Because the small angle regbn was highlighted, the average Fan veto velocity for angles greater than 10° is weighted against the momentum setting of the smaller angles and is sufficiently accurate for this correction. The correction for losses due to nuclear absorption and multiple scattering in counters and miscellaneous substances was made in two ways, depending on the location of the absorber. Inside the mag.net K(Z) is a linear combination of the s.sine and cosine of the remaining bend angle.
The fraction of particles that amount to 83 while meeting the other pion requirements was recorded for most data sets at laboratory angles greater than 14°. For this additional correction, measurements were made of the fraction, ·V, of pions that missed 83 with additional correction.
53 MISS RATE
This is important in the absorption correction for the rest of the system where the absorption cross section is taken to be independent of energy. To determine the "elementary" section measurements of the fraction of n + missing S3 due to plexiglass absorbers up to 32 cm thick were made with a momentum of 500 MeV /c. M = fraction of losses due to multiple scattering F = fraction of the beam that is n + (µ + inter-.
0 or D. 0 not zero), the factors in the integrand vary slowly, so they can be taken outside the integral. This would result in the integral being approximated by the integrand, evaluated at the center of the integration region, times the. The error in this approximation is of the second order in terms of the "size" of the integration region and consequently the approximation is sufficiently accurate.
The change in acceptability with horizontal position on the hydrogen target is neglected, and the spatial distribution of the photon beam is that given by BPAK 1 (23 . ) for typical values of K:::: 900 MeV and E. Due to the variation of dK/dP with angle, clearly, each of the four momentum channels does not remove the angular distribution at constant energy. Each data point was then shifted to the desired energy (dashed lines in Fig. 29), chosen so that each angular distribution came from only one channel; changing the cross-sectional value by the same amount changes the fit based on the distance moved.
The error assigned to the interpolated cross section is assumed to be the same as that of the original. As a summary point and to acknowledge the assistance of the computer programs written by others, Table 19 provides the relevant breakdown of the data analysis calculations.
