The photoproduction cross section of neutral pions from complex nuclei at small angles has been measured in an attempt to determine the '11'0 lifetime from the reaction where one of the photons is provided by the Coulomb field of the nucleus. The large production of shared nuclei indicates that the non-rotating part of the nucleon cross section is peaked at small angles. nuclear charge and inversely proportional to lifetime.
This experiment is an attempt to measure the production from the Coulomb field and from the size of the cross section to determine o. The cross section is measured by detecting both ,(-rays from the pion decay in energy-sensitive Cerenkov counters. From the angular and energy distribution of the ,(-rays) angular dependence lTo.
A more complete description of the equipment and procedure for data acquisition and analysis can be found in the appendices. Conclusions are presented in Section V and suggestions are made for improving the experiment.
LEA D CROSS SECTION
CO H ERENT NUCLEAR
DATA AND RESULTS
The spectrum of the sum of the energies of coincident y-rays is drawn in figure 9. Energy spectrum of the sum of the pulse heights from both Cerenkov counters from the main target at counter positions of 0.00 and 2.90 • The solid and broken histograms are the measured spectra for all events and for only IIpi likelt events respectively. The data were corrected for beam absorption in the target and in the paraffin in front of the detectors.
Fitting theoretical count rates was performed on this combination of 0 and e data. With this calculation we have tried to unfold the angular resolution of the detector system and reconstruct the original cross section. The main purpose is to show the shapes and sizes of the cross sections.
A reconstruction of the differential cross section calculated by unfolding the counting resolution as described in the text. The . statistical significance of the error flags is not correct as it is overestimated. The vertical scale is approximately the cross section in p.b/sr divided by A. The solid and dashed curves on the left are the best fits for the lower and upper limits for the lifetime of 2 x 10-17. sec and -16.
Fitting of the measured angular distributions to the theoretical rates calculated by the Monte-Carlo integral (see Appendix F) was performed using the maximum likelihood technique (12). The adjusted parameters are the amplitude for the Coulomb formation (defaulted to real), the real and imaginary parts of the coherent nuclear amplitude, and the incoherent cross section. The contribution to the cross section from this term was calculated and used in fitting the carbon and aluminum data.
For the same reason, it was also assumed that the phase of the interference term is independent of the angle. Parameters of the target kernels used in the calculation of cross sections to fit the data. The incoherent cross-section was therefore set to zero (actually a better fit slightly negative), resulting in an overestimation of the coherent nuclear amplitude and giving a shorter lifetime value.
Match with correlated incoherent and with pole. a) The entries in these positions are the same as the corresponding entries above since the pole term cont:-i.bution was calculated for the fit without a pole. A five percent gain change in one of the Cerenkov counters will change the count rate by two percent.
CONCLUSIONS AND SUGGESTIONS
If the front peak of the cross section is taken to indicate a pole due to the exchange of a neutral vector meson, then since the cross section appears to be large for elements with nearly equal numbers of protons and neutrons, we can conclude that the vector meson is isoscalar. This discrepancy, however, may only be due to our poor knowledge of the coupling constants. A measurement of coherent production from deuterium would help clarify this point.
This resolution can be reduced to ±1/20 if the gamma rays are converted in spark chambers placed before the Cerenkov counters. The lateral spread of the beatTIl has been excluded from the analysis of the data. Both decay gamma rays of the neutral pions produced in the target were detected in total absorption spectroTLeters.
The centers of the apertures were chosen to be 8040' on either side of the beam, as this 1S is the symmetrical angle of incidence of a rro. The charged particle background was eliminated by sweeping them in the vertical direction and with 4" x 7 If veto counters in front of the apertures. The background due to cosmic ray particles crossing both Cerenkov counters was reduced by the cosmic ray veto counters placed between the two Cerenkovs just to the left of the beam.
The signals from the cosmic ray veto counters are added to the 1A signal before the fast coincidence. The trigger turns on a twenty-channel pulse height analyzer (kick sorter), which records the pulse height of the A + B sum signal. At the same time, a blanking signal is applied to the grid of the cathode ray tube to turn on the electron beam.
The standard energy calibrations of the Cerenkov counters are performed on COSITlic beam IT luons passing vertically through the counter. The electronics gains are adjusted to standard values and the biases of the fast coincidence circuits are checked. This provides sensitive information about the energy calibration, because the electron spectrum decreases sharply with energy.
PULSE H EIGH T ( CHAN NELS )
The dot plots of the pulse height in the two Cerenkov counters recorded on Polaroid transparency film are read by projecting the photograph onto a rectangular grid. For each run, a parameter map is read that contains the target material and thickness, the counter position, the end point and calibration of the beam, and the energy calibration of the individual counters. The parameter card also shows the number of bips and triggers that occurred during the run and the duration of the run in minutes.
The coordinates of the events are then read and the kicksort channel and photon energy are calculated. The spectrum of pulse heights corresponding to that recorded for the sum pulses on the kick sorter is printed for comparison with the notebook. From the energy of the '{ beams in the two counters and the geometry of the counter apertures, the program calculates the maximum and minimum possible angles that the pion could be emitted to give.
This technique is useful for evaluating the count rate integral because we are able to duplicate the physics of the problem and get intermediate results such as angular and energy distributions. The functional dependence of the cross section can be easily specified and bias conditions on angles and energies similar to those in the analysis programs can be imposed. 1, CPl' A Lorentz transformation in the laboratory system along the pion direction is performed on the y-rays to see if they are both detected.
If both are, then their lab energies are calculated and the event parameters are saved to tape. The integration program reads the event parameters from the tape and calculates the cross section and the bremsstrahlung spectrum. To fold in the energy resolution of the counters, two new photon energies are calculated normally distributed around the energies recorded in the strip with a width given by (J = 61 IE Mev, where E is the energy of the incident photon in Gev.
The events are then handled exactly as in the data analysis programs to see if they match the angle and energy criteria. The pion angle is calculated as described above, and histograms are made of angle and energy distributions. An "experimental n value of the error on the integral is obtained by dividing the 2000 events into ten groups and finding the distribution in the distribution of count rates.
