The significance of these results for identifying the mechanism of the double pion charge exchange reaction is discussed. The probability that no resultant undergoes another single charge exchange in n+ is the pion-nucleon charge exchange cross section divided by 4 n r 2 (r, being defined as the root-mean-square separation between protons).
Exotic Mechanisms
In this work, due to Gibbs et a1 (Gi77), the outer-shell behavior was modeled by a simple analytical extrapolation of the on-shell transition amplitudes, the parameters of which were fitted to pion-deuteron absorption. 34;cloud" that surrounds the target nucleon from the nucleus, and is itself absorbed onto another nucleon.
It therefore appears that a realistic estimate of the contribution of this mechanism awaits more sophisticated calculations. This type of behavior indicates a two-step mechanism and provides further evidence in favor of the mating model.
Experimental Apparatus
General Laycut
The Beam Eine
For the purpose of the present measurement, a new cryostat system was mounted on the target cell by the UMPF cryogenic group. The target cell itself consists of a 7.57 crn diarneter bronze cylinder, segmented into two identical chambers, one above the other, as shown in.
The Dipole Magnet
The Magnetic Spectrometer
Due to the large dimensions of this plane, the arrival time of an optical pulse on the photomultiplier depends on the position of the intersection of the path with the scintillator. In fact, this setup calculated the average time for the release of 52 and 53, canceling the dependence on position.
The (krenk~v Detector
The counter top junction box section was segmented with aluminum dividers into 5 smaller sections, one for each pair of phototubes. A prototype single segment counter was constructed and used to evaluate the efficiency of the larger detector and the detection of muom cosmic rays.
The &am Monitor
The trigger and wire chamber circuitry was in the p3 pit, mounted on the spectrometer itself, while the rest of the electronics were outside the radiation shield in the data acquisition trailer. The occurrence of an event that caused a coincidence between S1, 52 and 53 triggered the recording of the event parameters (wire chamber outputs, fhght time and Cerenk output) to magnetic tape.
Experimental Procedure
Acceptance Scans
The relative acceptance thus defined is actually the angular acceptance of the spectrometer divided by the efficiency of the beam flux monitor. By using this relative acceptance in deriving the double charge exchange cross section, one eliminates the requirement of an absolute.
Dipole Magnet Calibration
The correction for pion energy loss in the carbon target (1.6 Mev cm2/g a t f 65 Me$, a sf value of 238.3 Mev/c for those pions due to ground state transitions was achieved. Seth et t al (Se78) finds the Rrst and second excited states at '%e at 2.139 and 2.71 Mev, respectively, which are excited at (nr",mg) almost as strongly as the ground state, and these are accounted for in the energy calibration .
Rehum Runs
U Snominal value of 25 msr (probably an overestimate, since the presence . ~b the circular dipole would certainly tend to reduce it), and the put k n o w value for n-p elastic scattering -with the acceptance sun results.
Backgmund Subtraction Runs
Each event buffer written to tape was processed by first converting the PCOS and TBC parameters of the wire chamber to physical positions in the chamber planes, two (one for x and one for y) for each of the four chambers, where these positions were defined relatively. to the central path of the spectrometer. Then, using the Kulaga and Geesaman algorithm (Ku8 1), the parameters of the event on the target were evaluated. Five parameters are sufficient to fully characterize an event; the x and y positions of the 'n on the target, zo and yo, the angles made by the -rr+ on the target relative to.
With these coefficients in hand, a multidimensional, weighted version of the Newton-Raphson method (So64,Br70) was used to recursively determine the value of a best fit to the measured elements of T, and an X2 "goodness of fit" parameter was evaluated for each event thus processed. The analysis software provided for the accumulation of each of the components of a, as well as any of the elements of the event buffers, in spectra of up to 2048 channels. It was also possible to window the events accumulated in each of the spectra on any of the other parameters of the event, such as time of flight, Cerenkov pulse or X 2 value.
Background Reduction
One can see that while the positrons are clearly separated from the pions based on time of flight alone, the relative count rates are such that the tail of the electron peak will still overwhelm the pion signal. These muon events were removed by placing an acceptance window on the 2 value of the event. Pions that decay in flight though the spectrometer will generally have sharp discontinuities in their directions up to the decay point and thus give poor fits to the measured T for any value of a, (remember that '6 is 8 elements being fitted on only 5 parameters), and can therefore be distinguished from the surviving peonies based on their large.
According to the Monte Carlo simulation of Colton (Co80), less than one muon in five will fall within the acceptance window. The relativistic expression for the number of pions gassing from the front thread chamber to the focal point. By folding in the above muon rejection factor of five, it is seen that less than 6% of the observed counts are due to muons, and due to the random Frnpulses imparted to the decay muon, those that are not rejected are unlikely to be any structure will not contribute. to the spectrum, which instead forms a relatively flat background.
Spectrometer Miciency
Therefore, the denominator of the expression indicates the number of times the other '7 room planes fired during the run, regardless of whether room 11: also fired, while the numerator is the number of events for which room 1 also fired. . The overall efficiency of the spectrometer can then be evaluated by simply taking the product of the 0% efficiency of the individual chambers. The n-decay man counts used for normalization purposes must be corrected for varying computer dead time and spectrometer efficiency before the counts for each run can be summed.
The x - + p e ~ values for each run were then summed to give an overall figwe for the Helium runs.
Background Subtraction
This curve, weighted by the ratio of the effective number of monitors of decaying antaons 4 ~ e to that of the background, was then subtracted from the summation of the helium spectrum. They also tried Dk-ect bin by bin by subtracting the background spectrum from the helium spectrum, giving results virtually indistinguishable from the indirect method.
Cross Section Extraction
Error Analysis
Systematic errors are mainly due to uncertainty in tke basic T T - p cross-section at t 0" , (k 3X), which entered into the acceptance determination, m d the thickness of the Helium target (k 4%). errors in quadrature give ' an overall uncertainty of 5%, which completely dominates it due to the beam monitor statistics, which contributed less than 1%.The final Dcx spectrum, shown in figure 14, drops to a cross section of zero at exactly the instant.
Some of these are due to positrons slipping through the flight and Cerenkov rejection windows. A contribution to these points is also due to 'm decay muons, as repulsion was not 100% efficient. A straight line was attached to the h g h momentum (r 240 Mev/c) points and this background curie was subtracted from the lower energy points.
Issues Relating to the DCX Reaction Mechanism
As previously discussed, positrons are produced either in pair production showers or by a two-step process involving no, and their number will increase nonlinearly with target thickness, making it impossible to eliminate them through subtraction simple. Summing the contributions of the data points between the 0 and 3.1 Mev link, a figure of 7k15 nb/sr is obtained for the tetraneutron production from this reaction. The cross sections measured in the present experiment are between 100 and 200 times larger than those found in the previous experiment at comparable excitation energies.
It seems impossible to reconcile the two measurements, and in view of similar discrepancies between Kaufman et al.'s data and those of other related experiments, it appears that the Ear-Ber experiment was an error, at least as far as standardization is concerned. . Given the excellent agreement between Kaufrnan's data and the theoretical predictions of Gibbs and d, it seems very unlikely that these calculations can reproduce the current experimental results. 1% no error can be found in the calculations, perhaps another mechanism should be used.
Shape of the Continuum
Using the average of neutron-neutron scattering length numbers cited by Preston and Bhaduri (Pr75), curves were calculated for the ease where only one of the two pairs of neutrons interacts, as well as the case where there are two such interacting pairs , and the results were least squarely fitted to the data and shown together with the results of the pure phase space calculation. Previous investigators of the 4~e(7r-, n+)4n reaction have also included the effects of ha 1-state interactions in their analyses. Becker and Schrnit (Be70) found in their analysis of the Gilly et al experiment that the influence of the A resonance in the pion-nucleon interaction.
As mentioned before, the usefulness of the results of that experiment is questionable, although if the discrepancy with other measurements is only due to an overall normalization error, their results may still be relevant to the question of the importance of final state interactions. In any case, a consistent treatment of final state interactions in a four-particle system would have to include the interactions between all the particles and not just one or two pairs, as well as Pauli effects, which all calculations show are more important. in 4He(n',~')4n than the pairwise final state interactions. M = reduced mass of the two dineutron system The decay width of the resonance is then given by.
Directiems for 'Furthm Investigation
Seth in Proceedings of the LAMPF Workshop o n R o n Single Caarge E x c h a n g e , Los APamos National Laboratory report LA-7892-C. The relative admittance, defined as the true angular admittance divided by the beam monitor efficiency, appears as a function after the spectrometer * moment range is divided into 256 channels.
WIRE CHAMBER EFFIICIENCES
SPACE FIT gV
Figure 2, by Stetz e% al, shows the measured and calculated total cross sections for the 4He(n+,x")4p reaction as a function of the 7r9 bombardment energy. The hatched area between the curves labeled 1 corresponds to the calculated r e s d t s of the pair mechanism of Becker and Schmit, while the ewves labeled 3 and 3' are the similar calculations of Gibbs et t al, neglecting bg and including the effects of the Pauli principle, respectively. The hard data points are measurements of F a l o d i n e t d , the point of open is that reported by Carayannopoulos et al, and the crosses are due to Stetz et al.
ALUMINUM
BEAM INTEGRATION MONITOR
TIME OF FLIGHT SPECTRUM
Correction was made for 0% pions in the target, and the background spectrum of Figure 13 was subtracted.
