of U „, in Proton-Proton Scattering in Pure Spin States*(

Squared time derivatives of output powers of the Argonne and Maryland gravitational radiation detectors are written on magnetic tapes at Argonne and Maryland every 0. 1 sec. A computer files the threshold crossing times. A coincidence is a pair of identical crossing times of both tapes. The accidentals rate is measured by repeating the procedure for a sequence of time delays in either channel. A significant excess of coincidences is found at zero delay. An experiment was done using the new accelerated polarized proton beam at the Argonne National Laboratory zero-gradient synchrotron and a polarized proton target. The total cross section for proton-proton scattering at 3. 5 GeV/c was measured in the spin states ft and tk perpendicular to the beam direction. The two cross sections were found to be equal within the experimental error of +5%.

ing times of both tapes. The accidentals rate is measured by repeating the procedure for a sequence of time delays in either channel. A significant excess of coincidences is found at zero delay.
&xPeriments. -Interaction of something with the antenna'"' will increase or decrease the energy depending on phase relations between the Brownian motion and the increase of velocity. To observe such changes, the derivative of the power is taken by an analog device, squared and written on magnetic tape every 0.1 sec with 6-bit accuracy (64 intervals). Without further filtering, the magnetic tape from recorders at both sites is read by the Univac 1108 computer. The computer lists the times each channel crosses a threshold which is chosen to give about 4000 crossings per day. The computer looks for identical crossing times, and prepares a list of coincidences. Then, one file is delayed by 0.1 sec and a new list of coincidences prepared, and so forth for other amounts of delay. All operations are performed by the computer. The number of coincidences is shown as a function of delay by the histogram of Fig. 1(a). The true coincidence rate is the number of coincidences found when no delay has been introduced minus the average value with various delays. For 21 days we observe an excess of 139 coincidences representing more than 5 standard deviations from the mean.
For most of the time of these experiments the telephone line was in use, and both Argonne and Maryland outputs were written on one tape at Maryland, while the Argonne output alone was written on tape at a second recorder at the Argonne National Laboratory. The histogram of Fig. 1(b) shows the number of coincidences recorded by the computer from a study of the single Maryland tape. The somewhat smaller number of coincidences at zero delay associated with Fig. 1 MARYLAND synchronization which introduce one -quantization-interval glitches (+0.1 sec) in one tape relative to the other. These irregularities are not present when all data are written on one tape.  1 includes all data for the periods listed which could be read by the computer. The excess of coincidences at zero delay varied between 12 and 40 per 4-day tape.
After these experiments were completed the telephone line was disconnected altogether and the zero-delay excess of coincidences remained. The use of isolated recorders with no telephone connection does not guarantee the validity of these results. We can imagine defective recorders which write spurious signals on tape at certain times, for example, at the beginning or end of a data block. Since these operations are controlled by synchronized clocks additional coincidences could be generated. For the experiments reported here the data were carefully searched for such effects. None were found. Furthermore, the telephone line enabled us to carry out a parallel experiment utilizing an on-line computer to record coincidences with and without a 4-sec delay. Results were consistent with Fig. 1.
Effect of thxesholds on coincidence rates. -A 4day tape with data giving a zero-delay coincidence excess of 40 was processed with a series of threshold crossing rates varying from one per minute to 11 per minute. At 2 crossings per minute the zero-delay excess is 30 and approximately equal to the accidentals. The zero-delay excess increases linearly to about 120 at 7 crossings per minute. The accidentals rate increases quadratically to about 480 at 7 crossings per minute. Beyond 8 crossings per minute the zerodelay excess decreases. The ratio of zero-delay excess to the accidentals can be increased if pulse heights are measured and a classification scheme for the coincidences employed following earlier work. ' Detectors and their sensitivity. ='The gravitational radiation detectors are the same aluminum cylinders described in earlier experiments. The equlpartltlon theorem predicts that the Brownian motion of the cylinder will give a noise current with mean squared value (Is ) = k T/L, . (2) We may measure N(v) in the following way. A calibrated noise generator is arranged to be a current source with power spectral density i ' v nẼ xtreme care is required to insure that connecting the noise generator does not degrade the noise performace. Let Z(v) be the impedance at terminals XX of Fig. 2(a). With noise generator turned on we observe increased power P' with p +dpi2 (1) The output power P will consist of three parts: The approximately square-law devices employed are those of earlier experiments. A 1. 6-Hz bandwidth is obtained by a two-stage Butterworth filter on the phase-sensitive detector. It has 12-dB rolloff per octave (0.8 Hz). The amplifier has a bandwidth of 12 Hz, centered at the cylinder mode frequency 1661 Hz. The differentiator is a resistance-capacitance filter. The noise performance and sensitivity are determined in the following way. Direct measurements and theory show that, in the viei ty Everything is known in (2) and (3) except N(v) which is, therefore, determined by observation of P and P' and a knowledge of Z'(v) and i"'(v). We observed that for bandwidth 6 v = 1.6 Hz, the ratio kT/4m'v"'L, g ' Equation (4) determines the sensitivity. ' This value was confirmed by a detailed study of the power spectrum making use of a very narrow band tunable filter, and by autocorrelation analysis of tape recordings of the output of a linear demodulator.
We can also calibrate by applying an electrostatic force to a plate close to one end of the cylinder. Pulses are applied at 830 Hz, since the force varies as the square of the field W k e now that the driving oscillator and associated circuits do not generate significant Fourier components within the amplifier pass band, since we observed no response from a 1.6-Hz band filter 78i detuned from the cylinder mode frequency. If the initial velocity is zero, the energy U gained by the cylinder after time I. is U= &o'8 S f /64M, where~, is the permittivity of free space, E is the peak value of the electric field, Ii s the cylinder mass, and S is the area of the plate. All calibration pulses referred to in the following discussion are the zero initial velocity values de-fined by (6).
The squared derivative of the power will vary over a wide range for calibration pulses of a given magnitude depending on phase relations between the added velocity and initial velocity associated with the Brownian motion. Thus a very small calibration pulse kT/60 may be seen as in Fig. 3 to appear in the output as a large squared derivative of power signal.
The following table summarizes our observations: of the noise performance of one of the gravitational radiation detectors, or additional noise introduced as a result of changes in computer program. These will increase the accidentals rate and leave such a small excess at zero delay that it vanishes in the fluctuations. For a period of about a month additional noise was inadvertently introduced in the following way.
A demodulator is employed to obtain the envelope of the amplified cylinder oscillations. There are two channels needed in consequence of the fact that the phase of the cylinder oscillations is a random variable. One channel is synchronously switched by a quartz oscillator tuned to the detector cylinder frequency. A second channel is switched by the same quartz oscillator with a phase shift of &m. To obtain the total power the two channel outputs are squared and summed.
It is desirable to record both channels separately on magnetic tape and prepare a computer program to search for changes in both amplitude and phase of the detector output. Study showed that the use of 64 quantization intervals for each channel introduced a large quantization error because one channel or the other frequently had small values of voltage, resulting in a large percentage error. Use of the computer to square and sum to give the power produced an unacceptable amount of noise, which was absent when the power was obtained by squaring and summing in an analog device without quantization. Figure 2(c) shows the power output of the analog device and Fig. 2(b) shows the additional noise obtained by squaring and summing the 64 interval quantized components of a test signal, with a computer.
The new experiment now is yielding about seven coincidences per day, corresponding to increases in energy exceeding hT/100. We are pleased to acknowledge valuable discussions with During recent years there has been an increasing interest in the importance of spin in high-energy strong interactions. This has come from the very successful experiments using polarized proton targets at Lawrence Berkeley Laboratory, ' CERN, ' and Argonne National Laboratory' (ANL).
For the past few years our group has worked together with the accelerator division at ANL on a project to accelerate polarized protons at the zero-gradient synchrotron (ZGS). A beam of 3x10' polarized protons has now been accelerated up to 6 GeV/c, with a polarization of (62 +15Pq. The polarized protons originate in a polarized ion source' which gives 8 p, A of 20-keV protons with a polarization of (75 +7Po. This source was placed in the new preaccelerator constructed by the ZGS staff' which accelerates the protons to 750 keg in a Cockcroft-%alton accelerating column. The protons are then fed into the main LIN-AC line by a switching magnet and then acceler-ated to 50 MeV by the LINAC. The polarization at 50 MeV is measured using a "polarimeter" which continuously measures the left-right asymmetry in proton-carbon elastic scattering at 60', where the measured asymmetry parameter is (85+ 7P~. ' We found the 50-MeV beam polarization to be (65+ 5)%. The polarized protons are then injected into the ZGS, accelerated, and then extracted and sent to the high-energy polarimeter, described below, where the polarization is measured.
The main problem in accelerating polarized protons in a synchrotron is "depolarizing resonances. "" These occur when the Larmor precessional frequency becomes equal to an integer multiple of the betatron oscillation frequency, so that the proton gets a similar perturbation each time it passes through a fringe field or imperfection with a horizontal component. These perturbations then add coherently and can rapidly de-