Results

After collecting all relevant data, the ratios R1, R2, and R3 were calculated for each run. The results are given in Tables 1, 2, and 3 respectively.

Table 1: Elastic monitor counts normalized to Faraday cup reading

Run	E$_{in}$	Pressure	FC4 (epA)	Livetime	Time (s)	Elastics	R1
7191	582.7	4.57	480	0.96	326	1421	702.2
7192	582.7	8.12	425	0.96	518	3726	740.6
7193	582.7	6.22	450	0.94	1160	6285	697.7
7194	582.7	6.21	430	0.92	748	4085	753.7
7202	471.9	5.82	387	0.90	696	4511	713.3
7210	784.2	7.42	350	0.95	2266	6696	740.1
7212	784.2	7.35	305	0.95	692	1758	734.6
7238	774.7	7.96	25	0.99	1150	203	540.4
7239	774.7	7.80	16	0.99	744	91	593.1
7240	774.7	7.80	17	1.00	394	21	242.2
7241	774.7	7.80	14	0.99	876	76	481.8
7242	774.7	7.86	13	0.99	1240	117	559.9
7243	774.7	7.73	15	0.99	1766	195	576.9
7244	774.7	7.77	13	0.99	2902	193	400.8

Table 2: Elastic monitor counts normalized to beta monitor

Run	E$_{in}$	Pressure	Charge Fraction	Livetime	Elastics	$\beta$ Scaler	R2
7191	582.7	4.57	0.34	0.96	61904	89.6M	18.3
7192	582.7	8.12	0.46	0.96	103794	91.8M	22.6
7193	582.7	6.22	0.40	0.94	39818	43.6M	21.0
7194	582.7	6.21	0.45	0.92	58324	68.5M	22.7
7202	471.9	5.82	0.41	0.90	71292	55.2M	22.8
7210	784.2	7.42	0.50	0.95	37058	65.5M	24.8
7212	784.2	7.35	0.47	0.95	16651	29.2M	23.7
7238	774.7	7.96	0.50	0.99	3391	4.92M	26.4
7239	774.7	7.80	0.51	0.99	981	1.42M	27.3
7240	774.7	7.80	0.37	1.00	194	3.57M	15.4
7241	774.7	7.80	0.45	0.99	3608	5.31M	23.6
7242	774.7	7.86	0.53	0.99	2946	4.39M	27.4
7243	774.7	7.73	0.42	0.99	1834	2.77M	21.6
7244	774.7	7.77	0.46	0.99	1201	1.74M	24.8

Table 3: Beta monitor counts normalized to Faraday cup reading

Run	E$_{in}$	FC4 (epA)	Charge Fraction	Time (s)	$\beta$ Scaler	R3
7191*	582.7	480	0.34	326	2.06M	38.5
7192	582.7	425	0.46	518	3.09M	30.7
7193	582.7	450	0.40	1160	7.07M	34.1
7194	582.7	430	0.45	748	4.52M	31.3
7202	471.9	387	0.41	696	3.43M	30.8
7210	784.2	350	0.50	2266	12.0M	30.2
7212*	784.2	305	0.47	692	2.75M	27.7
7238*	774.7	25	0.50	1150	0.27M	18.5
7239*	774.7	16	0.51	744	0.12M	19.4
7240	774.7	17	0.37	394	0.08M	30.6
7241*	774.7	14	0.45	876	0.14M	25.3
7242*	774.7	13	0.53	1240	0.17M	19.8
7243*	774.7	15	0.42	1766	0.32M	29.1
7244*	774.7	13	0.46	2902	0.39M	22.7

* Data had unstable beta monitor readings.

One of the most striking results of this study is the drop in the value of R1 at 774.7 keV/u. Run 7240 has the most abnormally low value of R1, possibly due to a statistical fluctuation in the elastic counts (though this too is unclear). Even if we exclude this run, however, all other runs at the energy show a significant decrease in R1 compared to those at 784.keV/u. There is no evidence of a strong resonance at this energy, so it is unclear what could be causing this anomaly. The beam intensity is fairly low at this energy, though, so the FC4 readings may be approaching the level of noise, making the error quite large.

R3 also had a large uncertainty associated with it. This may be partially a result of unstable beta readings which occurred in eight out of the fourteen runs (our time window was defined by the time in which the elastic monitor counts, not the beta monitor counts, were constant). Of the runs with stable beta readings, one included the anomalous run 7240. Left with only five reliable results, there does not seem to be enough data to make any conclusions about the reliability of R3.

The most constant ratio proved to be R2. Its largest source of deviation appeared to be caused by a scatter in the charge state fraction F. If we assumed a constant F, however, the scatter decreased, and if we omitted the outlier run 7240, R2 showed only a 3.7% variation at 582.7 keV/u, and a 1.9% variation at 774.7 keV/u. A constant value for R2 indicates that while the beam may fluctuate, the counters are stable, and measure the same value to a few percent. As energy increases, however, there appears to be a slight increase in R2, making it uncertain whether this value will be useful as a ``universal constant.''