--SRC Index


Ratios to 3He

In mid-september, there was a lot of work done to try and nail down the final A/3He ratios. I'll skip most of it and summarize where we are now. Note: for all this, we're using raw, finely binned cross sections (no rebinning).


Our issues

For cross sections with error bars greater than 25%, this is not a good way to get the errorbars:
error=ratio*sqrt[(err_A/sigma_A)**2+(err_3He/sigma_3He)**2]
Instead, we shift the 3He cross section up/down by 1 sigma and recalculate the ratio, and use those two (ratio_max, and ratio_min) to give us the error in the ratio. Unfortunately, it's asymmetric. Therefore, extracting a value for the ratio for x>2.4 (or some other threshold) is not straight-forward since some points have symmetric error bars and others don't.

Instead, John suggested we deal with ratios of 3He/A, where the denominator doesn't go to zero as fast, and its errorbars are usually manageable. Here, we work with symmetric errorbars until we extract the final ratio in a given x-range, then invert it to get the A/3He ratio and calculate the asymmetric errorbars for that final number.

Option 1

Take the ratio of integrated cross sections. So, add up all the 3He and A cross sections for xmin< x < xmax and take the ratio. So that ratio=sum(sigma_3He)/sum(sigma_A).

18 ... 4 ... 0.279941 +/- 0.0388449
18 ... 9 ... 0.177657 +/- 0.0242408
18 ... 12 ... 0.120225 +/- 0.0163779
18 ... 63 ... 0.0937415 +/- 0.0127339
18 ... 197 ... 0.0835292 +/- 0.0113302


Option 2

In this case, we take all the 3He/A ratios in a given x-range and perform an error-weighted average [Sum(r/err**2)/Sum(1/err**2)]

18 ... 4 ....... 0.283154 +/- 0.0384222
18 ... 9 ....... 0.17198 +/- 0.0241541
18 ... 12 ..... 0.104401 +/- 0.016072
18 ... 63 ..... 0.0817404 +/- 0.0126605
18 ... 197 ... 0.0692293 +/- 0.0110757

Decision time

While close, the two methods do not yield the same answer. And the disparity grows as one goes to heavier nuclei. In the end, there can be only one.