--SRC Index

Less madness at x>2.9, but not zero madness.

So, one of the big glaring issues was the size of the errorbars in the helium-3 cross sections seen here (last plot on the page).

The errors are constructed in the following way:

err-stat/MC_yield*rad_sigma*cc_cor*unrad_model

where err-stat is the error from the data yield (one plot up in the link, and that doesn't seem to have any strange anomalies), and everything else has the cross section model as the input in some manner.

Since that plot, this is what I have changed, and this impacts MC_yield, as well as rad_sigma (the latter only slighlty):

• --the 4-point x-theta interpolation in MC_yield was going too far back in x if it ran into a 0 (enough bins that it would get a wildly wrong slope for x-->3). This made the most difference as it was an actual mistake.
  
• --In the event of a zero, instead of interpolating the slope between the last 2 non-zero points, we take the last "real" non-zero value and interpolate to 0 at x=3 (by real, I mean, not equivalent to zero, so nothing like 1e-25 or something).
  
• --the 4-point interpolation was changed from a linear one to an exponential one (little change).
  
• --I regenerated the 2-d lookup table used by MC_yield (and also where the rad_model is looked up, but at the central angle) to do twice as many bins in E' as previously (which made almost no visible change here, but it addressed the wiggle issue).

As you can see in the plot below, the points that are affected are x>2.9, and they got better, but I don't think they're "correct", they're just better. For example, the unrad_model correction factor takes a big dive between the alst two points (12%), but it's not noticeable, because the other factors are changing even faster.

Also included is the analogous plot for deuteirum, which as I've mentioned before only has an issue at x=1.98.





Sure, but will this blend?

Let's check out the "new" 3He/A ratios.









Analogous plots of D/A ratios.
Note: I noticed that I only remade the cross sections for the last HMS setting for helium-3, so the plot is empty at low x. Redoing it.








Plateau Values

And now we extract the raw ratio in the plateau region.

Left Column: 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)]

Right Column: 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).

3He/A ratios, 2.5<=x<=2.9

18...4....... 0.282858 +/- 0.0383896 ;...... 0.279853 +/- 0.0388049
18...9....... 0.171882 +/- 0.0241501 ;...... 0.177602 +/- 0.0242152
18...12..... 0.104055 +/- 0.01605 ;.......... 0.120187 +/- 0.0163606
18...63..... 0.0815039 +/- 0.0126408 ;.... 0.0937121 +/- 0.0127204
18...197... 0.0690352 +/- 0.0110643 ;.... 0.083503 +/- 0.0113182

3He/A ratios, 1.4<=x<=1.9

18 ... 4 ...... 0.60191 +/- 0.0025868 ;....... 0.600497 +/- 0.00260542
18 ... 9 ...... 0.553134 +/- 0.00244216 ; ... 0.551894 +/- 0.00245845
18 ... 12..... 0.452585 +/- 0.00206333 ; ... 0.451594 +/- 0.00207639
18 ... 63 .... 0.422023 +/- 0.00193609 ; ... 0.420884 +/- 0.00194513
18 ... 197 .. 0.430087 +/- 0.00200943 ; ... 0.429117 +/- 0.00201801

3He/A ratios, 1.5<=x<=1.9

18 ... 4 ...... 0.586572 +/- 0.0035996 ;..... 0.586209 +/- 0.00362241
18 ... 9 ...... 0.536614 +/- 0.00337483 ; ..... 0.536383 +/- 0.00339618
18 ... 12..... 0.439975 +/- 0.00285449 ; .... 0.439711 +/- 0.00287086
18 ... 63 .... 0.403576 +/- 0.00262532 ; .... 0.402938 +/- 0.002636
18 ... 197 .. 0.407876 +/- 0.00269401 ; .... 0.407187 +/- 0.00270391

D/A ratios, 1.5<=x<=1.9

18... 3 ...... 0.470852 +/- 0.00405132 ; 0.470537 +/- 0.00407722
18... 4 ..... 0.276266 +/- 0.00214995 ; 0.275833 +/- 0.00216066
18... 9 ..... 0.252777 +/- 0.00199745 ; 0.252388 +/- 0.00200747
18... 12 ... 0.207221 +/- 0.0016707 ; 0.206901 +/- 0.00167835
18... 63 ... 0.190045 +/- 0.00153549 ; 0.189597 +/- 0.00153997
18... 197 ... 0.192015 +/- 0.00156732 ; 0.191596 +/- 0.00157145

Then, the wiggles

As part of the investigation into x>2.9 points, we loooked at the MC yield for a fixed x-value as a function of theta and noticed that it got weird near x-->A. It was my belief that there were two things that were conspiring to do this: model going to zero and large x-bins in the lookup table. To get a value out of the Y_MC lookup table (in x,theta), my code picks the 4-nearest neighbors and does an interpolation (or rather 2 of them). They used to be linear, but now they're exponential. When we're near x-->A, one, or more of the 4 lookup points can be zero (before it should be). What we try to do then is instead of interpolating between the nearest neighbors, we go from nearest non-zero neighbors to 0 at x=3. The model goes to zero noticeably before x=3. So, we have to do this "far" interpolation for data in the last several bins (the closer to 3, the larger fraction of the points that's affected). This is what I think I was making the wiggles. The lookup table is uniform in E' and theta, which obviously means the x-bins get bigger and bigger as you go to x-->A. That doesn't help.

To test this, I spent a few days trying to get the old code that makes the lookup table work again (Jlab switched compilers after I graduated and it hasn't worked since then). I made a new lookup table for 3He and deuterium at
18...degrees only, with twice as many points in E'. This took 2 days to run. Note: the cross sections were not really affected by this (I think it averages out), but the wiggles improved: