### We have 32 keV! NaI Detector Characterization, Lab Book 2014_08_13

Summary:
Spent the day characterizing the NaI detector.  The cool bit is that the 32 keV peak from Cs137 is visible in the spectrum.  It was distinguished from the background and the pedestal by subtracting a background spectrum from a spectrum with the source.  With the background subtracted out, the peak was clearly visible.  This is important because while the maximum predicted x-ray energy from the experiment is in the range of 150 keV, the radiation may be over a spectrum that contains lower energies.  The smaller the energy we can detect, the better.

It looks like the detector signal may not be linear with the PMT running at the high gain necessary to resolve the 32 keV peak.  This isn’t entirely unexpected.  Tomorrow lower gain tests will be run to see if the detector is any more linear at lower gains.  Linearity in this case means can the calculated voltage per channel on the detector predict where other peaks in the spectrum are.  For  more on this, read the entire entry, and stay tuned for a separate post on the basics of the detector and the PMT .

If you’re new to the experiment, then scroll to the bottom for all the background..

Background run 9:10 AM.

 Bias 1400 V Gate Wind0ow 0.5 uS Threshold 1.5mV Attenuation 6 dB Data set HBC_0002 Source Background Start Time 9:10 AM Stop Time 9:41 Date 2014_08_13 x-y scope V/div 1, 0.5 Shielded? No Tube/Detector Harshaw B-

Notes:  The QVT display/printer has to be bumped to print the first few channels.  I’m not sure if there’s a data inaccuracy to accompany this behavior or not.  When the start cursor is positioned at 0 and the print start button is pressed, the printer only prints the first four channels.  By advancing the cursor one position at a time you can get the printer to print additional channels.  After about three iterations of this process, the printer prints the rest of the data in the capture range correctly.  In the first ten channels, there is one more channel printed than fits in the range and there appear to be duplicates of the counts for two channels.
Spectrum picture:

Shielded Source Run
 Bias 1400 V Gate Wind0ow 0.5 uS Threshold 1.5mV Attenuation 6 dB Data set HBC_0003 Source Cs 137 Start Time 9:59 AM Stop Time 10:32 AM Date 2014_08_13 x-y scope V/div 1, 0.5 Shielded? Yes Tube Harshaw B-

Notes:  Run HBC_0003 was done with the source taped directly to the center of the detector window.  The plan is to determine the count rate from the detector using this data.
Spectrum picture

Shielded Background Run
 Bias 1400 V Gate Wind0ow 0.5 uS Threshold 1.5mV Attenuation 6 dB Data set HBC_0004 Source Background Start Time 10:42 AM Stop Time Date 2014_08_13 x-y scope V/div 1, 0.5 Shielded? Yes Tube Harshaw B-

Background Picture:

Source Signal minus Background from the previous two runs.

Made a  few rough estimates of the voltage per channel based on the assumption that the first peak shown above is the 32 keV Barium K peak.   The first calculation was done assuming that every channel down to 0 had useful information.  It gave the following results
 channel Count Voltage 80 5633 32000 400 980 9656 662000 675.5102 %error 29722.449 32 value on 662 V/channel 0.071173 377600 662 value on 32 V/channel 0.429607

The second method assumed that all the channels were useless below the pedestal peak of channel 36 and through them out.  The results had less error:

 Assume a pedastal at 36 and recalculate pedestal 36 channel Count Voltage 80 5633 32000 727.2727 980 9656 662000 701.2712 %error 30855.9322 32 value on 662 V/channel 0.035752 686545.455 662 value on 32 V/channel 0.037078

Finally, the last method is probably the most correct one and assumes the channels are linear and the peaks are at the correct locations.  It just constructs V/channel as the slope of a line between the two peaks.

 rise 630000 run 900 V/channel 700 offset -24000 pedestal voltage 25200 Barium K 32000 662 line 662000

Troublsome question of the day
Why does the 32 keV peak have fewer counts than the 622 keV peak with the higher gain setting?  Can this be reproduced?  Keep an eye on this during tomorrow’s low gain linearity test.

The values for the two edges of the Compton plateau were calculated using the last slope and offset determined above.  The equation was

$channel = \dfrac{energy-offset}{V/channel}$

The results indicate that the gain may not be linear at the current settings.
 Compton peak 291.4285714 Compton Plateau 720

The measured channel values were about 311 and 658 respectively.

Background
Hirsch's theory of hole superconductivity proposes a new BCS-compatible model of Cooper pair formation when superconducting materials phase transition from their normal to their superconducting state[1].  One of the experimentally verifiable predictions of his theory is that when a superconductor rapidly transitions, (quenches), back to its normal state, it will emit x-rays, (colloquially referred to here as H-rays because it's Hirsch's theory).

A superconductor can be rapidly transitioned back to its normal state by placing it in a strong magnetic field.  My experiment will look for H-rays emitted by both a Pb and a YBCO superconductor when it is quenched by a strong magnetic field.
This series of articles chronicles both the experimental lab work and the theory work that’s going into completing the experiment.

The lab book entries in this series detail the preparation and execution of this experiment… mostly.  I also have a few theory projects involving special relativity and quantum field theory.  Occasionally, they appear in these pages.

Call for Input
If you have any ideas, questions, or comments, they're very welcome!

References

1.  Hirsch, J. E., “Pair production and ionizing radiation from superconductors”, http://arxiv.org/abs/cond-mat/0508529

### Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

### Lost Phone

We were incredibly lucky to have both been in university settings when our kids were born.  When No. 1 arrived, we were both still grad students.  Not long after No. 2 arrived, (about 10 days to be exact), mom-person defended her dissertation and gained the appellation prependage Dr.

While there are lots of perks attendant to grad school, not the least of them phenomenal health insurance, that’s not the one that’s come to mind for me just now.  The one I’m most grateful for at the moment with respect to our kids was the opportunities for sheer independence.  Most days, we’d meet for lunch on the quad of whatever university we were hanging out at at the time, (physics research requires a bit of travel), to eat lunch.  During those lunches, the kids could crawl, toddle, or jog off into the distance.  There were no roads, and therefore no cars.  And, I realize now with a certain wistful bliss I had no knowledge of at the time, there were also very few people at hand that new what a baby…

### Lab Book 2014_07_10 More NaI Characterization

Summary: Much more plunking around with the NaI detector and sources today.  A Pb shield was built to eliminate cosmic ray muons as well as potassium 40 radiation from the concreted building.  The spectra are much cleaner, but still don't have the count rates or distinctive peaks that are expected.
New to the experiment?  Scroll to the bottom to see background and get caught up.
Lab Book Threshold for the QVT is currently set at -1.49 volts.  Remember to divide this by 100 to get the actual threshold voltage. A new spectrum recording the lines of all three sources, Cs 137, Co 60, and Sr 90, was started at approximately 10:55. Took data for about an hour.
Started the Cs 137 only spectrum at about 11:55 AM

Here’s the no-source background from yesterday
In comparison, here’s the 3 source spectrum from this morning.

The three source spectrum shows peak structure not exhibited by the background alone. I forgot to take scope pictures of the Cs137 run. I do however, have the printout, and…