Pin source calibration of HiRA telescopes
HiRA
High Resolution Array (HiRA), which consists of twenty identical detector telescopes ,Fig1, is capable of detecting charged particles with isotope resolutions for Z=1-8. It allows precise measurement of energy, charges and masses of various charged particle species with high angular resolution.
There are two silicon detectors in each telescope,Fig.2. The DE detector is a 65μm single-sided silicon detector for measurement of energy loss of the particle passing through it. The E detector is a 1.5mm double-sided silicon detector. The font side (EF) is divided into 32 vertical strips and the back side (EB) is divided into 32 horizontal strips. There are totally 1024 pixels (2mm x 2mm) for position determination.
If the array is set up at 35cm from the reaction target, the angular resolution achieved is +/-0.16degree.
Calibration of HiRA silicon detectors
Before the mounting of the telescopes, both silicon detectors are calibrated with the 228Th source, which is commercially available with well know alpha particles decay energies. The E detector is completely covered by the DE detector after mounting and the alpha particles cannot penetrate through the DE detector. Therefore, 228Th source calibration cannot be used for E detector after mounting. However, the mounting process may disturb the electronic system which makes the previous calibration no longer valid. Moreover, the stability of electronic system over time or after being disturbed is not guaranteed. Re-calibration for experiment running over a long time is needed. Pin source calibration is thus developed to calibrate the E detector to avoid the mounting and dismounting process, which may also damage the detectors.
Pin source
The pin is a 0.5 inchlong dowel pin. It is activated by electroplating the tip with daughternuclei from a 228Th source which can be generated in 24 hours or less. Theinactivated side of the pin is then glued onto the frame as shown in Fig.3 and put in between the DE and E detectors through a slot. The primary deposition on the pin is 212Pb isotope whichhas a half-life of 10.6 hours and provides strong energy peak at 8.785MeV and around 6.062MeV(6.050MeV(72%) and 6.089MeV(28%)). The energy spectrum is shown in Fig.4
1st calibration
The hit-pattern of the pin source on the E detector is as shown in Fig.5.Compared with the 1.95mm width of each strip, the pin source is close to the detector, around 2.72mm,therefore, the alpha particles hit the strips at very different angles and their energy loss in dead-layer is different. The difference in energy loss diminishes the energy resolution. Withenough data from reactions with the beam, the calibration of different strips in the E detector can be done by using only thepixel directly in front of the pin source, thus avoiding problem withdifference in dead-layer.
Given the nature of double-sided silicon detectors it is possible to calibrateall strips if one can accurately calibrate one single strip on the EFor on the EB. For example, suppose strips EF-17 and EB-16 are the strips closest to the pin source.
Requiring the events with only one coincident hit on both strips, it effectively selects alpha particles that hit the pixel, 17-16. This pixel should have the smallest incident angle giving the most accurate energy measurement. With the energy spectrum from one the strip, e.g. EF-17, gated on this pixel,16-16,and considering the energy of the peaks be 6.062 MeV and 8.785 MeV, the two peaks are fitted and a linear calibration is done for that strip.
For a particle detected by a pixel, the electronic channel of the EF and EB strip of that pixel should corresponds to the same energy. For strip EB-X, considering the events in the pixel, 17-X, as the energy is known from strip EF-17, a linear calibration can be done for strip EB-X. Therefore, all the EB strips can be calibrated with reference to a EF strip. Similarly, all the EF strips can be calibrated with reference to aEB strip.
If the pin source is a perfect point source, the pixel in front of the pin tip can be determined by finding the pixel of the highest counts because it has the largest solid angle from the tip, which is the main contaminated position, and thus should have the highest intensity.In practice, there are other weaker contaminated points on the pin body and the tip of the pin is not a perfect point source. The pixel with the highest counts (Pmax) may not be the pixel in front of the pin tip. However, it should be at most a slightly off for 1 pixel because the pin tip is very small and other contaminated points are much weaker. To make sure the pixel is the one closest to the pin, energies of different pixel across the EF and EB strips of Pmax are found, the pixel with the highest energy should be the one closest to the pin.
Dead-layer thickness and 2nd calibration
In the previous calibration the energy loss in the dead-layer is ignored, which leads to a systematic error in the calibration. A linear correction should be done with consideration of the dead-layer.
The dead-layer thickness (DL) can be determined by the 1st calibration.
Assume the dead-layer is even and the pin source is a point source
Consider Fig.6a
The energy of alpha particles (E) passing through the dead-layer is calculated by
whereEpin is the energy of the alpha particles of the pin source
is the stopping power of the dead-layer
DL is the thickness of the dead-layer that alpha particles pass through because of different entrance angles.
As the dead-layer is very thin in the silicon detector, the difference in energy loss of alpha particles with different energy is small. The correction factor A should be close to 1. The stopping power of an alpha particle is considered to be constant.
With the above relations and energy detected with 1st calibration across a line, DL can be determined by fitting the equation””with the energies and positions of corresponding pixels.
The energies from the strip in front of the pin tip and perpendicular to the pin are chose for fitting. It reduces the fitting equation from 3 dimensions to 2 dimensions and avoids the error from the difference in calibration of different strips and the problem of weak contaminated points in the pin body.
Consider Fig.6b
where C1 , C2 and C3 are the fitting parameters
C1 is the pin source energy in unit of 1st calibration
C2 is stopping power multiplied by dead-layer thickness in unit of 1st
calibration
C3 is the position of the pin in terms of strip
k is the conversion factor for to be in unit of strip width.
As the strip width and the distance of the pin from the detector are known, k =0.527.
Suppose the strip in front of pin tip and perpendicular to the pin is EF-17 and
at the centre of EB-0.
Consider the 8.785 MeV alpha particles.
From the energy spectrums of each pixel of strip EF-17, the corresponding energies of each pixel are found. C2 is found through fitting.
As A is close to 1 and is constant, consider energy difference of alpha particles penetrate the dead-layer perpendicularly and those penetrate at 60∘with equation “energy”.
Therefore, DL can be found by LISE++.
After DL is found, the energy loss of the alpha particles through dead-layer can be calculated and thus the systematic error is eliminate by adjusting the calibration energy of 1st calibration of the reference strip.
To have a more accurate value of dead-layer thickness and estimate the error from fitting in energy spectrum and fitting of the energy equation, the same fitting is done with the 6.062 MeV alpha particles.
DL(8.785 MeV) has more weight since the 6.062 MeV peak, which consists of 6.051 and 6.090 alpha particles, is less accurate. As the dead-layer thickness should be the same from both fitting, by comparing the difference in dead-layer thickness, the percentage error of fitting is estimated by
Considering the maximum value of |A-1| and Errfit, the maximum error of dead-layer thickness is calculated.
Data analysis
Pin source calibration and the 228Th source calibrations taken in experiments 06035 and 07037 (May & June, 2010). The E detectors were first calibrated with 228Th source before the DE detectors were mounted (May 4th and 5th, 2010).The DE detectors were mounted and calibrated (May 11th, 2010) .Data were taken during May and June in 2010.At the end of the experiment , pin source calibrations were done (June 16th & 17th, 2010)
The first rough calibration is done by 228Th source, whose alpha particles have to pass through the gold window of the source, mylar foil covering the detector and also the dead-layer of the detector. However, the energies used for calibration for the 5 peaks of 228Th source are 8.80, 6.80, 6.31, 5.70 and 5.44 which are higher than the real energies. The decay chain is shown in Fig7. Therefore, the correction term B is large but A is still expected to close to 1 since the difference in energy loss of the alpha particles in different layer is small. The result shows that |A-1|<0.05 for all the telescopes except a few with other problems.
Take telescope 13 as an example.
The strip in front of pin tip and perpendicular to the pin is EF-18. The energies of each pixels of EF-18 were found by Gaussian Fit of the energy spectrum as shown in Fig 8. And then the equation was fitted with Mathematica. The result is shown in Fig 9. With the value of C2, the energy loss of alpha particles was known and the dead-layer thickness of the telescope was calculated by LISE++. The energy loss and the dead-layer thickness of all the telescopes are shown in Fig. 10 and 11 respectively. The error in the dead-layer thickness figure is calculated by the maximum of the percentage error of dead-layer thickness with the equationand assuming 5% error
in A.
Electronic problems
As the energies of alpha particles from the 228Th after passing through the gold window of the source, mylar foil covering the detector and also the dead-layer (0.5μm) of the detector are calculated to be 8.584MeV, 6.539MeV, 6.036 MeV,5.417 MeV and 5.146 MeV, the 1st calibration is corrected.
However, it shows that there are electronic problems.
Consider fig.12,
The blue points are the maximum energy of the strip in front of pin tip and perpendicular to the pin from the fitting of every telescope, which are the energies of 8.785MeV alpha particles passing through the dead-layer of each telescope perpendicularly. The red line shows the expected value of that energy for 0.5μm dead-layer. Therefore, there are some changes during the period between two calibrations.
Telescopes 10, 11, 16, 17 and 19 are found that their electronic configuration was changed during that period. For the rest of them, a systematic shift of energy for around 70keV is observed but there is not a proper explanation. And it shows that re-calibration with procedures as described in 1st calibration of pin source should be done for the telescopes with consideration of dead-layer.
Conclusion
A pin source is relatively easy to make and convenient to use. It provides accurate calibrations to the E Si detectors placed behind a thin DE detector with minimum disturbance to the mechanical and electronic setup in nuclear physics experiments.
By placing a pin source close (~2.7 mm) to a two sided 2mm pitch Si strip detector, the dead-layer thickness of the Si detector is determined to be about 0.5+0.10 μm.
In the example we studied, the pin source was used to both check and correct the initial calibrations of the HiRA detectors. This is particular useful in experiments that run for a long time.