HPGe Analysis

General Overview
This pages is intended as a guide to help users to analyse data from the HPGe array at TAMU.

Peak Fitting
Ge spectrum, especially at high energy region (> 1 MeV), tends to have low-energy tail due to incomplete charge collection, etc. To handle this, skewed Gaussian fitting is recommended, which includes three components: 1) a Gaussian, 2) a skewed Gaussian, 3) a smoothed step (and polynomial) function for background (simply speaking, just a background). Typically contribution of 2) and 3) are small. For example, in Radware software, the contribution of 2) is suggested to set to 10%. For details, refer to http://radware.phy.ornl.gov/gf3/gf3.html (and see Fig. 1 in the website).

Doppler Correction
Formula, method used, new resolutions

Add-Back
method, type of add back, new efficiencies

Natural Background Subtraction
So far no certain way to evaluate the contribution in Ge spectrum from natural background has been established yet. Typical natural background gamma-rays are 1460.8 keV (40K->40Ar beta+decay), 1764.5 keV (214Bi->214Po beta(-) decay), 2614.5 keV (208Tl->208Pb beta(-) decay. *Some references identify the peak as 232Th maybe because this decays down to 208Tl via alpha and beta- decays?). We can normalize data from actual experiments to some of these peaks.

Other
(defective cores, segments.. etc..) Ge 2's right segment is currently not working (no signal).

Calibration
calibration coeff file, resolutions etc..

Available Sources
We can borrow following sources from Lawrence Livermore Lab group. Ones manufactured in 2015/1/1 with the original activity of about 37 kBq (more accurate activity values are provided in Curie by vendor).

- 152Eu (cover wide energy range of 121 - 1408 keV)

- 60Co (1173 and 1332 keV; useful for efficiency measurement (see below))

- 57Co (14, 122, 136 keV; note very short halflife (271 days), might be low activity)

- 132Cs (662 keV)

- 54Mn (834 keV; note very short halflife (312 days))

- 109Cd (88 keV; note short halflife (462 days))

- 133Ba (80, 276, 302, 356 keV)

- 22Na (511, 1274 keV)

Same sources manufactured in 2012/5/1 are available with the same original activity.

Additionally as a high energy gamma source,

- 241Am(9Be) (4438.91 keV)

is available through alpha + 9Be -> 12C* + n. However, due to long lifetime of the excited state (50 ns?), the doppler shift occurs and cause a broad distribution (1% or more), therefore this may not necessarily be a good source.

Tips in measuring the gamma sources
Most sources above still have a high radioactivity, which can be pros and cons. Pro is high statistics (small statistical error) and con is too large dead time (>90% sometimes), which causes a difficulty in determining detector's efficiency. To avoid this difficulty, one technique using 60Co is available (see below). One tip in this measurement is that you have to perform a long time run to obtain high statistics in coincidence gammas (see below for details). The other tip is use short half-life sources (e.g.,54Mn, 57Co, 109Cd) made in 2012/5/1 in determining efficiency, which gives low activity and less dead time. However, you may need a long run (1 day or more?), and more than that, still dead time could be larger than acceptable (remember TIARA DAQ's dead time is around 600 us, which means you are recommended to keep the CFD trigger count rate < 1000 Hz).

Efficiency curve
The absolute efficiency curve can be fitted with the following function:

eff_abs (E) = exp (((A + B * ln(E/100) + C * (ln(E/100))^2)^(-G) + (D + E * ln(E/1000) + F * (ln(E/1000))^2)^(-G))^(-1/G))

where E is energy of gamma-rays in keV. The first term including A,B, and C describes low energy part (< 100 keV) and the second term including D,E,and F describes high energy part (> 100 keV). Note, if we just use the high energy part (which is not unrealistic), the efficiency function simply turns into

eff_abs (E) = exp ((D + E * ln(E/1000) + F * (ln(E/1000))^2),

which is the same function as the one used in S. Brown's ph.D thesis. If your data do not include low energy gammas (<100 keV), this is much easier in fitting because there are few low energy gamma sources available (133Ba), which makes it difficult to obtain a good fitting using the equation on the top. One tip is, when you use Radware's effit code to obtain the efficiency curve, I suggest you to use it only when you have enough low energy source data, otherwise the fitting function doesn't work well in high energy side.

Angular Correlation (Simulation)
A simple Monte-Carlo simulation of two consecutive events hitting the wall of a rectangular box was made to estimate The number of correlated gammas in the cascade of Co-60. The source is placed in the centre at (0,0,0) an the events are simply The intersection between the 3D-line of the events and the plane of the detector. The sides of the box represents the planes of detectors and are placed at different positions perpendicular to the Cartesian axes: Figure 1 shows one such scenario taking into account the full clover detector (clover add-back scheme). Figure 2 shows another scenario taking into account only one core (singles). First particle A is generated and then particle B is generated with respect to A following this law of correlation: W(\theta) = 1 +  A22*L2  +  A44*L4; Where,
 * Detector 1 at x = (50+10.5) mm
 * Detector 2 at y = (50+15.3) mm
 * Detector 3 at x = -(50+6.3) mm
 * Detector 4 at y = -(50+11.5) mm
 * A22 = 0.1005
 * A44 = 0.0094
 * L2 = (1/2)*( 3*cos(\theta)^2 - 1 );   // Legendre polynomial order 2
 * L4 = (1/8)*( 35*cos(\theta)^4 - 30*cos(\theta)^2 + 3 ); // Legendre polynomial order 4

The detector shape is described accurately on the surface of every plane. No other efficiency other than geometrical (such as detection efficiency depending on energy) are taken into account The table below shows the correlation, for 10000000 events emitted.

Note that the numbers below are needed to correct for the angular correlation and final intrinsic efficiency.


 * A in Clover 1 = 1.04039e+06


 * A in Clover 2 = 932421


 * A in Clover 3 = 1.14775e+06


 * A in Clover 4 = 1.01684e+06


 * B in Clover 1 = 1.04062e+06


 * B in Clover 2 = 932696


 * B in Clover 3 = 1.14724e+06


 * B in Clover 4 = 1.01729e+06

For instance, in the table above, "While B in Clover 1" (the number of these events are 1.04062e+06 out of 1e7 source particles as above), A in Clover 2 = 94608.

Efficiency measurement at 1173, 1332 keV using 60Co
60Co (G.S. Jp=5+) decays into 60Ni with Q_beta = 2.822 MeV. Naturally, the decay goes to 2505.7 MeV (4+) in 60Ni and almost 100% decays to G.S. (0+) by emitting two E2 gamma radiations of 1173.2 and 1332.5 MeV via 1332.5 MeV (2+) level. These two gammas can be used for determining gamma-ray detection efficiency of detectors. Take the two gammas coincidence events in two different Ge clovers (e.g., Clover 1 and 2) and then determine the event ratio of one gamma (say 1173 keV) in coincidence to the other (1332 keV) in singles (i.e., no coincidence required), by which we can estimate the detector's absolute efficiency (eff_abs) without knowing absolute values of source activity and DAQ's dead time.

Below is the formulation of this method. Note, to use this method, we need the values obtained by simulation above (particle A is 1173 keV gamma and B is 1332 keV gamma now in this case).

Now N0 is the source activity of 60Co (or activity of decay branch via 2505keV->1332keV->GS. This case both are same since the decay branch is almost 100%) during the measurement. N1: 1332 keV gammas detected on a Ge Clover (say CL1). N12: 1173 keV detected on CL2 (or 3 or 4, whatever) in coincidence with the 1332 keV gamma. Dimension of time (i.e., measuring time) is not included below because it is not necessary as long as we perform this measurement at one single run (i.e., measurement period of time is same).

N1 = N0 * (Omega_1 / 4pi) * eff_int1 (1332 keV),

where Omega_1 is a solid angle contended with CL1 and eff_int1 (1332) is intrinsic efficiency of CL1 for 1332 keV gamma (i.e., efficiency without geometrical efficiency). Note, by Omega_1 / 4pi, it means the fraction of solid angle, and we can call it P1 for now. Just remember the relationship that absolute efficiency: eff_abs1 (1332) is obtained by P1 * eff_int1 (1332).

N12 = N1 * (Omega_2 / 4pi) * W(theta,Jpi) * eff_int2 (1173 keV),

where Omega_2 is a solid angle contended with CL2. W(theta,Jpi) is angular correlation - the theta is angle with respect to the 1332 keV gamma, so roughly the theta is now 90 degree (180 deg for CL3). eff_int2 is intrinsic efficiency of CL2. Since the complicated angular correlation part (i.e., (Omega_2 / 4pi) * W(theta,Jpi); note this should be more complicated than this expression) is already calculated by the above simulation, we can just call this part P12 for now.

Now obviously,

N12 / N1 = P12 * eff_int2 (1173 keV).

If we measure N12 / N1 experimentally, by combining with P12 given by the above simulation, we can get eff_int2 (1173 keV). From the simulation, P12 is, in this case, 94608 / 1040620 = 0.0909, where 94608 is taken from the above table (cross of While B in Clover 1 and While A in Clover 2) and 1040620 is from "B in Clover 1" above.

So,

eff_int2 (1173) = (N12 / N1) / P12.

Again, this is intrinsic efficiency. To obtain absolute efficiency (which is more useful in actual data analysis),

eff_abs2 (1173) = eff_int2 (1173) * P2 (geometrical fraction covered by CL2).

P2 is in this case, 932421 / 1e7, where 1e7 is total source activity in the simulation.

eff_abs2 (1332) is simply,

eff_abs2 (1332) = k * eff_int2 (1173),

where the coefficient k can be deduced by comparing the number of detected singles 1332 and 1173 keV gammas in CL2 (empirically, k= 0.95~0.98).

Do the same measurements for all the combination of CL1 (1332) and CL3 (1173), CL1 and CL4, CL2 and CL1, CL2 and CL3, CL2 and CL4, CL3 and CL1,..... etc. Each clover will get 3 values by coincidence with 3 different clovers, which will allow you to estimate the uncertainty of this measurement method. Since the uncertainty dominantly comes from the ones in measuring N12 experimentally (because these coincidence events are generally not detected well), it is recommended to take a long run for this measurement (say 12-24 hrs using our 37 KBq source to obtain N12 ~ 10,000 events).

Also note, this technique should be available for other coincident gammas as well (see the case of 22Na's two 511 keV gammas below).

Efficiency measurement at 511 keV using 22Na
22Na beta+ decay into 22Ne, which emit 1274 keV gamma-ray typically with two 511 keV gamma-rays (by anihilation). The two 511 keV gammas are emitted in 180 degree with respect to each other. Unlike 60Co gammas, therefore, only clovers facing each other (i.e., CL1 and CL3, CL2 and CL4) can detect the gammas in coincidence. First, gate on 511 keV gamma in a clover (say, CL1) and count the number of the gammas (N1). Next, see the coincident 511 keV gamma in the counterpart clover (CL3) and count the number of gammas (N12).

Due to the characteristic angular correlation, we can consider all the gammas in coincidence with CL1 are hitting the CL3 (and no gammas hit CL2 and 4 and anywhere else. Therefore,

eff_int2 (511) ~ N12 / N1

Note, this is still approximation because it is not 100% sure that the facing clovers are entirely symmetrical around the source. So there is very slight possibility you still miss some gammas in CL3 that coincide with CL1. But let's assume these are negligible (or you can do simulation using the real detectors geometry).

Now, the absolute efficiency of Clover 2 at 511 keV (eff_abs2) is

eff_abs2 (511) = P2 * eff_int2 (511)

where P2 is geometrical fraction covered by CL2. From the above simulation, P2 is 932421 / 1e7 = 0.0932.