NaI DETECTOR

CALIBRATION
In this part of the experience we want to calibrate the NaI detector; this inorganic scintillator is one of the most widely applied in gamma-ray spectroscopy not only for the good light output and linearity, but especially for the high Z-values and density leading to the predominance of the photoelectric effect on the Compton and the pair production.
First of all we have calibrated the detector with 22Na and 232Th sources. In image001 (l'ho rifatta moltiplicando l’errore fino a far uscire il chi quadro e con y e x scambiate, ve la incollo sotto) we can see the theoretical energy of the line (from the table of nuclides) versus channel. The data behave rather linearly; by (non metterei questo by) fitting them with the following function:
Ch = p₀ + p₁ * E

We obtain
p₀ = 15.62 ± 36.19 Channel
p₁ = 1.842 ± 0.02279 Channel /Kev

In order to verify the correctness of the fit parameters we have calculated the energies of another source (Radium troviamo anche il numero di isotopo!) and compared them with those provided by tables (http://atom.kaeri.re.kr). Since these values are all below 3% of relative displacement we can suppose (state, not only suppose!) that our detector behaves linearly. The results are reported in image002 (dal mio intervento su blog “NaI linearity”).

SHAPE PULSE AND SHAPING TIME

We now study the shape of the voltage pulse produced at the anode of the PM tube. We have to take into account the decay time of the scintillator and the time constant of the anode circuit. The PM tube anode circuit can be represented with a parallel RC circuit, where C is the capacitance of the anode itself, of the connetting cables and of the circuit connected to the anode and R is the input impedance of this circuit. The shape of the signal is represented by a simple exponential decay; this is possible because the PM tube has a small spread in transit time (this parameter determines the time width of the pulses of electrons reaching the anode, and it’s usually between 100 and 1000 ps, while the decay time of the scintillator is about 230 ns). By considering also the anode time constant we can write the following function:

V=a+b(exp (-(t-t0)/t_RC) –exp (-(t-t0)/T_scint))

In image 003 (da jack)we can see the anodic signal; from the fit we obtain
t_{RC =}
T_{scint =}

The NaI scintillator has another output, the preamplifier, which connect the detector to the pulse processing electronics. The output of this element is the typical pulse generated when the output of a radiation detector is collected, because this element doesn’t provide a pulse shaping; as we can see in image 004 (da jack) the pulses have a long tail compared with their leading edge (in fact they’re called “linear tail pulses”).
As we did with the anodic signal, we can study the preamplified one. From the previous fit function we have:

t_{RC =}
T_{scint =}

As we expected the rise time is rather short (it’s like that of the charge collection) while the decay time is larger (in order to enable the full collection of the charge with different collection times).
The fact that the output of the preamplifier is a linear tail pulse could be a problem in signal processing , because the pulses could “pile up” on the tail of precedent pulses and this overlap may lead to errors in measuring the amplitude. To solve this problem we’ll shape the pulse (with a linear amplifier), which means that the long tails are eliminated without affect (affecting?) the information carried by the maximum amplitude.
In order to keep at minimum the electronic noise we can adjust the shaping time by the following considerations: there are two contributions to the noise, a series noise , due to fluctuations in the current of the input stage (and more important for lower shaping time), and a parallel noise, mainly generated from fluctuations in the input voltage and in the amplifier itself (and more important for higher shaping time). By increasing the shaping time, we’ll reach a minimum in noise (where the two contributions are about equal), so, we study the resolution of the detector versus shaping time (image 005, qualcuno l'aveva messo sul blog? che io non l'ho trovata, se c'è già ditemelo che evito di rifarla) to determine the miles choice for this parameter.

We can see that the behavior of the data is pretty linear, so, for a detector like NaI the shaping time is not an useful method to improve the resolution. For the following measures we choose a shapig time of: non l’ho scritto da nessuna parte sul pc, dovrò andare a prendere il quaderno di lab