Teorías sobre la Inversión Extranjera Directa

To confirm that the HPGe crystal detector, coolant system, and pre-amplifier was working as expected and to the manufacturer’s calibration, a series of tests were conducted. The baseline confirmation tests were conducted using spectroscopic equipment used by the Department of Nuclear Physics at ANU that are frequently used for similar measurements and are well characterised.

The intent of the DBAR experiment is to measure the Doppler broadening of the positron annihilation photopeak, the effective measure of detector performance is the resolution at the 511keV region. The resolution can be determined by characterising the detector using well know emissions from radioactive isotopes and plotting the full-width at half-maximum as a function of photon emission energy — a standard method of detector characterisation used in spectroscopy.

The radioactive isotopes used to generate calibration spectra have energy variations which are vanishingly small in comparison to the resolution of the detector and therefore any broadening of emission lines can be attributed to the detector resolution alone.

4.4.1 Manufacturer’s Calibration

The cGe crystal has been calibrated by the manufacturer with radioisotopes 57_{Co and} 60_{Co, giving full-width at half-maximum (effective resolution) value. The measurements}

of the emission lines of these isotopes was performed using a spectroscopic amplifier with a shaping time of 4µs.

Isotope Energy (keV) fwhm_(keV)

57_{Co 122 0.976}

60_{Co 1332 1.794}

Calculated 511 1.24

Using a simple linear interpolation between the two stated resolutions from the manu- facturer (shown in table4.1), the estimated FWHM at 511keV is 1.24keV. This calibration is the reference with which to compare the various experimental methods outlined in this chapter.

The estimated efficiency for the Ge detector has been interpreted from the literature provided with the experimental equipment when purchased from Canberra, which has been reproduced and shown in figure 4.1.

0 200 400 600 800 1000 1200 1400 Energy (keV) 0 1 2 3 4 5 6 E ffi ci en cy (ar b . u n it s)

Figure 4.1: Typical absolute efficiency curve for coaxial Ge detector, with 10% relative efficiency and a 2.5cm source to end-cap spacing. Data estimated and interpreted from printed material “Germanium Detectors: User’s Manual”, provided by Canberra with detector purchase.

4.4.2 Experimental Set-up

The initial resolution benchmark experiment was set up using the following equipment, borrowed from the Department of Nuclear Physics. The equipment has previously been verified in similar applications, providing a consistent experimental set-up with which to benchmark the HPGe crystal.

The experimental configuration was the HPGe detector with CP5+ cooling system and built in Canberra 2002C pre-amplifier connected by shielded BNC cable to an Ortec 855 Dual Channel Spectroscopic Amplifier. The ouput of the amplifier was directed to a Pocket MCA 8000A multi-channel analyser [72] and the associated ADMCA software

was used for spectra collection [73]. The HPGe detector was cooled down over a 12 hour period before the high voltage bias supply connected to the pre-amplifier and any bias applied. The pre-amplifier was configured at a pre-set output gain of 100mV per MeV, and the output pulses were shaped and amplified by the Ortec 855 spectroscopic amplifier with a shaping time of 3µs. The bias on the high voltage supply at the pre-amplifier was set to the manufacturer recommended value of 4.2kV.

The radioactive source used for calibration was a “check source” of 152_{Eu, with well}

known spectra detailed in reference [74]. The source was placed approximately 10cm away from the detector end cap. Figure 4.2 shows the resulting spectrum of 152_{Eu that was}

collected under the specified conditions.

0 200 400 600 800 1000 1200 1400 1600

Energy (keV)

C

ou

n

ts

(a

rb

.

u

n

it

s)

Figure 4.2: Results of the calibration; the spectrum of 152_Eu

4.4.3 Calibrated results

The spectrum of152_{Eu as shown in figure4.2was accumulated for approximately 14×10}6

counts in total. The x-scale was calibrated using the well known peak positions for the most probable photon emissions in 152_{Eu [74]. The x-scale was then fit with a quadratic}

function to calibrate from bins to energy, in the form of equation (4.1):

A+Bx+Cx2 _(4.1)

parameters for the calibration, shown in equation (4.2).

A= 4.77758, B = 0.260488, C = 1.07727_×10−7 _(4.2)

Following the x-scale calibration, to measure the resolution of the system, the full- width at half-maximum of the calibration peaks was measured, with the results presented in table4.2:

Peak Position FWHM _{(keV) Uncertainty (keV)}

121.88 1.1504 0.15 244.86 1.1643 0.44 344.72 1.2431 0.17 778.16 1.5582 0.32 963.90 1.6657 0.3 1111.62 1.7379 0.33 1408.013 1.9185 0.23

Table 4.2: Calibration results

4.4.4 Conclusion

The calculated resolution at 511keV for this experimental benchmark is 1.37keV, interpo- lated from the results in table 4.2. Compared to the manufacturer’s supplied calibration and calculated resolution at 511keV of 1.24keV, the HPGe detector system is functioning as expected with the apparatus used in the benchmark measurement. The difference in resolution between this measurement and the manufacturer’s calibration is expected as the manufacturer’s calibration was performed using a spectroscopic amplifier shaping time of 4µs, which will result in a higher resolution.

The benchmark measurement performed confirms that the detector is performing as expected and will suitable to be used as part of the DBAR measurement.