696 Chapter 12. Radiation Spectroscopy
∆N
∆E
Eα
N 0
∆N
∆E
*
*
*
*
*
*
C=
N(MCA−bin)Figure 12.2.3: Typical calibration curve
obtained from a known source and an
pulser. The pulser helps in determining
the overall system linearity and the off-
set.Step-5:The MCA channel corresponding to the peak is identified. The peak
is generally symmetric but has a finite width due to statistical fluctuations of
various processes involved in the detection. The centroid of the peak is taken
to represent the expected energy of the particles.
Step-6:Next, the pulser is calibrated against this peak to determine the lin-
earity of the system and the offset. If the system is linear then the energy of
theα-particles will be related to the MCA channel numberNby
Eα=C(N−N 0 ), (12.2.1)whereC is the calibration factor in units of energy per channel (such as
MeV /MCA-bin). N 0 is the channel offset. Ideally there should not by any
offset, that is, zero energy should correspond to the zeroth channel. In prac-
tice, however, this is rarely seen and therefore it is always recommended to use
a pulser to determine the offset.
Before connecting the pulser to the preamplifier, the source should be taken
out of the container. The pulses are injected into the preamplifier and the
signal amplitude is varied until the oscilloscope shows the same pulse height
as in the case of the source. MCA spectrum of the pulser is then accumulated
and it is verified that the pulser peak is at the same channel number as the
source peak. This signal amplitude of the pulser is noted down.
Step-7:The signal amplitude of the pulser is varied in steps such that it spans
the whole expected range of particle energy. For example for a polonium-210
source it could be from 0 to 6MeV. At each step the MCA spectrum is obtained
and the channel number corresponding to the peak is recorded.
Step-8:The channel number is plotted against the energy corresponding to
the pulser’s signal amplitude.
Step-9:A straight line fit on these data points is performed. If there is no
offset, the line should end at the origin of the plot. If not, the offset is one of
the calibration parameters and must be included in any further calculations.
The slope of the straight line gives the required calibration constantCin terms
of energy per channel (see Fig.12.2.3).We mentioned earlier that a pulse generator is not always required to calibrate
the equipment. One can also use two or more sources instead to acquire more data