Pile-up pulse analysis

To obtain a better understanding of radioactive nuclei, one can study their decay properties, such as decay modes, energy of emitted radiation and half-life. However, some nuclei are much more short-lived than others and have been difficult to study with -now outdated- analogue electronic techniques. Recently, modern digitising electronics, denoted fast sampling ADCs, together with tailor-made algorithms have paved the way for the study of fast decaying nuclei. The development of one of such algorithms and the application of it to experimental data were the main tasks of the thesis.

Atomic nuclei consist of a number of protons, Z, and a number of neutrons, N. Together, they are called nucleons and govern the structure and property of an atomic nucleus. The combination of experimental data and theoretical models is the basis for our understanding of the atomic nucleus. Many nuclei are unstable and decay to a more stable state. From an experimental point of view, it is important to measure the properties of that decay. Decays can occur in different ways, through decay modes, such as, emission of an α-particle,  β-decays and decay by emission of a γ-ray. The energy and the life-time of the decay from unstable nuclei are examples of important properties of a nuclear state.

A basic principle of the measurement of energy of α-particles is the use of a semiconductor-based detector. The interaction between the ionizing particle and the semiconductor material creates many free charge carriers that can be collected as a current pulse. The amplitude of the pulse is proportional to the total collected charge in a preamplifier circuit which in turn is proportional to the energy of the ionizing particle. Samples of three preamplifier pulses are illustrated in the upper left inset of Figure 1. The lifetimes of the α-decaying nuclei, can be deduced from the time difference between the start of the different subsequent pulses.

The short lifetimes of certain nuclei have made them difficult to measure. This is because two (or more) α-decays very close in time could result in so called pile-ups with an analogue electronics experimental set-up. That is, the two (or more) decays are treated by the system as a single decay and results in corrupted data.

Fast sampling Analog-to-Digital converters, fADCs, have been recently employed in nuclear physics experiments and they have made possible to extract energies and times of pile-up signals with tailor-made algorithms. One of the main tasks of the thesis was to develop and implement such an algorithm. The other main task was to apply the algorithm to readily available experimental data from an experiment with the purpose of studying superheavy nuclei. The experiment was led by the Nuclear Structure Group from Lund University in November 2012 at the GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt, Germany. The synthesis of superheavy nuclei is very unlikely and most of the recorded data is, in a sense, undesired. However in the data set there are many of those pile-up pulses from fast subsequent α-decays which have not been analysed before. This thesis deals with the analysis of those potentially interesting undesired pulses.

The developed algorithm to treat the pile-ups was based on a method called Moving Window Deconvolution which is illustrated in Figure 1. The method consists of three steps, i) First the exponential decay of the signal is compensated for with a deconvolution. ii) A differentiation is performed to separate pulses. iii) A moving average is applied to the signal in order to remove noise, which results in a trapezoid. The energy of a pulse is extracted as the height of the resulting trapezoid.

Figure 1. A preamplifier pile-up signal with three pulses. (b) Deconvolved signal. The result of the deconvolution is three plateaus. The height of the last plateau corresponds to the sum of the amplitudes of all three pulses. (c) The differentiation resulting in three square-like pulses. The height of the square-like pulse represents the amplitude of the corresponding original one. (d) Averaged signal.


The developed pile-up routine was successfully applied to the experimental data. From the analysis a connection to the tabulated α-decay path of 219Ra to 215Rn could be firmly established, see Figure 2. The α-decay energy values agreed with the tabulated ones. A half-life of 2 µs was obtained with the newly developed algorithm and coincides within statistical uncertainties with the tabulated value. The decay path was confirmed by α-γ coincidences.

With the firmly established decay path, this thesis sets the proof-of-concept of energy and time extractions with a digital pulse processing system with a more generic algorithm to study the properties of very short-lived α-decaying nuclei. There is more data left to be analysed and new decay paths are being searched for.

Figure 2. Tabulated α-decay path of Ra-219. The yellow filled squares indicate the α-decaying mode. The black filled square indicates that the nucleus is stable towards any decay. Previously measured data of α-decays, half-lives and γ-rays, relevant to this work, are presented within the respective boxes. If not explicitly indicated, the energy of the emitted α-particle is presented in MeV and the emitted γ-ray in keV.