Schematic diagram showing the Pandemonium effect

The pandemonium effect is a problem that may appear when high-resolution detectors (usually germanium

semiconductor detector In ionizing radiation detection physics, a semiconductor detector is a device that uses a semiconductor (usually silicon or germanium) to measure the effect of incident charged particles or photons. Semiconductor detectors find broad applicati ...

s) are used in

beta decay In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which an atomic nucleus emits a beta particle (fast energetic electron or positron), transforming into an isobar of that nuclide. For example, beta decay of a neutron ...

studies. It can affect the correct determination of the feeding to the different levels of the daughter nucleus. It was first introduced in 1977.

Context

Typically, when a parent nucleus beta-decays into its daughter, there is some final energy available which is shared between the final products of the decay. This is called the ''Q'' value of the beta decay (''Q_β''). The daughter nucleus doesn't necessarily end up in the

ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state ...

after the decay, this only happens when the other products have taken all the available energy with them (usually as

kinetic energy In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...

). So, in general, the daughter nucleus keeps an amount of the available energy as excitation energy and ends up in an

excited state In quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Add ...

associated to some energy level, as seen in the picture. The daughter nucleus can only stay in that excited state for a small amount of time (the half life of the level) after which it suffers a series of gamma transitions to its lower energy levels. These transitions allow the daughter nucleus to emit the excitation energy as one or more

gamma ray A gamma ray, also known as gamma radiation (symbol ), is a penetrating form of electromagnetic radiation arising from high energy interactions like the radioactive decay of atomic nuclei or astronomical events like solar flares. It consists o ...

s until it reaches its ground state, thus getting rid of all the excitation energy that it kept from the decay. According to this, the energy levels of the daughter nucleus can be populated in two ways: * by direct beta feeding from the beta decay of the parent into the daughter (I_β), * by gamma transitions of higher energy levels (previously beta-populated from the direct beta decay of the parent) into lower energy levels (ΣI_i). The total

s emitted by an energy level (I_T) should be equal to the sum of these two contributions, that is, direct beta feeding (I_β) plus upper-level gamma de-excitations (ΣI_i). :I_T = I_β + ΣI_i (neglecting

internal conversion Internal conversion is an atomic decay process where an excited nucleus interacts electromagnetically with one of the orbital electrons of an atom. This causes the electron to be emitted (ejected) from the atom. Thus, in internal conversion (o ...

) The beta feeding I_β (that is, how many times a level is populated by direct feeding from the parent) can not be measured directly. Since the only magnitude that can be measured are the gamma intensities ΣI_i and I_T (that is, the amount of gammas emitted by the daughter with a certain energy), the beta feeding has to be extracted indirectly by subtracting the contribution from gamma de-excitations of higher energy levels (ΣI_i) to the total gamma intensity that leaves the level (I_T), that is: :I_β = I_T − ΣI_i (I_T and ΣI_i can be measured)

Description

The pandemonium effect appears when the daughter nucleus has a large ''Q'' value, allowing the access to many nuclear configurations, which translates in many excitation-energy levels available. This means that the total beta feeding will be fragmented, because it will spread over all the available levels (with a certain distribution given by the strength, the level densities, the

selection rule In physics and chemistry, a selection rule, or transition rule, formally constrains the possible transitions of a system from one quantum state to another. Selection rules have been derived for electromagnetic transitions in molecules, in atoms, in ...

s, etc.). Then, the gamma intensity emitted from the less populated levels will be weak, and it will be weaker as we go to higher energies where the level density can be huge. Also, the energy of the gammas de-excitating this high-density-level region can be high. Measuring these gamma rays with high-resolution detectors may present two problems: # First, these detectors have a very low

efficiency Efficiency is the often measurable ability to avoid making mistakes or wasting materials, energy, efforts, money, and time while performing a task. In a more general sense, it is the ability to do things well, successfully, and without waste. ...

of the order of 1–5%, and will be blind to a weak gamma radiation in most of the cases. # Second, their efficiency curve drops to very low values as it goes to higher energies, starting from energies of the order of 1–2

MeV In physics, an electronvolt (symbol eV), also written electron-volt and electron volt, is the measure of an amount of kinetic energy gained by a single electron accelerating through an electric potential difference of one volt in vacuum. When us ...

. This means that most of the information coming from gamma rays of huge energies will be lost. These two effects reduce how much of the beta feeding to the higher energy levels of the daughter nucleus is detected, so less ΣI_i is subtracted from the I_T, and the energy levels are incorrectly assigned more I_β than present: :ΣI_i ~ 0, → I_T ≈ I_β When this happens, the low-lying energy levels are the more affected ones. Some of the level schemes of nuclei that appear in the nuclear databasesEvaluated Nuclear Structure Data File (ENSDF) https://www.nndc.bnl.gov/ensdf/ suffer from this Pandemonium effect and are not reliable until better measurements are made in the future.

Possible solutions

To avoid the pandemonium effect, a detector that solves the problems that high-resolution detectors present should be used. It needs to have an efficiency close to 100% and a good efficiency for gamma rays of huge energies. One possible solution is to use a calorimeter like the total absorption spectrometer (TAS), which is made of a scintillator material. It has been shown that even with a high-efficiency array of germanium detectors in a close geometry (for example, the cluster cube array), about 57% of the total B(GT) observed with the TAS technique is lost.

Relevance

The calculation of the beta feeding, (I_β) is important for different applications, like the calculation of the residual heat in

nuclear reactors A nuclear reactor is a device used to initiate and control a fission nuclear chain reaction. They are used for commercial electricity, marine propulsion, weapons production and research. Fissile nuclei (primarily uranium-235 or plutonium-2 ...

nuclear structure Understanding the structure of the atomic nucleus is one of the central challenges in nuclear physics. Models The cluster model The cluster model describes the nucleus as a molecule-like collection of proton-neutron groups (e.g., alpha particl ...

studies.

References

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External links