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In 2020, the ICRU released a new report which includes the re-definition of the operational quantities used in radiation protection and new conversion coefficients from physical quantities to operational radiation protection quantities. An assessment of the ambient and personal dose conversion coefficients for the reference neutron fields of radionuclide sources at PTB is necessary based on these new definitions. In this work, a numerical estimation of the conversion coefficients of moderated and unmoderated 252Cf and 241Am-Be neutron sources based on ICRU57 and ICRU95 reports and using spectrum data available in the ISO 8529-1 standard and at PTB are discussed. Two numerical approaches are used for this estimation to ensure the reliability of the calculated values: a direct calculation using MCNP6, and cubic interpolation of conversion coefficients datasets written in Python. The results show large differences between the spectrum-averaged operational quantities for the current and new conversion coefficients of up to 23%. The choice of spectrum data affects conversion coefficient values by 6–8%.

Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run into difficulties of one sort or another. One of the first detailed descriptions was given by Sudarshan and his collaborators who, motivated by the measurement problem in quantum mechanics, proposed a Hilbert space formulation of classical-quantum interactions which made use of the Koopman-von Neumann description of classical systems. Here we use the approach of ensembles on configurations space to give a detailed account of a classical apparatus measuring the position of a quantum particle that is prepared in a superposition of two localized states. We show that the probability of the pointer of the classical apparatus is left in a state that corresponds to the probability of the quantum particle. A subsequent observation of the pointer leads to an update of its probability density. From this we can obtain information about the position of the quantum particle, leading to an update of its wave function. Since this formalism incorporates uncertainties and finite measurement precision, it is well suited for metrological applications. Furthermore, it resolves fundamental issues that appear in the case of a quantum description of the apparatus., Comment: 30 pages, 2 figures. 746. WE-Heraeus-Seminar "Koopman Methods in Classical and Classical-Quantum Mechanics"

Spectrum deconvolution is an important task in ionizing radiation measurements, as the pulse height spectra, or, in general, the measured data from spectrometers or other measuring instruments are usually determined by the convolution of the response function with the fluence spectra. The method presented here for obtaining fluence spectra from the measurements is an application of Bayesian parameter estimation to the deconvolution of X-ray emission data. The problem of choosing the optimal model among several possible models is also considered, as well as an approach to include contributions from various sources of uncertainty, both correlated and uncorrelated. The application is carried out using the Bayesian software WinBUGS.

Since the first particle accelerator’s construction in 1931, an exponential spread of these machines occurred worldwide, in different kinds of applications. Nowadays, these are mainly used for industrial (60%) and medical (35%) purposes and for scientific research (5%). High energy secondary mixed fields produced by the particle beams interaction with matter imply a complex environmental dosimetry and special radiation protection regulations able to guarantee workers and population safety. In the medical field, this aspect is particularly emphasized in hadrontherapy centres, where high energy charged particles such as protons and carbon ions modify environmental doses, with a significant increase in the neutron contribution. This work proposes a technique to identify points of losses of the primary particle beam around an acceleration ring and has been developed within the radiation protection section at the National Centre for Oncological Hadrontherapy situated in Pavia. In the first part, the radiation field produced by protons and carbon ions interactions with structural materials at different energies was investigated. The main instrument of analysis is the Monte Carlo code for particle transport FLUKA, supported by experimental measurements in the treatment room carried out with the rem counter LUPIN, designed for pulsed neutron fields dosimetry. This first step allowed an analysis of both the angular and energetic instrumental response and a comparison of experimental results with simulations. The second part proposes a description of the technique for beam loss positions reconstruction around the acceleration ring at CNAO based on the application of unfolding codes.

Currently, quality assurance measurements in mammography are performed on unprocessed images. For diagnosis, however, radiologists are provided with processed images. This image processing is optimised for images of human anatomy and therefore does not always perform satisfactorily with technical phantoms. To overcome this problem, it may be possible to use anthropomorphic phantoms reflecting the anatomic structure of the human breast in place of technical phantoms when carrying out task-specific quality assessment using model observers. However, the use of model observers is hampered by the fact that a large number of images needs to be acquired. A recently published novel observer called the regression detectability index (RDI) needs significantly fewer images, but requires the background of the images to be flat. Therefore, to be able to apply the RDI to images of anthropomorphic phantoms, the anatomic background needs to be removed. For this, a procedure in which the anatomical structures are fitted by thin plate spline (TPS) interpolation has been developed. When the object to be detected is small, such as a calcification-like lesion, it is shown that the anatomic background can be removed successfully by subtracting the TPS interpolation, which makes the background-free image accessible to the RDI. We have compared the detectability obtained by the RDI with TPS background subtraction to results of the channelized Hotelling observer (CHO) and human observers. With the RDI, results for the detectability d ′ can be obtained using 75% fewer images compared to the CHO, while the same uncertainty of d ′ is achieved. Furthermore, the correlation of d ′ (RDI) with the results of human observers is at least as good as that of d ′ (CHO) with human observers.

The neutron reference field produced by a heavy-water moderated 252Cf source is used at PTB for calibrating neutron-measuring devices. Knowledge of the precise neutron spectrum is very important for the investigation of operational radiation protection quantities. Recently, new fission spectrum data of 252Cf has been proposed based on the latest nuclear data library version. At PTB, earlier calculations for the D2O moderated 252Cf neutron source were carried out more than 20 years ago, thus updated and more detailed calculations are required. In this paper, a detailed simulation model of the PTB moderated 252Cf source assembly has been prepared and investigated using new spectral data and two different Monte Carlo transport codes MCNP6.1 and PHITS3.22, with ENDF/BVIII.0, ENDF/B-VII.1, ENDF/B-V, and ENDL85 evaluated nuclear data libraries. The results show that the evaluated nuclear data libraries influence the calculated operational quantities by (3-5) %. The dosimetric quantities calculated with the PHITS code and the ENDF/B-VII.1 data library agree well with the MCNP6 results.

Low-level neutron measurements are required for applications such as environmental monitoring, measurements of weak sources and the determination of neutron fluxes at underground laboratories. When analyzing low-level neutron measurements, it is important to be able to distinguish the signal due to neutrons from any background term that may originate within the detector. A solution to this problem has been developed for the case of measurements carried out with 3He spherical proportional counters of the type which are often used in Bonner sphere spectrometers. To determine this background, measurements were carried out in the former UDO underground laboratory of the Physikalisch-Technische Bundesanstalt located in the Asse salt mine. The analysis of the data was carried out using Bayesian parameter estimation. The result of the analysis is a very general parameterised function that can be used to describe the pulse height spectrum due to the background of the proportional counters.

The neutron field of the PTB Thermal Neutron Calibration Facility was characterised with the help of the Bonner sphere spectrometer of PTB, NEutron MUltisphere Spectrometer (NEMUS). For the analysis of the Bonner sphere data an analytical model of the neutron energy distribution was used. The unfolding of neutron spectra was performed via the method of Bayesian parameter estimation. Comparison of the results of thermal neutron fluence and thermal ambient dose equivalent with the results of the reference method of gold activation showed a very good agreement. For fast neutrons the results obtained with NEMUS will serve as reference values for this facility. The facility is ready for use as a thermal neutron reference field for calibrations of neutron measuring devices.

Measurement of the energy spectrum of secondary neutrons were carried out at the OncoRay Proton Therapy facility in Dresden, following an approach originating in neutron metrology which is well suited for both the characterization of secondary neutron fields at proton therapy facilities and the validation of Monte Carlo simulations. For the experiment, a brass target was placed in the proton beam and Bonner spheres measurements were made at a distance of 2 m from the target and at different angles, 15° to 120°, with respect to the incoming proton beam. The measured spectra were compared to Monte Carlo simulations.

One of the most promising approaches for evaluating CT image quality is task-specific quality assessment. This involves a simplified version of a clinical task, e.g. deciding whether an image belongs to the class of images that contain the signature of a lesion or not. Task-specific quality assessment can be done by model observers, which are mathematical procedures that carry out the classification task. The most widely used figure of merit for CT image quality is the area under the ROC curve (AUC), a quantity which characterizes the performance of a given model observer. In order to estimate AUC from a finite sample of images, different approaches from classical statistics have been suggested. The goal of this paper is to introduce task-specific quality assessment of CT images to metrology and to propose a novel Bayesian estimation of AUC for the channelized Hotelling observer (CHO) applied to the task of detecting a lesion at a known image location. It is assumed that signal-present and signal-absent images follow multivariate normal distributions with the same covariance matrix. The Bayesian approach results in a posterior distribution for the AUC of the CHO which provides in addition a complete characterization of the uncertainty of this figure of merit. The approach is illustrated by its application to both simulated and experimental data.

Organic NE213 liquid scintillator neutron detectors are commonly used at accelerator facilities for neutron beam diagnostics. In recent years, they have also been installed at nuclear fusion facilities to measure the neutron energy spectra from Deuterium (D) and Deuterium-Tritium plasmas, e.g., at the ASDEX Upgrade (Garching, Germany) and at the Joint European Torus (JET, Culham, UK). The NE213 equivalent scintillating material (now BC501A) of the detector is sensitive to neutron and gamma radiation, so pulse discrimination techniques are applied in order to obtain the measured neutron pulse height spectrum (PHS). If the neutron detector is stable, controlled, and well-characterized (i.e., its response function to incoming neutrons of known energy is determined with high accuracy), it can be used as a neutron spectrometer. The measured PHS can then be analyzed using standard techniques such as unfolding to determine the incoming neutron energy spectrum. This article focuses on the unfolding of neutron data measured in D plasma experiments at JET by a compact broadband neutron spectrometer using the maximum entropy unfolding code MAXED. A general method for optimizing MAXED input parameters is described and applied to the measured PHS to diagnose the effects of the auxiliary heating of JET D plasma on the neutron energy spectra.

CONUS is a novel experiment aiming at detecting elastic neutrino nucleus scattering in the fully coherent regime using high-purity Germanium (Ge) detectors and a reactor as antineutrino ($\bar\nu$) source. The detector setup is installed at the commercial nuclear power plant in Brokdorf, Germany, at a very small distance to the reactor core in order to guarantee a high flux of more than 10$^{13}\bar\nu$/(s$\cdot$cm$^2$). For the experiment, a good understanding of neutron-induced background events is required, as the neutron recoil signals can mimic the predicted neutrino interactions. Especially neutron-induced events correlated with the thermal power generation are troublesome for CONUS. On-site measurements revealed the presence of a thermal power correlated, highly thermalized neutron field with a fluence rate of (745$\pm$30)cm$^{-2}$d$^{-1}$. These neutrons that are produced by nuclear fission inside the reactor core, are reduced by a factor of $\sim$10$^{20}$ on their way to the CONUS shield. With a high-purity Ge detector without shield the $\gamma$-ray background was examined including highly thermal power correlated $^{16}$N decay products as well as $\gamma$-lines from neutron capture. Using the measured neutron spectrum as input, it was shown, with the help of Monte Carlo simulations, that the thermal power correlated field is successfully mitigated by the installed CONUS shield. The reactor-induced background contribution in the region of interest is exceeded by the expected signal by at least one order of magnitude assuming a realistic ionization quenching factor of 0.2., Comment: 28 pages, 28 figures

Radiation therapy with proton beams allows the deposition of high doses to the tumour while minimising dose to the surrounding tissue. During such treatment, the patient is also exposed to secondary radiation which produces an out-of-field dose that affects healthy tissue. The largest contribution to this out-of-field dose comes from neutron radiation; therefore, it is of interest to fully characterise the neutron field in the therapy room with measurements. This is usually done with Bonner sphere spectrometers using active detectors, typically 3He-filled proportional counters, as central thermal neutron sensors. Under the experimental conditions encountered in proton therapy facilities, a proper analysis of the measurements is impossible unless dead time corrections are implemented. In this paper, we present a method using a paralysable dead time model for carrying out such corrections for Bonner sphere measurements with 3He-filled proportional counters and apply it to data taken at the University Proton Therapy Dresden (UPTD) facility in double scattering mode. The neutron events were recorded with time stamps and, based on this time-resolved data, the measured neutron rate distribution was sampled. Since the neutron flux is proportional to the proton flux, the integral neutron flux is directly related to the proton dose. Hence, we were able to estimate the detector dead time from the measured rate distributions recorded for a set of measurements with different proton dose rates. Experimental measurements with different intensities of the proton field show that the corrections are in agreement within 0.5% for measured signal rates smaller than 15 × 103 counts per second and do not exceed 1% at 25 × 103 counts per second.

Radiation therapy is one of the most frequently used treatment modalities for cancer. While most patients receive photon therapy, a growing number of patients are treated with particles, mainly protons. Protons offer a more localized dose deposition compared to photon therapy. This allows a reduction of the dose that is applied by the primary beam to the healthy tissue outside the target volume. At the same time, the use of protons leads to a change in the composition of the secondary radiation field, when compared to photons. In most locations, the out-of-field dose is dominated by secondary neutrons. The out-of-field dose varies significantly in shape and magnitude. Currently, there is no established procedure to monitor the secondary neutron dose to the patients.This paper describes the simulation and measurement of the secondary neutron radiation field at the University Proton Therapy Dresden. The simulation uses a detailed model of the beam delivery system, an IBA universal nozzle. The simulations have been validated by a comprehensive set of extended range Bonner sphere spectrometer measurements, with the NEMUS spectrometer operated by the Physikalisch-Technische Bundesanstalt. The set of measurements covers all possible machine configurations for the double scattering mode. An excellent agreement between unfolded measurements and simulation predictions is achieved.The data show that the neutron field is varying strongly on the scale of a human body. This indicates that the use of fluence to dose conversion tables is not justified for neutron dose calculation in patients. Therefore, the presented data is of high importance for future studies of the organ doses in different treatment scenarios.

In computed tomography, there is a tradeoff between the quality of the reconstructed image and the radiation dose received by the patient. In order to find an appropriate compromise between the image quality of the reconstructed images and the radiation dose, it is important to have reliable methods for evaluating the quality of the reconstructed images. A successful family of methods for the assessment of image quality is task-based image quality assessment, which often involves the use of model observers, and which assesses the quality of the image reconstruction by deriving a figure of merit. Here, we present a Bayesian framework that can be used in task-based image quality assessment. Our framework is applicable to binary classification problems with normally distributed observations, and we make the additional assumption that the covariance matrix is the same in both image classes. We choose a particular non-informative prior for the parameters of our model, which allows us to derive an expression for the Bayes factor for the binary classification problem which to the best of our knowledge is novel. We introduce a novel model observer based on this Bayes factor. Further, we have developed a methodology for estimating the posterior distribution of the figure of merit for this type of classification problem. Compared with classical statistical approaches, our Bayesian approach has the advantage that it provides a full characterization of the uncertainty of the figure of merit. Our choice of prior allows us to design a simple Monte Carlo algorithm to efficiently sample the posterior of the figure of merit of the ideal observer, in contrast to common Bayesian procedures which rely on computationally expensive Markov chain Monte Carlo sampling. We have shown that for training samples of sufficient size, our estimated credible intervals for the figure of merit have coverage probabilities close to their credibility, so that our approach can reasonably be used within a classical statistical framework as well.

The emission of laser induced X-rays from materials processing ultra-short pulsed laser systems was measured. The absolute spectral photon fluence was determined using a thermoluminescence detector based few-channel spectrometer. The spectra at 10 cm from the laser focus were in the energy region between 2 and 25 keV with mean energies of ~4–6 keV (when weighted by fluence or directional dose equivalent) and up to 13 keV (when weighted by ambient dose equivalent). The operational quantities, H·′(0.07), H·′(3) and H·*(10), were determined to be in the order of 1600–7300, 16–71 and 1–4 mSv per hour processing time, respectively, depending on the material and condition of the workpiece. The dose contribution due to photons above 30 keV was for all quantities negligible, i.e. below 10−3.

Model observers are mathematical classifiers that are used for the quality assessment of imaging systems such as computer tomography. The quality of the imaging system is quantified by means of the performance of a selected model observer. For binary classification tasks, the performance of the model observer is defined by the area under its ROC curve (AUC). Typically, the AUC is estimated by applying the model observer to a large set of training and test data. However, the recording of these large data sets is not always practical for routine quality assurance. In this paper we propose as an alternative a parametric model observer that is based on a simple phantom, and we provide a Bayesian estimation of its AUC. It is shown that a limited number of repeatedly recorded images (10-15) is already sufficient to obtain results suitable for the quality assessment of an imaging system. A MATLAB® function is provided for the calculation of the results. The performance of the proposed model observer is compared to that of the established channelized Hotelling observer and the nonprewhitening matched filter for simulated images as well as for images obtained from a low-contrast phantom on an x-ray tomography scanner. The results suggest that the proposed parametric model observer, along with its Bayesian treatment, can provide an efficient, practical alternative for the quality assessment of CT imaging systems.

Fast neutron resonance radiography (FNRR) is an imaging method that exploits characteristic cross-section structures (peaks and troughs) of certainelements in the energy-range of 1-10 MeV to identify materials in a large volume object. In FNRR, the neutron energy spectrum transmitted through an object carries information about the elemental composition of thatobject. The principal elements present in most explosives are: carbon, oxygen, nitrogen andhydrogen. Explosives are characterized by high fractions of nitrogen and oxygen as well as low fractions of carbon and hydrogencompared to benign materials. Detection of explosives in cargo employing FNRRis based on determination of the local areal densities of these four elements and their ratios. In our measurements, the transmission spectrum is usually divided in 100 - 500 energy bins, representing 100 - 500 linear equations containing four unknown areal densities of HCNO. This is an overdetermined problem, which allows us to derive not only the fourexpectation values of their areal densitiesbut theirprobability distribution as well. For this purpose, a model was formulated and implemented within a software package which performs Bayesian analysis of complex statistical models using Markov chain Monte-Carlo (MCMC). This model was tested successfully both on simulated and experimental data. This work will describe the model and the outcome of elemental ratios reconstruction for several materials from experimental data.

Ratios of H(p)(10) and H*(10) were determined with reference instruments in a number of workplace fields within the nuclear industry and used to derive workplace-specific correction factors. When commercial survey meter results together with these factors were applied to the results of the locally used personal dosemeters their results improved and became within 0.7 and 1.7 of the reference values or better depending on the response of the survey meter. A similar result was obtained when a correction was determined with a prototype reference instrument for H(p)(10) after adjustment of its response. Commercially available survey instruments both for photon and neutron H*(10) measurements agreed with the reference instruments in most cases to within 0.5-1.5. Those conclusions are derived from results reported within the EC supported EVIDOS contract.

The availability of active neutron personal dosemeters has made real time monitoring of neutron doses possible. This has obvious benefits, but is only of any real assistance if the dose assessments made are of sufficient accuracy and reliability. Preliminary assessments of the performance of active neutron dosemeters can be made in calibration facilities, but these can never replicate the conditions under which the dosemeter is used in the workplace. Consequently, it is necessary to assess their performance in the workplace, which requires the field in the workplace to be fully characterised in terms of the energy and direction dependence of the fluence. This paper presents an overview of developments in workplace neutron dosimetry but concentrates on the outcomes of the EVIDOS project, which has made significant advances in the characterisation of workplace fields and the analysis of dosemeter responses in those fields. © The Author 2007. Published by Oxford University Press. All rights reserved.

EVIDOS ('evaluation of individual dosimetry in mixed neutron and photon radiation fields') is an European Commission (EC)-sponsored project that aims at a significant improvement of radiation protection dosimetry in mixed neutron/photon fields via spectrometric and dosimetric investigations in representative workplaces of the nuclear industry. In particular, new spectrometry methods are developed that provide the energy and direction distribution of the neutron fluence from which the reference dosimetric quantities are derived and compared to the readings of dosemeters. The final results of the project will be a comprehensive set of spectrometric and dosimetric data for the workplaces and an analysis of the performance of dosemeters, including novel electronic dosemeters. This paper gives an overview of the project and focuses on the results from measurements performed in calibration fields with broad energy distributions (simulated workplace fields) and on the first results from workplaces in the nuclear industry, inside a boiling water reactor and around a spent fuel transport cask.

Within the EC project EVIDOS (‘Evaluation of Individual Dosimetry in Mixed Neutron and Photon Radiation Fields’), different types of active neutron personal dosemeters (and some passive ones) were tested in workplace fields at nuclear installations in Europe. The results of the measurements which have been performed up to now are summarised and compared to our currently best estimates of the personal dose equivalent H p (10). Under- and over-readings by more than a factor of two for the same dosemeter in different workplace fields indicate that in most cases the use of field-specific correction factors is required.

The response of albedo dosemeters depends on the energy and angle of the incident neutron radiation. For their use as personal dosemeters, a field-calibration factor has to be applied. The presently used single sphere method for field calibration can be extended and optimised by putting five albedo dosemeters on the surface of a polyethylene sphere and two TL cards in the centre. To investigate the potential of this extension, reference measurements and Monte Carlo calculations were performed and the fluence response of the detectors at different positions on and within the sphere was determined. Calculated response functions demonstrate that information on the energy and directional distribution of neutron fluence can be extracted with this simple set-up for unknown neutron fields.

The analysis of Bonner sphere measurements is typically done using unfolding codes. However, it is very difficult to implement reliable uncertainty propagation in standard unfolding procedures. An alternative approach, which does provide reliable estimates of the uncertainties of neutron spectra leading to rigorous estimates of uncertainties of the dose, is to analyze the data using Bayesian parameter estimation. In this work, we extend previous approaches and apply this method to secondary neutrons from radiation therapy proton beams. This requires introducing a parameterized model which can describe the main features of the neutron spectra. We choose the parameterization based on information that is available from measurements and detailed Monte Carlo simulations. To demonstrate the validity of this approach, we consider the results of an experiment carried out at the experimental hall at the OncoRay proton therapy facility in Dresden.

We consider the coupling of quantum fields to classical gravity in the formalism of ensembles on configuration space, a model that allows a consistent formulation of interacting classical and quantum systems. Explicit calculations show that there are solutions for which two initially independent quantum fields evolve into an entangled state, even though their interaction occurs solely via a common classical gravitational field. Thus in contrast to recent suggestions, an observed generation of entanglement would not provide a definitive test of the nonclassical nature of gravity.

The formalism of ensembles on configuration space allows for a general description of interactions between quantum and classical ensembles. In this chapter, we consider such hybrid ensembles and focus on consistency requirements for models of quantum-classical interactions. We show how the configuration ensemble approach is able to satisfy desirable properties such as a Lie algebra of observables and Ehrenfest relations, while evading no-go theorems based in part on such properties. We then discuss issues concerning locality. It is found that, in principle, noninteracting ensembles of quantum and classical particles can be associated with nonlocal energy flows and nonlocal signaling. However, it is shown that such effects can be suppressed by a requirement of ‘classicality’, that localised classical systems have a very large number of degrees of freedom. Measurement aspects are also discussed and again ‘classicality’ plays an important role, this time ensuring an effective and irreversible decoherence. Finally, comparisons are briefly made with elements of the mean-field approach to quantum-classical interactions.

Given two systems with configuration spaces X and Y, we consider their joint description on the configuration space given by the set product \(X \times Y\). In the formalism of ensembles on configuration space, this description requires a probability distribution P(x, y) defined over the joint configuration space, the corresponding conjugate quantity S(x, y), and an ensemble Hamiltonian \(\mathcal{H}_{XY}[P,S]\). Once a composite system is defined, it becomes necessary to introduce a number of new concepts which must be defined carefully. For example, such systems may consist of subsystems which are independent or entangled, non-interacting or interacting, and one must give a precise mathematical formulation of these properties. Issues of locality must be taken into consideration. Observables which are ascribed to one of the subsystems (and are therefore initially defined on only one of the initial configuration spaces, X or Y) must be extended to the joint ensemble, but this can not be done in an arbitrary way. These concepts play an important role in the description of composite systems, and we address them in the first sections of this chapter. The remaining sections are devoted to a description of interactions between subsystems that model measurements, starting with basic measurement procedures followed by more elaborate procedures that describe weak measurements and measurement-induced collapse.

We consider ensembles on configuration space that consist of quantum fields which interact with and are the source of a classical gravitational field. These are hybrid systems where gravity remains classical while matter is described by quantized fields. There are some well known arguments in the literature which claim that such models are not possible. However, an examination of the most prominent ones, that are detailed enough to allow scrutiny, indicates that the hybrid models considered here are not excluded by any of the consistency arguments. We illustrate the approach with two examples. Our first example is a cosmological model. We consider the case of a closed Robertson–Walker universe with a massive quantum scalar field and solve the equations using a particular ansatz which selects a highly non-classical solution, one in which the scale factor of the Robertson–Walker universe is restricted to discrete values as a consequence of the interaction of the classical gravitational field with the quantized scalar field. We discuss this cosmological model in two approximations, that of a minisuperspace model and that of a midisuperspace model. Our second example concerns black holes. We consider CGHS black holes and show that we recover Hawking radiation from the equations that describe a hybrid system consisting of a classical CGHS black hole in a collapsing geometry interacting with a quantized scalar field. We also show that the hybrid model provides a natural resolution to the well known problem of time in quantum gravity.

The usual Heisenberg uncertainty relation may be replaced by an exact equality, valid for all states. This can be shown by carrying out a decomposition of the momentum of a quantum state into classical and nonclassical components and choosing suitable measures of position and momentum uncertainty. The exact uncertainty relation obtained in this way is sufficiently strong to provide the basis for moving from classical mechanics to quantum mechanics. In particular, the assumption of a nonclassical momentum fluctuation, having a strength which scales inversely with uncertainty in position, leads from the classical equations of motion to the Schrodinger equation. The approach based on the exact uncertainty principle is conceptually very simple, being based on the core notion of statistical uncertainty, intrinsic to any interpretation of quantum theory. This quantization procedure is not restricted to particles but can also be used to derive bosonic field equations. It is remarkable that the basic underlying concept, the addition of nonclassical momentum fluctuations to a classical ensemble, carries through from quantum particles to quantum fields, without creating conceptual difficulties, although significant technical generalizations are needed. This logical consistency and range of applicability is a further strength of the exact uncertainty approach.

We define ensembles on configuration space for classical gravitational fields that obey the Einstein equations. Our starting point is the Hamilton–Jacobi formulation of general relativity. After a brief review of the Einstein–Hamilton–Jacobi equation in the metric representation, we introduce the additional mathematical structure that is needed to formulate the theory of configuration space ensembles; i.e., a measure over the space of metrics and a probability functional. Then we define an appropriate ensemble Hamiltonian for the gravitational field, show that it leads to the correct equations, and recover the Einstein equations in the usual formulation. In addition, we show that the formalism of ensembles on configuration space provides a novel approach to solving the reconstruction problem; i.e., the derivation of the full set of Einstein equations from a Hamilton–Jacobi formulation of gravity. Having derived the equations for the general case, we move on to the simpler case of spherical symmetric spacetimes and derive the corresponding equations for midisuperspace models of spherically symmetric gravity. We consider the example of classical ensembles of black holes in this midisuperspace approximation.

The problem of defining hybrid systems comprising quantum and classical components is highly nontrivial, and the approaches that have been proposed to solve this problem run into various types of fundamental difficulties. The formalism of configuration-space ensembles is able to overcome many of these difficulties, allowing for a general and consistent description of interactions between quantum and classical ensembles. Such hybrid ensembles have a number of desirable features; e.g., quantum-classical interactions do not blur the fundamental distinction between the quantum and classical components; configuration separability is satisfied; and non-relativistic systems are Galilean invariant whenever the interaction potential itself is Galilean invariant. After demonstrating general properties of hybrid ensembles, we consider their application to the description of measurement of a quantum system by a classical apparatus, including examples of position and spin measurement; the scattering of a classical particle from a quantum superposition; and the definitions of Gaussian and coherent ensembles for quantum-classical oscillators. Finally, we generalise quantum Wigner functions to hybrid ensembles.

A description of ensembles on configuration space incorporates at least two geometrical structures which arise in a natural way: a metric structure, which derives from the natural geometry associated with a space of probabilities, and a symplectic structure, which derives from the symplectic geometry associated with a Hamiltonian description of motion. We show that these two geometrical structures give rise to a Kahler geometry. We first consider probabilities P and introduce the information metric. This leads to information geometry, a Riemannian geometry defined on the space of probabilities. We then bring in dynamics via a Hamiltonian formalism defined on a phase space with canonically conjugate coordinates P and S. This leads to more geometrical structure, a symplectic geometry defined on this phase space. The next step is to extend the information metric, which is defined over the space of probabilities only, to a metric over the full phase space. This requires satisfying certain conditions which ensure the compatibility of the metric and symplectic structures. These conditions are equivalent to requiring that the space have a Kahler structure. In this way, we are led to a Kahler geometry. This rich geometrical structure allows for a reconstruction of the geometric formulation of quantum theory. One may associate a Hilbert space with the Kahler space and this leads to the standard version of quantum theory. Thus the theory of ensembles on configuration space permits a geometric derivation of quantum theory.

The first part of this article provides a concise survey of some of the mathematical methods that have been proposed for neutron spectrum unfolding. The aim is to give a pedagogical introduction to the subject without going into a detailed discussion of technical issues. The second part of this article concerns the evaluation of uncertainties. Spectra derived using unfolding techniques (and any quantities computed from these spectra; e.g., fluences and doses) will be subject to uncertainties and it is important to provide estimates of these uncertainties. This is not straightforward, due in part to the special role played by the prior information. It is shown that an approach using Bayesian parameter estimation can overcome these difficulties.

Recent developments in accelerator physics have led to new challenges for radiation protection dosimetry. Doses have to be determined for workplace fields which are characterized by high-energy radiation, a dominant contribution from neutrons, high intensities and pulsed time structure This may present problems for active measuring devices. As is well known, the ambient dose equivalent is often underestimated by area monitors operating in high-energy neutron fields behind shielding. Therefore, it is desirable to calibrate survey monitors in a characterized neutron field with the type of spectral fluence distribution that is expected behind shielding, i.e. where the main dose from neutrons arises from two peaks with mean energies of about 1 MeV and 100 MeV, respectively. Such a neutron fluence distribution is produced by the irradiation of a Fe-target with 200 MeV/u 12C-ions. Measurements with the extended range Bonner sphere spectrometer NEMUS of PTB were performed at two positions inside the experimental area Cave A of the heavy-ion synchrotron SIS at GSI. The measured neutron spectra show different fluence contributions for the two peaks at the two positions. The results were compared to Monte Carlo Simulations with MCNPX and FLUKA.

A spin-half system may be characterised as having a set of two-valued observables which generate infinitesimal rotations in three dimensions. This abstract formulation can be given a concrete realization using ensembles on configuration space. We derive very general probabilistic models for ensembles that consist of one and two spin-half systems. In the case of a single spin-half system, there are two main requirements that need to be satisfied: the configuration space must be a discrete set, labelling the outcomes of two-valued spin observables, and these observables must provide a representation of so(3). These two requirements are sufficient to lead to a model which is equivalent to the quantum theory of a single qubit. The case of a pair of spin-half systems is more complicated, in that additional physical requirements concerning locality and subsystem independence must also be taken into account, and now the observables must provide a representation of \(so(3) \oplus so(3)\). We show in this case that, in addition to a model equivalent to the quantum theory of a pair of qubits, it may also be possible to have non-quantum local models.

Heisenberg introduced his famous uncertainty relations in a seminal 1927 paper entitled "The Physical Content of Quantum Kinematics and Mechanics". He motivated his arguments with a gedanken experiment, a gamma ray microscope to measure the position of a particle. A primary result was that, due to the quantum nature of light, there is an inherent uncertainty in the determinations of the particle's position and momentum dictated by an indeterminacy relation, $\delta q \delta p \sim h$. Heisenberg offered this demonstration as "a direct physical interpretation of the [quantum mechanical] equation $\textbf{pq} - \textbf{qp} = -i\hbar$" but considered the indeterminacy relation to be much more than this. He also argued that it implies limitations on the very meanings of position and momentum and emphasized that these limitations are the source of the statistical character of quantum mechanics. In addition, Heisenberg hoped but was unable to demonstrate that the laws of quantum mechanics could be derived directly from the uncertainty relation. In this paper, we revisit Heisenberg's microscope and argue that the Schr\"odinger equation for a free particle does indeed follow from the indeterminacy relation together with reasonable statistical assumptions., Comment: 17 pages, 1 figure European Journal of Physics (in press)

Extended-range Bonner sphere spectrometers are well suited for spectrometry in neutron fields that extend from thermal energies to a few hundred mega-electron-volts. The data analysis, however, is not straightforward, and it is of interest to evaluate how well the main features of the spectrum can be determined by the measurements and to estimate the uncertainties of integral quantities of interest, e.g., fluence and dose. In this paper, we apply Bayesian parameter estimation to this problem. We use simulated data that model measurements made in neutron fields behind shielding at high-energy accelerators.

Extended-Range Bonner sphere spectrometers (ERBSSs) are well suited for measurements in high-energy stray neutron fields, where neutron energies extend from thermal to a few hundred MeV. These fields typically have a thermal peak, a fairly flat intermediate region, a medium energy peak at ∼1 MeV and a high-energy peak at ∼ a few 100 MeV. The data analysis is not straightforward: it requires unfolding with response functions that have a substantial amount of overlap, and the responses of the modified spheres (which provide information about the fluence at high energies) increase dramatically above ∼100 MeV. In this paper, I try to determine which of the main features of the spectrum are well determined by the data given optimal methods of analysis, and which features are subject to ambiguity. To do this, I analyse ERBSS measurements using two methods of analysis that are particularly useful for this purpose, Bayesian parameter estimation and maximum entropy unfolding.

Within the EC project EVIDOS, 17 different mixed neutron-photon workplace fields at nuclear facilities (boiling water reactor, pressurised water reactor, research reactor, fuel processing, storage of spent fuel) were characterised using conventional Bonner sphere spectrometry and newly developed direction spectrometers. The results of the analysis, using Bayesian parameter estimation methods and different unfolding codes, some of them especially adapted to simultaneously unfold energy and direction distributions of the neutron fluence, showed that neutron spectra differed strongly at the different places, both in energy and direction distribution. The implication of the results for the determination of reference values for radiation protection quantities (ambient dose equivalent, personal dose equivalent and effective dose) and the related uncertainties are discussed.

Workplace neutron spectra from nuclear facilities obtained within the European project EVIDOS are compared with those of the simulated workplace fields CANEL and SIGMA and fields set-up with radionuclide sources at the PTB. Contributions of neutrons to ambient dose equivalent and personal dose equivalent are given in three energy intervals (for thermal, intermediate and fast neutrons) together with the corresponding direction distribution, characterised by three different types of distributions (isotropic, weakly directed and directed). The comparison shows that none of the simulated workplace fields investigated here can model all the characteristics of the fields observed at power reactors. © The Author 2007. Published by Oxford University Press. All rights reserved.

In this study, the interpolation problem for a set of Monte Carlo simulations of dose rate per activity of beta-emitting radionuclides is considered. The simulations were carried out for various conditions: for circular areal sources of different diameters and radionuclides, and for various distances from the source. Calculations were done for both operational quantities as well as organ doses: Hp(0.07), Hp(3), Hp(10), Hskin and Hlens Interpolation is needed for practical applications because it is often necessary to evaluate the dose quantities at parameter values that do not correspond exactly to the ones that were used for the simulation. To solve this problem, the method of radial basis function thin-plate spline interpolation is used. The method used for the interpolation and a software application called BetaDosim, which allows users to get the interpolated values, are described. BetaDosim is freely available.

Quantum mechanics has a rich geometrical structure which allows for a geometrical formulation of the theory. This formalism was introduced by Kibble and later developed by a number of other authors. The usual approach has been to start from the standard description of quantum mechanics and identify the relevant geometrical features that can be used for the reformulation of the theory. Here this procedure is inverted: the geometrical structure of quantum theory is derived from information geometry, a geometrical structure that may be considered more fundamental, and the Hilbert space of the standard formulation of quantum mechanics is constructed using geometrical quantities. This suggests that quantum theory has its roots in information geometry.

Detectors made from artificial chemical vapor deposition (CVD) single crystal diamond are very promising candidates for applications where high resolution neutron spectrometry in very high neutron fluxes is required, for example in fusion research. We propose a Bayesian method to estimate the neutron response function of the detector for a continuous range of neutron energies (in our case, 10 MeV ≤ En ≤ 16 MeV) based on a few measurements with quasi-monoenergetic neutrons. This method is needed because a complete set of measurements is not available and the alternative approach of using responses based on Monte Carlo calculations is not feasible. Our approach uses Bayesian signal-background separation techniques and radial basis function interpolation methods. We present the analysis of data measured at the PTB accelerator facility PIAF. The method is quite general and it can be applied to other particle detectors with similar characteristics.

Some recent JET campaigns, with the introduction of a trace amount (nT/nD < 5%) of tritium into D plasmas and third harmonic ICRH acceleration of 4He, provided unique opportunities to test 'burning plasma' diagnostics. In particular, new approaches and techniques were investigated for the detection of neutrons, ? particles and the fuel mixture. With regard to neutron detection, the recent activity covered aspects such as calibration and cross validation of the diagnostics, measurement of the spatial distribution of the neutrons, particle transport and neutron spectrometry. The first tests of some newneutron detection technologies were also undertaken during the Trace Tritium Experiment campaign. To improve JET's diagnostic capability in the field of ? particles, a significant development programme was devoted to the measurement of their confinement and imaging with ? -ray spectroscopy. A new approach for the fusion community to measuring the fast ion losses, based on the activation technique, was also attempted for the first time on JET. An assessment of the neutral particle analyser's potential to determine the fuel mixture and the particle transport coefficients is under way.