A new simulation of nuclear γ cascades by the Monte Carlo method is described. It makes it possible to generate artificially individual events of the γ-cascade decay of an isolated, highly excited initial level in a medium and heavy nucleus. A broad class of quantities, associated with the process of γ-cascade de-excitation, can be modelled. The main advantage of the method is the possibility of a full quantitative control over the influence of the Porter–Thomas fluctuations of partial radiation widths on uncertainties of the modelled cascade-related quantities. For assessment of these uncertainties and a control over the accuracy of the method, a special statistical formalism has been developed.

Simulation of γ cascades in complex nuclei with emphasis on assessment of uncertainties of cascade-related quantities

Five different statistics are compared with respect to parameter, error, and goodness-of-fit estimation in the case of counting experiments. In particular, maximum likelihood approaches are opposed to chi-square techniques. It could be shown that the maximum likelihood estimation derived for Poisson distributed data (Poisson MLE) produces the best statistic in order to estimate parameters. If goodness-of-fit estimations are to be done, Pearson's chi-square should be used. It is the only statistic that leads to the correct expectation value for chi-square. All the other statistics do not follow a chi-square distribution. It is discussed that the chi-square per degree of freedom is not well suited for judging the consistency of a model and the data. When estimating the mean of Poisson distributed data or the area under a peak, Poisson MLE was shown to be the only statistic that comes to consistent and unbiased results, two other statistics give asymptotically consistent results. The widely used Neyman's chi-square fails in all cases. Further, artificial Poisson distributed data have been created on the basis of known model functions. It is shown and discussed in which cases chi-square techniques fail to extract the correct parameter values and where they still can be used. Special emphasis is put on the evaluation of Doppler-broadened gamma line shapes as they are measured in the Crystal-GRID technique.

Comparison of maximum likelihood estimation and chi-square statistics applied to counting experiments

A high-resolution flat-crystal gamma-ray facility, GAMS4, has been constructed at the high-flux reactor at the Institut Laue-Langevin (ILL), Grenoble, France. The facility is located at the exit of a through-tube equipped to place sources in a neutron flux of ≈5.5×10 14 n cm −2 s −1 . Considerable care has been exercised to provide a precision gamma-ray metrology station including vibration isolation, temperature control, environmental monitoring, background suppression, and remote and automatic spectrometer control. The diffraction angles are controlled and measured interferometrically and absolute angle calibration is established with a relative uncertainty of ≈3×10 −7 . The crystals are nearly perfect specimens of Si and Ge whose lattice spacings are measured in meters and have a relative uncertainty of ≈5×10 −8 . The resolution obtained with this facility closely approaches dynamical diffraction predictions. Examples of measurements performed using this facility include (1) absolute wavelengths standards and neutron binding energies, (2) lifetimes of nuclear exited states, (3) determination of interatomic potentials, and (4) crystal structure factors. GAMS4 is a scheduled ILL instrument with beamtime being awarded through the ILL proposal process.

The GAMS4 flat crystal facility

http://koreascience.or.kr:80/article/JAKO200909651053675.pdf

Nuclear energy materials prediction: application of the multi-scale modelling paradigm

The binding energies of $^{29}\mathrm{Si}$, $^{33}\mathrm{S}$, and $^{36}\mathrm{Cl}$ have been measured with a relative uncertainty of $l0.59\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ using a flat-crystal spectrometer. The unique features of these measurements are (1) nearly perfect crystals whose lattice spacing is known in meters, (2) a highly precise angle scale that is derived from first principles, and (3) a \ensuremath{\gamma}-ray measurement facility that is coupled to a high-flux reactor with near-core source capability. The binding energy is obtained by measuring all \ensuremath{\gamma}-rays in a cascade scheme connecting the capture and ground states. The measurements require the extension of precision flat-crystal diffraction techniques to the 5- to 6-MeV energy region, a significant precision measurement challenge. The binding energies determined from these \ensuremath{\gamma}-ray measurements are consistent with recent highly accurate atomic-mass measurements within a relative uncertainty of $4.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$. The \ensuremath{\gamma}-ray measurement uncertainties are the dominant contributors to the uncertainty of this consistency test. The measured \ensuremath{\gamma}-ray energies are in agreement with earlier precision \ensuremath{\gamma}-ray measurements.

Precision measurement of the Si 29 , S 33 , and Cl 36 binding energies

The gamma ray induced Doppler broadening (GRID)-technique is reviewed. This experimental method, relying on ultra-high resolution gamma ray spectroscopy, involves the direct measurement of the Doppler broadening of gamma rays emitted when nuclei decay in-flight following recoil induced by preceding gamma rays. The technique permits the deduction of absolute transition rates in atomic nuclei formed after neutron capture and can therefore contribute to obtaining crucial information for sensitive tests of nuclear models. The method can be used for the study of lifetimes below a few picoseconds, but also, inversely, allows the investigation of interatomic collisions at very low energies. Thus one can probe the repulsive interatomic potential in solids. The characteristic features of the GRID technique are discussed and illustrated by some selected examples. Different approaches to model the slowing-down process at low energies are presented.

http://iopscience.iop.org/article/10.1088/0954-3899/19/2/006/pdf

H G Borner

Papers

Sub-picosecond lifetime measurements by gamma ray induced Doppler broadening