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Optical properties of relevance to nanomaterials
Published in Nils O. Petersen, Foundations for Nanoscience and Nanotechnology, 2017
In an earlier chapter (Section 5.1.2) we introduced the concept of electrons in a metal behaving like a gas — the free electron or Fermi gas model. These electrons in a metal should be able to interact with the oscillating electric field of the electromagnetic radiation.
Photonics
Published in Ajawad I. Haija, M. Z. Numan, W. Larry Freeman, Concise Optics, 2018
Ajawad I. Haija, M. Z. Numan, W. Larry Freeman
A collection of freely moving, noninteracting, fermions is called a Fermi gas. A collection of free electrons approximate such a gas and is also called a free electron gas. Fermi was able to find solutions to Schrödinger’s equation that allowed the development of a probability distribution function for electrons in a conductor, which is similar to a free electron gas. The distribution function f (ε) gives the probability that an electron will occupy the energy state ε. It takes the form fFε=expε−εF/kBT+1−1,where εF is the Fermi energy and is equal to the maximum occupancy energy allowed in the limit as T approaches absolute zero for ε < εF. We also note that for ε > εF in the same limit on T, fF = 0, which means there is no allowed occupancy above εF at a temperature of absolute zero. Further investigation of fF shows that for temperatures above absolute zero with ε = εf, fF is 1/2. This suggests that if there are N electrons, then N/2 will occupy states for which ε = εf. Futheremore, for ε > εF with the temperature above absolute zero, fermions from any state below εF will have a finite probability of occupying a state above εF.
JENDL photonuclear data file 2016
Published in Journal of Nuclear Science and Technology, 2023
Nobuyuki Iwamoto, Kazuaki Kosako, Tokio Fukahori
In the statistical model calculations, information of excitation energy and gamma-ray decay branching ratios for discrete levels was taken from RIPL-3 [39]. Nuclear level density above the discrete levels was calculated by the composite form of constant temperature and Fermi-gas models [40], in which the Fermi-gas model was revisited by Mengoni and Nakajima [41]. Emission particles are considered to be neutron, proton, deuteron, triton, 3He and -particle. Emission probabilities of these particles were obtained by optical model calculations with potentials of Koning and Delaroche (KD03) [42] for neutrons and protons, Han et al. [43] for deuterons, folding model based on KD03 for tritons, Xu et al. [44] for 3He, and Avrigeanu and Avrigeanu [45] for -particles. Gamma-ray strength function is an important factor to estimate the photo-absorption (and photo-neutron) cross sections. In this evaluation, E1, M1, and E2 transitions were taken into account for the gamma-ray decays from continuum states. For the E1 transition, modified Lorentzian model (MLO1) [46] was utilized. The GDR parameters were adjusted so as to reproduce measured photo-absorption, photo-neutron, and photo-neutron yield cross sections. When measured data were not available, the systematics of the GDR parameters taken from RIPL-3 was employed. For M1 and E2 transitions, the formulations of Kopecky and Uhl [47] were applied.
Improving Activation Cross Sections for Fusion Applications
Published in Fusion Science and Technology, 2018
N. Dzysiuk, A. J. Koning, D. Rochman, U. Fischer
One of the most difficult reaction channels in terms of fitting the cross section to experimental data is the (n, 2n) reaction channel because the shape of the cross section is insensitive to parameter variation. Normally, this cross-section value is very large and any changes will lead to deviation of other reaction channels as well. In this case it was important to choose the correct level-density model and type of OMP. In the TALYS system the constant temperature + Fermi gas model is used by default, but it was found that in many cases the “Ldmodel 2” (back-shifted Fermi gas model) is more reliable. In many cases the “gpadjust” and “gnadjust” parameters are set for the compound nucleus in certain reactions. For example, it is quite effective to fit (n, 2n) reaction but that may simultaneously influence the (n, p) channel. Thus, one of the options is to set “aadjust” (multiplier to adjust the level density parameter) for the target nucleus in order to fix (n, n′) and prevent the disagreement between (n, 2n) and (n, p). Additionally, “M2constant” is applicable since at energies over 8 MeV the preequilibrium processes become dominant. This parameter is overall constant for the matrix element, or the optical model strength, in the exciton model.
Grüneisen divergence near the structural quantum phase transition in ScF3
Published in Philosophical Magazine, 2019
R. Bhandia, T. Siegrist, T. Besara, G. M. Schmiedeshoff
Today, for a system with multiple energy scales , each with an associated specific heat , one defines an associated Grüneisen parameter , then becomes a weighted average of the with the (divided by the total specific heat) serving as weighting factors [6–8]. So, as an example, one expects the critical contribution to dominate near a continuous phase transition. A simple metal at low temperatures, as another example, can be modelled with two energy scales characterised by the Fermi and Debye temperatures respectively. If we take an ideal Fermi gas model for the electrons, because the Fermi temperature varies like . But for the phonons is less straightforward to access from the definition of the Debye energy as the limit of an integral, so to facilitate our example we consider the approximate form of Lindemann [9] who showed that where is the melting temperature, M is the molar mass, is a constant and is the Debye temperature; here . So evolves from at high temperatures where phonons dominate the specific heat to at low temperatures where the electrons do, multiple energy scales generally lead to a temperature dependent .