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Gold Nanoparticles
Published in Jay L. Nadeau, Introduction to Experimental Biophysics, 2017
Edward S. Allgeyer, Gary Craig, Sanjeev Kumar Kandpal, Jeremy Grant, Michael D. Mason
where the total cross section also equals the commonly used extinction cross section. The extinction cross section gives the rate at which energy is removed from an incoming beam of light due to scattering and absorption in a closed surface surrounding the scatterer via the so- called optical theorem. As the magnetic field (inherent in any light–matter interaction) has little effect on charged particles moving at nonrelativistic speeds, it is generally neglected in the physical picture of scattering. However, note that this is not true for extremely high-power sources, such as high-power lasers, which can accelerate charges to near-relativistic speeds. It is of note that there are a variety of semiredundant ways to present extinction measurements. Twelve of these are shown in Table 12.1. The extinction cross section of a homogeneous sample multiplied by the number density gives the extinction constant. The extinction constant, related to the molar absorptivity or (molar) extinction coefficient via Avogadro’s number, can be used in the familiar Beer–Lambert law to compute the attenuation of light traveling through a sample (neglecting multiple scattering events).
A set of basis functions to improve numerical calculation of Mie scattering in the Chandrasekhar-Sekera representation
Published in Waves in Random and Complex Media, 2021
Alexandre Souto Martinez, José Renato Alcarás, Tiago José Arruda
Using the following sum rules: and expanding the and functions up to around the backward and forward scattering directions one obtains the forwards/backwards scattering amplitudes: where From Equation (11), one obtains the following properties for the exact forward amplitude, which is used to calculate the total scattering cross section using the optical theorem: . Similarly, for the backward scattering amplitude, which gives the backscattering (radar) cross Section [1–4], one has . For future use, let us define the following quantity where is given by Equation (7). This quantity is central to correct the non-commutability of limits in the small particle approximation in the Chandrasekhar-Sekera representation.
Stealth and equiluminous materials for scattering cancellation and wave diffusion
Published in Waves in Random and Complex Media, 2021
S. Kuznetsova, J. P. Groby, L. M. Garcia-Raffi, V. Romero-García
The wave scattering by a distribution of scatterers can effectively be more precisely described by the MST [59,60]. The far-field expression of the scattered field provided by the MST (see Appendix 1 for more details) when the structure is radiated by a plane wave with wave vector , is given by where and the far-field scattered amplitude , at angle θ, reads as with , the azimuthal angle of the position vector of the i-th cylinder and , the scattering coefficients of the i-th cylinder calculated by MST. The scattered far-field intensity is thus proportional to . The scattering cross section of the scatterer distribution when excited by a plane wave is also computed by applying the Optical Theorem (see Appendix 1) via
Crucial importance of correlation between cross sections and angular distributions in nuclear data of 28Si on estimation of uncertainty of neutron dose penetrating a thick concrete
Published in Journal of Nuclear Science and Technology, 2022
Naoki Yamano, Tsunenori Inakura, Chikako Ishizuka, Satoshi Chiba
The random files generated by SANDY were created by processing only the data of the covariance files MF32, MF33 and MF34 (MT251 only) created by T6. On the other hand, the random files generated by T6 includes perturbations of the angular distribution of secondary neutrons and correlation to other quantities. Figure 7 shows the correlation between the total cross section and the elastic scattering cross section at 0 degree in the 1000 random files generated by T6. It is clear that there is a positive correlation between the total cross section and the forward elastic scattering cross section consistent with Wick’s limit derived from the optical theorem. This correlation gives rise to the cancellation of the variance of the dose of the penetrated neutrons in the following manner: in general, neutron transmission decreases as the total cross section increases. However, the forward scattering cross section, which is positively correlated with the total cross section, works to increase neutron transmission. Therefore, the forward elastic scattering cross section changes so as to cancel the change in neutron transmission caused by the change in the total cross section caused by the perturbation of the parameter. That is, the standard deviation of neutron dose was reduced when the correlation of the differential elastic scattering cross section to the total cross section was considered properly. This result was also confirmed with the calculation based on the third method, where the variance of the elastic scattering angular distribution was ignored, so its correlation to the total cross section was also ignored. Therefore, it was found that (1) uncertainty of the angular distribution data must be properly considered, (2) its correlation to other quantities like total cross section must also be considered properly, and (3) if the items (1) and (2) were ignored, the uncertainty of the dose of penetrated neutrons is overestimated. These conclusions may give an important warning to the interpretation of the neutron transport calculations which were thoroughly based on the ENDF-formatted files, where items (1) and (2) are not fulfilled in general. It has to be noticed at the same time that these conclusions are applicable to cases where the anisotropy of neutron scattering is highly important for the results like the deep penetration problems considered in this work.