اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدCorrection to the Molieres formula for multiple scattering
202
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The quasiclassical correction to the Molieres formula for multiple scattering is derived. The consideration is based on the scattering amplitude, obtained with the first quasiclassical correction taken into account for arbitrary localized but not spherically symmetric potential. Unlike the leading term, the correction to the Molieres formula contains the target density $n$ and thickness $L$ not only in the combination $nL$ (areal density). Therefore, this correction can be reffered to as the bulk density correction. It turns out that the bulk density correction is small even for high density. This result explains the wide region of applicability of the Molieres formula.
قيم البحث
اقرأ أيضاً
Frequency domain super-heterodyne laser light scattering is utilized in a low angle integral measurement configuration to determine flow and diffusion in charged sphere suspensions showing moderate to strong multiple scattering. We introduce an empir
ical correction to subtract the multiple scattering background and isolate the singly scattered light. We demonstrate the excellent feasibility of this simple approach for turbid suspensions of transmittance T>0.4. We study the particle concentration dependence of the electro-kinetic mobility in low salt aqueous suspension over an extended concentration regime and observe a maximum at intermediate concentrations. We further use our scheme for measurements of the self-diffusion coefficients in the fluid samples in the absence or presence of shear, as well as in polycrystalline samples during crystallization and coarsening. We discuss the scope and limits of our approach as well as possible future applications.
The Coulomb correction (difference from the 1st Born approximation) to the Moli`{e}re screening angle in multiple Coulomb scattering theory is evaluated with the allowance for inelastic contribution. The controversy between dominance of close- or rem
ote-collision contributions to Coulomb correction is discussed. For scattering centres represented by a Coulomb potential with a generic (not necessarily spherically symmetric) creening function, the Coulomb correction is proven to be screening-independent, by virtue of the eikonal phase cancellation in regions distant from the Coulomb singularity. Treating the atom %more self-consistently, as an assembly of pointlike electrons and the nucleus, and summing the scattering probability over all the final atom states, it is shown that besides the Coulomb correction due to close encounters of the incident charged particle with atomic nuclei, there are similar corrections due to close encounters with atomic electrons (an analog of Bloch correction). For low $Z eq1$ the latter contribution can reach $sim 25%$, but its observation is partly obscured by multiple scattering effects.
The muonic vacuum polarization contribution to the $g$-factor of the electron bound in a nuclear potential is investigated theoretically. The electric as well as the magnetic loop contributions are evaluated. We found these muonic effects to be obser
vable in planned trapped-ion experiments with light and medium-heavy highly charged ions. The enhancement due to the strong Coulomb field boosts these contributions much above the corresponding terms in the free-electron $g$-factor. Due to their magnitude, muonic vacuum polarization terms are also significant in planned determinations of the fine-structure constant from the bound-electron $g$-factor.
Kontsevichs formula is a recursion that calculates the number of rational degree $d$ curves in $mathbb{P}_{mathbb{C}}^2$ passing through $3d-1$ general positioned points. Kontsevich proved it by considering curves that satisfy extra conditions beside
s the given point conditions. These crucial extra conditions are two line conditions and a condition called cross-ratio. This paper addresses the question whether there is a general Kontsevichs formula which holds for more than one cross-ratio. Using tropical geometry, we obtain such a recursive formula. For that we use a correspondence theorem arXiv:1509.07453 that relates the algebro-geometric numbers in question to tropical ones. It turns out that the general tropical Kontsevichs formula we obtain is capable of not only computing the algebro-geometric numbers we are looking for, but also of computing further tropical numbers for which there is no correspondence theorem yet. We show that our recursive general Kontsevichs formula implies the original Kontsevichs formula and that the initial values are the numbers Kontsevichs fomula provides and purely combinatorial numbers, so-called cross-ratio multiplicities.
I argue that a version of the quantum-corrected Ryu-Takayanagi formula holds in any quantum error-correcting code. I present this result as a series of theorems of increasing generality, with the final statement expressed in the language of operator-
algebra quantum error correction. In AdS/CFT this gives a purely boundary interpretation of the formula. I also extend a recent theorem, which established entanglement-wedge reconstruction in AdS/CFT, when interpreted as a subsystem code, to the more general, and I argue more physical, case of subalgebra codes. For completeness, I include a self-contained presentation of the theory of von Neumann algebras on finite-dimensional Hilbert spaces, as well as the algebraic definition of entropy. The results confirm a close relationship between bulk gauge transformations, edge-modes/soft-hair on black holes, and the Ryu-Takayanagi formula. They also suggest a new perspective on the homology constraint, which basically is to get rid of it in a way that preserves the validity of the formula, but which removes any tension with the linearity of quantum mechanics. Moreover they suggest a boundary interpretation of the bit threads recently introduced by Freedman and Headrick.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
