Localization of the Essential Spectrum for Relativistic N-Electron Ions and Atoms
نویسنده
چکیده
The HVZ theorem is proven for the pseudorelativistic N electron Jansen-Hess operator (2 ≤ N ≤ Z) which acts on the spinor Hilbert space A(H1(R)⊗C) where A denotes antisymmetrization with respect to particle exchange. This ’no pair’ operator results from the decoupling of the electron and positron degrees of freedom up to second order in the central potential strength γ = Ze. 2000 Mathematics Subject Classification: 81Q10, 81V45
منابع مشابه
شبیهسازی نسبیتی معادله ولاسوف برای انبساط پلاسما به خلاء
In this study, relativistic Vlasov simulation of plasma for expansion of collisionless plasma for into vacuum is presented. The model is based on 1+1 dimensional phase space and electrostatic approximation. For this purpose, the electron dynamics is studied by the relativistic Vlasov equation. Regardless of the ions temperature, fluid equations are used for their dynamics. The initial electro...
متن کاملCalculation of the total cross section for the ionization of H, He, Ne and Ar atoms by bare ions at the high energy range
In the present work, the total cross-section for the ionization of H, He, Ne and Ar atoms by +He2+ ، H+ ، Li3 ions has been calculated. In these calculations, a binary encounter approximation in the form of a two-body process between projectile ions and atomic electrons at the high energy range has been implemented. In order to enter the nuclear role of the target atom, the atomic electron vel...
متن کاملThe essential spectrum of relativistic one-electron ions in the Jansen-Hess model
It is shown that the essential spectrum of the pseudo-relativistic Dirac operator according to Jansen and Hess which includes the Coulomb potential up to second order, extends from mc to infinity when the nuclear charge is below the critical value Ze ≈ 1.006. There is also no singular continuous spectrum in that case, and for small Z no embedded eigenvalues. This work is an extension of investi...
متن کاملThe Hvz Theorem for a Pseudo-relativistic Operator
The localization of the essential spectrum of a relativistic twoelectron ion is provided. The analysis is performed with the help of the pseudorelativistic Brown-Ravenhall operator which is the restriction of the CoulombDirac operator to the electrons’ positive spectral subspace.
متن کاملAn approximate analytical solution of the Bethe equation for charged particles in the range of radiotherapy energy
Charged particles such as protons and carbon ions are an increasing tool in radiation therapy. However, unresolved physical problems prevent optimal performance, including estimating the deposited dose in non-homogeneous tissue, is an essential aspect of optimizing treatment. The Monte Carlo (MC) method can be used to estimate the amount of radiation, but, this powerful computing operation is v...
متن کامل