On the essential spectrum of the Jansen-Hess operator for two-electron ions
نویسنده
چکیده
Based on the HVZ theorem and dilation analyticity of the pseudorelativistic no-pair Jansen-Hess operator, it is shown that for subcritical potential strength (Z ≤ 90) the singular continuous spectrum is absent. The bound is slightly higher (Z ≤ 102) for the Brown-Ravenhall operator whose eigenvalues λ are, by the virial theorem, confined to λ < 2m if Z ≤ 50.
منابع مشابه
The 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 کاملLocalization of the Essential Spectrum for Relativistic N-Electron Ions and Atoms
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 Su...
متن کاملThe single-particle pseudorelativistic Jansen–Hess operator with magnetic field
The pseudorelativistic no-pair Jansen–Hess operator is derived for the case where in addition to the Coulomb potential an external magnetic field B is permitted. With some restrictions on the vector potential, it is shown that this operator is positive provided the strength γ of the Coulomb potential is below a critical value (γc 0.35, depending on the magnetic field energy Ef ). Moreover, for ...
متن کاملSpectrum and essential spectrum of linear combinations of composition operators on the Hardy space H2
Let -----. For an analytic self-map --- of --- , Let --- be the composition operator with composite map --- so that ----. Let --- be a bounded analytic function on --- . The weighted composition operator --- is defined by --- . Suppose that --- is the Hardy space, consisting of all analytic functions defined on --- , whose Maclaurin cofficients are square summable. .....
متن کاملMeasure of non strict singularity of Schechter essential spectrum of two bounded operators and application
In this paper, we discuss the essential spectrum of sum of two bounded operators using measure of non strict singularity. Based on this new investigation, a problem of one-speed neutron transport operator is presented.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006