Atoms In Strong Magnetic Fields Research Articles

One-Dimensional Models for Atoms in Strong Magnetic Fields, II: Anti-Symmetry in the Landau Levels

Electrons in strong magnetic fields can be described by one-dimensional models in which the Coulomb potential and interactions are replaced by regularizations associated with the lowest Landau band. For a large class of models of these type, we show that the maximum number of electrons that can be bound is less than a Z + Z f(Z). The function f(Z) represents a small non-linear growth which is quadratic in log Z when the magnetic field strength grows polynomially with the nuclear charge Z. In contrast to earlier work, the models considered here include those arising from realistic cases in which the full trial wave function for N-electrons is the product of an N-electron trial function in one-dimension and an antisymmetric product of states in the lowest Landau level.

Theory of excitonic artificial atoms: InGaAs/GaAs quantum dots in strong magnetic fields

We develop a theory of excitonic artificial atoms in strong magnetic fields. The excitonic atoms are formed by N electrons and holes confined in a quantum dot. The single-particle levels are described by the Fock-Darwin spectrum in a magnetic field. The magnetic field induces crossing of energy levels and allows us to engineer degenerate shells. We apply exact diagonalization techniques to calculate the magnetic-field evolution of the ground state of the N-electron-hole complex and its emission spectra. We focus on degenerate shells and show that excitons condense into correlated states due to hidden symmetry. We relate the Fock-Darwin spectrum, hidden symmetries, and direct and exchange interaction among particles to the emission spectra as a function of number of electron-hole pairs (excitation power) and magnetic field.

High-|m|Rydberg states in strong magnetic fields

We calculate spectra and wave functions of Rydberg atoms in strong magnetic fields using adiabatic basis sets, which reflect the different time scales of the electronic motion parallel and transverse to the magnetic field. For large absolute values of the azimuthal quantum number m, nonadiabatic corrections are found to be negligible, and the adiabatic basis states and their energies are exact solutions. With decreasing value of $|m|,$ the system turns nonadiabatic, and the statistical behavior of the spectra changes from being consistent with classically regular to being consistent with classically chaotic motion. A relation describing the parameter region in which this transition occurs is obtained.

Decay rates of high-|m|Rydberg states in strong magnetic fields

We calculate the natural decay rates of Rydberg atoms in strong magnetic fields. We use adiabatic basis sets that exploit the different time scales of the electronic motion parallel and transverse to the magnetic field. For large absolute values of the azimuthal quantum number m, our approach is very efficient and naturally leads to a classification of the decay modes into magnetron, z-bounce, and cyclotron decays. We discuss the dependence of the decay rates on m, and study the enhancement of the decay rates due to thermal radiation.

On the Total Magnetic Moment of Large Atoms in Strong Magnetic Fields

We study the magnetic moment of neutral atoms in large magnetic fields. Asymptotic formulas for the energy exist with high precision in different regions depending on how large the nuclear charge Z is compared to the magnetic field strength B. All these formulas take the splitting of the kinetic energy into Landau levels as the principal feature and then treat the electric potential as a perturbation. We prove that these approximate formulas predict correctly'(to highest order) the total magnetic moment of the atom. The proof of this fact relies on a 'virial theorem' for Coulomb systems in a constant magnetic field.

Gradient corrections for semiclassical theories of atoms in strong magnetic fields

This paper is divided into two parts. In the first one the von Weizsäcker term is introduced to the magnetic Thomas–Fermi theory and the resulting MTFW functional is mathematically analyzed. In particular, it is shown that the von Weizsäcker term produces the Scott correction up to magnetic fields of order B≪Z2, in accordance with a result of Ivrii on the quantum mechanical ground state energy. The second part is dedicated to gradient corrections for semiclassical theories of atoms restricted to electrons in the lowest Landau band. We consider modifications of the Thomas–Fermi theory for strong magnetic fields (STF), i.e., for B≪Z3. The main modification consists in replacing the integration over the variables perpendicular to the field by an expansion in angular momentum eigenfunctions in the lowest Landau band. This leads to a functional (DSTF) depending on a sequence of one-dimensional densities. For a one-dimensional Fermi gas the analogue of a Weizsäcker correction has a negative sign and we discuss the corresponding modification of the DSTF functional.

Atomic dynamics in evaporative cooling of trapped alkali-metal atoms in strong magnetic fields

We investigate how the nonlinear Zeeman shift affects the dynamics of rf field-induced evaporative cooling in magnetic traps. We demonstrate for the ${}^{87}\mathrm{Rb}$ $F=2$ trapping state with wave-packet simulations how the cooling stops when the rf field frequency goes below a certain limit. We examine the applicability of semiclassical models for the strong-field case as an extension of our previous work [Phys. Rev. A 58, 3983 (1998)]. Our results verify many of the aspects observed in a recent ${}^{87}\mathrm{Rb}$ experiment [Phys. Rev. A 60, R1759 (1999)].

On the current of large atoms in strong magnetic fields

In this talk I will discuss recent results on the magnetisation/current of large atoms in strong magnetic fields. It is known from the work (E. Lieb, J.P. Solovej, and J. Yngvason, “Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions”, Commun. Math. Phys. (1994), no. 161, 77-124) of Lieb, Solovej and Yngvason that the energy and density of atoms in strong magnetic fields are given to highest order by a Magnetic Thomas Fermi theory (MTF-theory) when the magnetic field strength B and nuclear charge Z satisfy BZ -3 →0. It is, however, equally interesting to establish whether MTF-theory also gives the right asymptotic current. In this talk we will prove that this is indeed the case, at least for moderate magnetic fields. However, we will also prove that approximate ground states do not in general give the right asymptotics for the current.

Atoms in Strong Magnetic Fields:¶The High Field Limit at Fixed Nuclear Charge

Let E(B,Z,N) denote the ground state energy of an atom with N electrons and nuclear charge Z in a homogeneous magnetic field B. We study the asymptotics of E(B,Z,N) as $B\to \infty$ with N and Z fixed but arbitrary. It is shown that the leading term has the form $(\ln B)^2 e(Z,N)$, where e(Z,N) is the ground state energy of a system of N {\em bosons} with delta interactions in {\em one} dimension. This extends and refines previously known results for N=1 on the one hand, and $N,Z\to\infty$ with $B/Z^3\to\infty$ on the other hand.

A one-dimensional model for many-electron atoms in extremely strong magnetic fields: maximum negative ionization

We consider a one-dimensional model for many-electron atoms in strong magnetic fields in which the Coulomb potential and interactions are replaced by one-dimensional regularizations associated with the lowest Landau level. For this model we show that the maximum number of electrons is bounded above by 2Z+1 + c sqrt{B}. We follow Lieb's strategy in which convexity plays a critical role. For the case of two electrons and fractional nuclear charge, we also discuss the critical value at which the nuclear charge becomes too weak to bind two electrons.

Anisotropy of atoms in strong magnetic fields

The anisotropy of the atomic electronic density caused by strong magnetic fields is discussed here in the context of the statistical theory. In the framework of the current-density functional theory, a derivation is given of the gradient terms, necessary for anisotropy, based on the polarizability of free electrons in a magnetic field. Numerical results for the electronic density show a strong elongation of the electronic density along the field direction. In very high magnetic fields the electronic density is localized in thin columns along the field.

Ground state of the lithium atom in strong magnetic fields

The ground and some excited states of the Li atom in external uniform magnetic fields are calculated by means of our two-dimensional mesh Hartree-Fock method for field strengths ranging from zero up to $2.35\ifmmode\times\else\texttimes\fi{}{10}^{8}\phantom{\rule{0ex}{0ex}}\mathrm{T}$. With increasing field strength, the ground state undergoes two transitions involving three different electronic configurations: for weak fields, the ground-state configuration arises from the field-free ${1s}^{2}2s$ configuration; for intermediate fields, it arises from the ${1s}^{2}{2p}_{\ensuremath{-}1}$ configuration, and in high fields, the ${1s2p}_{\ensuremath{-}1}{3d}_{\ensuremath{-}2}$ electronic configuration is responsible for the properties of the atom. The transition field strengths are determined. Calculations on the ground state of the ${\mathrm{Li}}^{+}$ ion allow us to describe the field-dependent ionization energy of the Li atom. Some general arguments on the ground states of multielectron atoms in strong magnetic fields are provided.

Distribution of the absorption by chaotic states in quantum dots.

The mesoscopic fluctuations of the absorption at optical transitions from a low energy regular state to high energy chaotic states in an aggregate of semiconductor quantum dots is studied. We provide a universal dependence of the distribution of the absorption coefficient on the total number of dots and the ratio of the level broadening to the level spacing. The distribution remain broad even at large broadening, and the absorption spectrum should demonstrate a strong sensitivity to weak magnetic field in the region of large and weak absorption. The results can also apply to the absorption of Rydberg atoms in strong magnetic field at the pre-threshold ionization.

Hartree-Fock studies of atoms in strong magnetic fields.

We present comprehensive calculations of the electronic structure of selected first-row atoms in uniform magnetic fields of strength \ensuremath{\le}${10}^{10}$ G, within a flexible implementation of the Hartree-Fock formalism. Ground-state and low-lying excited state properties are presented for first-row atoms He, Li, C, and ion ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$. We predict and describe a series of ground-state quantum transitions as a function of magnetic field strength. Due to its astrophysical importance, highly excited states of neutral He are also computed. Comparisons are made with previous works, where available. \textcopyright{} 1996 The American Physical Society.

Observation of high angular momentum states of Rydberg atoms in strong magnetic and weak crossed electric fields

High angular momentum Rydberg states of atoms in strong magnetic fields or in strong magnetic and weak crossed electric fields correspond to classical regular drift trajectories around the positive ion core. The motion can be adiabatically separated in a fast cyclotron motion, an oscillation in magnetic field direction, and a slow drift motion. Some of the drift trajectories display huge electric-dipole moments induced by the weak electric field. Corresponding atomic drift states with large electric dipole moments are theoretically predicted. In the experiment drift states are excited by an optical one-photon transition. The excitation of drift-state atoms is very efficient in the vicinity of anti-crossings between Rydberg states with large photoexcitation cross section and drift states. The drift-state atoms are separated from other Rydberg atoms via electric-dipole deflection in an inhomogeneous electric field. The size of the observed dipole moments agrees quite well with theoretical values.

Atomic orbital basis set optimization for ab initio calculations of molecules with hydrogen atoms in strong magnetic fields

We present the results of the optimization of a recently established atomic orbital basis set for ab initio calculations of molecules in strong magnetic fields. The optimization is performed for the ground and many low-lying excited states of the hydrogen atom in the presence of a magnetic field of arbitrary strength. The behavior of the nonlinear variational parameters of the atomic orbitals is discussed as a function of the field strength. In order to demonstrate the suitability of our atomic orbital basis set for the calculation of molecular spectra and wave functions in a uniform magnetic field we present, as first results of a molecular calculation, electronic potential energy curves for the H+2 ion in a magnetic field.

Behaviour and spectroscopy of (anti) hydrogen atoms in strong magnetic fields

Since it has been demonstrated that antiprotons can be captured in sizeable amounts in ion traps, the intriguing question has been raised whether or not these antiprotons can be used for producingantihydrogen atoms. One route proposed is the merging of trapped antiprotons with a cold trapped plasma of positrons. In this case the formation of antihydrogen proceeds most likely through three-body recombination (p−e+e+→\(\bar H\) e+) into high Rydberg states of\(\bar H\), followed by a rapid cascade of transitions to low-lying states. To assess the influence of the trapping magnetic field (on the order of a few tesla) upon the formation process of\(\bar H\) we review the present knowledge of the behaviour and properties of hydrogen (and antihydrogen) atoms in strong magnetic fields — a subject which has been very topical in recent years because of its relation to the problem of “quantum” chaos.

Finite-Velocity Effects on Atoms in Strong Magnetic Fields and Implications for Neutron Star Atmospheres

view Abstract Citations (47) References (27) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Finite-Velocity Effects on Atoms in Strong Magnetic Fields and Implications for Neutron Star Atmospheres Pavlov, G. G. ; Meszaros, P. Abstract We consider the effects of a finite velocity on the properties of atoms in the strong magnetic field characteristic of neutron stars. Whereas in the absence of significant center-of-mass velocities the atomic structure is determined by the cylindrical symmetry, the electric field induced by the finite motion breaks this symmetry and distorts the atomic structure. The resulting dependence of the total energy on a generalized momentum of the atom can be interpreted in terms of a mass anisotropy the atom becomes "heavier" when it moves across the magnetic field, the transverse mass being higher for the more excited states. The field-dependent mass anisotropy, together with the field dependence of the binding energy of the atom, leads to a bending of the trajectories of neutral atoms in nonuniform magnetic fields, tending to channel and retain them in regions of high field. It also leads to a number of thermodynamic and spectroscopic effects. In particular, the mass anisotropy introduces both quantitative spectroscopic changes relative to the stationary magnetized atom, such as additional shifts and broadening of photoionization edges and lines, as well as qualitative changes, such as new selection rules for radiative processes and for the annihilation of magnetic positronium. The ionization balance of atoms and ions in pulsar atmospheres may also be strongly influenced, which together with the opacity changes could lead to effects of significant importance for the modeling of neutron star atmospheres in magnetic fields of strength B ≳109 G. Publication: The Astrophysical Journal Pub Date: October 1993 DOI: 10.1086/173274 Bibcode: 1993ApJ...416..752P Keywords: ATOMIC PROCESSES; MAGNETIC FIELDS; STARS: NEUTRON; STARS: PULSARS: GENERAL full text sources ADS | data products SIMBAD (2)

Relativistic variational calculations with finite nuclear size: Application to hydrogenic atoms in strong magnetic fields.

A finite-basis-set method is introduced for calculations involving an electron in the presence of a finite-size nucleus. It is found that the inclusion of powers of the form ${\mathit{r}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}+\mathit{n}}$ in the basis set, where \ensuremath{\gamma} is a real number and n an integer, is of fundamental importance, increasing the convergence in the energy eigenvalues by several orders of magnitude in the case of a large nuclear charge. This conclusion applies also to one-electron potential calculations such as Dirac-Hartree-Fock. The method is applied to calculations of the low-lying levels of hydrogenic atoms in strong magnetic fields. For B\ensuremath{\lesssim}${10}^{9}$${\mathit{Z}}^{2}$ G, the finite-nuclear-size correction is of the same order as that for B=0. For B\ensuremath{\gtrsim}${10}^{9}$${\mathit{Z}}^{2}$ G, the correction increases linearly with B for the ground state, and assumes a more complicated dependence for the excited states due to the presence of more than one peak in each radial wave function for B=0.

On the Structure of Atoms in Strong Magnetic Fields

AbstractThe problem of a multi‐electron atom in a strong magnetic field is treated within the framework of a new statistical model. Here, the charge density n is required to have axial symmmetry. The partial factorization ansatz, n(ϱ, z) = nϱ(ϱ) · nz(ϱ;z), when introduced into Kadomtsev's equation, leads to a second‐order, non‐linear partial differential equation for nz that is valid over an important range of field strengths. Analytical solutions for two limiting approximations are consistent with earlier qualitative studies. Some illustrative, numerical solutions for a less restrictive approximation reveal atomic structures analogous to accurate hydrogenic results, already in the literature.