arXiv 1004.52592010-04-29physics.atom-phmath-phmath.MP

Coupled tensorial form for atomic relativistic two-particle operator given in second quantization representation

Rytis Jursenas, Gintaras Merkelis

发表信息：: Central European Journal of Physics, 2009
DOI：: 10.2478/s11534-009-0126-5

英文摘要：

General formulas of the two-electron operator representing either atomic or effective interactions are given in a coupled tensorial form in relativistic approximation. The alternatives of using uncoupled, coupled and antisymmetric two-electron wave functions in constructing coupled tensorial form of the operator are studied. The second quantization technique is used. The considered operator acts in the space of states of open-subshell atoms.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Spin-other-orbit operator in the tensorial form of second quantization

The tensorial form of the spin-other-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements according to an approach, based on a combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique. One of the basic features of this approach is the use of tables of standard quantities, without which the process of obtaining matrix elements of spin-other-orbit interaction opera…

2004-05-18physics.atom-ph

On the fine structure photodetachment intensities using the irreducible tensorial expression of second quantization operators

The branching ratios of the fine-structure photodetachment intensities of S- have been calculated by Blondel et al. (J. Phys. B 39(2006)1409) using the standard irreducible tensorial operator techniques. They observed that the relative intensities were consistent with the well known Engelking-Lineberger formula (Phys. Rev. A19(1979)149) derived from the fractional parentage approach, and qualified this agreement as remarkable. In the present paper, we show that it can be understood from a general interesting angular momentum expression relating a weighted sum of squared 9j-symbols and a weight…

2008-08-26physics.atom-ph

An efficient approach for spin-angular integrations in atomic structure calculations

A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional parentage nor unit tensors. It is based on the combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique. The latter allows us to calculate graphically the irreducible tensorial products of the second quantization operators and their commutators, and …

2004-05-20physics.atom-ph

Revisiting Bohr's quantization hypothesis for the atomic orbitals

We deduce the quantization of the atomic orbit for the hydrogen's atom model proposed by Bohr without using his hypothesis of angular momentum quantization. We show that his hypothesis can be deduced from and is a consequence of the Planck's energy quantization.

2006-08-09physics.atom-ph

Integration over spin-angular variables in atomic physics

A review of methods for finding general expressions for matrix elements (non-diagonal with respect to configurations included) of any one- and two-particle operator for an arbitrary number of shells in an atomic configuration is given. These methods are compared in various aspects, and the advantages or shortcomings of each particular method are discussed. Efficient method to find the abovementioned quantities in LS coupling is presented, based on the use of symmetry properties of operators and matrix elements in three spaces (orbital, spin and quasispin), second quantization in coupled tensor…

2004-05-15physics.atom-ph

Secondly quantized multi-configurational approach for atomic databases

General method is suggested to find non-relativistic and relativistic matrix elements of one- and two-electron operators for any number of open shells in atom, requiring neither coefficients of fractional parentage nor unit tensors. It is based on second quantization in coupled tensorial form, angular momentum theory in orbital, spin and quasispin spaces and generalized graphical technique. All matrix elements (diagonal and non-diagonal with respect to configurations) differ then only by projections of quasispin of separate shells and are expressed via completely reduced (in three spaces) matr…

2004-05-14physics.atom-ph

更多相关论文收起更多论文

Frequency Light Shifts Caused by the Effects of Quantization of Atomic Motion in an Optical Lattice

Frequency light shifts resulting from the localization effects and effects of the quantization of translational atomic motion in an optical lattice is studied for a forbidden optical transition $J$=0$\to$$J$=0. In the Lamb-Dicke regime this shift is proportional to the square root from the lattice field intensity. With allowance made for magneto-dipole and quadrupole transitions, the shift does not vanish at the magic wavelength, at which the linear in intensity shift is absent. Preliminary estimates show that this shift can have a principal significance for the lattice-based atomic clocks wit…

2008-03-07physics.atom-phphysics.optics

Some new simplifications for general form of the orbit-orbit interaction operator

The general tensorial form of the orbit-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements with respect to configurations, in a uniform way. Some special cases are shown for which the orbit-orbit interaction operator reduces to simple form. The importance of different contributions to the Breit-Pauli hamiltonian is investigated in ground states and ionization potentials for Li isoelectronic sequency in the systematic way.

2004-05-14physics.atom-ph

Is the Bohr's quantization hypothesis necessary ?

We deduce the quantization of Bohr's hydrogen's atomic orbit without using his hypothesis of angular momentum quantization. We show that his hypothesis is nothing more than a consequence of the Planck's energy quantization.

2005-08-23physics.atom-phphysics.ed-ph

Optically detecting the quantization of collective atomic motion

We directly measure the quantized collective motion of a gas of thousands of ultracold atoms, coupled to light in a high-finesse optical cavity. We detect strong asymmetries, as high as 3:1, in the intensity of light scattered into low- and high-energy motional sidebands. Owing to high cavity-atom cooperativity, the optical output of the cavity contains a spectroscopic record of the energy exchanged between light and motion, directly quantifying the heat deposited by a quantum position measurement's backaction. Such backaction selectively causes the phonon occupation of the observed collective…

2011-11-29physics.atom-phphysics.opticsquant-ph

The library of subroutines for calculation of matrix elements of two-particle operators for many-electron atoms

In this paper a library for spin--angular integration in LS-coupling for many-electron atoms is presented. The software is an implementation of a methodology based on the second quantization in coupled tensorial form, the angular momentum theory in 3 spaces (orbital, spin and quasispin), and the graphical technique of angular momentum. This implementation extends applications of the relevant methodology to open f- shells and leads to faster execution of angular integration codes. The possibility of using some library routines for solving various angular momentum problems in atomic physics is a…

2004-05-14physics.atom-phphysics.comp-ph

Effects of Non-idealities and Quantization of the Center of Mass Motion on Symmetric and Asymmetric Collective States in a Collective State Atomic Interferometer

We investigate the behavior of an ensemble of $N$ non-interacting, identical atoms, excited by a laser. In general, the $i$-th atom sees a Rabi frequency $Ω_i$, an initial position dependent laser phase $ϕ_i$, and a motion induced Doppler shift of $δ_i$. When $Ω_i$ or $δ_i$ is distinct for each atom, the system evolves into a superposition of $2^N$ intercoupled states, of which there are $N+1$ symmetric and $(2^N-(N+1))$ asymmetric collective states. For a collective state atomic interferometer (COSAIN) we recently proposed, it is important to understand the behavior of all the collective stat…

2015-02-24physics.atom-phquant-ph

Pure spin-angular momentum coefficients for non-scalar one-particle operators in jj-coupling

A revised program for generating the spin-angular coefficients in relativistic atomic structure calculations is presented. When compared with our previous version [G.Gaigalas, S.Fritzsche and I.P.Grant, CPC 139 (2001) 263], the new version of the Anco program now provides these coefficients for both, scalar as well as non-scalar one-particle operators as they arise frequently in the study of transition probabilities, photoionization and electron capture processes, the alignment transfer through excited atomic states, collision strengths, and in many other investigations. The program is based o…

2004-05-31physics.atom-phphysics.comp-ph

Multiconfiguration electron density function for the ATSP2K-package

A new ATSP2K module is presented for evaluating the electron density function of any multiconfiguration Hartree-Fock or configuration interaction wave function in the non relativistic or relativistic Breit-Pauli approximation. It is first stressed that the density function is not a priori spherically symmetric in the general open shell case. Ways of building it as a spherical symmetric function are discussed, from which the radial electron density function emerges. This function is written in second quantized coupled tensorial form for exploring the atomic spherical symmetry. The calculation o…

2009-07-16physics.atom-phphysics.chem-phphysics.comp-ph

Quantum Electrodynamic Corrections to the g Factor of Helium P States

The Lande g factor describes the response of an atomic energy level to an external perturbation by a uniform and constant magnetic field. In the case of many-electron systems, the leading term is given by the interaction mu_B*(L+2S.B), where L and S are the orbital and spin angular momentum operators, respectively, summed over all electrons. For helium, a long-standing experimental-theoretical discrepancy for P states motivates a reevaluation of the higher-order terms which follow from relativistic quantum theory and quantum electrodynamics (QED). The tensor structure of relativistic correctio…

2012-09-24hep-phphysics.atom-ph

Cavity polaritons with Rydberg blockade and long-range interactions

We study interactions between polaritons, arising when photons strongly couple to collective excitations in an array of two-level atoms trapped in an optical lattice inside a cavity. We consider two types of interactions between atoms: Dipolar forces and atomic saturability, which ranges from hard-core repulsion to Rydberg blockade. We show that, in spite of the underlying repulsion in the subsystem of atomic excitations, saturability induces a broadband bunching of photons for two-polariton scattering states. We interpret this bunching as a result of interference, and trace it back to the mis…

2016-07-28physics.atom-phquant-ph