Calculation Of Transition Matrix Elements Research Articles

Calculation of Dipole Transition Matrix Elements and Expectation Values by Vibrational Coupled Cluster Method.

An effective operator approach based on the coupled cluster method is described and applied to calculate vibrational expectation values and absolute transition matrix elements. Coupled cluster linear response theory (CCLRT) is used to calculate excited states. The convergence pattern of these properties with the rank of the excitation operator is studied. The method is applied to a water molecule. Arponen-type double similarity transformation in extended coupled cluster (ECCM) framework is also used to generate an effective operator, and the convergence pattern of these properties is compared to the normal coupled cluster (NCCM) approach. It is found that the coupled cluster method provides an accurate description of these quantities for low lying vibrational excited states. The ECCM provides a significant improvement for the calculation of the transition matrix elements.

Computational strategy using improved virtual orbitals to ensure orthogonality of excited states to the ground state and to each other for calculation of transition matrix elements

Computational strategy using improved virtual orbitals to ensure orthogonality of excited states to the ground state and to each other for calculation of transition matrix elements

Engineered selection rules for tunable coupling in a superconducting quantum circuit

Engineering selection rules of transitions is a useful strategy for coupling and decoupling qubits in superconducting quantum circuits. Following this approach, we implement a tunable coupling scheme between two flux qubits. The qubits are coupled parametrically under microwave driving via the nonlinear inductance of a third qubit. The measured on-state coupling as well as the off-state residual coupling depends on the coupler bias and agrees quantitatively with a calculation of transition matrix elements of a three-qubit Hamiltonian.

Calculation of transition matrix elements by nonsingular orbital transformations

A general strategy is described for the evaluation of transition matrix elements between pairs of full class CI wave functions built up from mutually nonorthogonal molecular orbitals. A new method is proposed for the counter-transformation of the linear expansion coefficients of a full CI wave function under a nonsingular transformation of the molecular-orbital basis. The method, which consists in a straightforward application of the Cauchy–Binet formula to the definition of a Slater determinant, is shown to be simple and suitable for efficient implementation on current high-performance computers. The new method appears mainly beneficial to the calculation of miscellaneous transition matrix elements among individually optimized CASSCF states and to the re-evaluation of the CASCI expansion coefficients in Slater-determinant bases formed from arbitrarily rotated (e.g., localized or, conversely, delocalized) active molecular orbitals. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Shell model method for Gamow-Teller transitions in heavy, deformed nuclei

A method for calculation of Gamow-Teller transition rates is developed by using the concept of the Projected Shell Model (PSM). The shell model basis is constructed by superimposing angular-momentum-projected multiquasiparticle configurations, and nuclear wave functions are obtained by diagonalizing the two-body interactions in these projected states. Calculation of transition matrix elements in the PSM framework is discussed in detail, and the effects caused by the Gamow-Teller residual forces and by configuration-mixing are studied. With this method, it may become possible to perform a state-by-state calculation for beta-decay and electron-capture rates in heavy, deformed nuclei at finite temperatures. Our first example indicates that, while experimentally known Gamow-Teller transition rates from the ground state of the parent nucleus are reproduced, stronger transitions from some low-lying excited states are predicted to occur, which may considerably enhance the total decay rates once these nuclei are exposed to hot stellar environments.

Nonlinear optical approach to matrix-element spectroscopy of the 5s 2S1/2 → 5p 2Pj → 5d 2Dj′ transitions in 87Rb

We present in this paper results of a nonlinear optical spectroscopy approach to measurement of excited-state transition matrix elements. Recent advances in the quality of excited-state transition matrix elements have permitted renormalization of earlier measurements of transition amplitudes associated with the 5s 2S1/2 → 5p 2Pj → 5d 2D3/2 two-photon transitions in atomic 87Rb. Previous measurements were made to high precision, but further improvement of the accuracy was limited by uncertainties in data describing the influence of energetically distant transitions. Availability of more reliable matrix elements, including relativistic all-order calculations of transition matrix elements in alkali atoms, has since significantly improved the situation. In the present paper, we show that theoretical relative transition amplitudes for the excited state 5p 2Pj → 5d 2D3/2 doublet (ratio = 1.098(9)) are now in excellent agreement with experiment (ratio = 1.090(6)). This result, combined with our recent work on caesium, shows that it is possible to determine relative line strengths, for transitions connecting atomic excited states, with precision previously found only in state-of-the-art measurements of alkali resonance doublets. Detailed discussion of the experimental technique and supporting data, including polarization measurements on the 5s 2S1/2 → 5p 2Pj → 5d 2D5/2 transitions, is also presented.

Accurate Calculation of Mgii3s–npOscillator Strengths

A careful and accurate semiempirical calculation of transition matrix elements yielded the oscillator strengths of resonance lines for the lowest np configurations in Mg II. Through an extension of previous work, particular attention was given to the determination of branching ratios for the fine-structure levels in the upper states. The new f-values provide strong theoretical support to the recent astronomical determinations by Fitzpatrick (1997) and could settle the question of the Mg abundance in the interstellar medium. The branching ratio f(3s-4p3/2)/f(3s-4p1/2) = 1.78, a value that deviates from the assumed ratio of 2 used in earlier work.

Semiclassical calculation of transition matrix elements for atoms in external fields

Closed-orbit theory is generalized to the semiclassical calculation of cross-correlated recurrence functions for atoms in external fields. The cross-correlation functions are inverted by a high-resolution spectral analyzer to obtain the semiclassical eigenenergies and transition matrix elements. The method is demonstrated for dipole transitions of the hydrogen atom in a magnetic field. This is an alternative semiclassical calculation of individual quantum transition strengths from closed-orbit theory.

Nonlinear optical response of noble metals determined from first-principles electronic structures and wave functions: Calculation of transition matrix elements

We complete the second-harmonic generation (SHG) theory to a first-principle theory by calculating also the dipole matrix elements electronically. Thus, it is now possible to calculate the polarization dependence of the nonlinear susceptibility and the SH yield. Furthermore, the surface regions, where the SHG is generated, are analyzed. In particular, we calculate the nonlinear optical response and the second harmonic yield from a Cu(001) surface. The electronic structure and the wave functions are derived from first principles using a full-potential LAPW method. The results are compared with previous calculations neglecting the k dependence of the matrix elements.

Understanding the success of nonrelativistic potential models for relativistic quark-antiquark bound states

We investigate the connection between relativistic potential models for quark-antiquark bound states and the nonrelativistic models that have been used successfully to fit and predict the spectra of relativistic systems. We use Martin's operator inequality \sqrt{p^2+m^2} <= (p^2+M^2+m^2)/2M to motivate the approximation of the relativistic kinetic energy terms in the spinless Salpeter equation by expressions of the nonrelativistic form M+\epsilon+p^2/2M for each quark. To investigate the validity of the resulting approximation numerically, we generate energy spectra for q\bar{q} mesons composed of two light or two heavy quarks using the spinless Salpeter equation with the linear-plus-Coulomb potential, and then fit the lowest few states of each type using the effective Schr\"{o}dinger description with the same potential. We find good fits to the lowest four calculated c\bar{c} and the lowest three s\bar{s} states either taking M fixed at the value M_q=\sqrt{<p^2> +m_q^2}, or allowing M_q to vary in the fit. The energies of the lowest few c\bar{s} states are then predicted with similar accuracy. The reasons for the success of the nonrelativistic approximation are identified, and explain the success of Martin's nonrelativistic predictions for the spectra of relativistic light-heavy mesons. However, we note that the agreement between the nonrelativistic and relativistic wave functions is not good, a point of potential concern for the calculation of transition matrix elements.

Angular-momentum cranking applied to multiphonon anharmonic collective vibrations: Cranked bifurcation theory.

It is shown that the self-consistent angular-momentum cranking technique can be used to generate certain types of collective vibrational solutions of time-dependent mean-field equations. The method is suitable for systems having an equilibrium mean field with an axis of symmetry and is founded on a theorem (cranking bifurcation theorem) proposed in this paper, according to which cranking about an equilibrium axis of symmetry leads to new symmetry-breaking solutions that bifurcate from the axially symmetric solution at the critical cranking frequencies given by \ensuremath{\Omega}=${\mathrm{\ensuremath{\omega}}}_{\mathrm{\ensuremath{\mu}}}$/${\mathit{K}}_{\mathrm{\ensuremath{\mu}}}$, where ${\mathrm{\ensuremath{\omega}}}_{\mathrm{\ensuremath{\mu}}}$ is a random-phase-approximation (RPA) frequency for any mode carrying ${\mathit{K}}_{\mathrm{\ensuremath{\mu}}}$\ensuremath{\ne}0 units of angular momentum along the symmetry axis. The bifurcating solutions correspond to aligned multiphonon excitations including possible large-amplitude anharmonicities. A general heuristic proof of the method is provided, as well as a perturbative demonstration within the framework of the cranked Hartree-Fock (CHF) approximation, which includes a derivation of the RPA. The static CHF approach is then compared to a perturbative treatment of the time-dependent Hartree-Fock equations using the Lindstedt method. It is also shown that the cranking approach may be applied to phenomenological mean-field models to obtain anharmonic corrections to the vibrating potential model. Finally, the calculation of transition matrix elements is briefly discussed. \textcopyright{} 1996 The American Physical Society.

Quantum Monte Carlo diagonalization with angular momentum projection.

We present a description of the quantum Monte Carlo diagonalization method. This method has been introduced recently as an approach having both the advantage of the quantum Monte Carlo method and that of the direct diagonalization of the Hamiltonian matrix. In addition, the angular momentum projection is implemented so as to remove the degeneracy with regard to magnetic quantum number. We show that with this method the convergence of the eigenvalues is improved and that the wave functions of excited states can be obtained more easily. Moreover, the calculation of transition matrix elements becomes simpler. \textcopyright{} 1996 The American Physical Society.

Analytic representations of rovibrational dipole matrix elements for the CO molecule and its isotopomers

We report new calculations of transition matrix elements for more than thirty thousand infrared lines of the CO molecule and its isotopomers inside the X 1+ ground electronic state. These lines belong to the v=1, 2, 3 bands involving very high excited states such as v 0 41 and J 0 133. The transition matrix elements have been calculated from an accurate solution of the Schrodinger equation by using two dierent theoretical electric dipole moment functions (Werner 1981; Langho & Bauschlicher 1995). For low lying levels, our data compare satisfactorily with experimental ones and related works (Goorvitch & Chackerian 1994a, b; Chackerian et al. 1994, Goorvitch 1994). Moreover, we make predictions for oscillator strengths and Einstein coecients involving high excited transitions. In addition, we report simple analytic formulae that t our results for 12 C 16 O with an accuracy better than 10 2 as a function of m =( J 0 ( J 0 +1 ) J 00 (J 00 +1 )) =2 for each vibrational sequence and band. They oer an easy way to compute the various intensities of these rovibrational transitions whose transition energies may be introduced via the available Dunham coecients.

Mass of Light Neutrino and Right-Handed Current in 76Ge and 82Se 0νββ Decays11The project supported by National Natural Science Foundation of China under Grant No. 18975038B.

We discuss the 0νββ decay mediated by a light neutrino. Two-nucleon mechanism and shell-model wave function are used in this paper. Also we take into account the influences of both nuclear short-range correlation term and finite nucleon size on the calculations of transition matrix elements. The relation between the mixing parameter η of right-handed current and the Majorana neutrino mass mν is obtained by fitting the experimental data of 0νββ decay lifetimes of 76Ge and 82Se.

Simple Model Calculations for Optical Constants of Copper

AbstractA simple s‐d band model is used for the interpretation of ϵ2(ω) for copper. Fitting simple polynomials for transition matrix elments, analytical expressions are obtained for ϵ2(ω) in terms of band parameters of the s‐d model. This expression is used to study the effect of matrix elements and variation of relaxation energy on ϵ2(ω) of copper. It is shown that such a simple model is sufficient to study such a variation and, therefore, to study the qualitative variation of ϵ2(ω). The model is also used to explain the peaks in dϵ2(ω)/dω curve successfully. The effect of hybridization amongst s and d bands is also taken into account for the calculation of transition matrix elements and the resulting effects in ϵ2(ω) are calculated.

The solution of driven equations by R-matrix propagation methods

A method for the solution of the inhomogeneous (driven) Schrödinger equation is presented which is a generalization of the R-matrix propagation technique developed by Light and Walker. The method is numerically stable and allows the direct calculation of transition matrix elements for photodissociation (or photoionization) from the asymptotic form of the wave function. Thus, no additional integrals need to be computed. The method makes direct contact with the work of Freed et al. and Heller and demonstrates that straightforward modifications of standard collision theory can be used for the half-collision problem.

Nonadiabatic Quantum Theory of Interstitial Diffusion in Crystals

AbstractThe influence of the nonadiabaticity of interstitial motion on the quantum underbarrier diffusion is discussed. The wave functions of crystals with an impurity, localized in initial and final positions, are obtained and used for the calculation of the probability of interstitial transitions from one interstitial to another per unit time. The temperature dependence of this transition probability is analysed, taking into account the nonadiabaticity of impurity motion and the deviation from the Condon approximation which is used for the calculation of transition matrix elements.

Calculation of electronic transition matrix elements based on local atomic environment

In a wide variety of solids the electronic structure is well described in terms of local atomic environment by the recursion method. A theory of perturbations, directed towards the calculation of transition matrix elements, is developed in terms of the local environment using the recursion method as the unperturbed solution. As well as embodying this physical concept, the theory permits calculations on systems with many more degrees of freedom than other methods.

Radiative Transitions in Semiconductors

A multicomponent formalism similar to that of Adams is developed and applied to the calculation of transition matrix elements. The problem of the perturbed periodic potential is treated in the Bloch representation in such a way that the wave functions may be expressed in explicit form. First-order corrections to the effective mass theory are obtained, and matrix elements for radiative intraband and allowed and forbidden interband transitions are presented.

Holes and particles in shell models

The study of nuclear and atomic shell models involves the calculation of matrix elements of operators between many-body configurations. This paper shows how the occupation number representation of Dirac can be used in such calculations, especially for configurations near closed shells. Methods for the construction of many-body wave functions are given, and the equivalence of holes and particles discussed. Application is made to the calculation of transition matrix elements for holes and particles and to the investigation of two body interactions. In particular the interaction between holes and particles is considered.