Model Wave Functions Research Articles

TbW anomalous couplings in the Two Higgs Doublet Model

We make a complete one loop calculation of the $tbW$ couplings in the Two Higgs Doublet Model. We evaluate both the anomalous couplings $g_L$ and $g_R$ as well as left handed and right handed component of $tbW$. The computation is done in the Feynman gauge using the on-shell scheme renormalization for the Standard Model wave functions and parameters. We first show that the relative corrections to these anomalous couplings are rather small in most regions of the parameter space. We then analyze the effects of these anomalous couplings on certain observables such as top quark polarization in single top production through $t-$channel as well as $W^\pm$ boson helicity fractions in top decay.

Communication: Unambiguous comparison of many-electron wavefunctions through their overlaps.

A simple and powerful method for comparing many-electron wavefunctions constructed at different levels of theory is presented. By using wavefunction overlaps, it is possible to analyze the effects of varying wavefunction models, molecular orbitals, and one-electron basis sets. The computation of wavefunction overlaps eliminates the inherent ambiguity connected to more rudimentary wavefunction analysis protocols, such as visualization of orbitals or comparing selected physical observables. Instead, wavefunction overlaps allow processing the many-electron wavefunctions in their full inherent complexity. The presented method is particularly effective for excited state calculations as it allows for automatic monitoring of changes in the ordering of the excited states. A numerical demonstration based on multireference computations of two test systems, the selenoacrolein molecule and an iridium complex, is presented.

The longitudinal and transverse distributions of the pion wave function from the present experimental data on the pion–photon transition form factor

It is noted that the low-energy behavior of the pion-photon transition form factor $F_{\pi\gamma}(Q^2)$ is sensitive to the transverse distribution of the pion wavefunction, and its high-energy behavior is sensitive to the longitudinal one. Thus a careful study on $F_{\pi\gamma}(Q^2)$ can provide helpful information on the pion wavefunction precisely. In this paper, we present a combined analysis of the data on $F_{\pi\gamma}(Q^2)$ reported by the CELLO, the CLEO, the BABAR and the BELLE collaborations. It is performed by using the method of least squares. By using the combined measurements of BELLE and CLEO Collaborations, the pion wavefunction longitudinal and transverse behavior can be fixed to a certain degree, i.e. we obtain $\beta \in [0.691,0.757] \rm GeV$ and $B \in [0.00,0.235]$ for $P_{\chi^2} \geq 90\%$, where $\beta$ and $B$ are two parameters of a convenient pion wavefunction model whose distribution amplitude can mimic the various longitudinal behavior under proper choice of parameters. We observe that the CELLO, CLEO and BELLE data are consistent with each other, all of which prefers the asymptotic-like distribution amplitude; while the BABAR data prefers a more broad distribution amplitude, such as the CZ-like one.

Semiclassical-wave-function perspective on high-harmonic generation

We introduce a semi-classical wavefunction (SCWF) model for strong-field physics and attosecond science. When applied to high harmonic generation (HHG), this formalism allows one to show that the natural time-domain separation of the contribution of ionization, propagation and recollisions to the HHG process leads to a frequency-domain factorization of the harmonic yield into these same contributions, for any choice of atomic or molecular potential. We first derive the factorization from the natural expression of the dipole signal in the temporal domain by using a reference system, as in the quantitative rescattering (QRS) formalism [J. Phys. B. 43, 122001 (2010)]. Alternatively, we show how the trajectory component of the SCWF can be used to express the factorization, which also allows one to attribute individual contributions to the spectrum to the underlying trajectories.

Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect

The microscopic wave functions of the composite fermion theory can incorporate electron mass anisotropy by a trivial rescaling of the coordinates. These wave functions are very likely adiabatically connected to the actual wave functions of the anisotropic fractional quantum Hall states. We show in this article that they possess the nice property that their energies can be analytically related to the previously calculated energies for the isotropic states through a universal scale factor, thus allowing an estimation of several observables in the thermodynamic limit for all fractional quantum Hall states. The rather weak dependence of the scale factor on the anisotropy provides insight into why fractional quantum Hall effect and composite fermions are quite robust to electron mass anisotropy. We discuss how better, though still approximate, wave functions can be obtained by introducing a variational parameter, following Haldane [Phys. Rev. Lett. {\bf 107}, 116801 (2011)], but the resulting wave functions are not readily amenable to calculations. Our considerations are also applicable, with minimal modification, to the case where the dielectric function of the background material is anisotropic.

Coherent forward broadening in cold atom clouds

It is shown that homogeneous line-broadening in a diffuse cold atom cloud is proportional to the resonant optical depth of the cloud. Further, it is demonstrated how the strong directionality of the coherent interactions causes the cloud's spectra to depend strongly on its shape, even when the cloud is held at constant densities. These two numerical observations can be predicted analytically by extending the single photon wave-function model. Lastly, elongating a cloud along the line of laser propagation causes the excitation probability distribution to deviate from the exponential decay predicted by the Beer-Lambert law to the extent where the atoms in the back of the cloud are more excited than the atoms in the front. These calculations are conducted at low densities relevant to recent experiments.

Donor wave functions in Si gauged by STM images

The triumph of effective mass theory in describing the energy spectrum of dopants does not guarantee that the model wavefunctions will withstand an experimental test. Such wavefunctions have recently been probed by scanning tunneling spectroscopy, revealing localized patterns of resonantly enhanced tunneling currents. We show that the shape of the conducting splotches resemble a cut through Kohn-Luttinger (KL) hydrogenic envelopes, which modulate the interfering Bloch states of conduction electrons. All the non-monotonic features of the current profile are consistent with the charge density fluctuations observed between successive {001} atomic planes, including a counterintuitive reduction of the symmetry - a heritage of the lowered point group symmetry at these planes. A model-independent analysis of the diffraction figure constrains the value of the electron wavevector to $k_0 = (0.82 \pm 0.03)(2\pi/a_{Si})$. Unlike prior measurements, averaged over a sizeable density of electrons, this estimate is obtained directly from isolated electrons. We further investigate the model-specific anisotropy of the wave function envelope, related to the effective mass anisotropy. This anisotropy appears in the KL variational wave function envelope as the ratio between Bohr radii b=a. We demonstrate that the central cell corrected estimates for this ratio are encouragingly accurate, leading to the conclusion that the KL theory is a valid model not only for energies but for wavefunctions as well.

Variation after projection with a triaxially deformed nuclear mean field

We implemented a variation after projection (VAP) algorithm based on a triaxially deformed Hartree-Fock-Bogoliubov vacuum state. This is the first projected mean field study that includes all the quantum numbers (except parity), i.e., spin ($J$), isospin ($T$) and mass number ($A$). Systematic VAP calculations with $JTA$-projection have been performed for the even-even $sd$-shell nuclei with the USDB Hamiltonian. All the VAP ground state energies are within 500 keV above the exact shell model values. Our VAP calculations show that the spin projection has two important effects: (1) the spin projection is crucial in achieving good approximation of the full shell model calculation. (2) the intrinsic shapes of the VAP wavefunctions with spin projection are always triaxial, while the Hartree-Fock-Bogoliubov methods likely provide axial intrinsic shapes. Finally, our analysis suggests that one may not be possible to associate an intrinsic shape to an exact shell model wave function.

Extension of the wave packet molecular dynamics method towards the accurate quantum simulations of electron dynamics

In this paper, we review a multiple-wavepacket version of the Antisymmetrized Wave Packet Molecular Dynamics (AWPMD), that may be utilized to increase the accuracy and the performance of this quantum simulation method. The original WPMD method is based on parameterization of the electron wave function by a single Gaussian wave packet. It gives qualitatively better results than the classical Molecular Dynamics but the quantitative description of essentially quantum systems is rather poor. In this work, we describe a new technique based on multiple Gaussian expansion of the single-electron wave function, which is called Split Wave Packet Molecular Dynamics (SWPMD). The related theoretical formalism is given, followed by the analysis of static and dynamical properties of a quantum system of several particles, where the simulation results may be compared to the theoretical predictions. The tests are based on ionization of hydrogen atom under a strong laser pulse. We demonstrate that the SWPMD method may significantly improve the accuracy of the model wave function and enables one to simulate the quantum branching processes, including the tunneling, which was impossible in the single-wavepacket version of the method.

Choosing an atomic basis set for TD-DFT, SOPPA, ADC(2), CIS(D), CC2 and EOM-CCSD calculations of low-lying excited states of organic dyes

Aiming to pinpoint an atomic basis set providing accurate transition energies at a minimal computational cost, we investigate the evolution with basis set size of the energy of low-lying excited states in nine representative conjugated dyes with a wide panel of theoretical approaches, namely TD-DFT, SOPPA, ADC(2), CIS(D), CC2, EOM-CCSD, as well as several scaled opposite spin variants, namely SOS-CIS(D), SOS-CIS(D0) and SOS-ADC(2). At the exception of TD-DFT that displays the lowest basis set dependence, it turns out that the changes obtained when increasing the size of the basis set are rather independent of the selected wavefunction model, but strongly change according to the nature of the excited state considered. Reasonable compromises between accuracy and computational burden can be attained with 6-311+G(2d,p) that allows much faster calculations than the typical reference basis set, namely aug-cc-pVTZ, for an average loss of accuracy limited to ca. 0.02 eV.

Accuracy of Hourly Water Temperatures in Rivers Calculated from Air Temperatures

Water temperature is a critical variable for water quality control and management. The primary objective of this paper was to develop and compare simple methods to estimate hourly water temperatures in rivers. The wave function (WF) model, originally used to calculate hourly air temperature, was modified and applied to eight Alabama rivers. The results show significant improvement by using the modified WF model instead of direct linear and non-linear (polynomial and logistic) regression models with time lags (4–5 h). The average Nash–Sutcliffe coefficient (NS) used to evaluate model accuracy for the eight rivers improved from 0.71 for the linear model to 0.89 for the modified WF model with NS for most rivers exceeding 0.90. A lumped modified WF model was also developed by combining water temperature data for all eight rivers and can be applied for rivers in Alabama when no observed water temperatures are available to develop a site-specific WF model. The procedure to develop a modified WF model can be applied to other regions.

The Shell Model – Simplicity from Complexity

In order to apply the shell model to most nuclei, an effective ("residual") interaction between nucleons should be added to the single nucleon Hamiltonian. It cannot be the bare interaction which would introduce strong short range correlations into the shell model wave functions of nucleons moving independently in a potential well. For many years, many authors have been developing methods for calculating from the bare interaction, an effective interaction which may be used in the shell model. Only recently, the results seem to agree with experiment. During these years, successful shell model calculations have been carried out by using effective interactions determined consistently from measured energies of nuclei. Some old and some new results exhibit the success of this approach. In principle, shell model wave functions may be determined by a renormalized Hamiltonian which contains the effective interactions rather than the bare ones. Shell model wave functions may be used to calculate other observables if matrix elements are taken of renormalized operators. Such a program could succeed irrespective of the relation between shell model wave functions and the real ones. This would certainly be the case for ab initio calculations where a central potential well is not assumed and derivation of nuclear structure is attempted by using many body theory of nucleons interacting by the bare interaction. Still, there are observables which have been successfully calculated by shell model wave functions from real, un-renormalized operators. Several examples are briefly described below. This fact may be taken as some evidence that the "wounds" inflicted on shell model wave functions by the short range correlations occupy only a small volume and that there is a considerable overlap between shell model wave functions and the real ones. The calculated overlap between shell model and real wave functions may be obtained from derivations of the effective interaction. It is more difficult to see how the shell model may emerge as a good approximation from ab initio calculations. The question is whether the simplicity of the shell model as a good approximation will emerge from those complex calculations.

Covariant spectator theory ofnpscattering: Deuteron quadrupole moment

The deuteron quadrupole moment is calculated using two CST model wave functions obtained from the 2007 high precision fits to $np$ scattering data. Included in the calculation are a new class of isoscalar $np$ interaction currents automatically generated by the nuclear force model used in these fits. The prediction for model WJC-1, with larger relativistic P-state components, is 2.5% smaller that the experimental result, in common with the inability of models prior to 2014 to predict this important quantity. However, model WJC-2, with very small P-state components, gives agreement to better than 1%, similar to the results obtained recently from $\chi$EFT predictions to order N$^3$LO.

P-3He elastic scattering at 0.6–1 GeV: some short-range effects

Using a model wave function for 3He nucleus, where the two-body short-range correlation and three-nucleon force are considered, p-3He elastic scattering differential cross section is calculated using two different approaches, the multiple scattering formalism and the optical limit approximation, in the frame work of Glauber model at 0.6, 0.715 and 1 GeV. The results of the two approaches are similar. The principal contribution comes from the two-body short-range correlation and the effect of the three-nucleon force is relatively small. The observed results cannot describe the experimental data in the region, where the multiple scattering is dominant. These discrepancies between the theoretical and experimental results are interpreted as a result of the two-body short-range correlation and the three-nucleon force effects in the used wave function.

Описание радиационных распадов $V\to P\gamma^{*}$ в различных формах Пуанкаре-инвариантной квантовой механики

Работа посвящена описанию радиационных распадов $V \to P \gamma^{*}$ в различных основных формах Пуанкаре-инвариантной квантовой механики (ПИКМ). Для построения матричного элемента электромагнитного тока перехода используется специальная процедура, удовлетворяющая условиям лоренц-ковариантности и сохранения. В качестве иллюстрации развитого формализма в модифицированном релятивистском импульсном приближении проведено описание радиационного перехода $\rho \to \pi \gamma^{*}$. Получено аналитическое выражение для переходного формфактора $F_{\pi \rho}(Q^2)$, совпадающее во всех формах ПИКМ. Выполнены численные расчеты переходного формфактора с двумя типами модельных волновых функций.

Three-body asymptotic normalization factors for halo nuclei and their determination

The explicit forms of the true asymptotics of the three-body (312) bound state radial wave functions of halo nuclei a both with two loosely bound external neutrons and with two charged particles, valid in different parts of the asymptotic region of the configuration space, are presented. The results for three-body asymptotic normalization factors for α + n + n → 6He and n + α + α → 9Be obtained from the comparative analysis of these asymptotic forms with the specific approximate model wave functions for asymptotic regions are also given.

Be14(g.s.)and single-particle energies inBe13

Coupling two $sd$-shell neutrons to a pure $p$-shell $^{12}\mathrm{Be}$ ground state (g.s.), rather than to the physical g.s., removes difficulties in applying a previous simple model to $^{14}\mathrm{Be}$. I have calculated the g.s. wave function in this simple model, and have estimated the $2{s}_{1/2}$ single-particle energy.

Spectrum of edge states in theν=0quantum Hall phases in graphene

Edge excitations of the $\ensuremath{\nu}=0$ quantum Hall state in monolayer graphene are studied within the mean-field theory with different symmetry-breaking terms. The analytical expressions for the continuum (Dirac) model wave functions are obtained for the charge density wave, Kekul\'e distortion, ferromagnetic, and (canted) antiferromagnetic phases. The dispersion equations for each phase and boundary type (zigzag and armchair) are derived, numerically solved, and compared to the results of the corresponding effective tight-binding model. The effect of the next-to-nearest neighbor hopping parameter on the edge state spectrum is studied and revealed to be essential. The criteria for the existence of gapless edge states are established for each phase and edge type.

Container structure of alpha-alpha-Lambda clusters in 9-Lambda-Beryrium

A new concept of clustering is discussed in |$\Lambda$| hypernuclei using a new-type microscopic cluster model wave function, which has a structure in which constituent clusters are confined in a container, whose size is a variational parameter and which we refer to as a hyper-Tohsaki–Horiuchi–Schuck–Röpke (hyper-THSR) wave function. By using the hyper-THSR wave function, the |$2\alpha + \Lambda$|-cluster structure in |${{^9_\Lambda}\hbox{Be}}$| is investigated. We show that full microscopic solutions in the |$2\alpha + \Lambda$|-cluster system, which are given as |$2\alpha + \Lambda$| Brink-GCM (generator coordinate method) wave functions, are almost perfectly reproduced by the single configurations of the hyper-THSR wave function. The squared overlaps between both wave functions are calculated to be |$99.5$|%, |$99.4$|%, and |$97.7$|% for |$J^\pi =0^+ $|⁠, |$2^+ $|⁠, and |$4^+ $| states, respectively. We also simulate the structural change by adding the |$\Lambda$| particle, by varying the |$\Lambda N$| interaction artificially. With the increase of the |$\Lambda N$| interaction, the |$\Lambda$| particle gets to move more deeply inside the core and strongly invokes the spatial core shrinkage. Accordingly, distinct localized |$2\alpha$| clusters appear in the nucleonic intrinsic density, though, in the |${^8{\rm Be}}$| nucleus, a gaslike |$2\alpha$|-cluster structure is shown. The origin of the localization is associated with the strong effect of the Pauli principle. We conclude that the container picture of the |$2\alpha$| and |$\Lambda$| clusters is essential in understanding the cluster structure in |${^9_\Lambda{\rm Be}}$|⁠, in which the very compact spatial localization of clusters is shown in the density distribution.

Inelastic p9Be scattering and halo-structure of excited states of 9Be

The calculation of the differential cross section of the inelastic p9Be scattering (to the levels J = 1/2, 3/2) was made in the framework of the Glauber diffraction theory. We used the wave function of 9Be in the ground and excited states in the three-body 2alpha-n model. Expansion in series by gaussoids of the wave function of 9Be and presentation of the Glauber operator in the form, conjugated with three-body wave function, allow us to calculate analytically the matrix elements of inelastic scattering, taking into account all of the multiplicities of scattering and rescattering on clusters and nucleon, that are the components of 9Be. The drawn up profiles of excited state functions allow us to make conclusion on their extended neutron distributions. The differential cross section with the wave function in model 1 (with the alpha-alpha-Ali-Bodmer potential) is in a good agreement with available experimental data at E = 180 MeV.