Lowest-order Perturbation Theory Research Articles

Two- and Three-Photon Partial Photoionization Cross Sections of Li+, Ne8+ and Ar16+ under XUV Radiation

In this work, we present the photon energy dependence of the two- and three-photon cross sections of the two-electron Li+, Ne8+ and Ar16+ ions, following photoionization from their ground state. The expressions for the cross sections are based on the lowest-order (non-vanishing) perturbation theory for the electric field, while the calculations are made with the use of an ab initio configuration interaction method. The ionization cross section is dominated by pronounced single photon resonances in addition to peaks associated with doubly excited resonances. In the case of two-photon ionization, and in the non-resonant part of the cross section, we find that the 1D ionization channel overwhelms the 1S one. We also observe that, as one moves from the lowest atomic number ion, namely Li+, to the highest atomic number ion, namely Ar16+, the cross sections generally decrease.

Stimulated Raman scattering of an ultrashort XUV radiation pulse by a hydrogen atom

We consider the hydrogen atom $\mathrm{H}(1s)$ exposed to an ultrashort laser pulse with a central frequency ${\ensuremath{\omega}}_{0}$ ranging from several hundreds of eV to 1.5 keV ($\ensuremath{\approx}55$ a.u.) and a peak intensity of $3.51\ifmmode\times\else\texttimes\fi{}{10}^{16}\phantom{\rule{4pt}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$. We study the excitation of the atom by stimulated Raman scattering, a process involving pairs of frequencies (${\ensuremath{\omega}}_{1},{\ensuremath{\omega}}_{2}$). These frequencies are non-negligible components of the pulse Fourier transform and they satisfy the condition ${E}_{g}+\ensuremath{\hbar}{\ensuremath{\omega}}_{1}={E}_{b}+\ensuremath{\hbar}{\ensuremath{\omega}}_{2},{E}_{g}$ and ${E}_{b}\ensuremath{\equiv}{E}_{n}$ being the ground-state and the excited-state energy, respectively. The numerical results obtained by integrating the time-dependent Schr\odinger equation (TDSE) are compared with calculations in lowest order perturbation theory (LOPT). In LOPT we consider, in the second order of PT, the contribution of the term $\mathbf{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{P}$ in the dipole approximation and, in first order of PT, the expression of ${\mathbf{A}}^{2}$ taken for first-order retardation effects. ($\mathbf{A}$ denotes the vector potential of the field and $\mathbf{P}$ is the momentum operator.) We focus on the Raman excitation of bound states with principal quantum numbers $n$ up to $n=13$. The evaluation in perturbation theory of the $\mathbf{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{P}$ contribution to $1s\ensuremath{-}ns$ and $1s\ensuremath{-}nd$ transition probabilities uses analytic expressions of the corresponding Kramers--Heisenberg matrix elements. At fixed pulse duration $\ensuremath{\tau}=6\ensuremath{\pi}$ a.u. ($\ensuremath{\approx}0.48$ fs), we find that the retardation effects play an important role at high frequencies: they progressively diminish as the frequency decreases until the contribution of $\mathbf{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{P}$ dominates over the ${\mathbf{A}}^{2}$ contribution for ${\ensuremath{\omega}}_{0}$ values of a few a.u. We also study the dependence of the Raman process on the pulse duration for several values of ${\ensuremath{\omega}}_{0}$. In the case ${\ensuremath{\omega}}_{0}=13\phantom{\rule{4pt}{0ex}}\mathrm{a}.\mathrm{u}.\phantom{\rule{4pt}{0ex}}(\ensuremath{\approx}354\phantom{\rule{4pt}{0ex}}\mathrm{eV})$ where dipole and nondipole contributions are of the same order of magnitude, we present the Raman excitation probability as a function of the pulse duration for excited $ns,\phantom{\rule{4pt}{0ex}}np$, and $nd$ states.

A marked correlation function for constraining modified gravity models

Future large scale structure surveys will provide increasingly tight constraints on our cosmological model. These surveys will report results on the distance scale and growth rate of perturbations through measurements of Baryon Acoustic Oscillations and Redshift-Space Distortions. It is interesting to ask: what further analyses should become routine, so as to test as-yet-unknown models of cosmic acceleration? Models which aim to explain the accelerated expansion rate of the Universe by modifications to General Relativity often invoke screening mechanisms which can imprint a non-standard density dependence on their predictions. This suggests density-dependent clustering as a `generic' constraint. This paper argues that a density-marked correlation function provides a density-dependent statistic which is easy to compute and report and requires minimal additional infrastructure beyond what is routinely available to such survey analyses. We give one realization of this idea and study it using low order perturbation theory. We encourage groups developing modified gravity theories to see whether such statistics provide discriminatory power for their models.

Reflectance and transmittance of light for weakly inhomogeneous plates in the lower orders of perturbation theory

Reflectance and transmittance of light for weakly inhomogeneous plates in the lower orders of perturbation theory

Translation-rotation states of H2 in C60: New insights from a perturbation-theory treatment

We report an investigation of the translation-rotation (TR) level structure of H2 entrapped in C60, in the rigid-monomer approximation, by means of a low-order perturbation theory (PT). We focus in particular on the degree to which PT can accurately account for that level structure, by comparison with the variational quantum five-dimensional calculations. To apply PT to the system, the interaction potential of H2@C60 is decomposed into a sum over bipolar spherical tensors. A zeroth-order Hamiltonian, Hˆ0, is then constructed as the sum of the TR kinetic-energy operator and the one term in the tensor decomposition of the potential that depends solely on the radial displacement of the H2 center of mass (c.m.) from the cage center. The remaining terms in the potential are treated as perturbations. The eigenstates of Hˆ0, constructed to also account for the coupling of the angular momentum of the H2 c.m. about the cage center with the rotational angular momentum of the H2 about the c.m., are taken as the PT zeroth-order states. This zeroth-order level structure is shown to be an excellent approximation to the true one except for two types of TR-level splittings present in the latter. We then show that first-order PT accounts very well for these splittings, with respect to both their patterns and magnitudes. This allows one to connect specific features of the level structure with specific features of the potential-energy surface, and provides important new physical insight into the characteristics of the TR level structure.

Equilibration, particle production, and self-energy

The discontinuity, or imaginary part of a self-energy at finite temperature is proportional to the rate at which the corresponding particles are produced when very few of them are present, and also to the rate at which their phase space density approaches the thermal one. These relations were suggested by Weldon [1], who demonstrated them for low orders in perturbation theory. Here we show that they are valid at leading order in a linear coupling of the produced particles, and to all orders in all other interactions of the hot plasma, if there is a separation of the time scales for the production and for the thermalization of the bulk of the plasma.

Combining galaxy and 21-cm surveys

Acoustic waves traveling through the early Universe imprint a characteristic scale in the clustering of galaxies, QSOs and inter-galactic gas. This scale can be used as a standard ruler to map the expansion history of the Universe, a technique known as Baryon Acoustic Oscillations (BAO). BAO offer a high-precision, low-systematics means of constraining our cosmological model. The statistical power of BAO measurements can be improved if the `smearing' of the acoustic feature by non-linear structure formation is undone in a process known as reconstruction. In this paper we use low-order Lagrangian perturbation theory to study the ability of $21\,$cm experiments to perform reconstruction and how augmenting these surveys with galaxy redshift surveys at relatively low number densities can improve performance. We find that the critical number density which must be achieved in order to benefit $21\,$cm surveys is set by the linear theory power spectrum near its peak, and corresponds to densities achievable by upcoming surveys of emission line galaxies such as eBOSS and DESI. As part of this work we analyze reconstruction within the framework of Lagrangian perturbation theory with local Lagrangian bias, redshift-space distortions, ${\bf k}$-dependent noise and anisotropic filtering schemes.

Current noise of the interacting resonant level model

We study the zero-frequency current noise of the interacting resonant level model for arbitrary bias voltages using a functional renormalization group approach. For this we extend the existing nonequilibrium scheme by deriving and solving flow equations for the current-vertex functions. On-resonance artificial divergences of the latter found in lowest-order perturbation theory in the two-particle interaction are consistently removed. Away from resonance they are shifted to higher orders. This allows us to gain a comprehensive picture of the current noise in the scaling limit. At high bias voltages, the current noise exhibits a universal power-law decay, whose exponent is to leading order in the interaction identical to that of the current. The effective charge on resonance is analyzed in detail employing properties of the vertex correction. We find that it is only modified to second or higher order in the two-particle interaction.

Electron in three-dimensional momentum space

We study the electron as a system composed by an electron and a photon, using lowest order perturbation theory. We derive the leading-twist transverse-momentum-dependent distribution functions for both the electron and photon in the dressed electron, thereby offering a three-dimensional description of the dressed electron in momentum space. To obtain the distribution functions, we apply both the formalism of light-front wave function overlap representation and the diagrammatic approach. We perform the calculations both in light-cone gauge and Feynman gauge, and we present a detailed discussion of the role of the Wilson lines to obtain gauge-independent results. We provide numerical results and plots for many of the computed distributions.

Electron vortices in photoionization by circularly polarized attosecond pulses.

Single ionization of He by two oppositely circularly polarized, time-delayed attosecond pulses is shown to produce photoelectron momentum distributions in the polarization plane having helical vortex structures sensitive to the time delay between the pulses, their relative phase, and their handedness. Results are obtained by both abinitio numerical solution of the two-electron time-dependent Schrödinger equation and by a lowest-order perturbation theory analysis. The energy, bandwidth, and temporal duration of attosecond pulses are ideal for observing these vortex patterns.

Transition from perturbative to nonperturbative interaction in low-order-harmonic generation

We present results of ab initio numerical calculations for low-order-harmonic generation as well as calculations of the higher-order terms in the respective perturbative power-series expansions of the susceptibilities for third- and fifth-order-harmonic generation. We find that the transition from perturbative to nonperturbative interaction in these low-order nonlinear processes occurs at about ${10}^{13}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$. Our findings confirm previous results that any deviation from the predictions of lowest-order perturbation theory indicates that the perturbative series expansion is not applicable and, if required, needs to be replaced by a nonperturbative treatment of the interaction between the atom and the field. In particular, the results also show that the observation of low-order-harmonic yields cannot be considered as a test of higher-order Kerr effects.

Time-dependent calculations of transfer ionization by fast proton-helium collision in one-dimensional kinematics

We analyze a transfer ionization (TI) reaction in the fast proton-helium collision ${\mathrm{H}}^{+}+\mathrm{He}\ensuremath{\rightarrow}{\mathrm{H}}^{0}+{\mathrm{He}}^{2+}+ {e}^{\ensuremath{-}}$ by solving a time-dependent Schr\"odinger equation (TDSE) under the classical projectile motion approximation in one-dimensional kinematics. In addition, we construct various time-independent analogs of our model using lowest-order perturbation theory in the form of the Born series. By comparing various aspects of the TDSE and the Born series calculations, we conclude that the recent discrepancies of experimental and theoretical data may be attributed to deficiency of the Born models used by other authors. We demonstrate that the correct Born series for TI should include the momentum-space overlap between the double-ionization amplitude and the wave function of the transferred electron.

Electron structure: Shape, size, and generalized parton distributions in QED

The shape of the electron is studied using lowest-order perturbation theory. Quantities used to probe the structure of the proton---form factors, generalized parton distributions, transverse densities, Wigner distributions and the angular momentum content---are computed for the electron-photon component of the electron wave function. The influence of longitudinally polarized photons, demanded by the need for infrared regularization via a nonzero photon mass, is included. The appropriate value of the photon mass depends on experimental conditions, and consequently the size of the electron (as defined by the slope of its Dirac form factor) bound in a hydrogen atom is found to be about four times larger than when the electron is in a continuum scattering state. The shape of the electron, as determined from the transverse density and generalized parton distributions, is shown not to be round, and the continuum electron is shown to be far less round than the bound electron. An electron distribution function (analogous to the quark distribution function) is defined, and that of the bound electron is shown to be suppressed compared to that of the continuum electron. If the relative transverse momentum of the virtual electron and photon is large compared with the electron mass, the virtual electron and photon each carry nearly the total angular momentum of the physical electron ($1/2$), with the orbital angular momentum being nearly ($\ensuremath{-}1/2$). Including the nonzero photon mass leads to the suppression of end-point contributions to form factors. Implications for proton structure and color transparency are discussed.

Quantum field theoretic properties of Lorentz-violating operators of nonrenormalizable dimension in the fermion sector

In the current paper the properties of a quantum field theory based on certain sets of Lorentz-violating coefficients in the nonminimal fermion sector of the Standard Model extension are analyzed. In particular, three families of coefficients are considered, where two of them are $CPT$ even and the third is $CPT$ odd. As a first step the modified fermion dispersion relations are obtained. Then the positive- and negative-energy solutions of the modified Dirac equation and the fermion propagator are derived. These are used to demonstrate the validity of the optical theorem at tree level, which provides a cross-check for the results obtained. Furthermore unitarity is examined and seems to be valid for the first set of $CPT$-even coefficients. However for the remaining sets certain issues with unitarity are found. The article demonstrates that the adapted quantum field theoretical methods at tree level work for the nonminimal, Lorentz-violating framework considered. Besides, the quantum field theory based on the first family of $CPT$-even coefficients is most likely well behaved at lowest order perturbation theory. The results are important for future phenomenological investigations carried out in the context of field theory, e.g., the computation of decay rates and cross sections at tree level.

Giant resonances based on unitarily transformed two-nucleon plus phenomenological three-nucleon interactions

We investigate giant resonances of spherical nuclei on the basis of the Argonne V18 potential after unitary transformation within the similarity renormalization group or the unitary correlation operator method supplemented by a phenomenological three-body contact interaction. Such Hamiltonians can provide a good description of ground-state energies and radii within Hartree–Fock plus low-order many-body perturbation theory. The standard random phase approximation is applied here to calculate the isoscalar monopole, isovector dipole, and isoscalar quadrupole excitation modes of the , , and nuclei. Thanks to the inclusion of the three-nucleon interaction and despite the minimal optimization effort, a reasonable agreement with experimental centroid energies of all three modes has been achieved. The role and scope of the Hartree–Fock reference state in RPA methods are discussed.

Stable Eχtensions with(out) gravity

We investigate the vacuum stability as well as the gravitational corrections in extensions of the Standard Model featuring a new complex scalar, and two Dirac fermions for different choices of the hypercharge of the scalar and one of the two fermions. The neutral fermion acquires loop-induced magnetic interactions with the Standard Model and could be identified with a dark matter candidate. To the lowest order in perturbation theory we show that these extensions can save the electroweak vacuum from being metastable. We then add the gravitational corrections to the different beta functions and discover that the models can be compatible with the asymptotically safe gravity scenario at the price of a heavier Higgs and lighter top mass.

Femtosecond Two-Photon Detachment of Cu− Studied By Photoelectron Imaging

The wavelength dependence of photoelectron angular distributions (PADs) of two-photon detachment of Cu− has been directly studied by using the photoelectron map imaging. Results show that for the laser field intensity of 6.0×1010 W/cm2, PADs exhibit dramatic change with the external field wavelength. Comparison between the experimental observation and the lowest-order perturbation theory prediction indicates that the pattern of PADs can be explained by the interference of the s and d partial waves in the final state. Relative contributions of s and d partial waves in the two-photon detachment at different laser wavelengths are obtained.

Fully anharmonic IR and Raman spectra of medium-size molecular systems: accuracy and interpretation.

Computation of full infrared (IR) and Raman spectra (including absolute intensities and transition energies) for medium- and large-sized molecular systems beyond the harmonic approximation is one of the most interesting challenges of contemporary computational chemistry. Contrary to common beliefs, low-order perturbation theory is able to deliver results of high accuracy (actually often better than those issuing from current direct dynamics approaches) provided that anharmonic resonances are properly managed. This perspective sketches the recent developments in our research group toward the development of a robust and user-friendly virtual spectrometer rooted in second-order vibrational perturbation theory (VPT2) and usable also by non-specialists essentially as a black-box procedure. Several examples are explicitly worked out in order to illustrate the features of our computational tool together with the most important ongoing developments.

Phase transitions in three-dimensional bosonic systems in optical lattices

We formulate the collective quantum field theory for three-dimensional bosonic optical lattices and evaluate its consequences in a mean-field approximation to two collective fields, proposed by Cooper et al (2011 Phys. Rev. A 83 053622), and in a lowest-order variational perturbation theory. It is shown that the present mean-field approximation predicts some essential features of the experimentally observed dependence of the critical temperature on the coupling strength and a second-order quantum phase transition. In contrast to a recent prediction for atomic gases given by Cooper et al, our finding indicates no superfluid state with zero condensate fraction.

Comparison of the finite element method with perturbation theory and the small-slope approximation for acoustic scattering from one-dimensional rough poroelastic surfaces

The finite element method is used to address the problem of acoustic scattering from one-dimensional rough poroelastic surfaces. The poroelastic sediment is modeled following the Biot-Stoll formulation. The rough surfaces are generated using a modified power law spectrum. Both backscattering strengths and bistatic scattering strengths are calculated. These results are compared with lowest order perturbation theory and the lowest order small-slope approximation, as extended to the case of scattering from poroelastic surfaces. It is known that these approximate methods are sufficient for the study of rough surface scattering in the case of sediments modeled as fluids. This work seeks to assess whether or not these methods are accurate when applied to the case of poroelastic sediments. [Work supported by the Office of Naval Research, Ocean Acoustics Program.]