Excited-states and spectroscopic properties of superoxide anion: a theoretical study including spin–orbit coupling

ABSTRACT

The potential energy curves (PECs) of 24 Λ–S electronic states of superoxide anion (O₂^?), which correlated with the first dissociation channel, were calculated using a high-accuracy internally contracted multireference configuration interaction (icMRCI) methodology with the Davidson correction in conjunction with the correlation-consistent basis sets. The core electron correlation and scalar relativistic corrections as well as basis set extrapolation were included. The spin–orbit coupling was also taken into account by using the state interaction approach with the Breit–Pauli Hamiltonian. The PECs of 54 Ω states generated from the 24 Λ–S states were constructed and described in detail. The spectroscopic constants of the seventeen Λ–S and 37 Ω bound states were evaluated and the vibrational properties of some weakly bound states were predicted. Comparing with the available experimental and theoretical data shows that the computational strategy employed is suitable and highly accurate for this system.     

Spectral Analysis of the 2 + 1 Fermionic Trimer with Contact Interactions

We qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical fermions, plus a third particle of different species, with two-body interaction of zero range. For arbitrary magnitude of the interaction, and arbitrary value of the mass parameter (the ratio between the mass of the third particle and that of each fermion) above the stability threshold, we identify the essential spectrum, localise the discrete spectrum and prove its finiteness, qualify the angular symmetry of the eigenfunctions, and prove the increasing monotonicity of the eigenvalues with respect to the mass parameter. We also demonstrate the existence or absence of bound states in the physically relevant regimes of masses.     

Low Density Limit of BCS Theory and Bose–Einstein Condensation of Fermion Pairs

We consider the low-density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross–Pitaevskii functional, describing a Bose–Einstein condensate of fermion pairs.     

Similarity and differences between the radion and Higgs boson production and decay processes involving off-shell fermions

The radion is a scalar particle that occurs in brane world models and interacts with the trace of the energy–momentum tensor of the Standard Model (SM). The radion–SM fermion interaction Lagrangian differs from the Higgs boson–fermion interaction Lagrangian for off-shell fermions. It is shown that all additional, as compared to the Higgs boson, contributions to the amplitudes of radion production and decay processes involving off-shell fermions are canceled out for both massless and massive fermions. Thus, additional terms in the interaction Lagrangian do not change properties of these processes for the radion and the Higgs boson, except for the general normalization factors. This similarity is a consequence of gauge invariance for the processes with production of gauge bosons. When an additional scalar particle is produced, there are no apparent reasons for the above cancellation, as confirmed, for example, by the process with production of two scalar particles, which features an additional contribution of the radion in comparison with the Higgs boson.     

Bogolubov–Hartree–Fock Theory for Strongly Interacting Fermions in the Low Density Limit

We consider the Bogolubov–Hartree–Fock functional for a fermionic many-body system with two-body interactions. For suitable interaction potentials that have a strong enough attractive tail in order to allow for two-body bound states, but are otherwise sufficiently repulsive to guarantee stability of the system, we show that in the low-density limit the ground state of this model consists of a Bose–Einstein condensate of fermion pairs. The latter can be described by means of the Gross–Pitaevskii energy functional.     

Analytic Continuation with Pade Decomposition

The ill-posed analytic continuation problem for Green's functions or self-energies can be carried out using the Pade rational polynomial approximation. However, to extract accurate results from this approximation, high precision input data of the Matsubara Green function are needed. The calculation of the Matsubara Green function generally involves a Matsubara frequency summation, which cannot be evaluated analytically. Numerical summation is requisite but it converges slowly with the increase of the Matsubara frequency. Here we show that this slow convergence problem can be significantly improved by utilizing the Pade decomposition approach to replace the Matsubara frequency summation by a Pade frequency summation, and high precision input data can be obtained to successfully perform the Pade analytic continuation.     

A scalar-fermion model in the limit of infinitely heavy fermions

As a first step in the non-perturbative study of a chiralU(1)?U(1) Yukawa-model with explicit mirror fermions the limit of infinite bare fermion mass is considered. Non-perturbative information is obtained from 14th order scalar hopping parameter expansion, which is confronted with high statistics numerical data. A remarkable universality of the upper bound for the renormalized quartic coupling is observed. A new kind of first order phase transition surface is localized, which is characterized by a large jump in the average field length.     

Planck spectroscopy and quantum noise of microwave beam splitters

We use a correlation function analysis of the field quadratures to characterize both the blackbody radiation emitted by a 50 Ω load resistor and the quantum properties of two types of beam splitters in the microwave regime. To this end, we first study vacuum fluctuations as a function of frequency in a Planck spectroscopy experiment and then measure the covariance matrix of weak thermal states. Our results provide direct experimental evidence that vacuum fluctuations represent the fundamental minimum quantum noise added by a beam splitter to any given input signal.     

Functional renormalization group beyond the static approximation and its application to the two-dimensional Hubbard model

While the functional renormalization group is a powerful theoretical method, the static approximation has been usually adopted in which the Matsubara frequency dependence of vertex functions is ignored. We propose a formalism beyond the static approximation with an efficient parameterization in the Matsubara frequency space for the vertex functions to incorporate the self-energy.     

Hubbard模型中的相位弦效应与交互Chern-Simons理论

费米子符号在费米液体理论中至关重要. 然而, 在Mott绝缘体中, 很强的电子Coulomb相互作用抑制了体系的电荷涨落并消除了电子交换带来的费米子符号问题. 本文首先回顾二分晶格上Hubbard模型的相位弦理论, 从弱关联的费米液体到强关联的反铁磁Mott绝缘体的转变可以由此得到统一理解. 在任意Coulomb作用强度U下, 我们首先导出Hubbard模型的严格的符号结构. 在小U极限下, 它回到通常的费米子符号; 在大U极限下, 它给出了t-J模型的相位弦符号. 在半满情形下, 我们构造了一种电子分数化的表象, 其中, 电荷子与自旋子通过演生的交互Chern-Simons规范场相互耦合. 由此导出的基态波函数拟设与低能有效理论可以定性刻画Hubbard模型的基态相图. 在弱关联区域, 费米液体的准粒子由电荷子与自旋子的束缚态构成, 其长程相位相干性取决于背景自旋的关联性质. 体系的Mott转变可以通过电荷子打开能隙或是通过自旋子玻色凝聚来实现.     

Ab initio MRCI+Q study on the low-lying excited states of the PBr radical including spin–orbit coupling†

High-level ab initio calculations have been performed on the PBr radical by using multi-reference configuration interaction method plus Davidson correction (+Q) with correlation-consistent quadruple-ζ quality basis set. The potential energy curves (PECs) of the 22 Λ–S states of PBr have been obtained, most of which are reported for the first time. From the PECs of the bound states, the spectroscopic constants have been determined, in good agreement with the experimental results where available. Due to the large state density, there exhibits complicated interactions in the electronic excited states of PBr. The possible interactions by the spin–orbit coupling (SOC) effect have been discussed based on the evaluated R-dependent spin–orbit matrix elements. The 51 Ω states, generating from the 22 Λ–S states after taking SOC into account, have been computed. The Λ–S component analysis of the wavefunctions for the Ω states indicates the strong interaction of the Λ–S states especially at the avoided crossing points and near the dissociation limits. Finally, the transition dipole moments of several transitions arising from upper Ω states to the X₁0⁺ and X₂1 states and the corresponding radiative lifetimes have been studied. Our calculation results provide new information that should be valuable for further experimental studies on the electronic excited states of the PBr radical.     

Drude model and Lifshitz formula

Since nearly 10 years, it has been known that inserting the permittivity of the Drude model into the Lifshitz formula for free energy causes a violation of the third law of thermodynamics. In this paper we show that the standard Matsubara formulation for free energy contains a contribution that is non-perturbative in the relaxation parameter. We argue that the correct formula must have a perturbative expansion and conclude that the standard Matsubara formulation with the permittivity of the Drude model inserted is not correct. We trace the non-perturbative contribution in the complex frequency plane, where it shows up as a self-intersection or a bifurcation of the integration path.     

Transition to superfluidity in strongly coupled fermion systems: low density limit

The rôle of interacting bound pairs in strongly coupled fermion systems is considered in connection with the transition to superfluidity. Model calculations are performed for finite-range separable interaction potentials. The results of a cluster-Hartree-Fock approximation are compared with recent approaches improving the Nozières and Schmitt-Rink theory. In the low-density strong coupling limit, a first order transition to the superfluid phase is obtained.     

Fermion bound states in geometrically deformed backgrounds

This work deals with the behavior of fermions in the background of kinklike structures in the twodimensional spacetime. The kinklike structures appear from bosonic scalar field models that engender distinct profiles and interact with the fermion fields via the standard Yukawa coupling. We first consider two models that engender parity symmetry, one leading to the exclusion of fermion bound states, and the other to the inclusion of bound states, when the parameter that controls the bosonic structure varies from zero to unity. We then investigate a third model where the kinklike solution explicitly breaks parity symmetry, leading to fermion bound states that are spatially asymmetric.     

The Girardeau's fermion-boson procedure in the light of the composite-boson many-body theory

We reconsider the procedure developed for atoms a few decades ago by Girardeau, in the light of the composite-boson many-body theory we recently proposed. The Girardeau's procedure makes use of a so called “unitary Fock-Tani operator” which in an exact way transforms one composite bound atom into one bosonic “ideal” atom. When used to transform the Hamiltonian of interacting atoms, this operator generates an extremely complex set of effective scatterings between ideal bosonic atoms and free fermions which makes the transformed Hamiltonian impossible to write explicitly, in this way forcing to some truncation. The scatterings restricted to the ideal-atom subspace are shown to read rather simply in terms of the two elementary scatterings of the composite-boson many-body theory, namely, the energy-like direct interaction scatterings — which describe fermion interactions without fermion exchange — and the dimensionless Pauli scatterings — which describe fermion exchanges without fermion interaction. We here show that, due to a fundamental difference in the scalar products of elementary and composite bosons, the Hamiltonian expectation value for N ground state atoms obtained by staying in the ideal-atom subspace and working with boson operators only, differ from the exact ones even for N = 2 and a mapping to the ideal-atom subspace performed, as advocated, from the fully antisymmetrical atomic state, i.e., the state which obeys the so-called “subsidiary condition”. This shows that, within this Girardeau's procedure too, we cannot completely forget the underlying fermionic components of the particles if we want to correctly describe their interactions.     

Chemical potentials in gauge theories

One-loop calculations of the thermodynamic potential Ω are presented for temperature gauge and non-gauge theories. Prototypical formulae are derived which give Ω as a function of both (i) boson and/or fermion chemical potential, and in the case of gauge theories (ii) the thermal vacuum parameter A₀=const (A_μ is the euclidean gauge potential). From these basic abelian gauge theory formulae, the one-loop contribution to Ω can readily be constructed for Yang-Mills theories, and also for non-gauge theories.     

Polaron, molecule and pairing in one-dimensional spin-1/2 Fermi gas with an attractive Delta-function interaction

Using solutions of the discrete Bethe ansatz equations, we study in detail the quantum impurity problem of a spin-down fermion immersed into a fully ploarized spin-up Fermi sea with weak attraction. We prove that this impurity fermion in the one-dimensional (1D) fermionic medium behaves like a polaron for weak attraction. However, as the attraction grows, the spin-down fermion binds with one spin-up fermion from the fully-polarized medium to form a tightly bound molecule. Thus it is seen that the system undergos a crossover from a mean field polaron-like nature into a mixture of excess fermions and a bosonic molecule as the attraction changes from weak attraction into strong attraction. This polaron-molecule crossover is universal in 1D many-body systems of interacting fermions. In a thermodynamic limit, we further study the relationship between the Fredholm equations for the 1D spin-1/2 Fermi gas with weakly repulsive and attractive delta-function interactions.     

Two-Point Fermionic Correlators in External Constant Uniform Magnetic Field

The results of calculation of two-point correlation functions of fermionic currents in a constant uniform magnetic field are presented. The off-diagonal correlation functions including the tensor current (namely, the scalar-tensor and pseudoscalar-tensor) are calculated in addition to the correlators of scalar, pseudoscalar, vector, and axial-vector fermionic currents. The tensor fermionic current is a part of the Pauli term in the Lagrangian, which is responsible for the electromagnetic interaction of the fermion through an anomalous magnetic moment. In particular, if we take this interaction into account, we modify the frequency of axion-photon oscillations. In the future, it is planned to investigate this feature in details.     

Physical particles of the massive Schwinger model

The massive Schwinger model is considered in the infinite momentum frame. By assuming its physical particles consist of two fermion bound states, we compute a spectrum. For fermions with large bare masses, the method is reliable. For low-mass fermions, we find we must include states of higher fermion number to adequately describe excited states of the fundamental boson of the theory. We do this for the scalar state in the limit of small bare fermion mass. This representation of the theory provides a unified treatment of both the weak and strong coupling limits, remaining in the fermion representation throughout. We have checked our numerical results with exact calculations wherever possible, and find good agreement.     

费密子与Dirac双子系统的耦合问题

除了库仑耦合和Kazama-杨振宁耦合——кqβ∑·r/2Mr³外,本文同时讨论了费密子Dirac双子应当存在的另一耦合iкzz_de²γ·r/2Mr³。结果表明,对所有角动量态,费密子径向波函数具有物理上合理的原点渐近行为。定性地分析了束缚态的必要条件。发现,对于双子情形,当额外磁矩к→0时,存在费密子束缚态是可能的;但对于磁单极情形,当к→0时,必不存在费密子束缚态。 关键词：