Preferred shapes and modes of internal motion in a system of three identical fermions

The states havingL=0, even parity,S=1/2 or 3/2 of a model system of three identical fermions have beeninvestigated. The pairwise interaction adopted has a repulsive core and an attractive tail. Information on the preferred shapes and on internal motions have been extracted from the wave functions. A comparison is made among the states having symmetric, mixed-symmetric and antisymmetric spatial permutation symmetry. It is found that the symmetry plays an essential role in determining the microscopic structures.     

Structures of Two-Dimensional Three-Body Systems

Features of the structure of L = 0 states of a two-dimensional three-body model system have been investigated. Three types of permutation symmetry of the spartial part, namely symmetric, antisymmetric, and mixed, have been considered. A comparison has been made between the two-dimensional system and the corresponding three-dimensional one. The effect of symmetry on microscopic structures is emphasized. Received December 30, 1994; revised March 13, 1995; accepted for publication April 25, 1995     

Collision frequency shift of hyperfine transitions in atomic hydrogen at a low temperature

The experimental results on the collision frequency shift of ESR in diluted two-and three-dimensional atomic hydrogen at ultralow temperature have been analyzed. The apparent contradiction between experiment and theory is resolved by taking into account the relation between the symmetry of the state of two atoms and their total electron spin S. For example, transitions between symmetric and antisymmetric states of a pair of atoms induced by a symmetric perturbation are forbidden. If symmetric and antisymmetric states are, respectively, pure electronic triplets (S= 1) and singlets (S = 0), this results in the cancellation of the singlet-triplet transitions. Thus, the collision frequency shift of b → c and b → a transitions vanishes in a completely electron and nuclear spin-polarized gas (hyperfine state b). The comparison is performed with experiments in ultracold alkali vapors.     

The pairing correlations and nuclear shapes at very high angular momenta

The usual Strutinsky shell corrections include the pairing correlations in the BCS approach. At high-spin states the cranked intrinsic wave functions are not symmetric or antisymmetric under time reversal symmetry for general triaxial shapes. On the basis of the Hartree-Fock-Bogoliubov (HFB) approach two generalizations of the Strutinsky procedure are given to describe pairing correlations also for high-spin states and triaxial shapes. The method is applied to the neutron-deficient rare earth nucleus ¹⁵⁰Gd. It is found that pairing has an important effect on the change of nuclear deformation with increasing angular momentum. The proton pairing persists at least up to I ≈ 40.     

对称性对四体系统结构和内部运动的影响

文中用谐振子乘积基展开法求解了四体系统的Schrdinger方程.通过分析波函数及形状密度函数在多维坐标空间的分布,比较了四体全对称0⁺态,四体金对称0^－态和四体全反对称0⁺态,四体全反对称0^－态的结构和内部运动的差异;讨论了对称性的影响.     

Structure of 0+ states of 28Si and particle-hole conjugation

Full sd-shell calculations for the 0⁺ states of ²⁸Si have been performed in the SU(3) basis so that the intrinsic deformation of the shell model states can be deduced by inspection. The shell model Hamiltonian is decomposed in a symmetric part H_S and an antisymmetric part H_A with respect to particle-hole conjugation. It is shown that the splitting of prolate and oblate states is due to the spin-orbit part of H_A. The different prediction for ²⁸Si obtained with Kuo and with Preedom-Wildenthal matrix elements can be attributed to the difference in a single parameter: the strength of the spin-orbit part of H_A.     

Symmetry breaking in de Sitter spacetime by antipodal symmetric and antisymmetric fields

The symmetry behaviour of a ϵø⁴ model in the identified de Sitter space is considered. The different boundary conditions imposed on the quantum field correspond to antipodally symmetric and antisymmetric cases. For both cases, the variance of the quantum fluctuations around a constant background field is evaluated using a result on the conformal transformation of the effective action.     

Phenomenological theory of the s-wave state in superconductors without an inversion center

In materials without an inversion center of symmetry the spin degeneracy of the conducting band is lifted by an antisymmetric spin orbit coupling (ASOC). Under such circumstances, spin and parity cannot be separately used to classify the Cooper pairing states. Consequently, the superconducting order parameter is generally a mixture of spin singlet and triplet pairing states. In this paper we investigate the structure of the order parameter and its response to disorder for the most symmetric pairing state (A₁). Using the example of the heavy Fermion superconductor CePt₃Si, we determine characteristic properties of the superconducting instability. Depending on the type of the pairing interaction, the gap function is characterized by the presence of line nodes. We show that this line nodes move in general upon temperature. Such nodes would be essential to explain recent low-temperature data of thermodynamic quantities such as the NMR-T₁ ^-1, London penetration depth, and heat conductance. Moreover, we study the effect of (non-magnetic) impurity on the superconducting state.     

Fourier transform microwave spectroscopy of 1,1-dimethylsilacyclobutane. Interplay of two types of large-amplitude motions: two-top internal rotation and ring puckering

1,1-Dimethylsilacyclobutane, abbreviated as DMSCB, was investigated by Fourier transform microwave spectroscopy, by paying special attention to two types of large-amplitude motions in the molecule: two-top internal rotation and four-membered ring puckering and also to the coupling between the two. In order to clarify the unique feature of the internal dynamics in DMSCB in detail, two independent approaches were employed, one being a combination of a standard two-top theory of internal rotation and an established theory of ring puckering and the other a theory of large-amplitude motions developed by Hougen and his collaborators. In accordance with predictions by the two approaches based on symmetry consideration, the observed rotational spectra were found split into eight (or six when AE/EA lines were not resolved) components, which were assigned to the two-top states of AA, AE, EA, and EE symmetry, each being further split by puckering into two: the symmetric and antisymmetric states. The analyses by two approaches gave spectroscopic results, which were in good agreement with each other. The spectroscopic data on the normal species, combined with those on Si and C isotopic species, yielded molecular structure parameters including the puckering angle (the dihedral angle between the CSiC and CCC planes) of 28.64° or 30.26° (two possible sets). The splitting between the two lowest puckering states was determined to be 11.90(22) MHz, which led, with the equilibrium puckering angle, to the potential barrier to puckering of 395.3 or 347.0 cm⁻¹ for the two sets, respectively, which was slightly lower than the value 440 cm⁻¹ in a “parent” molecule: silacylcobutane. The first-order terms of the coupling between CH₃ internal rotation and overall rotation were converted to the barrier to internal rotation of 567.8 and 505.1 cm⁻¹ in the AE (two methyl groups rotating in the same direction, as viewed from Si) and EA (two methyl groups rotating in the opposite direction) states, respectively, which corresponded to the torsional frequencies of 154 and 144 cm⁻¹, at variance with the Raman data of 177 and 172 cm⁻¹, previously reported in literature.     

Beta decay of neutron-rich 118Rh and the lowest excited states in 118Pd

Beta decay of a refractory isotope ¹¹⁸Rh produced in symmetric fission and mass separated by the ion guide technique has been applied for the study of low-lying excited states of ¹¹⁸Pd. The yrast band in ¹¹⁸Pd has been observed up to a 6⁺ state and the lowest states of the asymmetric γ-band have been identified. The measured half-life of ¹¹⁸Rh is (300±60)ms. The systematics of the excited states in neutron-rich Pd-isotopes implies the saturation towards an O(6) symmetry at N = 70. Received: 19 June 2000 / Accepted: 1 August 2000     

Resonance fluorescence spectrum of two atoms,coherently driven by a strong resonant laser field

In Lehmberg's approach, we consider the resonance fluorescence spectrum of two radiatively interacting atoms. In the strong field limit we have obtained analytical solutions for the spectrum of the symmetric and antisymmetric modes without decoupling approximation. Our solutions are valid for all values of the distance r₁₂ separating the atoms. The spectrum of the symmetric modes contains additional sidebands in 2Ω (Ω is the Rabi frequency) with amplitude dependent on (a/Ω)², where a is a parameter dependent on r₁₂. The antisymmetric part of the spectrum has no additional sidebands in 2Ω. For small distances r₁₂ (a=1) our results for the symmetric modes are identical with those of Agarwal et al. apart from the so-called scaling factor. For large distances r₁₂ (a=0) the spectra of the symmetric and antisymmetric modes are identical with the well-known one-atom spectrum.     

Generalized thermoelastic Lamb waves in a plate bordered with layers of inviscid liquid

The propagation of thermoelastic waves in a homogeneous isotropic, thermally conducting plate bordered with layers of inviscid liquid or half-space of inviscid liquid on both sides is investigated in the context of generalized theories of thermoelasticity. Secular equations for the plate in closed form and isolated mathematical conditions for symmetric and antisymmetric wave modes in completely separate terms are derived. The results for coupled and uncoupled theories of thermoelasticity have been obtained as particular cases. The different regions of secular equations are obtained and special cases, such as Lame modes, thin plate waves and short wavelength waves of the secular equations are also discussed. The secular equations for thermoelastic leaky Lamb waves are also obtained and deduced. The amplitudes of displacement components and temperature change have also been computed and studied. Finally, the numerical solution is carried out for an aluminum-epoxy composite and aluminum materials plate bordered with water. The dispersion curves for symmetric and antisymmetric thermoelastic wave modes and amplitudes of displacement and temperature change in case of fundamental symmetric (S₀) and skew symmetric (A₀) modes are presented in order to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement. The results have been deduced and compared with the relevant publications available in the literature at the relevant stages of the work.     

The symmetry-breaking pattern of scalars in low dimension representations

We discuss the minimum problem of an SU(n) symmetric potential which has number of Higgs in fundamental, adjoint, second-rank symmetric and antisymmetric tensor representations. When there is only one scalar in the adjoint or tensor representation, the surviving symmetry cannot be chosen arbitrarily small by adjusting the parameters in the potential. When there is one more adjoint or tensor representation, the surviving symmetry after symmetry breaking can be diminished to nothing. However, when the two higher dimension representation scalars are diagonalized or quasi-diagonalized simultaneously at the local minimum, the surviving symmetry exists. We give the conditions for the existence of such a local minimum and its symmetry-breaking pattern. Our method is to transfer these problems to the relative orientation of vectors and the number of different eigenvalues.     

A simple class ofU(N) Racah coefficients and their application

Using permutation group techniques, a general expression is derived for the special class ofU(N) Racah coefficients for which the representations [f ¹] and [f ³] in the recoupling matrix for [f ¹]×[f ²]×[f ³][f] are either both totally antisymmetric or both totally symmetric. For the totally antisymmetric case further specialization gives a simple expression for aU(N) Racah coefficient which is needed in taking the average of the product of operators over the states of an irreducible representation ofU(N), where this result can be useful in the study of identical fermion systems by spectral distribution methods.Supported by the US National Science Foundation.     

Antisymmetric exchange in the CuB<Subscript>2</Subscript>O<Subscript>4</Subscript> A subsystem

The space distribution of the components of the microscopic Hamiltonian of the antisymmetric Dzyaloshinskii-Moriya exchange with respect to the exchange bond pairs of the A subsystem of Cu²⁺ ions in the crystallographic 4b positions of CuB₂O₄ has been obtained using symmetry analysis. The possibility of the coexistence of two different types of the exchange spatial distribution is demonstrated. The component of the antisymmetric exchange vector D parallel to the tetragonal axis has a weakly ferromagnetic distribution for all of the directions of the bonds between the nearest magnetic neighbors. Each exchange bond has an additional component of the antisymmetric exchange parallel to the bond projection on the tetragonal plane. The spatial distribution of these components is helicoidal with the modulation vector in the tetragonal crystal plane.     

Intense interactions of molecules with a short-wavelength electromagnetic radiation field: II. Resonance scattering of radiation and fluorescence

Within the framework of the nonadiabatic approach developed in the preceding paper, the resonance scattering, resonance Raman scattering, and resonance fluorescence are studied in detail for diatomic and triatomic molecules, and polyatomic symmetric and antisymmetric top molecules, which interact with the field of short-wavelength radiation with a wavelength λ ≥ Å and an intensity up to 10¹⁴ W/cm². The coherent excitations of high-lying Rydberg and autoionizing states are taken into account. Analytical expressions for calculating the tensors and cross sections of the above processes are derived.     

Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity

We present eight types of spatial optical solitons which are possible in a model of a planar waveguide that includes a dual-channel trapping structure and competing (cubic-quintic) nonlinearity. The families of trapped beams include “broad” and “narrow” symmetric and antisymmetric solitons, composite states, built as combinations of broad and narrow beams with identical or opposite signs (“unipolar” and “bipolar” states, respectively), and “single-sided” broad and narrow beams trapped, essentially, in a single channel. The stability of the families is investigated via the computation of eigenvalues of small perturbations, and is verified in direct simulations. Three species-narrow symmetric, broad antisymmetric, and unipolar composite states-are unstable to perturbations with real eigenvalues, while the other five families are stable. The unstable states do not decay, but, instead, spontaneously transform themselves into persistent breathers, which, in some cases, demonstrate dynamical symmetry breaking and chaotic internal oscillations. A noteworthy feature is a stability exchange between the broad and narrow antisymmetric states: in the limit when the two channels merge into one, the former species becomes stable, while the latter one loses its stability. Different branches of the stationary states are linked by four bifurcations, which take different forms in the model with the strong and weak coupling between the channels.     

The effective Hamiltonian for the coupling between inversion-torsion states in methylamine

The Hougen’s formalism of group-theoretical effective Hamiltonian has been extended to include the resonances between the wagging, ν₉, and third or fourth excited torsional, 3ν₁₅ and 4ν₁₅, states in methylamine. The presented Hamiltonian treats explicitly these couplings. For each of these bands the rovibrational sublevels belong to all symmetry species of the G₁₂ group of methylamine. On the other hand the vibrational states for ν₉ and 4ν₁₅ are symmetric with respect to reflection in the symmetry plane of the NH₂ group, and antisymmetric for 3ν₁₅. We have shown that the coupling terms between the ν₉ and 3ν₁₅ states are limited to Coriolis-like coupling, and no Fermi-type interactions are allowed. For the coupling between the ν₉ and 4ν₁₅ states all kind of interaction terms are possible.     

Frustration mechanism of formation of a helical magnetic structure in the CuB2O4 two-subsystem antiferromagnet

A new mechanism is proposed for forming an incommensurate magnetic structure of the transverse helix type owing to the removal of frustration through intersubsystem exchange in a two-subsystem antiferromagnet. The symmetry analysis of the distribution of the Dzyaloshinskii-Moriya interaction and comparison with the experimental data on the field dependence of magnetization indicate that antisymmetric exchange and competition between symmetric exchanges cannot be responsible for forming a helical magnetic structure in CuB₂O₄.     

The Pauli Exclusion Principle. Can It Be Proved?

The modern state of the Pauli exclusion principle studies is discussed. The Pauli exclusion principle can be considered from two viewpoints. On the one hand, it asserts that particles with half-integer spin (fermions) are described by antisymmetric wave functions, and particles with integer spin (bosons) are described by symmetric wave functions. This is a so-called spin-statistics connection. The reasons why the spin-statistics connection exists are still unknown, see discussion in text. On the other hand, according to the Pauli exclusion principle, the permutation symmetry of the total wave functions can be only of two types: symmetric or antisymmetric, all other types of permutation symmetry are forbidden; although the solutions of the Schrödinger equation may belong to any representation of the permutation group, including the multi-dimensional ones. It is demonstrated that the proofs of the Pauli exclusion principle in some textbooks on quantum mechanics are incorrect and, in general, the indistinguishability principle is insensitive to the permutation symmetry of the wave function and cannot be used as a criterion for the verification of the Pauli exclusion principle. Heuristic arguments are given in favor that the existence in nature only the one-dimensional permutation representations (symmetric and antisymmetric) are not accidental. As follows from the analysis of possible scenarios, the permission of multi-dimensional representations of the permutation group leads to contradictions with the concept of particle identity and their independence. Thus, the prohibition of the degenerate permutation states by the Pauli exclusion principle follows from the general physical assumptions underlying quantum theory.