A new representation of the interaction between an atom and an intense elliptically polarized electromagnetic field

A new representation of the interaction between a laser field and an atom is obtained. The Fourier component of the interaction is represented as a multipole expansion dependent on the force parameter of the field, a ₀=F/ω², and the degree of its ellipticity, η. This representation provides the analytical separation of the angles in the time-dependent Schrödinger equation. The stationary spherically symmetric part of the potential V ₀(r, a ₀, η) of a “field-dressed” atom is singled out. The application of the new representation to the calculation of nonlinear effects and electron scattering by an atom in a field are discussed     

Smooth mass corrections to massless theories

We analyze the transition from massive to massless theories in cases in which mass singularities are present. In massless theories these singularities are absorbed into densities or fragmentation functions. We define a subtraction procedure for massive theories which is a canonical generalization of the “minimal subtraction” in massless theories. We use this procedure to calculate smooth mass corrections to the structure functionsF ₂ andG ₁ of deep inelastic scattering. In particular we show how, in our scheme, heavy quarks affect the spin of the proton.     

Bad communities with high modularity

In this paper we discuss some problematic aspects of Newman and Girvan’s modularity function Q _N . Given a graph G, the modularity of G can be written as Q _N = Q _f ? Q ₀, where Q _f is the intracluster edge fraction of G and Q ₀ is the expected intracluster edge fraction of the null model, i.e., a randomly connected graph with same expected degree distribution as G. It follows that the maximization of Q _N must accomodate two factors pulling in opposite directions:Q _f favors a small number of clusters and Q ₀ favors many balanced (i.e., with approximately equal degrees) clusters. In certain cases the Q ₀ term can cause overestimation of the true cluster number; this is the opposite of the well-known underestimation effect caused by the “resolution limit” of modularity. We illustrate the overestimation effect by constructing families of graphs with a “natural” community structure which, however, does not maximize modularity. In fact, we show there exist graphs G with a “natural clustering” V of G and another, balanced clustering U of G such that (i) the pair (G, U) has higher modularity than (G, V) and (ii) V and U are arbitrarily different.     

Five-dimensional SU(2)-monopole: Continuous spectrum

Hyperspherical and parabolic wave functions are calculated for the five-dimensional “charge-SU(2) monopole” system in the continuous spectrum. It is shown that the coefficients of parabolic-hyperspherical and hyperspherical-parabolic transformations are proportional to the generalized hyperge-ometric function ₃ F ₂{...|1}.     

On sound transmission into a thin cylindrical shell under “flight conditions”

In the context of the transmission of airborne noise into an aircraft fuselage, a mathematical model for sound transmission into a thin cylindrical shell is used to study sound transmission under “flight conditions”: i.e., under conditions of external air flow past a pressurized cylinder at flight altitude. Numerical results for different incidence angles are presented for a typical narrow-bodied jet in cruising flight at 10 660 m (35 000 ft) with interior pressure at 2440 m (8000 ft). A comparison is made between no-flow sound transmission at standard conditions on the ground to sound transmission under flight conditions. It is shown that at M = 0, the cylinder transmission loss has dips at f_R (cylinder ring frequency) and f_c (critical frequency for a flat panel of same material and thickness as shell). Below f_R cylinder resonances affect TL. Between f_R and f_c, cylinder TL follows a masslaw behavior. Flow provides a modest increase in TL in the mass-law region, and strongly interacts with the cylinder resonances below f_R. For normally-incident waves, TL is unaffected by flow.     

Some unexpected proportionalities between components of the spin—other-orbit interaction in the f shell

The reduced matrix elements of the component z _i of the inter-electronic spin-other-orbit interaction have been calculated for all the states of the atomic f shell. Three of the z _i , each of which belongs to the irreducible representation (30) of Racah's group G₂, are found to exhibit matrix elements that are often related to one another in ways that go beyond what the Wigner-Eckart theorem, generalized to G₂, would predict. Examples are presented for matrix elements whose bras belong to the IR (20) of G₂ and whose kets belong to (31). The challenges to current theory are discussed.     

Spin forbidden transitions in the Ka = 0 subband of NO2 in the λ = 592.5 nm region

In a high resolution laser excitation spectrum of NO₂, lines were recorded which do not follow the selection rule ΔN = ΔJ = ΔF of “spin allowed” transitions. Line positions and intensities of these “spin forbidden” lines were investigated for all rotational lines up to N″ = 12 of the K_a = 0 subband around λ = 592.5 nm. While the observed line intensities of “spin allowed” transitions can be well described by the J-coupling scheme, neither the J- nor the G-coupling scheme sufficiently describes the “spin forbidden” transitions. The observations can be fitted satisfactorily by perturbation theory, in which the Fermi interaction in ²A₁ is treated as the perturber. This looks similar to a superposition of J and G scheme in the ²A₁ ground state.     

Shape transition in the neutron rich sodium isotopes

Mass spectrometer measurements of the neutron rich sodium isotopes show a sudden increase at ³¹Na in the values of the two-neutron separation energies. The spherical shell model naturally predicts a sudden decrease at ³²Na after the N = 20 shell closure. We propose that the explanation for this disagreement lies in the fact that sodium isotopes in this mass region are strongly deformed due to the filling of negative parity orbitais from the 1f_{$\text{7}\text{2}$} shell. Hartree-Fock calculations are presented in support of this conjecture.     

Simplified components of the spin-other-orbit interaction near the middle of the atomic f shell

To honour the memory of Brian Garner Wybourne, an analysis is presented of three components of the spin-other-orbit interaction for f electrons using the kind of Lie groups he would have been familiar with. The components have been named z ₆, z ₈ and z ₁₀. They all belong to the irreducible representation (IR) (30) of Racah’s group G₂. Near the middle of the f shell it is often found that fewer independent blocks of numbers are needed to express their matrix elements than the Wigner–Eckart theorem, generalized to the IRs U of G₂, would indicate. Each block corresponds to a given U and U?′, and possesses rows and columns labelled by the angular momenta L and L′. The number of independent blocks would be expected to be given by Racah’s multiplicity function c(UU?′ (30)); but near the middle of the shell the number c(UU?′ (20)) (or less) often suffices. For this to occur, z ₈ and z ₁₀ have to be replaced by linear combinations corresponding to IRs of the types (20)×(10) and (21)×(10) of the direct product group G_2A×G_2B, where A and B refer to electrons with their spins up (A) and spins down (B). A detailed example is provided by the IR (31) of G₂, which occurs in the configurations f ⁵ through f ⁹. In addition, two antiHermitian operators (z _a6 and z _a7) that also belong to the IR (30) of G₂ are discussed.     

Exotic mesons withJ PC=1−+, strange and non-strange

We analyse the QCD sum rules for the exotic quark-antiquark-gluon states called “glukonium” or “hermaphrodite” mesons. We predict a non-strange resonance of this type at ～1.5 GeV, a strange one at ～1.6 GeV and a strange-antistrange one at ～1.75 GeV. It should be noted that the above values of masses depend crucially on the vacuum expectation value of the gluon field operator <g ³ f _abc ·G _μv ^a G _vλ ^b G _λμ ^c >.     

Magnetoexcitons in core/shell quantum dots

The ground-state energies of the “bright” and “dark” excitons formed by an electron and a hole localized in a thin spherical shell subjected to a high magnetic field are calculated. This model corresponds to a core/shell quantum dot. The high-field condition implies that the magnetic length is much shorter than the radius of the sphere. It is found that the ground-state energy of the bright exciton exhibits an unusual magnetic-field dependence: E ₀ ～ H ^2/3.     

The structure of Heesch groups and its relation to material property tensors

The magnetic crystal point groups (Heesch groups) are classified according to their structure with respect to the three inversion operations: space, time, and total inversion. Accordingly the tensors are classified by the irreducible representations of the full inversion group. The groups and tensors are considered under the action of the elements A_i of the group of automorphisms of the full inversion group. The following correspondence theorem is proved: The matrix form of the tensor representation T of the group G coincides with the matrix form of the representation A_iT of the group A_iG. The theorem gives a clear explanation of the so-called “magic numbers” and provides a suitable short cut for the calculation and tabulation of material property tensors.     

Essential restriction on the symmetry of a unified theory for the case of massive gluons

In unified gauge theories with massive “color” gluons, the physical requirement of maintaining “color” SU(3) as a global classification symmetry is shown to lead to the following restrictions: (i) the local unifying symmetry group must be of the form G_flavor?G_color; (ii) quarks are to be integer charged; (iii) the number of flavors is an integral multiple of the number of “colors”.     

空间羣算符的矩阵元

本文首先通过对波失星直接乘积的分析指出,如果 ^*K″∈^*K?^*K′,则波矢峯G_k″可以有下面四种情况:A)G_k同G_k′,是G_k″的子峯,B)G_k=G_k′=G_k″,C)G_k″=G_s, D)G_s是G_k″的子峯。根据上述四种情况,分别考虑积分A=μ″^i″(k″)|f_μⁱ(k)|f_μ′^i′(k′)>的简约。并且证明,对所有四种情况,积分A的值均可由短阵U的矩阵元统一地表达出来。矩阵U是使可约表示Г′简约的转换矩阵,对四种情况,可约表示Г′分别是:A)(Г_kⁱ?Г_k′^i′)^(?),B)Гⁱ?Г_k′^i′,C)Г_k^i(s)?Г_k′^i′(s),D)(Г_k^i(s)?Г_k′^i′(s))^(?)。最后,利用准投影算符的方法,对矩阵U进行了计算,导出空间峯Wigner-Eckart定理的表式。     

Top-quark-mass enhancement in a seesaw-type quark mass matrix

We investigate the implications of a seesawtype mass matrix, i.e.,M _f?m _LM _F ^?1 m _R, for quarks and leptonsf under the assumption that the matricesm _L andm _R are common to all flavors (up-/down- and quark-/lepton-sectors) and the matricesM _F characterizing the heavy fermion sectors have the form [(unit matrix)+b _f (a democratic matrix)] whereb _f is a flavor parameter. We find that by adjusting the complex parameterb _f, the model can provide thatm _t?m _b while at the same time keepingm _u～m _d without assuming any parameter with hierarchically different values betweenM _U andM _D. The model with three adjustable parameters under the “maximal” top-quark-mass enhancement can give reasonable values of five quark-mass ratios and four KM matrix parameters.     

On unitary/antiunitary projective representations of groups

Unitary/antiunitary projective representations of groups (i.e., projective representations of groups where unitary as well as antiunitary operators in a separable complex Hilbert space are considered) are studied in a systematic way. Particular emphasis is put on continuous unitary/antiunitary projective representations of a Polish group G. It is shown that every continuous unitary/antiunitary projective representation of G can be lifted to a Borel unitary/antiunitary multiplier representation of G (namely, to a representation “up to a factor” which is a Borel mapping) and that this, in turn, can be derived from a continuous unitary/antiunitary (ordinary) representation of a Polish group obtained from an extension of G by the multiplicative group of all complex numbers of absolute value 1.     

The Reggeon Field Theory and finite scales at collider energies

The Reggeon Field Theory (RFT) with attention paid to finite “flavoring” rapidity scales is considered in the light of emerging SPS collider data. Predictions from a simple RFT perturbative model made in 1978 are shown to be consistent with σ_tot and other data, in both theP?f identity andP+f versions. The RFT scaling laws are judged not applicable without large non-leading terms, implying an asymptotic region beyond the collider.