Calculation of high-order rotational centrifugal-distortion matrix elements for a Hund's case (a) basis set

The derivation of explicit expressions for the Hund's case (a) matrix elements of R^2k is discussed, where R is the mechanical rotational angular momentum operator of the molecule. A recursion relation is developed that permits matrix elements of R^2k to be expressed in terms of those of R^2(k?1), thus affording a straightforward means of calculating the case (a) matrix elements of rotational centrifugal-distortion constants D_v, H_v, L_v, M_v, etc., to an arbitrarily high order. The explicit matrix elements of L_v are listed.     

Ten-fold degenerate d-electron correlation and the metal-nonmetal transition in a disordered binary system: Inclusion of Hund's rule coupling

The Yonezawa-Watabe (YW) study of the metal-nonmetal transitions in nondegenerate, s-electron disordered binary systems: doped semiconductors, metal-ammonia solutions, liquid metals and mixed crystals (alloys), is generalized to include ten-fold d-electron (hole) degeneracy. Such degeneracy automatically includes Hund's rule d-electron coupling and intra-site enhanced Coulomb and exchange interactions. Such a calculation is specifically relevant only to transition metal alloys, transition metal oxides and mixed transition metal oxides. It is seen that potential fluctuations exist in these systems and the possibility of Anderson localization in these disordered degenerate binary transition metal systems is explored. The YW CPA treatment of the effect of substitutional disorder (alloying) upon the mobility gap and quasiparticle states of the density of states at the extreme band edges and localization due to random spin configuration are generalized to these degenerate d-electron systems and it is shown that the disappearance of the mobility gap, not the density of states gap, causes the metal-nonmetal transition for degenerate d-electrons.     

The hyperfine structure of diatomic molecules: Hund's case (cα)

The hyperfine splitting in diatomic molecules is treated according to an unperturbed model that is denoted Hund's coupling case (c_α). The advantages of this model are: (i) Rapid convergence of the perturbation expansion (spin-orbit interaction is included in the unperturbed Hamiltonian), (ii) hyperfine interactions of the type ΔJ ≠ 0 are automatically included, (iii) simple rotational-independent matrix elements result for the hyperfine Hamiltonian, and (iv) it is rather easy to judge whether the various hyperfine parameters are correlated or not. Numberical diagonalization of a secular matrix of dimension (2S + 1)(2I + 1) (or less for singular levels) yields the hyperfine splittings. The interaction with remote electronic states is included through a Van Vleck transformation. The coupling case (c) matrix elements are readily specialized to coupling case (a), and the present method is applied to the a³Π₁ substate of InH (optical), the X³Σ^? state of ³³SO and ¹⁷O¹⁶O (microwave) and to the X²Π state of ⁷LiO (radio frequency).     

Λ-type doubling and term formulae for a 5Π state in the intermediate case between Hund's cases (a) and (b)

Explicit expressions valid for all values of Y intermediate between Hund's cases (a) and (b) are obtained for the multiplet term formula and for the width of the Λ-type doubling of a ⁵Π state.     

A simultaneous fit of b , c ,s (bcs Pairs) and c spectra

A previous fit of the J/ψ and γ levels and leptonic widths by a power-like phenomenological potential is modified to include systems containing strange quarks. In spite of the smallness of the strange quark mass, the fit is astonishingly good.     

A classical green's function approach to vibrational spectra of biopolymers

Classical green's function methods can be used to calculate the spectra of large molecules by essentially putting together the spectra of smaller parts. The methods are useful where the parts are connected by few valence bonds.     

Some acoustical properties of St Paul's Cathedral,London

The interior of St Paul's Cathedral has a volume of 152 000 m³ including the large dome. The average value of the reverberation time is 11 s at 500 Hz when the cathedral is empty and reduces to 7·8 s at the same frequency when the cathedral is full. These measurements have been confirmed by several methods, including the method of integrated impulses. For frequencies above 1250 Hz the reverberation time decreases, because of air absorption and the special effect of the dome. With a steady random noise source the energy density was not constant in the nave: at 1000 Hz the sound level fell away at an approximate rate of 3 dB per doubling of distance. The assumption of a Sabine space can be made to some extent, and based on this assumption it is possible to estimate the reverberation time when the cathedral is full from the results when empty. Speech intelligibility is poor and articulation tests showed that in the middle of the nave only 20–30% of words are understood.     

Some solutions for Yang's equations for self-dual SU(2) gauge fields

It is shown that a large class of solutions of Yang's equations for self-dual SU(2) gauge fields can be obtained from the solutions of two-dimensional and four-dimensional Laplace equations.     

Some anomalies in the regularities of the SER spectra of benzene and hexafluorobenzene

The paper is devoted to qualitative explanation of some anomalies in the SER spectra of benzene adsorbed on lithium and hexafluorobenzene absorbed on silver in the framework of the dipole-quadrupole SERS theory. These anomalies manifest in the most enhancement of the bands which do not belong to the breathing vibrations of symmetrical molecules. We consider, that these anomalies are associated with large influence of the totality of coefficients which characterize excitation of excited states of the molecule by separate vibrations. On the base of this assumption a conclusion is made about possible lower influence of electromagnetic factor and specific influence of electron structure of molecules in the considered systems.     

Negative linear gain and coupling in Lamb's two-mode laser theory

In laser theory one always supposes that the linear gain α of a mode should be positive for that mode to oscillate. We show here that, according to Lamb's theory, this assumption is not necessarry: in a two-mode laser, a mode with a negative linear gain can be brought to oscillation by a negative coupling with another mode.     

Structural, electronic and magnetic properties of the Mnben Ni(110) c(2×2) surface alloy

Using first-principles total energy method, we study the structural, the electronic and the magnetic properties of the MnNi(110) c(2×2) surface alloy. Paramagnetic, ferromagnetic, and antiferromagnetic surfaces in the top layer and the second layer are considered. It turns out that the substitutional alloy in the outermost layer with ferromagnetic surface is the most stable in all cases. The buckling of the Mn–Ni(110) c(2×2) surface alloy in the top layer is as large as 0.26á(1á=0.1 n13) and the weak rippling is 0.038 AA in the third layer, in excellent agreement with experimental results. It is proved that the magnetism of Mn can stabilize this surface alloy. Electronic structures show a large magnetic splitting for the Mn atom, which is slightly higher than that of Mn–Ni(100) c(2×2) surface alloy (3.41 eV) due to the higher magnetic moment. A large magnetic moment for the Mn atom is predicted to be 3.81 μ_B. We suggest the ferromagnetic order of the Mn moments and the ferromagnetic coupling to the Ni substrate, which confirms the experimental results. The magnetism of Mn is identified as the driving force of the large buckling and the work-function change. The comparison with the other magnetic surface alloys is also presented and some trends are predicted.     

Some highly excited states of the LiH molecule: Calculations relevant to core-hole initiated relaxation processes (CHIRP's) in ionic crystals

Results of calculations by the Unrestricted Hartree-Fock method of the total energy vs internuclear distance for the molecules LiH and (LiH)⁺ are presented in Figs. 1 and 2. These data are required for an investigation of a particularly interesting variety of CHIRP. Some implications of these results are considered. It appears that significant extensions of the theory of low energy atom-atom and atom-molecule collisions developed in recent years (largely by quantum chemists) may be required.     

Vibronic interaction in the case of quasidegenerate electronic states. Formation of vibrational structure of the fluorescence spectra (letters to the editor)

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 55, No. 3, pp. 359–361, September, 1991.     

Some anomalies in the Ne(I)(744/736 Å) photoelectron spectra of N2O

The Ne(I) 774/736 Å photoelectron spectra of N₂O are reported for the X?²Π state of N₂O⁺. The spectra in general do not show any autoionization behavior to the extent reported for CO₂ and CS₂. There is an apparent “enhancement” of the 101 level by the 744 Å line. In contrast to the He(I) 584 Å PES, the intensity ratio for the 100 and 001 levels are reversed when excited by Ne(I) 736 Å radiation.The spectra also show excitation to higher vibrational levels of N₂O⁺X²Π. This can be explained within the framework of autoionization of a Rydberg state whose core is similar to that of the B? state of N₂O⁺.     

A green's function analysis of atomic and molecular (e, 2e) reactions

Investigation of Atomic and molecular (e, 2e) spectra will be discussed in terms of a Green's function approach. The energy, intensity and momentum distribution of energy levels observed by electron coincidence ionization spectroscopy, are directly related to the poles, pole strengths and generalized overlap amplitude of the one particle propagator or Green's function. The theoretical calculation of these observable quantities via the Green's function technique will be discussed. In particular, the position and intensity of satellite (or “shakeup”) lines, relative to the main lines, will be analysed in some detail.     

Coriolis interaction in the local mode (n100;F2) combination states of GeH4

Coriolis interactions in local mode (n100) combination states of GeH₄ are studied. Three widely used local mode models, the normal mode model with Darling–Dennison resonance included (NMDD) model and the anharmonically coupled anharmonic oscillator (ACAO) model with two different kinds of bond stretching variable, were used to calculate the values of the interaction parameters. As a test of these three models, the Coriolis interaction parameters of the local mode (3100) combination bands of the ⁷⁴GeH₄,⁷²GeH₄ and ⁷⁰GeH⁴ species, recorded at a resolution of 0.015cm^-1 on a Bruker IFS120HR Fourier transform spectrometer, are compared with the calculated results. There is good agreement.