Emission spectrum of chlorine excited in the presence of argon

The spectrum of chlorine excited in the presence of argon has been photographed with a 21-ft. grating spectrograph in the first order. Two band systems in the region 2600–2390 Å and 2365–2239 Å are observed which appear to be respectively analogous to the 2950–2670 Å and 2660–2590 Å systems of bromine reported earlier by Venkateswarlu and Verma. The wavelengths and the wavenumbers of all the bands in the system 2600–2390 Å are given. The vibrational scheme along with the corresponding Franck-Condon parabola is also given. The analysis suggests that the lower state of the system is the 3π(O _u ⁺_ state established by Elliott at 17658 cm.^?1 and that the upper state is at 67773 cm.^?1 The vibrational constants obtained arew ₀′ = 246·6 cm.^?1,w ₀′x ₀′ = 0·615 cm.^?1,w ₀″ = 255·2 cm.^?1,w ₀″x ₀″ = 5·5 cm.^?1,w ₀″y ₀″ = ?0·0155 cm.^?1 andw ₀″z ₀″ = 0·00115 cm.^?1     

Emission spectrum of bromine excited in the presence of argon

The wavelengths and wavenumbers of the band heads of the system 3150–2970 Å as obtained from the plates taken on the first order 21′ grating spectrograph are given along with the vibrational analysis. This system is shown to be due to a transition from an upper electronic state at T_e = 48516 cm.^-1 with ω′ _e = 162·0 cm.^?1 and ω′ _e χ′ _e = 0·29 cm.^?1 to the well-known³ Π _u (O _u ⁺) state at T_e = 15918 cm.^-1 This lower state is common with that of the system 2950–2670 Å.     

Emission spectrum of bromine excited in the presence of argon

The wavelengths and wavenumbers of the band heads of the system 2660-2590 Å as obtained from the plates taken on the first order 21-feet grating spectrograph are given along with its vibrational analysis. This system is shown as the transition from an upper state at T _e =56776 cm.^?1 withω _e = 108·0 cm.^?1 to the³ Π _u (O _u ⁺) state at T _e =15918 cm.^?1 The lower state is the same as that of the two systems in the regions 2950-2670 Å and 3150-2970 Å reported earlier.     

The spectrum of iodine excited in the presence of argon

The band systems of iodine in the regions 3455-3015 Å, 2785-2750 Å and 2730-2520 Å obtained by earlier workers using prism spectrographs are now photographed in the first and second orders of a 21-ft. grating spectrograph. A large number of new bands are obtained in all these three systems which are now extended to the regions 3461-3015 Å, 2785-2731 Å and 2729-2486 Å. The wavelengths and wavenumbers of all the bands are recorded along with their visually estimated intensities. The Deslandres schemes for the three systems representing all the bands are given and are found to be supported by the corresponding intensity distributions of the expected type. It was found that the two systems 3460-3015 Å and 2785-2731 Å do not involve for their lower levels the ground state as assumed by the earlier workers but the³Π_u (O _u ⁺) state at 15642 cm.^?1, which is also the lower state for the 4420-4000 Å system. The band system in the region 2730-2486 Å has for its lower level the ground state of the molecule as reported by the earlier workers. A reanalysis of this system made to include all the bands observed in the present experiments, gave vibrational constants slightly different from those obtained by earlier workers. The vibrational constants of the upper states of the four different systems that one gets by exciting iodine in the presence of argon are

System	Te	ωe	ωeXe	ωeYe
4400-4000Å	41411 cm.-1	102·2 cm.-1	0·34 cm.-1	..
3460-3015Å	45937 cm.-1	103·7 cm.-1	0·95 cm.-1	..
2785-2731Å	51847 cm.-1	112·4 cm.-1	0·711 cm.-1	0·004 cm.-1
2730-2486Å	47207 cm.-1	96·5 cm.-1	0·510 cm.-1	0·0033 cm.-1

     

The emission spectrum of iodine bromide excited in the presence of Argon

IBr vapour was excited in the presence of argon by an uncondensed transformer discharge. Four band systems were obtained in the regions 5425–5360 Å, 4520–4415 Å, 4120–4010 Å and 3915–3540 Å of which the first three are discussed in this paper. The wavelengths and wavenumbers of the band heads in three systems as measured from the plates obtained with a 3-prism Steinheil glass spectrograph are given along with their visually estimated relative intensities. The three band systems, which are new, are analysed and the following vibrational constants expressed in cm.^?1 are obtained:

Band system	v e	w e ″	w e ″x e ″	w e ″y e ″	w e ′	w e ′x e ′
5425-5360 Å	18613	65·5	0·24	?0·01	43·0	0·026
4520-4415 Å	22312	65·5	0·24	?0·01	77·0	0·5
4120-4010 Å	24540	160·6	1·125	..	128·4	0·1

     

Emission spectrum of PrO

The bands of PrO at 8488.95 A and 7986.44 A of system I and at 7662.85 A of system III have been photographed on 6.6 meter concave grating spectrograph at a dispersion of 1.2 A/mm and their rotational structure analysed. They are assigned transitions fromv′ = 0 and 1 levels of A² Δ_5/2 andv′ = 0 level of B² Δ_5/2 to a commonv′’ = 0 level of the ground, X² Π_3/2 state.     

Emission spectrum of bismuth monochloride

Bismuth chloride has been excited in flowing condition with an uncondensed transformer discharge. About 390 bands are observed in the present experiments of which only 140 were recorded by earlier workers. The vibrational constants obtained are the same as those obtained by Morgan from obsorption experiments except for the addition of a cubic term for the upper state. It appears quite likely that the upper state of the system dissociates into Bi (⁴S_3/2) + Cl (²P_1/2) while the lower state, which is probably the ground state, dissociates into Bi (⁴S_3/2) + Cl (²P_3/2). The rough values of the dissociation energies obtained by extrapolations are D₀′=3750 cm.^?1 and D₀″=24614 cm.^?1     

Bose-Einstein condensation in the excited band and the energy spectrum of the Bose-Hubbard model

Based on the mean field approximation, we investigate the transition into the Bose-Einstein condensate phase in the Bose-Hubbard model with two local states and boson hopping in only the excited band. In the hard-core boson limit, we study the instability associated with this transition, which appears at excitation energies δ < |t ₀ |, where |t ₀ | is the particle hopping parameter. We discuss the conditions under which the phase transition changes from second to first order and present the corresponding phase diagrams (Θ,μ) and (|t ₀ |, μ), where Θ is the temperature and μ is the chemical potential. Separation into the normal and Bose-Einstein condensate phases is possible at a fixed average concentration of bosons. We calculate the boson Green’s function and one-particle spectral density using the random phase approximation and analyze changes in the spectrum of excitations of the “particle” or “hole” type in the region of transition from the normal to the Bose-Einstein condensate phase.     

Lower bound for the spectrum and the presence of pure point spectrum of a singular discrete Hamiltonian system

In this paper, criteria for limit-point (n) case of a singular discrete Hamiltonian system are established. Furthermore, the lower bound of the essential spectrum is obtained and the present of pure point spectrum is discussed for such system by using the spectral theory of self-adjoint operators in a Hilbert space.     

Singularly-perturbed boundary value problems in the presence of zeros in the spectrum of the limit operator

Translated fromSibirskii Matematicheskii Zhurnal, Vol. 35, No. 1, pp. 118–123, January–February, 1994.     

On a method for computing waveguide scattering matrices in the presence of point spectrum

A waveguide occupies a domain G in ? ⁿ⁺¹, n ? 1, having several cylindrical outlets to infinity. The waveguide is described by a general elliptic boundary value problem that is self-adjoint with respect to the Green formula and contains a spectral parameter µ. As an approximation to a row of the scattering matrix S(µ) we suggest a minimizer of a quadratic functional J ^R (·, µ). To construct such a functional, we solve an auxiliary boundary value problem in the bounded domain obtained by cutting off, at a distance R, the waveguide outlets to infinity. It is proved that, if a finite interval [µ₁, µ₂] of the continuous spectrum contains no thresholds, then, as R → ∞, the minimizer tends to the row of the scattering matrix at an exponential rate uniformly with respect to µ ∈ [µ₁, µ₂]. The interval may contain some waveguide eigenvalues whose eigenfunctions exponentially decay at infinity.     

Asymptotic properties of excited states in the Thomas-Fermi limit

Excited states are stationary localized solutions of the Gross-Pitaevskii equation with a harmonic potential and a repulsive nonlinear term that have zeros on a real axis. The existence and the asymptotic properties of excited states are considered in the semi-classical (Thomas-Fermi) limit. Using the method of Lyapunov-Schmidt reductions and the known properties of the ground state in the Thomas-Fermi limit, we show that the excited states can be approximated by a product of dark solitons (localized waves of the defocusing nonlinear Schrödinger equation with nonzero boundary conditions) and the ground state. The dark solitons are centered at the equilibrium points where a balance between the actions of the harmonic potential and the tail-to-tail interaction potential is achieved.     

Endpoints of gaps in the Markoff spectrum

If the interval (a, b) is a gap in the Markoff spectrum, then the numbera can be written as the sum of two quadratic irrationals. A similar result is obtained for one type of right endpointb.     

Continuous spectrum, point spectrum and residual spectrum of operator matrices

Let M_C denote a 2 × 2 upper triangular operator matrix of the form , which is acting on the sum of Banach spaces X⊕Y or Hilbert spaces H⊕K. In this paper, the sets and ?_C∈B(K,H)σ_r(M_C) are, respectively, characterized completely, where σ_c(·) denotes the continuous spectrum, σ_p(·) denotes the point spectrum and σ_r(·) denotes the residual spectrum. Moreover, some corresponding counterexamples are given.     

Synchronization of chaos in non-identical parametrically excited systems

In this paper, we investigate the synchronization of chaotic systems consisting of non-identical parametrically excited oscillators. The active control technique is employed to design control functions based on Lyapunov stability theory and Routh–Hurwitz criteria so as to achieve global chaos synchronization between a parametrically excited gyroscope and each of the parametrically excited pendulum and Duffing oscillator. Numerical simulations are implemented to verify the results.