Far-infrared spectrum of the internal rotation in methylamine

The far-infrared spectra of the Q branches of hindered rotation of CH₃NH₂ were studied in the 80 to 280 cm^?1 spectral region with resolutions up to 0.12 cm^?1. Through the theoretical analysis 11 of the 12 b-type parameters I_a1, I_a2, V₃, V₆, k₁, k₂, k₃, k₄, k₅, k₆, k₇, D_KK are determined using a nonlinear least-squares fit. The agreement between the observed and the final theoretical spectrum is satisfactory considering that only Q-branch lines were studied. Experimentally more lines, especially at low frequencies, were observed which probably belong to P- and R-branch lines of clusters thereof.     

Asymptotic inverse spectral problem for anharmonic oscillators

We study perturbationsL=A+B of the harmonic oscillatorA=1/2(??²+x ²?1) on ?, when potentialB(x) has a prescribed asymptotics at ∞,B(x)～|x|^?α V(x) with a trigonometric even functionV(x)=Σa _mcosω _m x. The eigenvalues ofL are shown to be λ _k =k+μ _k with small μ _k =O(k ^?γ), γ=1/2+1/4. The main result of the paper is an asymptotic formula for spectral fluctuations {μ _k }, $$\mu _k \sim k^{ - \gamma } \tilde V(\sqrt {2k} ) + c/\sqrt {2k} ask \to \infty ,$$ whose leading term \(\tilde V\) represents the so-called “Radon transform” ofV, $$\tilde V(x) = const\sum {\frac{{a_m }}{{\sqrt {\omega _m } }}\cos (\omega _m x - \pi /4)} .$$ as a consequence we are able to solve explicitly the inverse spectral problem, i.e., recover asymptotic part |x ^?α|V(x) ofB from asymptotics of {µ _k }. ₁ ^∞      

Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians

We consider the integrated density of states (IDS) ρ_∞(λ) of random Hamiltonian H_ω=?Δ+V_ω, V_ω being a random field on ? ^d which satisfies a mixing condition. We prove that the probability of large fluctuations of the finite volume IDS |Λ|^?1ρ(λ, H_Λ(ω)), Λ ? ? ^d , around the thermodynamic limit ρ_∞(λ) is bounded from above by exp {?k|Λ|},k>0. In this case ρ_∞(λ) can be recovered from a variational principle. Furthermore we show the existence of a Lifshitztype of singularity of ρ_∞(λ) as λ → 0⁺ in the case where V_ω is non-negative. More precisely we prove the following bound: ρ_∞(λ)≦exp(?kλ^?d/2) as λ → 0⁺ k>0. This last result is then discussed in some examples.     

Light-Front Zero-Mode Issue for the Transition Form Factors Between Pseudoscalar and Vector Mesons

We study the light-front zero-mode contribution to the transition form factors (g, f, a _±, T _i ) (i = 1, 2, 3) for the exclusive semileptonic P → V ?ν _? and rare P → V ? ⁺?^? decays using a covariant fermion field theory model in (3+1) dimensions. While the zero-mode contribution in principle depends on the form of the vector meson vertex Γ ^μ  = γ ^μ ? (2k ? P _V ) ^μ /D, the six form factors (g, f, a ₊, T ₁, T ₂, T ₃) are found to be free from the zero mode if the denominator D contains the term proportional to the light-front longitudinal momentum fraction factor (1/x) ⁿ of the struck quark with the power n > 0. Although the form factor a _? is not free from the zero mode, the zero-mode contribution comes only either from the simple vertex Γ ^μ  = γ ^μ term or from the other term just with a constant D (i.e. n = 0). We identify the zero-mode operator that is convoluted with the initial- and final-state valence wave functions to generate the zero-mode contribution to a _?.     

Longitudinal and transverse contributions to the threshold cross-section slope of single-pion electroproduction by a proton

The cross sections of inelastic electron scattering are measured near the threshold of single-pion production by a proton at k²=2.5, 3.5, 5.0 and 8.0 fm^? in the polarization range of the virtual photon ?=0.3–0.9. The separation of the |E₀₊|² and k²|S₀₊|² contributions to the cross-section slope at threshold is carried out and thus a new method of determining the F_A and F_π form factors is realized. The values for the axial mass and mean-square radius of the pion are obtained.     

Lower bounds to the I = 0, I = 2 ππ s-wave scattering lenghts

Roy's exact partial wave equations allow us to find bounds for any linear combination of the isospin I = 0 and s-wave scattering lengths, with positive coefficients. The bound is a function of the quantity a_D = a₂⁽⁰⁾ + a₂⁽²⁾, where a₂^(I) are the D-wave sacttering lengths. Thus, we can draw on the (a₀⁽⁰⁾, a₀⁽²⁾) plane an allowed domain whose boundary is fairly close to the phenomenological region. For a value of a_D = 1.7×10^?3, we find the following particular bounds: a₀⁽⁰⁾??0.49, a₀⁽²⁾??0.29.     

On-shell T-matrices in multiple scattering

The transition operator T for the scattering of a particle from N potentials V_j(x) can be expanded into a series featuring the transition operators t_j associated with the individual potentials. For V_j(x) both absolutely and square integrable in x, we show, using an analytic continuation argument, that if T is on-shell, i.e. in 〈k|T(k₀²±i0)|k′〉, |k| = |k′| = k₀, then each t_j is also on-shell.     

On the normalization of the Gamov resonant wave function in the configuration space

The regularization of the normalization integral for the resonant wave function, proposed by Zeldovich, is valid only when |Req _res| > |Imq _res|. A new normalization procedure is proposed and implemented, which is valid when this condition fails. First, an arbitrarily normalized vertex function g(k) is calculated using the formula with the potential V(r) in the integrand. This Fourier integral converges for a potential with the asymptotics V(r) → constr ^?n exp(?μr) if |Imq _res| < μ/2. Then the function g(k) is normalized using the generalized normalization rule, which is independent of the resonance pole position. The proposed method is approved by the example of calculation for a virtual triton.     

Study on the luminescence behavior of lanthanide ions using luminol as probe

Using luminol as the probe, the luminescence behavior of trivalent lanthanide ions (Ln³⁺=La³⁺, Ce³⁺, Pr³⁺, Nd³⁺, Sm³⁺, Eu³⁺, Gd³⁺, Tb³⁺, Dy³⁺, Ho³⁺, Er³⁺, Tm³⁺, Yb³⁺ and Lu³⁺) in aqueous solution was first investigated by fluorescence, and the sensitivity enhanced by 3–5 orders of magnitude compared with the Ln³⁺ intrinsic fluorescence. It was found that Ln³⁺ with luminol could form a 1:1 association complex which remarkably enhanced the fluorescence signal of luminol. The increment of fluorescence intensity was proportional to the concentration of Ln³⁺ in the range of 1.0–70.0 nmol L^?1, and the linear correlation equation, ΔI_F=AC_Ln+B, was given. The relationships of A (defined as sensitivity factor) with some physical parameters (atomic number Z, ionic radius γ_±, standard redox potential E^o and hydration enthalpy ΔH_hyd) were discussed. The good symmetry of A vs. Z plot for light lanthanides (LLG) and the heavy lanthanides (HLG) and linear relations of A with Z, γ_±, E^o and ΔH_hyd should originate in the special features of Ln³⁺ electronic configurations [Xe]4fⁿ (n=0–14). Using the proposed model of Ln³⁺–luminol interaction, lg[ΔI_F/(I_Fo–ΔI_F)]=rlg[Ln]+lg k, the association constant k was obtained over the range of 1.95×10⁶–2.63×10⁷ L mol^?1.     

Spin-lattice relaxation of the Vk-center in LiF

The angular and temperature dependences of the spin-lattice relaxation (SLR) rate of V_k-centers in LiF doped with Mg or Ag have been investigated. In the temperature interval 4.2–100 K the results can be fitted by the formula $\text{τ}{}^{\mathrm{?1}}\text{= A(θ)T + Be}{}^{\mathrm{<mtext>?\Delta </mtext><mtext>T</mtext>}}$ with A(0°) = 0.11 sec^?1K^?1, A(90°) = 1.3 sec^?1K^?1, B = 3 × 10⁵sec^?1 and Δ = (175 ± 15)K.A mechanism for the SLR is considered, assuming the modulation of the hyperfine interaction by phononinduced transitions between the ground and excited states of the resonant molecular vibrations of the V_k-center. This mechanism is found to explain the value, the temperature dependence and the isotropy of τ^?1 in the interval T = 20–100 K.The one-phonon SLR mechanisms of the V_k-center in the T < 10 K region are discussed.     

On the asymptotic behaviour of the mass operator near the Fermi energy

By taking due account of momentum conservation, it is shown that, when ω is near the Fermi energy ω_F, the imaginary part of the mass operator $\text{M(}\text{k}\text{, ω)}$ for an infinite Fermi system behaves like (ω ? ω_F)^p(k) where the exponent p(k) ? 2 depends on the interval in which $\text{|}\text{k}\text{|}$ is lying. In particular, the commonly asserted quadratic behaviour (ω ? ω_F² is shown to be true only for $\text{|}\text{k}\text{| ? 3k}{}_{\mathrm{<mtext>F</mtext>}}$. It is explicity assumed that the Fermi system admits a perturbative type treatment.     

The four quasi-particle 178Hf isomeric state,its excitation energy and multipolarities of deexciting transitions

The decay properties of the 31 y ¹⁷⁸Hf isomeric state have been investigated by means of a Ge(Li)-NaI(Tl) Compton suppression device and a Si(Li) detector, as well as with Ge(Li) and Ge(Li), intrinsic Ge and Si(Li) coincidence arrangements. From the E3 character of the unobserved isomeric transition (11.7 ≦ E_IT ≦ 16.7 keV), deduced from L-subshell and M/L ratios, I^π, K of the isomeric level was determined as 16⁺, 16. The {p[404] ↓ + p1514] ↑ + n[514] ↓ + n[624]↑}_16⁺ + four quasi-particle configuration was assigned to this level at 2447.5 ± 2.5 keV. As proposed earlier the isomeric E3 transition decays to the 13^? level of the band built upon the I^π = 8^? isomer. The |g_K?g_R| values derived from $\text{E}\text{2}\text{M}\text{1}$ ratios of interband transitions show that the 8^? isomer contains about 36 % of the p[404] ↓ + p[514] ↑ configuration and about 64 % of the n[624] ↑ + n[514] ↓ configuration.     

The theory of diffusion-limited recombination of donor—acceptor pairs

The asymptotics of the quasi-steady kinetics of diffusion-limited recombination of donor-acceptor (DA) pairs has been developed. The theory is based on the probability of DA pair recombination according to the relation w₀ exp [-(r/r_B)], where w₀ is constant, r is the separation between defects and r_B is the half Bohr radius of the more diffuse wavefunction. The reaction rate equation (for the thermal activation mechanism) includes the reaction constant as follows: k = 4πr_B[E_a/kT + ln (w₀r^2_B/D₀) + 1.54 + 2 K₀ (α)], α = 2r₀(w₀/D)$\text{1}\text{2}\text{,}$ where E_a is the activation energy, and K₀, I₀ are the modified Bessel functions. The quasi-steady recombination radius is introduced. The theory developed has been compared with the zone one. The interpretation of the activation energy and frequency factor have been presented for the diffusion model. An extension of the theory developed by taking into account Coulomb interaction between defects has also been presented. The applicability of the theory to the recombination of V_k centers with electronics centers is alkali halides has been shown. It is assumed that the theory is applicable to other centers of hole nature (H, proton, low symmetry exciton i.e. V_k + electron).     

Jahn-teller effects in (3d)2 ions in Al2O3

APR experiments have been carried out on V³⁺ and Cr⁴⁺ ions in Al₂O₃ partly to remove discrepancies in earlier measurements, and partly to provide additional information necessary for the theoretical analysis which follows. We find |G_-| ～ 45± 10 cm^?1 and ～ 160±30 cm^?1 for V³⁺ and Cr⁴⁺ respectively. It is shown that all the data for both ions can only be explained satisfactorily if a moderately strong Jahn-Teller effect operates in the cubic ³T₁, ground state of the ion. Full details are given, γ is found to be 0.14 and 0.36 for V³⁺ and Cr⁴⁺ respectively and important contributions from second-order Jahn-Teller effects are also present. The results also show that it is necessary to use a multimode full-lattice model of the Jahn-Teller effect as the constraints of the cluster model are broken. The implications of the proposed model on thermal conductivity, phonon spectroscopy and optical measurements are also briefly discussed. It is also pointed out that some important errors exist in the literature concerning the interpretation of experimental data for these systems.     

Theoretical calculation of the entropy change associated with substitutional anion defects in KCl

The entropy change S_d accompanying the substitution of a Cl^? ion in KCl by a F^?, Br^? or I^? ion has been calculated by a method that involves the whole phonon spectrum of the perfect crystal. The results are: $\text{S}{}_{\mathrm{d}}\text{k}\text{= -0.909}$ for KCl:F^?, 1.897 for KCl:Br^? and 4.055 for KCl:I^?. These figures are compared with the results obtained by approximate methods that have been used previously.     

Absence of Negative Energy Spectrum for N-Particle Hamiltonians

We consider the spectrum of the quantum Hamiltonian H for a system of N one-dimensional particles. H is given by $H = \sum\nolimits_{i = 1}^n { - \frac{1}{{2m_i }}\frac{{\partial ^2 }}{{\partial x_i^2 }}} + \sum {_{1 \leqslant i < j \leqslant N} } V_{ij} \left( {x_i - x_j } \right)$ acting in L ²(R ^N ). We assume that each pair potential is a sum of a hard core for |x|≤a, a>0, and a function V _ij (x), |x|>a, with $\smallint _a^\infty \left| {x - a} \right|\left| {V_{ij} \left( x \right)} \right|dx < \infty $ . We give conditions on V ^? _ij (x), the negative part of V _ij (x), which imply that H has no negative energy spectrum for all N. For example, this is the case if V ^? _ij (x) has finite range 2a and $$2m_i \smallint _a^{2a} \left| {x - a} \right|\left| {V_{ij}^ - \left( x \right)} \right|dx < 1.$$ If V ^? _ij is not necessarily small we also obtain a thermodynamic stability bound inf?σ(H)≥?cN, where 0<c<∞, is an N-independent constant.     

On the universality classes of the Henon map

Within an appropriate renormalization framework, we discuss a¹(b) and δ associated with the bifurcation road to chaos of a Hénon-like map generalized as follows: (x_t+1, y_t+1) = (1?a|x_t|^z + y_t, ?bx_t); (b?0, z?1). For fixed z, we obtained (i) only two universality classes, namely the conservative (b = 1) and non-conservative (b≠1) ones and (ii) $\text{a}{}^1\text{(}\text{1}\text{b}\text{) =}\text{a}{}^1\text{(b)}\text{b}{}^{\mathrm{z}}$. For b = 1, δ(z) presents a minimum, and diverges for z → 1 and z → ∞ (this contrasts with the b≠1 case).     

Study of the iterations of a mapping associated to a spin glass model

We study the iterations of the mapping $$\mathcal{N}[F(s)] = \frac{{(F(s))^2 - (F(0))^2 }}{s} + (F(0))^2 ,$$ with the constraintsF(1)=1,F(s)=∑a _nsⁿ,a _n≧0, and find that, except ifF(s)≡s,N[F(s)] approaches either 0 or 1 for |s|<1 ask→∞.     

ESR of Vk centers in CsI

V_k centers (self trapped hole I^?₂) have been obtained in CsI doped with Tl⁺ or Na⁺ by X-irradiation at low temperature and studied by ESR. Spin-Hamiltonian parameters are calculated and compared with those obtained for I^?₂ in the other alkali iodides, as well as the energy of the forbidden transition ²Σ⁺_u→²Π_u and the s and p components of the fundamental state.