Nuclear orientation study of the decay of204BiFe

The decay of²⁰⁴Bi nuclei (I =6⁺, T_1/2=11·22 h) oriented in an iron host was investigated on the JINR low-temperature nuclear orientation facility SPIN. The orientation parameterB ₂=1·17 (6) was obtained from the analysis of six prominent E1 gamma-transitions. From the measured normalized intensities of the gamma-rays observed some 70 values of multipole mixing ratios for the gamma-transitions in²⁰⁴Pb nucleus were determined for the first time. The spins 6, 6, 5 and 4 could be uniquely assigned to the²⁰⁴Pb negative parity levels at 3891·5 keV, 3768·4 keV, 3301·5 keV and 2338·2 keV, respectively. The spin-parity assignments of the levels at 4183·8 keV, 4094·2 keV, 3782·0 keV, 2506·9 keV and 2065·1 keV were confirmed as 6^–, 6^–, 5^–, 5^– and 5⁺, respectively. For the level at 3105·1 keV spin-parity 5^– was suggested and spinparity 7^– of the level at 2696·4 keV was called in question. The possible placements of the gammatransitions 3 1351·7 keV and 1353·4 keV in the decay scheme is discussed. The reorientation parameters for the long-living levels at 2264·2 keV (T _1/2=0·45 s) and 1273·9 keV (T _1/2= =265 ns) were determined asG ₂=0·41 (14) andG ₂=0·60 (17), respectively. For the isomeric level at 2185·7 keV (T _1/2=67·2 min) the value ofG ₂=0·88 (49) was proposed.The authors would like to express their thanks to T. I. Kracíková and M. Trhlík for the valuable discussions in the course of the evaluation of the experimental data.     

Clusters of cycles

A cluster of cycles (or (r,q)-polycycle) is a simple planar 2-connected finite or countable graph G of girth r and maximal vertex-degree q, which admits an (r,q)-polycyclic realization P(G) on the plane. An (r,q)-polycyclic realization is determined by the following properties: (i) all interior vertices are of degree q; (ii) all interior faces (denote their number by p_r) are combinatorial r-gons; (iii) all vertices, edges and interior faces form a cell-complex.An example of (r,q)-polycycle is the skeleton of (r^q), i.e. of the q-valent partition of the sphere, Euclidean plane or hyperbolic plane by regular r-gons. Call spheric pairs (r,q)=(3,3),(4,3),(3,4),(5,3),(3,5). Only for those five pairs, P((r^q)) is (r^q) without exterior face; otherwise, P((r^q))=(r^q).Here we give a compact survey of results on (r,q)-polycycles. We start with the following general results for any (r,q)-polycycle G: (i) P(G) is unique, except of (easy) case when G is the skeleton of one of the five Platonic polyhedra; (ii) P(G) admits a cell-homomorphism f into (r^q); (iii) a polynomial criterion to decide if given finite graph is a polycycle, is presented.Call a polycycle proper if it is a partial subgraph of (r^q) and a helicene, otherwise. In [ARS Comb. A 29 (1990) 5], all proper spheric polycycles are given. An (r,q)-helicene exists if and only if p_r>(q−2)(r−1) and (r,q)≠(3,3). We list the (4,3)-, (3,4)-helicenes and the number of (5,3)-, (3,5)-helicenes for first interesting p_r. Any outerplanar (r,q)-polycycle G is a proper (r,2q−2)-polycycle and its projection f(P(G)) into (r^2q−2) is convex. Any outerplanar (3,q)-polycycle G is a proper (3,q+2)-polycycle.The symmetry group Aut(G) (equal to Aut(P(G)), except of Platonic case) of an (r,q)-polycycle G is a subgroup of Aut((r^q)) if it is proper and an extension of Aut(f(P(G))), otherwise. Aut(G) consists only of rotations and mirrors if G is finite, so its order divides one of the numbers 2r, 4 or 2q. Almost all polycycles G have trivial AutG.Call a polycycle G isotoxal (or isogonal, or isohedral) if AutG is transitive on edges (or vertices, or interior faces); use notation IT (or IG, or IH), for short. Only r-gons and non-spheric (r^q) are isotoxal. Let T^*(l,m,n) denote Coxeter’s triangle group of a triangle on S², E² or H² with angles π/l, π/m, π/n and let T(l,m,n) denote its subgroup of index 2, excluding motions of 2nd kind. We list all IG- or IH-polycycles for spheric (r,q) and construct many examples of IH-polycycles for general case (with AutG being above two groups for some parameters, including strip and modular groups). Any IG-, but not IT-polycycle is infinite, outerplanar and with same vertex-degree, we present two IG-, but not IH-polycycles with (r,q)=(3,5),(4,4) and AutG=T(2,3,∞)PSL(2,Z), T^*(2,4,∞). Any IH-polycycle has the same number of boundary edges for each its r-gon. For any r≥5, there exists a continuum of quasi-IH-polycycles, i.e. not isohedral, but all r-gons have the same 1-corona.On two notions of extremal polycycles:

1. We found for the spheric (r,q) the maximal number n_int of interior points for an (r,q)-polycycle with given p_r; in general case, (p_r/q)≤n_int<(rp_r/q) if any r-gon contains an interior point.

2. All non-extendible (r,q)-polycycles (i.e. not a proper subgraph of another (r,q)-polycycle) are (r^q), four special ones, (possibly, but we conjecture their non-existence) some other finite (3,5)-polycycles, and, for any (r,q)≠(3,3),(3,4),(4,3), a continuum of infinite ones.

On isometric embedding of polycycles into hypercubes Q_m, half-hypercubes and, if infinite, into cubic lattices Z_m, : for (r,q)≠(5,3),(3,5), there are exactly three non-embeddable polycycles (including (4³)−e, (3⁴)−e); all non-embeddable (5,3)-polycycles are characterized by two forbidden sub-polycycles with p₅=6.     

Estimates of general Mayer graphs. IV. On the computation of Gaussian integrals by the star-mesh transformation

We point out that, to compute by hand a Gaussian integral exp · (– _LL y _l r _ij ² d r _n+1 ...d r _n+k , where the sum runs over all linesL = (i,j) of a graph andr _ij = ¦r _i –r _j ¦, the simplest way is to use the star-mesh transformation, well known in electrical network theory. We apply this to test, on a relatively complicatedn-graph, the accuracy of an estimation method that we proposed elsewhere [Phys. Lett. 62A:295 (1977)].     

The ideal polymer chain near planar hard wall beyond the Dirichlet boundary conditions

We present a new ab initio approach to describe the statistical behavior of long ideal polymer chains near a plane hard wall. Forbidding the solid half-space to the polymer explicitly (by the use of Mayer functions) without any other requirement, we derive and solve an exact integral equation for the partition function G _D(r,r′, N) of the ideal chain consisting of N bonds with the ends fixed at the points r and r′ . The expression for G(r,r′, s) is found to be the sum of the commonly accepted Dirichlet result G _D(r,r′, N) = G ₀(r,r′, N) - G ₀(r,r”, N) , where r” is the mirror image of r′ , and a correction. Even though the correction is small for long chains, it provides a non-zero value of the monomer density at the very wall for finite chains, which is consistent with the pressure balance through the depletion layer (so-called wall or contact theorem). A significant correction to the density profile (of magnitude 1/is obtained away from the wall within one coil radius. Implications of the presented approach for other polymer-colloid problems are discussed.     

Pitfalls in the Use of Common Luminescent Probes for Oxidative and Nitrosative Stress

Lucigenin (LC²⁺, bis-N-methylacridinium) and 2,7-dichlorofluorescin (DCFH₂) are widely used as chemiluminescent or fluorescent probes for cellular oxidative stress, to reflect levels of superoxide (O₂ ^·–) and hydrogen peroxide, respectively. We report mechanistic studies that add to the growing evidence for the unsuitability of either probe except in very well-defined circumstances. The ability for lucigenin to generate superoxide via reduction of LC²⁺ to LC^·+ and redox cycling with oxygen depends on the reduction potential of the LC²⁺/LC^·+ couple. Redox equilibrium between LC^·+ and the redox indicator benzyl viologen is established in microseconds after generation of the radicals by pulse radiolysis and indicated E(LC²⁺/LC^·+) –0.28 V vs. NHE. Reaction of LC^·+ with O₂ to generate O₂ ^·– was also observed directly similarly, occurring in milliseconds, with a rate constant k 3 × 10⁶ M ^–1 s^–1. Quinones act as redox mediators in LC^·+/O₂ redox cycling. Oxidation of DCFH₂ to fluorescent DCF is not achieved by O₂ ^·– or H₂O₂, but NO₂ ^·) reacts rapidly: k 1 × 10⁷ M ^–1 s^–1. Oxidation by H₂O₂ requires a catalyst: cytochrome c (released into the cytosol in apoptosis) is very effective (even 10 nM). Fluorescence reflects catalyst level as much as O₂ ^·–) production.     

Born Reciprocity and the 1/r Potential

Many structures in nature are invariant under the transformation pair, (p,r)→(b  r,−p/b), where b is some scale factor. Born’s reciprocity hypothesis affirms that this invariance extends to the entire Hamiltonian and equations of motion. We investigate this idea for atomic physics and galactic motion, where one is basically dealing with a 1/r potential and the observations are very accurate, so as to determine the scale b≡mΩ. We find that an Ω∼1.5×10⁻¹⁵ s⁻¹ has essentially no effect on atomic physics but might possibly offer an explanation for galactic rotation, without invoking dark matter.     

Analysis of the High-Resolution Infrared Spectrum of the PHD2 Molecule: ν1 and 2ν1 Bands

The results of investigation into the infrared spectra of the PHD₂ molecule including the ₁ fundamental band centered at 2324.005 cm^–1 (with a resolution of 4.2·10^–3 cm^–1) and the first 2₁ valence overtone centered at 4563.634 cm^–1 (with a resolution of 8.8·10^–3 cm^–1) are given in the present paper. Based on an analysis of the results obtained, 1340 and 1020 lines are referred to the ₁ and 2₁ bands, respectively. This data are used to calculate 316 and 248 vibrational-rotational energies of the (100000) and (200000) excited vibrational states, respectively. Since both bands can be considered as isolated, we take advantage of the Watson Hamiltonian (the reduction A in the I ^r representation) to describe their rotational structure. The calculated spectroscopic parameters of the examined states of the PHD₂ molecule correlate well with each other and with the corresponding parameters of the ground vibrational state.     

Diagonal and Off-Diagonal Recursion Relation for the General Potential V(r) = Arp

A recursion relation is derived for the potential V(r) = Ar ^p. Generally, this connects off-diagonal matrix elements of r ^k–2, r ^k+p, r ^k, and r ^k+2. The diagonal case is obtained by setting m = n in this relation. The relation is derived by elementary methods and without recourse to specific properties of the eigenstates. Finally, this relation is studied for the familiar potentials p = –1, 1, 2.     

In {2 2} vacuums,the null-datum on null rays is exactlyr −5

It is shown, by a simple argument, that in any {2 2} (i.e. type D) vacuum space-time, the complex component of the Weyl curvature (spinor abcd) along any light ray is precisely proportional tor ^–5, wherer is the standard Schwarzschild radial coordinate, or its natural complex generalization for the arbitrary {2 2} case.     

Photoinduced Electron Transfer From Carbazole to Halomethanes in a Gas Phase

Intermolecular photoinduced electron transfer (PET) in a gas phase was studied using carbazole vapor fluorescence quenching by halomethanes (CHCl₃, CH₂Br₂, CCl₄, CHBr₃). The fluorescence quenching rate constants k _q changing from 2.3·10⁵ sec^–1·torr^–1 in mixtures with CHCl₃ to 4.6·10⁶ sec^–1·torr^–1 in mixtures with CHBr₃ at a constant temperature of 403 K were estimated. The dependence of the carbazole fluorescence decay rates in the presence of halomethanes on the free energy change G during transfer of the electron from carbazole to halomethanes is considered. It is suggested to take into account the influence of the vibrational energy of the carbazole molecule E _vib and its temperature changes in estimation of the G values. The differences between PET in the gas and liquid phases were analyzed. It is found that for mixtures with CCl₄ and CHBr₃ the negative temperature dependence of k _q is observed, when the decay rates and efficiencies of the intermolecular PET decreased with temperature increase in the range 403–573 K, i.e. these mixtures the electron transfer is not a barrier-restricted process.     

Exact Solutions of the Two-Dimensional Schrödinger Equation with Certain Central Potentials

By applying an ansatz to the eigenfunction, an exact closed-form solution of theSchrödinger equation in two dimension is obtained with the potentials V(r) =ar ² + br ⁴ + cr ⁶,V(r) = ar + br² + cr ^–1,and V(r) = ar ² + br ^–2+ cr ^–4 + dr ^–6,respectively. The restrictions on the parameters of the given potential andthe angular momentum m are obtained.     

Ionic Synthesis of Ga1–x In x As Solid Solution Films

The Ga_1–x In _x As compound obtained by In-ion implantation (100 keV and (0.45–6)·10¹⁷ cm^–2) followed by thermal (800 °C and 15') or high-energy electron-beam (1 MeV, 0.6 mA·cm^–2, 660 °C, and 16 s) annealing is investigated by Rutherford backscattering, optical absorption, and capacitor photoelectromotive force. It is shown that x increases from 0.07 up to 0.21, and the band gap decreases from 1.34 down to 1.21 eV as the implantation dose increases. The surface potential decreases from 0.79 down to 0.58 V. A high efficiency of electron-beam annealing is pointed out.     

Determination of the Constants of Binding of Acridine Dyes with Micelles of Sodium Dodecyl Sulfate Using the Quenching of Delayed Fluorescence by Heavy Atoms

The constants of binding dye molecules with the micelles of sodium dodecyl sulfate are determined using quenching of delayed fluorescence of acridine dyes by sodium iodide in aqueous–micellar solutions. Kinetic equations have been composed that describe the processes of deactivation of the excited states of dyes. By solving these equations at the concentration of the quencher sodium iodide corresponding to the minimum lifetime of triplet states and at the concentration of micelles corresponding to the least value of the delayed fluorescence quenching rate constants, we obtained the constants of binding dyes with micelles equal to 1.3·10⁷, 2.9·10⁷, and 3.1·10⁷ M^–1 for trypaflavine, acridine orange, and acridine yellow, respectively. We calculated the rate constants of quenching of the triplet states of the molecules of dyes by iodide ions (I ^–) that decreased in transition from trypaflavine to acridine orange and acridine yellow.     

Polarization measurements in high energy elastic scattering of pions,kaons, protons and antiprotons on protons and comparison with regge phenomenology

The polarization parameterP has been measured for elastic scattering on polarized protons, of ^–, K^– and ¯p at 40 GeV/c and of ⁺, K⁺ and p at 45 GeV/c. Four-momentum transfer ranges from –0·08 to –1·8 (GeV/c)² for ^–p, and from –0·08 to about –1sd0(GeV/c)² for p, ⁺, K^± and ¯p.The angular distribution of the polarization in ^–p exhibits the well known non sense double zero att=–0·6 (GeV/c)². The K^–p and ¯pp results are compatible with exchange degeneracy for ¦t¦_r <0·5 (GeV/c)². The energy dependence of the polarizationP(t) in ^–p and in K⁺p above 10 GeV/c incident momentum is compatible with interference between Pomeron and Regge poles. On the contrary, the polarization in pp elastic scattering decreases faster than ordinary Regge model predictions. This result can be explained by interference between non flip and flip amplitudes of the Pomeron, leading to negative values for the polarization.Presented by A.de Lesquen at the Symposium on Hadron-Hadron Scattering at High Energies, Liblice, Czechoslovakia, June 16–21, 1975.     

New explicit nonperiodic solutions of the homogeneous wave equation

We exhibit a newansatz for the solution of the homogeneous three-dimensional time-dependent wave equation in spherical coordinates of the form Φ(r,t)=Y(θ, φ)(I(r)+G(g)), whereg ≡ct/r. FunctionG(g) has explicit solution in terms of three independent nonperiodic functionss _ℓ,t _ℓ,u _ℓ (s _ℓ andt _ℓ are related to the associated Legendre functions of the first and second kinds).G(g) is nonperiodic and may be cast as a superposition of incoming and outgoing waves. To obtainG(g), we solved a nonhomogeneous associated Legendre equation (this solution, to our knowledge, is also new).G(g) may prove useful in many microscopic and macroscopic problems, representable by homogeneous wave equations.     

Investigation of the Fiban K-1 Sulfocationite by the IR Spectroscopy Method

Using the IR spectroscopy method, we have studied the state of water, sulfogroups, and adsorbed methanol in a Fiban K-1 fibrous cationite under different conditions of preparation of a sample. It is shown that on an air-dried cationite protonation of methanol is performed by the ionic pair [(H_2n+1O _n )⁺·SO₃ ^–] after vacuum treatment at 20°C and by the ionic pair [H⁺·SO₃ ^–] after vacuum treatment at 90°C.     

Characterization of a a-Si:H thin-film transistors and the effect of thermal annealing

An analysis of characteristics of a-Si:H thin-film transistors were performed. The mobility of electrons in the accumulation layer induced by a gate voltage was in a order of 0.5 cm²/V · s at a field strength lower than 1×10⁴V/cm, and proportional toE ^–r at higher electric field, wherer was 0–0.2.The effect of thermal annealing at the temperatures 100–160°C on the parametersV _T andr are discussed. The activation energies for the variation of both parameters were 0.31 eV and 0.33 eV, respectively, that suggests the mechanism influencing both parameters may be the same. The mechanism is discussed in relation to the carrier hopping through the network of localized states.     

The electrodynamics and statistical mechanics of linear plasma response functions

The purpose of this paper is to review and to extend, wherever possible, the Kramers-Kronig relations, sum rules, and symmetry properties for the electrodynamic transport tensors of a linear plasma medium. For complete generality, we consider both nonrelativistic and relativistic plasmas with and without external magnetic fields. Our study is carried out first within the framework of classical electrodynamics. We then exploit the statistical-mechanical fluctuation-dissipation theorem to further obtain the Onsager symmetry relations and Kubo sum-rule frequency moments. Of special significance is the emergence of a variety of new Kramers-Kronig formulae andf-sum rules for the inverse dispersion tensor.Nomenclature E(k,) electric field intensity - Ê(k,) electric field in absence of plasma particles, - (k,) electric field due to the plasma particles (=E-Ê) - B(k,) magnetic induction - D(k,) electric induction - H(k,) magnetic field strength - B ₀ constant external magnetic field - A ₀ vector potential corresponding toB ₀ - (k,),j(k, co) charge and current densities due to the plasma particles - (k,),J(k,) charge and current densities of the external agency - (k,,B ₀) dielectric tensor of the plasma medium in the presence of B₀ - (k,,B ₀) diamagnetic tensor - (k, co,B ₀) (k,,B ₀) – 1, electric polarizability tensor - (k,,B ₀) magnetic polarizability tensor - (k,,B ₀) ordinary conductivity tensor - (k,,B ₀) external conductivity tensor - D(k,,B ₀) n²T–(k,,B ₀), dispersion tensor, where T=1-kk is the transverse projection tensor (k being the unit vector in the direction ofk) andn = kc/ the index of refraction - n²T – 1, = vacuum wave operator (value of D in vacuum) - 1/2( + ), Hermitian part of - ^{^} 1/2( – ), Anti-Hermitian part of a - , real and imaginary parts of a - R(r,t) dissipated power per unit volume of plasma - U total energy absorbed by the plasma - R(k,) E^*(k,) · (k,,b ₀) ·E(k,) corresponding spectral energy density - W(r,t) 1/2₀E²(r, 0 + (l/2₀) B²(r,t), field energy density - W(k,) 1/2₀E^*k,) ·E(k,) + (l/2₀)B ^*(k,) · B(k,), energy content in a certain domain of (k,)-space for a single mode - x _i,p _i,v _i coordinate, momentum, and velocity of ith electron - _i [1–(_i ²/c²)]^–1/2 - X _j,P _j,V _j coordinate, momentum, and velocity of jth ion - {A _q}, {E_q} field coordinates and momenta - j_k(t),J _k(t) perturbations in the microscopic electron and ion current densities due to the presence of the small external vector potential agencyâ(r,t) = (1/L³) â_k(t) expi k ·r - Liouville distribution function = ⁰ + - ⁰ macrocanonical distribution function characterizing the equilibrium state of the system in the infinite past - small perturbation due toA - H⁰ Hamiltonian of equilibrium system which includes interaction - H Hamiltonian for the interaction between the system and the small external perturbing agencyA - ⁰ = d^R()⁰ expectation value of any quantity over the equilibrium ensemble (d^R is an element of hypervolume in -phase space) - G(12) two-particle distribution function - F(1) one-particle distribution function - g(¦x₂ – x₁ ¦) [G(12)/F(1)F(2)] – 1, pair correlation function - N total number of electron in volume L³ - n ₀ equilibrium density (of electrons) - ^–1 temperature (in energy units) - ₀ (n₀e²/m₀)^1/2, equilibrium electron plasma frequency - _c ¦e ¦–B ₀/m, electron frequency - ^–1 ( ₀/n₀e²)^1/2, Debye length - ₀ (n₀Ze²/M₀)^1/2, equilibrium ion plasma frequency - _c ZeB₀/M, ion cyclotron frequency     

On the Distribution of Free Path Lengths for the Periodic Lorentz Gas III

 For r(0,1), let Z _r ={xR ² |dist(x,Z ²)>r/2} and define τ _r (x,v)=inf{t>0|x+tv∂Z _r }. Let Φ _r (t) be the probability that τ _r (x,v)≥t for x and v uniformly distributed in Z _r and §¹ respectively. We prove in this paper that

The dependence of the neutron temperature on the geometric parameter for water and loose diphenyl

The dependence of the neutron temperatureT _n on the geometric parameterB ² was measured by the pulse method in water and loose diphenyl. The measurements were made on a moderator poisoned by cadmium sulphate, a substance whose absorption cross-section is non 1/v.The following results were obtained: For waterT _n [eV]=–(0·00391±0·00045)B ² [cm^–2]+(0·02537±0·00035) for loose diphenyl:T _n [eV]=–(0·01014±0·00152)B ² [cm^–2]+(0·02518±0·00054).We are indebted to J. Jirou and J. Jadavan for their assistance in the measurements, the accelerator operation and electronic apparatus maintenance.