The Kepler-Coulomb problem on SO(2, 2) hyperboloid

In this note the Kepler-Coulomb problem in hyperbolic space H ₂ ² : z ₀ ² + z ₁ ² ? z ₂ ² ? z ₃ ² = R ² is discussed.     

Excitation of the giant monopole resonance and coulomb excitation of the giant dipole resonance in hadron inelastic scattering from208Pb

It is shown that the charge varianceσ _z ² observed in the low energy fission is consistent with the quantum mechanical zero point motion of an isovector giant dipole resonance. Theσ _z ² is determined at the ‘exit point’, where the neck radius ≈2.4 fm.     

The decay of the Bethe-Salpeter kernel inP(ϕ)2 quantum field models

We extend methods of high temperature expansions to show that for even weakly coupledP(?)₂ quantum field models the Bethe-Salpeter kernel has 4 particle decay. More precisely ifK denotes the Euclidean Bethe-Salpeter kernel $$|K(x_1 ,x_2 ,x_3 ,x_4 )| \leqq Oe^{ - m_0 (1 - \varepsilon )d_2 } ,$$ wherex=(x ⁰,x ¹),d ₂=2|x ₁ ⁰ +x ₂ ⁰ ?x ₃ ⁰ ?x ₄ ⁰ |+|x ₁ ⁰ ?x ₂ ⁰ |+|x ₃ ⁰ ?x ₄ ⁰ | and ε(λ)→0 as λ→0. Our methods apply to otherr particle irreducible kernels.     

Upon the determination of heavy quark fragmentation functions ine + e − annihilation

Results on the fragmentation of heavy quarks from analyses of inclusive lepton production ine ⁺ e ^? annihilation are studied. The use of various fragmentation variables is closely examined and their differences resolved, providing a common basis for comparison of experimental results. The mean value of the fraction of available energy-momentum carried by the primary heavy hadron, defined as $$z = \frac{{(E + p_\parallel )_{hadron} }}{{(E + p)_{quark} }},$$ is determined to be 〈z〉=0.67±0.02±0.02 and 〈z〉_b=0.83±0.01±0.02 for an unknown mixture of charmed and bottom flavoured hadrons respectively. The corresponding values of the parameter? _Q of the Peterson fragmentation function are $$\varepsilon _c = 0.06_{ + 0.02 + 0.02}^{ - 0.01 - 0.01} and \varepsilon _b = 0.06_{ + 0.001 + 0.02}^{ - 0.001 - 0.02} .$$ The ratio? _c /? _b can be approximately related toM _b ² /M _c ² giving a value of 10 _?2?4 ⁺⁴⁺⁵ , in agreement with an expectation of ～10. Measurements of the charged multiplicity of hadronic events containing heavy quark jets are investigated in terms of the mean value ofz.     

E2 andE3 transition strengths in some rare-earth nuclei

Coulomb excitation byα-particles of vibrational-like states in even-mass rare-earth nuclei is used to determine the reduced transition probabilitiesB(E2; 0 _gs ⁺ →2 _γ ⁺ ),B(E2; 0 _gs ⁺ →2 _β ⁺ ),B(E2; 2 _gs ⁺ →0 _β ⁺ ) andB(E2; 0 _gs ⁺ →3 _oct ^? ) in¹⁵⁰Nd,^{152, 154}Sm,^{154, 158}Gd,¹⁶⁴Dy and¹⁶⁶Er. TheB(Eλ; 0 _gs ⁺ →I=λ)-values range from 2.4 to 6.5 single-particle units for transitions to the 2 _γ ⁺ -states, 0.8 single-particle units for the 2 _β ⁺ -states and from 14.1 to 21.7 single-particle units for the 3^?-states.     

Pion photoproduction on197Au to ground and isomeric states in197Hg

The lifetime of the 331.3 keV 0 ₂ ⁺ state in¹⁰⁰Zr has been measured at the gas-filled recoil separator for fission products JOSEF. By observing the delayed coincidences between theβ-particles populating the level and theE0 conversion electrons from its decay into the ground state, a half-life of 3.37±0.30 ns has been obtained. From the measured lifetime and the relative intensities of the 0 ₂ ⁺ →0 ₁ ⁺ and 0 ₂ ⁺ →2 ₁ ⁺ transitions, values of 0.493±0.015 for theE0 strength parameterρ, and of 16 single particle units forB(E2,2 ₁ ⁺ → 0 ₂ ⁺ ) have been deduced. The enhanced nature of theE0 transitions suggests mixing of the 0 ₁ ⁺ and 0 ₂ ⁺ states which may be estimated by comparing the experimentalB(E2) values for the 2 ₁ ⁺ →0 ₁ ⁺ and 2 ₁ ⁺ →0 ₂ ⁺ transitions with the predictions of the asymmetric VMI model.     

On the free energy of the hopfield model

The general theory of inhomogeneous mean-field systems of Raggio and Werner provides a variational expression for the (almost sure) limiting free energy density of the Hopfield model $$H_{N,p}^{\{ \xi \} } (S) = - \frac{1}{{2N}}\sum\limits_{i,j = 1}^N {\sum\limits_{\mu = 1}^N {\xi _i^\mu \xi _j^\mu S_i S_j } } $$ for Ising spinsS _i andp random patterns ξ^μ=(ξ ₁ ^μ ,ξ ₂ ^μ ,...,ξ _N ^μ ) under the assumption that $$\mathop {\lim }\limits_{N \to \gamma } N^{ - 1} \sum\limits_{i = 1}^N {\delta _{\xi _i } = \lambda ,} \xi _i = (\xi _i^1 ,\xi _i^2 ,...,\xi _i^p )$$ exists (almost surely) in the space of probability measures overp copies of {?1, 1}. Including an “external field” term ?ξ _μ ^p h^μμξ _i=1 ^N ξ _i ^μ S_i, we give a number of general properties of the free-energy density and compute it for (a)p=2 in general and (b)p arbitrary when λ is uniform and at most the two componentsh ^μ1 andh ^μ2 are nonzero, obtaining the (almost sure) formula $$f(\beta ,h) = \tfrac{1}{2}f^{ew} (\beta ,h^{\mu _1 } + h^{\mu _2 } ) + \tfrac{1}{2}f^{ew} (\beta ,h^{\mu _1 } - h^{\mu _2 } )$$ for the free energy, wheref ^cw denotes the limiting free energy density of the Curie-Weiss model with unit interaction constant. In both cases, we obtain explicit formulas for the limiting (almost sure) values of the so-called overlap parameters $$m_N^\mu (\beta ,h) = N^{ - 1} \sum\limits_{i = 1}^N {\xi _i^\mu \left\langle {S_i } \right\rangle } $$ in terms of the Curie-Weiss magnetizations. For the general i.i.d. case with Prob {ξ _i ^μ =±1}=(1/2)±?, we obtain the lower bound 1+4?²(p?1) for the temperatureT _c separating the trivial free regime where the overlap vector is zero from the nontrivial regime where it is nonzero. This lower bound is exact forp=2, or ε=0, or ε=±1/2. Forp=2 we identify an intermediate temperature region between T_*=1?4?² and T_c=1+4?² where the overlap vector is homogeneous (i.e., all its components are equal) and nonzero.T _* marks the transition to the nonhomogeneous regime where the components of the overlap vector are distinct. We conjecture that the homogeneous nonzero regime exists forp≥3 and that T_*=max{1?4?²(p?1),0}.     

Off-shell effects in nucleon-deuteron polarization observables

A separable representation of theS-wave Paris potential and a phase-shift equivalent Yamaguchi-type potential significantly differing in their off-shell behaviours are used to calculate second-order polarization observables of elastic nucleon-deuteron scattering atE _D=10 and 20MeV. Off-shell effects are found that stem from differences in the nuclear interaction in the inner regionr?1.2 fm. Adding approximate Coulomb-distortion contributions to the purely nuclear Faddeev amplitudes proton-deuteron predictions are obtained. Coulomb effects are not found to be negligible. Comparison with experimental data, in particular, the spin-correlation parameterC _y,y of the reaction \({}^1\vec H(\vec d,d)^1 H\) forE _D=10MeV vector-polarized deuterons and the spin-transfer coefficientsK _y ^y′ ,K _x ^x′ andK _z ^x′ for \({}^2H(\vec p,\vec p)^2 H\) atE _p=10MeV, prefer the interaction model that contains an intermediate-range repulsion.     

Spin states of cobalt and the thermodynamics of Sm1 − x Ca x CoO3 − δ solid solutions

In the rare-earth SmCoO₃ perovskite, Co³⁺ ions at low temperatures appear to be in the low-spin state with S = 0, t _2g ² e _g ⁰ . If Ca²⁺ ions partially substitute Sm³⁺ ions, oxygen deficient Sm_{1 ? x} Ca _x CoO_{3 ? δ} solid solutions with δ = x/2 appear. The oxygen deficiency leads to the formation of pyramidally coordinated cobalt ions Co _pyr ³⁺ in addition to the existing cobalt ions Co _oct ³⁺ within the oxygen octahedra. Even at low temperatures, these ions have a magnetic state, either S = 1, t _2g ⁵ e _g ¹ or S = 2, t _2g ⁴ e _g ² . At low temperatures, the magnetization of Sm_{1 ? x} Ca _x CoO_{3 ? δ} is mainly determined by the response of Co _pyr ³⁺ ions. Owing to the characteristic features of the crystal structure of the oxygen deficient perovskite, these ions form a set of nearly isolated dimers. At high temperatures, the magnetization of Sm_{1 ? x} Ca _x CoO_{3 ? δ} is mainly determined by the response of Co _oct ³⁺ ions, which exhibit a tendency to undergo the transition from the S = 0, t _2g ⁶ e _g ⁰ state to the S = 1, t _2g ⁵ e _g ¹ or S = 2, tt _2g ⁴ e _g ² state. In addition, the magnetization and specific heat of the solid solutions under study include the contribution from the rare-earth subsystem, which undergoes a magnetic ordering at low temperatures.     

Electric properties of levels of 156Dy rotational bands

The nonadiabaticity of E0 transitions from 0 ₂ ⁺ states and 2 ₁ ⁺ bands in ¹⁵⁶Dy is examined within a phenomenological model that takes into account the mixing of K ^π = 0 ₁ ⁺ , 0 ₂ ⁺ , 0 ₃ ⁺ , 2 ₁ ⁺ states and 1⁺-bands. It is shown that the nonadiabaticity of E0 transitions is due primarily to the mixing of 0 ₂ ⁺ and 0 ₃ ⁺ bands.     

Xα-SW-calculation of the chemically induced decay constant variation of Tc-99m in the tetrahedral oxy-complex ion and the octahedral halogen-complex ions

The tetrahedral and octahedral complex ions TcO ₄ ^? , TcCl ₆ ^2? , TcBr ₆ ^2? , TcI ₆ ^2? , which exhibit experimentally determined decay constant variations of Tc-99m [1], meet the conditions for the application of the X_α-SW-method. The results of the calculations are given, including the case of TcF ₆ ^2? . The decay constant variations are evaluated using the one-electron functions in a partial-wave expansion. The results are compared with the measured values and a detailed discussion gives a comprehensive picture of the decay constant variation induced by the chemical surroundings considered.     

Production and loss of N 2 + , Ne+ and Ne 2 + during the decay period of plasmas produced in neon-nitrogen mixtures

Studies of the time dependencies of the number density of N ₂ ⁺ , Ne⁺ and Ne ₂ ⁺ ions have been made during the decay period of plasmas produced in neon containing various concentrations of nitrogen molecules. Reaction rate constants were obtained for N ₂ ⁺ +N₂+Ne→N ₄ ⁺ +Ne((1.2±0.2)×10^?29 cm⁶ sec^?1) and Ne⁺+N₂→N ₂ ⁺ + Ne ((2.9±0.3) × 10^?12 cm³ sec^?1). The ambipolar diffusion coefficient of N ₂ ⁺ in neon was found to beD _a p _o =350±20 cm² sec^?1 Torr.     

Electronic color centers in SrF2-Na crystals

It was shown that optical bleaching of M _A ⁺ color centers at 80 K in SrF₂-Na crystals causes the core of an M _A ⁺ -center to transform into the V _a ⁺ Me ⁺ V _a ⁺ configuration, in which all three point defects are arranged diagnonally in the cube cell. Reirradiation of an optically bleached crystal by x-rays generates F _D centers in it: V _a ⁺ Me ⁺ V _a ⁺ + e ^? → V _a ⁰ Me ⁺ V _a ⁺ ≡ F _D. The F _D → M _A ⁺ transformation in SrF₂-Na crystals proceeds at T = 135 K, in contrast to the F _A → M _A ⁺ transformations, which take place at T > 200 K.     

Domain wall theory of elementary excitations in anisotropic antiferromagneticS=1 chains

We present a theoretical investigation of elementary excitations in anisotropic antiferromagneticS=1 chains using the concept of domain walls in string (hidden) order. Domain walls are classified by the internal spin projectionS _dw ^z . We calculate energies and string correlation functions of low lying excited states of the domain wall type in the Haldane phase and compare the results to those of numerical computations. The boundaries of the Haldane phase are determined from the instability of these excitations with respect to the ground state. The interaction between two domain walls is found to be proportional to the productS _dw ^z , S _dw ^z ₂, it is effectively repulsive for equal spin projections.     

Description of the properties of the low-lying energy states in 100Mo with IBM2

The properties of the low-lying energy states for the 100Mo isotope is investigated within the framework of the proton-neutron interacting model IBM2.By considering the relative energy of the d proton boson to be diferent from that of the neutron boson and taking into account the dipole interacting among like-boson LπLπand LνLν,the low-lying energy spectrum is reproduced well.Particularly,the relative position of the energies for 2+1,0+2,2+2 and 4+1states shifted correctly fit the experimental data.The electromagnetic properties,including the key observable B(E2)reduced transition branching ratios and the E2 reduced matrix elements of the experimental data,are well described.Our calculations show possible shape coexistence in the 100Mo nucleus.     

Ground-state energy of quantum liquids

The kinetic (K ₄ ⁰ (n) and K ₃ ⁰ (n)) and potential (V ₄ ⁰ (n) and V ₃ ⁰ (n)) energies of ⁴He and ³He atoms have been found from the law of corresponding states and the experimental data on the dependence of the ground-state energies E ₄ ⁰ (n) and E ₃ ⁰ (n) on the density of the isotopes ⁴He and ³He. In the approximation of structureless quantum liquid, the potential energies are equal, V ₄ ⁰ V ₃ ⁰ (n) = (n), and the kinetic energies are inversely proportional to the atomic mass, $K_4^0 (n) = \frac{3} {4}K_3^0 (n)$ . The potential energy given by the expression V ⁰ = 4E ₄ ⁰ ? 3E ₃ ⁰ to a high accuracy is linear in the density n, which is associated with nearly an absence of short-range order in liquid helium. The kinetic energy of liquid ⁴He is given by the expression K ₄ ⁰ = 3(E ₃ ⁰ ? E ₄ ⁰ ), which agrees with the experimental data on neutron scattering in liquid ⁴He. The quantities K ₄ ⁰ (n) and K ₃ ⁰ (n) determine the scale of all thermodynamic characteristics in the temperature range where the effects of the particle statistics can be neglected.     

Roles played by an oxygen atom and out-of-plane high-frequency vibrational modes of a dibenzofuran molecule in the nonradiative deactivation of the lowest triplet state

We have studied the deactivation of the triplet sublevels s = z, y, and x of the lowest triplet state T ₁ ^s of the dibenzofuran molecule, which is determined by radiative (dipole) and nonradiative (degradation) transitions with the rate constants K _rad ^s and K _dg ^s . The main attention is paid to the nonradiative transitions T ₁ ^s ? S ₀ from the in-plane spin states (s = z, y), which are determined by the intramolecular interaction along the coordinates of out-of-plane vibrational modes. The roles played by the many-electron atom (oxygen) and high-frequency out-of-plane vibrational modes in the intramolecular interaction have been evaluated theoretically. Estimates of K _dg ^s based on three known approaches (three models) that describe the nonradiative transition in the approximation of adiabatic and nonadiabatic interactions are presented.     

Simultaneous electrochemical and electron paramagnetic resonance studies of fullerene anion radicals C 60 1− and C 60 3−

Simultaneous electrochemical and electron paramagnetic resonance experiments have been carried out on the reduced C₆₀ fullerene to examine theg-factor assignment of the radical species. C ₆₀ ^1? and C ₆₀ ^3? show the following EPR characteristics at room temperature: C ₆₀ ^1? :g _1?=2.0002±0.0001, 2ΔB _1s=0.17 mT, and C ₆₀ ^3? :g _{3?=2.0008±0.0002}, 2ΔB _1s=0.07 mT. EPR linewidths are apparently narrower compared to those in most of the spectra previously reported. Variable temperature EPR study on solution containing C ₆₀ ^1? has shown thatg _1? value is not while the linewidth is only slightly temperature dependent.     

Gyromagnetic ratios of excited states in186W

The gyromagnetic ratios of the 4 ₁ ⁺ , 6 ₁ ⁺ , and 2 ₂ ⁺ states in¹⁸⁶W were measured relative to that of the 2 ₁ ⁺ level by means of the transient field implantation perturbedγ-ray angular distribution technique. The nuclei in the states of interest were Coulomb excited using a beam of 220-MeV⁶³Cu projectiles and recoiled swiftly through a thin, polarized Fe foil. The present measurements yielded ratiosg(4 ₁ ⁺ )/g(2 ₁ ⁺ )=1.04±0.07,g(6 ₁ ⁺ )/g(2 ₁ ⁺ )=1.03 ±0.20 andg(2 ₂ ⁺ )/g(2 ₁ ⁺ )=0.63±0.13. The sizable disparity between the measuredg-factors of the ground- and excited-band is examined within the context of the interacting boson approximation model.