Single-particle levels of nuclei in the vicinity of the doubly magic nuclei 2048 Ca28 and 2856 Ni28

Isotonic and isotopic dependences of single-particle energies of neutron and proton states in 20 ≤ Z ≤ 28 and 24 ≤ N ≤ 32 nuclei are investigated, these energies being determined by matching data on nucleon-stripping and nucleon-pickup reactions on the same nucleus. Regularities of the formation of the spectra of single-particle levels in Z, N = 20, 28 magic nuclei are demonstrated. A distinctive feature is found in the isotonic dependence of the energy of the 1 f _5/2 neutron level, this feature being consistent with the assumption that j _>-j _< interaction is operative in nuclei. The single-particle energies calculated by using the potential of the dispersive optical model are found to be consistent with experimental data within their errors. Original Russian Text ? O.V. Bespalova, I.N. Boboshin, V.V. Varlamov, T.A. Ermakova, B.S. Ishkhanov, E.A. Romanovsky, T.I. Spasskaya, T.P. Timokhina, 2008, published in Yadernaya Fizika, 2008, Vol. 71, No. 1, pp. 37–49.     

Analysis of single-particle energies of the neutron states in the 64,66,68,70Zn isotopes within a mean field model with dispersive optical potential

The dynamics of the shell parameters of ^{64, 66, 68, 70}Zn nuclei close to the Fermi energy, obtained by the joint evaluation of data from the stripping and pick-up reaction of a nucleon on one and the same nucleus, demonstrates how the difference between the neutron single-particle spectra of the levels of ⁷⁰Zn and ⁶⁸Ni nuclei with the number N = 40 arises. The experimental data are analyzed within a mean field model with dispersive optical potential. The calculation results describe very well the dimunution of the energy gap between the 1g _9/2 and 2p _1/2 levels in Zn isotopes, in comparison with Ni isotopes.     

Analysis of the neutron single-particle energies of Zn, Ge, and Se isotopes within a mean field model with dispersive optical potential

The parameters of the neutron dispersive optical potential of even-even Zn, Ge, and Se isotopes (both stable and unstable) are determined from an analysis of experimental and estimated neutron single-particle energies. The imaginary part of the potential depends on the shell structure of the isotopes. The calculated energies are found to be in good agreement with the experimental and estimated energies.     

Allowance for the shell structure of the 42100 Mo and 46110 Pd nuclei in the synthesis of 84200 Po, 88210 Ra, and 92220 U

The effect of the shell structure of colliding nuclei in calculating the entrance channel on the ensuing evolution of the product system is investigated. The entrance channel is calculated under the assumption of the nose-to-nose orientation of colliding nuclei. The following three reactions involving nuclei that are deformed in the ground state are considered: ₄₂¹⁰⁰Mo + ₄₂¹⁰⁰Mo → ₈₄¹⁰⁰Po, ₄₂¹⁰⁰Mo + ₄₆¹⁰⁰Pd → ₈₈²¹⁰Ra, and ₄₆¹¹⁰Pd + ₄₆¹¹⁰Pd → ₉₂²²⁰U. The state of the system at the point of touching is determined by the results obtained by calculating the entrance reaction channel. The shape of the system is specified by three collective coordinates (deformation parameters). The evolution of collective coordinates of the system is described in terms of Langevin equations. The potential energy of the system of colliding nuclei is calculated with allowance for their shell structure. It is shown that allowance for individual features of interacting nuclei in the entrance channel of the fusion-fission reactions makes it possible to obtain, for the reactions being considered, cross sections for evaporation-residue formation that are closer to available experimental data than their liquid-drop counterparts.     

Transition densities between the 01+, 21+, 41+, 02+, 22+, 11− and 31− states in 12C derived from the three-alpha resonating-group wave functions

All the multipole transition densities between the seven T = 0 states in ¹²C are calculated with the use of the microscopic 3α resonating-group wave functions which are obtained by dynamically solving the 3α relative motion with the total antisymmetrization taken into account exactly. The observed elastic and inelastic electron scattering form factors for the transition to the 2₁⁺, 4₁⁺, 0₂⁺, 1₁^?and 3₁^? states are well reproduced with no additional effective charge. The existence of a deformed intrinsic state for the 0₁⁺, 2₁⁺and 4₁⁺states is deduced by the analysis of the transition densities between them which are derived by the weak-coupling-type 3α wave functions; the intrinsic density distribution is illustrated. The monopole density distribution of the 0₂⁺, 2₂⁺ and 1₁^?, states is found to be much longer ranged than that of the 0₁⁺, 2₁⁺ and 4₁⁺ states; the 3₁^? state case is intermediate. On the basis of the transition densities between the 0₁⁺, 2₁⁺, 0₂⁺ and 2₂⁺ states, analysis is made of the transition between the shell-like states and the molecule-like states with a large spatial-structure change. Specific, effective nucleon-nucleon interactions are folded into the transition densities here obtained. The evident dependence of the radial shape of the folded nucleon-¹²C form factors on the choice of the interactions and the multi-step form factors for the excitation of the 0₂⁺, 1₁^? and 3₁^? states are discussed.     

Analysis of single-particle energies of doubly magic <Superscript>100,132</Superscript>Sn nuclei within the dispersive optical model

Extrapolation of the single-particle energies E _nlj of the bound states of neutrons and protons in the ^{112,116,118,120,124}Sn isotopes has been performed to estimate the values of E _nlj for unstable doubly magic ₅₀ ¹⁰⁰ Sn₅₀ and ₅₀ ¹³² Sn₈₂ nuclei. The estimates obtained are compared with the data derived from the analysis of the decay spectra of neighboring radioactive nuclei and with the results of the calculation within the dispersive optical model.     

Electromagnetic decay of the 02+ state in the doubly closed shell nucleus 64146Gd82

The existence of the 0₂⁺ state in ¹⁴⁶Gd at 2165.0 (4) keV is established through observation of the E0(0₂⁺ → 0₁⁺ transition. The measured half-time 375 (40) ps of this state corresponds to a monopole strength of ?² = 0.0122 (13) which is taken as evidence against a strong state dependence of the effective proton monopole charge.     

Calculation of single-particle energies in the <Stack><Subscript>38</Subscript><Superscript>96</Superscript></Stack>Sr nucleus within the mean field model with the dispersive optical potential

Evaluated and experimental neutron single-particle energies of the ^{88, 94, 96}Sr and ^{90, 96, 98}Zr nuclei near the Fermi energy are compared. A possibility of formation of a considerable particle-hole gap in the ^{94, 96}Sr typical of traditional magic nuclei is investigated. Agreement is obtained between the single-particle energies calculated within the mean field model with the dispersive optical potential and the evaluated energies for the ^{94, 96}Sr nuclei.     

Unitary version of the single-particle dispersive optical model and single-hole excitations in medium-heavy spherical nuclei

A unitary version of the single-particle dispersive optical model was proposed with the aim of applying it to describing high-energy single-hole excitations in medium-heavy mass nuclei. By considering the example of experimentally studied single-hole excitations in the ⁹⁰Zr and ²⁰⁸Pb parent nuclei, the contribution of the fragmentation effect to the real part of the optical-model potential was estimated quantitatively in the framework of this version. The results obtained in this way were used to predict the properties of such excitations in the ¹³²Sn parent nucleus.     

Further investigation of the γ-transitions in Λ4H and Λ4 hypernuclei

The γ-spectra induced by stopped K^? mesons in ⁶Li and ⁷Li targets in coincidence with the accompanying charged pions and π⁰ mesons. The γ-line at (1.04 ± 0.04) MeV observed with charged pions was identified as a γ-transition in _Λ⁴H, whereas the γ-line at (1.15 ± 0.04)_MeV observed with π⁰ mesons was ascribed to a γ-transition in _Λ⁴He. Using these new values for the excitation energies of the 1⁺ levels of _Λ⁴H and _Λ⁴He hypernuclei, the phenomenological ΛN potential for the s-state interaction was recalculated.     

The g-factor difference for the 61+ and 88+ states in 210Po

The difference in g-factors for the 6₁⁺ and 8₁⁺$\text{(πh}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}{}^2\text{)}$ states in ²¹⁰Po has been measured as $\text{(g}{}_6\text{? g}{}_8\text{)}\text{g}{}_8\text{= 2.0 ± 0.7\%}$. This result represents a small violation of additivity. A value of g₈ = 0.909 ± 0.011, independent of g₆, was also obtained.     

Comparison between the spin polarization energies for VSi− in silicon and VGa0 in gallium phosphide

We compare the gain in energy upon spin polarization for the undistorted V_Si^- in silicon and V_Ga⁰ in gallium phosphide. We show that this gain in energy is mainly related to the magnitude of the electron-electron interactions on the first neighbors of the vacancy. These interactions being larger for phosphorous atoms than for silicon atoms, the spin polarization energy is larger for V_Ga⁰ than for V_Si^?; this explains why the former is spin polarized while the latter is Jahn-Teller distorted.     

Oxygen vacancy model for the E1′ center in SiO2

An (oxygen)^- vacancy model of the E₁^≈ center in alpha quartz, featuring an asymmetric relaxation of the two silicons adjacent to the oxygen vacancy, is presented and analyzed. This model is shown to be consistent with both theoretical calculations and experimental hyperfine data, in contrast with any model previously proposed for the E₁^≈ center.     

On the renormalized coupling constant and the susceptibility in φ44 field theory and the Ising model in four dimensions

We discuss the euclidean φ₄⁴ field theory, and the critical behavior in ferromagnetic systems in four dimensions. It is rigorously shown that there are at most logarithmic corrections to the mean field law in the behavior of the magnetic susceptibility _X = ΣS₂(0, x). Furthermore, if any such corrections are present in a continuum limit which is used to construct a φ₄⁴ field theory, the limiting theory would be non-interacting. Our analysis extends to ferromagnetic systems of variables which belong to the Griffiths-Simon class.     

Vibrational study of layered ZnPS3 compounds intercalated with [Co(η5 -C5H5)2+] and [Cr(η6 -C6H6)2+] CATIONS

Infrared and Raman spectra (10–3100 cm^?1) of the layered ZnPSs compound and of intercalates with [Co(η⁵ ? C₅H₅)₂⁺] and [Cr(η⁶ ? C₆H₆)₂⁺] cations in the polycrystalline state have been recorded 300–10 K temperature range. A complete assignment of the spectra is proposed in terms of PSs group motions, Zn²⁺ ion translations and [Co(η⁵ ? C₅H₅)₂⁺] or [Cr(η⁶ ? C₆H₆)₂⁺] internal vibrations. New low frequency for the [Co(η⁵-C₅H₅)₂⁺] intercalate at low temperature are assigned to librational and torsional modes of C₅H₅ rings. Moreover, the preresonance Raman spectra of this intercalate show a selective enhancement for the metal-ligand vibrations when the charge transfer band of the cobalticenium is approached. One concludes that guest molecules are intercalated under their cationic form, are weakly interacting with the host lattice and seem to be dynamically disordered at room temperature.     

The radiative characteristics of the rovibronic states of the hydrogen molecule: IV. Relative probabilities of the r 3Π g ? , s 3Δ g ? → c 3Π u ± spontaneous transitions of the H2 molecule

A statistical analysis of the available literature data and data obtained in this work on the wave numbers of the lines that appear in triplet-triplet rovibronic transitions of the H₂ molecule was performed. This allowed us to verify and refine the controversial identification of spectral lines and find the optimum rovibronic level energy values for the c ³Π _u ^±, r ³Π _g ⁻, and s ³Δ _g ⁻ states. The ratios between the line strengths of the P, Q, and R branches of the (4dπ)r ³Π _g ⁻, (4dδ)s ³Δ _g ⁻ → (2pπ)c ³Π _u ^± band systems of the H₂ molecule were measured systematically. The calculation results obtained in the Frank-Condon approximation differed substantially (by up to two orders of magnitude) from the experimental data. The dependences of the ratios between rovibronic line strengths of the r ³Π _g ⁻ → c ³Π _u ^± and s ³Δ _g ⁻ → c ³Π _u ^± transitions on the rotational quantum number N′ of the upper level were found to correlate with each other. The deviations of adiabatic theory increase as N′ grows, which is evidence of an important role played by electronic-rotational interactions in the perturbation of transition probabilities. The experimental ratios between the probabilities of rovibronic transitions satisfactorily agree with the results of calculations within the framework of the simple nonadiabatic model taking into account electronic-rotational interaction of radiating adiabatic states in the approximation of pure precession. The dependences of transition probabilities on N′ were obtained for the first time for the first four diagonal bands of the r ³Π _g ⁻, s ³Δ _g ⁻ → c ³Π _u ^± transitions. Original Russian Text ? S.A. Astashkevich, B.P. Lavrov, A.V. Modin, I.S. Umrikhin, 2008, published in Khimicheskaya Fizika, 2008, Vol. 27, No. 2, pp. 22–38.     

High field magnetization in Pr(Ni1-xCox)5 single crystals

Magnetization measurements in fields up to 38 T performed at low temperature on single crystals of the hexagonal Pr(Ni_1-xCo_x)₅ compounds for x = 0, 0.05, 0.10 and 0.20 are presented. In PrNi₅ we observe highly original behaviour predicted by the knowledge of the Crystalline Electric Field parameters and arising from the existence of a non-magnetic singlet ground state; namely transitions associated with the field induced “anticrossing” and “crossing” of the two lowest states along the [100] and [120] directions, respectively. The measurements performed on the other compounds have allowed us to study the dependence of this behaviour on Co substitutions.     

Calculation of radiative transition probabilities and radiative recombination rate coefficients for H2, OH, H 2+ and OH+ molecules

A method is presented to calculate the radiative transition probabilities and the radiative recombination rate coefficients between electronic molecular states. Total transition probabilities are determined from vibrational transition probabilities without considering the detailed rotational structure of the molecular electronic states. Radiative recombination rate coefficients are obtained from the computation of vibrational photo-ionisation cross sections. Concerning spontaneous emission, Lyman (B → X) and Werner (C → X) band systems of H₂ and Meinel (A → X), (B → A) and (B → X) band systems of OH are investigated. For radiative recombination, transitions between H₂⁺ (X) and H₂(X), and between OH⁺(X, a, A, b, and c) and OH(X) are considered. Transition probabilities and recombination rate coefficients are calculated as a function of temperature in the range 1500–15 000 K.     

Calculation of the spectroscopic constants for the electronic states A1Σ u+ , B1Πu, C1Πu, D1Σ u+ , and E1Σ u+ of the cesium dimer

The vibrational, rotational, and centrifugal distortion constants have been calculated for the electronic states A ¹Σ _u ⁺ , B ¹Π_u, C ¹Π_u, D ¹Σ _u ⁺ , and E ¹Σ _u ⁺ of the Cs₂ molecule. The calculation was performed on the basis of the semiempirical potential energy curves constructed in this paper. The calculated spectroscopic constants are compared with the experimental data. Original Russian Text ? A.D. Smirnov, 2007, published in Optika i Spektroskopiya, 2007, Vol. 102, No. 1, pp. 23–27.     

Calculation of the probability of the 4 T 2→4 A 2 transition in luminescence spectra of the Mn4+ ion in gadolinium-gallium garnet

The ⁴ T ₂→⁴ A ₂ transition of the Mn⁴⁺ ion has been observed in the luminescence spectrum of Mn⁴⁺:Cd₃Ga₅O₁₂ upon intense laser pumping. It is shown that an increase in the intensity of the ⁴ T ₂→⁴ A ₂ transition with respect to the ² E→ ⁴ A ₂ transition in these crystals with increasing pumping power relates to the increased role of induced transitions. The intensity of this process is greater in the region where the ² E→⁴ A ₂ and ⁴ T ₂→⁴ A ₂ transition bands overlap most, which leads to an increase of the zero-phonon line of the latter transition, peaking at a wavelength of 694 nm. The rates of radiative and nonradiative recombination involving the ⁴ T ₂, ² E, and ⁴ A ₂ terms of the Mn⁴⁺ ion in gallium-gadolinium garnet (GGG) are calculated using data from luminescence spectra measured at different temperatures. The Mn⁴⁺:GGG crystal is proposed for use as an active element of lasers with continuous frequency tuning. __________ Translated from Optika i Spektroskopiya, Vol. 94, No. 4, 2003, pp. 590–596. Original Russian Text Copyright ? 2003 by Bulyarskiĭ, Zhukov, Prikhod’ko.