Properties of8Be and12C deduced from the folding-potential model

Theα-α differential cross sections are analyzed in the optical model using a double-folded potential. With the knowledge of this potential bound and resonance-state properties ofα-cluster states in⁸Be and¹²C as well as astrophysical S-factors of⁴He(α,γ)⁸Be and⁸Be(α,γ)¹²C are calculated. Γ_γ-widths and B(E2)-values are deduced.     

Elastic scattering of α-particles on10B forE α = 5−50 MeV

Experimental data of the elastic scattering ofα-particles on¹⁰B forE _α = 30?50.6 MeV are presented. They are analysed together with the data of a previous measurement forE _α = 5?30 MeV in the frame of the optical model including spin-orbit coupling. The interaction radii of theα-¹⁰B-systems are determined with the Inopin-Ericson model forE _α = 5?50 MeV. The mean free path ofα-particles in¹⁰B is calculated.     

Local density approximation in effective density-dependentαN-interactions

Different forms of a local density approximation (LDA) in effective density-dependent αN-interactions are compared in single-folding optical model analyses of elastic α particle scattering by^{40, 42, 44, 48}Ca atE _α=104 MeV and by⁴⁰Ca atE _α=140 MeV. It is shown that the form of the LDA considerably influences the results on folded optical potentials. A variable form of the LDA is suggested and discussed which includes previous forms as limiting cases. The new form leads to better fits to the data and to full consistency with the best available “model-independent” optical potentials.     

Investigation of large angle structure in α-scattering from calcium isotopes betweenE α=36–61 MeV

Elasticα-scattering angular distributions have been measured atE _α=36.2 MeV, 39.6 MeV, 42.6 MeV, 49.5 MeV, 61.0 MeV for⁴⁰Ca and atE _α=36.2 MeV, 42.6 MeV, 49.5 MeV and 61.0 MeV for⁴⁴Ca, respectively. At backward angles the data display an oscillatory structure forE _α<50 MeV and more smoothly decreasing slopes atE _α =61.0 MeV resembling the data obtained at higher energies. The⁴⁰Ca data belowE _α =50 MeV show the well known backward enhancement, which at 42.6 MeV and 49.5 MeV can be fitted by aP ₁₄ ² and aP ₁₆ ² respectively. Together with previous data,P _L ²-structures have now been observed for allL-values betweenL=8 andL=16. The slope of the curveL(L+1) versus excitation energy is slightly smaller forL>12 than forL<12. Optical model analyses (within a Woods-Saxon-folding model) lead to large differences between the⁴⁴Ca and⁴⁰Ca parameters. Furthermore, in our parametrization, the⁴⁰Ca real potential depth shows dramatic changes with energy. This feature seems outside the domain of the optical model and requires consideration of additional effects (e.g. antisymmetrization) not included in the standard optical model. Present microscopic calculations on the basis of the Resonating Group Method are discussed in connection with the characteristic features ofα-scattering from⁴⁰Ca.     

Picosecond nonlinearity of GeO2–Bi2O3–PbO–TiO2 glasses at 532 and 1,064 nm

The third-order optical properties of GeO₂–Bi₂O₃–PbO–TiO₂ glasses at 532 nm and 1,064 nm were studied to evaluate their potential for optical limiting and all-optical switching. The Z-scan technique was used to determine the nonlinear (NL) refractive index, n ₂, and the NL absorption coefficient, α ₂, of samples with different amounts of the constituent oxides. Values of n ₂ ≈ + 0.7 × 10^?14 cm²/W at 1,064 nm and ≈+1.5 × 10^?14 cm²/W at 532 nm were measured. The NL absorption coefficient, α ₂, was smaller than the minimum that our apparatus can measure (α ₂ < 0.01 cm/GW) in the near-infrared (1,064 nm); in the visible region (532 nm), we obtained α ₂ ≈ 4.4 cm/GW. The set of NL parameters measured indicates the potential usefulness of the GeO₂–Bi₂O₃–PbO–TiO₂ glasses for all-optical switching at 1,064 nm and for optical limiting at 532 nm.     

The 56Fe(α, γ)60Ni reaction cross section

The yield of 1.332 MeV γ-rays from the reaction ⁵⁶Fe(α, γ)⁶⁰Ni has been measured as a function of α-particle bombarding energy in the range 4.2–7.1 MeV. This energy region includes the (α, n) threshold at E_α = 5.46 MeV. The energy dependence of this γ-ray cross section, as well as the (α, nγ) cross section, is compared with statistical model calculations. Good agreement is achieved between these data and calculations using global optical model parameters to determine the transmission functions. In particular, the pronounced threshold effect in the (α, γ) yield, at the opening of the (α, n) channel, is well represented.     

Optical potential calculations for the 1s level in pionic atoms

The Ericson-Ericson optical potential for theπ-nucleuss-wave interaction was extended to be applicable also for light nuclei. In particular, terms of order A^?1 were evaluated and the (π2N) dispersion was considered. From comparison with experimental data we found that considerable improvement could be achieved by introducing terms of order A^?1. The (π2N) dispersion was found to be repulsive and of the same magnitude as the absorption. The (πN) scattering lengths were deduced to be α₃?α₁=0.258±0.008m _π ^?1 and α₁+2α₃=?0.018±0.008m _π ^?1 .     

Spin and parity assignments for 35Cl levels from the 31P(α, p)34S reaction

³⁵Cl states at excitation energies between 9.9 and 11.8 MeV have been identified through sharp resonances in the ³¹P(α, p_o)³⁴S excitation functions at 25°, 105° and 155° for E_α = 3.25–5.50 MeV. Forty-eight on-resonance angular distributions, normalized to an absolute cross section scale, have been subjected to single-level and two-level analyses resulting in spin and parity assignments for each resonance. Approximately half the resonances were of the pure single-state type, having unique angular distribution shapes. Data from 12 resonances of an earlier experiment ¹) were analyzed with the same theory, extending the diagnostics down to a ³⁵Cl excitation energy of 9.1 MeV. A set of optical potentials consistent in all four reactions that this experimental program encompasses has been incorporated in the present analysis. Validity of the optical potential is demonstrated for α-particles elastically scattered by ³¹P.     

The alpha-branching ratios of the188,190,192Pb isotopes

Theα-branching ratios (b _α ) of^192,190,188Pb are measured using mass-separated sources. Different experimental set-ups are used — one detector as well as two detector set-ups — thereby detecting theα particles from the parent and/or viaα decay formed daughter nuclei, theβ-delayed gamma radiation from the parent and/or viaβ decay formed daughter nuclei and the Tl KX rays from electron capture decay. Values forb _α of 6.2(6) 10^?5 and 4.0(4) 10^-3 were found for^192,190Pb respectively. For¹⁸⁸Pb, limits on theb _α values were obtained: 0.03<b _α <0.10. A careful analysis of the previously reportedb _α values showed that the discrepancies in theb _α values were not due to inadequate correction procedures, as was suggested, but to experimental uncertainties in the efficiency determination of the different detection set-ups and to an unreliableβ-decay scheme for¹⁸⁸Pb. Theb _α obtained in this work show that the leadα decay is not faster than the Hgα decay and that there is no need to assume a disappearance of theZ=82 shell closure halfway betweenN=82 andN=126.     

Helium burning of 18O

The ¹⁸O(α, γ)²²Ne capture reaction has been studied at E_α = 0.6?2.3 MeV. The known resonance at E_α = 2.20 MeV has been established and fourteen new resonances have been found in the energy range covered. The E_α = 1.16, 1.32, 1.45, 1.53, 1.87, 1.96 and 2.15 MeV resonances correspond to resonances observed previously in the ¹⁸O(α, n)²¹Ne reaction. The E_α = 0.77, 1.25 and 1.27 MeV resonances represent new compound states in ²²Ne. Information on branching ratios, ωγ values and total widths is reported. Transition strength arguments and analyses of γ-ray angular distribution data together with results from previous work resulted in the most likely J^π assignments for the resonances.The E_α = 1.66 and 1.78 MeV resonances are good candidates for the two J^π = 8⁺ states predicted at E_x ≈ 11–12 MeV and are probably members of the K^π = 0⁺ (ground state) and K^π = 2⁺ rotational bands in ²²Ne.The investigated energy range of E_α together with that of previous work corresponds to stellar temperatures of T = (0.3?4.3) × 10⁹ K. The astrophysical reaction rate determined from these data is compared with predictions based in part on the nuclear optical model. The rate is also compared with that of the competing ¹⁸O(α, n)²¹Ne reaction.     

Precise measurement of the 23P0−23P2 fine structure interval in helium

A measurement of the 2³P₀?2³P₂ fine structure interval in the helium has beeen made using the optical microwave atomic beam magnetic resonance technique. The result is 31.908 040 (20) GHz (0.6ppm), which establishes an internal consistency in measurements of the helium fine structure and verifies the theory to order α⁴Ry. When the theory is used together wit our experimental result we obtain a value for the fine structure constant α by α^-1=137.03613(11) (0.8 ppm).     

Optical Stark effects in the stimulated Raman spectrum of molecular oxygen

High-resolution stimulated Raman spectroscopy has been used to observe optical Stark effects in pure-spin, rotational, and rotational-vibrational transitions in molecular oxygen (X³Σ_g^?). Recorded spectra in both polarized and depolarized configurations demonstrate some striking differences in the Stark splitting of ³Σ ground state molecules from that reported previously for ¹Σ molecules. An analysis of the position of a number of normal and satellite rotational-vibrational lines in both the polarized and depolarized spectra has led to a measurement of a value for the v = 1 excited state polarizability anisotropy and to a more accurate value for the band origin of the v = 1 ← 0 transition: γ₁ = (α_| ? α_|)₁ = (1.36 ± 0.17) × 10^?24 cm³, and ν₀ = 1556.385 ± 0.001 cm^?1.     

Nonlinear optical properties and phase-relaxation processes in single-walled carbon nanotubes

We have investigated third-order nonlinear optical properties of bundled and isolated semiconducting single-walled carbon nanotubes (SWNTs) by means of Z-scan method, pump-probe method, and two-beam time-resolved degenerate four-wave mixing (DFWM) method. The figures of merit Im χ⁽³⁾/α in both bundled and isolated SWNTs samples were found to be enhanced with increasing tube diameter. The measured Im χ⁽³⁾/α value in the bundled SWNTs was an order of magnitude smaller than that in the isolated SWNTs. Both population relaxation time T₁ and phase-relaxation time T₂ for bundled samples were smaller than those in the isolated samples. These experimental results can be explained by an increase in nonradiative recombination rate and phase-relaxation rate in the bundled sample. The phase-relaxation time T₂ is considered to have a significant role in the enhancement of Im χ⁽³⁾/α.     

Structural and optical properties of lithium borobismuthate glasses

Glasses with compositions 25Li₂O-(75−x)Bi₂O₃-x B₂O₃, with 0?x?30 mol%, have been prepared using the melt quenching technique. The density and the molar volume have been determined. IR spectroscopy is used as a structural probe of the nearest neighbor environment in the glass network. The optical transmittance and reflectance spectrum of the glasses have been recorded in the wavelength range 400-1100 nm. The values of the optical band gap E_g^opt for indirect transition and refractive index have been determined for 0?x?30 mol%. The average electronic polarizability of the oxide ion α_o²⁻ and the optical basicity have been estimated from the calculated values of the refractive indices. Variations in the different physical parameters such as the density, molar volume, optical band gap, refractive index, average electronic polarizability of the oxide ion and optical basicity with B₂O₃ content have been analyzed and discussed in terms of the changes in the glass structure.     

Quantum electrodynamic corrections to the 23S1 → 11S0 + one photon transition rate in helium and helium-like lons

The order (Zα)⁵, α(Zα)⁴, and α(Zα)⁴ log(Zα) energy denominator and recoil corrections to the leading order (Zα)⁴ decay amplitude for the 2³S₁ → 1¹S₀ + one photon transition are considered. It is found that order α(Zα)⁴ terms arise in the individual diagrams but exactly cancel upon summation. In view of the results of this and other recent theoretical work it is concluded that the rates predicted by pure quantum electrodynamics are known to considerable precision. The recent discrepancy between theory and experiment in the decay rate for several helium-like ions appears to have been resolved by placing the detector farther downstream from the foil where the metastable states are produced. At present, all the experimental values are in good agreement with the theory.     

Pressure dependence of the absorption edge for Cd1-xMnxTe

The effect of pressure on the optical absorption edge of mixed crystals Cd_1-xMn_xTe with different manganese concentrations is reported. The observed absorption edge shifts to higher energy with increasing pressure at a rate of α=7?8×10^?3 eV/kbar and a second order coefficient of β=-4×10^?5 eV/kbar² for x<0.5, to lower energy with increasing pressure at a rate of α=-5.0 ×10^?3 eV/kbar for x?0.5. A phase transition occurs for all the samples studied. The absorption edge of the new phase is outside the wavenumber range of the instrument. The physical origins of different pressure coefficients are discussed in the light of the deformation potentials of energy band states and the hybridization of the Mn²⁺ 3d levels with the p-like states in the valence band.     

Relationship between the thermal expansion coefficient, plasmon energy, and bond length of ternary chalcopyrite semiconductors

A simple relation between the average bond length and plasmon energy, that is, d=15.30(?ω_p)^−2/3, has been proposed for A^IIB^IVC^V₂ and A^IB^IIIC^VI₂ chalcopyrite semiconductors. The average linear thermal expansion coefficient (α_L) of these semiconductors has been calculated using plasmon energy data. The linear expansion coefficients (α_a) and (α_c) of the lattice parameters a and c, respectively, have also been calculated. The calculated values of d, α_L, α_a and α_c have been compared with the experimental values and the values reported by different workers. A fairly good agreement has been obtained between them.     

Hyperpolarizabilities of alkaline-earth metal ions Be+, Mg+, and Ca+

The knowledge of the hyperpolarizabilities of atoms and ions is helpful for the analysis of the high order effects of the frequency shifts in precision spectroscopy experiments. Liu et al. [Phys. Rev. Lett. 114, 223001(2015)] proposed to establish all-optical trapped ion clocks using laser at the magic wavelength for clock transition. To evaluate the high-order frequency shifts in this new scheme of optical clocks, hyperpolarizabilities are needed, but absent. Using the finite field method based on the B-spline basis set and model potentials, we calculated the electric-field-dependent energy shifts of the ground and low-lying excited states in Be+, Mg+, and Ca+ in the field strength range of 0.0-6×10.5 a.u.. The scalar and tensor polarizabilities(α0, α2) and hyperpolarizabilities(γ0, γ2, γ4) were deduced. The results of the hyperpolarizabilities for Be+ showed good agreement with the values in literature, implying that the present method can be applied for the effective estimation of the atomic hyperpolarizabilities,which are rarely reported but needed in experiments. The feasibility of optical trapping of Ca+ is discussed, and the contributions of hyperpolarizabilities to the transition frequency shift for Ca+ in the optical dipole trap are estimated using quasi-electrostatic approximation.     

Application of the method of integral equations for calculating the vertex constants for an α-particle

The vertex constants G²_αTN and G²_αdd for the virtual decays α → t(τ) + p(n) and α → d + d are calculated by solving the Faddeev-Yakubovsky equations for four nucleons. A spin-dependent separable potential with the Hulthén form factor is used as the NN interaction. The resonant Hilbert-Schmidt expansion is applied to solve the integral equations. The values obtained G²_αTN = 17.9 ± 1.7 fm and G²_αdd = 18.1 ± 1.3 fm are compared with the phenomenological values extracted from data on nuclear reactions.     

Third-order nonlinear optical response in double-walled carbon nanotubes

Resonant behavior and magnitudes of third-order nonlinear optical susceptibilities in double-walled carbon nanotubes (DWNTs) have been investigated by means of femtosecond pump-probe spectroscopy with different pump-photon energies. With the selective excitation of the E₂₂ exciton transition of the inner tubes labeled by the chiral vector indices (7,5) and (7,6), the imaginary part of nonlinear susceptibility Imχ⁽³⁾ has shown the resonant enhancement compared with the case of the nonresonant excitation of the specific tube. The nonlinear response signal at the E₂₂ transition energy of the (8,7) tube has been also enhanced for the excitation of the G-band phonon sideband of its E₂₂ transition. This result is consistent with the phonon-mediated nonlinear optical process observed for the E₂₂ transitions in single-walled carbon nanotubes (SWNTs). It has been also found that the values of the figure of merit Im χ⁽³⁾/α (α: absorption coefficient) of the inner tubes in DWNTs are smaller than those of the corresponding SWNTs, which is interpreted in terms of decay time shortening due to the energy relaxation between the inner and outer tubes.