Quantification of Entanglement Entropy in Helium by the Schmidt–Slater Decomposition Method

In this work, we present an investigation on the spatial entanglement entropies in the helium atom by using highly correlated Hylleraas functions to represent the S-wave states. Singlet-spin 1sns ¹ S ^e states (with n = 1 to 6) and triplet-spin 1sns ³ S ^e states (with n = 2 to 6) are investigated. As a measure on the spatial entanglement, von Neumann entropy and linear entropy are calculated. Furthermore, we apply the Schmidt–Slater decomposition method on the two-electron wave functions, and obtain eigenvalues of the one-particle reduced density matrix, from which the linear entropy and von Neumann entropy can be determined.     

Natural radiative lifetimes in the2S1/2 and2D5/2,3/2 sequences of aluminum

Natural radiative lifetimes have been measured for the 3s ² ns ² S _1/2 (n≦10) and 3s ² nd ² D _5/2,3/2 (n≦11) sequences of aluminum using pulsed laser excitation of an atomic beam. The investigated states were populated from the ground configuration using UV pulses of wavelength down to 210 nm produced by a Nd: YAG- or an excimer-pumped dye-laser system. TheS-state lifetimes increase regularily with increasing principal quantum number but this is not the case for theD sequence.     

Lifetime measurements in the triplet system of Mg I

In an atomic beam the metastable 3s3p ³ P-states of Mg I were populated by electron impact. A pulsed tunable dye laser was used to excite the metastable atoms to the 3snd³ D-(n=3–7) and to the 3sns³ S ₁-states (n=4and 6). Observing the time dependence of the reemitted resonance light the lifetimes of these states were measured.     

Lifetimes and oscillator strengths in the triplet system of ZnI

Selective laser excitation was used to measure the radiative lifetimes of the ZnI triplet states 4sns ³ S ₁(n=5–7) and 4snd ³ D ₃,³ D ₂ and³ D ₁(n=4–6). These states were excited from the metastable 4s4p ³ P states, which were collisionally populated in an atomic beam. The values are compared with the results of other experimental methods (beam-foil, pulsed electron excitation, Hanle effect) and with theoretical calculations. The corresponding oscillator strengths are discussed with respect to the astrophysical determination of the Zn photospheric abundance.     

Postcollision interaction upon electron excitation of the 5sns 1 S 0 and 5snd 3 D j levels of the cadmium atom

The optical excitation functions (OEFs) for two series of spectral lines of the Cd atom originating from the 5sns ¹ S ₀ (n = 6?11) and 5snd ³ D _{1, 2, 3} (n = 5 and 6) levels excited by an ultramonoenergetic (ΔE _1/2 < 0.05 eV) electron beam with energies exceeding the single ionization threshold are presented. In the energy range from 10.8 to 12.9 eV, the energy dependences of the excitation cross sections of the studied spectral transitions exhibit the effect of postcollision interaction of slow scattered and fast emitted electrons. This process leads to an additional population of the initial levels of the spectral transitions due to the capture of a scattered electron into an excited atomic level. The energies and widths of the electronic decay of autoionizing states are estimated in the classical approach by two methods, namely, by the least squares method and by direct calculation. Calculations are performed using approximate formulas valid for different relations between the postcollision shifts of the OEF maxima and the binding energies of the atomic levels. The terms of the autoionizing atomic states responsible for the maxima observed in the OEFs of the spectral transitions are determined.     

Radiative lifetimes of Zn I highly excited states

The energy levels and lifetimes of 4sns³S₁ (n=5-25), 4snd³D₁ (n=4-25) and 4snp¹P₁ (n=5-15) of Zn I have been evaluated using the multichannel quantum defect theory (MQDT). The calculated lifetimes of 4sns³S₁ and 4snd³D₁ characterized by the effective quantum ν are given by the formula and , respectively.     

Observations of the collision-induced dipole transitions and of a quadrupole transition for barium in krypton

For Ba perturbed by Kr, collision-induced dipole transitions 6s²¹S₀ – 6snd¹D₂ (8?n?10) have been observed. The effective oscillator strength per unit Kr density was found to be 1.8–1.0 x 10^-23 cm³. For the electric-quadrupole transition 6s²¹S₀ -6s6d¹D₂, the oscillator strength is (2.0±0.4) x 10^-6.     

Impact broadening of Sr 5sns 1 S 0, 5snd 1D2 and 5snd 3 D 2 levels by He and Xe

The impact broadening of strontium 5sns ¹ S ₀, 5snd ¹ D ₂ and 5snd ³ D ₂ levels by He and Xe have been studied by measuring the collisional half-widths of Doppler-free two-photon absorption lines from the 5s ^{2 1} S ₀ ground state in a thermionic diode. Large inelastic contributions to the broadening rates of the levels have been found where the moduli of the quantum defects of different level series are close to each other. A similar but continuousn-mixing behaviour along the series has also been found in our recent investigation on the broadening of Rb levels by noble gases. The broadening rates of the very high levels in Sr were found to be independent on the principal quantum number and the angular momentum of the levels and in good agreement with our recent broadening data of the Rb-He and Rb-Xe systems and the data for Na-He and Na-Xe found by the Columbia group.     

Low mass-scale parity restoration in expanded gauge theories

It is shown that schemes of grand unification withSU(2n)⁴ gauge symmetry permit the embedding of the left-right symmetricSU(2) _L ×SU(2) _R ×U(1)×SU(3) ^c intermediate symmetry at relativelylow energies [between 250 GeV and a few TeV] as well as allows light unification mass-scales (≦10⁵ TeV) ifn≧3 for values of the weak angle Sin² θ _W and the strong coupling α _S in the ranges 0.20≦Sin² θ _W ≦0.25, 0.10≦α _S ≦0.15.     

Classical stability of direct products of spheres in gravitational systems

Classical stability of Einstein spaces S^d₁ ×?×S^d_n(d_j ? 2) against all fluctuations is investigated in euclidean gravity with a cosmological constant. It is shown that S^d is classically stable, while S^d₁ ×?× S^d_n(n ? 2) is classically unstable. As a generalization of this analysis it is proved that a compact Einstein space B₁ ×?× B_n(n ? 2) which is a direct product of each Einstein space is classically unstable. Non-Einstein spaces M² × S⁴ (M² × S² × S²) are also considered in six- dimensional Einstein-Maxwell theory and are shown to be classically stable (unstable).     

Evidence for three microscopically different kinds ofE1 transition in lead-region nuclei

A survey of electric dipole transition rates, or B(E1) values, is done for lead-region nuclei with 82≦Z≦90 and 112≦N≦134. It is found that the major part of the E1 transitions are hindered by a factor of about 10⁶–10⁷ and these transitions are interpreted to proceed via admixtures of the collective 1^? state. A second group, which is generally 10–100 times less hindered and is involving the πi_13/2 orbital in the initial states, is suggested to proceed via the allowed πi_11/2→πh_9/2 admixtures in the wave functions. These two groups are compared to a third newly established category, the α-cluster or IBAp-boson mode, of the so-called vibron model.     

Description of charge-exchange resonances in deformed nuclei

The (p, n) and (n, p) transition strength functions with excitation of the GT resonance, other 1⁺ states, spin-dipole with λ^π=0^- andE1 charge-exchange resonances in deformed nuclei in the regions 156≦A≦168 and 236≦A≦240 are calculated in the RPA. It is shown that the GT resonance has a maximum at 18–20 MeV, and in the region of 5–6 MeV around maximum (60–70)% of strength is concentrated. The spindipole resonance with λ^π=0^-, 1^- and 2^? strength is distributed within 14–33 MeV and theE1 strength within 25–29 MeV. The latter is splitted withΔE equal to 0.6–2 MeV into two peaks withI ^π I=1^-0 and 1^?1. In the region of 4–7 MeV around maximum 73–77% ofE1 strength is concentrated. The total (n,p) transition strength is 10–200 times as small as the total (p, n) transition strength.     

The vuv photoelectron spectra of atomic In and Tl

The photoelectron spectra of atomic indium and thallium have been obtained using a pseudo-atomic beam technique. Ionizations from the np, ns and (n ? 1)d shells (n = 5 for In and n = 6 for Tl) were observed using He(I) and HE(II) radiation. The (np)^?1 ionization results in a single ¹S₀ ionized state, whereas the (ns)^?1 and ((n ? 1)d)^?1 ionizations both result in states additional to those allowed for a one-electron ionization process. This is attributed to configuration interaction in the final ionized state.     

Calculation of absorption coefficient for the ν1 band of sulfur dioxide

The absorption coefficients S/d of sulfur dioxide have been calculated for the ν₁ band for temperatures from 300 ～ 1500°K, taking the major isotopic species S³⁴O₂ into consideration. The total number of the vibrational transitions considered were 4, 10, 23, 41 and 70 for the temperatures of 300, 600, 900, 1200 and 1500°K, respectively. The vibrational energy was calculated to the second order, and the rotational energy and matrix element were calculated exactly with consideration for the asymmetry of the sulfur dioxide molecule. The line intensities greater than 1·0 × 10^-8 cm^-2 atm^-1 STP were included in the calculations. The wavenumber regions of 1000 ～ 1300 cm^-1 were divided into small intervals of Δω = 10 cm^-1 and the S/d averaged over the Δω were obtained. The S/d and some of the line intensities and positions at 300°K were compared with the experimental results of other workers and good agreement was obtained.     

Excitation functions of nuclear reactions producing11C

Excitation functions of the reactions⁹Be(³He,n),¹⁰B(d,n),¹¹B(p,n),⁹Be(α,2n),¹¹B(d,2n) and¹²C(n,2n), all leading to the residual nucleus¹¹C, were measured with activation techniques. Projectile energies have been chosen to populate the composite systems¹²C^* and¹³C^* in energy ranges overlapping for 31MeV≦E ^*(¹²C)≦38MeV and 26 MeV≦E ^*(¹³C)≦33Mev, respectively. The attainable thick target yields are highest forp+¹¹B. Statistical model calculations fail to quantitatively reproduce the experimental data although preequilibrium decay modes have been taken into account.     

Self-duality and octonionic analyticity of S7-valued antisymmetric fields in eight dimensions

We exhibit two octonionic extensions of the Kalb-Ramond type fields with rank two and four in eigth dimensions. By analogy to the d = 4 (anti-) self-duality of the SU(2) ≈ S³ quaternionic gauge field we consider the respective d = 8 (anti-) self-duality equations for these nonlinear, S⁷-valued antisymmetric fields. By way of an octonionic 't Hooft ansatz these equations reduce to the same generalized Fueter-Cauchy-Riemann equations over S⁸. Explicit (9n + 8) parameter S⁷ → S⁷ mapping solutions, n being a winding number, are found in terms of holomorphic functions of the spacetime octonion. An infinite number of local continuity equations results.     

On the Existence of the Anomaly in the2 H(d,n) and2 H(d,p) Reactions atE d ≈100 keV

All data which are concerned with the existence of an anomaly in the excitation functions of the² H(d, n)- and² H(d, p)-reactions nearE _d =100 keV are discussed. New experimental data for the² H(d,p)- reactions using tensor polarized deuterons (90≦E _d ≦190 keV) are presented.     

Highly resolved electronic absorption and luminescence spectra of some phenanthrolines in Shpolskii matrices: Part II. Fluorescence and S1←S0 absorption spectra

Highly resolved fluorescence and S₁←S₀ absorption spectra of some phenanthrolines in n-alkane matrices were obtained at 77 K. The vibrational analysis of the spectra was carried out. Mirror symmetry distortions of the fluorescence and absorption spectra were attributed to vibronic coupling between ¹(π, π¹) states. It was shown that vibronic mixing of S₁(π, π¹) and S₂(π, π¹) states occurs in phenanthroline molecules with S₁-S₂ energy gap not exceeding 3000 cm^-1 (i.e., 4,7-, 1,7- and 1,10-Phen), whereas in other phenanthrolines the coupling of S₁ and S₃(π, π¹) plays a dominant role. Fluorescence quantum yields of phenanthroline liquid solutions were measured. Changes of luminescence efficiencies due to the change of the polarity of the media point to a weak coupling of the lowest ¹(π, π¹) and ¹(n, π¹) states.     

Investigation of inclusive production ofK 0 andK * (892)0 mesons inK + A interactions at 11.2 GeV

Inclusive production ofK ⁰ andK ^* (892)⁰ mesons inK ⁺ A-interactions (A=Be, Cu, Pb) at the energy 11.2 GeV has been investigated to study hadronisation of the leading \(\bar s\) -quark; the results are presented. Double differential cross sections d²σ/dx _f dp _t ² were measured in the region of incident particle fragmentation (0.4≦x _f ≦1,p _t ≦0.5 GeV/c). The experimental data obtained were analysed on the basis of the Lund model FRITIOF and a quark-gluon model that takes into account colour screening and hadron formation length effects. The experimental data confirm the picture of hadronisation of the leading \(\bar s\) -quark developed in the latter model.     

Hyperfine anomaly in the spectrum of the osmium atom. effect of the spatial distribution of nuclear charge

Contributions of the superposition of configurations ns ²5d ⁸+ns5d ⁸ n′s (n=1–5, n′=6–10) and ns ²5d ⁶+ns5d ⁶ n′s (n=1–6, n′=7–10) to parameters a _5d ⁰¹ , a _5d ¹² , and a _5d ¹⁰ of the hyperfine structure in the spectrum of the osmium atom OsI are calculated. It is shown that the nonzero contribution is made only to a _5d ¹⁰ . The effect of the spatial distribution of nuclear charge on the parameters of the hyperfine structure in the spectra of ¹⁸⁷Os and ¹⁸⁹Os isotopes and on the hyperfine anomaly for the 5d ⁷6s levels in the spectrum of these isotopes is estimated.