Theoretical study of photoionization of the isoelectronic sequence Rb<Superscript>+</Superscript>, Sr<Superscript>2+</Superscript>, and Y<Superscript>3+</Superscript>

The photoionization cross sections for the 4p shell of ions of the Kr isoelectronic sequence Rb⁺, Sr²⁺, and Y³⁺ are calculated. The configuration interaction theory and the perturbation theory are used to describe the many-electron effects. The relativistic effects are taken into account in the Pauli-Fock approximation. The calculated resonance structure of photoionization cross sections for the 4p shell in the region below the 4s threshold associated with the autoionization of the 4s-np singly excited states and the 4p4p-nln′l′ doubly excited states reproduces the results of recent measurements of total photoabsorption cross sections for the Rb⁺, Sr²⁺, and Y³⁺ ions. It is found that, as the nuclear charge in the isoelectronic sequence increases, the ratio between the direct and correlation parts of amplitudes of the 4s-(n/?)p transition changes and, as the consequence, the minimum of the photoionization cross section of the 4s shell shifts from the continuous spectrum to the region of states of discrete spectrum. This accounts for the strong changes in the shape of the 4s-np resonances in the photoionization cross sections for the 4p shell of Rb⁺, Sr²⁺, and Y³⁺, as well as the distinction between the shapes of the 4s-6p _1/2 mirror resonance in the partial 4p _1/2 and 4p _3/2 photoionization cross sections for the Y³⁺ ion which do not suppress each other in the total photoionization cross section, as is the case for similar resonances in Rb⁺ and Sr²⁺.     

4<Emphasis Type="Italic">p</Emphasis><Superscript>5</Superscript>4<Emphasis Type="Italic">d</Emphasis><Superscript>2</Superscript> configuration in the spectra of rubidium-like Ru VIII and Rh IX ions

The spectra of ruthenium and rhodium excited in a low-inductive vacuum spark have been obtained using a vacuum grazing-incidence spectrograph with a grating of 3600 lines/mm 3 m in radius in the range of 180–350 Å. The bidium-like spectra of Ru VIII and Rh IX were analyzed. Ten spectral lines of the 4p ⁶4d-4p ⁵4d ² transitions are identified and six energy levels in the 4p ⁵4d ² configuration with an excited internal electron were found for each ion for the first time.     

Restricting Positive Energy Representations of Diff<Superscript>+</Superscript>(<Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript>) to the Stabilizer of <Emphasis Type="Italic">n</Emphasis> Points

Let G _n ? Diff⁺(S ¹) be the stabilizer of n given points of S ¹. How much information do we lose if we restrict a positive energy representation \(U^c_h\) associated to an admissible pair (c, h) of the central charge and lowest energy, to the subgroup G _n ? The question, and a part of the answer originate in chiral conformal QFT. The value of c can be easily “recovered” from such a restriction; the hard question concerns the value of h. If c ≤ 1, then there is no loss of information, and accordingly, all of these restrictions are irreducible. In this work it is shown that \(U^c_{h}|_{G_n}\) is always irreducible for n =  1 and, if h =  0, it is irreducible at least up to n ≤  3. Moreover, an example is given for c >  2 and certain values of \(h \neq \tilde{h}\) such that \(U^c_{h}|_{G_1}\simeq U^c_{\tilde{h}}|_{G_1}\) . It is also concluded that for these values \(U^c_{h}|_{G_n}\) cannot be irreducible for n ≥  2. For further values of c, h and n, the question is left open. Nevertheless, the example already shows that, on the circle, there are conformal QFT models in which local and global intertwiners are not equivalent.     

Line shape of <Superscript>57</Superscript>Co sources exhibiting self absorption

The effect of selfabsorption in Mössbauer sources is studied in detail. Spectra were measured using an old ⁵⁷ C o/R h source of 74M B q activity with an original activity of ca. 3.7G B q and a 0.15G B q ⁵⁷ C o/α ? F e source magnetized by an in-plane magnetic field of 0.2 T. The ⁵⁷ C o/α ? F e source of a thickness of 25 μ was used both from the active and the inactive side giving cause to very different selfabsorption effects. The absorber was a single crystal of ferrous ammonium sulphate hexahydrate (FAS). Its absorption properties were taken over from a detailed study (Bull et al., Hyperfine Interact. 94(1–3), 1; Spiering et al. 2). FAS (space group P21/c) crystallizes as flat plates containing the (\(\overline {2}\)01) plane. The γ-direction was orthogonal to the crystal plate. The ⁵⁷ C o atoms of the ⁵⁷ C o/R h source were assumed to be homogeneously distributed over a 6μ thick Rh foil and to follow a one dimensional diffusion profile in the 25 μ Fe-foil. The diffusion length was fitted to 10 μ. The theory follows the Blume-Kistner equations for forward scattering (Blume and Kistner, Phys. Rev. 171, 417, 3) by integrating over the source sampled up to 128 layers.     

Neutron single-particle structure of <Superscript>48</Superscript>Ca, <Superscript>50</Superscript>Ti, <Superscript>52</Superscript>Cr, <Superscript>54</Superscript>Fe,and <Superscript>56</Superscript>Ni nuclei

The change in the neutron single-particle structure of (1f?2p)-shell magic nuclei near the Fermi energy with an increase in the number of protons in the 1f _7/2 subshell from 0 for ⁴⁸Ca to 8 for ⁵⁶Ni has been investigated. Good agreement of the experimental and estimated values of the single-particle energies E _nlj of the bound states of neutrons in these nuclei with the results of calculations within the dispersive optical model is obtained.     

Elastic and inelastic scattering of 800-MeV protons on <Superscript>16</Superscript>O and <Superscript>20</Superscript>Ne nuclei

Differential cross sections and polarization observables for the elastic and inelastic scattering of 800-MeV protons on ¹⁶O and ²⁰Ne nuclei are calculated on the basis of the theory of multiple diffractive scattering and the α-cluster model involving dispersion. The single-particle nucleon-density distributions obtained within the α-cluster model involving dispersion are used in the calculations. The differential cross sections and polarization calculated for elastic and inelastic p¹⁶O and p²⁰Ne scattering are compatible with available experimental data. The spin-rotation functions calculated for elastic p¹⁶O and p²⁰Ne scattering within the independent-nucleon model differ qualitatively from their counterparts calculated within the α-cluster model involving dispersion.     

Many-electron character of Rydberg series converging to the ionization thresholds of the 4<Emphasis Type="Italic">p</Emphasis><Superscript>4</Superscript>5<Emphasis Type="Italic">s</Emphasis> states of KrII

The photoionization cross sections of the 4p shell and the 4s main level and 4p ⁴(³ P) 5s ⁴ P _{5/2, 3/2} satellite subvalence levels of KrII have been calculated in the 4s-near-threshold range of excitation energies from 28.48 to 28.70 eV. The calculation takes into account the core relaxation by the methods of the theory of non-orthogonal orbitals, the interaction between resonant states through autoionization channels by solving the complex secular equation, and the interaction between the channels of the continuous spectrum in all orders of the perturbation theory by the K-matrix method. Good quantitative agreement between the energy-integrated theoretical and experimental photoionization cross sections for the satellite levels has been obtained for the first time. It is shown that only simultaneous consideration of the above-mentioned effects leads to such agreement. The resonant structure of the photoionization cross sections in this excitation energy range is related to the autoionization decay of the 4p ⁴5s(⁴ P _1/2)np and 4p ⁴5s(² P _3/2)np Rydberg series. The specificity of this process is that both series manifest themselves not independently but owing to their strong electrostatic interaction with the prominent 4p ⁴(¹ D)5s ² D _5/2 6p _3/2 resonance, which lies in this excitation energy range.     

Hyperfine magnetic anomaly in isotopic pairs <Superscript>151, 152</Superscript>Eu and <Superscript>152, 153</Superscript>Eu

High-resolution laser spectroscopy measurements of optical hyperfine splitting on the ^{151, 152, 153}Eu isotopes were performed on the atomic transition 4f ⁷6s ^{2 8} S _7/2 → 4f ⁷6s6p ⁶ P _5/2 at λ ≈ 564.58 nm. Values of the nuclear magnetic dipole and electric quadrupole moments are obtained from the measured hyperfine splitting and the magnetic hyperfine anomalies in the isotope pairs ^{151, 152}Eu and ^{152, 153}Eu are deduced. The absolute values of the hyperfine anomaly in both cases are unusually large: 5 (1)%. The possible sources causing these anomalies are discussed.     

Study of <Superscript>179</Superscript>Hf<Superscript><Emphasis Type="Italic">m</Emphasis>2</Superscript> excitation

Isomeric ratios of ¹⁷⁹Hf ^m2,g yields in the (γ, n) reaction and the cross section for the ¹⁷⁹Hf ^m2 population in the (α, p) reaction are measured for the first time at the end-point energies of 15.1 and 17.5 MeV for bremsstrahlung photons and 26 MeV for alpha particles. The results are σ = (1.1 ± 0.11) × 10^?27 cm² for the ¹⁷⁶Lu(α, p)¹⁷⁹Hf ^m2 reaction and Y _m2/Y _g = (6.1 ± 0.3) × 10^?6 and (3.7 ± 0.2) × 10^?6 for the ¹⁸⁰Hf(γ, n)¹⁷⁹Hf ^m22 reaction at Е _ep =15.1 and 17.5 MeV, respectively. The experimental data on the relative ¹⁷⁹Hf ^m2 yield indicate a single-humped shape of the excitation function for the ¹⁸⁰Hf(γ, n)¹⁷⁹Hf ^m2 reaction. Simulation is performed using the TALYS-1.4 and EMPIRE-3.2 codes.     

Two-Neutron Alignment in <Superscript>127</Superscript>Xe

High spin states in ¹²⁷Xe have been investigated via ⁹Be induced fusion-evaporation reaction at 48 MeV. Spin and parity of excited states up to \( \sim \frac {47}{2} \hbar \) have been confirmed from angular correlation and linear polarization results. Rotational alignment of the second pair of h _11/2 neutrons has been observed at \(\hbar \omega \sim \) 0.44 MeV; beyond that, the band is associated with ν[h _11/2]³ configuration. The alignment phenomena has been discussed in comparison with the neighboring ^125,129Xe.     

Extreme-ultraviolet emissivity from Xe<Superscript>8+</Superscript> to Xe<Superscript>12+</Superscript> by using a detailed line-by-line method

A theoretical model has been developed to calculate the emissivity of low densityxenon plasmas (from Xe⁸⁺ to Xe¹²⁺) by employing a detailed lineaccounting formalism. A complete set of atomic datasuch as transition probabilities for electric (magnetic) dipoleand quadruple E1, E2, M1 and M2 and electron impact excitationcollision strength, which is accurate to fine-structure level,was calculated using a full configuration interaction formalismand was used to solve the rate equation which determines thepopulation of different levels. Detailed results are given forpure Xe¹⁰⁺ ion, which is essential for extreme-ultravioletemission at 13.5 nm, and for low density plasmas (the electron densitywas taken to be 10¹² cm^-3) at temperatures of 30, 45, 55, 65and 75 eV. The fraction of different ionization stages was obtained by acompletely coupled rate equation from neutral atom to Xe²⁰⁺ by usinga detailed configuration accounting method. The results show that theemissivity of the dipole forbidden lines of transition array4s ²4p ⁶4d ⁷5s \(\rightarrow\) 4s ²4p ⁶4d ⁸ of Xe¹⁰⁺is very sensitive to the temperature, which should be a useful tool todiagnose the temperature in EBIT plasmas.     

Charge-transfer bands in crystals of alkaline earth fluorides with Eu<Superscript>3+</Superscript> and Yb<Superscript>3 + 1</Superscript>

The absorption, luminescence, and excitation spectra of CaF₂, SrF₂, and BaF₂ crystals with EuF₃ or YbF₃ impurity have been investigated in the range 1–12 eV. In all cases, strong wide absorption bands (denoted as CT₁) were observed at energies below the 4f ⁿ -4f ^{n ? 1}5d absorption threshold of impurity ions. Weaker absorption bands (denoted as CT₂) with energies 1.5–2 eV lower than those of the CT₁ bands have been found in the spectra of CaF₂ and SrF₂ crystals with EuF₃ or YbF₃ impurities. The fine structure of the luminescence spectra of CaF₂ crystals with EuF₃ impurities has been investigated under excitation in the CT bands. Under excitation in the CT₁ band, several Eu centers were observed in the following luminescence spectra: C _4v , O _h , and R aggregates. Excitation in the CT₂ bands revealed luminescence of only C _4v defects.     

Experimental Study and Analysis of Absorption Spectra of Ni<Superscript>2+</Superscript> Ions in Nickel Orthoborate Ni<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>2</Subscript>

The results of studies of the absorption spectra of nickel orthoborate Ni₃(BO₃)₂ in the range of electronic d–d-transitions are reported. The obtained data are analyzed in the framework of the crystal field theory. The Ni²⁺ ions are located in two crystallographically nonequivalent positions 2a and 4f with point symmetry groups C_2h and C₂, respectively, surrounded by six oxygen ions forming deformed octahedra. The absorption spectra exhibit three intense bands corresponding to spin-resolved transitions from the ground state of nickel ion ³A_2g (³F) to the sublevels of the ³T_2g (³F), ³T_1g (³F) and ³T_1g (³P) triplets split by the spinorbit interaction and the rhombic component of the crystal field. At temperatures below 100 K, the spectra exhibit a thin structure, in which phonon-free lines can be distinguished. Comparison of the calculated frequencies of the zero-phonon transitions with the experimental data allows estimating parameters of the crystal field acting on the nickel ions in the 2a- and 4f-positions, as well as the parameters of electrostatic interaction between the 3d electrons and spin-orbit interaction constants.     

Data on photoneutron reactions from various experiments for <Superscript>133</Superscript>Cs, <Superscript>138</Superscript>Ba and <Superscript>209</Superscript>Bi nuclei

Basic methods for determining cross sections for photoneutron partial reactions are examined. They are obtained directly in experiments with quasimonoeneregetic annihilation photons or from the cross section for the (γ, xn) = (γ, 1n) + 2(γ, 2n) + 3(γ, 3n) +... neutron-yield reaction in experiments with bremsstrahlung photons by introducing corrections based on statistical nuclear-reaction theory. The difference in the conditions of these experiments, which leads to discrepancies between their results because of sizable systematic errors, is analyzed. Physical criteria are used to study the reliability of data on the photodisintegration of ¹³³Cs, ¹³⁸Ba, and ²⁰⁹Bi nuclei. The cross sections for partial and total reactions satisfying the reliability criteria are evaluated within the experimental–theoretical method (σ^eval(γ, in) = F_i^theor × σ^expt(γ, xn)) on the basis of the experimental cross sections σ^expt(γ, xn) and the results of the calculations within the combined model of photonuclear reactions.     

Formation of cumulative nuclei of <Superscript>4</Superscript>He in <Superscript>16</Superscript>O<Emphasis Type="Italic">p</Emphasis> collisions at a momentum of 3.25 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon

The formation of cumulative nuclei of ⁴He in ¹⁶Op collisions at a momentum of 3.25 GeV/c per nucleon was investigated for the first time under conditions of 4π acceptance. The slope parameter of the invariant cross sections for the formation of cumulative nuclei of ⁴He was determined, and new data on the correlations between the yield of these cumulative nuclei and the yield of charged particles and fragments in ¹⁶Op interactions were obtained.     

Two-proton correlations in <Superscript>4</Superscript>He<Emphasis Type="Italic">p</Emphasis> interactions at a primary momentum of 5 GeV/<Emphasis Type="Italic">c</Emphasis>

Correlations of secondary protons in ⁴Hep interactions are investigated in an exclusive experiment with the aid of a 2-m liquid-hydrogen bubble chamber exposed to an alpha-particle beam of momentum 5 GeV/c the kinetic energy of primary protons in the rest frame of the nucleus is T_p=620 MeV). By using data obtained in 4π geometry for six basic channels of ⁴Hep interaction that lead to the production of two protons, the total correlation function for the pp system is determined, along with two-proton correlation functions for individual channels. Experimental results are compared with the predictions of the modified Lednicky-Lyuboshitz model. The value of R=1.6±0.3 fm is obtained for the root-meansquare spacetime radius of pp emission in ⁴Hep interactions. The dependence of the correlation function on the total momentum of two emitted protons and on the momentum-transfer direction is investigated.     

Searching for signatures around 1920 MeV of a N<Superscript>*</Superscript> state of three hadron nature

We provide a series of arguments which support the idea that the peak seen in the \( \gamma\) p \( \rightarrow\) K ⁺ \( \Lambda\) reaction around 1920MeV should correspond to the recently predicted state of J ^P = 1/2⁺ as a bound state of K \( \bar{{K}}\) N with a mixture of a ₀(980)N and f ₀(980)N components. At the same time we propose polarization experiments in that reaction as a further test of the prediction, as well as a study of the total cross-section for \( \gamma\) p \( \rightarrow\) K ⁺ K ^- p at energies close to threshold and of dσ/dM _inv for invariant masses close to the two-kaon threshold.     

Polar Phase of Superfluid <Superscript>3</Superscript>He: Dirac Lines in the Parameter and Momentum Spaces

The time reversal symmetric polar phase of the spin-triplet superfluid ³He has two types of Dirac nodal lines. In addition to the Dirac loop in the spectrum of the fermionic Bogoliubov quasiparticles in the momentum space (p _x , p _y , p _z ), the spectrum of bosons (magnons) has Dirac loop in the 3D space of parameters—the components of magnetic field (H _x ,H _y ,H _z ). The bosonic Dirac system lives on the border between the type-I and type-II.     

Band interaction in <Superscript>162</Superscript>Dy, <Superscript>168</Superscript>Er,and <Superscript>172</Superscript>Yb

Coriolis interaction between levels of two rotational bands in ¹⁷²Yb with K ^π = 2⁺ and 3⁺ and in ¹⁶⁸Er between levels with K ^π = 0^?, 1^?, and 2^? is studied. The values of the interaction parameters are obtained. The mutual influence of two bands in ¹⁶²Dy with ΔK = 2, K _i ^π = 0 ₂ ⁺ and 2 ₁ ⁺ due to Coriolis interaction is demonstrated.     

Investigation of <Emphasis Type="Italic">pn</Emphasis> correlations in <Superscript>4</Superscript>He<Emphasis Type="Italic">p</Emphasis> interactions at a momentum of 5 GeV/<Emphasis Type="Italic">c</Emphasis>

Proton-neutron correlations in ⁴Hep interactions are studied in an exclusive experiment by using a 2-m bubble chamber exposed to a 5-GeV/c beam of α particles (the kinetic energy of the protons in the nucleus rest frame is T _p = 620 MeV). Data on the production of pn pairs in 4π geometry for three channels, where it is possible to reconstruct the neutron momentum unambiguously, are used to determine the pn correlation function in ⁴Hep interactions. The experimental results are compared with the predictions of a modified Lednicky-Lyuboshitz model. The value obtained for the root-mean-square radius of the pn-emission region is R _pn = 2.1 ± 0.3 fm. The dependence of the correlation function on the modulus of the total momentum of the emitted nucleon pair and on the direction of the momentum transfer is studied. An indication that the emission of a pn pair proceeds predominantly through the production of a virtual deuteron is obtained.