Parametrization of two-body perturbation on atomic fine and hyperfine structure. The configuration (6p)3 in the bismuth atom

A method of simultaneous parametrization of one- and two-body interactions on atomic hyperfine structure of configurationl ^N is proposed and applied for the analysis of the configuration (6p)³ in the bismuth atom. For this purpose, the hyperfine structure splittings of the levels²D ₃ ^2/0 ,²D ₅ ^2/0 and²P ₁ ^2/0 were measured. The finally obtained values of HFS parameters are: for one-body parameters (in MHz):a _p ⁰¹ =2,537(9),a _p ¹² =5,182 (12),a′¹⁰=?2,019(10),b _p ⁰² =?3,198(53),b _p ¹¹ =2,816(54); for two-body parameters (in MHz):x _pp ^′/01 ,₂=284(3),x _pp ^′/12 ,₂=581(5),x _pf ^′/12 ,₂=170(70),x _pp ^′/02 ,₂=?359(36),x _pf ^′/02 ,₂=?33(100). The value of the quadrupole moment of the nucleus ₈₃ ²⁰⁹ Bi is also discussed.     

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.     

Low-frequency dispersion of the effective transverse conductivity in inhomogeneous media in strong magnetic field

On crystalline silicon specimens with a nonuniform carrier concentration distribution produced by an optical method, a dispersion of the effective transverse conductivity σ _⊥ ^eff (ω) is observed near the frequency ω≈ω_c=τ _⊥ ^?1 ≡ε/4πσ _⊥ ^eff . At ω<ω_c, an anomalous transverse effective conductivity is observed: σ _⊥ ^eff (ω) is greater than the transverse conductivity of a homogeneous specimen σ _⊥ ^h (ω) (in the frequency range studied in the experiment σ _⊥ ^h (ω) = const). Near ω≈ω_c, the conductivity σ _⊥ ^eff decreases, and, at ω>ω_c it coincides with σ _⊥ ^h .     

B(E2)-values of even-a nuclei with 82 neutrons

Coulomb excitation of the first excited 2⁺-state was measured usingα-particles to determine reduced transition probabilities,B(E2; 0 _gs ⁺ →2 ₁ ⁺ ), in nuclei with a closed shell of 82 neutrons. TheB(E2; 0 _gs ⁺ →2 ₁ ⁺ -values are 10.2 single-particle units (spu) for¹³⁸Ba, 13.5 spu for¹⁴⁰Ce, 11.9 spu for¹⁴²Nd and 11.6 spu for¹⁴⁴Sm. The uncertainty ranges from 1.3 % to 2.3 %.     

Relative tensor calculus and the tensor time derivative

A relative tensor calculus is formulated for expressing equations of mathematical physics. A tensor time derivative operator ▽ _b ^a is defined which operates on tensors λ^ia...ib. Equations are written in a rigid, flat, inertial or other coordinate system a, altered to relative tensor notation, and are thereby expressed in general flowing coordinate systems or materials b, c, d, .... Mirror tensor expressions for ▽ _b ^a λ^ic...id and ▽ _b ^a λ_ic...id exist in a relative geometry G if and only if a rigid coordinate system a exists in G, where ▽ _b ^a λ^ic = λ _,0c ^ic + λ^kev _ckc ^aic + λ _kc ^ic v _b ^ckc , ▽_jcλ^ic = λ _,jc ^ic + λ^kcΓ _{jc kc} ^ie , and v _b ^aic is the velocity of b relative to a with components in c. These operators are convenient in theoretical analyses and can be incorporated into machine programs for the numerical solution of physical problems.     

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.     

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

In the present work, the problem of the motion of the classical particle in the Kepler-Coulomb field in three-dimensional hyperbolic space H ₂ ² : z ₂ ⁰ + z ₂ ¹ ? z ₂ ² ? z ₂ ³ = R ² is solved in the framework of Hamilton-Jacobi equation. The requirements for the existence of bounded motion of particle are formulated. The equation of the trajectory of particle is obtained, and it is shown that all the finite trajectories are closed. It is also demonstrated that under the certain values (zero or negative) of the separation constant A the fall of the particle onto the center takes place.     

Microscopic foundation of the interacting boson model in thes d-shell nuclei

Starting from an isospin invariant shell-model hamiltonian, we describe a method for deriving microscopically the IBM-hamiltonian appropriate to lights d-shell nuclei. The key ingredients of our approach are:a) the Belyaev-Zelevinsky-Marshalek (BZM) bosonization procedure;b) two successive unitary transformations that extract the “maximally decoupled” collective bosons with angular momentaJ=0(s _ππ ⁺ ,s _νν ⁺ ,s _πν ⁺ ) andJ =2(d _ππ ⁺ ,d _νν ⁺ ,d _πν ⁺ (T=0),d _πν ⁺ (T=1)). The method is applied to obtain the low-energy spectra and the electron scattering form factors for the 0 ₁ ⁺ →2 ₁ ⁺ transitions in²⁰Ne and²⁴Mg. Good agreement with the exact shell-model results is achieved. The inclusion of proton-neutron bosons (s _πν ⁺ ,d _πν ⁺ (T=1),d _πν ⁺ (T=0)), as well as the renormalization of boson parameters due to the non-collective degrees of freedom, are shown to play a crucial role.     

Measurements of lifetime andg-factor of the 32S(4 1 + ) state at 4.459 MeV

Precessions of the very short-lived 2 ₁ ⁺ - and 4 ₁ ⁺ -states in³²S have been measured using the transient field technique. The deducedg-factor of the 4 ₁ ⁺ -state g=+0.40(15) agrees with the known value of the 2 ₁ ⁺ -state and with theoretical predictions. In addition, the lifetimes of both states were redetermined and are consistent with previous results.     

New isomers in83Br,85Rb,85Kr and86Kr

Using methods of in-beam spectroscopy in connection with 35 MeV⁷Li bombardment of⁸²Se targets four new isomers have been identified. They are observed in⁸³Br at 3070 keV (T_1/2=0.6±0.2 μs), in⁸⁵Rb at 2826 keV (T_1/2=12.5±0.6 ns), in⁸⁵Kr at 1991 keV (T_1/2=1.2+ _0.4 ^1.0 μs) and in⁸⁶Kr at 2250 keV (T_1/2=3.1±0.6 ns). Spin and parity 19/2^? have been assigned to the new isomer in⁸⁵Rb that is interpreted as the coupling of a p_3/2 proton to the g ₉ ^2/?2 two-neutron excitation of the N=48 neutron system. Using the TDPAD method an upper limit for the g-factor of ¦g¦≦0.17 has been estimated for this isomer. The same two-neutron excitation is also believed to be responsible for the new isomer in⁸³Br. The new isomers in⁸⁵Kr and⁸⁶Kr are interpreted as configurations containing the two-proton excitation (f ₅ ^2/?1 , p ₃ ^2/?1 ) where in the isomeric 17/2⁺ level of⁸⁵Kr an additional g_9/2 neutron hole is involved.     

Hyperfine structure of EPR spectra of Gd3+ odd isotopes in PbMoO4, Pb5Ge3O11, YVO4, and quadrupole interaction (temperature dependence)

A hyperfine structure of EPR signals of odd isotopes Gd³⁺ in Pb₅Ge₃O₁₁, PbMoO₄, and YVO₄ single crystals has been investigated at different temperatures. The observation of forbidden (with the nuclear spin flip) transitions has made it possible to determine quadrupole interaction P ₂ ⁰ associated with the gradient of the electric field of ligands at the impurity. It has been shown for the first time that, under the condition |P ₂ ⁰ | ≥ |A _{x, y} | (A _i are the tensor components), not only the magnitudes of splitting but also the observed asymmetry in a hyperfine structure (in perpendicular orientations of the magnetic field) depends on mutual signs of parameters of initial splitting b ₂ ⁰ and P ₂ ⁰ . Results of studying the spectra have demonstrated that |b ₂ ⁰ (T)|/|P ₂ ⁰ (T)| ～ const for a concrete single crystal, which assumes the similarity of physical mechanisms determining these parameters.     

g-factor of the second 4+ state in24Mg

The transient field technique has been used to determine theg-factor of the 4 ₂ ⁺ state at 6.010MeV excitation in²⁴Mg. The deduced value ofg=+0.5(4) is consistent with collective model expectations. Further, the equality within experimental accuracies, of the g-factors of the 2 ₁ ⁺ , 2 ₂ ⁺ , 4 ₁ ⁺ and 4 ₂ ⁺ states agrees with theoretical predictions for thisT=0 self-conjugate nucleus, in contrast to the results for²⁰Ne.     

MeanM-subshell fluorescence yields atZ=88, 90, 92, and 94

M x-ray —L x-ray coincidence measurements with high resolution, cooled Si(Li) x-ray detectors were made on transitions following the alpha decays of²²⁸Th,²³²U,²³⁸Pu, and²⁴⁴Cm, in order to determine the meanM-subshell fluorescence yields. The values obtained are:v ₄ ^M =0.032±0.002, andv ₅ ^M =0.024±0.002 atZ=88;v ₁ ^M =0.038±0.003,v ₄ ^M =0.042±0.002, andv ₅ ^M =0.038±0.002 atZ=90;v ₁ ^M =0.047±0.002,v ₄ ^M =0.048±0.002, andv ₅ ^M =0.044±0.002 atZ=92;v ₁ ^M =0.066±0.002,v ₄ ^M =0.062±0.002, andv ₅ ^M =0.063±0.002 atZ=94. The quantityΩ ₁ ^M +f ₁₂ ^MΩ ₂ ^M was measured as (56±10)×10^?4, (62±12)×10^?4, (99±18) ×10^?4, and (93±15)×10^?4 forZ=88, 90, 92, and 94, respectively, which agree well with the calculations of McGuire. The radiativeL ₁-L ₃ transition intensity was measured for the four atomic numbers and found to be consistently less than the calculations of Scofield by about 45 percent.     

A new many-body solution of the Friedel resonance problem

It is numerically shown that the groundstate of the Friedel problem (consisting of a conduction band and a dresonance), occupied with (n+ 1) electrons, can be written as Ψ = (A a ₀ ^* +Bd*) Π _v=1 ⁿ a _v ^* Φ₀, where a ₀ ^* represents a localized conduction electron state, d* is the Friedel resonance state and Π _v=1 ⁿ a _v ⁸ Φ₀ is a Slater determinant of n single electron states a _t ^* , (Φ₀ is the vacuum state). The a _i ^* together with a ₀ ^* are part of a full ortho-normalized basis of the conductions band.     

Paramagnetische Resonanz des dreiwertigen Gadoliniums in YPO4, YVO4 und YAsO4

The EPR spectra of Gd³⁺-doped isostructural single crystals of YPO₄, YVO₄, and YAsO₄ have been measured in X-band at room temperature and at nitrogen and helium temperatures. The zero-field splitting can be described by the five crystal-field parametersb ₂ ⁰ ,b ₄ ⁰ ,b _6/0,b ₄ ⁴ , and b ₆ ⁴ fitted to a tetragonal spin-Hamiltonian corresponding to the point symmetry D_2d of the Gd³⁺ site. The values ofg and b ₂ ⁰ vary significantly with host lattice and with temperature.     

Structural analysis of three-spin systems of photosystem II by PELDOR

The pulsed electron electron double resonance (PELDOR) pulse sequence is applied to a three-spin system consisting of three radicals (Y _D ^· , Y _Z ^· and Q _A ^? ) generated in spinach PS II. The distance between Y_Z and Q_A has been determined to be 3.4 nm with the previously derived distances of the other radical pairs, 2.9 nm for Y _D ^· -Y _Z ^· and 3.9 nm for Y _D ^· -Q _A ^? . This distance has been derived from the Y _Z ^· -Q _A ^? radical pair trapped in Y_D-less mutants ofChlamydomonas reinhardtii. Furthermore the method was applied to the Y _D ^· -Q _A ^? -Chl _Z ⁺ system to find the unknown distance between Q_A and Chl_Z. The derived distance was 3.4 nm. A triangular configuration was found in the membrane system that gives the relative positions of the electron transfer components.     

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.     

Confrontation between the quasiparticle-phonon nuclear model and the interacting boson model for deformed nuclei

TheK ^π=0⁺, 2⁺ and 4⁺ states are considered in doubly even deformed nuclei. It is shown that in the quasiparticle-phonon nuclear model (QPNM) and in the interacting boson model (IBM) a vibrational state has one dominating component. The states withK _n ^π =0 ₃ ⁺ , 0 ₄ ⁺ 0 ₅ ⁺ 2 ₂ ⁺ , 2 ₃ ⁺ , 4 ₁ ⁺ and 4 ₂ ⁺ have a dominating one-phonon component within the QPNM and a two- or three-boson component within the IBM. According to the QPNM the contribution of two-phonon components to the wave functions of these states is less than 10%, i.e. there is a qualitative discrepancy in describing the structure of these states within the QPNM and the IBM. The experimental data indicate the existence in these states of one-phonon or two-quasiparticle components. They are rather well described within the QPNM. These states cannot be described within the IBM. This is due to the fact that the IBM takes into account only a small part of the space of two-quasiparticle states, just the one entering intoΒ- andγ-vibrational states.