Isomer shifts and changes of the nuclear charge radii in99Ru and101Ru

The recoilless nuclear gamma resonance of the 127 keV γ-rays of¹⁰¹Ru was observed in ruthenium metal, RuO₂ and [Ru(NH₃)₄(HSO₃)₂]. By comparison of the isomer shifts observed in these materials for the 127 keV absorption line with the corresponding shifts of the 90keV γ-rays of⁹⁹Ru one obtains δ〈r ²〉 [127 keV]/ δ〈r ²〉 [90 keV]=1.78±0.26 for the ratio of the changes of the mean square nuclear charge radii between the first excited and the ground states in these nuclei. An estimate of electron density differences based on free-ion relativistic self-consistent field calculations yields δ〈r ²〉[90keV]≈+1.4·10^?3 for⁹⁹Ru and δ〈r ²〉/〈r ²〉 [127 keV]≈+2.4·10^?3 for the¹⁰¹Ru case. These results are discussed in terms of the core excitation model.     

Observation of new nuclides37Si,40P,41S,42S produced in deeply inelastic reactions induced by40Ar on238U

A non-relativistic quantum-mechanical system is studied which consists ofN identical bosons interacting by pair potentials of the form 〈r¦V¦r ¹〉=?π/2ν ₀ a ^?3 f(r/a)f ^*(r ¹/a). General upper and lower bounds to the ground-state energyE _N are provided for alla, V ₀ andN, and detailed results are given in the case of the Yamaguchi potential for whichf(x)=e ^?x/x. It is shown that the ratioE _N /E ₂ diverges both under the limit (i) a↓0,E ₂ =arbitrary constant <0, and (ii) (V ₀ a ²)↓(V ₀ a ²)_c, where (V ₀ a ²) _c corresponds toE ₂=0. The results complement recent studies of the Efimov effect via scattering theory.     

n-shell Thomas-Fermi model: Coulomb atom

A simple expression for the electron density of then-shell of the Coulomb atom with the nuclear charge Zρ _n(r)=Z ³ π ^?2 n ^?3(2Z ^?1 r ^?1?n ^?2)^1/2 is found in the semi-classical approximation. It is used for the asymptotic estimation of averages 〈r ^a 〉 (?2<a<∞). An explicit dependence of the leading oscillatory contribution to 〈r ^a 〉 due to angular moments on the electron number is also obtained.     

The inverse problem for the third order equation uxxx + q(x)ux + r(x)u = −iζ3u

The spectral problem u_xxx + q(x)u_x + r(x)u = ?iξ³u is considered. A set of spectral data which is sufficient for the reconstruction of the potentials q(x) and r(x) is found and the problem of this reconstruction, this inverse problem solved.     

High multipolarity nuclear excitations in the continuum

The strength distributions of particle-hole isoscalar transitions with high multipolarities are considered in the framework of the independent particle model using the Woods-Saxon potential. It is shown that for the multipole operatorsj _L (qr)Y _LM withL?A ^1/3 andq?p _F the distributions are peaked at the relatively low energy for allL, and their widths decrease asL ^?1/2. In contrast to that, for the surface external fields (?U/?r)Y _LM the centroid excitation energy is proportional toL ² and the distribution widths increase asL ^4/3. The conclusion is drawn that the p-h excitations might be responsible for the structures in the excitation function observed in heavy ion collisions in the energy region up to ≈2ε _F .     

Analytical solution of the double-logarithmic integral equation with QCD running coupling

The analytical solution of the double-logarithmic integral equation with QCD running coupling describing small-x behaviour of the non-singlet structure function ? _NS(x,Q ²) has been found for any cut-off parameter μ. Analytical properties of the solution and a position of the right-most singularity in the complex ρ-plane which determines the asymptotics of ? _NS(x,Q ²) at small x have been studied. The asymptotical formula ? _NS(x,Q ²) = C ₁ x ^-λ1{ln^κ1(Q ²/Λ²) —ln^κ1 (μ ²/Λ²) + κ ₁ ln^κ1-1(Q ²/Λ²)[ψ(1) - ψ(λ₁)]} valid if x ? 1 and ln(Q ²/Λ²) ? 1 has been obtained where C ₁, λ₁ are constants, κ ₁ = g/λ₁, λ₁ < g = 8/(33 - 2gh _f), gh _f is a number of active flavours and ψ(ξ) denotes the digamma function.     

Decay of helicity in homogeneous turbulence

The self-similar relaxation of helicity in homogeneous turbulence has been considered taking into account integral invariants ∫ ₀ ^∞ r ^m 〈u(x)ω(x + r)〉 dr = I _m ^h (where ω = curlu and r = |r|). It has been shown that integral invariants with m = 3 for both helicity and energy are possible in addition to helical analogs of Loitsyanskii (m = 4) and Birkhoff-Saffman (m = 2) invariants associated with the conservation laws of momentum and angular momentum, respectively. Helicity always relaxes more rapidly than the energy. Its decay exponent is in the interval from ?3/2 to ?5/2 versus the interval from ?6/5 to ?10/7 for the energy.     

Models of superfrustration

Earlier studies of the triangular lattice antiferromagnet and the fully frustrated model on the square lattice proved that in these models the pair correlation 〈S ₀ S _r 〉 decreases asymptotically asr ^?1/2 at zero temperature. In the present paper the existence of two and higher dimensional models is shown in which the frustration is so strong that it destroys the phase transition even atT=0: the correlation length remains finite. The influence of this “superfrustration” on the free energy and on the ground state properties is also discussed.     

Infrared contribution to the double-logarithmic small-x asymptotics of structure functions

The role playing by the “soft” (κ _T < 1 GeV/c) region in the small-x behaviour ofg ₁(x,Q ²) and the non-singlet structure functionf _{1, NS}(x, Q²) has been studied with the help of the effective QCD Lagrangian which takes into account the lightest degrees of freedom — the constituent quarks and the π-mesons (Goldstone bosons). It has been shown that the quark-quark interaction due to the pion exchange has a negative couplingg for the isovector component (I = 1 in thet-channel) off ₁(x,Q ²) and isosinglet component ofg ₁(x, Q²). Here the pion induced interaction changes mainly the normalization of the quark distribution (it decreasesf _1,NS ^{I = 1} (x,Q ²) two times atx < 3·10^?3) and changes slightly the effective exponents λ (?_1,NS ,g ₁ ～x ^?λ atx → 0). On the other hand due to a positive value of couplingg the value of λ increases by 15% for the isovector part ofg ₁ (x,Q ²) and up to λ ≈ 0.5 (instead of λ ≈ 0.2 without the pion contribution) for the isoscalar non-singlet structure functionf _1,NS ^{I = 0} (x,Q ²).     

Möβbauereffekt am61Ni

With the Möβbauer technique the hyperfine splittings of the 67.4 keV transition of⁶¹Ni in compounds and alloys have been studied. A magnetic momentΜ _61,4=+ (0,477 ±0.031)Μ _n of the first excited state has been determined. From isomer shifts an order of magnitude estimate of the change in radius ofδ〈r ²〉/〈r ²〉=?6· 10^?4 can be inferred. The electric quadrupole interaction of the first excited level has been observed in Ni-J-boracite. In addition the hyperfine fields at the nickel sites were determined in the alloy series Ni _x Fe_1-x (0≦x≦1). In one case an effect of polarization in a high external field is measured. The fields in some rare earth (RE) intermetallic compounds of the form RENi₂ were deduced from linewidth to be less than 15 kOe.     

The hyperfine structure of they 8 p-multiplet of 4f 7(8 S) 6s 6p in EuI

The hyperfine splitting constants of the 4f ⁷ 6s 6p y ⁸ P _7/2 level of Eul were determined using the level crossing method. These values and those for the hyperfine splittings of the other 4f ⁷ 6s 6p levels are compared to theoretical values calculated with eigenfunctions of Smith and Collins. For the quadrupole coupling constants a better agreement between theory and experiment is obtained if different 〈r ^?3〉 _p -parameters are assumed for 4f(⁸ S) 6s 6p(³ P) and for 4f ⁷(⁸ S) 6s 6p(¹ P).     

Nuclear gamma-transitions via the accompanying atomic excitations

The nuclearγ-transitions via excitation of the atomic electrons (electronic bridges) is considered in the framework of the strong coupling channels method. The nuclearM4 transitions from the lowest isomeric level of nuclei⁹³Nb and¹⁹³Ir in the both mechanisms of elastic and inelastic electronic bridges are investigated. The comparison between the semiclassical and selfconsistent Dirac-Hartree-Fock-Slater calculations is presented. The derived valuesκ _f of a relative probability of nuclearγ-transition via the atomic excitation (inelastic electronic bridge)κ _f(⁹³Nb)=6.9·10^?2 andκ _f(¹⁹³Ir)=1.4·10^?2 are in agreement with the experimental data.     

Änderung des quadratischen Kernladungsradius bei Rotationsanregung

Isomer shifts ofγ rays from rotational bands of deformed nuclei have been determined in Mössbauer effect measurements. The following changes of the mean square nuclear charge radii have been deduced:Δ〈r ²〉(¹⁵⁶Gd, 89keV)=(+2.6±0.8)·l0^?3fm²,Δ〈r ²〉(¹⁷⁰Yb, 84keV)=(+1.2±0.3)·10^?3fm²,Δ〈r ²〉(¹⁷¹Yb, 67keV)=(+1.1±0.2)·10^?3fm². The results are compared with theoretical calculations and additional experimental data, to study the effect of the Coriolis and centrifugal forces in rotational excitation on the motion of the nucleons.     

Isomerieverschiebungen der 81 keV γ-Linie des133Cs

Isomer shifts of the 81.0 keVγ-transition in¹³³Cs have been measured by the Mössbauer technique for eight ionic Cs compounds, and for the intermetallic compound CsBi₂. The source was¹³³Ba in CaF₂. The shifts, relative to CsCl, range from ?1.4 · 10^?8 eV for CsNO₃ to +1.6 · 10^?8 eV for CsBi₂. The difference in electron density at the Cs nucleus between CsBi₂ and CsNO₃ is discussed using chemical bonding arguments. For the Cs halides, this difference is estimated from the overlap of outer electron shells in the lattices. A relative change of the mean square charge radiusδ〈r ²〉/〈r ²〉=+2 · 10^?4 is derived.     

Crystalline fields,exchange interactions and spin reorientations in TmxHo1−xFe2 systems,studied by a Yb170 Mössbauer probe

Mössbauer studies of the 84.3 keV gamma ray of Yb¹⁷⁰ emitted from Yb in Tm_xHo_1?xFe₂ at various temperatures were performed. These yield the crystalline field parameters (A₄〈r⁴〉 = 36 ± 5 K, A₆〈r⁶〉 = -3 ± 2K, the exchange field (μ_BH_exch = 116 ± 4 K) and the Yb³⁺ free ion hyperfine constants (H_4f = 4100 ± 150 kOe, eqQ = 2400 ± 250 MHz and H (conduction electrons) = 350±100 kOe). Spin relaxation phenomena observed in TmFe₂ at low temperatures give a value of ～ 0.03 for |?(E_F)J_sf|. Spectra observed in Tm_0.2Ho_0.8Fe₂ in the spin reorientation transition region indicate that the transition is of second order.     

Ultra-high energy neutrino-nucleon and neutrino-electron cross-sections in the standard model,in supersymmetric and superstring models

The neutrino-nucleon cross-section is calculated for energies up to 10¹⁵ GeV in the framework of the standard model assuming that the nucleon structure functionF ₂(x, Q ²) goes like ln²(a/x) asx→0. The cross-sections forv _μ e ^?(v _e e ^?)-interactions rise linearly with energy up toE _ν～10⁷ GeV and amount at this energy to ～10% of the neutrino-nucleon cross-section. The νN-cross-sections with production of supersymmetric particles in the framework of a supersymmetric model with minimal particle content are estimated. Photino-nucleon and photino-electron interactions are considered for masses of the squarks and sleptons in the range of 80–300 GeV. In superstring inspired unified models an estimation is made of the νN-interaction with an exchange of light leptoquarks.     

An SO(10) model with 54 + 126 + 10 higgs

We find an absolute minimum of an SO(10) symmetric potential with SU(3) × U(1) invariance. By fixing the higher scales M_R(〈126〉) ? M_x(〈54〉), the model is consistent with the experimental knowledge about matter stability and the value of sin²θ_w. We determine the spectrum of scalar particles and show that their tree-diagram contributions to nucleon decay amplitudes are proportional to 1/M_x².