Rotational band crossings in the actinides

In the actinides bothi _13/2 protons andj _15/2 neutrons are close to the Fermi surface. At rapid rotation these high-j particles will unpair and align their orbital angular momentum along the axis of rotation giving rise tos-bands that cross the ground-state band. Coulomb excitation of the odd nuclei ₂₃₇ ⁹³ Np (established up to the 45/2⁺ state) and ₂₃₅ ⁹² U (established up to the 51/2^? state) provides specific information about these band crossings: From the saturating alignment of the odd high-j particle in both nuclei at intermediate rotational frequencies we find the aligned angular momentum of thei _13/2 protons-band to be 6.6? while the corresponding value for thej _15/2 neutrons-band is 5.5?. At more rapid rotation above ?ω=0.18 MeV we observe additional alignment in²³⁵U. This is ascribed to the interaction of the protons-band. From the gradual onset of the additional alignment we deduce that forZ=92 the protons-band interacts strongly with the ground-state band and from a comparison of the actual amount of alignment with the full value of 6.6? we estimate the crossing to occur around ?gw _c ^p =0.25 MeV.     

Untersuchung der Struktur desu-u-Kerns142Pr durch (α, n γ)- und (p,n γ)-Reaktionen und Bestimmung von Matrixelementen der effektiven Proton-Neutron-Restwechselwirkung

The structure of the odd-odd nucleus¹⁴²Pr has been studied at the Erlangen Tandem Van de Graaff accelerator by using the nuclear reactions¹³⁹La(α, nγ) and¹⁴²Ce(p, n γ). Neutron-gamma and gamma-gamma coincidence measurements have been performed. In the frame work of the shell model the low lying states up to energies of 400 keV can be described as two mixed multiplettsC _1i ^I ¦j′ _p ,j _n ;I>+C _2i ^I ¦j″ _p ,'j _n ; I> (i=1, 2;j′ _p =2d5/2,j″ _p =1g 7/2^?1 andj _n =2f 7/2). From a fit of experimentally determinedγ-branching ratios to theoretical transition probabilities we have derived the amplitudes of the wavefunctions. From these wavefunctions and the energies of states and configurations in¹⁴²Pr we have obtained matrixelements of the effective residualp, n-interaction.     

One-electron relativistic molecules with Coulomb interaction

As an approximation to a relativistic one-electron molecule, we study the operator \(H = ( - \Delta + m^2 )^{1/2} - e^2 \sum\limits_{j = 1}^K {Z_j } |x - R_j |^{ - 1}\) withZ _j ≧0,e ^?2=137.04.H is bounded below if and only ife ² Z _j ≦2/π allj. Assuming this condition, the system is unstable whene ²∑Z _j >2/π in the sense thatE ₀=inf spec(H)→?∞ as the R _j →0, allj. We prove that the nuclear Coulomb repulsion more than restores stability; namely \(E_0 + 0.069e^2 \sum\limits_{i< j} {Z_i Z_j } |R_i - R_j |^{ - 1} \geqq 0\) . We also show thatE ₀ is an increasing function of the internuclear distances |R _i ?R _j |.     

On asymptotic behaviour of four spin correlation functions in a linear chain of spins

Second and fourth moments of the four spin frequency correlation functions S^Z_i(t) S^Z_i+1 (t) S^Z_j+1 〉_k,ω and 〈S^x_i(t) S^z_i+1 (t) S^x_jS^z_j+1 〉_kω have been calculated in the high temperature limit for an arbitrary spin with an isotropic Heisenberg Hamiltonian.     

SUSY-QCD corrections to scalar quark pair production in e+e− annihilation

We calculate the supersymmetric O(α_s) QCD corrections to the cross section e⁺e⁻ → q̃_iq̃_j (i, j = 1,2) within the Minimal Supersymmetric Standard Model. We pay particular attention to the case of the left-right squark mixing and to the renormalization of the mixing angle. The corrections due to gluino exchange turn out to be smaller than those due to gluon exchange, but they can be significant at higher energies, even for a gluino mass of a few hundred GeV.     

TheE1 transitions in kaonic atoms

The electric dipole transition rates in kaonic atoms are calculated by using distorted relativistic wave functions. The kaon-nucleus strong interaction which is responsible for the distortion of atomic states is considered to be proportional to the nuclear density and the effective isospin-averaged kaon-nucleon scattering length. Six atoms have been studied for which the last observed X-rays correspond to 3d-2p, 4f-3d, 5g-4f, 6h-5g, 7i-6h and 8j-7i transitions. It is found that the electric dipole transition rate is enhanced by an amount (0.3–7.6)×10¹³s^?1     

Effective gauge theory and the effect of heavy quarks in Higgs boson decays

A general framework is given for evaluating the contributions of as yet undiscovered heavy quarks to the gluonic decay rate of the Weinberg-Salam type Higgs boson. Since the Yukawa coupling of the Higgs boson to a quark pair is proportional to the quark mass, loop graphs involving heavy quarks have a non-vanishing effect on the gluonic decay width of the Higgs boson. This effect of heavy quarks with massesM _j(j=t,...) much greater than the Higgs boson massm _H is calculated in an effective gauge theory. The effects of two different kinds of large logarithms, lnM _j ² /μ m _h ² /μ ² are separated and summed up by the renormalization group method. It is found that the higher order QCD corrections are large and that the gluonic contribution to the hadronic decay width is significant if there are more than three generations. The Higgs decay width can therefore be used to probe the number of generations of heavy quarks.     

An analytic approach to the measurement of nestedness in bipartite networks

We present an index that measures the nestedness pattern of bipartite networks, a problem that arises in theoretical ecology. Our measure is derived using the sum of distances of the occupied elements in the incidence matrix of the network. This index quantifies directly the deviation of a given matrix from the nested pattern. In the simplest case the distance of the matrix element a_i,j is d_i,j=i+j, the Manhattan distance. A generic distance is obtained as d_i,j=(i^χ+j^χ)^1/χ. The nestedness index is defined by ν=1−τ, where τ is the “temperature” of the matrix. We construct the temperature index using two benchmarks: the distance of the complete nested matrix that corresponds to zero temperature and the distance of the average random matrix where the temperature is defined as one. We discuss an important feature of the problem: matrix occupancy ρ. We address this question using a metric index χ that adjusts for matrix occupancy.     

Polarized deuteron structure functions at small x

We investigate shadowing corrections to the polarized deuteron structure functions g ₁ ^d and b₁. In the kinematic domain of current fixed target experiments we observe that shadowing effects in g ₁ ^d are approximately twice as large as for the unpolarized structure function F ₂ ^d . Furthermore, we find that b₁ is surprisingly large at x < 0.1 and receives dominant contributions from coherent double scattering.     

Integrals involving Euler-Bernoulli flexure and Saint-Venant torsion eigenfunctions

Tables of the integral ∝₀^LX_i(x)θ_j(x) dx where X_i(x) and θ_j(x) are Euler-Bernoulli and Saint-Venant eigenfunctions respectively are presented for 1?i, j?5 for beams with combinations of clamped, pinned and free ends. These integrals arise in application of the Rayleigh-Ritz and Ritz-Galerkin methods to free vibration and dynamic stability problems involving coupled torsion and bending.     

Leptonic and hadronic corrections to mass and propagator ofW andZ bosons

Using the propagator formalism we establish more precisely the effects of fermion loops on the boson mass ratioM _W ² /M _Z ² cos² θ and on the energy dependence of the form factors associated to time-like or space-likeW, Z and γ exchanges. We calculate the corrections due to higher doublets of quarks including vector meson formation and to higher doublets of leptons for example a large number of neutrino types.     

Phenomenology of composite colored weak bosons

In composite models of quarks, leptons and weak bosons whereW-constituents are colored objects, color octet partners ofW ^± andZ ⁰ are predicted. We study in detail the phenomenology of these particles. Independent of the specific model one expects a color octet isotriplet of vector bosons (W ₈ ^± ,Z ₈ ⁰ ) with mass in the range of 100–200 GeV, and a color octet isosinglet vector bosonV ₈ ⁰ with substantially larger mass, due to mixing with the gluon. Moreover, relatively light color octet excitations of the leptons appear, while the existence of “color exotic” partners of the quarks is model dependent. These particles decay mainly into a lepton (quark) and a gluon. We construct the couplings ofW ₈ ^± ,Z ₈ ⁰ andV ₈ ⁰ to ordinary and “color exotic” fermions. The signals of color octet weak bosons in low energy weak reactions are explored in detail. The production cross section ofW ₈ ^± (Z ₈ ⁰ ) in hadron-hadron collisions is calculated for \(0.54TeV \leqq \sqrt s \leqq 20TeV\) . Various decay modes of colored weak bosons are studied. The most prominent decay signatures ofW ₈ ^± andZ ₈ ⁰ are events of the type (l ^+-: charged lepton;j: hadronic jet; : missing transverse momentum). The present CERN \(p\bar p\) collider data on such events are discussed in the light ofW ₈ ^± andZ ₈ ⁰ decays. If colored weak bosons are not found with a mass less than ～250 GeV composite model building will be strongly restricted.     

Recurrence of random walks in the Ising spins

Consider the 1/2-Ising model inZ ². Let σ _j be the spin at the site (j, 0)∈Z ² (j=0, ±1, ±2, ...). Let \(\{ X_n \} _{n = 0}^{ + \infty } \) be a random walk with the random transition probabilities such that $$P(X_{n + 1} = j \pm 1|X_n = j) = p_j^ \pm \equiv 1/2 \pm v(\sigma _j - \mu )/2$$ We show a case whereE[p _j ⁺ ≧E[p _j ^? ], but \(\mathop {\lim }\limits_{n \to \infty } X_n = - \infty \) is recurrent a.s.     

Near and far infrared vibrational absorption ofH i − andD i − centres in KBr

Near infrared absorption measurements by Gross and Bron led to the suggestion that the threefold degeneracy of the localized vibration ofH _i ^? andD _i ^? centres in KI is completely lifted in KBr. Using thermal annealing procedures,H _i ^? -D _i ^? substitution and far infrared techniques we found that the lines at 794, 840, and 896 cm^?1 cannot be interpreted as a splitting of the main line. Only the 794 cm^?1 line can be correlated with the direct excitation of theH _i ^? oscillator. The absence of any splitting in this line (its halfwidth at 9 °K is only 1.5 cm^?1) indicates that also in KBrH _i ^? centres have at most only slightly perturbedT _d symmetry.     

Head-on collision of dust-ion-acoustic solitons in electron-dust-ion quantum plasmas

In this paper, we study the head-on collision between two dust-ion-acoustic (DIA) solitons in quantum electron-dust-ion plasma. Using the extended Poincaré–Lighthill–Kuo (PLK) method, we obtain the Korteweg–de Vries (KdV) equations, the phase shifts and the trajectories after the head-on collision of the two DIA solitons. We investigate the effect of quantum diffraction parameters for electrons and ions (H _e, H _i), the Fermi temperature ratio (σ) and the dust charged number density (n _d0) on the phase shifts. Different values of μ?=?z _d0(n _d0/n _i0) and μ _d?=?z _d0(m _i/m _d) are taken to discuss the effects on phase shifts, where z _d0 denotes the dust charge number, n _j0 represents the equilibrium number density and m _j is the mass of the jth species (j?=?e, i, d for electrons, ions and dust particles, respectively). It is observed that the phase shifts are significantly affected by the plasma parameters.     

Relativistic calculations of ground states of single-electron diatomic molecular ions

We have performed relativistic calculations of ground-state energies for a series of single-electron homonuclear dimers A ₂ ^(2Z?1)+ with nucleus charge Z = 1, 2, 10, 20, 30, 40, 50, 60, 70, 80, 90, 92, and 100 and internuclear distances R = 2/Z. The work involves the Born-Oppenheimer approximation and the single-electron two-center Dirac Hamiltonian, which describes the interaction between an electron and two immovable point charges. Analysis of the convergence process and comparison with data presented in other works for H ₂ ⁺ and Th ₂ ¹⁷⁹⁺ dimers shows that the relative error of the obtained results is on the order of 10^?11–10^?12. High-accuracy values of ground-state energies for some dimers other than Z = 1 and 90 have been obtained in this work for the first time.     

U(3)-family nonet Higgs boson and its phenomenology

In a model where quark and lepton masses and family-mixings are caused not by a variety of Yukawa couplingsy _ij (i,j=1, 2, 3: family indices) with one vacuum expectation value (VEV)ν=〈φ _L ⁰ 〉₀, but by a variety of VEV’s of a U(3)-family nonet Higgs bosonφ _L ,v _i ^j =〈φ _Li ^0j 〉₀, with a single coupling constant, the following problems are investigated: what constraints on the Higgs potential are imposed in order to provide realistic quark and lepton mass spectra and mixings and what constraints on the Higgs boson masses are required in order to suppress unwelcome flavor-changing neutral current effects. Lower bounds of the physical Higgs boson masses ofφ _L are deduced from the present experimental data and new physics from the present scenario is speculated.     

Harness Processes and Non-Homogeneous Crystals

We consider the Harmonic crystal, a measure on with Hamiltonian H(x)=∑ _i,j J _i,j (x(i)−x(j))²+h∑ _i (x(i)−d(i))², where x, d are configurations, x(i), d(i)∈ℝ, i,j∈ℤ ^d . The configuration d is given and considered as observations. The ‘couplings’ J _i,j are finite range. We use a version of the harness process to explicitly construct the unique infinite volume measure at finite temperature and to find the unique ground state configuration m corresponding to the Hamiltonian.     

Signatures for neutralinos at theZ 0

We calculate the visible and invisible width for production of neutralinos,Z ⁰→χ _i ⁰ χ _k ⁰ , and all possible decay rates of the neutralinos. We systematically study their dependence on the supersymmetry parameters and work out the domains where detectable signatures occur. These are the one-sided eventsZ ⁰→e ⁺ e ^?+p _miss,Z ⁰→jets+p _miss,Z ⁰→γ+p _miss andZ ⁰→H _2,3 ⁰ +p _miss, and the two-sided eventsZ ⁰→γ+γ+p _miss,Z ⁰→γ+l ⁺ l ^?+p _miss andZ ⁰→γ+jets+p _miss.     

Analyticity properties and a convergent expansion for the inverse correlation length of the high-temperatured-dimensional Ising model

We show that the inverse correlation lengthm(β) (= mass of the fundamental particle of the associated lattice quantum field theory) of the spin-spin correlation function 〈s _x s _y 〉,x, y εZ ^d , of thed-dimensional Ising model admits the representation $$m(\beta ) = - ln\beta + r(\beta )$$ for small inverse temperaturesβ > 0.r(β) is ad-dependent function, analytic atβ = 0.c _n , the nth β = 0 Taylor series coefficient of r(β) can be computed explicitly from the Z^d limit of a finite number of finite lattice A spin-spin correlation functions 〈s₀s_x〉t>Afor a finite number ofx = (x ₁,x₂, ..., x_d), ¦x¦ = ∑ _i ^d 1¦x_i¦< R(n), where R(n) increases withn. Furthermore, there exists aβ' > 0, such that for eachβ ε (0,β')m(β) is analytic. Similar results are also obtained for the dispersion curve ω(p), ω(p)=ω(0)=m, pε(-π, π]^d?1, of the fundamental particle of the associated lattice quantum field theory.