The sensitivity of allowed β-decay to the nuclear radius

The sensitivity to the nuclear radius of the phase-space factor for allowed β-decay is investigated as a function of energy release and Z for Z < 40 using a definition of the phasespace factor that takes into account in detail finite-size effects on the lepton wave functions and their convolution with the nucleon wave functions.     

Finite-size corrections to the energy levels of light muonic atoms

An analytic expression is developed in perturbation theory for the nuclear finite-size correction to the s-state energy levels of light muonic atoms. Using first-, second- and third-order perturbation theory, the finite-size corrections of order (Zα)⁴, (Zα)⁵, and (Zα)⁶ are calculated analytically for an arbitrary charge distribution. Application is made to the case of the μ? ⁴He atom, where the error in our finite-size expression is shown to be less than 10ppm.     

Watson representation for the amplitude of lepton-pair production in nucleus-nucleus collisions

An expression for the amplitude of lepton pair production in nucleus-nucleus collisions is obtained in terms of the amplitudes of lepton-nucleus scattering. By using this representation an approximate compact expression for this amplitude valid to terms of the order (Zα)⁵ is obtained.     

über die Streuung relativistischer Elektronen im Coulombfeld

An approximative method for summing the partial wave series for the scattering amplitude of the relativistic scattering of electrons by an atomic nucleus is investigated in the simplest case of a point charge nucleus for electron energies not less 10 MeV. In the course of the computationΒ=1 is assumed (Β=v/c,v andc denote the velocity of the electron and of light, respectively). The Sommerfeld-Watson-transformation is the starting point. The method consists in setting up an asymptotic expansion in 1/sin² (θ/2) (θ is the scattering angle) of the amount coming from the Regge-poles. Two further amounts, the dependence of which on the scattering angle especially for easy nuclei is little, are computed numerically without simplification, which should be possible. The method is developed from a special way of summing the partial wave series for the non-relativistic Rutherford scattering, which may be done analytically.Mott's scattering formula is verified and finally the applicability of the method is examined for summing the relativistic partial wave series with the exact S-Matrix. The results are as exact as the expension of the cross section to order (Z/137)⁵ (Z is the nuclear charge). The method should in principle be applicable for an extended nucleus, but in this case there remain still several problems.     

Fragmentation of12C nuclei in emulsion at 50 GeV/c

A total of 852¹²C-emulsion nucleus interactions at 4.2 GeV/c per incident nucleon was investigated. At least one charged projectile fragment was observed in 733 events, in which the multiplicity and angular distributions ofZ=1,2, and ≧3 projectile fragments were studied. Five events were observed in which¹²C projectile nuclei were fragmented into twoZ=3 fragments. Thus the cross section of this process is about 6×10^?3 of the inelastic cross section. The angular distribution of projectile fragments becomes narrower as the fragment charge increases. At all values of fragment charges, a pronounced peak in the angular distribution can be observed at zero emission angle. In this paper, only the projectile-fragmentation events possessing no heavily ionizing particle (n _h =0 events) have been investigated. Our sample contains 84 of these events, i.e., about 10% of the total inelastic events. The number of events withZ _max, the charge of the emitted principal fragment, equal to 1, 2, 3, 4, and 5 are 11, 52, 13, 4, and 4, respectively. Of these 84 events, 36 interactions have a total charge of emitted projectile fragmentsZ ^* equal to 6, i.e., as much as the beam chargeZ _p . Of the 36 events, 17 produce no charged pions and of the 17 events, 10 only represent the dissociation of¹²C→3α, i.e., 1.2% of the total inelastic interactions. The number of events withZ ^*=5, 4, 3, 2, and 1 are 27, 14, 4, 2, and 1, respectively. The average number of produced charged pions per one interacting projectile nucleon was estimated to be 1.2±0.1. This value agrees with the corresponding one in elementary interaction at the same energy per nucleon, a result pertaining to the incoherent production model in collision of two nuclei. In this class of events,n _h =0, the number of stars in which H, He, Li, Be, and B isotopes were detected are 59, 58, 13, 4, and 4, respectively. The projected angular distributions ofZ=1 and 2 projectile fragments are Gaussian shaped, narrow, consistent with isotropy, and depend on the fragment. These distributions are consistent with quantum mechanical calculations using the sudden approximation and shell-model functions. From the angular measurements ofα-particle tracks in the dissociation¹²C→3α events, the distribution ofα-particle transverse momentum inside the carbon projectile nucleus was deduced. It seems that the dissociation of¹²C→3α happens via an intermediate⁸Be state.     

High Z effects in accounting for radiative component of the electron magnetic moment in hydrogen-like atoms

The behavior of electron energy levels in hydrogen-like atoms is studied while taking into account the nonperturbative interaction between the radiative component of the magnetic moment of a free electron Δg _free and the Coulomb field of an atomic nucleus with charge Z, including those with Z > 137. It is shown that for Zα ? 1 the energy-level shift is rather effectively determined through the matrix elements of the corresponding Dirac-Pauli operator with relativistic Coulomb wave functions. At the same time, for superheavy nuclei with Z ～ 170, this shift, generated by Δg _free, is genuinely nonperturbative, behaves like ～Z ⁵ near the threshold of negative continuum, exceeds all the estimates of radiative corrections coming from vacuum polarization and electron self-energy known so far, and turns out to be at least of the same order as the effects of nuclear charge screening by filled electron shells.     

Two-photon collisions in deep inelastic lepton-nucleon and lepton-nucleus scattering

We have calculated the μ-pair production via photon-photon collisions in deep-inelastic charged lepton scattering on proton and nuclei, using the equivalent photon approximation. Specific parametrizations were assumed for the proton and the nuclei form factors and the QED photon structure function. Results are given for lepton energies below 300 GeV and virtual photon massesQ ² less than 50 GeV², as functions of the μ-pair mass, the scaling variablex and the electric chargeZ of the hadron target. Using a photon structure function derived from QPM and VDM we also estimate the contribution of γγ collisions to hadron production in these deep inelastic processes.     

Forward-backward asymmetry of hadroproduced heavy quarks in QCD

It has been argued that higher order 2→3 O(α_s³ QCD processes play an important role in the hadroproduction of heavy quarks. We propose forward-backward or charge conjugation asymmetry as a distinctive signature of the higher-order QCS production mechanism. We analyse the physical origin of the asymmetries and show that observed forward-backward asymmetries for the heavy quark or decay lepton are 5% or less for realistic experimental conditions. Observation of asymmetries in excess of our calculated values would signal the production of heavy quarks via unconventional mechanisms.     

Neutral heavy lepton candidate in e+e− interactions

An event of the form e⁺e^? → μ⁺μ^? + (2 jets) recently observed at √s = 43.45 GeV is interpreted as production of a pair of neutral heavy leptons N, each with mass 20.5 ± 1.0 Gev/c². Two possibilities are explored: (i) the lepton is a wak isodoublet neutrino, produced in pairs by virtual Z⁰ decay. In this case, one expects $\text{B(}\text{Z}{}^0\text{→}\text{N}\text{N}\text{) ≈ 5\%}$; (ii) the lepton is a “right-handed neutrino”, produced in pairs via a new vector boson Z_χ. In this case, in one model, the Z_χ must lie between about 50 and 67 GeV/c². More generally, it must be very weakly coupled to ordinary quarks and leptons in order not to conflict with low-q² neutral-current data. Suggestions are made for further observation of N$\text{N}$ pairs and other effects of Z_χ in forthcoming e⁺e^? and p$\text{p}$ collisions.     

A study of B meson oscillations using hadronic Z0 decays containing leptons

An event sample enriched in semileptonic decays of b hadrons is selected using an inclusive lepton selection from approximately 3.0 million hadronic Z⁰ decays collected with the OPAL detector. This sample is used to investigate B meson oscillations by reconstructing a proper decay time for the parent of each lepton, using a jet charge method to estimate the production flavour of this parent, and using the lepton charge to tag the decay flavour. We measure the mass difference between the two B⁰ _d mass eigenstates     

Electroweak interactions probing the nucleon structure

The possibility is studied of isolating single electroweak structure functions in deep inelastic lepton-nucleon scattering atQ ² aroundM _Z ² . Utilizing the cross-section dependence on the lepton charge and longitudinal polarization λ it is shown that the most-conclusive results follow from measurements of σ⁺(?λ)±σ^?(+λ). Considerable simplifications of the problem are possible if λ can be tuned to sin² θ dependent values of about 0.2. New quark-parton model relations are derived.     

Measurement of B d 0 - oscillations

B _d ⁰ meson oscillations are measured in hadronic Z⁰ decays using the charge of a lepton or the mean charge of an event hemisphere to sign the presence of a b or a b? quark when it is produced, and using the charge of a lepton emitted at large pt or of a D*^± to sign the presence of a B or a B? meson when it decays. With 3.2 million hadronic Z⁰ decays registered by DELPHI between 1991 and 1994, the mass difference Δm _d between the two physical B _d ⁰ states is measured in four channels: Taking into account the statistical overlap between these measurements and the common systematic uncertainties, the combined result is:      

One-Dimensional Models for Atoms in Strong Magnetic Fields,II: Anti-Symmetry in the Landau Levels

Electrons in strong magnetic fields can be described by one-dimensional models in which the Coulomb potential and interactions are replaced by regularizations associated with the lowest Landau band. For a large class of models of this type, we show that the maximum number of electrons that can be bound is less than aZ+Zf(Z). The function f(Z) represents a small non-linear growth which reduces to A _p Z(logZ)²when the magnetic field B=O(Z ^p ) grows polynomially with the nuclear charge Z. In contrast to earlier work, the models considered here include those arising from realistic cases in which the full trial wave function for N-electrons is the product of an N-electron trial function in one-dimension and an antisymmetric product of states in the lowest Landau level.     

Nuclear matrix elements for the coherent μ-e conversion process

The lepton flavor-violating coherent (μ⁻, e⁻) conversion is investigated. Photonic and nonphotonic contributions arising in various gauge models are considered. The dependence of the conversion rate on the structure of the nucleus is given by the elastic form factors. These are obtained in the context of shell model taking into account finite-size effects or extracted from the electron scattering data whenever possible. The relevant branching ratios are studied throughout the periodic table.     

Mechanism of independent neutron transfer in elastic <Emphasis Type="Italic">α</Emphasis><Superscript>6</Superscript>He scattering and structure of the <Superscript>6</Superscript>He nuclear wave function

The presence of two topologically different configurations, a dineutron and a cigar-like one, in the spatial wave function for the neutron-rich nucleus ⁶He is predicted. In elastic α ⁶He scattering, the dineutron configuration leads to the appearance of backward maxima in the cross section for elastic α ⁶He scattering. The cigar-like configuration is responsible for the scattering mechanism involving independent sequential neutron transfer and the formation of the ⁵He-⁵He virtual system. In order to estimate the contribution of this mechanism, the matrix element for the two-step sequential particle transfer is calculated by a method that takes into account delay in the interaction and which is realized in the QUADRO code. Calculations performed on this basis make it possible to estimate the weight of the cigar-like component in the wave function for the ⁶He nucleus.     

Analysis of elastic and inelastic hadron scattering on 6,7Li nuclei within diffraction theory

Within Glauber-Sitenko multiple-scattering theory, the differential cross sections for elastic and inelastic proton, positive-pion, and positive-kaon scattering on ^6,7Li nuclei are calculated at incident-hadron energies ranging between 0.143 and 1.0 GeV. The ⁶Li and ⁷Li wave functions are taken in, respectively, the α2N and the αt clustermodel. The resulting cross sections are investigated as functions of the scattered-particle energy, parameters of the model wave functions, and various scattering multiplicities. It is concluded that a partial filling of the diffraction minimum in the cross section is due to the D-wave contribution to the wave function for the ⁶Li target nucleus.     

Method for calculating the relativistic Coulomb scattering amplitudes of electrons

The scattering amplitudes for the scattering of electrons by a point charge nucleus can be represented by power series in the variables (sin Θ/2)² or (cos Θ/2)², whereΘ is the scattering angle. A method for calculating the coefficients of these series including all terms up to an arbitrarily high order in (Z/137)², whereZ is the nuclear charge, is described. The method makes extensively use of recurrence relations and does not contain any approximation. Since all power series occurring in the course of the computation converge rapidly, very accurate results can be obtained with the help of a computer. The method is particularly advantageous for small and large scattering angles, where other methods fail to give accurate results.     

Bond-stretching and bond-bending force constant of binary tetrahedral (AB and AB) semiconductors

In this Letter we present the two expressions relating the bond-stretching force constant (α in N/m) and bond-bending force constant (β in N/m) for the A^IIIB^V and A^IIB^VI semiconductors with the product of ionic charges (Z₁Z₂) and nearest neighbor distance d (Å). Interatomic force constants of these compounds exhibit a linear relationship when plotted on a log-log scale against the nearest neighbor distance d (Å), but fall on different straight lines according to the ionic charge product of the compounds. A fairly good agreement has been found between the observed and calculated values of the α and β for binary tetrahedral semiconductors.     

Soft x-ray PHA measurement of the long pulse discharge in HT-7 tokamak

By analyzing the soft x-ray energy spectrum measured by the soft x-ray pulse height analysis (PHA) system, the electron temperature (Te) and the effective charge number (Zeff) of the ultra-long pulse discharge driven by lower hybrid wave (LHW) were obtained in the HT-7 tokamak. Moreover, the information of medium-Z impurities such as Ti, Cr, Fe, and Ni intrinsic to HT-7 tokamak can also be inspected. The accuracy of the electron temperature derived from the soft x-ray energy spectrum measurements is verified by comparing with the temperature measured by the Thomson scattering system for various plasmas and electron cyclotron emission diagnostic system for ohmic plasmas. The bulk electron temperature of about 1 keV and Zeff≈2 were achieved for long pulse plasma. The appreciable Kα lines of Ti, Cr, Fe and Ni metallic impurities released from the antennas of radio frequency wave and/or the first wall and Ar injected into plasma can be observed, and they kept stable during the long duration discharges. As a result, the longest pulse discharge with relatively high temperature of Te(0)∼1 keV, and ne(0)∼0.5×¹⁰¹⁹ m−3 has been achieved with a duration of 400 s in the HT-7 experimental campaign in 2008.     

Cluster knockout reactions

Cluster knockout reactions are expected to reveal the amount of clustering (such as that of α, d and even of heavier clusters such as¹²C, ¹⁶O etc.) in the target nucleus. In simple terms, incident medium high-energy nuclear projectile interacts strongly with the cluster (present in the target nucleus) as if it were existing as a free entity. Theoretically, the relatively softer interactions of the two outgoing particles with the residual nucleus lead to optical distortions and are treated in terms of distorted wave (DW) formalism. The long-range projectile–cluster interaction is accounted for, in terms of the finite range (FR) direct reaction formalism, as against the more commonly adopted zero-range (ZR) distorted wave impulse approximation (DWIA) formalism. Comparison of the DWIA calculations with the observed data provide information about the momentum distribution and the clustering spectroscopic factor of the target nucleus. Interesting results and some recent advancements in the area of (α, 2 α) reactions and heavy cluster knockout reactions are discussed. Importance of the finite-range vertex and the final-state interactions are brought out.