Electron shells in over-critical external fields

When the charge of a nucleus exceedsZ=Z _cr≈ 164–172 the energy of the 1s-electron level is lowered beyond the critical value of ?m _e c ². Then this bound level is degenerated with negative energy continuum solutions of the Dirac equation and becomes a resonance, whose shape varies and is approximately of Breit-Wigner type forZ?Z _cr?5. The physical meaning of this resonance can be understood most easily if the 1s-level is unoccupied (K-hole). In this case a positron may escape ifZ>Z _cr, a process, that can be interpreted as auto-ionization of the positron. This fundamentally new process of quantum electrodynamics of strong fields can be tested experimentally by scattering very heavy ions (Z≧80) on each other since in such collisions superheavy electronic molecules occur (superheavy quasimolecules).     

Systematic studies of positron production in heavy-ion collisions near the Coulomb barrier

We present the results obtained from systematic studies of positron creation for a series of heavy-collision systems, with united chargeZ _u =Z ₁ +Z ₂ ranging fromZ _u =164 (Pb + Pb) toZ _u =184 (U+U) at bombarding energies close to the Coulomb barrier, using the Orangeβ-spectrometer at GSI. For each collision system studied, the dominating continuous distributions due to quasiatomic and nuclear positron emission are determined accurately. This is essential in obtaining the characteristics of the still unexplained monoenergetic positron lines which appear in the energy range between 200 keV and 400 keV. Our results are compared with coupled-channels calculations for quasi-atomic positron creation. The latter describe quite well the global features of the measured spectra, but overestimate systematically their absolute values. From the comparison, a common normalization factor of about 0.75 can be established for the calculated spectra. In particular, the dependence onZ _u of the measured emission probabilities was found to follow a power law (∝Z _u ^195±1), in fair agreement with the theoretical prediction.     

Critical charge in quantum electrodynamics

The critical nuclear charge Z _cr and the critical distance R _cr in the system of two colliding heavy nuclei—they are defined as those at which the ground-state level of the electron spectrum descends to the boundary of the lower continuum, with the result that beyond them (that is, for Z>Z _cr or R<R _cr) spontaneous positron production from a vacuum becomes possible—are important parameters in the quantum electrodynamics of ultrastrong Coulomb fields. Various methods for calculating Z _cr and R _cr are considered, along with the dependence of these quantities on the screening of the Coulomb field of a nucleus by the electron shell of the atom, on an external magnetic field, on the particle mass and spin, and on some other parameters of relevance. The effective-potential method for the Dirac equation and the application of the Wentzel-Kramers-Brillouin method to the Coulomb field for Z>137 and to the two-body Salpeter equation for the quark-antiquark system are discussed. Some technical details in the procedure for calculating the critical distance R _cr in the relativistic problem of two Coulomb centers are described.     

Positron lines from subcritical heavy ion-atom collisions

Positron lines were observed in heavy ion-atom collisions at bombarding energies close to the Coulomb barrier in subcritical systems with the sum of the atomic numbers of the colliding nucleiZ _u =Z ₁+Z ₂ being smaller thanZ _u =172. Each collision system, studied,²⁰⁸Pb +²⁰⁸Pb(Z_u=164),²³⁸U+¹⁸¹Ta(Z_u=165), and²³⁸Au(Z_u=171), exhibits the emission of two positron lines withZ _u -independent c.m. energies of ～ 258 keV and ～ 340 keV, and with widths of about 30 keV, superimposed on continuous positron spectra from nuclear pair decay and pair emission induced by the time changing Coulomb field of the collision. The production cross section of thee ⁺-lines rises with a high power ofZ _u (ocZ _u ²²), which is comparable to theZ _u ²⁰-dependence for the collision induced positrons.     

Z1 and Z2 variations in the stopping powers of Z1=10 to 18 ions deduced from Dsam lifetime measurements

From lifetime measurements of the ²²Ne(3.26 MeV), ¹³P(2.23 MeV) levels and published data, deviations from theory of the stopping powers for Ne and other ions in many materials have been deduced; they correlate strongly with electron densities deduced from positron lifetimes. The data also indicate that Z₁ deviations for s-d shell nuclei are Z₂ dependent.     

Positrons from supercritical fields of giant nuclear systems

During collisions of heavy nuclei with a combined chargeZ?160 the electronic 1s-state is deeply bound due to the strong Coulomb field, forZ≧173 it even enters as a resonance the lower continuum of the Dirac-Hamiltonian. In pure Rutherford scattering no qualitative indication for the filling of a dynamically createdK-hole by the spontaneous positron creation process is predicted, but the study of heavy-ion collisions with nuclear time delay due to the attractive nuclear force promises clear signatures for the decay of the vacuum. Emphasis is laid also on the quantitative influence of the electron-electron interaction and ofE0-transitions in the giant nuclear system on positron emission, the latter treated in a classical approximation. We compare our results with recent experimental data of two different groups at GSI, Darmstadt.     

Finite-temperature quantum field theory in Minkowski space

We formulate finite-temperature quantum field theories in Minkowski space (real time) using Feynman path integrals. We show that at non-zero temperature a new field arises which plays the role of a ghost field and is necessary for unambiguous Feynman rules. Consequently, the finite-temperature Lagrangian is different from the zero-temperature one and a new, discrete Z₂ symmetry arises. We discuss the functional formalism and spontaneous symmetry breakdown at finite temperature and also the possibility of spontaneous breakdown of the (thermal) Z₂ symmetry.     

Identification of extra neutral gauge bosons at the International Linear Collider

Heavy neutral gauge bosons, Z ^′s, are predicted by many theoretical schemes of physics beyond the Standard Model, and intensive searches for their signatures will be performed at present and future high energy colliders. It is quite possible that Z ^′s are heavy enough to lie beyond the discovery reach expected at the CERN Large Hadron Collider LHC, in which case only indirect signatures of Z ^′ exchanges may occur at future colliders, through deviations of the measured cross sections from the Standard Model predictions. We here discuss in this context the foreseeable sensitivity to Z ^′s of fermion-pair production cross sections at an e ⁺ e ^? linear collider, especially as regards the potential of distinguishing different Z ^′ models once such deviations are observed. Specifically, we assess the discovery and identification reaches on Z ^′ gauge bosons pertinent to the E ₆, LR, ALR and SSM classes of models, that should be attained at the planned International Linear Collider (ILC). With the high experimental accuracies expected at the ILC, the discovery and the identification reaches on the Z ^′ models under consideration could be increased substantially. In particular, the identification among the different models could be achieved for values of Z ^′ masses in the discovery (but beyond the identification) reach of the LHC. An important role in enhancing such reaches is played by the electron (and possibly the positron) longitudinally polarized beams. Also, although the purely leptonic processes are experimentally cleaner, the measurements of c- and b-quark pair production cross sections are found to carry important, and complementary, information on these searches.     

The decay of the vacuum in the field of superheavy nuclear systems

In the strong Coulomb field of a nucleus or quasimolecule withZ?172 a change of the QED vacuum has been predicted, signalled by the spontaneous emission of positrons if holes in theK-shell are available. The dynamical semiclassical theory of positron excitation in heavy ion scattering is presented and extended to collisions with nuclear contact. Interference patterns in the energy spectrum of the emitted positrons and, for sufficiently long reaction timeT, the emerging of a characteristic line at the position of the 1sσ-resonance is predicted. The position and width of the 1sσ-resonance is calculated in dependence on the nuclear configuration, the effect of electron screening is taken into account. Recent experimental indications [1, 2] for structures in the spectra of positrons emitted in U-U collisions at energies close to the Coulomb barrier are discussed in terms of spontaneous positron creation. The observed spectra could be explained under the assumption of long lasting nuclear reactions (T?4·10^?20 s) with a cross section in the millibarn region. Various consequences of this interpretation are discussed.     

Anomaly in the lattice partition function

The lattice partition function Z(T)=σ_(Si) exp(−H/k_BT), where H, k_B and T are the Hamiltonian of the system, the Boltzmann constant and the absolute temperature, respectively, leads to a vanishing spontaneous magnetisation for all temperatures, independently of the lattice considered. This feature is related to the symmetry breaking in these systems. In comparing this relation to the well-known partition function Z(T)=σ_n exp(−E_n/k_BT) where E_n is energy, we observe an incompatibility which could be the reason that this partition function leads to a vanishing spontaneous magnetisation.     

Z2 oscillation of mean charge states of fast Si and Cl ions after passage through thin foils

Z₂ (target atomic number) oscillation of equilibrium charge states has been observed for 30–110 MeV Si and 70 and 110 MeV Cl ions after the passage through 22 different Z₂ foils. This oscillation may be related to the Z₂ oscillation of electron capture cross sections into the projectile K vacancy.     

Z–Z' mixing effects in W boson pair production processes at hadron and lepton high-energy colliders

Potential possibilities to detect the effects of Z–Z' mixing in the W-pair production process in proton-proton and electron–positron collisions at the Large Hadron Collider (LHC) and International Linear Collider (ILC) have been studied. It has been established that the processes of W boson pair production are very sensitive to the angle of Z–Z' mixing and their measurements in current and future experiments will make it possible to improve modern restrictions on the angle of Z–Z' mixing in the models with extended gauge sector. At a nominal energy of 14 TeV and an integral luminosity of 100 fb^–1, the LHC collider can offer much more precise information on the parameter of Z–Z' mixing and the mass M ₂ than can be obtained using the ILC leptonic collider (0.5 TeV).     

Phenomenology of a four generation superstring model

We discuss the quark-lepton phenomenology of a superstring model compactified on aCP ⁴-based Calabi-Yau manifold defined by? _i Z _i ⁵ = 5 _c Z ₁ Z ₂ Z ₃ Z ₄ Z ₅ leading to four fermion generations using the Yukawa couplings calculated by us in a previous paper. We note that maintaining supersymmetry implies that forc?1, one of theU(1)-subgroup ofE ₆ must break at the Planck scale; on the other hand forc?10⁺⁴, an intermediate scale of about 10¹¹ GeV or 10¹⁴ GeV may be generated without destabilizing the gauge hierarchy. The model may have problems with fast proton decay for some choice ofc; however, understanding small neutrino masses remains a problem.     

An effective theory of a compositeZ

It is shown that the experimental value of sin² θ_w can be obtained if theZ is a bound state of two haplons provided that the haplons carry a new hypercolour quantum number in addition to colour. This approach also leads to the prediction that the electromagnetic couplings of theZ are substantially larger than they are in standard electroweak theory. It may be possible to observe these anomalous couplings in the processe ⁺ e ^? →Zγ at LEP 200 where theZ is longitudinally polarised.     

Mean field approach to finite temperature gauge systems

We apply a mean field treatment to theZ ₂ andZ ₃ gauge systems at finite temperature. In the lowest order the deconfinement of fixed electric charges is a second order transition forZ ₂ and a first order transition forZ ₃. Higher order corrections can be calculated using the steepest descent method.     

Coulomb Problem for <Emphasis Type="Italic">Z</Emphasis> &gt; Z<Subscript>cr</Subscript> in Doped Graphene

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Z_cr(J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z < Z_cr (J, n = 0), the energy of a level is presented as a function of charge Z for the lowest values of orbital angular momentum M, the level with J = 0 being the first to descend to the band edge. For Z>Z_cr (J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions ε₀ and widths γ of quasistationary states as a function of supercriticality. The values of ε₀* and width γ* are pointed out for which quasidiscrete levels may show up as Breit–Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Z_cr. In this single-particle approximation, there is no spontaneous creation of electron–hole pairs, and the impurity charge cannot be screened by this mechanism.     

Fragmentation of gold projectiles: From evaporation to total disassembly

We have studied the fragmentation of Au projectiles interacting with targets of C, Al and Cu at an incident energy ofE/A=600 MeV. The employed inverse kinematics allowed a nearly complete detection of projectile fragments with chargeZ≧2. The recorded fragmentation events were sorted according to three observables, the multiplicityM _lp of light charged particles, the largest atomic numberZ _max within an event, and a new observable,Z _bound, representing the sum of the atomic numbersZ of all fragments withZ≧2. Using these observables, the impact parameter dependence of the fragmentation process was investigated. For all three targets, a maximum mean multiplicity of 3 to 4 intermediate mass fragments (IMFs) is observed. The corresponding impact parameters range from central collisions for theC target to increasingly peripheral collisions for the heavier targets. It is found that the correlation between the IMF multiplicity andZ _bound, extending from evaporation type processes (largeZ _bound) to the total disassembly of the projectile (smallZ _bound), is independent of the target nucleus. This universal behaviour may suggest an — at least partial — equilibration of the projectile fragment prior to its decay.     

One-loop electro-weak corrections to three-jet observables of <Emphasis Type="Italic">b</Emphasis>-quarks <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilations

We compute the full one-loop EW contributions of \({\mathcal{O}}(\alpha_{\mathrm{S}}\alpha_{\mathrm{EM}}^{3})\) entering the electron–positron into two b-quarks and one gluon cross section at the Z peak and LC energies. We include both factorisable and non-factorisable virtual corrections, photon bremsstrahlung but not the real emission of W ^± and Z bosons. Their importance for the measurement of α _S from jet rates and shape variables is explained qualitatively and illustrated quantitatively. Their impact on the forward–backward asymmetry is also analysed.     

Der Zerfall des84Rb und die Fluoreszenzausbeute von Krypton

The electron capture decay and the positron decay of⁸⁴Rb were investigated using NaJ (Tl)-detectors and a Ge (Li)-detector. Measurements of all intensities and of some informative double and triple coincidences were performed. From coincidence measurements betweenK-X-radiation and the following γ-radiation we got theK-fluorescence yield of Krypton Ω_itK=0.653 ± 0.004. Taking in consideration former measurements¹ one concludes a continuous behaviour of Ω_itK(Z) forZ=36, 37 and 38 within an uncertainty of 1%. For the branching ratios of the decay of⁸⁴Rb we obtained The half-life of⁸⁴Rb was determined to beT _1/2=(34.5 ± 0.2) d.     

On physics beyond standard model

In this review we do not try to cover all the aspects of physics besnd tile standard model （BSM）, instead our latest understanding on tile BSM will be presented： i） Tile Higgs sector is likely related to BSM, which can be confirmed at current running large hadron collider （LHC） or tile fllture eolliders. Furthermore we pointed out that spontaneous CP violation can be closely related to the lightness of the Higgs boson, ii） Top quark forward-backward asymmetry, which was mea.sured by Tewttron, might be the sign of BSM.2; proposed a new color-octet particle Zcr to account fi）r the observation and Z can be fllrther studied at the LHC. iii） If dark matter （DM） is utilized to accommodate astrophysical obserwtions, it ought to be observed at the high energy LttC and DM produced at colliders should be tile slnoking gun signal, iv） Lithium puzzle might also be the sign of the BSM. We briefly review tile newly proposed solution to Lithium puzzle, i.e.. the existonce of non-thermal component during the big bang nuclei-synthesis （BBN）. The possible origins of the non-thermal coinponent can be dark matter or the new accelerating mechanism of normal particles.