Calculation of the positron bound state with the copper atom

A new relativistic method for calculation of positron binding to atoms is presented. The method combines a configuration interaction treatment of the valence electron and the positron with a many-body perturbation theory description of their interaction with the atomic core. We apply this method to positron binding by the copper atom and obtain the binding energy of 170 meV (+ - 10%). To check the accuracy of the method we use a similar approach to calculate the negative copper ion. The calculated electron affinity is 1.218 eV, in good agreement with the experimental value of 1.236 eV. The problem of convergence of positron-atom bound state calculations is investigated, and means to improve it are discussed. The relativistic character of the method and its satisfactory convergence make it a suitable tool for heavier atoms.Comment: 15 pages, 5 figures, RevTe

Multipositronic systems

The stability of Coulombic systems containing positrons are investigated by the stochastic variational method. The existence of several new exotic atoms are predicted, including HPse+, LiPs2e+, or (H-,Ps2). Similar systems (replacing the positrons by holes) might be observed in semiconductors.Comment: Phys. Rev. Lett., in pres

Nonlinear dynamics of a solid-state laser with injection

We analyze the dynamics of a solid-state laser driven by an injected sinusoidal field. For this type of laser, the cavity round-trip time is much shorter than its fluorescence time, yielding a dimensionless ratio of time scales $\sigma \ll 1$. Analytical criteria are derived for the existence, stability, and bifurcations of phase-locked states. We find three distinct unlocking mechanisms. First, if the dimensionless detuning $\Delta$ and injection strength $k$ are small in the sense that $k = O(\Delta) \ll \sigma^{1/2}$, unlocking occurs by a saddle-node infinite-period bifurcation. This is the classic unlocking mechanism governed by the Adler equation: after unlocking occurs, the phases of the drive and the laser drift apart monotonically. The second mechanism occurs if the detuning and the drive strength are large: $k =O(\Delta) \gg \sigma^{1/2}$. In this regime, unlocking is caused instead by a supercritical Hopf bifurcation, leading first to phase trapping and only then to phase drift as the drive is decreased. The third and most interesting mechanism occurs in the distinguished intermediate regime $k, \Delta = O(\sigma^{1/2})$. Here the system exhibits complicated, but nonchaotic, behavior. Furthermore, as the drive decreases below the unlocking threshold, numerical simulations predict a novel self-similar sequence of bifurcations whose details are not yet understood.Comment: 29 pages in revtex + 8 figs in eps. To appear in Phys. Rev. E (scheduled tentatively for the issue of 1 Oct 98

Monopoles near the Planck Scale and Unification

Considering our (3+1)-dimensional space-time as, in some way, discrete or l attice with a parameter $a=\lambda_P$, where $\lambda_P$ is the Planck length, we have investigated the additional contributions of lattice artifact monopoles to beta-functions of the renormalisation group equations for the running fine structure constants $\alpha_i(\mu)$ (i=1,2,3 correspond to the U(1), SU(2) and SU(3) gauge groups of the Standard Model) in the Family Replicated Gauge Group Model (FRGGM) which is an extension of the Standard Model at high energies. It was shown that monopoles have $N_{fam}$ times smaller magnetic charge in FRGGM than in SM ($N_{fam}$ is the number of families in FRGGM). We have estimated al so the enlargement of a number of fermions in FRGGM leading to the suppression of the asymptotic freedom in the non-Abelian theory. We have shown that, in contrast to the case of AntiGUT when the FRGGM undergoes the breakdown at $\mu=\mu_G\sim 10^{18}$ GeV, we have the possibility of unification if the FRGGM-breakdown occurs at $\mu_G\sim 10^{14}$ GeV. By numerical calculations we obtained an example of the unification of all gauge interactions (including gravity) at the scale $\mu_{GUT}\approx 10^{18.4}$ GeV. We discussed the possibility of $[SU(5)]^3$ or $[SO(10)]^3$ (SUSY or not SUSY) unifications.Comment: 49 pages, 7 figure