Return probability: Exponential versus Gaussian decay

We analyze, both analytically and numerically, the time-dependence of the return probability in closed systems of interacting particles. Main attention is paid to the interplay between two regimes, one of which is characterized by the Gaussian decay of the return probability, and another one is the well known regime of the exponential decay. Our analytical estimates are confirmed by the numerical data obtained for two models with random interaction. In view of these results, we also briefly discuss the dynamical model which was recently proposed for the implementation of a quantum computation.Comment: 9 pages, 7 figures; revised version accepted for publicatio

Many-body corrections to the nuclear anapole moment II

The contribution of many-body effects to the nuclear anapole moment were studied earlier in [1]. Here, more accurate calculation of the many-body contributions is presented, which goes beyond the constant density approximation for them used in [1]. The effects of pairing are now included. The accuracy of the short range limit of the parity violating nuclear forces is discussed.Comment: 18 pages, LateX2e, 7 figure

Statistical Theory of Finite Fermi-Systems Based on the Structure of Chaotic Eigenstates

The approach is developed for the description of isolated Fermi-systems with finite number of particles, such as complex atoms, nuclei, atomic clusters etc. It is based on statistical properties of chaotic excited states which are formed by the interaction between particles. New type of ``microcanonical'' partition function is introduced and expressed in terms of the average shape of eigenstates $F(E_k,E)$ where $E$ is the total energy of the system. This partition function plays the same role as the canonical expression $exp(-E^{(i)}/T)$ for open systems in thermal bath. The approach allows to calculate mean values and non-diagonal matrix elements of different operators. In particular, the following problems have been considered: distribution of occupation numbers and its relevance to the canonical and Fermi-Dirac distributions; criteria of equilibrium and thermalization; thermodynamical equation of state and the meaning of temperature, entropy and heat capacity, increase of effective temperature due to the interaction. The problems of spreading widths and shape of the eigenstates are also studied.Comment: 17 pages in RevTex and 5 Postscript figures. Changes are RevTex format (instead of plain LaTeX), minor misprint corrections plus additional references. To appear in Phys. Rev.

Many Body Corrections to Nuclear Anapole Moment

The many body contributions to the nuclear anapole moment of $^{133}$Cs, $^{205}$Tl, $^{207,209}$PB, and $^{209}$Bi from the core polarization are calculated in the random-phase approximation with the effective residual interaction. Strong reduction of a valence nucleon contribution was found provided by the core polarization effects. The contribution of the core particles to the anapole moment compensates this reduction to large extent keeping the magnitude of nuclear anapole moment close to its initial single particle value.Comment: 14 pages, latex, no figures, ps-file available at http://www.inp.nsk.su/preprint/prep95.htm

Calculation of nuclear-spin-dependent parity nonconservation in s-d transitions of Ba+^+, Yb+^+ and Ra+^+ ions

We use correlation potential and many-body perturbation theory techniques to calculate spin-independent and nuclear spin-dependent parts of the parity nonconserving amplitudes of the transitions between the $6s_{1/2}$ ground state and the $5d_{3/2}$ excited state of Ba$^+$ and Yb$^+$ and between the $7s_{1/2}$ ground state and the $6d_{3/2}$ excited state of Ra$^+$. The results are presented in a form convenient for extracting of the constants of nuclear-spin-dependent interaction (such as, e.g., anapole moment) from the measurements.Comment: 9 pages, 8 tables, no figure

Nuclear Anapole Moments in Single Particle Approximation

Nuclear anapole moments of \;^{133}Cs, \;^{203,205}Tl, \;^{207}Pb, \;^{209}Bi are treated in the single-particle approximation. Analytical results are obtained for the oscillator potential without spin-orbit interaction. Then the anapole moments are calculated numerically in a Woods-Saxon potential which includes spin-orbit interaction. The results obtained demonstrate a remarkable stability of nuclear anapole moment calculations in the single-particle approximation.Comment: 20 pages, LateX, One figure available upon request, BINP-93-11

Schiff Theorem Revisited

We carefully rederive the Schiff theorem and prove that the usual expression of the Schiff moment operator is correct and should be applied for calculations of atomic electric dipole moments. The recently discussed corrections to the definition of the Schiff moment are absent.Comment: 6 page

Variation of fundamental constants in space and time: theory and observations

Review of recent works devoted to the temporal and spatial variation of the fundamental constants and dependence of the fundamental constants on the gravitational potential (violation of local position invariance) is presented. We discuss the variation of the fine structure constant $\alpha=e^2/\hbar c$, strong interaction and fundamental masses (Higgs vacuum), e.g. the electron-to-proton mass ratio $\mu=m_e/M_p$ or $X_e=m_e/\Lambda_{QCD}$ and $X_q=m_q/\Lambda_{QCD}$. We also present new results from Big Bang nucleosynthesis and Oklo natural nuclear reactor data and propose new measurements of enhanced effects in atoms, nuclei and molecules, both in quasar and laboratory spectra.Comment: Proceeding of ACFC, BadHonnef, 2007: to be published in EP

The nuclear Schiff moment and time invariance violation in atoms

Parity and time invariance violating (P,T-odd) nuclear forces produce P,T-odd nuclear moments. In turn, these moments can induce electric dipole moments (EDMs) in atoms through the mixing of electron wavefunctions of opposite parity. The nuclear EDM is screened by atomic electrons. The EDM of an atom with closed electron subshells is induced by the nuclear Schiff moment. Previously the interaction with the Schiff moment has been defined for a point-like nucleus. No problems arise with the calculation of the electron matrix element of this interaction as long as the electrons are considered to be non-relativistic. However, a more realistic model obviously involves a nucleus of finite-size and relativistic electrons. In this work we have calculated the finite nuclear-size and relativistic corrections to the Schiff moment. The relativistic corrections originate from the electron wavefunctions and are incorporated into a ``nuclear'' moment, which we term the local dipole moment. For mercury these corrections amount to about 25%. We have found that the natural generalization of the electrostatic potential of the Schiff moment for a finite-size nucleus corresponds to an electric field distribution which, inside the nucleus, is well approximated as constant and directed along the nuclear spin, and outside the nucleus is zero. Also in this work the plutonium atomic EDM is estimated.Comment: 16 pages, 1 figure, minor misprints correcte