Collective T- and P- Odd Electromagnetic Moments in Nuclei with Octupole Deformations

Parity and time invariance violating forces produce collective P- and T- odd moments in nuclei with static octupole deformation. Collective Schiff moment, electric octupole and dipole and also magnetic quadrupole appear due to the mixing of rotational levels of opposite parity and can exceed single-particle moments by more than a factor of 100. This enhancement is due to two factors, the collective nature of the intrinsic moments and the small energy separation between members of parity doublets. The above moments induce T- and P- odd effects in atoms and molecules. Experiments with such systems may improve substantially the limits on time reversal violation.Comment: 9 pages, Revte

Enhanced T-odd P-odd Electromagnetic Moments in Reflection Asymmetric Nuclei

Collective P- and T- odd moments produced by parity and time invariance violating forces in reflection asymmetric nuclei are considered. The enhanced collective Schiff, electric dipole and octupole moments appear due to the mixing of rotational levels of opposite parity. These moments can exceed single-particle moments by more than two orders of magnitude. The enhancement is due to the collective nature of the intrinsic moments and the small energy separation between members of parity doublets. In turn these nuclear moments induce enhanced T- and P- odd effects in atoms and molecules. First a simple estimate is given and then a detailed theoretical treatment of the collective T-, P- odd electric moments in reflection asymmetric, odd-mass nuclei is presented and various corrections evaluated. Calculations are performed for octupole deformed long-lived odd-mass isotopes of Rn, Fr, Ra, Ac and Pa and the corresponding atoms. Experiments with such atoms may improve substantially the limits on time reversal violation.Comment: 28 pages, Revte

Parity Doubles in Quark Physics

There are numerous examples of very nearly degenerate states of opposite parity in molecular physics. The ammonia maser is based on one such double. Theory shows that these parity doubles can occur if the nuclear shape in the molecule is reflection-asymmetric because the time scales of the shape and the electronic cloud are well-separated. Parity doubles occur in nuclear physics as well for odd $A \sim 219-229$. We discuss the theoretical foundation of these doubles and on that basis suggest that parity doubles should occur in particle physics too. In particular they should occur among baryons composed of $cbu$ and $cbd$ quarks.Comment: minor changes made; to appear in Phys.Rev.Let

Nearby Doorways, Parity Doublets and Parity Mixing in Compound Nuclear States

We discuss the implications of a doorway state model for parity mixing in compound nuclear states. We argue that in order to explain the tendency of parity violating asymmetries measured in $^{233}$Th to have a common sign, doorways that contribute to parity mixing must be found in the same energy neighbourhood of the measured resonance. The mechanism of parity mixing in this case of nearby doorways is closely related to the intermediate structure observed in nuclear reactions in which compound states are excited. We note that in the region of interest ($^{233}$Th) nuclei exhibit octupole deformations which leads to the existence of nearby parity doublets. These parity doublets are then used as doorways in a model for parity mixing. The contribution of such mechanism is estimated in a simple model.Comment: 11 pages, REVTE

Nuclear Octupole Correlations and the Enhancement of Atomic Time-Reversal Violation

We examine the time-reversal-violating nuclear ``Schiff moment'' that induces electric dipole moments in atoms. After presenting a self-contained derivation of the form of the Schiff operator, we show that the distribution of Schiff strength, an important ingredient in the ground-state Schiff moment, is very different from the electric-dipole-strength distribution, with the Schiff moment receiving no strength from the giant dipole resonance in the Goldhaber-Teller model. We then present shell-model calculations in light nuclei that confirm the negligible role of the dipole resonance and show the Schiff strength to be strongly correlated with low-lying octupole strength. Next, we turn to heavy nuclei, examining recent arguments for the strong enhancement of Schiff moments in octupole-deformed nuclei over that of 199Hg, for example. We concur that there is a significant enhancement while pointing to effects neglected in previous work (both in the octupole-deformed nuclides and 199Hg) that may reduce it somewhat, and emphasizing the need for microscopic calculations to resolve the issue. Finally, we show that static octupole deformation is not essential for the development of collective Schiff moments; nuclei with strong octupole vibrations have them as well, and some could be exploited by experiment.Comment: 25 pages, 4 figures embedded in tex

Time invariance violating nuclear electric octupole moments

The existence of a nuclear electric octupole moment (EOM) requires both parity and time invariance violation. The EOMs of odd $Z$ nuclei that are induced by a particular T- and P-odd interaction are calculated. We compare such octupole moments with the collective EOMs that can occur in nuclei having a static octupole deformation. A nuclear EOM can induce a parity and time invariance violating atomic electric dipole moment, and the magnitude of this effect is calculated. The contribution of a nuclear EOM to such a dipole moment is found, in most cases, to be smaller than that of other mechanisms of atomic electric dipole moment production.Comment: Uses RevTex, 25 page

Gamow-Teller Strength in the Region of 100^{100}Sn

New calculations are presented for Gamow-Teller beta decay of nuclei near $^{100}$Sn. Essentially all of the $^{100}$Sn Gamow-Teller decay strength is predicted to go to a single state at an excitation energy of 1.8 MeV in $^{100}$In. The first calculations are presented for the decays of neighboring odd-even and odd-odd nuclei which show, in contrast to $^{100}$Sn, surprisingly complex and broad Gamow-Teller strength distributions. The results are compared to existing experimental data and the resulting hindrance factors are discussed.Comment: 12 pages (latex) and 2 figures available on reques

Staggering effects in nuclear and molecular spectra

It is shown that the recently observed Delta J = 2 staggering effect (i.e. the relative displacement of the levels with angular momenta J, J+4, J+8, ..., relatively to the levels with angular momenta J+2, J+6, J+10, ...) seen in superdeformed nuclear bands is also occurring in certain electronically excited rotational bands of diatomic molecules (YD, CrD, CrH, CoH), in which it is attributed to interband interactions (bandcrossings). In addition, the Delta J = 1 staggering effect (i.e. the relative displacement of the levels with even angular momentum J with respect to the levels of the same band with odd J) is studied in molecular bands free from Delta J = 2 staggering (i.e. free from interband interactions/bandcrossings). Bands of YD offer evidence for the absence of any Delta J = 1 staggering effect due to the disparity of nuclear masses, while bands of sextet electronic states of CrD demonstrate that Delta J = 1 staggering is a sensitive probe of deviations from rotational behaviour, due in this particular case to the spin-rotation and spin-spin interactions.Comment: LaTeX, 16 pages plus 30 figures given in separate .ps files. To appear in the proceedings of the 4th European Workshop on Quantum Systems in Chemistry and Physics (Marly-le-Roi, France, 1999), ed. J. Maruani et al. (Kluwer, Dordrecht

Photometric Monitoring of Open Clusters I. The Survey

Open clusters, which have age, abundance, and extinction information from studies of main-sequence turn off stars, are the ideal location in which to determine the mass-luminosity-radius relation for low-mass stars. We have undertaken a photometric monitoring survey of open clusters in the Galaxy designed to detect low-mass eclipsing binary systems through variations in their relative light curves. Our aim is to provide an improved calibration of the mass-luminosity-radius relation for low-mass stars and brown dwarfs, to test stellar structure and evolution models, and to help quantify the contribution of low-mass stars to the global mass census in the Galaxy. In this paper we present our survey, describing the data and outlining the analysis techniques. We study six nearby open clusters, with a range of ages from $\sim 0.2$ to 4 Gyr and metallicities from approximately solar to -0.2dex. We monitor a field-of-view of > 1 square degree per target cluster, well beyond the characteristic cluster radius, over timescales of hours, days, and months with a sampling rate optimised for the detection of eclipsing binaries with periods of hours to days. Our survey depth is designed to detect eclipse events in a binary with a primary star of \lesssim 0.3~M_{\sun}. Our data have a photometric precision of $\sim 3$ mmag at $I\approx 16$.Comment: 50 pages, 18 figures, accepted for publication in A

Systematic Construction of Nonlinear Product Attacks on Block Ciphers

A major open problem in block cipher cryptanalysis is discovery of new invariant properties of complex type. Recent papers show that this can be achieved for SCREAM, Midori64, MANTIS-4, T-310 or for DES with modified S-boxes. Until now such attacks are hard to find and seem to happen by some sort of incredible coincidence. In this paper we abstract the attack from any particular block cipher. We study these attacks in terms of transformations on multivariate polynomials. We shall demonstrate how numerous variables including key variables may sometimes be eliminated and at the end two very complex Boolean polynomials will become equal. We present a general construction of an attack where multiply all the polynomials lying on one or several cycles. Then under suitable conditions the non-linear functions involved will be eliminated totally. We obtain a periodic invariant property holding for any number of rounds. A major difficulty with invariant attacks is that they typically work only for some keys. In T-310 our attack works for any key and also in spite of the presence of round constants