Exact solutions of the radial Schrodinger equation for some physical potentials

By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrodinger equation for the pseudoharmonic and Kratzer potentials in two dimensions. The energy levels of all the bound states are easily calculated from this eigenfunction ansatz. The normalized wavefunctions are also obtained.Comment: 13 page

Electron spin relaxation by nuclei in semiconductor quantum dots

We have studied theoretically the electron spin relaxation in semiconductor quantum dots via interaction with nuclear spins. The relaxation is shown to be determined by three processes: (i) -- the precession of the electron spin in the hyperfine field of the frozen fluctuation of the nuclear spins; (ii) -- the precession of the nuclear spins in the hyperfine field of the electron; and (iii) -- the precession of the nuclear spin in the dipole field of its nuclear neighbors. In external magnetic fields the relaxation of electron spins directed along the magnetic field is suppressed. Electron spins directed transverse to the magnetic field relax completely in a time on the order of the precession period of its spin in the field of the frozen fluctuation of the nuclear spins. Comparison with experiment shows that the hyperfine interaction with nuclei may be the dominant mechanism of electron spin relaxation in quantum dots

Exponential Metric Fields

The Laser Interferometer Space Antenna (LISA) mission will use advanced technologies to achieve its science goals: the direct detection of gravitational waves, the observation of signals from compact (small and dense) stars as they spiral into black holes, the study of the role of massive black holes in galaxy evolution, the search for gravitational wave emission from the early Universe. The gravitational red-shift, the advance of the perihelion of Mercury, deflection of light and the time delay of radar signals are the classical tests in the first order of General Relativity (GR). However, LISA can possibly test Einstein's theories in the second order and perhaps, it will show some particular feature of non-linearity of gravitational interaction. In the present work we are seeking a method to construct theoretical templates that limit in the first order the tensorial structure of some metric fields, thus the non-linear terms are given by exponential functions of gravitational strength. The Newtonian limit obtained here, in the first order, is equivalent to GR.Comment: Accepted for publication in Astrophysics and Space Science, 17 page

Deviation of Neutrino Mixing from Bi-maximal

We have studied how observables of the neutrino mixing matrix can link up with the ones in the quark sector. The deviation from the bi-maximal flavor mixing is parameterized using a 3 x 3 unitary matrix. The neutrino mixings are investigated supposing this unitary matrix to be hierarchical like the quark mixing matrix. We obtain the remarkable prediction |U_{e3}| >= 0.03 from the experimentally allowed range tan^2 theta_{sol} = 0.24 ~ 0.89. The CP violation in neutrino oscillations is expected to be very small.Comment: Some references are adde

Possible Flavor Mixing Structures of Lepton Mass Matrices

To search for possible textures of lepton mass matrices, we systematically examine flavor mixing structures which can lead to large lepton mixing angles. We find out 37 mixing patterns are consistent with experimental data, taking into account phase factors in the mixing matrices. Only six of the patterns can explain the observed data without any tuning of parameters, while the others need particular choices for the phase values. It is found that these six mixing patterns are those predicted by the models which have been proposed to account for fermion mass hierarchies. On the other hand, the others may give new flavor mixing structures of lepton mass matrices and therefore new possibilities of model construction.Comment: 21 page

Lepton Flavor Violating Process in Bi-maximal texture of Neutrino Mixings

We investigate the lepton flavor violation in the framework of the MSSM with right-handed neutrinos taking the large mixing angle MSW solution in the quasi-degenerate and the inverse-hierarchical neutrino masses. We predict the branching ratio of $\mu \to e+\gamma$ and $\tau \to \mu+\gamma$ processes assuming the degenerate right-handed Majorana neutrino masses. We find that the branching ratio in the quasi-degenerate neutrino mass spectrum is 100 times smaller than the ones in the inverse-hierarchical and the hierarchical neutrino spectra. We emphasize that the magnitude of $U_{e3}$ is one of important ingredients to predict BR($\mu \to e +\gamma$). The effect of the deviation from the complete-degenerate right-handed Majorana neutrino masses are also estimated. Furtheremore, we examine the S_{3\sL}\times S_{3\sR} model, which gives the quasi-degenerate neutrino masses, and the Shafi-Tavartkiladze model, which gives the inverse-hierarchical neutrino masses. Both predicted branching ratios of $\mu\to e+\gamma$ are smaller than the experimantal bound.Comment: Latex file, 38 pages, 10 figures, revised versio

Bound state solutions of the Dirac-Rosen-Morse potential with spin and pseudospin symmetry

The energy spectra and the corresponding two- component spinor wavefunctions of the Dirac equation for the Rosen-Morse potential with spin and pseudospin symmetry are obtained. The $s-$wave ($\kappa = 0$ state) solutions for this problem are obtained by using the basic concept of the supersymmetric quantum mechanics approach and function analysis (standard approach) in the calculations. Under the spin symmetry and pseudospin symmetry, the energy equation and the corresponding two-component spinor wavefunctions for this potential and other special types of this potential are obtained. Extension of this result to $\kappa \neq 0$ state is suggested.Comment: 18 page

Status of a Supersymmetric Flavour Violating Solution to the Solar Neutrino Puzzle with Three Generations

We present a general study of a three neutrino flavour transition model based on the supersymmetric interactions which violate R-parity. These interactions induce flavour violating scattering reactions between solar matter and neutrinos. The model does not contain any vacuum mass or mixing angle for the first generation neutrino. Instead, the effective mixing in the first generation is induced via the new interactions. The model provides a natural interpretation of the atmospheric neutrino anomaly, and is consistent with reactor experiments. We determine all R-parity violating couplings which can contribute to the effective neutrino oscillations, and summarize the present laboratory bounds. Independent of the specific nature of the (supersymmetric) flavour violating model, the experimental data on the solar neutrino rates and the recoil electron energy spectrum are inconsistent with the theoretical predictions. The confidence level of the $\chi^2$-analysis ranges between $\sim 10^{-4}$ and $\sim 10^{-3}$. The incompatibility, is due to the new SNO results, and excludes the present model. We conclude that a non-vanishing vacuum mixing angle for the first generation neutrino is necessary in our model. We expect this also to apply to the solutions based on other flavour violating interactions having constraints of the same order of magnitude.Comment: 17 pages, Latex fil

Is prenatal diet associated with the composition of the vaginal microbiome?

Background: The vaginal microbiome has been associated with adverse pregnancy outcomes, but information on the impact of diet on microbiome composition is largely unexamined. Objective: To estimate the association between prenatal diet and vaginal microbiota composition overall and by race. Methods: We leveraged a racially diverse prenatal cohort of North Carolina women enrolled between 1995 and 2001 to conduct this analysis using cross-sectional data. Women completed food frequency questionnaires about diet in the previous 3 months and foods were categorised into subgroups: fruits, vegetables, nuts/seeds, whole grains, low-fat dairy, sweetened beverages and red meat. We additionally assessed dietary vitamin D, fibre and yogurt consumption. Stored vaginal swabs collected in mid-pregnancy were sequenced using 16S taxonomic profiling. Women were categorised into three groups based on predominance of species: Lactobacillus iners, Lactobacillus miscellaneous and Bacterial Vaginosis (BV)-associated bacteria. Adjusted Poisson models with robust variance estimators were run to assess the risk of being in a specific vagitype compared to the referent. Race-stratified models (Black/White) were also run. Results: In this study of 634 women, higher consumption of dairy was associated with increased likelihood of membership in the L. crispatus group compared to the L. iners group in a dose-dependent manner (risk ratio quartile 4 vs. 1: 2.01, 95% confidence interval 1.36, 2.95). Increased intake of fruit, vitamin D, fibre and yogurt was also associated with increased likelihood of membership in L. crispatus compared to L. iners, but only among black women. Statistical heterogeneity was only detected for fibre intake. There were no detected associations between any other food groups or risk of membership in the BV group. Conclusions: Higher consumption of low-fat dairy was associated with increased likelihood of membership in a beneficial vagitype, potentially driven by probiotics