We propose a new texture for the light neutrino mass matrix. The proposal is based upon imposing zerotrace condition on the two by two sub-matrices of the complex symmetric Majorana mass matrix in the flavor basis where the charged lepton mass matrix is diagonal. Restricting the mass matrix to have two traceless sub-matrices may be found sufficient to describe the current data. Eight out of fifteen independent possible cases are found to be compatible with current data. Numerical and some approximate analytical results are presented.

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We use a power-series expansion to calculate the eigenvalues of anharmonic oscillators bounded by two infinite walls. We show that for large finite values of the separation of the walls, the calculated eigenvalues are of the same high accuracy as the values recently obtained for the unbounded case by the inner-product quantization method. We also apply our method to the Morse potential. The eigenvalues obtained in this case are in excellent agreement with the exact values for the unbounded Morse potential.

A numerical method of high precision is used to calculate the energy eigenvalues and eigenfunctions for a symmetric double-well potential. The method is based on enclosing the system within two infinite walls with a large but finite separation and developing a power series solution for the Schrödinger equation. The obtained numerical results are compared with those obtained on the basis of the Zinn-Justin conjecture and found to be in an excellent agreement.

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We show that for the triple well potential with non-equivalent vacua, instantons generate for the low lying energy states a singlet and a doublet of states rather than a triplet of equal energy spacing. Our energy splitting formulas are also confirmed numerically. This splitting property is due to the presence of non-equivalent vacua. A comment on its generality to multi-well is presented.Instantons are non-trivial classical solutions of Euclidean field equations for which the action is finite. 1 Their importance, besides being topological configurations, comes from their finite contributions to Feynman path integral. In quantum mechanics instantons correspond to non-trivial finite classical solutions of classical equations of motion with inverted potential. 2 The uses of instanton calculations have proven to be useful in analyzing nonperturbative aspects of quantum mechanical systems with degenerate vacua, this is because instanton solutions contribute to the quantum tunnelling phenomena, which can be calculated with the aid of the dilute gas approximation. A celebrated example is the splitting of energy level in the symmetric double well case. 2 To our knowledge only a few recent papers attempted to apply the instanton method to the triple well potential with non-equivalent vacua. 3-5 This problem is rather involved compared to the symmetric double well case. It has been suspected that in the presence of non-equivalent vacua the dilute gas approximation may break down. 5 Moreover, it has been claimed 3,4 that the average of the harmonic frequencies over the non-equivalent vacua of the potential serves as the central § Corresponding author 2103 Mod. Phys. Lett. A 2004Lett. A .19:2103Lett. A -2112. Downloaded from www.worldscientific.com by UNIVERSITY OF BRITISH COLUMBIA on 10/24/12. For personal use only.

Strong decay constants of the heavy tensor to heavy pseudoscalar (vector) and light pseudoscalar mesons are estimated within the light cone QCD sum rules. It is observed that the values of these coupling constants show a significant dependence on the choice of the Lorentz structure. Additionally, the decay widths of these mesons are calculated and discussed within the light of experimental data. A comparison of our results on these coupling constants with the predictions from the 3-point sum rules is performed.

A modified version of the previously proposed exponential model with pairing attenuation for the well deformed even-even nuclei has been applied to predict the energy levels of doubly even actinide nuclei. Satisfactory results are obtained by that model as compared with the experimental results. The backbending phenomena are successfully described and discussed. A further comparison with the main previous models has been undertaken to confirm its validity in the heavy nuclei region.