Modern Physics Letters A

We give a formulation unifying the discussion of the spherical harmonics and the monopole harmonics. As a demonstration of the potency of this approach, we exhibit via this method a symmetry of the exchange of the quantum numbers m and q in the monopole harmonics.

The mixing of the photon with a hypothetical sterile paraphotonic state would have consequences on the cosmological propagation of photons. The absence of distortions in the optical spectrum of distant Type Ia supernovae allows to extend by two orders of magnitude the previous limit on the Lorentz-violating parameter δ associated to the photon–paraphoton transition, extracted from the absence of distortions in the spectrum of the cosmic microwave background. The new limit is consistent with the interpretation of the dimming of distant Type Ia supernovae as a consequence of a nonzero cosmological constant. Observations of gamma-rays from active galactic nuclei allow to further extend the limit on δ.

First we extract the long-distance (LD) weak matrix element <π|H_W|K> from K → 2π, K → 3π, K_L → 2γ, K⁺ → π⁺e⁺e^-, K⁺ → π⁺μ⁺ μ^- and K_L → μ⁺ μ^- data and give compatible theoretical estimates. We also link this LD scale to the single-quark-line (SQL) transition scale β_W and then test the latter SQL scale against the decuplet weak decay amplitude ratio <π^-Ξ⁰| H_W|Ω^->/<Ξ^- |H_W|Ω^->. Finally, we study LD K_S → 2γ decay. All of these experimental and theoretical values for <π|H_W|K> are in good agreement. We deduce an average value from 11 experimental determinations of <π|H_W|K> = (3.59 ± 0.05) × 10^-8GeV², while the theoretical SQL values average to (3.577 ± 0.004) × 10^-8GeV².

We calculate the equation of state of strongly coupled Hamiltonian lattice QCD at finite density by constructing a solution to the equation of motion corresponding to an effective Hamiltonian describing the ground state of the theory with Wilson fermions. To lowest order in N_c we find that the pressure of the quark Fermi sea can be negative indicating its mechanical instability. This new mean field result is in qualitative agreement with continuum models and should be verifiable by future numerical simulations.

Based on a relativistic mean field (RMF) framework, we analyze the BCS approximation to the relativistic Hartree–Bogoliubov (RHB) approach for the case of nuclei close to the drip line. In the BCS calculations the single particle continuum corresponding to RMF is replaced by a set of discrete positive energy states generated by enclosing the nucleus in a box. It is found that the main contribution to the pairing correlations for the neutron-rich nuclei is given by the low-lying resonant states, in addition to the contributions coming from the states close to the Fermi surface. Towards this end we present the results of our calculations for the entire chain of even–even ^48–98Ni isotopes. Results for the neutron-rich nucleus ⁸⁴Ni is discussed in detail as a prototype. A detailed comparison of our results for the nucleus ⁸⁴Ni with those obtained in similar studies using RHB, nonrelativistic Hartree–Fock–Bogoliubov (HFB), and a recently proposed resonant continuum HF+BCS method provides strong evidence for the applicability of the RMF+BCS approach for the treatment of neutron-rich nuclei as well. Additional results of extensive calculations for the isotopes of O, Ca, Zr, Sn and Pb nuclei further reinforce our conclusions. From amongst these calculations, the results of the even–even ^32–76Ca isotopes with two different RMF force parametrizations, and their agreement with the recent continuum relativistic Hartree–Bogoliubov (CRHB) results are discussed briefly for illustration purposes.

Vaidya–Tikekar²⁰ model has been generalised to describe cold compact stars having concentric layers of different phases. We illustrate the model by considering a star whose inner core has a deconfined quark phase, enveloped by less compact baryonic constituents.