Next-to-next-leading order correction to 3-jet rate and event-shape distribution

The hadronic events from the e ⁺ e ⁻ annihilation data at the centre-of-mass energies ranging from 60 to 197 GeV were studied. The AMY and OPAL Collaborations offered a unique opportunity to test QCD by measuring the energy dependence of different observables. The coupling constant, α _s, was measured by two different methods: first by employing the three-jet observables. Combining all the data, the value of as at next-to-next leading order (NNLO) was determined to be 0.117 ± 0.004(hard) ± 0.006(theo). Secondly, from the event-shape distributions, the strong coupling constant, α _s, was extracted at NNLO and it’s evaluation was tested with the energy scale. The results were consistent with the running of α _s, expected from QCD predictions. Averaging over different observables, α _s was determined to be 0.115 ± 0.007(hard) ± 0.003(theo).     

Structural and optical properties of the M@C59X cages (X=N,B and M=Li,Na)

Using B3LYP/6-31G* density functional level of theory, the structural and optical properties of the C₆₀ and M@C₅₉X cages have been investigated. Results indicate that the charge on C atoms and band gap of C₆₀ cage are changed dramatically with the substitution of one B or N atom at one of the C sites and the Li and Na atom encapsulations in the C₆₀ cage. The Mulliken analyses show that the charge is transferred completely between the alkali atoms and the C₅₉X cage. The substitutional and encapsulation doping (SED) reduce the optical gaps of the C₆₀ cage. Also, the oscillator strengths of the absorption peaks are dependent on dopant types.