Properties of Fe, Ni and Zn isotope chains near the drip-line

The location of proton and neutron drip-lines and the characteristics of the neutron-deficient and the neutron-rich isotopes Fe, Ni and Zn on the basis of Hartree-Fock method with Skyrme forces (Ska, SkM*, Sly4) taking into account deformation was investigated. The calculations predict a big jump of deformation parameter up to β ~ 0.4 for Ni isotopes in the neighborhood of N ~ 62. The manifestation of magic numbers for isotopes ⁴⁸Ni, ⁵⁶Ni, ⁷⁸Ni and also for the stable isotope in the respect to neutron emission ¹¹⁰Ni which is situated beyond the neutron drip-line is discussed.На основі метода Хартрі-Фока з силами Скірма (Ska, SkM*, Sly4) при врахуванні деформації досліджено положення протонної і нейтронної границі стабільності і характеристики нейтронодефіцітних і нейтрононадлишкових изотопів Fe, Ni и Zn. Розрахунки зазбачають, що для изотопів Ni в околі N ~ 62 спостерігається великий стрибок величини параметра деформації до β ~ 0.4. Обговорюються прояви магічних чисел для изотопів нікеля ⁴⁸Ni, ⁵⁶Ni, ⁷⁸Ni, а також для нейтроностабільного изотопа ¹¹⁰Ni , який знаходиться за межами границі стабильності.На основе метода Хартри-Фока с силами Скирма (Ska, SkM*, Sly4) при учете деформации исследовано положение протонной и нейтронной границы стабильности и характеристики нейтронодефицитных и нейтроноизбыточных изотопов Fe, Ni и Zn. Расчеты предсказывают, что для изотопов Ni в окрестности N ~ 62 наблюдается большой скачок величины параметра деформации до β ~ 0.4. Обсуждается проявление магических чисел для изотопов никеля ⁴⁸Ni, ⁵⁶Ni, ⁷⁸Ni, а также для нейтроностабильного изотопа ¹¹⁰Ni, который находится за пределами границы стабильности

Hadronic τ\tau decay, the renormalization group, analiticity of the polarization operators and QCD parameters

The ALEPH data on hadronic tau-decay is throughly analysed in the framework of QCD. The perturbative calculations are performed in 1-4-loop approximation. The analytical properties of the polarization operators are used in the whole complex q^2 plane. It is shown that the QCD prediction for R_{tau} agrees with the measured value R_{tau} not only for conventional Lambda^{conv}_3 = (618+-29) MeV but as well as for Lambda^{new}_3 = (1666+-7) MeV. The polarization operator calculated using the renormgroup has nonphysical cut [-Lambda^2_3, 0]. If Lambda_3 = Lambda^{conv}_3, the contribution of only physical cut is deficient in the explanation of the ALEPH experiment. If Lambda_3 = Lambda^{new}_3 the contribution of nonphysical cut is very small and only the physical cut explains the ALEPH experiment. The new sum rules which follow only from analytical properties of polarization operators are obtained. Basing on the sum rules obtained, it is shown that there is an essential disagreement between QCD perturbation theory and the tau-lepton hadronic decay experiment at conventional value Lambda_3. In the evolution upwards to larger energies the matching of r(q^2) (Eq.(12)) at the masses J/psi, Upsilon and 2m_t was performed. The obtained value alpha_s(-m^2_z) = 0.141+-0.004 (at Lambda_3 = Lambda^{new}_3) differs essentially from conventional value, but the calculation of the values R(s) = sigma(e+e- -> hadrons)/sigma(e+e- -> mu+mu-), R_l = Gamma(Z -> hadrons)/Gamma(Z -> leptons), alpha_s(-3 GeV^2), alpha_s(-2.5 GeV^2) does not contradict the experiments.Comment: 20 page

The check of QCD based on the tau-decay data analysis in the complex q^2-plane

The thorough analysis of the ALEPH data on hadronic tau-decay is performed in the framework of QCD. The perturbative calculations are performed in 3 and 4-loop approximations. The terms of the operator product expansion (OPE) are accounted up to dimension D=8. The value of the QCD coupling constant alpha_s(m_tau^2)=0.355 pm 0.025 was found from hadronic branching ratio R_tau. The V+A and V spectral function are analyzed using analytical properties of polarization operators in the whole complex q^2-plane. Borel sum rules in the complex q^2 plane along the rays, starting from the origin, are used. It was demonstrated that QCD with OPE terms is in agreement with the data for the coupling constant close to the lower error edge alpha_s(m_tau^2)=0.330. The restriction on the value of the gluonic condensate was found =0.006 pm 0.012 GeV^2. The analytical perturbative QCD was compared with the data. It is demonstrated to be in strong contradiction with experiment. The restrictions on the renormalon contribution were found. The instanton contributions to the polarization operator are analyzed in various sum rules. In Borel transformation they appear to be small, but not in spectral moments sum rules.Comment: 24 pages; 1 latex + 13 figure files. V2: misprints are corrected, uncertainty in alpha_s is explained in more transparent way, acknowledgement is adde

On the Behavior of the Effective QCD Coupling alpha_tau(s) at Low Scales

The hadronic decays of the tau lepton can be used to determine the effective charge alpha_tau(m^2_tau') for a hypothetical tau-lepton with mass in the range 0 < m_tau' < m_tau. This definition provides a fundamental definition of the QCD coupling at low mass scales. We study the behavior of alpha_tau at low mass scales directly from first principles and without any renormalization-scheme dependence by looking at the experimental data from the OPAL Collaboration. The results are consistent with the freezing of the physical coupling at mass scales s = m^2_tau' of order 1 GeV^2 with a magnitude alpha_tau ~ 0.9 +/- 0.1.Comment: 15 pages, 4 figures, submitted to Physical Review D, added references, some text added, no results nor figures change