Comparison of big event with calculations of the air shower development

The incidence of high energy hadrons and electron-photons in air showers at various stages of development is calculated. Numerical calculation is used to solve the diffusion equation for a nuclear cascade and analytical calculation for cascade shower induced gamma rays. From these calculations, one can get the longitudinal development of the high energy hadron and electron-photon components, and the energy spectra of these components at various depths of air shower development. The total number of hadrons (N sub H) and electron-photon components (N sub gamma) are related according to stages of the air shower development and primary energy. The relation of the total energy of hadron and electron-photon component above the threshold energy is given. The energy balance between both components is also a useful parameter to study high energy events accompanying air showers. The relation of N sub H and fractional hadronic energy E (sum E sub H sup gamma/sum E sub H sup gamma + Sum E sub gamma) is calculated. This relation is helpful to understand the stage of air shower development(t) and primary energy (E sub p)

Anisotropic spin fluctuations and multiple superconducting gaps in hole-doped Ba_0.7K_0.3Fe_2As_2: NMR in a single crystal

We report the first ^{75}As-NMR study on a single crystal of the hole-doped iron-pnictide superconductor Ba_{0.7}K_{0.3}Fe_2As_{2} (T_c = 31.5 K). We find that the Fe antiferromagnetic spin fluctuations are anisotropic and are weaker compared to underdoped copper-oxides or cobalt-oxide superconductors. The spin lattice relaxation rate 1/T_1 decreases below T_c with no coherence peak and shows a step-wise variation at low temperatures, which is indicative of multiple superconducting gaps, as in the electron-doped Pr(La)FeAsO$_{1-x}$F$_{x}$. Furthermore, no evidence was obtained for a microscopic coexistence of a long-range magnetic and superconductivity

Pressure-induced unconventional superconductivity near a quantum critical point in CaFe2As2

75As-zero-field nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements are performed on CaFe2As2 under pressure. At P = 4.7 and 10.8 kbar, the temperature dependences of nuclear-spin-lattice relaxation rate (1/T1) measured in the tetragonal phase show no coherence peak just below Tc(P) and decrease with decreasing temperature. The superconductivity is gapless at P = 4.7 kbar but evolves to that with multiple gaps at P = 10.8 kbar. We find that the superconductivity appears near a quantum critical point under pressures in the range 4.7 kbar < P < 10.8 kbar. Both electron correlation and superconductivity disappear in the collapsed tetragonal phase. A systematic study under pressure indicates that electron correlations play a vital role in forming Cooper pairs in this compound.Comment: 5pages, 5figure

Hydration-induced anisotropic spin fluctuations in Na_{x}CoO_{2}\cdot1.3H_{2}O superconductor

We report ^{59}Co NMR studies in single crystals of cobalt oxide superconductor Na_{0.42}CoO_{2}\cdot1.3H_{2}O (T_c=4.25K) and its parent compound Na_{0.42}CoO_{2}. We find that both the magnitude and the temperature (T) dependence of the Knight shifts are identical in the two compounds above T_c. The spin-lattice relaxation rate (1/T_1) is also identical above T_0 \sim60 K for both compounds. Below T_0, the unhydrated sample is found to be a non-correlated metal that well conforms to Fermi liquid theory, while spin fluctuations develop in the superconductor. These results indicate that water intercalation does not change the density of states but its primary role is to bring about spin fluctuations. Our result shows that, in the hydrated superconducting compound, the in-plane spin fluctuation around finite wave vector is much stronger than that along the c-axis, which indicates that the spin correlation is quasi-two-dimensional.Comment: 4 pages, 5 figure

Na content dependence of superconductivity and the spin correlations in Na_{x}CoO_{2}\cdot 1.3H_{2}O

We report systematic measurements using the ^{59}Co nuclear quadrupole resonance(NQR) technique on the cobalt oxide superconductors Na_{x}CoO_{2}\cdot 1.3H_{2}O over a wide Na content range x=0.25\sim 0.34. We find that T_c increases with decreasing x but reaches to a plateau for x \leq0.28. In the sample with x \sim 0.26, the spin-lattice relaxation rate 1/T_1 shows a T^3 variation below T_c and down to T\sim T_c/6, which unambiguously indicates the presence of line nodes in the superconducting (SC) gap function. However, for larger or smaller x, 1/T_1 deviates from the T^3 variation below T\sim 2 K even though the T_c (\sim 4.7 K) is similar, which suggests an unusual evolution of the SC state. In the normal state, the spin correlations at a finite wave vector become stronger upon decreasing x, and the density of states at the Fermi level increases with decreasing x, which can be understood in terms of a single-orbital picture suggested on the basis of LDA calculation.Comment: version published in J. Phys. Condens. Matter (references updated and more added

59-Co and 75-As NMR Investigation of Electron-Doped High Tc Superconductor BaFe(1.8)Co(0.2)As(2) (Tc = 22K)

We report an NMR investigation of the superconductivity in BaFe(2)As(2) induced by Co doping (Tc=22K). We demonstrate that Co atoms form an alloy with Fe atoms and donate carriers without creating localized moments. Our finding strongly suggests that the underlying physics of iron-pnictide superconductors is quite different from the widely accepted physical picture of high Tc cuprates as doped Mott insulators. We also show a crossover of electronic properties into a low temperature pseudo-gap phase with a pseudo-gap Delta 560K, where chi(spin) constant and resisitivty T. The NMR Knight shift below Tc decreases for both along the c-axis and ab-plane, and is consistent with the singlet pairing scenario.Comment: Accepted for publication in J. Phys. Soc. Jpn. (4 pages

Evidence for Unconventional Superconductivity in Arsenic-Free Iron-Based Superconductor FeSe : A ^77Se-NMR Study

We report the results of $^{77}$Se--nuclear magnetic resonance (NMR) in $\alpha$-FeSe, which exhibits a similar crystal structure to the LaFeAsO$_{1-x}$F$_x$ superconductor and shows superconductivity at 8 K. The nuclear-spin lattice relaxation rate $1/T_1$ shows $T^3$ behavior below the superconducting transition temperature $T_c$ without a coherence peak. The $T_1T=$ const. behavior, indicative of the Fermi liquid state, can be seen in a wide temperature range above $T_c$. The superconductivity in $\alpha$-FeSe is also an unconventional one as well as LaFeAsO$_{1-x}$F$_x$ and related materials. The FeAs layer is not essential for the occurrence of the unconventional superconductivity.Comment: 4pages, 4figures, to be published in J. Phys. Soc. Jpn. 77 No.11 (2008

Magnetism and Superconductivity in the Two-Dimensional 16 Band d-p Model for Iron-Based Superconductors

The electronic states of the Fe2As2 plane in iron-based superconductors are investigated on the basis of the two-dimensional 16-band d-p model which includes the Coulomb interaction on a Fe site: the intra- and inter-orbital direct terms U and U', the Hund's coupling J and the pair-transfer J'. Using the random phase approximation (RPA), we obtain the magnetic phase diagram including the stripe and the incommensurate order on the U'-J plane. We also solve the superconducting gap equation within the RPA and find that, for large J, the most favorable pairing symmetry is extended s-wave whose order parameter changes its sign between the hole pockets and the electron pockets, while it is dxy-wave for small J.Comment: 4 pages, 5 figure

Selfsimilar solutions in a sector for a quasilinear parabolic equation

We study a two-point free boundary problem in a sector for a quasilinear parabolic equation. The boundary conditions are assumed to be spatially and temporally "self-similar" in a special way. We prove the existence, uniqueness and asymptotic stability of an expanding solution which is self-similar at discrete times. We also study the existence and uniqueness of a shrinking solution which is self-similar at discrete times.Comment: 23 page

Spin Fluctuations and Unconventional Superconductivity in the Fe-based Oxypnictide Superconductor LaFeAsO_0.7 probed by 57Fe-NMR

We report $^{57}$Fe-NMR studies on the oxygen-deficient iron (Fe)-based oxypnictide superconductor LaFeAsO$_{0.7}$ ($T_{c}=$ 28 K) enriched by $^{57}$Fe isotope. In the superconducting state, the spin component of $^{57}$Fe-Knight shift $^{57}K$ decreases almost to zero at low temperatures and the nuclear spin-lattice relaxation rate $^{57}(1/T_{1})$ exhibits a $T^{3}$-like dependence without the coherence peak just below $T_{c}$, which give firm evidence of the unconventional superconducting state formed by spin-singlet Cooper pairing. All these events below $T_c$ are consistently argued in terms of the extended s$_{\pm}$-wave pairing with a sign reversal of the order parameter among Fermi surfaces. In the normal state, we found the remarkable decrease of $1/T_1T$ upon cooling for both the Fe and As sites, which originates from the decrease of low-energy spectral weight of spin fluctuations over whole ${\bm q}$ space upon cooling below room temperature. Such behavior has never been observed for other strongly correlated superconductors where an antiferromagnetic interaction plays a vital role in mediating the Cooper pairing.Comment: 4 pages, 4 figures,Accepted for publication in J. Phys. Soc. Jpn., vol.78, No.1 (2009