Optimal bounds for ratios of eigenvalues of one-dimensional Schrödinger operators with Dirichlet boundary conditions and positive potentials

Consider the Schrödinger equation –u+V(x)u=u on the intervalI, whereV(x)0 forxI and where Dirichlet boundary conditions are imposed at the endpoints ofI. We prove the optimal bound

The structure of28Si above 10 MeV excitation energy I: gamma-decay modes and radiative widths of levels

The systematics of-decay modes and radiative widths of highly excited states in²⁸Si has been extended by taking-ray spectra on 60 resonances of the²⁷Al(p,) reaction in the range 1097 keVE _p 4492 keV (12643 keVE _x 15915 keV) and on the²⁴Mg(,) resonances atE =3355, 3431, 4003 keV (E _x =12860, 12925, 13 415 keV). The-decay modes of levels in the sub-resonance region (E _x =10–12.5 MeV) were studied with both the²⁷ A1(p, ) reaction and the²⁷ A1(d, n) reaction at E_d=4,5,6 MeV. Information on radiative widths of levels was obtained by measuring the resonance strengthsS =(2I+1) _p / for 52 resonances of the²⁷Al(p, ) reaction with an emphasis on prospective T=1 states.     

High spin states in77Se populated by the74Ge(α,n γ) reaction

⁷⁷Se has been investigated by the reaction⁷⁴Ge(,n) at 14 MeV. Gamma singles spectra, gamma angular distributions and gamma-gamma coincidences have been taken. A level scheme has been established, spins and parities have been assigned. States of a rotational band on the 1/2^– ground state, a rotational band on the 5/2^– 249.7 keV state and an anormal band have been identified. Nuclear Reaction ⁷⁴Ge(,n )E =14 MeV; measuredE ,I ,--Coin.,-ang. distr.⁷⁷Se deduced levels,J, . Enriched target, Ge (Li).     

LargeP T P−P collisions to probe the gluonic and sea spin distribution in the proton

We parametrise the polarised gluon and sea distribution functions incorporating the interpretation of the EMC experiment that, due to the axial anomaly the observed quark contribution to proton spin at Q ²>=10.7 GeV². Typical processes to isolate the gluonic and sea content of the proton studied here are the largeP _T direct photon production processes (a) using single polarized protonPPX and (b) polarized beam and target protonPPX. In both the above process the dominant contribution comes from the Compton subprocess and so can be used as a clean probe of the gluonic content of the proton. LargeP _T muon pair production PP(^+–)X are also studied and we find that the annihilation subprocess dominates, but not much larger than the Compton subprocess and so may not be a clean probe of the sea content of the proton. The effect of two loop corrections to the parametrisation and asymmetries are also considered, and are found to be negligible.     

Mössbauer study of mixed valent silicides Eu(Ir1−x Pd x )2Si2

The solid solutions Eu(Ir_1–x Pd _x )₂Si₂, which exist for 0x0.125 and 0.75x1. cristallize with the tetragonal ThCr₂Si₂-type structure. The variation of the europium valence with composition has been thoroughly studied at temperatures 4.2T293 K by¹⁵¹Eu Mössbauer resonance. For 0x0.125 the europium valence at room temperature decreases asx increases. For 0.75x1 the valence transition temperature Eu³⁺Eu²⁺ increases asx increases.     

Fast-hadron formation mechanism in leptoproduction in nuclei

The mechanism of fast-hadron leptoproduction in nuclei in deep inelastic region is considered. Different possible mechansims of fast-hadron formation in the virtual-photon fragmentation region and the process of transition of the quark (quark-gluon system) through nuclear matter is analysed. The range of consistency of the SLAC and EMC CERN data on meson leptoproduction in different nuclei is obtained to be 0.2 GeV²m _c ² 0.5 GeV². It is shown that the kinematic region 0.05x _B 0.3 and (3–5)Q ²/m _c ² 100 is the most favourable for an investigation of the growth law (evolution) of the transverse dimensions of quark (quark-gluon system) produced by the virtual photon.     

Photon-deuteron diffractive scattering

One expects a similarity of the energy dependence of the difference _tot(*p)– _tot(*n) for virtual (deep inelastic scatteringQ ²m ²) and real (Q ²=0) photons. Previous analysis of D structure functions with allowence for nuclear shadowing (NS) in the deuteron has led to conclusion that _tot(*p)– _tot(*n)<0>x<0.015. the=" early=" evidence=" from=" the=" real=" photoproduction=" data="> _tot(p)– _tot(n)<0. we=" critically=" reexamine=" determinations=" of=" the="> _tot(p)– _tot(n), using more accurate calculations of NS correction to _tot(D), and discuss a possibility of _tot(n) _tot(p) at moderately high energies.     

Emissivity of CO2-H2O mixtures at temperatures up to 1000° K

The emissivity in the 2.7 m range is examined with a spectrometer having 25 cm^–1 for 2.5, ,7.5 cm·atm,4 8cm·atm, 400T1000° K; 150P730 mm Hg. It is found that relation (1) is obeyed to within /0.1, though the calculated transmission is usually less than the measured value. It is shown that the relation is obeyed on account of the mutual position of the CO₂ and H₂O lines in the band, i.e., one gas may be considered as unselective relative to the other.     

Extended operator expansion method for neutrinoless double beta decay

Reliable calculations of nuclear matrix elements are a prerequisite for the determination of the effective neutrino mass and other particle physics parameters from neutrinoless double beta decay. Here, the operator expansion method is improved by including Coulomb, tensor and central interactions simultaneously. Furthermore, the formalism of the OEM is extended to those matrix elements necessary to extract the right-handed parameters and from 0 decay. OEM includes the dependence of the nuclear matrix elements on the intermediate states implicitly and can therefore be understood as a step beyond the closure approximation. Numerical studies are carried out for the isotope⁷⁶Ge combining the OEM expressions with ground-state wave functions calculated within a proton-neutron quasiparticle Random Phase Approximation (pn-QRPA) model. The influence and relative importance of central, tensor and Coulomb interactions is investigated. Within the OEM, contributions from the Coulomb force are found to be negligible in 0 decay, while the tensor force leads to a moderate change of the results, of the order of (10–30)%, giving a better agreement between sets of calculations which employ different NN-interactions. Generally, results of the OEM+QRPA calculation are similar to previous calculations of 0 decay matrix elements, indicating that 0 decay is not sensitive to model approximations and might therefore be more accurately calculated than the strongly suppressed 2 decay matrix elements.     

Magnetic states of Cu1 sublattice in YBa2Cu3Oy high Tc compounds at different oxygen content

Magnetic states of Cu1 sublattice in YBa₂Cu₃O _y : 1%⁵⁷Fe compounds with 6.09 y6.98 were investigated by⁵⁷Fe Mössbauer spectroscopy at 1.68T300 K. It has been found that, upon reducingy, the magnetic transition temperatureT _ml changes from 3.3 to 12 K aroundy6.4 where the superconductivity disappears. The magnetic phase diagram for the Cu1 sublattice is plotted.     

The decays of theρ′1 andω′1 mesons

New measurements of the reactione ⁺ e ^– confirm previous evidence for the decay₁ and provide a strong constraint on the mass of the₁. The results from a detailed analysis of these data are compared with those from a corresponding analysis of new data on the reactione ⁺ e ^–. It is shown that in accord with expectation. This identification of a strong₁ decay supports a previous claim that the₁ and theC(1480), observed in the channel, cannot be different manifestations of the same particle.     

Studies of the reactionπ − p→η ′ π 0 n at 38 and 100 GeV/c

The production of ⁰ system in ^– _p charge-exchange interactions at ^– momenta 38 GeV/c and 100 GeV/c has been studied. The 2 and ^{0 0} decay modes of leading to 4 and 8 final states respectively have been detected. No statistically significant peak is observed in the ⁰ mass spectrum in the range of 1.2 GeV÷2.1 GeV. An upper limit of 6·10^–3 has been established for thea ₂ ⁰ (1320) ⁰ branching ratio.     

Effect of hydrogen doping on the magnetic properties of Gd2CuO4

We report the results of ac-susceptibility and dc-magnetization measurements for H_yGd₂CuO₄ (0y0.54). It is shown thatH doping lowers the weak ferromagnetic component in the material. The distinct hysteresis loops observed atT=77 K for both non- and hydrogenated samples change its shape withy. The magnetic ordering temperatures T _N ^Cu and T _N ^Gd , as determined from the temperature dependencies of ac-susceptibility, remain unchanged with sample's hydrogenation. This result seems to indicate that extra electrons are not doped onto the Cu-O planes of Gd₂CuO₄. The frequency dependencies ofx(, T) andx(, T) for bothy=0 andy=0.15 samples are analysed., The maximums ofx andx found at about 200K are considered in terms of susceptibility dependence on the spin-lattice relaxation time (). The anomalies in ac-susceptibility found recently in Gd₂CuO₄ atT _a=8 K andT _b=9.5 K decrease significantly withy. Results are discussed in the context of available data on 214T-type compounds.     

Dynamics of vector spin glasses: The Gabay-Toulouse line

The dynamics of ann-component vector spin glass with infinite range interactions are investigated near and above the Gabay-Toulouse (GT) line. The local transverse susceptibility _T for 0 varies along the whole GT lineT _c1 (H) as ^v , with a field and temperature independent critical exponentv=1/2. The longitudinal susceptibility _L () remains analytic for all (T, H)T _c1 (H), except for a cross-over fromv=1 tov=1/2 forH0 at the freezing temperatureT=T _f . The dynamic susceptibilities _T () and _L () are already coupled above the GT line via self-energy terms. BelowT _c1 (H), this coupling is strongly enhanced by other mechanisms.     

A mini transmissionγ-ray Compton polarimeter and measurements of the sign of magnetic moments of radioactive nuclei

A mini transmission-ray Compton polarimeter was developed for the measurement of the sign of magnetic moments of radioactive nuclei with low-temperature nuclear orientation. The signs of the magnetic moments of the following isotopes were determined:¹⁹³Os [=+0.7297(16) _N];^191m Ir [=+6.20(9) _N];¹⁹²Ir [=+1.924(10) _N];¹⁹⁴Ir [=+0.39(1) _N];^195m Pt [=–0.605(15) _N].Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday     

28Si(32S) fragmentation at 3.7 A, 14.6 A and 200 A GeV

The fragmentation topology of²⁸Si at 3.7A GeV and 14.6A GeV and³²S at 200A GeV in reactions with emulsion nuclei is presented. The fragmentation cross sections are very similar at all three energies. A statistical percolation model can qualitatively describe the data forZ 6. The He production is underestimated and the 3 Z 5 fragments overestimated by this model.