Nuclear magnetic resonance on oriented189,191 Pt in iron

Nuclear magnetic resonance measurements have been performed for¹⁸⁹Pt and¹⁹¹Pt oriented at 7 and 15 mk in iron host. The magnetic hyperfine splitting frequencies, ν=¦μB_HF/Ih¦, of the¹⁸⁹Pt and¹⁹¹Pt ground states were determined to be 277.61(5) and 319.88(3) MHz. With the hyperfine field of B_HF=-1280(26) kG the nuclear magnetic moments were deduced to be: ¦μ(¹⁸⁹Pt;3/2^?)¦=0.427(9) μ^N; ¦μ(¹⁹¹Pt,3/2^?) ¦=0.492(10) μ_N. The effective spinlattice relaxation time for¹⁹¹PtFe at 7 mK in a polarizing magnetic field of 2 kG has been found to be 30(2) s using a single-exponential fit.     

Magnetic moment of the 5/2−1/2[541] ground state of 14h 185Ir

The magnetic and electric hyperfine splitting frequencies ¦gμ _N B _HF/h¦ ande ² qQ/h of the 5/2^?1/2[541] ground state of 14h ¹⁸⁵Ir in Ni were measured with nuclear magnetic resonance on oriented nuclei to be 360.8(7) MHz and +6.7(2.0) MHz, respectively. The ground state magnetic dipole moment and electric quadrupole moment of¹⁸⁵Ir are deduced to be ¦μ¦=2.601 (14)μ _N andQ=?1.9(5)b, taking values for the hyperfine field and electric field gradient of B_HF=?454.9 (2.3) kG and eq=?0.151(4) × 10¹⁷ V/cm², respectively. The negative quadrupole moment is in agreement with nuclear-orientation data and proves again theI ^π K=5/2^? 1/2 ground state configuration.     

Nuclear magnetic resonance on oriented 11/2− 129mXe and131mXe in Fe

The magnetic hyperfine splitting frequenciesν _M=¦gμ _NB_HF/h.¦ of the 11/2^? isomeric states^129m Xe (T_1/2=8.9d) and^131mXe (T_1/2=11.8d) in Fe were measured with nuclear magnetic resonance on oriented nuclei at temperatures of 10–15 mK as 188.0(1) MHz and 209.8(1) MHz, respectively, the samples being prepared with the technique of recoil implantation after (α, x n) reactions. The magnetic moments of^129m Xe and^131m Xe are deduced to be (?)0.8914(6)μ _N and (?)0.9943(6)μ _N, respectively. The missing γ-anisotropies for allγ-transitions following the decay of 36.4d ¹²⁷Xe indicateI=1/2 for the ground state spin of¹²⁷Xe.     

On the coexistence of oblate and prolate deformed bands in83Zr

Deformation parameters of the positive parity yrast band and negative parity bands in⁸³Zr are deduced from lifetimes andE2/M1 mixing ratios. Lifetimes of high spin states have been determined from recoil distance Doppler shift and Doppler shift attenuation measurements using the⁵⁴Fe(³²S,2pnγ) ⁸³Zr reaction. Ten lifetimes and five lifetimes limits were determined. The positive parity band, built on theg _9/2 K=5/2 orbital has an average deformation ¦β ₂¦=0.28(2), and shows a reduction ofE2 transition strengths in the observed backbend region at I^π≈21/2⁺. In contrast, theE2 strengths in the negative parity states show a steady increase up to I^π≈=15/2^?. These states are more strongly deformed than the positive parity states (¦β ₂¦=0.33(3)). TheE2/M1 mixing ratios show that the negative parity band hasK=3/2 and is prolate, and favour oblate deformation for the positive parity yrast band. In theK=1/2^? band theE2 strength of the 7/2^?→3/2^? transition yields a deformation ¦β ₂¦=0.26(5). The band structure is compared with calculations within the Hartree-Fock Bogoliubov cranking model.     

Stark-Effekt-Untersuchungen in der Hyperfeinstruktur der 3s 2 3d 2 D 5/2- und2 D 3/2-Terme des Al I-Spektrums

The resonance fluorescence of the transitions 3d ² D _5/2,3/2 3p ² P _3/2,1/2 in the Al I-spectrum was observed as a function of a magnetic field. Adding an electric field parallel to the magnetic field the shifts of level crossing signals caused by the Stark effect of the electric field were used to separate overlapping signals of the 3d ² D _5/2- and 3d ² D _3/2-states. The following values of the Stark parametersβ of both states and the hyperfine structure constantsA andB of the 3d ² D _3/2-states were deduced: 3d ² D _3/2∶ ¦A¦=99(1) Me/sec · g_J/0,8,B/A=?0,22(12), ¦β¦=0.45 (8) Mc/sec/(kV/cm)² · g_J,/0.8, A/β< 0 3d²D_5/2∶ ¦β¦=0.16 (4) Mc/sec/(kV/cm)² · g_J/1.2, A/β>0. Some qualitative aspects of interconfiguration mixing in the 3d²D-states are discussed.     

Nuclear magnetic resonance on oriented194Ir (T 1/2=19.4 h) in Fe and Ni

The hyperfine interaction of¹⁹⁴Ir (j ^π =1^?;T _1/2=19.4 h) in Fe and Ni has been investigated with the technique of nuclear magnetic resonance on oriented nuclei. For both systems the electronic-orbital-momentum induced electric quadrupole splitting could be resolved. The magnetic and electric hyperfine splitting frequencies,v _M =¦gμ _N ^B _HF/h¦ andv _Q =e ² qQ/h, respectively, were measured as:¹⁹⁴IrFe:v _m =408.54 (23) MHz;v _q =?2.47(20) MHz;¹⁹⁴IrNi:v _M =135.24(5) MHz;v _q =?1.23 (3) MHz. Taking into account a 3% uncertainty arising from hyperfine anomalies theg-factor is deduced as ¦g¦=0.39 (1). The electric quadrupole moment,Q=+0.352 (18)b, is slightly smaller than expected from the known systematics of deformation parameters in this mass region.     

Bounds for a Bose condensate in dimensions v ⩾ 3

A stronger version of the Bogoliubov inequality is used to derive an upper bound for the anomalous average ¦x)>|s of an interacting nonrelativislic Bose fielda(x) at a finite temperature. This bound is ¦a(x)²|s <pR, whereR satisfies 1 -R = (RT/2T _c ^v/2, withv the dimensionality, andT _c the critical temperature in the absence of interactions. The formation of nonzero averages is closely related to the Bose-Einstein condensation and ¦|·² is often believed to coincide with the mean densitypa of the condensate. We have found nonrigorous arguments supporting the inequality po ? ¦|·², which parallels the result of Griffiths in the case of spin systems.     

Decay of the positronium molecule into a positronium atom and photons

Decays of the positronium molecule Ps₂ into para- or orthopositronium Ps in the ground state and photons are investigated. The differential probabilities of the decays are determined. The total probabilitiesw _2γ ^(Ps2) andw _3γ ^(Ps2) of Ps₂ annihilation with the production of two and three photons and positronium are calculated to be $$w_{2\gamma }^{(P_{S_2 } )} = 1.6 \cdot 10^{10} \sec ^{ - 1} ,w_{3\gamma }^{(P_{S_2 } )} = 0.43 \cdot 10^8 \sec ^{ - 1} $$ . The curve of the angular correlation of the γ rays on the decay of Ps₂ into two photons and parapositronium is studied. The width of this curve is Δ¦P¦=0.128 a.u. (¦P¦ is the total photon momentum), which corresponds to a deviation of the emission angle of the γ rays from π: θ ? 0.934 mrad. The maximum in the distribution of the photons with respect to the momenta ¦P¦ in the center of mass of the annihilating pair is attained at ¦P¦=0.175 a.u. The calculations were made on an M-222 computer, and their accuracy is determined by the choice of the wave function of the positronium molecule and the accuracy in the computer calculation of the integrals.     

Static electric quadrupole interaction of Ta- and Hf-ions in barium and lead titanate

The static electric quadrupole interaction of¹⁸¹Ta and¹⁷⁸Hf in polycrystalline barium and lead titanate at the site of titanium has been measured using time differential PAC and the Mössbauer effect. The electric field gradients (EFG) at room temperature at the¹⁸¹Ta nucleus are ¦V _zz¦=(3.6±0.2)·10¹⁷V/cm² in BaTiO₃ and ¦V _zz¦=(14.6±0.6)·10¹⁷ V/cm² in PbTiO₃. The temperature dependence of the quadrupole interaction has been studied giving the following EFG values: ¦V _zz¦=(2.4±0.2)·10¹⁷ V/cm² in the monoclinic and ¦V _zz¦=(1.1±0.3)·10¹⁷ V/cm² in the rhomboedral phase of BaTiO₃, and ¦V _zz¦=(15.7±0.6)·10¹⁷ V/cm² for¹⁸¹Ta/PbTiO ₃ at 77 °K. The EFG of¹⁷⁸Hf in PbTiO₃ has been derived from a Mössbauer effect experiment to beV _zz=+(10.7±0.5)·10¹⁷ V/cm². The results are compared with EFG's calculated in a point charge model and with experimental EFG's measured at⁴⁴Sc and⁵⁷Fe in the same titanates by other authors. Contributions of covalent bonds to the effective EFG's in perovskit crystals are discussed.     

Level-Crossing-Experimente zur Untersuchung der Hyperfeinstruktur des 5d 2 D 5/2-Terms im Indium I-Spektrum

The resonance fluorescence of the transition 5d ² D _5/2?5p ² P _3/2 (λ=3256Å) in the In I-spectrum was observed as a function of an external magnetic field. From the level crossing signals the following values of the hyperfine constantsA andB of the 5d ² D _5/2-state were deduced: ¦A¦=148(8) Mc/sec·g _J/1.2 and ¦B/A¦≦0.3. The widths of the signals yielded the mean lifetimet=7.1 (6)·10^?9 sec · 1.2/g _J . From the shifts of the signals caused by a constant electric field parallel to the magnetic field the value of the Stark parameter ¦β¦=0.19(4) Mc/sec/(kV/cm)² ·g _J /1.2 and the sign of the ratioA/β<0 were determined. Calculations with Coulomb wave functions show that the Stark shifts of the electric field are mainly due to admixtures of the 6p ² P _3/2-state.     

Field theory,curdling, limit cycles,and cellular automata

It is suggested that the process of curdling is an important question for the science of fractals. A field equation which displays nucleation (curdling) of particles out of a pure radiation field is discussed. The particle formation arises naturally from the nonlinear character of the equation rather than from imposed quantization conditions. The relativistically invariant equation is $$div(\rho ^\mu (r,t,\Omega _1 )) = \int {[\rho _\mu (r,t,\Omega ),\rho ^\mu (r,t,\Omega _2 )]d} \Omega _2 $$ where ¦, ¦ denotes commutator.ρ ^μ (r,t,Ω) is both a 4-vector and a 2×2 matrix. It represents substance atr, t traveling with the velocity of light in direction Ω. A unique feature is that the scattering ofρ(Ω ₁) byρ(Ω ₂) as determined by the right-hand side of the above equation results in fields that persist at a given place even thoughρ itself represents substance traveling always at the speed of light. Explicit solutions are given for the case of one dimension. Fields representing particles are obtained and shown to have specially oscillatory structure with incipient fractal character.     

Investigation of224Ra in the226Ra(α, α′ 2n) reaction

Positive and negative parity bands have been followed up to 10⁺ (possibly 12⁺) and 11^? in²²⁴Ra and are compared to the corresponding bands in the isotone²²⁶Th. If a constant value of the intrinsic quadrupole moment is assumed for allE2 transitions in²²⁴Ra theE1/E2 branching ratios are consistent with an intrinsic dipole moment of ¦Q₁¦=0.032(3)e·fm. This small value, as compared to ¦Q₁¦=0.30(2)e·fm for²²⁶Th, can be explained by an almost complete cancellation of large positive liquid-drop and negative shell-model contributions.     

Collisional depolarization and redistribution of laser radiation in near resonance with a2 P 3/2↔2 S 1/2 transition

We have investigated experimentally and theoretically the spectral distribution and collisional depolarization of laser light near resonant to the Na transition 3² S _1/2?3² P _3/2 scattered from a Na/Ar mixture in a cell (n _Na≈4.0×10¹⁰cm^?3,n _Ar≈1.0×10¹⁷cm^?3). In particular, at excitation intensity of ≈3mW/mm² and bandwidth of <10 MHz, intensityI _F and linear polarization degreeP _F of theD ₂-fluorescence component of the scattered spectrum have been measured as functions of the laser detuningΔλ _L from theD ₂-resonance within two regions: 1) ¦Δλ _L ¦-Doppler-width; 2) 20≧¦Δλ _L ¦/Δλ _D ≧1. Within the first region the influence of hyperfine splitting as well as pumping of the hyperfine and Zeeman sublevels of 3² S _1/2 was studied in detail. Using an overall, total collision cross section for depolarization of 3² P _3/2 state atoms, calculations on the basis of the theory of redistribution reproduce qualitatively, but in a consistent manner, the experimental functionsI _F(Δλ_L) andP _F (Δλ _L ). The possibility to derive differential cross sections fromP _F (Δλ_L) is discussed.     

L ∞ estimates for the space-homogeneous Boltzmann equation

This paper studies the boundedness of solutionsf of the initial-value problem for the space-homogeneous Boltzmann equation for inverse kth power forces, whenk>5, and under angular cutoff. The main result is that if the initial value isf ₀ ? 0 with (1 + ¦υ¦²)φ₀ εL ¹ and (1 + ¦υ¦)^s f ₀ε L^∞ for somes > 2, then (1 + ¦υ¦^s'f _tεL ^∞ fort>0 and ess_υ,t sup(1 + ¦υ¦)^s'f(υ, t,) < ∞ for anys′ ? s whens ? 5, and anys′ ? s ifs > 5.     

Measurements of tau decay modes and a precise determination of the mass

The cross sections for e⁺e^? → e⁺(μ⁺ + non showering track + any photons have been measured for cm energies between 3.1 GeV and 5.2 GeV. We observe τ-pair production below the thresholdfor charm production and determine the τ mass to be 1.807 ± 0.020 GeV from a fit to the energy dependence of the cross section. The ration of the leptonic branching ratios B_μ/B_e = 0.92 ± 0.32 is consistent with eμ-universality. The following branching ratios are determined for a V-A coupling: $\text{B(τ → ν}{}_{\mathrm{\tau }}\text{e}\text{ν}\text{) = B(τ → ν}{}_{\mathrm{\tau }}\text{μ}\text{ν}\text{) = 0.182 + 0.028}$. B(τ → ν_τ + charged hadron + any photons) = 0.29 ± 0.11, B(τ → ν_τ + three or more charged hadrons + any photons) = 0.35 ± 0.11.     

Experimentelle untersuchung der 5d6s6pz 2 F 5/2,7/2-Terme im Lanthan I-Spektrum unter Verwendung von Levelcrossing-Spektroskopie

The hyperfinestructure-interaction-constantsA/g _J andB/g _J of the 5d 6s6p z ² F _5/2,7/2 terms in the La I-spectrum were measured by levelcrossing technique. Using a La-atomic beam many levelcrossings between magnetic sublevels with ¦Δm¦=2 were detected in both terms by resonance scattering. Values for the lifetime of each state were deduced from the widths of Hanle-effect- and levelcrossing-signals.     

Microwave spectrum and rotational isomerism of 3,3-difluoropropene CHF2CHCH2

The analysis of the microwave spectrum of 3,3-difluoropropene has confirmed the existence of two rotational isomers, cis and gauche. The rotational constants in the ground vibrational state are A = 9126.08 MHz, B = 3722.120 MHz, and C = 2946.598 MHz for the cis form and A = 8901.64 MHz, B = 4192.759 MHz, and C = 3107.718 MHz for the gauche form. The dipole moment and its components along the principal axes of intertia are μ_a = 2.369 ± 0.015 D, μ_c = 0.70 ± 0.03 D, and μ_t = 2.47 ± 0.03 D for the cis form and μ_a = 1.535 ± 0.015 D, μ_b = 0.53 ± 0.04 D, μ_c = 1.36 ± 0.03 D, and μ_t = 2.12 ± 0.05 D for the gauche form. The relative intensity measurement indicates that the cis form is more stable than the gauche form by 260 ± 80 cm^?1. The energy of the first excited state with respect to the ground state was found to be 63 ± 8 cm^?1 for the cis form and 85 ± 10 cm^?1 for the gauche form. Two Fourier coefficients of the potential function restricting the torsion around the CC bond were determined to be V₁ = 266 ± 40 cm^?1 and V₃ = 508 ± 200 cm^?1, using the available data. The potential function thus obtained is compared to a prediction model which is derived assuming additivity of the potential as a function of substitution.     

Spectral characteristics and nonlinear studies of methyl violet 2B dye in liquid and solid media

Solid-state dye-doped polymers are attractive alternatives to the conventional liquid-dye solutions. In this paper, the spectral characteristics and nonlinear properties of the dye Methyl violet 2B has been studied. The third-order nonlinear optical properties of Methyl violet 2B dye in ethanol and a dye-doped polymer film were measured by the Z-scan technique. This material exhibits a negative optical nonlinearity. The dye exhibited a nonlinear refractive coefficient (n ₂ = ?4.14 × 10^?7 and ?4.291 × 10^?7 cm²/W in liquid and solid media, respectively), nonlinear absorption coefficient (β = ?4.634 × 10^?3 and ?4.66 × 10^?3 cm/W in liquid and solid media, respectively), and susceptibility (χ⁽³⁾ = 1.88 × 10^?5 and 1.963 × 10^?5 esu in liquid and solid media, respectively). These results show that Methyl violet 2B dye has potential applications in nonlinear optics.     

New values of pion-nucleon scattering lengths and f2

From fixed t dispersion relations we have obtained more accurate values for the pion nucleon coupling constant and s-wave scattering lengths, using our recent low energy πN angular distribution and total cross section data. The results are: f² = 0.0790 ± 0.0010, a₁ ? a₃ = 0.262 ± 0.004μ^?1, a₁ + 2a₃ = ? 0.014 ± 0.005μ^?1.