Renormalization problem in nonrenormalizable massless Φ4 theory

Nonrenormalizable massless Φ⁴ theory is made finite by regularization via higher derivatives in the kinetic part of the Lagrangean. The theory is shown to remain finite in the infinite cutoff limit if certain integrals over functions of one variable, with computable Taylor expansion at the origin, are finite. The values of these integrals are the only unknowns in the double series in powers ofg andg ^2/ε obtained for the Green's functions in massless (Φ⁴)_4+ε with generic ε. For ε=1 and ε=2, these series reduce to double series in powers ofg and lng. The problems of extension to (Φ⁴)_4+ε with mass, of causality and unitarity, of the relation to the BPHZ formalism, and of the indeterminacy of the result are discussed.     

Pressure-volume-temperature relations of a poly-ε-caprolactam and its nanocomposite

The equation of state of a poly-ε-caprolactam melt, PA-6, of molar mass M _n = 22 kg/mol was investigated in a Gnomix apparatus (Gnomix Inc., Boulder, Colorado) between 300 and 560 K, and pressures up to 150 MPa. Corresponding measurements were performed with addition of 1.6 wt% of montmorillonite exfoliated particles. Reductions in specific volume of about 1.0 and 1.4%, respectively, at 10 and 150 MPa, are observed. For the melt, excellent agreement between experiment and the results from lattice-hole theory is found for both systems. Addition of the nanoparticles reduced the hole (free volume) fraction by 14%. Evidently, the hole fraction is a sensitive indicator of structural changes. It is noteworthy that such a small quantity of added nanoparticles increases the tensile strength by about 14% and modulus by 26%, at a cost of reduction in the elongation at break by about 25%. For a treatment of the PNC, and as an approximation, our earlier model of a particulate composite was adopted. To calculate the binary interaction parameters it was assumed that: (1) the clay particles are in form of flat disks, 100 nm diameter and 1 nm thick; (2) the hard core segments of polymer and of solid occupy the same lattice volume, i.e. v ^* ₁₁ = v ^* ₂₂; (3) the energetic interactions of polymer with solid are given by the geometric average between the two self-interactions. These assumptions lead to the following results ('11' represents polymer-polymer, '22' represents clay-clay and '12' represents polymer-clay interactions): ε ^* ₁₁= 32.09; ε ^* ₁₂ = 313.54 and ε ^* ₂₂ = 3063 (kJ/mol) v ^* ₁₁ = 24.89; v ^* ₁₂ = 33.53 andv ^* ₂₂ = 24.89 (ml/mol)     

Analyticity properties and a convergent expansion for the inverse correlation length of the high-temperatured-dimensional Ising model

We show that the inverse correlation lengthm(β) (= mass of the fundamental particle of the associated lattice quantum field theory) of the spin-spin correlation function 〈s _x s _y 〉,x, y εZ ^d , of thed-dimensional Ising model admits the representation $$m(\beta ) = - ln\beta + r(\beta )$$ for small inverse temperaturesβ > 0.r(β) is ad-dependent function, analytic atβ = 0.c _n , the nth β = 0 Taylor series coefficient of r(β) can be computed explicitly from the Z^d limit of a finite number of finite lattice A spin-spin correlation functions 〈s₀s_x〉t>Afor a finite number ofx = (x ₁,x₂, ..., x_d), ¦x¦ = ∑ _i ^d 1¦x_i¦< R(n), where R(n) increases withn. Furthermore, there exists aβ' > 0, such that for eachβ ε (0,β')m(β) is analytic. Similar results are also obtained for the dispersion curve ω(p), ω(p)=ω(0)=m, pε(-π, π]^d?1, of the fundamental particle of the associated lattice quantum field theory.     

Generalization of the radiative corrections to β and μ decays in the SU(2)L × U(1) gauge model

Previous results for the radiative corrections to the ratio of decay probabilities of β and μ decays are generalized to the case of arbitrary symmetry breaking in the framework of the SU(2)_L × U(1) gauge model. In this more general case, the results remain very simple: the corrections are given by the corresponding expressions of the local V-A theory with m_W substituted for the cutoff Λ plus a positive definite contribution which depends on θ_W and R = m_W²/m_Z².Thus, the corrections in the general case are still constrained to have large values as required by Cabibbo universality and the present experimental values on β and μ decays. For reasonable values of m_Z and m_W the results in the general case are numerically close to those previously obtained in the simplest version of the theory. To illustrate this point the corrections are compared for two different choices of the parameters of the theory. In an appendix we discuss, rather briefly, the theoretical arguments that allow us to generalize pprevious discussions the case of fractionally charged quarks.     

Rigid lattice NMR spectra of proton conductors H(H2O)nSbO3

The “rigid lattice” ¹H NMR spectra of H(H₂O)_nSbO₃ have been interpreted for n=0.20, 0.92 and 1. For n?0.92 the compounds contain deformed H₃O⁺ ions and OH groups. For n=1 the real formula is (H₃O)_0.7H_0.3SbO₃,0.3 H₂O. The results are discussed in relation to the level of proton conductivity.     

Paramagnetic resonance of some three-nuclear clusters of iron

ESR of exchange-coupled iron triads in carboxilates [Fe₃O(RCOO)₆(H₂O)₃·(RCOO)_n where R = ClCH₂, FCH₂, Cl₂CH or Cl₃C is studied at 4.2 K (microwave frequency v = 9.5 kMc/sec). ESR spectra and observed values of g-factors are discussed according to the model of a symmetrical cluster. Fine structure δ splittings of the triad ground state are determined on bases of the theory and ESR data: δ ≈ 0.03-0.16 cm^?1.     

Optical absorption due to paraexciton of Cu2O

In Cu₂O a new absorption line is observed at 97 cm^?1 below the n =1 of the yellow exciton (triply degenerate orthoexciton) under a strong magnetic field at 4.2 K. The line is assigned as a transition to a nondegenerate spin triplet state Γ⁺₂ (paraexciton). An analysis including the effects due to the n =1 of the green exciton yields 364 cm^?1 as the exchange energy, and 2.68 and ?1.02, or 1.02 and ?2.68 as the g-factors of the conduction and valence bands forming the yellow exciton.     

Electron beam interactions with CO on W {100} studied by Auger electron spectroscopy

The interaction of 2500 eV electrons with carbon monoxide chemisorbed on tungsten {100} was investigated by rapid-scan Auger electron spectroscopy. When no α state was present the O and C signals from the β state of CO were invariant during electron bombardment, giving an upper limit estimate for the electron stimulated desorption cross section, Q_β of 2 × 10^?21 cm². With the crystal at room temperature and saturated with CO, however, electron-beam induced accumulation of carbon was observed and characterised, the rate of the process being independent of CO pressure at pressures above 2 × 10^?8 Torr. At 450 K the rate was found to be pressure dependent up to at least 6 × 10^?7 Torr. A model is proposed for the accumulation process, which is based on electron beam dissociation of α₂-CO to form adsorbed carbon and gaseous O and the creation of new sites for further α₂-CO adsorption; it is in quantitative agreement with the results and yields a cross section for ESD of α₂-CO (Q_α2 = 1.55×10^?18cm²) in close agreement with direct measurements.     

Diode-laser measurements and calculations of CO 1-0 P(4) line broadening in the 294- to 765-K temperature range

We present first diode-laser measurements of C¹²O¹⁶ 1-0 P(4) line broadening by Ar, N₂ and H₂O at high temperatures, together with the line-intensity value at 300 K. A T^-β dependence of line-widths on temperature is deduced from measurements in the 294- to 765-K and 0.2- to 1.2- atm ranges (β = 0.69±0.02, β = 0.69±0.02, β = 0.59±0.05 for Ar, N₂ and H₂O broadening, respectively). Calculations for CO-Ar and CO-N₂ with the model proposed by Robert and Bonamy give very satisfactory results.     

Crack propagation and initiation in low cycle strain controlled fatigue

Experimental techniques for crack extension measurements in cylindrical specimens, subjected to tension-compression strain cycling, are described. Both electrical resistivity and compliance techniques are applicable and yield information on crack growth as well as crack initiation. Crack propagation follows the relationship $$dc/dN = A.c.(\varepsilon _{TR} /\varepsilon _F )^{n + 1} - \frac{{\rho ^* }}{2}$$ withn close to unity. (Herec is the crack length,A a constant andε _F a critical strain characteristic of the material;ε _TR is the total strain range.) The Manson-Coffin equation could be regarded as a consequence of this crack propagation relationship, though the value of the strain hardening exponentn 1 will require further verification and clarification. From preliminary tests it appears that crack initiation in notched specimens is also governed by a Manson-Coffin type relationship, especially if the effective plastic strain at the notch root can be properly computed from $$\varepsilon _{TR,effective} = K_\varepsilon .\varepsilon _{TR} - \varepsilon _e^ + $$ whereK _? is the proper strain concentration factor,ε _TR the total nominal strain range andε _e ⁺ the elastic component under consideration of the plastic constraint at the notch root.     

On the optical absorption due to particle-hole excitations in thin metal films

We present here a qualitative discussion on the optical absorption due to particle-hole excitations in thin metal films. We show that in sufficiently thin films, such excitations yield resonant absorption, when P-polarized light is obliquely incident on the metal surface. For instance, for frequency ω #62; ε_F where ε_F is the Fermi-energy, such resonances occur whenever ω satisfies the condition ω/ε_F = (1 + nπ/dq_F)² - 1, where n = 1,3,5,…,q_F is the Fermi wave-vector and d is the thickness of the film. The experimental observability of this effect is also discussed.     

Fluorescence resolue dans le temps des niveax de singulet et d du zinc

The time resolved spectroscopy technique is applied to investigate the (4s, nd) ¹D₂ series of Zn I using a selective stepwise excitation via the resonant 4¹P₁ state. Radiative lifetimes of n¹S₀ (n = 6?8) and n¹D₂ (n = 4,5) levels are measured. Upper limits for transition probabilities 4¹P₁?n¹S₀ (n = 9?12) and 4¹P₁?n¹ (n = 6?10 ) are obtained. Strong configuration interaction effects are observed in the ¹D₂ series and compared with those in Mg I and Cd I.     

The magnetooptical properties of InSe near the band gap

We have studied the magnetooptical properties of InSe near the band gap by wavelength modulation spectroscopy at 10 K with the electric vectorE perpendicular to theC-axis of the crystal. For the first time, Landau levels have been observed from which we obtain the reduced effective mass perpendicular to $\overrightarrow{C}$, μ_⊥ = (0.090 ± 0.010)m₀. The n = 1, 2 and 3 exciton lines along with a diamagnetic shift of the n = 1 level have been resolved from which we evaluate the Rydberg constant R = 15.0 ± 0.5 meV, the diamagnetic shift σ₁ = 14 ± 2 meV/(kG)² and ε_⊥ε_∥ = 81 ± 8. Evidence of the presence of the γ and ε polytypes in the sample due to stacking faults is given.     

119Sn Mössbauer characterization of self assembled organotin(IV) complexes with Schiff bases containing amino acetate skeletons

Several organotin(IV) compounds, viz., diorganotin(IV) compounds of the types Ph₂SnLH (monomer), ⁿBu₂SnLH·OH₂ (monomer), [Me₂SnLH·OH₂]₂ (centrosymmetric dimer), [ⁿBu₂SnLH]₃ (cyclic trinuclear), [Ph₂SnLH] _n (polymer), {[ⁿBu₂Sn(LH)]₂O}₂ (centrosymmetric tetranuclear), dinuclear di-/tri-mixed organotin(IV) compounds Ph₂SnLH·Ph₃SnCl (monomer) and triorganotin(IV) compounds of the types [Bz₃SnLH]₂ (centrosymmetric dimer) and [Me₃SnL¹H] _n (Polymer) (LH = Schiff base carboxylate) have been studied in the solid state at liquid nitrogen temperature using ¹¹⁹Sn Mössbauer spectroscopy. The tin coordination geometry of the compounds determined from crystallography was correlated with the ¹¹⁹Sn Mössbauer results.     

Time-dependent density functional theory study on electronic excited states of the hydrogen-bonded solute-solvent phenol-(H2O)n (n=3-5) clusters

The solute-solvent interactions of hydrogen-bonded phenol-(H₂O)_n (n=3-5) clusters in electronic excited states were investigated by means of the time-dependent density functional theory (TDDFT) method. The geometric structures and IR spectra in ground state, S₁ state, and T₁ state of the clusters, were calculated using the density functional theory (DFT) and TDDFT methods. Only the ring form isomer, the most stable one of the cluster, was considered in this study. Four, five and six intermolecular hydrogen bonds were formed in phenol-(H₂O)₃, phenol-(H₂O)₄, and phenol-(H₂O)₅ clusters, respectively. Based on the analysis of IR spectra, it is revealed that the “window region” between unshifted and shifted absorption bands in both S₁ and T₁ state becomes broader compared with that in ground state for the corresponding clusters. Furthermore, two interesting phenomenon were observed: (1) with the anticlockwise order of the ring formed by the intermolecular hydrogen bonds in the H-bonded phenol-(H₂O)_n (n=3-5) clusters, the strengths of the intermolecular hydrogen bonds decrease in all the S₀, S₁ and T₁ states; (2) upon electronic excitation, the smaller the distance between phenol and water is, the larger the change of intermolecular hydrogen bonds strength is. Moreover, the intermolecular hydrogen bond (phenolic OH is the H donor) is strengthened in excited state compared with that in ground state. But the intermolecular hydrogen bond (phenolic OH is the H acceptor) is weakened in excited state.     

Theory of nonstoichiometric ordering of Pb-containing relaxors with perovskite structure

Conditions that are imposed on the interatomic interaction and under which a certain ordered state of AB _x ^′ B _1?x ^″ perovskites arises are determined with allowance for effectively pairwise interactions and the configuration entropy of interchanges of B′ and B″ ions. It is shown that, for the interaction potential u(R) = u ₀/R ⁶, the highest temperature of ordering of the 1: 2 type (T _ord (1: 2)) corresponds to a structure observed at A ≡ Ba. The highest temperature of ordering of the 1: 1 type (T _ord (1: 1)) corresponds to a structure that typically occurs in the case of A ≡ Pb. Within the approximation used, it is found that T _ord (1: 1) > T _ord (1: 2) for all compositions and that the 1: 1-ordered phase is most stable. For models with u(R) = u ₀/R ⁿ (n = 1–6) including the interaction in the first m coordination shells (m = 3, 6, 8, 11), it is shown that the ground state of AB _x ^′ B _1?x ^″ O₃ corresponds either to a decomposed solid solution or to an ordered state similar to that observed in PbMg_1/3Nb_2/5O₃.     

Beta decays of 128Ce and 128La

Low-lying states in ₅₇ ¹²⁸ La and ₅₆ ¹²⁸ Ba have been investigated by γ-ray spectroscopy after the β decays of ₅₈ ¹²⁸ Ce and ₅₇ ¹²⁸ La. For the EC+β⁺ decay of ¹²⁸Ce, a new halflife has been determined to be 4.1 ± 0.3 min. In ¹²⁸La a new β-unstable isomeric state with a halflife shorter than 2 min is suggested in addition to a previously known isomeric state with the halflife of 5.2 min. A tentative level scheme of ¹²⁸La at low excitation energies has been constructed from the γ?γ coincidence measurement after the β decay of ¹²⁸Ce. The γ?γ angular correlation for γ rays from ¹²⁸Ba after the β decay of ¹²⁸La suggests that the spin-parity assignment of I ^π = 4^? or 5⁺ is preferable for the 2424.9 keV level which is populated via the β decay of the 5.2-min isomeric state with a log ft value of 5.6. For the 2877.1 keV level observed with log ft = 5.8, a preferable spin-parity assignment is 5^? or 6⁺. On the basis of these decay properties and low-lying excited states in neighboring odd mass nuclei, the spins and parities of isomeric states in ¹²⁸La are proposed to be (1⁺ or 2⁺) for the low-spin state, while (5± or 6⁺) for the high-spin state, within the limit of zero order approximation to the proton-neutron couplings.     

直流偏置电场下BaTiO３基陶瓷介电常数非线性机理的研究

采用传统固相法制备了Ba_0.6Sr_0.4TiO_３(BST)和BaZr< sub>xTi_１-xO_３(x=0.25，0.3，0.35，0.4)（ＢＺＴ）陶瓷 ，并对其在直流偏置电场下的介电常数非线性行为进行了系统、详细的研究.结果表明，基 于Devonshire的宏观相变理论(phenomenological theory)提出的公式ε_r(app) ε_r(0)=1［1+αε^{３_{r(0)E２ ］1/3和ε(E)=ε1－ε2E2+ε3E4，均可定量地解释BST体系顺电相的介电常数非线性行为，其中εr (app)表示材料在电场下的介电常数，εr(0)表示不加电场即静态下材料 的介电常数，α是非谐性因子，E表示电场强度，ε(E)表示材料在电场下的介电常数，ε１，ε２，ε３分别表示线性、非线性和高阶介电常数. 而对于处于铁电相和居里温度附近的BST体系，则需要考虑铁电畴对介电常数非线性的贡献 ，这种贡献随着外加直流偏置电场强度的增大逐步减小.对于弛豫铁电体BZT体系，即使处于 顺电相，也必须考虑由极性微区的冻结与合并引起的介电常数的下降，极性微区对介电常数 非线性的贡献随着电场强度和温度的上升而有所下降. 关键词： BST x}Ti_１-xO_３')" href="#">BaZr_xTi_１-xO_３ 可调性 介电 常数非线性 直流偏置电场}     

Structure of ZnZrF<Subscript>6</Subscript> · <Emphasis Type="Italic">n</Emphasis>H<Subscript>2</Subscript>O (<Emphasis Type="Italic">n</Emphasis> = 6–2) and ZnZrF<Subscript>6</Subscript> crystallohydrates according to vibrational spectroscopy data

Fluoridezirconate crystallohydrates ZnZrF₆ · nH₂O (n = 6–2) and anhydrous ZnZrF₆ are investigated by vibrational spectroscopy and thermography. The influence of the hydrate number on the structure of the cationic and anionic sublattices of the crystallohydrates is studied. The changes in the strength of HOH···F and HOH···O hydrogen bonds of coordinated and outer-sphere water molecules occurring with variations in the hydrate number are determined by changes in the IR spectra. The IR spectra of ZnZrF₆ · nH₂O (n =6, 4) compounds, which have isolated complex anions [ZrF₆]^2– in their structure, revealed a band with two peaks in the range of 3470–3430 cm^–1, which corresponds to stretching vibrations of coordinated water molecules. The spectra of ZnZrF₆ · nH₂O (n = 5, 3, 2, 1) crystallohydrates with a polymeric structure show a high-frequency shift of this band, which corresponds to weakening of hydrogen bonds. The vibrations of crystallization water molecules involved in the network of strong O–H···F and O–H···O hydrogen bonds manifest themselves in the spectra of ZnZrF₆ · nH₂O (n =5, 3) crystallohydrates by broad structureless bands in the region of stretching, bending, and libration vibrations.     

H, C NMR and JCH coupling constants investigation of 4-Phenylpyridine: A combined experimental and theoretical study

Proton coupled and uncoupled ¹³C, ¹H, DEPT, COSY and HETCOR NMR spectra of 4-Phenylpyridine (4-Phpy) have been reported for the first time except for its ¹H NMR spectrum. In order to provide a precise structural elucidation for carbon atoms those have very close chemical shifts to each other, the magnitude of ⁿJ_CH (n=1,2,3) coupling constants of 4-Phpy (C₁₁H₉N) have also been investigated. ¹³C, ¹H NMR chemical shifts and ^1-3J_CH coupling constants of 4-Phpy have been calculated by means of B3LYP density functional method with 6-311++G(d,p) basis set. Moreover, the optimized parameters (bond lengths, bond and torsion angles) of 4-Phpy have been calculated with B3LYP at 6-31G(d) level in methanol (ε=32.63). Comparison between the experimental and the theoretical results indicates that density functional B3LYP method is able to provide satisfactory results for predicting NMR properties.