Polar smectic subphases: Phase diagrams, structures and X-ray scattering

We analyze a discrete phenomenological model accounting for phase transitions and structures of polar Smectic-C* liquid-crystalline phases. The model predicts a sequence of phases observed in experiment: antiferroelectric SmC _A ^* –ferrielectric SmC _FI1 ^* –antiferroelectric SmC _FI2 ^* (three-and four-layer periodic, respectively)–incommensurate SmC _α ^* –SmA. We find that, in the three-layer SmC _FI1 ^* structure, both the phase and the module of the order parameter (tilt angle) differ in smectic layers. This modulation of the tilt angle (and therefore of the layer spacing d) must lead to X-ray diffraction at the wave vectors Q _s =2πs/d(s=n±1/3) even for the nonresonant scattering.     

A new many-body solution of the Friedel resonance problem

It is numerically shown that the groundstate of the Friedel problem (consisting of a conduction band and a dresonance), occupied with (n+ 1) electrons, can be written as Ψ = (A a ₀ ^* +Bd*) Π _v=1 ⁿ a _v ^* Φ₀, where a ₀ ^* represents a localized conduction electron state, d* is the Friedel resonance state and Π _v=1 ⁿ a _v ⁸ Φ₀ is a Slater determinant of n single electron states a _t ^* , (Φ₀ is the vacuum state). The a _i ^* together with a ₀ ^* are part of a full ortho-normalized basis of the conductions band.     

Scaling for a random polymer

LetQ _n ^β be the law of then-step random walk on ?^d obtained by weighting simple random walk with a factore ^?β for every self-intersection (Domb-Joyce model of “soft polymers”). It was proved by Greven and den Hollander (1993) that ind=1 and for every β∈(0, ∞) there exist θ^*(β)∈(0,1) and such that under the lawQ _n ^β asn→∞: $$\begin{array}{l} (i) \theta ^* (\beta ) is the \lim it empirical speed of the random walk; \\ (ii) \mu _\beta ^* is the limit empirical distribution of the local times. \\ \end{array}$$ A representation was given forθ ^*(β) andµ _β ^β in terms of a largest eigenvalue problem for a certain family of ? x ? matrices. In the present paper we use this representation to prove the following scaling result as β?0: $$\begin{array}{l} (i) \beta ^{ - {\textstyle{1 \over 3}}} \theta ^* (\beta ) \to b^* ; \\ (ii) \beta ^{ - {\textstyle{1 \over 3}}} \mu _\beta ^* \left( {\left\lceil { \cdot \beta ^{ - {\textstyle{1 \over 3}}} } \right\rceil } \right) \to ^{L^1 } \eta ^* ( \cdot ) . \\ \end{array}$$ The limitsb ^*∈(0, ∞) and are identified in terms of a Sturm-Liouville problem, which turns out to have several interesting properties. The techniques that are used in the proof are functional analytic and revolve around the notion of epi-convergence of functionals onL ²(?⁺). Our scaling result shows that the speed of soft polymers ind=1 is not right-differentiable at β=0, which precludes expansion techniques that have been used successfully ind≧5 (Hara and Slade (1992a, b)). In simulations the scaling limit is seen for β≦10^?2.     

Renormalization group fixed points in the local potential approximation ford≧3

In the Local Potential Approximation, renormalization group equations reduce to a semilinear parabolic partial differential equation. Felder [8] has derived this equation and has constructed a family of non-trivial fixed pointsu _2n ^* (n=2,3,4,...) which have the form ofn-well potentials and exist in the ranges of dimensions 2<d<2+2/n–1. In this paper we show that ifd4, then these non-trivial fixed points disappear, and if 3d<4 then we have only theu ₄ ^* fixed point.Research supported by CNPq, Brazil     

Multiple quantum coherences: New NMR tools to study materials and living systems

Intermolecular multiple-quantum coherences have been proven in recent years to provide a novel contrast mechanism to study heterogeneity in liquid systems. This subject represents a source of remarkable interest in the fields of physics of matter and biomedicine. Recent results achieved on intermolecular double-quantum signal transverse relaxation decay in confined liquid systems (such as in vivo bone marrow in trabecular bone, and doped water in glass capillary pipes) are reported and discussed in this paper. Correlated two-dimensional spectroscopy revamped by asymmetricz-gradient echo detection-like sequences were implemented in order to perform intermolecular doublequantum transverse relaxationT _2DQ andT _2DQ ^* measurements. Our experimental results indicated that the relationshipT _2,n ^* =T ₂ ^* /n betweenn-quantum transverse relaxation time and the conventional singlequantumT ₂ ^* only applies for homogeneous systems and fails in the case of highly heterogeneous systems like porous systems.     

Observation of perturbations in the rovibronic transition probabilities for the (4d)r 3Π g − , (4d) s 3 Δ g − → (2p) c 3Π u ± band systems of the H2 molecule

The ratios of the radiative transition probabilities for the lines of the P, Q, and R branches of the (4d)r ³Π _g ^? , (4d)s ³Δ _g ^? → (2p) c ³Π _u ^± band systems of the H₂ molecule have been measured for the first time. Significant (to two orders of magnitudes) differences are found between the experimental values and the adiabatic theory predictions. It is established that the results of the nonadiabatic calculation performed by us in the pure-precession approximation taking into account the electronic-rotational interaction of the 4d ³Π_g and 4d ³Δ_g states are in agreement with the experimental data. The optimal energies of rovibronic levels of the r ³Π _g ^? , s ³Δ _g ^? , c ³Π _u ^? , and c ³Π _u ⁺ states have been found and reidentification of 11 from 54 spectral lines, assigned previously to the (0-0) and (1-1) bands, was performed.     

Microscopic foundation of the interacting boson model in thes d-shell nuclei

Starting from an isospin invariant shell-model hamiltonian, we describe a method for deriving microscopically the IBM-hamiltonian appropriate to lights d-shell nuclei. The key ingredients of our approach are:a) the Belyaev-Zelevinsky-Marshalek (BZM) bosonization procedure;b) two successive unitary transformations that extract the “maximally decoupled” collective bosons with angular momentaJ=0(s _ππ ⁺ ,s _νν ⁺ ,s _πν ⁺ ) andJ =2(d _ππ ⁺ ,d _νν ⁺ ,d _πν ⁺ (T=0),d _πν ⁺ (T=1)). The method is applied to obtain the low-energy spectra and the electron scattering form factors for the 0 ₁ ⁺ →2 ₁ ⁺ transitions in²⁰Ne and²⁴Mg. Good agreement with the exact shell-model results is achieved. The inclusion of proton-neutron bosons (s _πν ⁺ ,d _πν ⁺ (T=1),d _πν ⁺ (T=0)), as well as the renormalization of boson parameters due to the non-collective degrees of freedom, are shown to play a crucial role.     

Comparative study of the semiempirical three-parameter potential energy functions for diatomic molecules

A comparative study is made of four three-parameter semiempirical potential energy functions for 32 electronic states of diatomic molecules and their ions:n ₂:X¹gS _g ⁺ ,B ³π_g,A ³ gS_u,C ³ _u,B′ ³ gS_u.a ¹ π_g, a′gS _u ^? ,Ω ¹δ_u N ₂ ⁺ :X ² gS _g ^gS +A ² π,C ² gS _u ⁺ ,B ² gS _u ⁺ CO:X¹gS⁺,a ³ π, a′³ gS_u,e ³ gS^?,d ³gD₁,A ¹π CO⁺:X²gS⁺,A ² π,B ²gS⁺ O₂:X³gS _g ^? ,B ³ gS_u,c ¹ gS _u ^? ,b ¹gS _g ^s ,a ¹ δ_g,c ³ δ_u O ₂ ⁺ :X ²π_g,A ² π_g, a¹ π_g,b ⁴ gS _g ^? A program for numerically integrating the radial Schrödinger equation by the Cooley method is worked out. Certain additional units are introduced to conserve computer time. The resulting vibrational levels are compared with the experimental levels for all the electronic states studied. It is concluded on the basis of this analysis that it is not possible to describe equally well all the electronic states of various molecules on the basis of any single three-parameter potential function. A method for choosing a potential function for describing some particular electronic state of a diatomic molecule is proposed.     

Vacuum energy ingϕ d /4 -theory forg→∞

In the nonlocalg? _d ^/4 (d≧1) and localg? ₂ ⁴ theory theS-matrix is obtained in a form of the functional integral which is proved to exist. The density of vacuum energy $$E(g) = - \mathop {\lim }\limits_{V \to \infty } \frac{1}{V}\ln \left\langle {0\left| {S_V (g)} \right|0} \right\rangle $$ is investigated. It is proved to be analytic through the whole complexg-plane except for the negative real axis and pointg=0. Its asymptotic behaviour forg→∞ is found.     

On the free energy of the hopfield model

The general theory of inhomogeneous mean-field systems of Raggio and Werner provides a variational expression for the (almost sure) limiting free energy density of the Hopfield model $$H_{N,p}^{\{ \xi \} } (S) = - \frac{1}{{2N}}\sum\limits_{i,j = 1}^N {\sum\limits_{\mu = 1}^N {\xi _i^\mu \xi _j^\mu S_i S_j } } $$ for Ising spinsS _i andp random patterns ξ^μ=(ξ ₁ ^μ ,ξ ₂ ^μ ,...,ξ _N ^μ ) under the assumption that $$\mathop {\lim }\limits_{N \to \gamma } N^{ - 1} \sum\limits_{i = 1}^N {\delta _{\xi _i } = \lambda ,} \xi _i = (\xi _i^1 ,\xi _i^2 ,...,\xi _i^p )$$ exists (almost surely) in the space of probability measures overp copies of {?1, 1}. Including an “external field” term ?ξ _μ ^p h^μμξ _i=1 ^N ξ _i ^μ S_i, we give a number of general properties of the free-energy density and compute it for (a)p=2 in general and (b)p arbitrary when λ is uniform and at most the two componentsh ^μ1 andh ^μ2 are nonzero, obtaining the (almost sure) formula $$f(\beta ,h) = \tfrac{1}{2}f^{ew} (\beta ,h^{\mu _1 } + h^{\mu _2 } ) + \tfrac{1}{2}f^{ew} (\beta ,h^{\mu _1 } - h^{\mu _2 } )$$ for the free energy, wheref ^cw denotes the limiting free energy density of the Curie-Weiss model with unit interaction constant. In both cases, we obtain explicit formulas for the limiting (almost sure) values of the so-called overlap parameters $$m_N^\mu (\beta ,h) = N^{ - 1} \sum\limits_{i = 1}^N {\xi _i^\mu \left\langle {S_i } \right\rangle } $$ in terms of the Curie-Weiss magnetizations. For the general i.i.d. case with Prob {ξ _i ^μ =±1}=(1/2)±?, we obtain the lower bound 1+4?²(p?1) for the temperatureT _c separating the trivial free regime where the overlap vector is zero from the nontrivial regime where it is nonzero. This lower bound is exact forp=2, or ε=0, or ε=±1/2. Forp=2 we identify an intermediate temperature region between T_*=1?4?² and T_c=1+4?² where the overlap vector is homogeneous (i.e., all its components are equal) and nonzero.T _* marks the transition to the nonhomogeneous regime where the components of the overlap vector are distinct. We conjecture that the homogeneous nonzero regime exists forp≥3 and that T_*=max{1?4?²(p?1),0}.     

QCD analysis of non-singlet electromagnetic structure functions

A direct analysis of all data on the nonsinglet combination of electromagnetic structure functionsF ₂ ^p ?F ₂ ⁿ is shown to yield a value of the QCD scale-breaking parameter \(\Lambda _{\overline {{\rm M}S} } = 0.36 \pm 0.16\) Gev, in good agreement with that obtained from non-singlet neutrino data. The ratiod _v /u _v , extracted using the results of a previous neutrino analysis, shows an excess of up-quarks to down-quarks of about a factor of five at largex.     

Polarized deuteron structure functions at small x

We investigate shadowing corrections to the polarized deuteron structure functions g ₁ ^d and b₁. In the kinematic domain of current fixed target experiments we observe that shadowing effects in g ₁ ^d are approximately twice as large as for the unpolarized structure function F ₂ ^d . Furthermore, we find that b₁ is surprisingly large at x < 0.1 and receives dominant contributions from coherent double scattering.     

The decay of the Bethe-Salpeter kernel inP(ϕ)2 quantum field models

We extend methods of high temperature expansions to show that for even weakly coupledP(?)₂ quantum field models the Bethe-Salpeter kernel has 4 particle decay. More precisely ifK denotes the Euclidean Bethe-Salpeter kernel $$|K(x_1 ,x_2 ,x_3 ,x_4 )| \leqq Oe^{ - m_0 (1 - \varepsilon )d_2 } ,$$ wherex=(x ⁰,x ¹),d ₂=2|x ₁ ⁰ +x ₂ ⁰ ?x ₃ ⁰ ?x ₄ ⁰ |+|x ₁ ⁰ ?x ₂ ⁰ |+|x ₃ ⁰ ?x ₄ ⁰ | and ε(λ)→0 as λ→0. Our methods apply to otherr particle irreducible kernels.     

Spin effects in two-body hadronic decays of the B c mesons

Spin effects in the weak two-body hadronic decays of the B _c and B _c ^* mesons into J/ψ and ρ(π) mesons are considered within the model of hard one-gluon exchange between quarks at high momentum transfers. It is shown that the polarization of the J/ψ meson in the decays of the B _c ^* meson differs substantially from that in the decays of the B _c ^* meson. The decay widths of the B _c ^* meson differ significantly from the widths of the B _c ^* meson.     

Ab initio calculation of transition dipole moments for transitions between valence states in oxygen molecules

Results of ab initio calculations of potential-energy curves for 20 singlet and 20 triplet valence states of oxygen with configuration interaction taken into account in the 6-31G basis are presented. Transition dipole moments of triplet-triplet (1³Π_g ← B ³Σ _u ^? , 1³Π_g ← A ³Σ _u ⁺ , 1³Π_g ← A′ ³Δ_u, B ³Σ _u ^? ← X ³Σ _g ^? , 2³Π_u ← 1³Π _g, 2³Σ _g ^? ← B ³Σ _u ^? , 1³Π_u ← X ³Σ _g ^? , 2³Π_u ← X ³Σ _g ^? , 2³Π _g ← A′³Δ_u, 3³Π_g ← A′ ³Δ _u, 2³Δ_u ← 2³Π_g, 3³Π_g ← B ³Σ _u ^? , and 2³Π_g ← A ³Σ _u ⁺ ) and singlet-singlet (2¹Σ _g ⁺ ← 2¹Π_u, 2¹Π_u ← 1¹Π ^g, ¹Π_u ← 2¹Δ_g, 1¹Π_g ← c ¹Σ _u ^? , ¹Π_u ← b ¹Σ _g ⁺ , 1¹Δ _u ← a ¹Δ_g, 2¹Π_u ← a ¹Δ_g, 2¹Δ_g ← 1¹Δ_u, ¹Π _u ← a ¹Δ _g, 1¹Π_u ← b ¹Σ _g ⁺ , 2¹Π_g ← 1¹Π_u, 2¹Π _g ← c ¹Σ _u ^? , 1¹Δ _u ← 1¹Π _g, f′Σ _u ⁺ ← b ¹Σ _g ⁺ , 2¹Σ _g ⁺ ← f ′¹Σ _u ⁺ , 3¹Π_g ← 1¹Δ_u) radiative transitions are calculated as functions of internuclear separation. The possibility of observing these transitions under experimental conditions is discussed.     

EPR studies on the di-nitrogen centers with nonequivalent atoms in a reddish-brown plastically deformed diamond

Two new di-nitrogen centers, which were labeled M2 and M3, were found together with known W7 and N4 centers in an unusual reddish-brown natural diamond. The following magnetic hyperfine interaction parameters (expressed in MHz) were determined for the two nitrogen atoms:A ₁ ⁽¹⁾ =117.95(5),A ₁ ⁽²⁾ =A ₁ ⁽³⁾ =84.48(5),A ₂ ⁽¹⁾ =7.1(1),A ₂ ⁽²⁾ =A ₂ ⁽³⁾ =6.6(1) for M2 andA ₁ ⁽¹⁾ =121.55(5),A ₁ ⁽²⁾ =A ₁ ⁽³⁾ =85.90(5),A ₂ ⁽¹⁾ =6.0(1),A ₂ ⁽²⁾ =5.4(1),A ₂ ⁽³⁾ =5.1(1) for M3. Hyperfine interaction tensors for the nitrogen atom N₁ with a larger interaction have axial symmetry about the <111> direction, but those for the other nitrogen atom, N₂, appear to be small, almost isotropic. Probable models of the M2 and M3 centers are suggested and discussed.     

Hyperfine anomaly in the spectrum of the osmium atom. effect of the spatial distribution of nuclear charge

Contributions of the superposition of configurations ns ²5d ⁸+ns5d ⁸ n′s (n=1–5, n′=6–10) and ns ²5d ⁶+ns5d ⁶ n′s (n=1–6, n′=7–10) to parameters a _5d ⁰¹ , a _5d ¹² , and a _5d ¹⁰ of the hyperfine structure in the spectrum of the osmium atom OsI are calculated. It is shown that the nonzero contribution is made only to a _5d ¹⁰ . The effect of the spatial distribution of nuclear charge on the parameters of the hyperfine structure in the spectra of ¹⁸⁷Os and ¹⁸⁹Os isotopes and on the hyperfine anomaly for the 5d ⁷6s levels in the spectrum of these isotopes is estimated.     

Study of the lowest electronic states of Xe2, XeKr, and XeAr molecules by the method of multiphoton resonance ionization

The spectra of Xe₂, XeKr, and XeAr molecules in the range 66 500–68 800 cm^?1 are obtained by the methods of (2 + n) and (3 + n) (n = 1, 2, 3) resonance multiphoton ionization during the registration of molecular and atomic ions. The combining of two-and three-photon resonance excitations of Xe₂ molecules makes it possible to obtain the spectra caused by transitions from the ground state X0 _g ⁺ to the excited states of Xe*6s[3/2] _1,2 ^o Xe¹ S ₀ molecules both of the even (0 _g ⁺ , 1 _g ) and of the odd (B0 _u ⁺ , B′1 _u , 2 _u ) symmetries. The data on the Ω = 2 _u state of the Xe₂ molecule with the dissociation limit Xe*6s[3/2] ₂ ^o + Xe¹ S ₀ and on the Ω = 1 state of the XeAr molecule with the dissociation limit Xe*6s[3/2] ₁ ^o + Ar¹ S ₀ are obtained for the first time. The potential curve of the excited 2 _u state of the Xe*6s[3/2] ₂ ^o Xe¹ S ₀ molecule is repulsive and intersects the potential curve of the B0 _u ⁺ state of the Xe*6s[3/2] ₁ ^o Xe¹ S ₀ molecule. In the case of the three-photon excitation, it is observed that all the bands in the spectra of XeKr and XeAr molecules are broadened and are shifted, which indicates that, in an intense light field, the influence of the dynamic Stark effect is significant.     

Effective hamiltonian of Bloch electrons in a homogeneous electrical field

In order to construct a band mechanics of Bloch electrons in a homogeneous electrical field E with the interband interaction taken into account, a method of determining the exact single-band Hamiltonian $$H_q = \varepsilon _q^F (\kappa ) + Fi\frac{\partial }{{\partial \kappa }}$$ is proposed, where ε _q ^F (κ) is the renormalized (effective) electron dispersion law for R = 0 and the q-th Bloch band,F= ¦e¦·E. The function ε _q ^F (κ) is expressed in terms of the interband element coordinates as well as in terms of periodic solutions of the system of ordinary differential equations which degenerateinto a common Riccati equation in a two-band approximation. A solution of the system and the form of ε _q ^F (κ), in agreement with the Wanhier result, is found in the quasiclassical approximation.     

Spin-1 particle in a homogeneous magnetic field

The Corben-Schwinger theory gives imaginary values of the energy, forS ₃ ² =1 states, in very intensive magnetic fields. The theory proposed by the author, which is most satisfactory in the nonrelativistic approximation, does not have this defect forS ₃ ² =1 states, but it appears forS ₃ ² =0 states.