Zeros of tree amplitudes at rest and symmetries of mechanical systems

We consider the tree amplitudes of production of $n_2$ scalar particles by $n_1$ particles of another kind, where both initial and final particles are at rest and on mass shell, in a model of two scalar fields with $O(2)$ symmetric interaction and unequal masses. We find that these amplitudes are zero except for the lowest possible $n_1$ and $n_2$, and that the cancellation of the corresponding Feynman graphs occurs due to a special symmetry of the classical mechanical counterpart of this theory. This feature is rather general and is inherent in various other scalar field theories.Comment: 11 pages Preprint INR-830/93, August 199

Linear in temperature correction to the Casimir force

We discuss the temperature correction to the Casimir force between nonideal metallic bodies which caused disagreement in the literature. A general method to find the troubling term is proposed that does not require a direct reference to the Lifshitz formula. The linear in temperature correction is shown to survive for nonideal metals. It is important for small separations between bodies tested in the recent experiments.Comment: 5 pages, REVTEX, to be published in Phys. Lett.

Tree amplitudes at multiparticle threshold in a model with softly broken O(2)O(2) symmetry

Tree amplitudes of the production of two kinds of scalar particles at threshold from one virtual particle are calculated in a model of two scalar fields with $O(2)$ symmetric quartic interaction and unequal masses. These amplitudes exhibit interesting factorial and exponential behaviour at large multiplicities. As a by-product we observe that the kinematically allowed decay of one real particle into $n$ real particles of another kind, all at rest, has zero tree amplitude in this model for $n>2$.Comment: 17 pages. Preprint INR-823/9

On the nullification of threshold amplitudes

The nullification of threshold amplitudes is considered within the conventional framework of quantum field theory. The relevant Ward identities for the reduced theory are derived both on path-integral and diagrammatic levels. They are then used to prove the vanishing of tree-graph threshold amplitudes.Comment: 16 page

Anomalous Behavior of 2+ Excitations around 132Sn

In certain neutron-rich Te isotopes, a decrease in the energy of the first excited 2+ state is accompanied by a decrease in the E2 strength to that state from the ground state, contradicting simple systematics and general intuition about quadrupole collectivity. We use a separable quadrupole-plus-pairing Hamiltonian and the quasiparticle random phase approximation to calculate energies, B(E2,0+ -> 2+) strengths, and g factors for the lowest 2+ states near 132Sn (Z >= 50). We trace the anomalous behavior in the Te isotopes to a reduced neutron pairing above the N = 82 magic gap.Comment: 1 figure added. to be published in Phys. Rev.

Solution of the microscopic gap equation for a slab of nuclear matter with the Paris NN-potential

The gap equation in the $^1S_0$-channel is solved for a nuclear slab with the separable form of the Paris potential. The gap equation is considered in the model space in terms of the effective pairing interaction which is found in the complementary subspace. The absolute value of the gap $\Delta$ turned out to be very sensitive to the cutoff $K_{max}$ in the momentum space in the equation for the effective interaction. It is necessary to take $K_{max}=160-180 fm^{-1}$ to guarantee 1% accuracy for $\Delta$. The gap equation itself is solved directly, without any additional approximations. The solution reveals the surface enhancement of the gap $\Delta$ which was earlier found with an approximate consideration. A strong surface-volume interplay was found also implying a kind of the proximity effect. The diagonal matrix elements of $\Delta$ turned out to be rather close to the empirical values for heavy atomic nuclei.Comment: 17 pages, 12 figure

Charge ordering and structural distortions at low temperature in La<SUB>2-2x</SUB>Sr<SUB>1+2x</SUB>Mn₂O₇ (x=0.475 and 0.5)

In this paper we present x-ray scattering results of charge and orbital ordering in the bilayer manganite La222xSr112xMn2O7 with doping levels x50.5 and x50.475. Using high-energy x-ray scattering, the structural modulation due to the Jahn-Teller ordering and the charge ordering due to the Mn31/Mn41 pattern have been measured. Both the x50.5 and x50.475 samples are found to display charge and Jahn-Teller order. We have confirmed that the wave vectors of the Jahn-Teller order, charge order, and orbital order are QW 5(0.25,0.25,0), QW 5(0.5,0.5,0) and QW 5(0.25,0.25,0). The origin of these has been confirmed by resonant x-ray scattering in the vicinity of the Mn K edge using polarization analysis. Contrary to previous studies, the Jahn-Teller order is found to be not reentrant, but is found to reduce in intensity at temperatures below 140 K for both samples. Charge ordering was also detected in the x50.5 sample below this temperature

UK export performance research - review and implications

Previous research on export performance has been criticized for being a mosaic of autonomous endeavours and for a lack of theoretical development. Building upon extant models of export performance, and a review and analysis of research on export performance in the UK for the period 1990-2005, an integrated model of export performance is developed and theoretical explanations of export performance are put forward. It is suggested that a multi-theory approach to explaining export performance is viable. Management and policy implications for the UK emerging from the review and synthesis of the literature and the integrated model are discussed

Collectivity, Phase Transitions and Exceptional Points in Open Quantum Systems

Phase transitions in open quantum systems, which are associated with the formation of collective states of a large width and of trapped states with rather small widths, are related to exceptional points of the Hamiltonian. Exceptional points are the singularities of the spectrum and eigenfunctions, when they are considered as functions of a coupling parameter. In the present paper this parameter is the coupling strength to the continuum. It is shown that the positions of the exceptional points (their accumulation point in the thermodynamical limit) depend on the particular type and energy dependence of the coupling to the continuum in the same way as the transition point of the corresponding phase transition.Comment: 22 pages, 4 figure

Common determinants of dental caries and obesity in children : a multi-ethnic nested birth cohort study in the United Kingdom

The article examines the common determinants of childhood dental caries and obesity. Longitudinal data from the Born in Bradford cohort study (BiB1000) (n = 1735) and dental data (dental general anaesthetics (GA) and oral health survey 2014/15) (n = 171) were used to test a framework on the social determinants of childhood dental caries (decayed, missing, filled teeth (dmft) index) and obesity (body mass index (BMI)). The BiB1000 data were collected at pregnancy week 26–28 and after birth at 6, 12, 18, 24 and 36 months. The determinants were demographics, wellbeing, socio-economic status (SES), dietary behaviours and physical activity behaviour of the children. Missing data were accounted for through multiple imputation (MI). The framework was tested through structural equation modelling. Overall, the model fit was adequate. No alcohol consumption of the mother after giving birth, higher frequency of child drinking sugar-sweetened beverages, emotional and behavioural difficulties of the child and being male were directly associated with both BMI and dental caries. Caregivers uninvolved or indulgent feeding style were associated with higher BMI and less dental caries. Social deprivation was associated with lower BMI and higher dmft. Five determinants were directly associated with BMI only. Fifteen indirect paths were significant for both child dental caries and BMI. The findings suggest common determinants for both childhood obesity and dental caries. Common risk factor approach seems appropriate for planning future health promotion programmes