Pairing gaps in Hartree-Fock Bogoliubov theory with the Gogny D1S interaction

As part of a program to study odd-A nuclei in the Hartree-Fock-Bogoliubov (HFB) theory, we have developed a new calculational tool to find the HFB minima of odd-A nuclei based on the gradient method and using interactions of Gogny's form. The HFB minimization includes both time-even and time-odd fields in the energy functional, avoiding the commonly used "filling approximation". Here we apply the method to calculate neutron pairing gaps in some representative isotope chains of spherical and deformed nuclei, namely the Z=8,50 and 82 spherical chains and the Z=62 and 92 deformed chains. We find that the gradient method is quite robust, permitting us to carry out systematic surveys involving many nuclei. We find that the time-odd field does not have large effect on the pairing gaps calculated with the Gogny D1S interaction. Typically, adding the T-odd field as a perturbation increases the pairing gap by ~100 keV, but the re-minimization brings the gap back down. This outcome is very similar to results reported for the Skyrme family of nuclear energy density functionals. Comparing the calculated gaps with the experimental ones, we find that the theoretical errors have both signs implying that the D1S interaction has a reasonable overall strength. However, we find some systematic deficiencies comparing spherical and deformed chains and comparing the lighter chains with the heavier ones. The gaps for heavy spherical nuclei are too high, while those for deformed nuclei tend to be too low. The calculated gaps of spherical nuclei show hardly any A-dependence, contrary to the data. Inclusion of the T-odd component of the interaction does not change these qualitative findings

Mass Detection with Nonlinear Nanomechanical Resonator

Nanomechanical resonators having small mass, high resonance frequency and low damping rate are widely employed as mass detectors. We study the performances of such a detector when the resonator is driven into a region of nonlinear oscillations. We predict theoretically that in this region the system acts as a phase-sensitive mechanical amplifier. This behavior can be exploited to achieve noise squeezing in the output signal when homodyne detection is employed for readout. We show that mass sensitivity of the device in this region may exceed the upper bound imposed by thermomechanical noise upon the sensitivity when operating in the linear region. On the other hand, we show that the high mass sensitivity is accompanied by a slowing down of the response of the system to a change in the mass

ESTIMATING SITE-SPECIFIC NITROGEN CROP RESPONSE FUNCTIONS: A CONCEPTUAL FRAMEWORK AND GEOSTATISTICAL MODEL

Confirming the precision agriculture hypothesis for variable rate nitrogen applications (VRA) is challenging. To confront this challenge, researchers have used increasingly sophisticated statistical models to estimate and compare site-specific crop response functions (SSCRFs). While progress has been made, it has been hampered by the lack of a conceptual framework to guide the development of appropriate statistical models. This paper provides such a framework and demonstrates its utility by developing a heteroscedastic, fixed and random effects, geostatistical model to test if VRA can increase nitrogen returns. The novelty of the model is the inclusion of site, spatial, treatment, and treatment strip heteroscedasticity and correlation. Applied to data collected in 1995 from two corn nitrogen response experiments in South Central Minnesota, results demonstrate the importance of including site, spatial, treatment, and treatment strip effects in the estimation of SSCRFs. Results also indicate a significant potential for VRA to increase nitrogen returns and that these potential returns increase as the area of the management unit decreases. At one location, there was greater than a 95% chance that VRA could have increased profitability if the cost of implementing VRA was less than 14.5 $ha-1. At the other location, if implementation costs were less than 48.3$ ha-1, there was greater than a 95% chance of increased profitability.Crop Production/Industries,

High frequency electro-optic measurement of strained silicon racetrack resonators

The observation of the electro-optic effect in strained silicon waveguides has been considered as a direct manifestation of an induced $\chi^{(2)}$ non-linearity in the material. In this work, we perform high frequency measurements on strained silicon racetrack resonators. Strain is controlled by a mechanical deformation of the waveguide. It is shown that any optical modulation vanishes independently of the applied strain when the applied voltage varies much faster than the carrier effective lifetime, and that the DC modulation is also largely independent of the applied strain. This demonstrates that plasma carrier dispersion is responsible for the observed electro-optic effect. After normalizing out free carrier effects, our results set an upper limit of $8\,pm/V$ to the induced high-speed $\chi^{(2)}_{eff,zzz}$ tensor element at an applied stress of $-0.5\,GPa$. This upper limit is about one order of magnitude lower than the previously reported values for static electro-optic measurements

A Lattice Study of the Gluon Propagator in Momentum Space

We consider pure glue QCD at beta=5.7, beta=6.0 and beta=6.3. We evaluate the gluon propagator both in time at zero 3-momentum and in momentum space. From the former quantity we obtain evidence for a dynamically generated effective mass, which at beta=6.0 and beta=6.3 increases with the time separation of the sources, in agreement with earlier results. The momentum space propagator G(k) provides further evidence for mass generation. In particular, at beta=6.0, for k less than 1 GeV, the propagator G(k) can be fit to a continuum formula proposed by Gribov and others, which contains a mass scale b, presumably related to the hadronization mass scale. For higher momenta Gribov's model no longer provides a good fit, as G(k) tends rather to follow an inverse power law. The results at beta=6.3 are consistent with those at beta=6.0, but only the high momentum region is accessible on this lattice. We find b in the range of three to four hundred MeV and the exponent of the inverse power law about 2.7. On the other hand, at beta=5.7 (where we can only study momenta up to 1 GeV) G(k) is best fit to a simple massive boson propagator with mass m. We argue that such a discrepancy may be related to a lack of scaling for low momenta at beta=5.7. {}From our results, the study of correlation functions in momentum space looks promising, especially because the data points in Fourier space turn out to be much less correlated than in real space.Comment: 19 pages + 12 uuencoded PostScript picture

Nonlocal Scalar Quantum Field Theory: Functional Integration, Basis Functions Representation and Strong Coupling Expansion

Nonlocal QFT of one-component scalar field $\varphi$ in $D$-dimensional Euclidean spacetime is considered. The generating functional (GF) of complete Green functions $\mathcal{Z}$ as a functional of external source $j$, coupling constant $g$, and spatial measure $d\mu$ is studied. An expression for GF $\mathcal{Z}$ in terms of the abstract integral over the primary field $\varphi$ is given. An expression for GF $\mathcal{Z}$ in terms of integrals over the primary field and separable Hilbert space (HS) is obtained by means of a separable expansion of the free theory inverse propagator $\hat{L}$ over the separable HS basis. The classification of functional integration measures $\mathcal{D}\left[\varphi\right]$ is formulated, according to which trivial and two nontrivial versions of GF $\mathcal{Z}$ are obtained. Nontrivial versions of GF $\mathcal{Z}$ are expressed in terms of $1$-norm and $0$-norm, respectively. The definition of the $0$-norm generator $\varPsi$ is suggested. Simple cases of sharp and smooth generators are considered. Expressions for GF $\mathcal{Z}$ in terms of integrals over the separable HS with new integrands are obtained. For polynomial theories $\varphi^{2n},\, n=2,3,4,\ldots,$ and for the nonpolynomial theory $\sinh^{4}\varphi$, integrals over the separable HS in terms of a power series over the inverse coupling constant $1/\sqrt{g}$ for both norms ($1$-norm and $0$-norm) are calculated. Critical values of model parameters when a phase transition occurs are found numerically. A generalization of the theory to the case of the uncountable integral over HS is formulated. A comparison of two GFs $\mathcal{Z}$, one in the case of uncountable HS integral and one obtained using the Parseval-Plancherel identity, is given.Comment: 26 pages, 2 figures; v2: significant additions in the text; prepared for the special issue "QCD and Hadron Structure" of the journal Particles; v3: minimal corrections; v4: paragraphs added related to Reviewer comment

S\mathcal{S}-Matrix of Nonlocal Scalar Quantum Field Theory in the Representation of Basis Functions

Nonlocal quantum theory of one-component scalar field in $D$-dimensional Euclidean spacetime is studied in representations of $\mathcal{S}$-matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is formulated on coupling constant $g$ in the form of an infrared smooth function of argument $x$ for space without boundary. Nonlocality is given by evolution of Gaussian propagator for the local free theory with ultraviolet form factors depending on ultraviolet length parameter $l$. By representation of the $\mathcal{S}$-matrix in terms of abstract functional integral over primary scalar field, the $\mathcal{S}$ form of a grand canonical partition function is found. And, by expression of $\mathcal{S}$-matrix in terms of the partition function, the representation for $\mathcal{S}$ in terms of basis functions is obtained. Derivations are given for discrete case where basis functions are Hermite functions, and for continuous case where basis functions are trigonometric functions. The obtained expressions for the $\mathcal{S}$-matrix are investigated within the framework of variational principle based on Jensen inequality. Equations with separable kernels satisfied by variational function $q$ are found and solved, yielding results for both the polynomial theory $\varphi^{4}$ and the nonpolynomial sine-Gordon theory. A new definition of the $\mathcal{S}$-matrix is proposed to solve additional divergences which arise in application of Jensen inequality for the continuous case. Analytical results are illustrated numerically. For simplicity of numerical calculation: the $D=1$ case is considered, and propagator for the free theory $G$ is in the form of Gaussian function typically in the Virton-Quark model. The formulation for nonlocal QFT in momentum $k$ space of extra dimensions with subsequent compactification into physical spacetime is discussed.Comment: 38 pages, 18 figures; v2: significant text editing; v3: text and plots edited, references and acknowledgments added; prepared for the special issue of the journal Particles in memory of G.V. Efimo

The origin of the LMC stellar bar: clues from the SFH of the bar and inner disk

We discuss the origin of the LMC stellar bar by comparing the star formation histories (SFH) obtained from deep color-magnitude diagrams (CMDs) in the bar and in a number of fields in different directions within the inner disk. The CMDs, reaching the oldest main sequence turnoffs in these very crowded fields, have been obtained with VIMOS on the VLT in service mode, under very good seeing conditions. We show that the SFHs of all fields share the same patterns, with consistent variations of the star formation rate as a function of time in all of them. We therefore conclude that no specific event of star formation can be identified with the formation of the LMC bar, which instead likely formed from a redistribution of disk material that occurred when the LMC disk became bar unstable, and shared a common SFH with the inner disk thereafter. The strong similarity between the SFH of the center and edge of the bar rules out significant spatial variations of the SFH across the bar, which are predicted by scenarios of classic bar formation through buckling mechanisms.Comment: MNRAS Letters, accepte

Finite-volume two-pion energies and scattering in the quenched approximation

We investigate how L\"uscher's relation between the finite-volume energy of two pions at rest and pion scattering lengths has to be modified in quenched QCD. We find that this relation changes drastically, and in particular, that ``enhanced finite-volume corrections" of order $L^0=1$ and $L^{-2}$ occur at one loop ($L$ is the linear size of the box), due to the special properties of the $\eta'$ in the quenched approximation. We define quenched pion scattering lengths, and show that they are linearly divergent in the chiral limit. We estimate the size of these various effects in some numerical examples, and find that they can be substantial.Comment: 22 pages, uuencoded, compressed postscript fil

Pion-Nucleon Phase Shifts in Heavy Baryon Chiral Perturbation Theory

We calculate the phase shifts in the pion-nucleon scattering using the heavy baryon formalism. We consider phase shifts for the pion energy range of 140 to $200$ MeV. We employ two different methods for calculating the phase shifts - the first using the full third order calculation of the pion-nucleon scattering amplitude and the second by including the resonances $\Delta$ and $N^*$ as explicit degrees of freedom in the Lagrangian. We compare the results of the two methods with phase shifts extracted from fits to the pion-nucleon scattering data. We find good to fair agreement between the calculations and the phase shifts from scattering data.Comment: 14 pages, Latex, 6figures. Revised version to appear in Phys.Rev.