Short-range Cutoff Research Articles

Equilibrium configuration of self-gravitating charged dust clouds: Particle approach

A three dimensional Molecular Dynamics (MD) simulation is carried out to explore the equilibrium configurations of charged dust particles. These equilibrium configurations are of astrophysical significance for the conditions of molecular clouds and the interstellar medium. The interaction among the dust grains is modeled by Yukawa repulsion and gravitational attraction. The spherically symmetric equilibria are constructed which are characterized by three parameters: (i) the number of particles in the cloud, (ii) Γg (defined in the text) where Γg−1 is the short range cutoff of the interparticle potential, and (iii) the temperature of the grains. The effects of these parameters on dust cloud are investigated using a radial density profile. The problem of equilibrium is also formulated in the mean field limit where total dust pressure, which is the sum of kinetic pressure and the electrostatic pressure, balances the self-gravity. The mean field solutions agree well with the results of MD simulations. The astrophysical significance of the results is briefly discussed.

Molecular dynamics calculation of the spectral densities of plasma fluctuations

Spectral densities of plasma fluctuations are calculated for the thermal case using classical molecular dynamics (MD) assuming Coulomb interactions and a short-range cutoff radius. The aim of the calculation is to verify limits and performances of such calculations in the light of possible generalizations, e.g. collisional or non-ideal plasmas. Results are presented for ideal, collisionless, fully ionized thermal plasmas. Comparison with the analytical theory reveals a generally satisfactory agreement with possibility for improvement when more strict numerical parameters are used albeit with a strong increase in computational cost. The largest deviations have been observed in the vicinity of the weakly damped eigenmodes. The agreement is strong in other parts of the spectrum, where Landau damping is prominent, and overcomes the effects stemming from the excess collisionality and coupling as well as from the exclusion of short-range collisions.

Local chiral potentials with Δ -intermediate states and the structure of light nuclei

We present fully local versions of the minimally non-local nucleon-nucleon potentials constructed in a previous paper [M.\ Piarulli {\it et al.}, Phys.\ Rev.\ C {\bf 91}, 024003 (2015)], and use them in hypersperical-harmonics and quantum Monte Carlo calculations of ground and excited states of $^3$H, $^3$He, $^4$He, $^6$He, and $^6$Li nuclei. The long-range part of these local potentials includes one- and two-pion exchange contributions without and with $\Delta$-isobars in the intermediate states up to order $Q^3$ ($Q$ denotes generically the low momentum scale) in the chiral expansion, while the short-range part consists of contact interactions up to order $Q^4$. The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database in two different ranges of laboratory energies, either 0--125 MeV or 0--200 MeV, and to the deuteron binding energy and $nn$ singlet scattering length. Fits to these data are performed for three models characterized by long- and short-range cutoffs, $R_{\rm L}$ and $R_{\rm S}$ respectively, ranging from $(R_{\rm L},R_{\rm S})=(1.2,0.8)$ fm down to $(0.8,0.6)$ fm. The long-range (short-range) cutoff regularizes the one- and two-pion exchange (contact) part of the potential.

Mechanical properties of silica glass predicted by a pair-wise potential in molecular dynamics simulations

Pair-wise BKS potential for silica glass was modified by changing the short-range cutoff to improve the prediction of mechanical properties. Classical molecular dynamic (MD) simulations were carried out by using this modified potential and better prediction of mechanical properties at ambient conditions and their changes with pressure at room temperature were shown. It was further observed that there was no major change in structural properties when different short-range cutoffs were used to relax the glass. To better understand the contribution of structure to the mechanical properties, samples quenched under various cooling rates and one structure optimized in first principles calculations were used. It was seen that the improvement of structure has a less effect than improving the interaction potential in determining the mechanical properties of BKS silica glass. The strength and weakness of the BKS potential for silica glass was discussed.

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange includingΔresonances

We construct a coordinate-space chiral potential, including $\Delta$-isobar intermediate states in its two-pion-exchange component. The contact interactions entering at next-to-leading and next-to-next-to-next-to-leading orders ($Q^2$ and $Q^4$, respectively, $Q$ denoting generically the low momentum scale) are rearranged by Fierz transformations to yield terms at most quadratic in the relative momentum operator of the two nucleons. The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database, consisting of 2309 $pp$ and 2982 $np$ data (including, respectively, 148 and 218 normalizations) in the laboratory-energy range 0--300 MeV. For the total 5291 $pp$ and $np$ data in this range, we obtain a $\chi^2$/datum of roughly 1.3 for a set of three models characterized by long- and short-range cutoffs, $R_{\rm L}$ and $R_{\rm S}$ respectively, ranging from $(R_{\rm L},R_{\rm S})=(1.2,0.8)$ fm down to $(0.8,0.6)$ fm. The long-range (short-range) cutoff regularizes the one- and two-pion exchange (contact) part of the potential.

Interaction of half-quantized vortices in two-component Bose-Einstein condensates

We study the asymptotic interaction between two half-quantized vortices in two-component Bose-Einstein condensates. When two vortices in different components are placed at distance $2R$, the leading order of the force between them is found to be $(\mathrm{ln}R/\ensuremath{\xi}\ensuremath{-}1/2)/{R}^{3}$, in contrast to $1/R$ between vortices placed in the same component. We derive it analytically using the Abrikosov ansatz and the profile functions of the vortices, confirmed numerically with the Gross-Pitaevskii model. We also find that the short-range cutoff of the intervortex potential linearly depends on the healing length.

Error and timing analysis of multiple time-step integration methods for molecular dynamics

Molecular dynamics simulations of biomolecules performed using multiple time-step integration methods are hampered by resonance instabilities. We analyze the properties of a simple 1D linear system integrated with the symplectic reference system propagator MTS (r-RESPA) technique following earlier work by others. A closed form expression for the time step dependent Hamiltonian which corresponds to r-RESPA integration of the model is derived. This permits us to present an analytic formula for the dependence of the integration accuracy on short-range force cutoff range. A detailed analysis of the force decomposition for the standard Ewald summation method is then given as the Ewald method is a good candidate to achieve high scaling on modern massively parallel machines. We test the new analysis on a realistic system, a protein in water. Under Langevin dynamics with a weak friction coefficient ( ζ = 1 ps −1 ) to maintain temperature control and using the SHAKE algorithm to freeze out high frequency vibrations, we show that the 5 fs resonance barrier present when all degrees of freedom are unconstrained is postponed to ≈ 12 fs . An iso-error boundary with respect to the short-range cutoff range and multiple time step size agrees well with the analytical results which are valid due to dominance of the high frequency modes in determining integrator accuracy. Using r-RESPA to treat the long range interactions results in a 6× increase in efficiency for the decomposition described in the text.

Thermal roughening of a solid-on-solid model with elastic interaction

We analyze the effects of a long-ranged interaction between surface defects on thermal roughening within the framework of a solid-on-solid model of a crystal surface by means of Monte Carlo simulation. Below roughening the interaction can be understood in terms of a repulsive step-step interaction, which is modeled by elastic dipoles located on sites adjacent to the steps. In order to reduce the computational effort involved in calculating interaction energy based on long-ranged potentials, we employ a multigrid scheme. As a result of the long-range character of the repulsive step interaction, the roughening temperature increases drastically compared to a system with short-range cutoff as a consequence of anticorrelations between surface defects.

Nucleon-Nucleon Phase Shifts in the ExtendedQuark-Delocalization Colour-Screening Model

An alternative method is applied to the study of nucleon-nucleon scattering phase shifts within the framework of the extended quarkdelocalization colour-screening model, in which the one-pion exchangewith short-range cutoff is included.

Is there a Di-Ω State?**The project partly supported by the Foundation of the Heavy Ion Research Facility Laboratory, National Natural Science Foundation of China, and the Foundation of the Education Ministry of China

Resonating-group method has been applied to calculate the dibaryon state in the framework of the extended quark-delocalization color-screening model. The mass of the di-Ω is predicted to be about 45 MeV lower than the threshold. The effect of channel coupling due to the tensor force and sensitivity to meson exchange short-range cutoff radius, have also been studied.

Di-Ω in the extended quark delocalization, color screening model

The \ensuremath{\Omega}\ensuremath{\Omega} $(SIJ=\ensuremath{-}6,0,0)$ dibaryon state is studied with the extended quark-delocalization color-screening model including a \ensuremath{\pi}-meson exchange tail, which reproduces the properties of the deuteron quantitatively. We find the mass of the di-\ensuremath{\Omega} to be about 45 MeV lower than the \ensuremath{\Omega}-\ensuremath{\Omega} threshold. The effect of channel coupling due to the tensor force has been calculated and found to be small in this case. We have also studied the effect of other pseudoscalar meson exchanges and sensitivity to the short-range cutoff radius ${r}_{0}$ for the meson exchanges.

Collapse in systems with attractive nonintegrable potentials.

Collapse, or a gravitational-like phase transition, is found in microcanonical ensembles of particles with an attractive 1/r(alpha) potential not only for alpha = 1 but for all 0<alpha<3. The phase behavior of the system is complex: If an effective sufficiently short-range cutoff is applied, the density of the collapsed phase is finite everywhere; if not, the collapse results in a density singularity. Also, with increasing effective cutoff range, the gravitational phase transition will cross over to a normal first-order phase transition.

Phase transitions in systems with 1/r(alpha) attractive interactions.

Collapse, or a gravitational-like phase transition is studied in a microcanonical ensemble of particles with an attractive 1/r(alpha) potential. A mean-field continuous integral equation is used to determine a saddle-point density profile that extremizes the entropy functional. For all 0 < alpha < 3, a critical energy is determined below which the entropy of the system exhibits a discontinuous jump. If an effective short-range cutoff is applied, the entropy jump is finite; if not, the entropy diverges to +infinity. A stable integral equation solution represents a state with maximal entropy; the reverse is always true only for a modified integral equation introduced here.

Realistic models of pion-exchange three-nucleon interactions

We present realistic models of pion-exchange three-nucleon interactions obtained by fitting the energies of all the 17 bound or narrow states of $3&lt;~A&lt;~8$ nucleons, calculated with less than 2% error using the Green's function Monte Carlo method. The models contain two-pion-exchange terms due to $\ensuremath{\pi}N$ scattering in S and P waves, three-pion-exchange terms due to ring diagrams with one $\ensuremath{\Delta}$ in the intermediate states, and a phenomenological repulsive term to take into account relativistic effects, the suppression of the two-pion-exchange two-nucleon interaction by the third nucleon, and other effects. The models have five parameters, consisting of the strength of the four interactions and the short-range cutoff. The 17 fitted energies are insufficient to determine all of them uniquely. We consider five models, each having three adjustable parameters and assumed values for the other two. They reproduce the observed energies with an rms error $&lt;1%$ when used together with the Argonne ${v}_{18}$ two-nucleon interaction. In one of the models the $\ensuremath{\pi}N$ S-wave scattering interaction is set to zero; in all others it is assumed to have the strength suggested by chiral effective-field theory. One of the models also assumes that the $\ensuremath{\pi}N$ P-wave scattering interaction has the strength suggested by effective-field theories, and the cutoff is adjusted to fit the data. In all other models the cutoff is taken to be the same as in the ${v}_{18}$ interaction. The effect of relativistic boost correction to the two-nucleon interaction on the strength of the repulsive three-nucleon interaction is estimated. Many calculated properties of $A&lt;~8$ nuclei, including radii, magnetic dipole, and electric quadrupole moments, isobaric analog energy differences, etc., are tabulated. Results obtained with only Argonne ${v}_{8}^{\ensuremath{'}}$ and ${v}_{18}$ interactions are also reported. In addition, we present results for seven- and eight-body neutron drops in external potential wells.

An Ordered Phase with Slow Decay of Correlations in Continuum $1/r^2$ Ising Models

For continuum $1/r^2$ Ising models, we prove that the critical value of the long range coupling constant (inverse temperature), above which an ordered phase occurs (for strong short range cutoff), is exactly 1. This leads to a proof of the existence of an ordered phase with slow decay of correlations. Our arguments involve comparisons between continuum and discrete Ising models, including (quenched and annealed) site diluted models, which may be of independent interest.

Recent advances in pressure broadening: experiment and theory

Recent measurements of pressure broadened linewidths at both ambient and cryogenic temperatures are presented. For simple systems, such as CO broadened by He, accurate molecular scattering theory calculations give quantitative agreement. Results for more complex systems, which are not yet amenable to accurate calculations, are discussed in the context of Anderson-like theories; these suggest that a short-range cutoff procedure based on the infinite order sudden scattering approximation might prove useful.

The excluded-volume expansion in polymer chains: Evaluation of the Flory exponent in the Gaussian approximation

The self-consistent excluded-volume chain-expansion problem is reexamined, in the Gaussian approximation. The integral equation resulting from minimization of the free energy is solved analytically on the basis of a conjecture that is shown to be logically consistent. The mean-square distance between atoms separated by k bonds (k≫1) within an infinitely large chain is 〈r2(k)〉∝k6/5{∏∞n=1Ln [ln(k/k̄)]}2/5, where Ln(x) =1+an ln Ln−1(x), L1=1+a1x; k̄ is a short-range cutoff and the ai’s are suitable constants, generally comprised between 0 and 1, while limn→∞ an =1. Accordingly, the divergence associated with the short-range cutoff is explicitly evaluated instead of being removed through renormalization techniques. For (k/k̄)→∞ the above function is independent of k̄ and we have ln〈r2(k)〉∝6/5 ln k, thus reobtaining Flory’s asymptotic exponent. Numerical results obtained from the integral equation in the nonasymptotic regime give support to the above analytic solution.

Geometry of polymer chains near the theta-point and dimensional regularization

We consider the ab initio continuum theory of polymer chains in a theta solvent, interacting via two- and three-body forces, with a short range cutoff s0 and in continuous space dimension d(2&amp;lt;d≤3). We calculate the full expression in terms of d and s0 of the squared end-to-end distance R2 of a single chain, and of its squared radius of gyration R2G, to first order in the interactions. We show explicitly how the cutoff is removed in any d, up to d=3, to yield an effective three-parameter theory. We show how this procedure is exactly equivalent to dimensional regularization. This completely disproves recent claims that for polymers in a θ solvent, cut-off theories and dimensional regularization would not be equivalent near three dimensions, or in three dimensions. We locate numerical errors in calculations by others, which explain the discrepancies. We also give to all orders the general relation existing between cut-off and dimensional regularizations for the three-parameter model, for 2&amp;lt;d&amp;lt;3.

Shallow-deep instabilities of chalcogen donors in silicon

Recent experiments show the occurrence of shallow-deep instabilities for the binding energies of the many-valley ground-state multiplets of all substitutional chalcogen donors in Si. We now analyze these experiments in terms of our previous theory, which predicted the possibility of such instabilities. We then study the theoretical dependence of the shallow-deep instability on a short-range cutoff in the impurity potential. We find such a dependence to be strongly nonlinear in a very narrow cutoff interval. That can explain why such a wide range of binding energies occurs in nature for the ${A}_{1}(1s)$ levels of donors and excitons, as opposed to the $E(1s)$ and ${T}_{2}(1s)$ levels.

The interaction of nucleons with antinucleons. III. Photon and pion emission from bound states

We calculate widths and branching ratios for the emission of γ rays or pions from a bound state of the nucleon-antinucleon (NN) system, leading to another NN bound state. We use a realistic potential model to describe the medium- and long-range parts of the NN interaction, and parametrize the short-range behavior. The general features of γ and π transitions, based on the selection rules, are emphasized. We illustrate these features with typical results for several choices of the short-range cutoff. The observation of pions is a necessary supplement to the γ-ray experiments, in order to significantly constrain the possible quantum number assignments of final states. We investigate transitions between quasiatomic (QA) and more deeply bound quasinuclear (QN) states, and also QN to QN γ or π emission. The former may have been seen in experiments involving the pp atom, while the latter are in some optimum cases accessible in pd spectator experiments, although there is no evidence for these QN to QN transitions as yet. The role of isospin mixing in QA states is discussed, as well as the importance of maintaining orthogonality of the QA and QN wave functions.