Range R0 Research Articles

Coulomb-free 1S0p − p scattering length from the quasi-free p + d → p + p + n reaction and its relation to universality

The Coulomb-free 1S0 proton-proton (p-p) scattering length relies heavily on numerous and distinct theoretical techniques to remove the Coulomb contribution. Here, it has been determined from the half-off-the-energy-shell p-p scattering cross section measured at center-of-mass energies below 1 MeV using the quasi-free p + d → p + p + n reaction. A Bayesian data-fitting approach using the expression of the s-wave nucleon-nucleon scattering cross section returned a p-p scattering length {a}_{pp}=-18.1{7}_{-0.58}^{+0.52}{| }_{stat}pm 0.0{1}_{syst} fm and effective range r0 = 2.80 ± 0.05stat ± 0.001syst fm. A model based on universality concepts has been developed to interpret this result. It accounts for the short-range interaction as a whole, nuclear and residual electromagnetic, according to what the s-wave phase-shift δ does in the description of low-energy nucleon-nucleon scattering data. We conclude that our parameters are representative of the short-range physics and propose to assess the charge symmetry breaking of the short-range interaction instead of just the nuclear interaction. This is consistent with the current understanding that the charge dependence of nuclear forces is due to different masses of up-down quarks and their electromagnetic interactions. This achievement suggests that these properties have a lesser than expected impact in the context of the charge symmetry breaking.

Computational Simulation of Basic Reproductive Strength on Covid 19

The basic reproduction number (R0), is presented to be an indicator of the contagiousness or transmissibility of infectious and parasitic agents. On the inception of a covid-19 epidemic, there’s a period admitted as the the susceptible, exposed or infected duration, earlier than an affected person can spread the virus to every other person. We enhance mathematical fashions to file for this period and observe version to the covid-19 contamination in china. We take a look at the epidemiological constants within the version, such as the transmigration charge and the simple reproductive variety, the usage of statistics of launched cases. We therefore estimate the act of the inclined, exposed or latency length inside the symptoms of a covid-19 infection. Through this critical version giant range R0, has been used to count on the sphere of persons right now infected with the contagious human and categorized the intensity of prone, exposed, and infected populations as quickly because the infectious is over, it can be immediately used to degree the contaminated regions. Primarily based at the power of R0, inclined, uncovered, and infected human being’s price has been calculated through Runge Kutta Felhberg method, maple 18. By using this investigation, the susceptible human’s infectious rates from covid-19 are strongly multiplied because the infected human being’s price moves up and down and the uncovered humans price decelerates with the boom of the basic reproductive wide variety. The transmissibility of covid-19 infection is related to the respiration lack of information of conventional humans and global warming.

Optimal control strategies for dengue transmission in pakistan

This paper presents a deterministic model for dengue virus transmission. The model is parameterized using data from the 2017 dengue outbreak in Pakistan. We estimated the basic reproduction number (R0) without any interventions for the 2017 dengue outbreak in Peshawar district of Pakistan as R0≈2.64, the distribution of the reproduction number lies in the range R0∈[1.21,5.24] (with a mean R0≈2.64). Optimal control theory is then applied to investigate the optimal strategy for curtailing the spread of the disease using two time-dependent control variables determined from sensitivity analysis. These control variables are insecticide use and vaccination. The results show that the two controls avert the same number of infections in the district regardless of the weights on the costs this is due to the reciprocal relationship between the cost of insecticide use and vaccination. A strong reciprocal relationship exists between the use of insecticide and vaccination; as the cost of insecticide increases the use of vaccination increases. The use of insecticide on the other hand slightly increases when vaccination level decreases due to increase in cost.

Influence of Hydrogen-like impurity and thickness effect on quantum transition of a two-level system in an asymmetric Gaussian potential quantum dot

Considering hydrogen-like impurity and the thickness effect,the eigenvalues and eigenfunctions of the electron ground state and first exited state in a quantum dot (QD) are derived by using the Lee-Low-Pines-Pekar variational method with a parabolic confinement potential well (PCPW) and an asymmetric Gaussian functional confinement potential well (AGFCPW) serving as the transverse and longitudinal confinement potential,respectively.Based on the above two states,a two-level system is constructed.Then,the electron quantum transition affected by a magnetic field is discussed in terms of the two-level system theory.The numerical calculations indicate that the electron transition probability Q deceases with the range R0 of the PCPW decreasing.With R0 decreasing,the amplitude of the transition probability Q decreases greatly when R0 is small (R0 2.5rp),but the decrease becomes small when R0 is large (R0 2.5rp).The transition probability Q decreases with the dielectric constant ratio increasing.For different values of the well width L of the AGFCPW,the change forms of the transition probability Q with the well width L are different:the transition probability Q decreases monotonically with the decreasing of the well width L when L is large (L 1.3rp), which is similar to the trend of the transition probability Q changing with the range R0 of the PCPW,but the oscillation of the transition probability Q is small with the decreasing of the well width L when L is small (L 1.3rp).Whereas, both changes are consistent basically when the range of the confinement potential (the value of R0 or L) is large since the AGFCPW can be approximated by the PCPW when z/L ≪ 1.For the electronic state and its change in the QD with a confinement potential,in any case,the results are rough without regard to the influence arising from the thickness of the QD.This shows that the AGFCPW is more accurate than the PCPW in reflecting the real confinement potential. This conclusion is in accordance with the experimental results.In addition,the transition probability Q decreases with increasing V0.The amplitude of the transition probability Q decreasing with increasing the dielectric constant ratio is enlarged with reducing the coupling strength .This indicates that the phonon (the polarization of the medium) effect cannot be ignored when investigating the change of the electronic state in the QD.The transition probability Q periodically oscillates and goes up with increasing the cyclotron frequency c.The external magnetic field is a kind of inducement causing the quantum transition of electronic state.The transition probability Q periodically oscillates and goes up with increasing the cyclotron frequency c,and is affected dramatically by the coupling strength :with increasing the coupling strength ,the oscillation period of Q increases,but the oscillation amplitude decreases.In a word,the transition probability of the electron is influenced significantly by some physical quantities,such as the coupling strength ,the dielectric constant ratio ,the resonant frequency of the magnetic field c,the well depth V0, and the well width L of AGFCPW.

Structure and dynamics of few-helium clusters using soft-core potentials

In this work we investigate the structure and dynamics of small clusters of Helium atoms. We consider bound states of clusters having A = 2, 3, 4, 5, 6 atoms and continuum states in the three-atom system. Motivated by the fact that the He-He system has a very large scattering length a compared to the range r0 of the He-He potential (r0/a < 1/10), we propose the use of a soft-core interparticle potential. We use an attractive gaussian potential that reproduces the values of the dimer binding energy and the atomatom scattering length obtained with one of the widely used He-He interactions, the LM2M2 potential. In addition, we include a repulsive three-body force to reproduce the trimer binding energy. With this model, consisting in the sum of a two- and a three-body potential, we show the spectrum of the four, five, and sixparticle systems and phase-shifts and inelasticities in the three-atom system. Comparisons to calculations using realistic He-He potentials are given. In addition some universal relations are explored.

Effective field theory as a limit ofR-matrix theory for light nuclear reactions

We study the zero channel radius limit of Wigner's R-matrix theory for two cases, and show that it corresponds to non-relativistic effective quantum field theory. We begin with the simple problem of single-channel n-p elastic scattering in the 1S0 channel. The dependence of the R matrix width and level energy on the channel radius, "a" for fixed scattering length a0 and effective range r0 is determined. It is shown that these quantities have a simple pole for a critical value of the channel radius. The 3H(d,n)4He reaction cross section, analyzed with a two-channel effective field theory in the previous paper, is then examined using a two-channel, single-level R-matrix parametrization. The resulting S matrix is shown to be identical in these two representations in the limit that R-matrix channel radii are taken to zero. This equivalence is established by giving the relationship between the low-energy constants of the effective field theory (couplings and mass) and the R-matrix parameters (reduced width amplitudes and level energy). An excellent three-parameter fit to the observed astrophysical factor S is found for "unphysical" values of the reduced widths.

Low-energy D*+D̄10 scattering and the nature of resonance-like structure Z+ (4430)

Low-energy scattering of D*+ and D̄10 meson is studied using quenched lattice QCD with improved lattice actions on anisotropic lattices. The threshold scattering parameters, namely the scattering length a0 and the effective range r0, for the s-wave scattering in JP = 0− channel are extracted: a0 = 2.52(47) fm and r0 = 0.7(1) fm. It is argued that, albeit the interaction between the two charmed mesons being attractive, it is unlikely that they can form a shallow bound state in this channel. Our calculation provides some useful information on the nature of the newly discovered resonance-like structure Z+(4430) by the Belle Collaboration.

Low-energy universality and scaling of van der Waals forces

At long distances interactions between neutral ground state atoms can be described by the Van der Waals potential V(r) =-C6/r^6-C8/r^8 - ... . In the ultra-cold regime atom-atom scattering is dominated by s-waves phase shifts given by an effective range expansion p cot d0 (p) = -1/a0 + r0 p^2/2 + ... in terms of the scattering length a0 and the effective range r0. We show that while for these potentials the scattering length cannot be predicted, the effective range is given by the universal low energy theorem r0 = A + B/a0+ C/a0^2 where A,B and C depend on the dispersion coefficients Cn and the reduced di-atom mass. We confront this formula to about a hundred determinations of r0 and a0 and show why the result is dominated by the leading dispersion coefficient C6. Universality and scaling extends much beyond naive dimensional analysis estimates.

Nucleosynthesis driven by Coulomb explosion of nanodroplets

This paper presents a computational and theoretical study of the yields for the C12(p,γ)N13 and C12(d,n)N13 nucleosynthesis reactions driven by high-energy (MeV) Coulomb explosion (CE) of (CH4)n and (CD4)n nanodroplets (n=104–107, radii R0=100–500Å) in ultraintense near-infrared Gaussian laser fields (peak intensities IM=1018–1019Wcm−2, pulse length τ=25fs). Efficient nucleosynthesis with C12 nuclei requires the production of protons and deuterons in the energy range of 0.5–2.0MeV, which is accomplished by CE of nanodroplets. The energy distributions of the nuclei were obtained from scaled molecular dynamics simulations and were utilized to calculate the energy averaged cross sections and the reaction yields for nucleosynthesis. Two distinct reaction modes were established pertaining to reactions inside the plasma filament volume (IF), and to reactions outside the plasma filament volume (OF). The dominating contribution to the total yields originates from the OF mode. The time resolved γ-ray emission for C12(p,γ)N13 will be exhibited in distinct time intervals of 2–100ps for the OF mode and of 65fs–3ps for the IF mode. Estimates of the yields were provided by incorporating the effects of nanodroplet size distributions that result in a slow size dependence of the yields in the range R0&amp;gt;250Å, and the effects of laser intensity attenuation in an assembly of nanodroplets that result in the decrease of the OF and IF yields due to the decrease of the effective plasma filament volume. For 400Å nanodroplets at IM=4×1018–1019Wcm−2, under realistic experimental conditions, the C12(p,γ)N13 nucleosynthesis driven by CE of (CH4)n nanodroplets is characterized by a yield (per laser pulse) of ∼100, while the yield for the C12(d,n)N13 nucleosynthesis driven by CE of (CD4)n clusters is ∼9×104. Table-top nucleosynthesis driven by nanodroplet CE is amenable to experimental observation.

Abundances of Metal‐rich HiiRegions in M51

We have obtained multiobject spectroscopy of H II regions in the spiral galaxy M51 with the Keck I telescope and the Low Resolution Imaging Spectrometer. For 10 objects we have detected the auroral line [N II] λ5755, while [S III] λ6312 has been measured in seven of these. This has allowed us to measure the electron temperature of the gas and to derive oxygen, sulfur, and nitrogen abundances for the 10 H II regions. Contrary to expectations from previous photoionization models of a few H II regions in M51 and from strong-line abundance indicators, the O/H abundance is below the solar value for most objects, with the most metal-rich H II regions, P203 and CCM 72, having log(O/H) = -3.16 [~1.4(O/H)☉] and log(O/H) = -3.29 [~1.0 (O/H)☉], respectively. The reduction of O/H by factors of up to 2 or 3 with respect to previous indirect determinations has important consequences for the calibration of empirical abundance indicators, such as R23, in the abundance and excitation range found in the central regions of spiral galaxies. The abundance gradients in these galaxies can therefore be considerably flatter than those determined by using such empirical calibrations. The H II regions with a measured electron temperature span the range (0.19-1.04) R0 in galactocentric radius and indicate a shallow abundance gradient for M51: -0.02 ± 0.01 dex kpc-1. The S/O abundance ratio is found to be similar to previous determinations of its value in other spiral galaxies, log(S/O) ≈ -1.6. Therefore, we find no evidence for a variation in massive-star initial mass function or nucleosynthesis at high oxygen abundance. An overabundance of nitrogen is measured, with log(N/O) -0.6. On the basis of our new abundances, we revise the effective yield for M51, now found to be almost 4 times lower than previous estimates, and we discuss this result in the context of chemical evolution in galactic disks. Features from Wolf-Rayet stars (the blue bump at 4660 A and the C III line at 5696 A) are detected in a large number of H II regions in M51, with the C III λ5696 line found preferentially in the central, most metal-rich objects.

On the Connectivity of Ad Hoc Networks

This paper presents a framework for the calculation of stochastic connectivity properties of wireless multihop networks. Assuming that n nodes, each node with transmission range r0, are distributed according to some spatial probability density function, we study the level of connectivity of the resulting network topology from three viewpoints. First, we analyze the number of neighbors of a given node. Second, we study the probability that there is a communication path between two given nodes. Third, we investigate the probability that the entire network is connected, i.e. each node can communicate with every other node via a multihop path. For the last-mentioned issue, we compute a tight approximation for the critical (r0 ,n )pairs that are required to keep the network connected with a probability close to one. In fact, the problem is solved for the general case of a k-connected network, accounting for the robustness against node failures. These issues are studied for uniformly distributed nodes (with and without ‘border effects’), Gaussian distributed nodes, and nodes that move according to the commonly used random waypoint mobility model. The results are of practical value for the design and simulation of wireless sensor and mobile ad hoc networks.

Topology properties of Ad hoc networks with random waypoint mobility

Given is a wireless multihop network with n nodes moving according to the random waypoint model on a system area of size A. Each node has a fixed transmission range r0. We derive a closed-form approximation for the critical (r0, n)-pairs that are needed to keep the mobile network connected during at least P(con)=99% of the time. In addition, we calculate the average degree μ experienced by a node during its movement and the node-to-node distance distribution f s(s).

Competing predissociation and preionization in the photoabsorption of H2 above the ionization threshold

We present a straightforward multichannel quantum defect theory (MQDT) procedure to calculate the broadening of preionization resonances due to competing predissociation in the ionization continuum of molecular hydrogen. We discretize the dissociative continuum by forcing the ionic vibrational basis functions to vanish at a boundary R0, after which we average the differential oscillator strength over a range R0+dR. The relevant averaging range dR depends on the density of discrete vibrational levels in the vicinity of selected preionization resonances. This approach yields directly the full spectral linewidth including the effect of predissociation. We apply the method to regions of the photoabsorption spectrum of para-H2 (v″=0, J″=0) between the photon wavelengths 782.0 and 786.0 Å. This spectral region exhibits extensive resonance structures due to preionization and predissociation. We obtain semiquantitative agreement with linewidths and branching ratios for ionization and dissociation obtained from experiment, and the MQDT/R-matrix method of Jungen [Phys. Rev. Lett. 53, 2394 (1984)].

Matched mode method of passive source localization

Source range and depth localization in a waveguide are accomplished by matching the measured mode amplitudes to predicted mode amplitudes. The matching function is F(r,z) = Σn = 1M an(r0,z0)an*(r,z), where an(r0,z0) is the measured amplitude of the nth mode due to a source at a range r0 and depth z0, an(r,z) is the predicted mode amplitude due to a source at a range r and depth z, and the sum extends over M measured modes. The values of r and z that produce the maximum of the magnitude of F(r,z) are taken to be the estimates of the true range and depth r0 and z0. Simulations were performed for an ocean environment using a range invariant normal mode propagation model. The sound field measured by a vertical string of hydrophones was simulated and a least‐squares method was used to estimate the measured mode amplitudes from the simulated hydrophone outputs. The predicted mode amplitudes were computed from the propagation model. The effects of array length, hydrophone spacing, number of modes resolved, and the presence of multiple sources were examined. It was found that accurate ranging could be achieved, but only if the vertical aray extended over essentially the entire water column. It was also found that accurate depth resolution required the measurement of a larger number of modes than was necessary for accurate range resolution. [This work was supported by Naval Sea Systems Command, Code 63R.]

Augmented adiabatic mode theory for upslope propagation from a point source in variable‐depth shallow water overlying a fluid bottom

A uniform asymptotic solution is presented for sound propagation from a constant frequency point source in shallow water whose depth H(r) decreases monotonically with cylindrical distance r. The water has constant sound speed c1 and density ρ1; the bottom fluid extends indefinitely in depth and has sound speed c2 and density ρ2, where c2>c1. The interface depth has constant value H0 up to range r0 and thereafter decreases linearly to zero. The solution appears as a sum of modal terms, each such mode eventually encountering a critical depth Hc(n) (at which modal phase velocity equals c2) at a critical range rc(n). A previously derived local solution for a modal term near its critical range is modified such that it automatically reduces to the adiabatic mode solution at nearer ranges and such that it is valid at arbitrary distances beyond the critical range. Bulk attenuation is incorporated into the model using an appropriate modal average over depth. Numerical results are compared with four parabolic equat...

Generation and propagation of the coherently scattered boundary wave over a ridge

Recent theoretical studies by I. Tolstoy and experiments by H. Medwin and co‐workers have shown that a low‐frequency sound at near grazing incidence to a surface of rigid hemispherical bosses generates a coherently scattered boundary wave which can be much larger than the spherically divergent direct radiation wave. In the present experiment the axial grazing diffraction of the boundary wave over a slightly rough wedge is measured. Two components of the boundary wave are identified in the shadow region of the wedge: one (RS) develops along the rough upslope then diffracts over the crest in the same manner as the volume wave; the ratio of this boundary wave amplitude to the volume wave amplitude (BWA/VWA) grows as range r01/2 upslope and is constant with increasing range r beyond the crest. The other component (SR) is generated by the diffracted volume wave along the rough downslope and BWA/VWA grows initially as range r0.6 from the crest. For both components the amplitude ratio has a frequency dependence ∫2. Low wave‐number grazing propagation over a rough wedge thereby produces a boundary wave in the shadow region whose amplitude can be several times greater than that of a diffracted volume wave over a smooth wedge. [Work supported by Office of Naval Research.]

Integrated bandpass filters

The letter presents some new results associated with one bandpass (b.p.) filter configuration of the integrated uniform R0-C0KR0 structure consisting of two rectangular resistive films, one having per-unit-length (p.u.l.) constant series resistance R0 and the other KR0 (where K is a dimensionless constant), separated from each other by a dielectric film having p.u.l. constant shunt capacitance C0. It is shown that the output voltage in the b.p. region may be made almost constant for the load fluctuations in the wide range R0 ≤ Rt < ∞ (where Rt = load resistance) by selecting K ≤ 0.3. The range of variation of Rt producing constant output voltage in the b.p. region is found to be narrower for increasing value of K.

Change in the transparency of a water aerosol under the action of CO2laser pulses

An analysis of a system of hydrothermodynamics equations, describing the evaporation of a water drop by laser radiation, is used to find the threshold for explosive evaporation of drops with initial radii in the range R0 = 0.1–10 μ. The results obtained are applied in estimation of the sudden change in the bulk attenuation coefficient of an aerosol at wavelengths λ = 0.63 and 10.6 μ. due to drop fragmentation under the action of rectangular laser pulses. This change may increase the λ = 0.63 μ attenuation tens of times and may reduce slightly the λ = 10.6 μ attenuation.

Percolation in a continuous two-dimensional medium

In a preceding paper, we presented a Monte Carlo method and two branching process models, used for the study of clusters of atoms randomly distributed and bounded by an interaction of given range r0. Similar methods are used here for the two-dimensional case. We find that the infinite cluster appears when the mean number of atoms in a circle of radius r 0 is about 4.1.

Extrapolated and Projected Ranges of 4- to 24-MeV Electrons in Elemental Materials

The extrapolated range Rex and the projected range Rpr of 4- to 24-MeV electrons in Be, Al, Cu, Ag, and Au have been determined from the experimental data for the charge-deposition distribution produced by the electrons in the effectively semiinfinite absorber. While the results for Rex show no significant difference from the data obtained by Harder and Poschet and by Ebert et al. for the absorber configuration of finite slab, the present values of Rpr for the absorbers of high atomic number are slightly smaller than the results of Harder and Poschet. In the energy region considered here, Rex has been found to obey an empirical equation of the form Rex = A(E0−B)C, where A, B, and C are expressed by simple functions of atomic number, and E0 is the incident kinetic energy of the electron. A semiempirical relation previously found between Rpr and the continuous slowing-down approximation range R0 has been modified so as to show a better agreement with the present data.