Barrier Positions Research Articles

The parametrization of Coulomb barrier heights and positions using the double folding model

Abstract The Coulomb barrier heights and positions are systematically shown with mass numbers and charge radii of the interacting nuclei. The nuclear potential is calculated by using the double folding model with the density-dependence nucleon–nucleon interaction (CDM3Y6). The pocket formulas are obtained for the Coulomb barrier heights and positions by analyzing several hundreds of heavy-ion systems with mass numbers from light nuclei to heavy nuclei. The parameterized formulas can reproduce the calculated barrier heights and positions by using the double folding model within the accuracy of ±1%. Moreover, the results are agreeable with the experimental data. The relation between the barrier height and the barrier position is also studied.

α-decay and fusion phenomena in heavy ion collisions using nucleon-nucleon interactions derived from relativistic mean-field theory

Nucleus-nucleus potentials are determined in the framework of the double-folding model for a new microscopic nucleon-nucleon (NN) interaction relativistic mean field-3-Yukawa (R3Y) derived from the popular relativistic mean-field theory Lagrangian, and the results are compared for the use of Michigan-3-Yukawa (M3Y) effective NN interactions. The double-folding potentials so obtained are further taken up in the context of the preformed cluster model (PCM) of Gupta and collaborators and the barrier penetration model to study respectively the ground-state (g.s.) {alpha}-decay and low-energy fusion reactions. In this paper, using PCM, we deduce empirically the {alpha} preformation probability P{sub 0}{sup {alpha}(emp)} from experimental data on a few g.s. {alpha} decays in the trans-lead region. For fusion reactions, two projectile-target systems {sup 12}C+{sup 208}Pb and {sup 16}O+{sup 208}Pb are selected for calculating the barrier energies as well positions, fusion cross sections ({sigma}{sub fus}), and fusion barrier distribution [D(E{sub c.m.})]. The barrier energies and positions change for the R3Y NN interactions in comparison with those of the M3Y NN interactions. We find that in the {alpha}-decay studies the values of P{sub 0}{sup {alpha}(emp)}(R3Y) are similar to those of P{sub 0}{sup {alpha}(emp)}(M3Y). Further, both NN interactions give similar {sigma}{sub fus} values using the Wong formula specifically when more » the R3Y NN interaction calculated {sigma}{sub fus} values are reduced by 1.5 times, and the results are in agreement with the experimental data for both the systems, especially for the higher energies. Results for D(E{sub c.m.}) are also quite similar for both choices of NN interaction. « less

Multiphoton fluorescence recovery after photobleaching in bounded systems.

Multiphoton fluorescence recovery after photobleaching (MP-FRAP) is a laser microscopy technique used to measure diffusion coefficients of macromolecules in biological systems. The three-dimensional resolution and superior depth penetration within scattering samples offered by MP-FRAP make it an important tool for investigating both in vitro and in vivo systems. However, biological systems frequently confine diffusion within solid barriers, and to date the effect of such barriers on the measurement of absolute diffusion coefficients via MP-FRAP has not been studied. We have used Monte Carlo simulations of diffusion and MP-FRAP to understand the effect of barriers of varying geometries and positions relative to the two-photon focal volume. Furthermore, we supply ranges of barrier positions within which MP-FRAP can confidently be employed to measure accurate diffusion coefficients. Finally, we produce two new MP-FRAP models that can produce accurate diffusion coefficients in the presence of a single plane boundary or parallel infinite plane boundaries positioned parallel to the optical axis, up to the resolution limit of the multiphoton laser scanning microscope.

Analytical parametrization of fusion barriers using proximity potentials

Using the three versions of proximity potentials, namely proximity 1977, proximity 1988, and proximity 2000, we present a pocket formula for fusion barrier heights and positions. This was achieved by analyzing as many as 400 reactions with mass between 15 and 296. Our parametrized formula can reproduced the exact barrier heights and positions within an accuracy of $\pm1%$. A comparison with the experimental data is also in good agreement.

Full distance-resolved folding energy landscape of one single protein molecule

Kinetic bulk and single molecule folding experiments characterize barrier properties but the shape of folding landscapes between barrier top and native state is difficult to access. Here, we directly extract the full free energy landscape of a single molecule of the GCN4 leucine zipper using dual beam optical tweezers. To this end, we use deconvolution force spectroscopy to follow an individual molecule's trajectory with high temporal and spatial resolution. We find a heterogeneous energy landscape of the GCN4 leucine zipper domain. The energy profile is divided into two stable C-terminal heptad repeats and two less stable repeats at the N-terminus. Energies and transition barrier positions were confirmed by single molecule kinetic analysis. We anticipate that deconvolution sampling is a powerful tool for the model-free investigation of protein energy landscapes.

Laser-Manipulating Macroscopic Quantum States of a Bose–Einstein Condensate Held in a Kronig–Penny Potential

We investigate the boundary value problem (BVP) of a quasi-one-dimensional Gross–Pitaevskii equation with the Kronig–Penney potential (KPP) of period d, which governs a repulsive Bose–Einstein condensate. Under the zero and periodic boundary conditions, we show how to determine n exact stationary eigenstates {Rn} corresponding to different chemical potentials {μn} from the known solutions of the system. The n-th eigenstate Rn is the Jacobian elliptic function with period 2d/n for n = 1,2,…, and with zero points containing the potential barrier positions. So Rn is differentiable at any spatial point and Rn2 describes n complete wave-packets in each period of the KPP. It is revealed that one can use a laser pulse modeled by a δ potential at site xi to manipulate the transitions from the states of {Rn} with zero point x ≠ xi to the states of {Rn} with zero point x = xi. The results suggest an experimental scheme for applying BEC to test the BVP and to observe the macroscopic quantum transitions.

Temperature Softening of a Protein in Single-molecule Experiments

Mechanical flexibility is crucial for the function of proteins. However, such material properties are not easily accessible experimentally. We used single-molecule force spectroscopy to study the stiffness of a single domain of Dictyostelium discoideum filamin (ddFLN4) in a temperature range from 5 degrees C to 37 degrees C. Analyzing the distributions of unfolding forces allowed us to extract transition barrier heights and positions of the underlying energy landscape. We found a marked narrowing of unfolding force distributions with increasing temperature. This narrowing reflects an increase in transition state position from 2.7 A to 7.8 A and thus a reduction of the molecular spring constant of the protein by a factor of 7. We suggest this temperature softening reflects a shift in the nature of the interactions responsible for mechanical stability from hydrogen bonds to hydrophobic interactions. This result has important consequences for all interpretations of protein mechanical studies if experimental results obtained at room temperature are to be transferred to physiological temperatures.

Isotopic dependence of fusion probabilities for neutron-deficient and -rich colliding nuclei

Isotopic dependence of the fusion dynamics is studied by analyzing the collision of a large number of isotopes of Ca and Ni with 0.6 \( \leqslant\)N/Z\( \leqslant\) 2. This study, which results from the Skyrme energy density formalism, reveals that the addition of neutrons favors fusion of reacting partners, whereas the reverse happens with the removal of neutrons. The fusion barrier heights and positions follow a non-linear second-order dependence on (\( {\frac{{{N}}}{{{Z}}}}\)-1 ), whereas fusion cross-sections can be parameterized by a straight line.-1

Influence of high-permittivity barriers on PD activity in three-layer dielectrics

It is a well-known fact that the breakdown voltage of dielectrics in a divergent field may be increased by using an additional insulating layer (a barrier) placed at the optimal position between the electrodes. This paper is devoted to the investigation of the barrier effect in solid dielectrics in a quasi-uniform electric field, i.e. the study of the relationship between partial discharge (PD) activity and the barrier position in the insulating gap. It is established that the PD parameters depend on the barrier position in the gap. In particular, the ignition voltage of critical PDs is increased by more than 50% at the optimal barrier position compared to that for other barrier positions.

FORCE MEASUREMENTS IN WELFARE EVALUATION OF CATTLE HOUSING DESIGN

The force exerted on housing equipment by an animal may be used as a physical welfare parameter in the evaluation of housing design. This article is concerned with the force on a cow’s chest as she pushes against a self–locking feed barrier, as well as the force on the forelegs as she presses on the rear curb of the manger to reach her feed. The forces were determined in two experiments carried out with non–lactating cows of heavy breed. In the first experiment the force on the feed barrier was determined with the feed barrier placed either vertically or in a 20. inclined position combined with a manger width of either 1.20 or 0.62 m. The experiment showed that the force on the feed barrier remained low as long as the feed was kept within the cows’ reach in the narrow manger. With the wide manger, unacceptable forces were measured for both feed barrier positions. The inclined feed barrier allowed the cow to reach the feed at larger distances than the vertical feed barrier, however. In the second experiment the forces on both the feed barrier and the curb were determined for the same two feed barrier positions combined with a 135–, 200–, or 300–mm wide curb. Here a permanent manger width of 1.20 m was used. No serious forces were recorded on the curb in the case of inclined feed barrier as long as the curb width did not exceed 135 mm. For vertical feed barrier a curb width of up to 300 mm proved to be acceptable. For inclined feed barrier a curb width of 200 and especially 300 mm proved to be unacceptable. To avoid unacceptable forces on the cow’s chest a maximum manger width of 0.65 m is recommended for vertical feed barriers and 0.80 m for inclined feed barriers. To avoid unacceptable forces on the cows’ forelegs, a curb width of less than 200 mm is recommended for vertical feed barriers and 150 mm for inclined feed barriers.

Undulations in potential curves analyzed using the Fermi model: LiH, LiHe, LiNe, andH2examples

The interaction of a Rydberg electron with a ground-state atom is modeled using the Fermi approximation to obtain long-range potentials for various excited diatomic molecules. Particular attention is paid to cases of degenerate and near-degenerate atomic Rydberg levels. Extensive comparisons are performed with recent ab initio calculations for 1 Σ + and 3 Σ + states of LiH and H 2 , also 2 Σ + states of LiHe, for up to the ninth state of a specified symmetry. Results for LiNe are also discussed. Overall, good qualitative and in some cases quantitative agreement is found. For isolated states, the undulations in the potentials clearly reflect the nodal pattern of the Rydberg state involved and the magnitude is fixed in the Fermi approach by the electron-ground-state atom scattering length. When several states are close in energy, in the Fermi model because of the factorizable nature of the interaction, only a single nonzero potential emerges from the remaining flat manifold. Such behavior explains, for example, the presence of high barriers at large distances seen in ah initio calculations for the 1 , 3 Σ + g , u n=3 states of molecular hydrogen. For the systems involving H the Fermi results are generally better for the weaker, triplet interactions than the singlets. In the case of near-degenerate levels the weaker interactions are normally described better than the stronger interaction, where avoided crossings (not included in this simple model) may be important. In LiHe, where the interactions are weaker, generally for separations larger than about 10a 0 the Fermi model obtains barrier positions within 1a 0 and maxima within 10 cm - 1 . For LiNe, because of the very small scattering length for electrons in neon, largely qualitative results are obtained. The Fermi model is also shown to yield a physically sound diabatic approach for excited states of diatomic molecules, allowing for a deeper understanding of the unusual shapes of the adiabatic curves. Limitations of the Fermi model are also discussed.

Analytical calculation of fusion cross-sections

We analyse the fusion cross-sections, calculated by using two different analytical parameterisations and compare them with the experimental data. Both the parameterisations are based on ion-ion potentials calculated within the framework of Skyrme energy density formalism. In the first case, the ion-ion potential (including the spin-density term) was parameterised and then, by adding the Coulomb potential, one could compute the fusion barrier analytically. In the second case, the calculated fusion barrier heights and positions were parameterised directly. Both of these (previously) reported parameterisations are used here to calculate the fusion barriers and fusion excitation functions for more than 50 reactions belonging to the s-d and f-shell nuclei. A detailed comparison of these parametrisations with the experimental and several other theoretical results shows that both of these parameterisations are able to reproduce the experimental data equally well. As the (second) direct parameterisation depends only on the charges and masses of colliding nuclei, it is very useful for predicting/ understanding the fusion process in low energy heavy-ion reactions.

Role of Tail−Tail Interactions versus Head-Group−Subphase Interactions in Pressure−Area Isotherms of Fatty Amines at the Air−Water Interface. 2. Time Dependence

The dependence of the surface pressure vs area (π−A) isotherms of fatty primary amine monolayers spread on a subphase of an aqueous solution of various Hn[MO4]n- acids (M = S6+, P5+, Cl7+) under ionic conditions of low pH on several temporal parametersincluding compression/expansion rateshave been studied as a function of the chain length of the fatty amines. A parameter, RT/C, has been used as a qualitative measure of the relative strengths of the tail−tail interaction as compared to the subphase−head-group (acid−base) complex-forming interaction. The changes in the π−A isotherm due to waiting for different periods of time after spreading as well as the changes in the surface pressure, π, with time at various barrier positions have been studied. The results show an increase in the lift-off area, ALO, with time that is not due to an external contaminant. The compression/expansion curves always show hysteresis, the extent of which may decrease (for larger RT/C) or show a counterintuitive increase (for smaller RT/C) with decreasing compression/expansion rates. The results are analyzed in terms of a new two-state model involving clusters and individual complexed amine molecules.

Algebraic expressions for effective potential characteristic parameters in heavy ion scattering

In this paper, we obtain reliable expressions to calculate the barrier and pocket positions of the real part of the effective phenomenological optical potential having Woods-Saxon form factor, for different partial waves. The comparison of the results obtained from these formulae, when compared with the numerical results obtained using Newton-Raphson iterative procedure are found to be quite accurate, with error less than 1%. We also obtain algebraic expressions for estimatinglpoc, the angular momentum at which the potential pocket vanishes, the accuracy of which is tested with the exact calculations, using self-consistent iterative procedures. These and other expressions deduced in this paper provide simple and useful methods for calculating critical parameters of heavy ion effective potentials like barrier and pocket positions, curvatures at the barrier and pocket positions,lpoc and the grazing angular momentumlg to carry out the analysis of heavy ion scattering.

Statistical mechanics of a correlated energy landscape model for protein folding funnels

In heteropolymers, energetic correlations exist due to polymeric constraints and the locality of interactions. Pair correlations in conjunction with the a priori specification of the existence of a particularly low energy state provide a method of introducing the aspect of minimal frustration to the energy landscapes of random heteropolymers. The resulting funneled landscape exhibits both a phase transition from a molten globule to a folded state, and the heteropolymeric glass transition in the globular state. We model the folding transition in the self-averaging regime, which together with a simple theory of collapse allows us to depict folding as a double-well free energy surface in terms of suitable reaction coordinates. Observed trends in barrier positions and heights with protein sequence length and thermodynamic conditions are discussed within the context of the model. We also discuss the new physics which arises from the introduction of explicitly cooperative many-body interactions, as might arise from sidechain packing and nonadditive hydrophobic forces.

Fusion barriers using the energy-density formalism: Simple analytical formula and the calculation of fusion cross sections.

Fusion barriers are calculated within the sudden approximation, using the Skyrme interaction energy-density model. Both the closed and unclosed shell nuclei are considered and the role of spin-density term is studied in detail. For unclosed shell nuclei, the fusion cross sections are found to decrease by as much as {similar to}50 mb when spin-density effects are included. Very accurate, simple analytical expressions, in terms of only the masses and charges of the reacting nuclei, are obtained for the barrier heights and positions. This introduces a great simplification for the fusion barrier calculations.

大気圧SF<sub>6</sub>ガス中不平等電界下のバリア効果

Generally, it is known that insertion of a barrier under a nonuniform field in air increases the flashover voltage. This is called the barrier effect. However, there are many uncertainties that remain to be clarified about the barrier effect in SF6 gas. Therefore, the influence of the barrier shapes and positions on the flashover voltage for the lightning impulse voltages and voltages (50 Hz) is examined by inserting a barrier between a hemispheric-end rod and a plate in SF6 gas under near-atmospheric pressure. As a result, the following findings were obtained:. (1) Insertion of a disk-shaped barrier reduces the flashover voltage; a cup-shaped barrier whose surface curves almost along the equipotential line increased the flashover voltage by 30 to 40 percent;. (2) trapped charge on the barrier surface is of the same polarity as the applied voltage and the magnitude of positive charge was greater than that of negative charge. It was found also that there is a correlation between the amount of trapped charge and the flashover voltage; and. (3) application of a barrier under a nonuniform field in the atmospheric pressure SF6 gas helps reduce the size of, for example, a cubic-type gas-insulated switchgear.

Barrier effect under nonuniform field in atmospheric pressure SF6 gas

Generally, it is known that insertion of a barrier under a nonuniform field in air increases the flashover voltage. This is called the barrier effect. However, there are many uncertainties that remain to be clarified about the barrier effect in SF6 gas. Therefore, the influence of the barrier shapes and positions on the flashover voltage for the lightning impulse voltages and voltages (50 Hz) is examined by inserting a barrier between a hemispheric-end rod and a plate in SF6 gas under near-atmospheric pressure. As a result, the following findings were obtained:. (1) Insertion of a disk-shaped barrier reduces the flashover voltage; a cup-shaped barrier whose surface curves almost along the equipotential line increased the flashover voltage by 30 to 40 percent;. (2) trapped charge on the barrier surface is of the same polarity as the applied voltage and the magnitude of positive charge was greater than that of negative charge. It was found also that there is a correlation between the amount of trapped charge and the flashover voltage; and. (3) application of a barrier under a nonuniform field in the atmospheric pressure SF6 gas helps reduce the size of, for example, a cubic-type gas-insulated switchgear.

Catalysis of Friedel-Crafts reactions by electric fields

The effects of uniform and nonuniform electric fields on the HF+CH 4 reaction have been investigated by using an ab initio RHF method with the 3-21+G basis set. It is found that barrier heights and positions of stationary points along the reaction coordinate are dramatically altered upon introduction of such electric fields. The changes are analyzed in terms of modifications in atomic charges and variations of electron densities at the main bond critical points. The electric fields are found to belong to the reaction coordinate of this chemical process

Cation permeation through the voltage-dependent potassium channel in the squid axon. Characteristics and mechanisms.

Characteristics of cation permeation through voltage-dependent delayed rectifier K channels in squid giant axons were examined. Axial wire voltage-clamp measurements and internal perfusion were used to determine conductance and permeability properties. These K channels exhibit conductance saturation and decline with increases in symmetrical K+ concentrations to 3 M. They also produce ion- and concentration-dependent current-voltage shapes. K channel permeability ratios obtained with substitutions of internal Rb+ or NH+4 for K+ are higher than for external substitution of these ions. Furthermore, conductance and permeability ratios of NH+4 or Rb+ to K+ are functions of ion concentration. Conductance measurements also reveal the presence of an anomalous mole fraction effect for NH+4, Rb+, or Tl+ to K+. Finally, internal Cs+ blocks these K channels in a voltage-dependent manner, with relief of block by elevations in external K+ but not external NH+4 or Cs+. Energy profiles for K+, NH+4, Rb+, Tl+, and Cs+ incorporating three barriers and two ion-binding sites are fitted to the data. The profiles are asymmetric with respect to the center of the electric field, have different binding energies and electrical positions for each ion, and (for K+) exhibit concentration-dependent barrier positions.