Soft-core Potential Research Articles

Dynamics of highly supercooled liquids: Heterogeneity, rheology, and diffusion

Highly supercooled liquids with soft-core potentials are studied via molecular dynamics simulations in two and three dimensions in quiescent and sheared conditions.We may define bonds between neighboring particle pairs unambiguously owing to the sharpness of the first peak of the pair correlation functions. Upon structural rearrangements, they break collectively in the form of clusters whose sizes grow with lowering the temperature $T$. The bond life time $\tau_b$, which depends on $T$ and the shear rate $\gdot$, is on the order of the usual structural or $\alpha$ relaxation time $\tau_{\alpha}$ in weak shear $\gdot \tau_{\alpha} \ll 1$, while it decreases as $1/\gdot$ in strong shear $\gdot\tau_{\alpha} \gg 1$ due to shear-induced cage breakage. Accumulated broken bonds in a time interval ($\sim 0.05\tau_b$) closely resemble the critical fluctuations of Ising spin systems. For example, their structure factor is well fitted to the Ornstein-Zernike form, which yields the correlation length $\xi$ representing the maximum size of the clusters composed of broken bonds. We also find a dynamical scaling relation, $\tau_b \sim \xi^{z}$, valid for any $T$ and $\gdot$ with $z=4$ in two dimensions and $z=2$ in three dimensions. The viscosity is of order $\tau_b$ for any $T$ and $\gdot$, so marked shear-thinning behavior emerges. The shear stress is close to a limiting stress in a wide shear region. We also examine motion of tagged particles in shear in three dimensions. The diffusion constant is found to be of order $\tau_b^{-\nu}$ with $\nu=0.75 \sim 0.8$ for any $T$ and $\gdot$, so it is much enhanced in strong shear compared with its value at zero shear. This indicates breakdown of the Einstein-Stokes relation in accord with experiments. Some possible experiments are also proposed.

Electromagnetic production of the hypertriton

Kaon photoproduction on 3He, γ + 3 He → K + + Λ 3 H , is studied in the framework of the impulse approximation. Realistic 3He wave functions obtained as solutions of Faddeev equations with the Reid soft-core potential are used along with different Λ 3H wave functions. Results are compared for several elementary operator models, which can successfully describe the elementary kaon production off the proton up to a photon lab energy of k = 2.2 GeV. It is found that the corresponding cross sections are small, of the order of several nanobarns. It is also shown that the influence of Fermi motion is important, while the effect of different off-shell assumptions on the cross section is not too significant.

Kinetic heterogeneities and non-linear rheology of highly supercooled liquids

Supercooled liquids with soft-core potentials are studied via molecular dynamics simulations in two and three dimensions in quiescent and sheared conditions. We demonstrate that bond breakage events among particle pairs occur collectively in clusters. The average life time, τ b ( γ ̇ ) , of bonds tends to the α relaxation time, τ α, for weak shear, γ ̇ ≪1/τ α , and decreases as 1/ γ ̇ for strong shear, γ ̇ ≫1/τ α . The structure factor, S b( q), of the broken bonds may be fitted to the Ornstein–Zernike form. The correlation length, ξ, is uniquely expressed in terms of τ b ( γ ̇ ) as ξ∼τ b ( γ ̇ ) 1/4 in two dimensions and ξ∼τ b ( γ ̇ ) 1/2 in three dimensions for any T and γ ̇ in glassy states. The viscosity is of order τ b ( γ ̇ ) for any γ ̇ , so the shear stress tends to a limiting stress for γ ̇ τ α ≫1 .

Jost function for coupled partial waves

An exact method for direct calculation of the Jost functions and Jost solutions for non-central potentials which couple partial waves of different angular momenta is presented. A combination of the variable-constant method with the complex coordinate rotation is used to replace the matrix Schrodinger equation by an equivalent system of linear first--order differential equations. Solving these equations numerically, the Jost functions can be obtained to any desired accuracy for all complex momenta of physical interest, including the spectral points corresponding to bound and resonant states. The effectiveness of the method is demonstrated using the Reid soft-core and Moscow nucleon-nucleon potentials which involve tensor forces.

Lyapunov Instability in One-Dimensional Lennard-Jones System

We study a transition from quasiperiodic to stochastic motion in one-dimensional classical systems consisting of N particles with the nearest-neighbor Lennard–Jones interaction, extensively by computer simulation. We find a new feature in the change of the Lyapunov spectrum and the maximal Lyapunov exponent by changing its energy in the intermediate region between quasiperiodic and stochastic motions. The characteristics of the Lennard–Jones system in the intermediate region is considered by means of properties of Hessian matrix of potential function. The applicability of random matrix approximation for high energy region is also investigated, comparing with the case of soft-core potential.

Photoproduction of the hypertriton

In the framework of the impulse approximation we study the photoproduction of the hypertriton Λ 3H by using realistic 3He wave functions obtained as solutions of Faddeev equations with the Reid soft-core potential for different Λ 3H wave functions. We obtain relatively small cross sections of the order of 1 nb. We also find that the influence of Fermi motion is important, while the effect of different off-shell assumptions on the cross section is not too significant.

Describing the Properties of Chains of Segments Interacting Via Soft-Core Potentials of Variable Range with the SAFT-VR Approach

We present a general development for the equation of state (EOS) of chain molecules composed of tangent spherical segments interacting with a soft repulsive potential and an attractive well. The method is based on a recent version of the statistical associating fluid theory for chain molecules with interaction potentials of variable range (SAFT-VR). In this communication we focus our attention on the properties of Lennard–Jones chains (LJC), using SAFT-VR and a sample recipe for the evaluation of the chain free energy that requires only a knowledge of the contact value of the cavity function of a Sutherland-6 system. We study the liquid–vapor coexistence properties for different values of the chain length. The results obtained are of similar accuracy to other EOS for LJC, but our approach is simpler and more general. We show that standard perturbation theories developed for simple liquids can also be used for chain molecules.

In-medium dependence and Coulomb effects of the pion production in heavy ion collisions

The properties of the high energy pions observed in heavy ion collisions, in particular in the system Au on Au at 1 GeV/nucleon are investigated. The reaction dynamics is described within the Quantum Molecular Dynamics (QMD) approach. It is shown that high energy pions freeze out early and originate from the hot, compressed matter. N*-resonances are found to give an important contribution toward the high energy tail of the pion. Further the role of in-medium effects in the description of charged pion yields and spectra is investigated using a microscopic potential derived from the Brueckner G-matrix which is obtained with the Reid soft-core potential. It is seen that the high energy part of the spectra is relatively more suppressed due to in-medium effects as compared to the low energy part. A comparison to experiments further demonstrates that the present calculations describe reasonably well the neutral (TAPS) and charged (FOPI) pion spectra. The observed energy dependence of the π−/π+ ratio, i.e. deviations from the isobar model prediction, is due to Coulomb effects and again indicate that high energy pions probe the hot and dense phase of the reaction. These findings are confirmed independently by a simple phase space analysis.

Lyapunov exponent and the solid-fluid phase transition

We study changes in the chaotic properties of a many-body system undergoing a solid-fluid phase transition. To do this, we compute the temperature dependence of the largest Lyapunov exponents λmax for both two- and three-dimensional periodic systems of N-particles for various densities. The particles interact through a soft-core potential. The two-dimensional system exhibits an apparent second-order phase transition as indicated by a λ-shaped peak in the specific heat. The first derivative of λmax with respect to the temperature shows a peak at the same temperature. The three-dimensional system shows jumps, in both system energy and λmax, at the same temperature, suggesting a first-order phase transition. Relaxation phenomena in the phase-transition region are analyzed by using the local time averages.

Parity conservingγasymmetry inn-pradiative capture

The importance of n-p radiative capture, utilizing polarized cold neutrons, as a means of measuring the weak pion coupling constant is reviewed. Parity conserving processes of the form k_gamma*[s_n,k_n] can contribute to the s_n*k_gamma photon asymmetry in any such experiment, if the apparatus is not perfectly symmetric. For an incident laboratory neutron energy of 0.003 eV a value of A^{PC}_{gamma}=0.67*10^{-8} is obtained for two different potential models (Argonne AV14 and Nijmegen Reid93). Serving as an extreme test case, the Reid soft core potential yields 0.61*10^{-8}, close to the result of the contemporary forces. Implications for extracting the weak pion coupling constant and for monitoring the beam polarization are discussed.

Lowest-order constrained variational calculation for hot asymmetric nuclear matter

The method of lowest-order constrained variational that reasonably predicts the nuclear matter saturation data is used to calculate the equation of state of asymmetric nuclear matter at finite temperature. The Reid soft-core potential with and without the N - interaction, which fits N - N scattering data, is taken as the nuclear Hamiltonian. The calculation is performed for a wide range of density, asymmetry parameter and nuclear temperature, which are of interest in heavy-ion collisions and astrophysics. Beside spin, isospin, total angular momentum and density dependence of the correlation functions, they are also arranged to depend on the temperature and asymmetry parameter of the system. The free energy, pressure, effective mass etc of asymmetric nuclear matter are calculated. It is shown that while the calculated symmetry coefficient defined in the semi-empirical mass formula is roughly constant and is near its empirical value at zero temperature, it depends on the proton-to-neutron ratio at finite temperature. Finally, the dependence of the liquid - vapour phase transition, as well as the effective mass dependence on the temperature and asymmetry parameter, is investigated.

Delta excitations in compressed finite nuclei. II. Nucleon-nucleon interaction dependence.

Spherical Hartree-Fock calculations at equilibrium and under radial compression are presented for $^{40}\mathrm{Ca}$ and $^{90}\mathrm{Zr}$ in a model space of seven major oscillator shells. We employ an effective baryon-baryon interaction which includes the \ensuremath{\Delta}(1236) resonance explicitly. The nucleon-nucleon (N-N) interactions are based on the Nijmegen and Reid soft core potentials. The results indicate a significant dependence on the choice of the N-N interaction at large nuclear compression. We found mixing between nucleons and \ensuremath{\Delta}'s even at equilibrium in $^{90}\mathrm{Zr}$ with either choice of potentials, but not in $^{40}\mathrm{Ca}$. Substantial amounts of the excitation energy induced by compression goes to the creation of \ensuremath{\Delta} excitations. \textcopyright{} 1996 The American Physical Society.

ELASTIC SCATTERING OF 28Si–27Al IN A REALISTIC OPTICAL POTENTIAL

Within a realistic model for the optical potential between nuclei based on the solution of the Bethe-Goldstone equation with the Reid soft-core potential, the differential cross-sections of the 28 Si –27 Al system, recently measured at energies around the Coulomb barrier, are calculated. The experimental data are well-reproduced over the entire energy range without any adjustable parameters to fit the cross-section.

Heavy-ion collisions and the density dependence of the local mean field

We study the effect of the density dependence of the scalar and the vector part of the nucleonic self-energy in relativistic quantum molecular dynamics (RQMD) on observables like the transversal flow and the rapidity distribution. Linear and non-linear density dependences of the mean field are studied. The latter case can either be restricted to the scalar part of the mean field or be taken into account in both the scalar and vector parts. The mean field is determined from a non-linear extension of the Walecka model or from the Brueckner-Hartree-Fock G -matrix with the Reid soft-core potential. The transversal flow is very sensitive to these different approaches. In particular, a linear scaling of the flow with the effective mass of the considered models is observed. For the reaction Ar + KC1 at 1.8 GeV/nucleon a comparison with the data is given.

Folding model description of fusion reaction

The shape, separation and orientation dependence of the interaction potential and fusion cross section of the system are investigated within the double-folding model of deformed nuclei. The effective nucleon - nucleon interaction is taken to be the M3Y, which has been derived from G-matrix elements and based upon the Reid soft-core potential. A deformed Fermi shape with quadrupole and hexadecapole deformations is considered for the density distribution of . It is found that both the interaction potential and fusion cross section strongly depend on the deformations and orientations. The integrated fusion cross section over all orientation angles yields an excellent agreement with the experiment data.

Thermodynamic Perturbation Approach to Freezing of the Classical One-Component Plasma

Systematic investigations are made of the thermodynamic perturbation approach to freezing, which has proved successful for systems interacting through soft-core or long-ranged potentials. The classical one-component plasma (OCP) is taken as the extreme case of such systems and the investigations focus on the reference systems employed in this approach and on the approximation schemes used to treat that system. It is confirmed that good results are obtained for the freezing properties of the OCP if a system with repulsive, short-ranged potential is properly chosen as the reference system, and both this system and the remaining part due to the long-range interaction are separately treated by the modified weighted-density approximation (MWDA) using accurate input data. However, if we adopt the hard spheres as the reference system in this approach and use either the MWDA or the generalized effective-liquid approximation (GELA) for this system, we cannot get similar results unless we use the input data in the ...

Quantum signatures in the stabilization dynamics.

We investigate the phase-space dynamics of a hydrogenic atom in a very intense, high-frequency laser field, by comparing the time-dependent quantum Wigner functions with the corresponding classical distributions calculated using the Monte Carlo method. In both cases we model the atom by a one-dimensional soft-core potential in order to simplify the calculation. We demonstrate the importance of nonclassical interferences in the Wigner function and show how negative parts of it observed at the peak of the pulse are associated with the formation of a coherent superposition of dressed ``Kramers-Henneberger'' (KH) eigenstates. These signatures of the quantum dynamics are eliminated towards the end of the pulse when the coherence between the KH eigenstates degrades so that the classical and the quantum mechanical phase-space distributions come into agreement.

Wave-packet dynamics and photoionization in the Coulomb potential.

We study the dynamics of radial wave packets in the singular Coulomb potential by solving the time-dependent Schr\"odinger equation numerically. A propagation scheme involving fast-Fourier transforms is used. We concentrate on the simple radial motion of the hydrogen atom to test the numerical method. In particular, we calculate the dynamics under the influence of a strong laser pulse and document how above-threshold-ionization peaks can be interpreted in terms of momentum-space wave functions. The results are compared to those obtained from a calculation that uses a soft core potential.

Unusual nuclear shapes and neutron specific heat of neutron star crusts.

We investigate the specific heat of superfluid neutrons in the region of the crust of a neutron star characterized by unusual nuclear shapes, whose possible existence has been recently proposed. To describe pairing properties the results from Reid soft-core potential for nucleon-nucleon interaction are used. It is found that the presence of unusual nuclei causes a sizable increase in the specific heat. The results can have consequences in the study of thermal evolution of young neutron stars.

Complex Kohn Variational Principle for Two-Nucleon Bound-State and Scattering with the Tensor Potential

Complex Kohn variational principle is applied to the numerical solution of the fully off-shell Lippmann-Schwinger equation for nucleon-nucleon scattering for various partial waves including the coupled 3S1 -3D1 channel. Analytic expressions are obtained for all the integrals in the method for a suitable choice of expansion functions. Calculations with the partial waves 1S0 , 1P1, 1D2 , and 3S1 -3D1 of the Reid soft core potential show that the method converges faster than other solution schemes not only for the phase shift but also for the off-shell t matrix elements. We also show that it is trivial to modify this variational principle in order to make it suitable for bound-state calculation. The bound-state approach is illustrated for the 3S1 -3D1 channel of the Reid soft-core potential for calculating the deuteron binding, wave function, and the D state asymptotic parameters.