Shell-structure inertia for slow collective motion

The modified shell correction method is suggested for the calculation of transport coefficients in a slow nuclear collective dynamics. For the multipole low-lying vibrations near the spherical shape of a nucleus, the smooth transport coefficients corresponding to the extended Thomas-Fermi approach are used as a macroscopic background. The time-dependent mean field is approximated through the infinitely deep square-well potential for the calculation of the shell corrections. Significant shell effects in stiffness and inertia are found at small temperatures. These effects disappear approximately at the same large enough temperature as in the free energy. It is shown that the collective inertia is substantially larger than that of irrotational flow owing to the consistency condition of particle density and potential variations. The collective vibration energies and reduced friction and effective damping coefficients with accounting for the shell effects are in better agreement with allowance data than that found from the hydrodynamic model. The text was submitted by the authors in English.     

Self-consistent transport coefficients for average collective motion at moderately high temperatures

Linear response theory is applied to compute the coefficients for inertia, friction and local stiffness for slow, large scale nuclear collective motion. It is shown how these coefficients can be defined within a locally harmonic approximation. The latter allows to study the implications arising from a finite local collective frequency. It is only for temperatures around 2 MeV that the zero frequency limit becomes a fair approximation. Friction is found to have a marked temperature dependence. The numerical computations are performed on the basis of a two-center shell model, but allowing the particles and holes to become dressed through effects of the medium. The dependence of the transport coefficients on the parameters of these self-energies is studied. It is argued that the uncertainties are smaller than a factor of 2.     

Role of nuclear surface vibrations in low energy heavy ion collisions

Nuclear surface vibrations cause dissipation as well as fluctuations of the relative motion between heavy ions. Viewing these as transport phenomena, we derive explicit formulae for the induced force and the correlation functions in terms of the spectrum of the nuclear vibrations and the coupling form factor. We provide a general proof that the path integral approach and the density operator formalism lead to equivalent transport coefficients as long as the influence functional takes a standard form. As an illustration, we then analyze⁸⁴Sr+²⁰⁸Pb scattering. We discuss the properties of the potential renormalization, and explain the mechanism of the high lying vibrations becoming dominant in dissipation with increasing bombarding energy by examining the properties of the retarded friction function.     

Coupling of the rotational motion with the axial vibrations of multipolarity 2 and 4

The unadiabatic effects related to the coupling between the rotational and vibrational degrees of freedom are investigated. The collective Hamiltonian is constructed using the concepts of the Bohr theory and includes the degrees of freedom corresponding to the axial quadrupole and hexadecapole vibrations. The coupling of the nuclear vibrations with the rotational motion is so strong that one has to multiply the inertial parameters and the moment of inertia by the factor 1.7 in order to get the experimental energies spacing in the ground state bands. The dynamical effects to the electric quadrupole and hexadecapole moments are considered. The parameter of unadiabaticityα calculated within the model agrees well with the experimental data.     

Generalized cranking model for collective nuclear motion

The Inglis cranking model is generalized to take into account effects of any velocity dependence present in the single-particle potential and the reaction of the pairing field to the collective motion. The generalized model is applied to translations, rotations and some special types of vibrations. Some of our results and our numerical calculations are obtained with a harmonic-oscillator single-particle potential. Unlike the inertia calculated with the Inglis cranking model, the inertia calculated with the generalized cranking model is independent of the effective mass and approaches the irrotational value in the limit of large pairing.     

A numerical analysis of the heavy-ion reaction based on the linear response theory

Taking the relative distanceR and the deformationδ of each nucleus as the collective variables, we solve the two dimensional coupled dynamical equations of motion with friction in the framework of the linear response theory. In solving the equations of motion, we approximately replace the inertia tensor with the hydrodynamical one and use the modified liquid-drop one as the collective potential energy. As the frictional coefficients we use the microscopically calculated ones in the previous paper. The calculation is done for the reaction of²⁸Si+²⁰Ne, in which the incident energy of²⁰Ne is 120 MeV. Results show that our microscopically calculated friction gives the large value of energy dissipation which amounts to the “completely damped” collision. Besides it, growths of the oblate deformation in the entrance channel and the prolate deformation in the exit channel are clearly seen. They give a large influence on the time development of the energy dissipation. We compare our calculated results with the experimental data for the reactions of 120 MeV²⁰Ne with²⁷Al. The agreement between them is found to be reasonably good.     

Microscopic calculation of the restoring force for scissor isovector vibrations

The restoring force for scissor isovector vibrations is calculated microscopically with the wave functions of an axially symmetric Woods-Saxon potential from a density-dependent symmetry energy. The experimental energies of the low-lying magnetic dipole states in rare-earth nuclei are well reproduced. It is found that only outer particles, which contribute to the nuclear moment of inertia, take part in this collective vibration. They are about half of the total number of nucleons.     

Application of the theory of open quantum systems to nuclear physics problems

Quantum diffusion equations with transport coefficients explicitly depending on time are derived from the generalized non-Markovian Langevin equations. The asymptotic behavior of the friction and diffusion coefficients is investigated in the case of the FC and RWA couplings between the collective and internal subsystems. An asymptotic expression is obtained for the propagator of the density matrix of the open quantum system with the general quadratic Hamiltonian, linearly coupled (in coordinate and momentum) to internal degrees of freedom. The effect of different sets of transport coefficients on the decoherence and decay rate of the metastable state is investigated using the master equation for the reduced density matrix of open quantum systems. The developed approach is used to study the capture of the projectile nucleus by the target nucleus at energies near the Coulomb barrier. Capture cross sections in asymmetric reactions are well described with allowance for the calculated capture probabilities. Particular cases where dissipation favors penetration through the potential barrier are found. The generalized Kramers formula for the quasi-stationary decay rate of the quantum metastable systems is analytically derived.     

A theoretical model for the collective motion of proteins by means of principal component analysis

A coarse grained model in the frame work of principal component analysis is presented. We used a bath of harmonic oscillators approach, based on classical mechanics, to derive the generalized Langevin equations of motion for the collective coordinates. The dynamics of the protein collective coordinates derived from molecular dynamics simulations have been studied for the Bovine Pancreatic Trypsin Inhibitor. We analyzed the stability of the method by studying structural fluctuations of the C _a atoms obtained from a 20 ns molecular dynamics simulation. Subsequently, the dynamics of the collective coordinates of protein were characterized by calculating the dynamical friction coefficient and diffusion coefficients along with time-dependent correlation functions of collective coordinates. A dual diffusion behavior was observed with a fast relaxation time of short diffusion regime 0.2–0.4 ps and slow relaxation time of long diffusion about 1–2 ps. In addition, we observed a power law decay of dynamical friction coefficient with exponent for the first five collective coordinates varying from −0.746 to −0.938 for the real part and from −0.528 to −0.665 for its magnitude. It was found that only the first ten collective coordinates are responsible for configuration transitions occurring on time scale longer than 50 ps.     

Possible nature of oscillations in the time dependences of the internal friction and effective shear modulus in Al-Cu alloys

The conditions of the appearance of in-phase oscillations in the time dependences of the low-frequency internal friction and effective shear modulus G _eff in Al-0.01 wt% Cu and Al-0.001 wt % Cu alloys are studied. The in-phase oscillations are shown to appear in the alloys only when their dislocation-impurity structure is disturbed from equilibrium and the impurity concentration near a dislocation is optimum. This fact suggests that the in-phase oscillations are due to a collective character of dislocation-impurity interactions, which leads to a transfer of energy of translational dislocation motion to transverse dislocation vibrations in the main slip plane.     

金属型脉冲堆惯性效应计算

金属型脉冲堆的反应性负反馈主要来自燃料的热膨胀。当脉冲堆爆发短周期脉冲时,由于燃料的热膨胀不能及时响应温度的变化,致使负反馈滞后,产生惯性效应。采用ANSYS程序计算了在突然热加载条件下的振荡特性,同时采用随机中子输运程序计算了平均关闭系数,然后把带有振荡特性的热反馈带入点堆动力学方程,采用数值方法求解得到了考虑惯性效应的裂变脉冲波形。计算结果与Godiva实验测量结果一致。采用的数值方法中,脉冲周期与振荡效应存在定量关系。由计算结果可知,脉冲周期短,惯性效应明显;脉冲周期越长,惯性效应的影响越小,金属型脉冲堆爆发脉冲时应尽量避免短周期脉冲。     

Vortex mutual friction in rotating superfluid<Superscript>3</Superscript>He

The Manchester rotating cryostat has been used to measure the longitudinal and transverse coefficients of vortex mutual friction in the A and B phases of superfluid³He. In the B phase the dominant contribution to the mutual friction is scattering of excitations off occupied bound states in the vortex core. The A phase results are explained quantitatively by assuming that doubly quantised continuous vortices are created with a dynamics determined by the equation of motion of the orbital vectorI; the measurements enable us to put an upper limit on the orbital inertia of less than 0.01h per Cooper pair. History-dependent textural effects which had to be overcome in order to make meaningful measurements in the A phase are explained by noting that for a given rotation direction the most stable vortices can be formed more easily from one direction of uniformI texture than the other.     

The adiabatic cranking model for large amplitudes

A simple model of slow large scale collective nuclear motion is developed. Starting with the equation for the single-particle density matrix extended by approximate incorporation of particle collisions in the relaxation time approach the classical equation of motion for the collective variables specifying the shape of nuclear surface is derived. The coefficients of equation of motion are related to the microscopic quantities: single-particle energies, occupation numbers, derivatives of s.-p. energies with respect to the deformation parameters. The one- and two-body contributions to the collective mass and friction parameters are discussed.     

New quasiparticles hystons and coherent photoinduced dynamics of molecules in polar disordered media

Using methods of statistical thermodynamics, it is shown that after pulse excitation the evolution of a “polar luminescent probe—polar disordered medium” system is described by an equation of damping vibrations. This allows the conclusion that in the solvate shell of the probe molecule synchronous rotational vibrations (librations) of the molecules of the medium occur, whose damping is caused by dielectric friction. Such a collective synchronous motion is considered as a motion of a quasiparticle called a hyston. The moment of inertia J_n and mass M_h of a hyston are defined as J_h=2m² ₁a^-3Ω₀ ^-2(ε-1)/(2ε+1), M_h=J_hM_s/J_s, where m₁ is the dipole moment of the probe molecule in the excited S₁-stute; a is the Onsager radius; Ω₀ is the cyclic frequency of harmonic vibrations of the hyston; ε is the dielectric constant; M_s and J_s are the mass and moment of inertia of a molecule of the medium, respectively. The correlation function of the motion of the molecules c(t) is a solution of the equation of hyston motion. The fluorescence response s(t) in measurements with time resolution coincides with the correlation function: s(t)=c(t). The concepts concerning hystons make it possible to describe macroscopic photoinduced coherent motion that is manifested against a background of thermal motion of the medium molecules. Institute of Molecular and Atomic Physics, National Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnei Spektroskopii, Vol 65, No. 2, pp. 176–183, March–April, 1998.     

Nonlinear dynamics of a rub-impact micro-rotor system with scale-dependent friction model

Scale effects in dry friction at microscale and the coefficients of friction due to adhesion force and two- and three-body deformations are considered. A rub-impact micro-rotor model with scaling nonlinear rub-impact force is presented and the nonlinear dynamic characteristics of the system in micro-electro-mechanical systems (MEMS) are investigated when the rotating speed, imbalance, damping coefficient, scale length and fractal dimension are regarded as the control parameters. Effects of scale length, fractal dimension, velocity-dependent impact factor and contact form on the coefficients of dry friction are investigated and discussed, and used to study the nonlinear behavior of rub-related vibrations with a large number of numerical simulations. The effects of rotating speed, imbalance, damping coefficient, and friction coefficient on the micro-rotor system responses are studied. It is indicated that the rub-impact micro-rotor system with the scale effects in friction alternates among the periodic, quasi-periodic and chaotic motions as the system parameters change. The results can be effectively used to diagnose the rub-impact fault, reduce the failure and improve the characteristics of a micro-rotor system, and optimize the design of micro-rotating machinery in MEMS.