One-body nuclear friction

We have calculated the velocity dependent forces acting between two nuclei that arise due to one-body mechanism of nuclear excitation when they are dragged against one another with constant velocity. The nuclear friction coefficients are then extracted from the velocity dependence of these forces which is found to be strongly linear. The one-body force is calculated by solving the time-dependent Schrödinger equation for all the occupied single-particle states of a nuclear system in a central collision. Each nucleus in this model is assumed to be described by a single-particle Woods-Saxon potential filled with 40 nucleons each. The magnitude of the resulting one-body friction is found to be in between the proximity and surface frictions. The proximity-friction is too small by about an order of magnitude. To check this result, we calculated the one-sided flux from one nucleus to the other. The friction force connected to this flux (i.e. the one-body exchange friction) turns out to be about half or less than the one body friction. We conclude that theproximity-friction grossly underestimates the one-body exchange friction. Furthermore,inelastic excitations are at least as important for one-body dissipation at distances beyond the touching point as is particle exchange.     

Holomorphic curves from matrices

Membranes holomorphically embedded in flat non-compact space are constructed in terms of the degrees of freedom of an infinite collection of 0-branes. To each holomorphic curve we associate infinite-dimensional matrices which are static solutions to the matrix theory equations of motion, and which can be interpreted as the matrix theory representation of the holomorphically embedded membrane. The problem of finding such matrix representations can be phrased as a problem in geometric quantization, where ϵ ∝ l_P³/R plays the role of the Planck constant and parametrizes families of solutions. The concept of Bergman projection is used as a basic tool, and a local expansion for the action of the projection in inverse powers of curvature is derived. This expansion is then used to compute the required matrices perturbatively in ϵ. The first two terms in the expansion correspond to the standard geometric quantization result and to the result obtained using the metaplectic correction to geometric quantization.     

One- and two-body dissipation in heavy-ion collisions

A microscopic theory has been formulated for one- and two-body dissipation in collisions between two heavy nuclei. With a nucleon-nucleon interaction as the basic perturbation in a density matrix approach with “linear response” approximations, the one- and two-body nuclear friction coefficients for the ⁴⁰Ca + ⁴⁰Ca system have been calculated and their dependence on relative kinetic energy and smearing of nuclear single-particle states was obtained. The results of our calculation show that: (a) the combined one- and two-body friction coefficients compare favourably with phenomenological values, (b) the one-body dissipation is more effective than two-body in kinetic energy damping, while both the mechanisms are comparable for the damping of relative angular momentum, (c) the importance of the two-body friction compared to one-body increases at higher relative kinetic energies and (d) the effect of introducing a smearing in nuclear levels appears as a lowering of nuclear friction.     

Field of linear frames as a fundamental self-interacting system

We present some philosophical and physical arguments supporting the hypothesis that the most fundamental self-interacting field in an amorphous space-time is the field of linear frames, i.e. the quadruple of vector bosons. We construct a wide class of Lagrangian dynamical models invariant under the total group of diffeomorphisms and under the natural action of the proper linear group GL⁺ (4, R) on the tetrad field. There exist some links between these models and the Hamiltonian dynamical systems on GL⁺ (3, R) (the mechanics of affinely-rigid bodies [23] [27]). We present the general form of field equations, conservation laws and Bianchi identities. There exist some formal similarities between our Lagrangians and those used in non-linear electrodynamics, in particular in the Born–Infeld theory [21]. We also give a few rough remarks concerning models invariant under natural subgroups of GL⁺ (4, R), i.e. under SL(4, R) and SO(1, 3; R) (special linear group and Lorentz group). The latter class includes the conventional Einstein relativity and the more general metrical-parallelism models. It turns out that there are GL⁺ (4, R)-invariant Lagrangians which are structurally alike the conventional Einstein Lagrangian.We have not derived as yet either mathematical or physical consequences of the presented model. Nevertheless, it seems to follow from our discussion that, a priori, the GL⁺ (4, R)-invariant tetrad models could be competitive with the Einstein theory. The next thing to be done would be a careful mathematical analysis of these models and attempts to compare their consequences with those of the Einstein relativity and of other field theories.     

Improved higher order phase-integral approximations of the JWKB type in the vicinity of zeros and singularities of the “wave number”

This paper treats the local behaviour of certain phase-integral approximations (PIA) of arbitrary order. This is done for the vicinities of zeros and poles of the coefficient Q²(z) in the wave-equation d²ψ/dz²+Q²(z)ψ = 0. This coefficient can be complex on the real axis. A simple formula relating the cumulative error of PIA (μ-integral) to the first truncated correction in the phase-integral expansion is derived. For a simple model of a zero or pole of Q²(z), PIA of arbitrary order are determined explicitly. Their phase-integrals exhibit certain symmetry properties which justify the “loop integrals” often used in the JWKB formulae when applied in higher orders. We demonstrate the asymptotic character of the phase-integral expansion explicitly and determine its optimum order and accuracy. The well-known connection formulae are shown to retain their one-directional character in higher orders. Modifications which improve PIA at their critical points are also discussed in detail both at the modification point and elsewhere. Some quantum mechanical applications are also discussed.     

Langevin fission dynamics of hot rotating nuclei: Systematic application to Z 2/A=34–42 heavy nuclei

A stochastic approach that treats fission dynamics on the basis of three-dimensional Langevin equations is used to calculate the mass-energy distributions of fragments originating from the fission of compound nuclei whose fissility parameter lies in the range Z ²/A=34–42. In these calculations, use was made of the liquid-drop model allowing for finite-range nuclear forces and the diffuseness of the nuclear surface in calculating the potential energy and a modified one-body mechanism of viscosity in describing dissipation. The emission of light prescission particles is taken into account on the basis of the statistical model. The calculations performed within three-dimensional Langevin dynamics reproduce well all parameters of the experimental mass-energy distributions of fission fragments and all parameters of the prefission-neutron multiplicity for various parameters of the compound nucleus. The inclusion of the third collective coordinate in the Langevin equations leads to a considerable increase (by up to 40–50%) in the variances of mass-energy distributions in relation to what was previously obtained from two-dimensional Langevin calculations. For the parameters of the mass-energy distributions of fission fragments and the parameters of the prefission-neutron multiplicity to be reproduced simultaneously, the reduction coefficient K _s must be diminished at least by a factor of 2(0.2≤K _s ≤0.5) in relation to that in the case of total one-body viscosity (K _s =1).     

Effects of band structure and matrix element on RKKY interaction

The effects of band structure and matrix elements on the RKKY interaction J(R) are separately investigated. When the Fermi surface has planes perpendicular to R, effects appear on the period of oscillation, the phase shift and the amplitude of J(R). The applicable region of the asymptotic form for large R and the validity of the free electron approximation are also examined. If there are no tangential planes perpendicular to R, it is found that: 1) when two interacting localized spins are on lattice points in the crystal, exponential damping appears even for the constant matrix element model and the matrix element effects introduce competing terms causing a sign change; 2) when one of the spins is at an interstitial position, the constant matrix model gives a weaker J(R) ∝ R^-2 damping, but the character of this term changes into the exponential damping by taking into account matrix elements.     

Modified gravity in contemporary universe

Astronomical data in favor of cosmological acceleration and possible explanations of accelerated expansion of the universe are discussed. Main attention is paid to gravity modifications at small curvature which could induce accelerated cosmological expansion. It is shown that gravitating systems with mass density rising with time evolve to a singular state with infinite curvature scalar. The universe evolution during the radiation-dominated epoch is studied in the R ²-extended gravity theory. Particle production rate by the oscillating curvature and the back reaction of particle production on the evolution of R are calculated in one-loop approximation. Possible implications of the model for cosmological creation of non-thermal dark matter are discussed.     

Probabilistic scission of a fissile nucleus into fragments

A probabilistic criterion is proposed for the scission of a fissile nucleus into fragments. The probability of the rupture of the neck between would-be fragments is estimated by considering scission as a fluctuation. The energy of the prescission configuration and the energy of the separated-fragment configuration are computed on the basis of a macroscopic model that takes into account a finite range of nuclear forces and the diffuseness of the nuclear surface. The effect of the probabilistic criterion of nuclear scission on fission-process observables, such as the moments of the mass-energy distribution of fission fragments, the mean multiplicity of prescission neutrons, and mean fission times, is demonstrated. It is shown that the Strutinsky criterion, according to which nuclear scission occurs at a finite neck radius of 0.3R₀, is a rather good approximation to the probabilistic scission criterion in Langevin dynamical calculations employing the one-body nuclear-viscosity mechanism modified in such a way that the wall-formula contribution is reduced, the reduction factor satisfying the condition k _s <05.     

Shape selection in non-Euclidean plates

We investigate isometric immersions of disks with constant negative curvature into R³, and the minimizers for the bending energy, i.e. the L² norm of the principal curvatures over the class of W^2,2 isometric immersions. We show the existence of smooth immersions of arbitrarily large geodesic balls in H² into R³. In elucidating the connection between these immersions and the non-existence/singularity results of Hilbert and Amsler, we obtain a lower bound for the L^∞ norm of the principal curvatures for such smooth isometric immersions. We also construct piecewise smooth isometric immersions that have a periodic profile, are globally W^2,2, and numerically have lower bending energy than their smooth counterparts. The number of periods in these configurations is set by the condition that the principal curvatures of the surface remain finite and grow approximately exponentially with the radius of the disk. We discuss the implications of our results on recent experiments on the mechanics of non-Euclidean plates.     

Monte Carlo studies of triangulated spherical surfaces in the two-dimensional space

We numerically study a triangulated surface model in R²${\mathbf{R}}^2$ by taking into account a viewpoint of string model. The models are defined by a mapping X from a two-dimensional surface M   to R²${\mathbf{R}}^2$, where the mapping X and the metric g of M are the dynamical variables. The sum over g in the partition function is simulated by the sum over bond lengths and deficit angles by using the Regge calculus technique, and the sum over g is defined to be performed independently of the sum over X. We find that the model undergoes a first-order transition of surface fluctuations, which accompanies a collapsing transition, and that the transitions are reflected in the internal geometry of surface. Fluid surface models are also studied on dynamically triangulated surfaces, and the transitions are found to be of second order. The order of the transition remains unchanged from that of the conventional model defined only by the variable X both in the fixed-connectivity and the fluid models.     

Bivariate distributions in statistical spectroscopy studies: III. Non interacting particle strength densities for one-body transition operators

In statistical spectroscopy, it was shown by French et al. (Ann. Phys., N.Y. 181, 235 (1988)) that the bivariate strength densities take a convolution form with the non interacting particle (NIP) strength density being convoluted with a spreading bivariate Gaussian due to interactions. Leaving aside the question of determining the parameters of the spreading bivariate Gaussian, one needs good methods for constructing the NIP bivariate strength densitiesI _O ^h (E,E′) (h is a one-body hamiltonian andO is a transition operator) in large shell model spaces. A formalism for constructingI _O ^h is developed for one-body transition operators by using spherical orbits and spherical configurations. For rapid construction and also for applying the statistical theory in large shell model spacesI _O ^h is decomposed into partial densities defined by unitary orbit configurations (unitary orbit is a set of spherical orbits). Trace propagation formulas for the bivariate momentsM _rs with r+s ≤2 of the partial NIP strength densities, which will determine the Gaussian representation, are derived. In a large space numerical example with Gamow-Tellerβ ^? transition operator, the superposition of unitary orbit partial bivariate Gaussian densities is shown to give a good representation of the exact NIP strength densities. Trace propagation formulas forM _rs with r+<—4 are also derived inm-particle scalar spaces which are useful for many purposes.     

Collisional excitation of neon-like Ni XIX using the Breit-PauliR-matrix method

Collision strength for the transition within the first five fine-structure levels in Ni XIX are calculated using the Breit-PauliR-matrix method. Configuration interaction wave functions are used to represent the target states included in theR-matrix expansion. The relativistic effects are incorporated in the Breit-Pauli approximation by including the one-body mass correction, Darwin and spin-orbit interaction terms in scattering equations.     

Test of correlation expansions for inelastic scattering of protons from 16O and 40Ca in Glauber theory

Two different versions of a correlation expansion for the A-body nuclear transition density required to evaluate the Glauber amplitude for inelastic proton-nucleus scattering are tested. Antisymmetrized oscillator wave functions, containing only Pauli correlations, are used to calculate the “exact” amplitude as well as various terms in the correlation expansions for the excitation of the 3^? (6.13 MeV) state of ¹⁶O and the 5^? (4.49 MeV) state of ⁴⁰Ca. The leading term in both expansions, which ignores all correlations and corresponds to the Glauber theory version of the DWIA, leads to errors which are larger than present experimental errors, especially at large momentum transfers. In one version of the correlation expansion, due to Alkhazov et al., the first-order correction contains both elastic and inelastic two-body correlations and leads to satisfactory results. In the other version, used by Abgrall et al., the first-order correction contains only inelastic two-body correlations. In this case the first- and second-order corrections are needed to obtain accuracy comparable to that of the latest experiments.     

Dynamic model for alpha particle emission during fission

We investigate the motion of anα-particle in the average time depencent potentialV(R _α ,t) of a fissioning nucleus. The emission process is treated quantum mechanically via a numerical solution of the one-body Schroedinger equation withV(R _α ,t). This solution yields the distribution of initial conditions for classical trajectories describing theα-particles outside the Coulomb barrier. The time and shape dependence ofV(R _α,t) is shown to have significant influence on the observable angle and energy distribution of theα-particles emitted during fission.     

Two-loop self-energy correction in a strong Coulomb nuclear field

The two-loop self-energy correction to the ground-state energy levels of hydrogen-like ions with nuclear charges Z≥10 is calculated without the Zα expansion, where α is the fine-structure constant. The data obtained are compared with the results of analytical calculations within the Zα expansion; significant disagreement with the analytical results of order α²(Zα)⁶ has been found. Extrapolation is used to obtain the most accurate value for the two-loop self-energy correction for the 1s state in hydrogen.     

A generalization of Wigner's R-matrix method

A generalization of the Wigner's non-relativistic R-matrix theory of scattering by a central potential field is proposed. The idea is to use an R-matrix expansion basis generated by a Sturm-Liouville problem with an eigenparameter included both in a differential equation and in a boundary condition (in the standard theory an R-matrix basis is obtained by solving an eigenvalue problem with fixed boundary conditions). A partial fraction expansion of an R^(η)-matrix introduced is derived and shown to converge faster than a partial fraction expansion of Wigner's R-matrix used in the standard theory.     

The geometric SO(3) × D model

The geometric SO(3) × D model is formulated as a computationally viable submodel of the algebraic sp(3, R) model containing the Sp (1, R) model of Arickx et al. as a submodel. It is basically a scheme for constructing a space of states (like the space of Slater determinants) which can be employed either directly, for constrained variational quantal dynamics of the Hartree-Fock, RPA and TDHF type, or to construct a shell-model basis for the diagonalization of a microscopic hamiltonian. The results of HF calculations, restricted to SO(3) × D surfaces, are reported for the nuclei ⁴He, ⁸Be, ¹⁶O and ²⁰Ne.