Semiclassical treatment of fusion processes in collisions of weakly bound nuclei

We describe a semiclassical treatment of nuclear fusion reactions involving weakly bound nuclei. In this treatment, the complete fusion probabilities are approximated by products of two factors: a tunneling probability and the probability that the system is in its ground state at the strong absorption radius. We investigate the validity of the method in a schematic two-channel application, where the channels in the continuum are represented by a single resonant state. Comparisons with full coupled-channels calculations are performed. The agreement between semiclassical and quantal calculations isquite good, suggesting that the procedure may be extended to more sophisticated discretizations of the continuum.Comment: 11 pages, 5 figure

Quality quantification model of basic raw materials

Basic raw materials belong to the key input sources in the production of pig iron. The properties of basic raw materials can be evaluated using a variety of criteria. The essential ones include the physical and chemical properties. Current competitive pressures, however, force the producers of iron more and more often to include cost and logistic criteria into the decision-making process. In this area, however, they are facing a problem of how to convert a variety of vastly different parameters into one evaluation indicator in order to compare the available raw materials. This article deals with the analysis of a model created to evaluate the basic raw materials, which was designed as part of the research

Addition Spectra of Chaotic Quantum Dots: Interplay between Interactions and Geometry

We investigate the influence of interactions and geometry on ground states of clean chaotic quantum dots using the self-consistent Hartree-Fock method. We find two distinct regimes of interaction strength: While capacitive energy fluctuations $\delta \chi$ follow approximately a random matrix prediction for weak interactions, there is a crossover to a regime where $\delta \chi$ is strongly enhanced and scales roughly with interaction strength. This enhancement is related to the rearrangement of charges into ordered states near the dot edge. This effect is non-universal depending on dot shape and size. It may provide additional insight into recent experiments on statistics of Coulomb blockade peak spacings.Comment: 4 pages, final version to appear in Phys. Rev. Let

Body Fixed Frame, Rigid Gauge Rotations and Large N Random Fields in QCD

The "body fixed frame" with respect to local gauge transformations is introduced. Rigid gauge "rotations" in QCD and their \Sch equation are studied for static and dynamic quarks. Possible choices of the rigid gauge field configuration corresponding to a nonvanishing static colormagnetic field in the "body fixed" frame are discussed. A gauge invariant variational equation is derived in this frame. For large number N of colors the rigid gauge field configuration is regarded as random with maximally random probability distribution under constraints on macroscopic--like quantities. For the uniform magnetic field the joint probability distribution of the field components is determined by maximizing the appropriate entropy under the area law constraint for the Wilson loop. In the quark sector the gauge invariance requires the rigid gauge field configuration to appear not only as a background but also as inducing an instantaneous quark-quark interaction. Both are random in the large N limit.Comment: 29 pages LATEX, Weizmann Institute preprint WIS-93/40/Apr -P

Spin and interaction effects in quantum dots: a Hartree-Fock-Koopmans approach

We use a Hartree-Fock-Koopmans approach to study spin and interaction effects in a diffusive or chaotic quantum dot. In particular, we derive the statistics of the spacings between successive Coulomb-blockade peaks. We include fluctuations of the matrix elements of the two-body screened interaction, surface-charge potential, and confining potential to leading order in the inverse Thouless conductance. The calculated peak-spacing distribution is compared with experimental results.Comment: 5 pages, 4 eps figures, revise

Functional determinants for general Sturm-Liouville problems

Simple and analytically tractable expressions for functional determinants are known to exist for many cases of interest. We extend the range of situations for which these hold to cover systems of self-adjoint operators of the Sturm-Liouville type with arbitrary linear boundary conditions. The results hold whether or not the operators have negative eigenvalues. The physically important case of functional determinants of operators with a zero mode, but where that mode has been extracted, is studied in detail for the same range of situations as when no zero mode exists. The method of proof uses the properties of generalised zeta-functions. The general form of the final results are the same for the entire range of problems considered.Comment: 28 pages, LaTe

Inelastic semiclassical Coulomb scattering

We present a semiclassical S-matrix study of inelastic collinear electron-hydrogen scattering. A simple way to extract all necessary information from the deflection function alone without having to compute the stability matrix is described. This includes the determination of the relevant Maslov indices. Results of singlet and triplet cross sections for excitation and ionization are reported. The different levels of approximation -- classical, semiclassical, and uniform semiclassical -- are compared among each other and to the full quantum result.Comment: 9 figure

Density functional theory of spin-polarized disordered quantum dots

Using density functional theory, we investigate fluctuations of the ground state energy of spin-polarized, disordered quantum dots in the metallic regime. To compare to experiment, we evaluate the distribution of addition energies and find a convolution of the Wigner-Dyson distribution, expected for noniteracting electrons, with a narrower Gaussian distribution due to interactions. The tird moment of the total distribution is independent of interactions, and so is predicted to decrease by a factor of 0.405 upon application of a magnetic field which transforms from the Gaussian orthogonal to the Gaussian unitary ensemble.Comment: 13 pages, 2 figure

Landau-Ginzburg method applied to finite fermion systems: Pairing in Nuclei

Given the spectrum of a Hamiltonian, a methodology is developed which employs the Landau-Ginsburg method for characterizing phase transitions in infinite systems to identify phase transition remnants in finite fermion systems. As a first application of our appproach we discuss pairing in finite nuclei.Comment: 14 pages, 4 figure