Resonances and Fluctuations in Nuclear Reaction Cross Sections

On the basis of the continuum shell model, an expression for the S-matrix is derived. The external mixing between shape resonances and resonance states of complicated nuclear structure is investigated. It is shown that the doorway properties of the shape resonances may lead to an l-dependent transparency of the optical potential and, consequently, to an energy dependence of large back angle scattering if the unitarity of the S-matrix is taken into account.     

Can QCD Be a Perturbation Theory of Hadrons?

We have found that the S-matrix for atoms and hadrons depends on a gauge as the elementary particles are off mass-shell in the bound states. The S-matrix for bound states one should to construct by the projection of the Belinfante energy-momentum tensor on the Gauss equation solution for the time component with the time-axis chosen as the eigenvector of the bound state total momentum operator. We have shown that this QCD Hamiltonian determined in infrared region by the rising potential ansatz, besides the parton model in the specific gauge, contains also the nonrelativistic potential model for heavy quarkonia, the chiral Lagrangians for light quarkonia with their spectrum, the glueball physics, and the small effective coupling constant in the whole region of transversal momenta.     

Time-dependent mean field S-matrix theory

By using the path integral approach to many-body systems, we formulate a time-dependent mean field S-matrix theory of nuclear reactions. Many-body channel eigenstates are constructed by using projection techniques. In this way the S-matrix between the channel eigenstates is expressed as a superposition of S-matrix elements between wave-packet-like states localized in space and time. A field operator representation of the interaction picture S-matrix is derived which enables one to apply the path integral approach. Applying the stationary phase approximation to the path integral representation of the interaction picture S-matrix between the localized states an asymptotically constant time-dependent mean field approximation to this S-matrix is obtained. Finally, the S-matrix between the projected channel eigenstates is obtained by evaluating the integral, arising from the projections, over the space-time positions of the localized states in the stationary phase approximation. The stationary phase conditions select those localized states from the projected channel states for which the mean field values of energy and momentum coincide with their corresponding channel eigenvalues.     

Photoionization of excited states of neon-like Mg III

The close coupling R-matrix method is used to calculate cross-sections for photoionization of Mg III from its first three excited states. Configuration interaction wave functions are used to represent two target states of Mg III retained in the R-matrix expansion. The positions and effective quantum numbers for the Rydberg series converging to the excited state 2s ²2p ^{6 2} S ^e of the residual ion, are predicted.     

Conserved currents and symmetry transformations in local scattering theory

The relation between conserved currents and symmetries of theS-matrix is investigated within the framework of Wightman field theory. Assuming a complete particle interpretation with no massless particles, it is shown that every conserved current yields a self-adjoint charge operator which acts additively onn-particle states and commutes with theS-matrix. For currents satisfying current algebra relations of a groupG, the corresponding charges generate a unitary representation ofG.     

Three-Body Phase Shift in One-Dimensional 2 + 1 Scattering

For a model of three particles on a line, subject to attractive delta-function interactions, we consider the phase shift. We do this from the point of view of the calculation of the S-matrix in a hyperspherical adiabatic basis (an adiabatic S-matrix), and for energies ranging from the (negative) energy of the two-body bound state to a total energy of zero. We derive analytical expansions and present numerical work, for different approximations, and compare with the exact results that we obtain from the work of McGuire, whose model we have borrowed. We show that the simplest adiabatic approximation gives results that are qualitatively wrong, but that better approximations yield, for most of our range, excellent agreement with the exact result. Understanding the threshold behaviour, however, requires a zero-energy three-body bound state, or resonance, previously unsuspected for this model. The methods developed for the case of the simplest adiabatic approximation also yield threshold and low-energy results applicable to the two-body problem in two dimensions. Received December 23, 1996; revised May 13, 1997; accepted for publication June 19, 1997     

The (d,p)-reaction treated by the formalism of Green's functions

The full energy dependence of the two-particle Green's function is taken into account in deriving theS-matrix for a (d, p)-reaction leading from an even-even nucleus in the ground state to a single-particle residual state in the even-odd nucleus. The resultingT-vertex of many-body theory is discussed with the Bethe-Salpeter equation in the particle-particle channel, which allows for a renormalization in the same sense as for bound state problems but now in a different range of energy. Special attention is paid to the problems arising in expanding the deuteron (two particles in the continuum) into shell model wave functions.     

Interplay of quark and meson degrees of freedom in a near-threshold resonance: Multi-channel case

We investigate the interplay of quark and meson degrees of freedom in a physical state representing a near-threshold resonance for the case of multiple continuum channels. The aim is to demonstrate the full complexity of possible near-threshold phenomena. It turns out that those are especially rich, if both quark and meson dynamics generate simultaneously weakly coupled near-threshold poles in the S-matrix. We study the properties of this scenario in detail, such as t-matrix and production amplitude zeros, as well as various effects of the continuum channels interplay.     

Electron Conductance and Lifetimes in a Ballistic Electron Waveguide

Ballistic electron waveguides are open quantum systems that can be formed at very low temperatures at a GaAs/AlGaAs interface. Dissipation due to electron–phonon and electron–electron interactions in these systems is negligible. Although the electrons only interact with the walls of the waveguide, they can have a complicated spectrum including both positive energy bound states and quasibound states which appear as complex energy poles of the scattering S-matrix or energy Green's function. The quasibound states can give rise to zeros in the waveguide conductance as the energy of the electrons is varied. The width of the conduction zeros is determined by the lifetimes of the quasibound states. The complex energy spectrum associated with the quasibound states also governs the survival probability of electrons placed in the waveguide cavities.     

Partial wave analysis of dilatation-invariant relativisticS-matrix

Free particle states andS-matrix are defined on carrier spaces of representations of the Weyl groupW (Poincaré group extended by dilatations). By using Clebsch-Gordan coefficients ofW the extension of the relativistic partial wave analysis of the two-bodyS-matrix is obtained. Scattering of particles with arbitrary masses and spins is treated and a comparison with relativistic case is discussed.One of the authors (J. N.) would like to thank Professor M.Flato for a stimulating discussion.     

The relativistic bound and scattering states of the Manning-Rosen potential with an improved new approximate scheme to the centrifugal term

The approximately analytical bound and scattering state solutions of the arbitrary l-wave Klein-Gordon equation for the mixed Manning-Rosen potentials are carried out by an improved new approximation to the centrifugal term. The normalized analytical radial wave functions of the l-wave Klein-Gordon equation with the mixed Manning-Rosen potentials are presented and the corresponding energy equations for bound states and phase shifts for scattering states are derived. It is shown that the energy levels of the continuum states, reduce to the bound states of those at the poles of the scattering amplitude. Some useful figures are plotted to show the improved accuracy of our results and the special case for wave is studied briefly.      

Three-nucleon calculations without the explicit use of two-body potentials

Using as two-nucleon interaction input the ³S₁-³D₁ and ¹S₀ partial waves, the Faddeev equations are solved for the three-nucleon bound state. The ³S₁³D₁T-matrix is calculated from the Reid potential. Avoiding the usual potential fit, the ¹S₀T-matrix is directly continued off-shell and is constructed consistent with the ¹S₀ phase shift of elastic two-nucleon scattering. The off-shell part of the ¹S₀T-matrix is parametrized and with this parametrization the dependence of the three-nucleon bound-state properties is studied. As a result it is found that the binding energy varies only between 6.2 MeV and 6.8 MeV, while the minimum in the charge form factor for electron scattering from ³He lies between 12.9 fm^?2 and 18.7 fm^?2. The larger (smaller) ³He binding energy is accompanied by a ³He charge form factor whose minimum is at larger (smaller) momentum transfers.     

A modified RPA for open-shell nuclei

A modified RPA suitable for open-shell nuclei is constructed using the Green function method. Unlike the standard RPA, this modification makes allowance for the spread of bound single-particle and single-hole states over more complex configurations which is done due to a more realistic approximation of single-particle Green functions. The calculations of the nucleon-nucleus S-matrix and of the probability amplitudes for the single-particle transitions of the nucleus from the ground state into scattering states are examined. For the separable effective forces these quantities are expressed in closed form.     

Calculation of the energy density function by the method of steepest descent

We present a unified theory of diatomic molecules which reconciles bound state spectroscopy and atomic scattering theory. The total wave-function is expanded in a complete set of atomic channel states which is entirely equivalent to an expansion in Hund's case (e) electronic-rotational states. An analysis of the coupled radial, that is vibrational, functions places strong constraints on the asymptotic properties of the molecular wave-functions. These are presented in terms of the reactance K and scattering S matrices of atomic scattering theory which offers a uniform treatment for open channels (inelastic scattering and continuum spectroscopy), closed channels (bound state spectroscopy) and mixtures of both (predissociation). The normalization of the total wavefunction is derived and related to the asymptotic boundary conditions both for continuum and bound states.     

Multiphoton detachment from a zero-range potential revisited

Direct detachment of an electron bound by a regularized zero-range potential is reinvestigated. For the definition of the S-matrix amplitude for detachment, the wave function of the electron after the laser pulse has passed through is projected on an exact scattering state of the zero-range potential rather than a plane-wave state, which is normally used. The exact scattering state generates an additional contribution to the amplitude, which leads to an isotropic term in the angle-resolved energy spectrum.     

Continuum states of modified Morse potential

Using a proper approximation scheme to the centrifugal term, we study any l-wave continuum states of the Schrdinger equation for the modified Morse potential. The normalised analytical radial wave functions are presented, and a corresponding calculation formula of phase shifts is derived. It is shown that the energy levels of the continuum states reduce to those of the bound states at the poles of the scattering amplitude. Some numerical results are calculated to show the accuracy of our results.     

Q¯ modes in the Quark-Gluon Plasma

We study the evolution of heavy quarkonium states with temperature in a Quark-Gluon Plasma (QGP) by evaluating an in-medium Qˉ T-matrix within a reduced Bethe-Salpeter equation in S- and P-wave channels. The interaction kernel is extracted from finite-temperature QCD lattice calculations of the singlet free energy of a Qˉ pair. Quarkonium bound states are found to gradually move across the Qˉ threshold after which they rapidly dissolve in the hot system. We calculate Euclidean-time correlation functions and compare to results from lattice QCD. We also study finite-width effects in the heavy-quark propagators.     

Non-Relativistic Treatment of a Generalized Inverse Quadratic Yukawa Potential

A bound state solution is a quantum state solution of a particle subjected to a potential such that the particle's energy is less than the potential at both negative and positive infinity. The particle's energy may also be negative as the potential approaches zero at infinity. It is characterized by the discretized eigenvalues and eigenfunctions,which contain all the necessary information regarding the quantum systems under consideration. The bound state problems need to be extended using a more precise method and approximation scheme. This study focuses on the non-relativistic bound state solutions to the generalized inverse quadratic Yukawa potential. The expression for the non-relativistic energy eigenvalues and radial eigenfunctions are derived using proper quantization rule and formula method, respectively. The results reveal that both the ground and first excited energy eigenvalues depend largely on the angular momentum numbers, screening parameters, reduced mass, and the potential depth. The energy eigenvalues,angular momentum numbers,screening parameters,reduced mass,and the potential depth or potential coupling strength determine the nature of bound state of quantum particles. The explored model is also suitable for explaining both the bound and continuum states of quantum systems.     

Strength functions for fragmented doorway states

Coupling a strongly excited “doorway state” to weak “hallway states” distributes its strength into micro-resonances seen in differential cross sections taken with very good energy resolution. The distribution of strength is shown to be revealed by reduced widths of the K-matrix rather than by the imaginary part of poles of the S-matrix. Different strength functions (SF) constructed by averaging the K-matrix widths are then investigated to determine their dependences on energy and on parameters related to averages of microscopic matrix elements. A new sum rule on the integrated strength of these SF is derived and used to show that different averaging procedures actually distribute the strength differently. Finally, it is shown that the discontinuous summed strength defines spreading parameters for the doorway state only in strong coupling, where it approximates the indefinite integral of the continuous SF of MacDonald-Mekjian-Kerman-De Toledo Piza. A new method of “parametric continuation” is used to relate a discontinuous sliding box-average, or a finite sum, of discrete terms to a continuous function.     

Double S- and P-wave charmonium production in e+e? annihilation

On the basis of perturbative QCD and the relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of S-wave and P-wave charmonium states. Relativistic factors in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave function to the reference frame of the moving S- and Pwave mesons are taken into account. For the gluon and quark propagators entering the production vertex function we use a truncated expansion in the ratio of the relative quark momenta to the center-of-mass energy $ \sqrt s $ \sqrt s up to the second order. Relativistic corrections to the quark bound state wave functions in the rest frame are considered by means of the Breit-like potential. It turns out that the examined effects change essentially the nonrelativistic results of the cross section for the considered reactions at the center-of-mass energy $ \sqrt s $ \sqrt s = 10.6 GeV.