A non-relativistic model of two-particle decay II. Reduced resolvent

We continue discussion of the Lee-type decay model described in the first part of this paper. After separation of the centre-of-mass motion, we deduce meromorphic structure of the reduced resolvent for small values of the coupling constant.Presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

A non-relativistic model of two-particle decay III. The pole approximation

In the third part of the paper, we are concerned mostly with the problem of justifying the approximation in which the reduced resolvent is replaced by the pole term alone. Imposing additional regularity assumptions on the function, which specifies the interaction, we are able to estimate the difference of the corresponding reduced propagators. This result is used further to derive an estimate of the deviations from the exponential decay law which results from the pole approximation. With exception of very small and very large times, the obtained bound is proportional to fourth power of the coupling constant. We prove also Fermi golden rule for the model under consideration, and compare the present method to the one previously used by Demuth.     

Bound states and scattering from bound states in the light-front field theory dynamics

Starting from the Weinberg rules we derive a covariant form of the relativistic Schrödinger equation and formulate the bound state problem in the light-front field theory dynamics. We present an explicit rule for embodying the two-body subsystem in the three-body space and demonstrate that the cluster decomposition property is explicitly preserved in the light front field theory dynamics. As an application of these results we write amplitudes forπd→nN ^*, πd→πpn, andπd→πd, in the impulse approximation, in terms of the internal bound state wave functions and two-body reducedt-matrix elements.     

An energy-independent nonlocal potential model for bound and scattering states

The general expression of the nucleon-nucleus optical potential has been obtained using Watson's multiple scattering theory and Wolfenstein's parametrization of the nucleon-nucleon scattering amplitude. The resulting theoretical potential is nonlocal and consists of an energy-independent central volume plus surface real and imaginary potential and of a Thomas-like spin-orbit term. The analysis has been restricted to N = Z spherical nuclei, so that neither isospin-isospin nor spin-spin interactions have been included. The widely used Perey-Buck, Greenlees, and Watson expressions of the optical potential are easily obtained as particular cases. For practical purposes, the nonlocal potential has been parametrized in the Frahn-Lemmer form, using Woods-Saxon radial form factors, and the equivalent local potential (ELP) has been calculated by a Perey-Buck-like transformation.The ELP has a radial behavior very similar to the original nonlocal one, but the potential depths and radii are energy dependent. The six free parameters in the ELP have been adjusted to fit the available experimental data in the ?70 to + 150 MeV range of interest in nuclear reactions, namely, energies of single hole and single particle states, charge distributions, proton elastic scattering cross sections, and polarizations. The fitted potential depths show an energy dependence in remarkable agreement with the model predictions with a central nonlocality range β ? 1 F and a spin-orbit nonlocality range β₃ ? 0.8 F. The relative importance of surface and volume dependence in the real central potential in also discussed.     

Unified theory of bound and scattering molecular Rydberg states as quantum maps

Using a representation of multichannel quantum defect theory in terms of a quantum Poincaré map for bound Rydberg molecules, we apply Jung's scattering map to derive a generalized quantum map, that includes the continuum. We show that this representation not only simplifies the understanding of the method, but moreover produces considerable numerical advantages. Finally we show under what circumstances the usual semi-classical approximations yield satisfactory results. In particular we see that singularities that cause problems in semi-classics are irrelevant to the quantum map.     

Simultaneous measurement of beta- decay to bound and continuum electron states

We report the first measurement of a ratio lambda(beta(b))/lambda(beta(c)) of bound-state ((lambda(beta(b))) and continuum-state (lambda(beta(c))) beta(-)-decay rates for the case of bare 207Tl81+ ions. These ions were produced at the GSI fragment separator FRS by projectile fragmentation of a 208Pb beam. After in-flight separation with the Brho-deltaE-Brho method, they were injected into the experimental storage-ring ESR at an energy of 400.5A MeV, stored, and electron cooled. The number of both the 207Tl81+ ions and their bound-state beta(-)-decay daughters, hydrogen-like 207Pb81+ ions, were measured as a function of storage time by recording their Schottky-noise intensities. The experimental result, lambda(beta(b))/lambda(beta(c)) = 0.188(18), is in very good agreement with the value of 0.171(1) obtained from theory employing spectra of allowed transitions.     

A variational approach to bound states in quantum field theory

We consider here in a toy model an approach to bound state problem in a nonperturbative manner using equal time algebra for the interacting field operators. The potential is replaced by offshell bosonic quanta inside the bound state of nonrelativistic particles. The bosonic dressing is determined through energy minimisation, and mass renormalisation is carried out in a nonperturbative manner. Since the interaction is through a scalar field, it does not include spin effects. The model however nicely incorporates an intuitive picture of hadronic bound states in which the gluon fields dress the quarks providing the binding between them and also simulate the gluonic content of hadrons in deep inelastic collisions.     

The classical field limit of scattering theory for non-relativistic many-boson systems. II

We study the classical field limit of non relativistic many-boson theories in space dimensionn3, extending the results of a previous paper to more singular interactions. We prove the expected results: when tends to zero, the quantum theory tends in a suitable sense to the corresponding classical field theory, and the quantum fluctuations are governed by the equation obtained by linearizing the quantum evolution equation around the classical solution. These results hold uniformly in time and therefore apply to scattering theory. The interactions considered here are so singular as to require a change of domain in order to define the generator of the evolution of the fluctuations, but sufficiently regular so that no energy renormalization is needed.     

Some comments on heavy quark bound states,production and decay

We suggest that mixed heavy quark bound states like \(b\bar c\) may offer very good testing ground for Q.C.D. We make a prediction within ≈0.3% for the \(b\bar c\) ground state mass and discuss its possible production in weak decays. Various general features of non leptonic decays of heavey flavors and in particular the prediction of absence ofK _* ⁰ resonance inD ⁰→K ^-→⁺→⁰ arte discussed, and finally we close by commenting on the importance of associated heavy flavor production as a crucial test for the recently advanced preconfinment notion.     

The classical field limit of scattering theory for non-relativistic many-boson systems. I

We study the classical field limit of non-relativistic many-boson theories in space dimensionn≧3. When ?→0, the correlation functions, which are the averages of products of bounded functions of field operators at different times taken in suitable states, converge to the corresponding functions of the appropriate solutions of the classical field equation, and the quantum fluctuations are described by the equation obtained by linearizing the field equation around the classical solution. These properties were proved by Hepp [6] for suitably regular potentials and in finite time intervals. Using a general theory of existence of global solutions and a general scattering theory for the classical equation, we extend these results in two directions: (1) we consider more singular potentials, (2) more important, we prove that for dispersive classical solutions, the ?→0 limit is uniform in time in an appropriate representation of the field operators. As a consequence we obtain the convergence of suitable matrix elements of the wave operators and, if asymptotic completeness holds, of theS-matrix.     

Resonances,metastable states and exponential decay laws in perturbation theory

Resonances which appear as perturbed bound states are discussed in the framework of Balslev-Combes theory. The corresponding metastable states are constructed using the formal perturbation expansion to orderN–1 for the (nonexistent) perturbed bound states. They are shown to have exponential decay in time governed by the complex resonance energies, up to a background of order 2N in the perturbation parameter. The results apply in lowest orderN=1 to the perturbation of bound states embedded in the continuum and in arbitrary order to cases like the Stark effect.Dedicated to Res Jost and Arthur Wightman     

Effect of beta decay to bound states in ionized atoms on the fraction of delayed neutrons

The ionization of an atom leads to the appearance of an additional beta-decay channel to a bound state of an electron. It is shown that, for nuclei that are products of uranium fission and which are emitters of delayed neutrons, the fraction of delayed neutrons increases upon taking into account the additional beta-decay channel to bound states.     

Dispersion and symmetry of bound states in the shastry-sutherland model

Bound states made from two triplet excitations on the Shastry-Sutherland lattice are investigated. Based on the perturbative unitary transformation by flow equations quantitative properties like dispersions and qualitative properties like symmetries are determined. The high order results [up to (J2/J1)(14)] permit one to fix the parameters of SrCu2(BO3)(2) precisely: J1 = 6.16(10) meV, x J2/J1 = 0.603(3), J( perpendicular) = 1.3(2) meV. At the border of the magnetic Brillouin zone a general double degeneracy is derived. An unexpected instability in the triplet channel at x = 0.63 indicates a transition towards another phase. The possible nature of this phase is discussed.     

Approximate,non-relativistic scattering phase shifts,bound state energies,and wave function normalization factors for a screened Coulomb potential of the Hulthén type

Non-relativistic scattering phase shifts, bound state energies, and wave function normalization factors for a screened Coulomb potential of the Hulthén type are presented in the form of relatively simple analytic expressions. These formulae have been obtained by a suitable renormalization procedure applied to the quantities derived from an approximate Schrödinger equation which contains the exact Hulthén potential together with an approximate angular momentum term. When the screening exponent vanishes, our formulae reduce to the exact Coulomb expressions. The interrelation between our formulae and Pratt's ‘analytic perturbation theory for screened Coulomb potentials’ is discussed.     

Multiple scattering theory of the density of states in semiconductors

A method for calculating the electronic density of states of a semiconductor in the presence of impurity scattering is given. The approach is based on a low density multiple scattering expansion. The calculation treats the density of states of the conduction band, shifts of the band edge, and the profiles of the impurity bands. It is performed for a simple model, using a spherical well potential for the individual impurity centers, but could be extended to any scattering potential. The first impurity band forms when the potential is sufficiently strong that one center can bind an electron. The impurity bands are of finite width, have a flat upper edge, and an asymmetrically broadened tail on the low energy side.