Connected kernel methods in nuclear reactions: (III). Effective interactions

The recently derived connected kernel equation (CKE) for N-body scattering operators is applied to direct nuclear reactions. A spectral representation is derived for the kernel of the CKE in order to obtain manageable approximations. This allows the kernel to be split into orders corresponding to the propagation of different numbers of bound clusters. By formally solving one part of the kernel at a time, the CKE is written as a hierarchy of nested equations in increasingly many variables. The first equation of this hierarchy is a set of coupled channel Lippmann-Schwinger equations coupling together all two-cluster channels. These equations reduce to the usual coupled channel equations for inelastic scattering and to the coupled channel Born approximation for rearrangement reactions when weak coupling assumptions are made. The second equation of the hierarchy is a two-variable integral equation for the effective interactions appearing in the coupled channel equations. The driving terms and kernel of this integral equation are obtained from the third equation of the hierarchy which is a three-variable integral equation and so forth. The use of the spectral expansion results in a renormalized theory in the sense that the bound state and reaction problems are separated. This permits the inclusion of nuclear models in the theory in a straightforward manner. The hierarchy is applied to a particular example, that of nucleon-nucleus scattering. For this case the hierarchy is truncated at the level allowing no more than three clusters in the continuum. By suppressing exchange and keeping only one-particle transfer and single-nucléon knockout channels, a set of equations for the optical potentials and transfer operators is obtained. These equations provide a three-body treatment of the single scattering approximation to the optical potential. Iteration of the equations yields the usual single scattering approximation in first order including three-body off-shell effects. After suppression of Fermi motion and off-shell effects, the standard impulse approximation is recovered. Modifications of the method for other cases are discussed and other possible applications suggested.     

Time structure and atomic excltation spectra in heavy-ion collisions with nuclear contact

From a quantum mechanical model for quasielastic nuclear scattering, employing a pocket in the internuclear potential at close distances, a distribution of nuclear delay times is derived. The influence of this time structure on atomic excitation spectra is demonstrated using positron emission from supercritical collisions as an example. In a narrow regime of beam energies close to the Coulomb barrier, a considerable probability for collisions with long nuclear delay times is found, associated with a sharp peak in the positron spectrum which is due to enhanced spontaneous positron production. It is pointed out that quasielastic nuclear scattering alone cannot account for the absolute numbers of spontaneous positrons as extracted from recent experiments. A possible generalization of the theory to include inelastic nuclear processes is briefly discussed.     

General N-Body Theory of Nonrelativistic Quantum Scattering

 The two-Hilbert-space theory of scattering is reviewed with particular reference to its application to nonrelativistic multichannel quantum- mechanical scattering theory. In Part I the abstract assumptions of the theory are collected, transition operators (both on- and off-energy-shell) are defined, the dynamical equations that determine the off-shell transition operators are presented and their real-energy limits examined, and the convergence of sequences of approximate transition operators is established. A section on how to incorporate group symmetries into the formalism reports new work. The material of Part I is relevant to a variety of both classical and quantum scattering systems. In Part II attention is directed specifically to N-body nonrelativistic quantum scattering systems in which the particles interact via short-range pair potentials. A method of constructing approximate transition operators is presented and shown to satisfy all the abstract assumptions of Part I. The dynamical equations that determine the half-on-shell approximate transition operators are shown to be coupled one-dimensional integral equations that have compact kernels and unique solutions when considered as operators on a Hilbert space of H?lder continuous functions. Moreover, the on-shell parts of those approximate transition amplitudes are shown to converge to the exact on-shell amplitudes as the order of the approximation increases. Detailed formulas for the kernels of the integral equations are written down for systems of particles that are distinguishable and for systems containing identical particles. Finally, some important open problems are described. Received July 2, 1999; accepted in final form October 27, 1999     

Vibrational excitation by positron collisions with molecular gases: a study of O and NO targets

The scattering of slow positrons from and NO molecules is treated using exact static interactions and a model potential for correlation-polarisation forces. The quantum coupled equations for the elastic scattering are extended to vibrationally inelastic processes and the different excitation probabilities are evaluated. Comparison with existing experiments for the NO target indicates that the present calculations provide a realistic treatment of positron scattering below Ps formation and give computational estimates on the efficiency of such projectiles in producing vibrationally excited molecules in the ambient gas. Received: 23 April 1999 / Received in final form: 3 June 1999     

Vortex scattering

The geodesic approximation to vortex dynamics in the critically coupled abelian Higgs model is studied. The metric on vortex moduli space is shown to be Kähler and a scheme for its numerical computation described. The scheme is applied to the 2-vortex system and the geodesic scattering compared with previous simulations of the full field theory. The quantum scattering is also analysed.     

Complex paths and uniform approximations in a semi-classical description of direct reactions

The semi-classical (WKB) approximation in three dimensions is considered for scattering processes. Complex solutions of the classical equations of motion are included. They represent contributions to the quantal wave in classically forbidden regions, and in particular describe diffractive effects in the cases where the scattering potential varies appreciably within a wavelength. Special emphasis is given to inelastic and transfer processes, including multistep transitions within a coupled channel frame. Uniform approximation techniques are discussed and widely generalized. Especially, it is shown that when the semi-classical approximations are done consistently at every step of the calculation, there is no need for uniform treatments in the intermediate stages of the calculation, but only at the far end. This simplifies considerably the calculations. Applications to nuclear physics are considered by comparing quantum mechanical and semi-classical cross sections for the scattering of two heavy ions. Excellent agreement is obtained between the two calculations. The new insight brought by the complex semi-classical approximation is used in order to obtain phase rules for the angular distribution, and matching rules. Transition probabilities in their dependence on energy and angle are discussed. They turn out to depend dominantly on ΘE and not on both variables separately.     

Quantum theory of the Raman effect

A quantum mechanical analysis is made of higher order processes in Raman scattering. In particular the examples of coupled Stokes and Antistokes radiation and the generation of 1st and 2nd Stokes radiation are considered. All fields, electromagnetic and phonons, are quantized and the Schrödinger equation for the system is solved exactly. This completely quantum mechanical approach eliminates discrepancies which occur when linearization procedures such as the parametric approximation are employed. The theory applies to both stimulated and spontaneous Raman scattering.     

Effective potential theory of atom-solid surface elastic scattering

A new quantum mechanical theory of atom-solid surface elastic scattering is formulated, based on the idea of effective potentials. Two such quantities are defined in the present approach, one, the “optical potential”, regulating specular scattering, and the second, the “transition potential”, responsible for diffractive scattering. Rigorous equations are obtained for the above mentioned quantities, by using field-theoretic techniques, and an approximation scheme is worked out explicitly. The main computational aspect of the present theory requires the solution of an uncoupled integro-differential equation and the formulation can be easily extended to consider more complicated scattering processes.     

Spin-flip and domain wall magnetoresistance in quantum magnetic nanocontacts

The theory of nanosize point contacts made of ferromagnetic metals is developed. A general quantum scattering theory is applied to calculate magnetoresistance of a nanocontact with a domain wall located in the constriction. The exact solution of the electron motion in a potential of the linear domain wall is used as a zero-order approximation. Spin-flip and spin-conserving quantized conductances of the nanocontact are calculated by the perturbation theory by the difference between the model and the Cabrera-Falicov potentials of the domain wall. It is explicitly shown that spin-flip conductance imposes natural limitation on magnetoresistance of the point contact, which otherwise diverges in the regime of complete spin-rectified conductance through the contact.     

Selected topics of quantum computing for nuclear physics

Nuclear physics,whose underling theory is described by quantum gauge field coupled with matter,is fundamentally important and yet is formidably challenge for simulation with classical computers.Quantum computing provides a perhaps transformative approach for studying and understanding nuclear physics.With rapid scaling-up of quantum processors as well as advances on quantum algorithms,the digital quantum simulation approach for simulating quantum gauge fields and nuclear physics has gained lots of attention.In this review,we aim to summarize recent efforts on solving nuclear physics with quantum computers.We first discuss a formulation of nuclear physics in the language of quantum computing.In particular,we review how quantum gauge fields(both Abelian and non-Abelian)and their coupling to matter field can be mapped and studied on a quantum computer.We then introduce related quantum algorithms for solving static properties and real-time evolution for quantum systems,and show their applications for a broad range of problems in nuclear physics,including simulation of lattice gauge field,solving nucleon and nuclear structures,quantum advantage for simulating scattering in quantum field theory,non-equilibrium dynamics,and so on.Finally,a short outlook on future work is given.     

Radiational corrections and two-photon transfer in elastic electron-electron and electron-positron scattering

The radiational corrections to the differential cross section of elastic electron—electron and electron—positron scattering in the center-of-mass system are determined in the fourth order of perturbation theory by quantum-electrodynamic methods. The contribution of two-photon exchange is determined in the static approximation for one of the colliding particles, taking subsequent account of the deflection of the second particle in the center-of-mass system. The presence of an annihilation channel in the two-photon exchange of electron—positron scattering leads to more intense soft-photon emission than in electron—electron scattering. Data from modern electron—positron colliders permit experimental verification of quantum electrodynamics at high energies.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 77–83, August, 1993.     

Properties of nuclear and neutron matter in a relativistic Hartree-Fock theory

Relativistic Hartree-Fock (HF) equations are derived for an infinite system of mesons and baryons in the framework of a renormalizable relativistic quantum field theory. The derivation is based on a diagrammatic approach and Dyson's equation for the baryon propagator. The result is a set of coupled, nonlinear integral equations for the baryon self-energy with a self-consistency condition on the single-particle spectrum. The HF equations are solved for nuclear and neutron matter in the Walecka model, which contains neutral scalar and vector mesons. After renormalizing model parameters to reproduce nuclear matter saturation properties, HF results at low to moderate densities are similar to those in the mean-field (Hartree) approximation. Self-consistent exchange corrections to the Hartree equation of state become negligible at high densities. Rho- and pi-meson exchanges are incorporated using a renormalizable gauge-theory model. A chiral transformation of the lagrangian is used to replace the pseudoscalar πN coupling with a pseudovector coupling, for which one-pion exchange is a reasonable first approximation. This transformation maintains the model's renormalizability so that corrections may be evaluated. Pion exchange has a small effect on the HF results of the Walecka model and brings HF results in closer agreement with the mean-field theory. The diagrammatic techniques used here retain the mesonic degrees of freedom and are simple enough to be extended to more refined self-consistent approximations.     

Three-dimensional electrostatic waves in a nonuniform quantum electron-positron magnetoplasma

The dispersion properties of three-dimensional electrostatic waves in a nonuniform quantum electron-positron magnetoplasma are examined. A new dispersion relation is derived using the electron and positron densities response arising from the balance between the quantum Bohm and electrostatic forces, and from the electron and positron continuity and Poisson equations. In the local approximation regime, the dispersion relation admits both oscillatory and purely growing instabilities those depend on the quantum parameters as well as the density, velocity and magnetic field inhomogeneities.     

Nuclear time delay in resonant heavy ion collisions

From a quantum mechanical model for quasielastic nuclear scattering, involving a pocket in the internuclear potential, we derive a distribution of nuclear delay times. We show that coherent excitation of states in a rotational band of nuclear resonances leads to a lighthouse effect in the nuclear scattering cross section. Its influence on atomic excitations is shortly discussed for the case of positron creation in supercritical heavy ion collisions.     

One-loop approximation of Møller scattering in generalized Krein-space quantization

It has been shown that the negative-norm states necessarily appear in a covariant quantization of the free minimally coupled scalar field in de Sitter spacetime. In this processes ultraviolet and infrared divergences have been automatically eliminated. A natural renormalization of the one-loop interacting quantum field in Minkowski spacetime (λφ ⁴) has been achieved through the consideration of the negative-norm states defined in Krein space. It has been shown that the combination of quantum field theory in Krein space together with consideration of quantum metric fluctuation, results in quantum field theory without any divergences. Pursuing this approach, we express Wick’s theorem and calculate Møller scattering in the one-loop approximation in generalized Krein space. The mathematical consequence of this method is the disappearance of the ultraviolet divergence in the one-loop approximation.     

The dynamics of triple-well trapped Bose-Einstein condensates with atoms feeding and loss effects

In this paper, we consider the macroscopic quantum tunnelling and self-trapping phenomena of Bose-Einstein condensates （BECs） with three-body recombination losses and atoms feeding from thermal cloud in triple-well potential. Using the three-mode approximation, three coupled Gross-Pitaevskii equations （GPEs）, which describe the dynamics of the system, are obtained. The corresponding numerical results reveal some interesting characteristics of BECs for different scattering lengths. The self-trapping and quantum tunnelling both are found in zero-phase and ：r-phase modes. Furthermore, we observe the quantum beating phenomenon and the resonance character during the self-trapping and quantum tunnelling. It is also shown that the initial phase has a significant effect on the dynamics of the system.     

The Boltzmann equation from quantum field theory

We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff–Baym equations. Our method applies to a generic quantum field, coupled to a collection of background fields and sources, in a homogeneous and isotropic spacetime. The analysis is based on analytical solutions to the full Kadanoff–Baym equations, using the WKB approximation. This is in contrast to previous derivations of kinetic equations that rely on similar physical assumptions, but obtain approximate equations of motion from a gradient expansion in momentum space. We show that the system follows a generalized Boltzmann equation whenever the WKB approximation holds. The generalized Boltzmann equation, which includes off-shell transport, is valid far from equilibrium and in a time dependent background, such as the expanding universe.     

Differential cross sections for chemically reactive systems

A quantum mechanical theory is developed for the differential and total elastic and reactive scattering cross sections for an electronically adiabatic bimolecular exchange reaction, with the restriction that the three atoms are constrained to move on a straight line, but with the whole system free to rotate in three dimensions. The introduction of a set of natural collision coordinates, together with a vibrationally adiabatic approximation, is used to reduce the scattering problem to the solution of one-dimensional Schrödinger equations. Semi-classical expressions for the elastic and reactive phase shifts are derived. The partial wave summations that occur in the theory are evaluated by semi-classical techniques and elastic and reactive differential cross sections are calculated for three different kinds of potential surface. A feature of the calculations is the appearance of a new kind of rainbow, which is named a ‘cubic’ rainbow since it arises when the deflection function varies cubically with impact parameter. The classical and semi-classical theory of cubic rainbows is developed.