On the Asymptotic Dynamics of a Quantum System Composed by Heavy and Light Particles

We consider a non-relativistic quantum system consisting of K heavy and N light particles in dimension three, where each heavy particle interacts with the light ones via a two-body potential α V. No interaction is assumed among particles of the same kind. Choosing an initial state in a product form and assuming α sufficiently small we characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. In the case K = 1 the result is extended to arbitrary α. The proof relies on a perturbative analysis and exploits a generalized version of the standard dispersive estimates for the Schrödinger group. Exploiting the asymptotic formula, an application to the problem of the decoherence effect produced on a heavy particle by the interaction with the light ones is also outlined.     

A multilayer ΔE-ER telescope for breakup reactions at energies around the Coulomb barrier

The breakup reactions of weakly-bound nuclei at energies around the Coulomb barrier and the corresponding coupling effect on the other reaction channels are hot topics nowadays. To overcome the difficulty in identifying both heavier and lighter fragments simultaneously, a new kind of ionization-chamber based detector telescope has been designed and manufactured. It consists of a PCB ionization chamber and three different thickness silicon detectors installed inside the chamber, which form a multilayer ΔE-E_R telescope. The working conditions were surveyed by using an α source. An in-beam test experiment shows that the detector has good particle identification for heavy particles like ¹⁷F and ¹⁶O as well as light particles like protons and alpha particles. The measured quasi-elastic scattering angular distribution and the related discussions for ¹⁷F+²⁰⁸Pb are presented.     

Amplification of the scattering cross section due to non-trivial topology of the spacetime

In [1, 2] it was demonstrated that the total cross section of the scattering of two light particles (zero modes of the Kaluza-Klein tower) in the six-dimensional λφ ⁴ model differs significantly from the cross section of the same process in the conventional λφ ⁴ theory in four space-time dimensions even for the energies below the threshold of the first heavy particle. In the present article the analytical structure of the cross section in the same model with torus compactification for arbitrary radii of the two-dimensional torus is studied. Also, further amplification of the total cross section due to interaction of the scalar field with constant background Abelian gauge potential in the space of extra dimensions is shown.     

Anomalous resistivity and the origin of heavy mass in the two-band Hubbard model with one narrow band

We search for marginal Fermi-liquid behavior [1] in the two-band Hubbard model with one narrow band. We consider the limit of low electron densities in the bands and strong intraband and interband Hubbard interactions. We analyze the influence of electron polaron effect [2] and other mechanisms of mass enhancement (related to momentum dependence of the self-energies) on the effective mass and scattering times of light and heavy components in the clean case (electron-electron scattering and no impurities). We find the tendency towards phase separation (towards negative partial compressibility of heavy particles) in the 3D case for a large mismatch between the densities of heavy and light bands in the strong-coupling limit. We also observe that for low temperatures and equal densities, the homogeneous state resistivity R(T) ∼ T ₂ behaves in a Fermi-liquid fashion in both 3D and 2D cases. For temperatures higher than the effective bandwidth for heavy electrons T > W _* ^h , the coherent behavior of the heavy component is totally destroyed. The heavy particles move diffusively in the surrounding of light particles. At the same time, the light particles scatter on the heavy ones as if on immobile (static) impurities. In this regime, the heavy component is marginal, while the light one is not. The resistivity saturates for T > W _* ^h in the 3D case. In 2D, the resistivity has a maximum and a localization tail due to weak-localization corrections of the Altshuler-Aronov type [3]. Such behavior of resistivity could be relevant for some uranium-based heavy-fermion compounds like UNi₂Al₃ in 3D and for some other mixed-valence compounds possibly including layered manganites in 2D. We also briefly consider the superconductive (SC) instability in the model. The leading instability is towards the p-wave pairing and is governed by the enhanced Kohn-Luttinger [4] mechanism of SC at low electron density. The critical temperature corresponds to the pairing of heavy electrons via polarization of the light ones in 2D.     

Adiabatic approximation on the impact-parameter model

In this paper we study the impact-parameter model for the scattering of a light particle by two heavy ones in the case when the coupling constants of the potentials acting on the light particle due to the presence of the two heavy ones are the same. We study the asymptotic behavior of the transition probability when the relative velocity of the heavy particles goes to zero. We show that the probability of a transition can be arbitrarily close to the one of no transition.     

Scattering off of an instanton

We consider the scattering of a classical colored particle off an instanton. That is, we investigate Wong's equations (or equivalently, the Kaluza-Klein geodesic equations) for a colorSU(2) particle under the influence of a Euclidean instanton. We solve the equations in the limit in which the instanton becomes singular. Our main result is that particles with head-on trajectories scatter off the instanton with a scattering angle of π/3. This angle is independent of the magnitude of the color charge and velocity of the particle as long as both are nonzero. The plane in which the scattering takes place is determined by the particle's initial position and color charge. We also solve for the geodesics for the corresponding (singular) Kaluza-Klein metric onS ⁷.     

Light scattering by Gaussian random ellipsoid particles: First results with discrete-dipole approximation

We introduce the stochastic geometry of a Gaussian random ellipsoid (GE) and, with the discrete-dipole approximation, carry out preliminary computations for light scattering by wavelength-scale GE particles. In the GE geometry, we describe the base ellipsoid by the three semiaxes a?b?c. The axial ratios b:a and c:a appear as two shape parameters additional to those of the Gaussian random sphere geometry (GS). We compare the scattering characteristics of GE particles to those of ellipsoids. Introducing irregularities on ellipsoids smoothens the angular scattering characteristics, in a way analogous to the smoothening of spherical particle characteristics in the case of GS particles.     

Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas

We study a system consisting of a heavy quantum particle, called the tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density ${\to \infty}$ ). Our estimates allow us to interchange the thermodynamic with the mean-field limit.     

Spin flip due to the spin–orbit interaction of colliding slow charged particles

The scattering amplitudes of point charged particles is calculated analytically taking into account the spin–orbit interaction. We have considered two cases typical of a hydrogen-like plasma: scattering of an electron by a heavy ion and scattering of an electron by a free electron. The results have been obtained taking into account the ranges of low collision energies smaller than α² m _e c ², where α is the fine structure constant.     

Heavy SUSY Higgs bosons at e + e − linear colliders

The production mechanisms and decay modes of the heavy neutral and charged Higgs bosons in the Minimal Supersymmetric Standard Model are investigated at future e ⁺ e ^? colliders in the TeV energy regime. We generate supersymmetric particle spectra by requiring the MSSM Higgs potential to produce correct radiative electroweak symmetry breaking, and we assume a common scalar mass m₀, gaugino mass m_1/2 and trilinear coupling A, as well as gauge and Yukawa coupling unification at the Grand Unification scale. Particular emphasis is put on the low tan β solution in this scenario where decays of the Higgs bosons to Standard Model particles compete with decays to supersymmetric charginos/neutralinos as well as sfermions. In the high tan β case, the supersymmetric spectrum is either too heavy or the supersymmetric decay modes are suppressed, since the Higgs bosons decay almost exclusively into b and τ pairs. The main production mechanisms for the heavy Higgs particles are the associated AH production and H ⁺H^? pair production with cross sections of the order of a few fb.     

The Thermodynamic Pressure of a Dilute Fermi Gas

We consider a gas of fermions with non-zero spin at temperature T and chemical potential μ. We show that if the range of the interparticle interaction is small compared to the mean particle distance, the thermodynamic pressure differs to leading order from the corresponding expression for non-interacting particles by a term proportional to the scattering length of the interparticle interaction. This is true for any repulsive interaction, including hard cores. The result is uniform in the temperature as long as T is of the same order as the Fermi temperature, or smaller.     

Light scattering in a layer of correlatively arranged optically soft particles

The light scattering by an ensemble of monodisperse spatially correlated optically soft spherical particles is studied in the interference approximation. A model of the interaction of particles is proposed in which the spatial correlation between particles is determined by a radius R _c exceeding the particle radius R _p. The radial distribution function is calculated in the Percus-Yevick approximation for hard spheres of the radius R _c. To simulate the radiation scattering from an individual particle of the radius R _p, the Mie equations are used. It is shown that, in a medium of correlated small nonabsorbing particles of the radius R _c > R _p, an abnormal wavelength dependence of the refractive index is possible at a low volume concentration of particles. The results obtained explain some experimentally observed features of the scattering in sodium borosilicate glasses with a small concentration of scattering centers.     

Multichannel scattering of a particle in a quantum wire of cylindrical symmetry

The Schrödinger equation for a scattering particle in a quantum wire is considered. We discuss two geometrical forms of cross-section of the wire: the rectangular section and the cylindrical one. It is shown that scattering of the particle on an arbitrary potential V = V (x, y, z,), given in the wire, can be considered as a multichannel scattering, where the index of the channel coincides with the index which determines energy levels of the confined transverse motion of the particle. A method for determination of the amplitudes of transmission T _i and reflection R _i in the case of multichannel scattering is proposed. The case of two-channel scattering is considered in detail and a method for determination of the scattering amplitudes T ₁, T ₂ and R ₁, R ₂ is proposed.     

Class of model problems in three-body quantum mechanics that admit exact solutions

An approach to solving scattering problems in three-body systems for cases where the mass of one of the particles is extremely small in relation to the masses of the other two particles and where the pair potentials of interaction between the particles involved are separable is developed. Exact analytic solutions to such model problems are found for the scattering of a light particle on two fixed centers and on two interacting heavy particles. It is shown that new resonances and a dynamical resonance enhancement may appear in a three-body system.     

Quantum-coherent transport of a heavy particle in a fermionic bath

In this review, a detailed discussion of the behaviour of a heavy particle interacting with a Fermi sea is given. Particular emphasis is put on the issue of how strong correlations influence coherence and transport of the particle. First, we investigate the question of whether the heavy particle is a well defined quasiparticle at low temperatures. While in one dimension ( D = 1) and at a van Hove singularity in D = 2 the coherence of the particle is destroyed, the quasiparticle weight is finite in higher dimensions. The most important transport quantity is the diffusion constant or mobility of the heavy particle. We are able to describe both the well known high-temperature properties and the cross-over to the lowest temperatures in a unified approximation scheme based on a self-consistent evaluation of an effective action. Two strong-correlation effects of independent origin are discussed. The first arises if the scattering of the fermions from the heavy particle is nearly resonant, that is, if one of the scattering phase shifts δ is close to π/2. In this regime an anomalous exponent is observed in the temperature dependence of the mobility μ(T). In D = 3, for instance, the mobility is proportional to T^-3/2 rather than to T^-2. The second effect is a giant mass renormalization in the case of a large particle. In this situation, the low-temperature effective mass M* increases up to an exponentially large value, M* exp[c(r/λF)³], where r is the effective radius of the particle, λF the Fermi wavelength and c a non-universal constant of order one.     

Fission dynamics with the 4π detector 8πLP

A 4π light charged particle spectrometer, named 8πLP, is in operation at the Laboratori Nazionali di Legnaro (Italy) for the study of the reaction mechanisms produced in low-energy heavy-ion reactions. The spectrometer has recently been used in a study of fission dynamics that involves the detection of light charged particles in the fission and evaporation residue channel in a system of intermediate fissility, as well as in a study of multinucleon transfer to heavy target. Data on the system 240 MeV ³²S + ¹⁰⁰Mo are presented. Dynamical effects extracted as a consequence of the comparison of the data to the statistical model calculations are discussed.     

Critical scattering and pionic instabilities in heavy ion collisions

We investigate the effect of collective instabilities in heavy ion collisions. The focus is on critical scattering phenomena associated with pionic instabilities. The decay rate Γ of excited many-body systems is calculated in RPA. Γ is shown to give the rate of spontaneous “phonon” pair production. We express Γ as a sum of a collective, Γ_col, and a scattering, Γ_scat, rate. Γ_col is the pair production rate of phonons in unstable states. In the case of pionic instabilities, Γ_col is the condensation rate of π⁺π^? and π⁰π⁰ pairs into unstable states. Γ_scat is the pair production rate of phonons in the particle-hole excitation region and gives the two-body scattering rate in the medium. An effective (density-dependent) two-body cross section is obtained. The difference between critical scattering of external particles in a system near equilibrium and that of constituents of systems far from equilibrium is investigated. A model calculation suggests the existence of pionic instabilities in heavy ion collisions. Growth rates of unstable modes and the effective cross sections displaying critical scattering are calculated. Finally, we estimate Γ_scat and Γ_col.     

光学与粒径耦合多分散性的动态光散射研究

研究了满足Rayleigh-Gans-Debye(RGD)近似条件的球形稀溶液的光学和粒径多分散性耦合的动态光散射技术检测问题.在分析中采用了球壳L和球核R-L都连续变化且壳层变化满足L=αR (其中α<1和R是壳球半径)的壳-核硬球模型.得出了在溶剂折射率n_m和壳层折射率n_s匹配时,即n_m=n_s,平均散射强度I(q)和等效扩散系数D_e(q)与散射矢q间的关系.给出了用以检测窄分散系统小多分散性 关键词：     

Faddeev-Born-Oppenheimer equations for molecular three-body systems: Adiabatic calculation of 9Be

The low-lying states of ⁹Be are calculated in the α-particle cluster model. The calculation is performed using a rotationally invariant molecular formulation of the three-body problem based on the Faddeev equations, which are solved for the α + n + α system in the adiabatic limit with the α-α interaction turned off. The resulting two-centre wave function is used to formulate an ansatz for the solution of the full hamiltonian of the system where all three particles interact. Unlike the traditional molecular approach, the ansatz we propose allows for the coupling between the movement of the light particle and the rotational motion of the heavy particles. This leads to a set of coupled ordinary differential equations for the three-body wave function that has good total angular momentum and parity. Although only one Born-Oppenheimer molecular energy curve is considered, all adiabatic corrections due to Coriolis coupling effects, mass polarization and derivatives of the two-centre wave function with respect to the separation distance between the α-particles are taken into account. Comparison with exact Faddeev results is presented for the ground-state energies of ⁹Be in a model problem where the α-α interaction is turned off. The validity of the molecular approach for small mass ratios between the heavy particle and the light particle is studied in a very general framework.     

Relativistic non-Hamiltonian mechanics

Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u_μu^μ + c² = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton’s principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton’s principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton’s principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton’s principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.