Electron-phonon interaction in a local region

It has been shown that the formation of a bound state is possible in the region with a local electron-phonon interaction. Carbon nanostructures are considered as an example of the material in which this effect can be implemented. Based on the developed concepts, it has become possible to explain the anomalously high field emission in such structures not only phenomenologically but also at the microscopic level.     

The effective interaction for unbound nucleons and the optical potential

The effective interaction for an unbound nucleon in a complex nucleus is studied with particular emphasis upon the relationship of the unbound state interaction with the interaction for bound states. A successful unified treatment of unbound and bound states is given, and the unbound state effective interaction is related to the standard “optical model”. The attractive force for an unbound nucleon is shown to be of an exchange type and is best represented by a non-local, energy-independent potential which can be calculated, at least for not too high incident nucleon energy, from the attractive interaction between bound nucleons in a nucleus. We relate the unbound state potential to the bound state effective force as calculated by Negele using Hartree-Fock theory.

A non-local potential used by Elton, Webb, and Barrett in a successful analysis of electron scattering is shown, with minor modification, to work remarkably well in an analysis of elastic scattering of protons. Excellent agreement with experiment is obtained for the differential cross section and the polarization of protons with an incident energy up to 60 MeV scattered from ⁴⁰Ca, ⁵⁸Ni, ¹²⁰Sn and ²⁰⁸Pb. The real potential parameters are shown to be independent of the incident energy and physically reasonable; the imaginary potential parameters agree with expectations from Fermi gas and collective models. Bound state energy levels are also calculated with no readjustment of the real potential parameters in order to check the consistency of the interaction with the bound states, and the results are in good agreement with Negele.

The interaction of Skyrme as modified by Vautherin and Brink is also used in an analysis of elastic proton scattering. Good results are obtained for the differential cross section and the polarization for 20 MeV protons scattered from ⁵⁸Ni. At higher incident proton energy, and for larger nuclei, the results are poorer.     

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.     

Effects of interface bound states on the shot noise in normal metal–low-dimensional Rashba semiconductor tunnel junctions with induced s-wave pairing potential

We consider the effects of interface bound states on the electrical shot noise in tunnel junctions formed between normal metals and one-dimensional(1 D) or two-dimensional(2 D) Rashba semiconductors with proximity-induced s-wave pairing potential. We investigate how the shot noise properties vary as the interface bound state is evolved from a non-zero energy bound state to a zero-energy bound state. We show that in both 1 D and 2 D tunnel junctions, the ratio of the noise power to the charge current in the vicinity of zero bias voltage may be enhanced significantly due to the induction of the midgap interface bound state. But as the interface bound state evolves from a non-zero energy bound state to a zero-energy bound state, this ratio tends to vanish completely at zero bias voltage in 1 D tunnel junctions, while in 2 D tunnel junctions it decreases smoothly to the usual classical Schottky value for the normal state. Some other important aspects of the shot noise properties in such tunnel junctions are also clarified.     

Effect of so-phonon on the ground state energy of the surface impurity atom

We calculate by means of variational principle the ground state energy of the surface optical polaron bound to an impurity atom centered on the surface, and find that such surface bound polaron may be more stable than expected.     

The threshold anomaly and the effective interaction for nuclear nonelastic scattering

Previously, a dispersion relation has been used to elucidate the energy dependence of one-channel optical potentials, especially the “threshold anomaly” that is observed at low energies. We show that this dispersion relation is also applicable to the elements of the potential matrix which is needed for a coupled-channels treatment. Consequently, the off-diagonal couplings which produce nonelastic transitions may also exhibit such anomalies. We discuss how the energy dependences of the various matrix elements may be related, and provide some arguments that the potential in an excited state is similar to that in the ground state evaluated at a bombarding energy reduced by the excitation energy. We also examine the collective, or deformed potential, model to see whether the way it is commonly applied is consistent with the dispersion relation.     

The production of narrow Σ-hypernuclear states

It has been suggested that some of the observed narrow Σ hypernuclear states may be “bound states in the continuum” of the Σ interacting with the host nucleus formed when that interaction is strongly absorptive. It is shown that the S matrix for such a process vanishes at the complex energy of such a bound state. Some general properties of the S matrix in the presence of absorption are derived.     

Mixing of scalar meson and baryon-baryon interaction

At quark level,we study the effect of ideal mixing of singlet σ 0 and octet σ 8 scalar mesons on baryon-baryon interaction in the chiral SU(3) quark model.We solve the resonating group method equation for scattering process and bound state.The results show that the binding energy of deuteron and nucleonnucleon and hyperon-nucleon scattering data can be reasonably described for ideal mixing.Taking the same parameters we used in the scattering calculation,we further investigate the possible dibaryons and find the binding energy of (ΩΩ) ST =00 and (Ξ *Ω) ST =0 1 2 can be reduced a lot for ideal mixing.     

Physisorption of positronium on quartz surfaces

Whether positronium (Ps) can be physisorbed on a material surface is of great fundamental interest, since it can lead to new insight regarding quantum sticking and is a necessary first step to try to obtain a Ps2 molecule on a material host. Experiments in the past have produced evidence for physisorbed Ps on a quartz surface, but firm theoretical support for such a conclusion was lacking. We present a first-principles density-functional calculation of the key parameters determining the interaction potential between Ps and an alpha-quartz surface. We show that there is indeed a bound state with an energy of 0.14 eV, a value which agrees very well with the experimental estimate of approximately 0.15 eV. Further, a brief energy analysis invoking the Langmuir-Hinshelwood mechanism for the reaction of physisorbed atoms shows that the formation and desorption of a Ps2 molecule in that picture is consistent with the above results.     

非对称量子点中弱耦合束缚极化子的性质

采用线性组合算符和幺正变换方法研究了非对称量子点中弱耦合束缚极化子的性质。导出了非对称量子点中弱耦合束缚极化子的振动频率和基态能量随量子点的横向和纵向有效受限长度,库仑束缚势和电子-声子耦合强度的变化关系。通过数值计算,结果表明:非对称量子点中弱耦合束缚极化子的振动频率和基态能量随量子点的横向和纵向有效受限长度的减小而迅速增大。     

Model studies of the interaction of h atoms with bcc iron

Ab initio/effective core potential cluster studies are reported for the interaction of H atoms with bcc iron. The calculations use a one-electron ECP based on the 4s¹3d⁷ state of the Fe atom. Two-fold and four-fold sites on the (100) surface as well as octahedral, tetrahedral, and trigonal interior sites were studied. Four-fold surface sites are found to be bound by ~1.5 eV with the H atom ~ 0.5a₀ above the surface. Penetration of the surface at a four-fold site involves movement toward a second layer atom and is expected to be unfavorable. Two-fold surface sites have small binding energies ～ 0.25 eV. Penetration of the surface at this site involves movement toward a tetrahedral interior site and is downhill in energy. Tetrahedral interior sites are found to be bound by ～1.3 eV and are a minimum on the potential energy surface. Octahedral sites are a maximum on the potential energy surface and are estimated to be ～ 0.2 eV higher (including lattice relaxation effects). Trigonal sites are found to be a saddle point connecting adjacent tetrahedral sites and this pathway leads to an estimated barrier to diffusion of ～ 0.1 eV (including lattice relaxation effects). The volume expansion for a H atom in a tetrahedral site is calculated to be 21%.     

Screening of the electron-hole interaction in quantum well structures

Recent optical non-linearities in GaAs/Ga_1?xAl_xAs quantum well structures have been attributed to the screening of the electron-hole interaction in such structures by the free carriers created. We here present the results of a variational calculation of the ground state energy of an electron-hole pair confined to move in two dimensions when screening of the Coulomb interaction between the electron-hole pair by the free carriers present is taken into account by using the screened potential obtained by Stern and Howard for hydrogenic impurities in semiconducting inversion layers. It is found that the binding energy of the 2D exciton decreases less rapidly with the screening parameter than is the case for a 3D exciton and that the 2D exciton remains bound even for large values of the screening parameter. This is in contrast to the case in bulk semiconductors where the electron-hole pair no longer bind into an exciton when the screening length of the free carriers becomes less than the Bohr radius of the exciton.     

Exchange dipole interaction in a multilevel cooperative system of atoms

Atomic systems with three or more equidistant energy levels, in which a cascade process is possible, are considered. Hamiltonians obtained for such systems are analogous to Heisenberg Hamiltonians, but for systems with integral spins. For Dicke states in multilevel systems, quantum-mechanical mean values of the energy of a cooperative system are calculated taking into account weak interactions between atoms. The type of emission preceding superradiant avalanche emission of the system is analyzed. It can be expected that a coherent state may be formed, in which collective processes affect one another not only via population of the intermediate common layer, but also via phasing of pure quantum states. The single superfluorescence pulse that can be formed in this case is not a simple superposition of two or more pulses of sequential superradiant transitions in two-level systems.     

An upper bound for the ground-state energy of an antiferromagnetic chain with next-nearest-neighbor interaction

A trial function for the ground state of the antiferromagnetic linear chain leads to an equation for an upper bound of the ground-state energy per spin. This equation is solved exactly.     

Focussed inelastic resonances in particle scattering from surfaces

Particles, such as atoms or electrons, inelastically scattered from a crystal surface in resonance with a bound state are predicted to focus around a discrete set of final angles with a defined energy for each angle. The final angle and energy of such focussed inelastic resonances (FIR) are shown to be independent of the initial state. A calculation of the FIR amplitude indicates favorable conditions for the observation of the so far elusive bound states of He on low-index metal surfaces and of image states on stepped metal surfaces.     

Polarization's interaction and bound states of like charged particles in plasma

It has been shown that, as a result of the plasma polarization, there appears a minimum of potential energy of interaction of small like charged particles. With a use of the quasi-classical approximation, an existence condition of the bound state of two like unit charges has been obtained. An opportunity of electron pairs formation caused by the plasma polarization in high temperature superconductors is evaluated.     

The effective interaction in a nuclear model

The effective interactionU belonging to a given subspace ofn unperturbed model functions can be related to the free nucleon-nucleon interaction by means of an exact integral equation. The conditions for a Born-v. Neumann expansion ofU and for an approximation by a slowly energy dependent interaction with adjustable parameters are investigated. It appears that effective interactions which have been used successfully in shell model calculations of bound state properties do not necessarily describe the actual dynamics of a nucleus.     

温度对抛物量子点中弱耦合束缚磁极化子的影响

采用线性组合算符和幺正变换方法研究温度对量子点中弱耦合束缚磁极化子性质的影响,导出了弱耦合束缚磁极化子的振动频率、基态能量和声子平均数随温度的变化关系。取CdTe晶体为例进行数值计算,结果表明:弱耦合束缚磁极化子的振动频率、基态能量和声子平均数随温度的升高而增大,基态能量随量子点的受限强度的增强而迅速增大。     

Exact and approximate results for the Anderson impurity model

This paper provides exact and rigorous upper and lower bounds to the ground state energy of the Single Impurity Anderson Model in the limit of infiniteU. The upper bound approximates the ground state energy very well and the corresponding state may be used as a starting point for further investigations. The energy spectrum of the Single Impurity Anderson Model is calculated exactly for a special non-trivial model density of states describing the bare band electrons. All approaches introduced here are compared to this exact result and to other ground state energy calculations.     

Black holes as collapsed polymers

We propose that a large Schwarzschild black hole (BH) is a bound state of highly excited, long, closed strings at the Hagedorn temperature. According to our proposal, the interior of the BH consists, on average, of a uniform distribution of matter with low curvature and large quantum fluctuations about the average. This proposal represents a dramatic departure from any conventional state of matter and from the longstanding expectation that the interior of a BH should look like empty space except for a very small, dense core (the singularity). Standard effective field theory in terms of the metric and other quantum fields is incapable of describing such a state in a meaningful way. However, in polymer physics, such states can be described by a mean field theory in terms of the polymer concentration. We therefore propose that the interior of the BH be described in terms of an effective free‐energy density which is a function of the string concentration or entropy density; this density being a highly non‐perturbative quantity in terms of the metric and other quantum fields. For a macroscopic BH, our proposed free‐energy density contains only linear and quadratic terms, in analogy with that of the theory of collapsed polymers. We calculate the coefficient of the linear term under the accepted assumption that the dominant interaction of the strings at large distances is the gravitational interaction and the coefficient of the quadratic term by relying on explicit string calculations to determine the rate of interaction in terms of the string coupling. Using the effective free energy, we find that the size of the bound state is determined dynamically by the string attractive interactions and derive scaling relations for the entropy, energy and size of the bound state. We show that these agree with the scaling relations of the BH; in particular, with the area law for the BH entropy. The fact that the entropy is not extensive is a result of having strong correlations in the interior state, and the specific form of the entropy‐area law originates from the inverse scaling of the effective temperature with the bound‐state radius. We also find that the energy density of the bound state is equal to its pressure.