Electromagnetically induced alpha-emission in an analytically solvable model

Alpha emission induced byγ-absorption or inelastic electron scattering on²⁰Ne is examined in an analytically solvable model. The exact results are compared with an approximation recently proposed by Fliessbach. The model is used as a testing case to decide which definition of alpha-spectroscopic amplitudes is appropriate. A method for handling center of mass effects is presented.     

Multi-channel scattering problems: an analytically solvable model

We have proposed a general method for finding an exact analytical solution for the multi-channel scattering problem in the presence of a delta function coupling. Our solution is quite general and is valid for any set of potentials, if the uncoupled diabatic potential has an exact solution. We have also discussed a few examples, where our method can easily be applied.     

Multi-channel curve crossing problems: analytically solvable model

We have proposed a general method for finding the exact analytical solution for the multi-channel curve crossing problem in the presence of delta function couplings. We have analysed the case where a potential energy curve couples to a continuum (in energy) of the potential energy curves.     

Glass-glass transition and new dynamical singularity points in an analytically solvable p-spin glasslike model

We introduce and analytically study a generalized p-spin glasslike model that captures some of the main features of attractive glasses, recently found by mode coupling investigations, such as a glass-glass transition line and dynamical singularity points characterized by a logarithmic time dependence of the relaxation. The model also displays features not predicted by the mode coupling scenario that could further describe the attractive glasses behavior, such as aging effects with new dynamical singularity points ruled by logarithmic laws or the presence of a glass spinodal line.     

Proton radioactivity with analytically solvable potential

The phenomenon of proton emission is treated as a process of asymmetric fission through a one-dimensional potential barrier developed due to combined effects of the Coulomb potential, centrifugal potential and various renormalization processes. The barrier is simulated to an asymmetric, smooth and analytically solvable potential with adjustable depth, shape and range. The half-lives of proton emitters in the mass range A = 105–171 have been calculated using exact expression for the transmission coefficients. Good agreement with the experimental data is obtained by the adjustment of just one parameter in all the cases.      

Curve crossing problem with Gaussian type coupling: analytically solvable model

We give a general method for finding an exact analytical solution for the two state curve crossing problem. The solution requires the knowledge of the Green's function for the motion on the uncoupled potentials. We use the method to find the solution of the problem in the case of parabolic potentials coupled by Gaussian interaction. Our method is applied to this model system to calculate the effect of curve crossing on the electronic absorption spectrum and the resonance Raman excitation profile.     

New analytically solvable models of relativistic point interactions

Two new analytically solvable models of relativistic point interactions in one dimension (being natural extensions of the nonrelativistic , resp. , interactions) are considered. Their spectral properties in the case of finitely many point interactions as well as in the periodic case are fully analyzed. Moreover, we explicitly determine the spectrum in the case of independent, identically distributed random coupling constants and derive the analog of the Saxon and Hutner conjecture concerning gaps in the energy spectrum of such systems.     

An analytically solvable model of confined electrons in a magnetic field and its relation to Landau diamagnetism

Here we present analytic results for the Slater sum and the magnetic moment for arbitrary magnetic field strengths for an assembly of harmonically confined, but initially free, electrons. The relevance of the results to the generalized Landau diamagnetism of such confined electrons is emphasized.     

Efimov effect in Dirac semi-metals

The Efimov effect is defined as a quantum state with discrete scaling symmetry and a universal scaling factor. It has attracted considerable interests from nuclear to atomic physics communities. In a Dirac semi-metal, when an electron interacts with a static impurity through a Coulombic interaction, the same kinetic scaling and the interaction energy results in the Efimov effect. However, even when the Fermi energy lies exactly at the Dirac point, the vacuum polarization of the electron-hole pair fluctuation can still screen the Coulombic interaction, which leads to deviations from the scaling symmetry and eventually breaks down of the Efimov effect. This energy distortion of the Efimov states due to vacuum polarization is a relativistic electron analogy of the Lamb shift for the hydrogen atom. Motivated by the recent experimental observations in two- and three-dimensional Dirac semi-metals, we herein investigate this many-body correction to the Efimov effect and the conditions that allow some of the Efimov-like quasi-bound states to be observed in these condensed matter experiments.     

Heat flow in an exactly solvable model

A chain of one-dimensional oscillators is considered. They are mechanically uncoupled and interact via a stochastic process which redistributes the energy between nearest neighbors. The total energy is kept constant except for the interactions of the extremal oscillators with reservoirs at different temperatures. The stationary measures are obtained when the chain is finite; the thermodynamic limit is then considered, approach to the Gibbs distribution is proven, and a linear temperature profile is obtained.     

Correlation functions in an exactly solvable tefface-ledge-kink model

We solve exactly a terrace-ledge-kink (TLK) model describing a vicinal section of a crystal surface at a microscopic level, with either repulsive or attractive interactions between the ledges. As expected there is a faceting, or reconstructive, phase transition, driven either by temperature or by the chemical potential, that controls the mean slope of the surface. In the rough phase we carry out a thorough investigation of microscopic thermal fluctuations of the interface. This is done by combining Bethe ansatz and Conformal Field Theory methods in order to calculate appropriately defined correlators.     

Efimov effect in 2-neutron halo nuclei

This paper presents an overview of our theoretical investigations in search of Efimov states in light 2-neutron halo nuclei. The calculations have been carried out within a three-body formalism, assuming a compact core and two valence neutrons forming the halo. The calculations provide strong evidence for the occurrence of at least two Efimov states in ²⁰C nucleus. These excited states move into the continuum as the two-body (core-neutron) binding energy is increased and show up as asymmetric resonances in the elastic scattering cross-section of the n-¹⁹C system. The Fano mechanism is invoked to explain the asymmetry. The calculations have been extended to ³⁸Mg, ³²Ne and a hypothetical case of a very heavy core (A = 100) with two valence neutrons. In all these cases the Efimov states show up as resonances as the two-body energy is increased. However, in sharp contrast, the Efimov states, for a system of three equal masses, show up as virtual states beyond a certain value of the two-body interaction.     

The Efimov effect in a four-body system

It is shown, using a Born-Oppenheimer model, that the four-body Efimov effect may occur in a system consisting of three identical heavy particles and one light particle, if the light-heavy interaction leads to a zeroenergy two-heavy-one-light bound state.     

Efimov effect in nuclear three-body resonance decays

We investigate the effects of the nearly fulfilled Efimov conditions on the properties of three-body resonances. Using the hyper-spheric adiabatic expansion method we compute energy distributions of fragments in a three-body decay of a nuclear resonance. As a realistic example we investigate the 1- state in the halo nucleus 11Li within a three-body model 9Li + n +n model. Characteristic features appear as sharp peaks in the energy distributions. Their origin, as in the Efimov effect, is in the large two-body s-wave scattering lengths between the pairs of fragments.     

The reduced α-amplitude in an exactly solvable model

In recent work by Fliessbach the removal of an α-particle from a nucleus under the influence of a perturbation was considered. Using certain approximations the many-body transition matrix element was reduced to a one-body matrix element. This one-body matrix element showed that the appropriate bound α-amplitude in the initial nucleus (reduced amplitude) depends on the energy transferred to the removed α-particle. The present paper deals with an analytic model in which the one-body transition matrix element as given in that work can be derived exactly from the original microscopic matrix element.     

A model search for Efimov states

A search for Efimov states is carried out in terms of a one-dimensional model three-body problem. A numerically exact solution is obtained that allows scanning through the resonance condition. No evidence is found for the existence of an infinite number of such bound three-body states. It is deduced from one-dimensional results that such an infinity of bound states should also not arise in a complete three-dimensional calculation.