Planned research (Dr. S. Rakityansky)

Ongoing and planned future research

Currently I am working on the topics described on the other pages of this CV
(see Accomplished Research and Scientific Competitiveness) as well as on few new projects. This includes the following:

Semiconductor nanostructures

Thanks to advances in the epitaxial growth technology, it has become possible in the last two decades to make crystal structures called superlattices, nanostructures, nanodevices, mesoscopic devices, or semiconductor heterostructures. These artificially grown crystals are composed of alternating layers of different semiconductor materials with nanometer thickness. The materials used in them, have different energy-gaps between the valence and conduction bands. As a result, for the conducting electrons and holes, the layers represent a one-dimensional alternating sequence of potential wells and barriers.

By adjusting chemical composition and thickness of the layers, it is possible, in principle, to construct a device with a given potential profile. This so-called "wave function engineering" requires not only the sophisticated technology of crystal growing but also reliable methods for setting targets for such growing, i.e. methods for optimising the potential profile that generates desired spectrum of bound states and resonances of the charge carriers in the conduction band.

For this purpose, I am developing an exact method for direct calculation of the Jost function together with the Jost solutions of a one-dimensional Schroedinger equation that describes the motion of a particle on an infinite line. A combination of the variable-constant method with the complex coordinate rotation is used to replace the Schroedinger equation by an equivalent system of linear first-order differential equations. By solving these equations numerically, the Jost function can be obtained with any desired accuracy for all complex momenta of physical interest, including the spectral points corresponding to bound and resonant states. The effectiveness of the method has been tested by applying it to an Al(x)Ga(1-x)As heterostructure.

In contrast to the existing methods for locating resonances in such structures, the Jost function approach is exact (within the envelope-function approximation, of course) and treats the bound and all types of resonant states in a uniform way as the S-matrix poles in the complex energy plane. The effect of the external electric field can also be included in an exact way.

Theory of resonances

At present I am developing Jost function theory for locating quantum resonances generated by non-local potentials. Such a theory could find applications in molecular and nuclear physics where the realistic interactions often include non-local terms caused by anti-symmetrization of the wave function.
I am writing a monograph with tentative title: "Jost Function in Quantum Mechanics: theory and guide for practical applications".

$\eta$ -meson physics

Recent experiments by Uppsala and Giessen-Mainz groups who found the enhancement of near-threshold $\eta$ production in the reactions $np\to d\eta$ and $\gamma d\to np\eta$ , urged us to study the processes of $\eta$ production on light nuclei in a microscopic model with the adequate treatment of the few-body dynamics.

Collaboration: Prof. S. A. Sofianos (UNISA), Prof. V. B. Belyaev (Dubna), Ms. N. V. Shevchenko (Irkutsk), Prof. W. Sandhas (Bonn)

Nuclear astrophysics

Formation of deuterons is the "bottle-neck" process at the earliest stages of the Big Bang nucleosynthesis. Since at these stages the temperature and density were extremely high, we expect that the three-body reactions, such as npe--->de, could have done a notable contribution to the deuteron production. If it was so, then the whole network of the

-chain reactions would be affected as well as the resulting primordial abundancies of the light elements. We are currently working on this problem. Another reaction which could increase the deuteron production is, in a sense, analogous to the double $\beta$ -decay processes well-known in physics of heavy nuclei. One of the protons in the

collision can undergo a virtual $\beta^+$ -decay, $p\to ne^+\nu$ , which effectively reduces their Coulomb repulsion and facilitates the fusion $pp\to de^+\nu$ . We are planning to consider various such modifications of the standard

-chain model.

Collaboration: Prof. S. A. Sofianos (UNISA), Prof. V. B. Belyaev (Dubna), Dr. N. V. Shevchenko (Dubna), Dr. D. E. Monakhov (Dubna)

Nuclear fusion in molecules

Nuclear fusion could be a very powerful and practically inexhaustible source of energy. For a fusion event to occur, the nuclei must be close enough to each other to feel the strong attraction. They, however, are kept away from each other by the Coulomb barrier. Instead of lifting the particles against the barrier (which means increasing the temperature), it seems to be more promising to attempt to make the barrier itself thinner or to keep the particles near the barrier for such a long time that even a low penetration probability would work. The idea is to put the nuclei we want to fuse, inside a molecule where they can stay close to each other for a long time and, in addition, the Coulomb barrier becomes thinner because of electron screening. In this way fusion may proceed even at room temperature. The nuclear systems of particular interest are those which have near-threshold resonances that significantly increase the tunneling probability. An amazing example of such a system is the nucleus 18Ne that has an excited state exctly at the threshold energy of the system consisting of two protons and the oxygen nucleus 16O.
We are planning to estimate the rate of the reaction $pp^{16}{\rm O}\longrightarrow {}^{18}{\rm Ne}^*(1^-)$ in the water molecule H

O ("burning of water") and few other fusion reactions in several diatomic molecules.

Collaboration: Prof. V. B. Belyaev (Dubna), Mr. J. Dicks (MSc student, UNISA)

In addition to these topics on which I have been working during the last five years, the following new items are added to my research plan:

Effective cluster-cluster potentials in few-nucleon systems

Since the N-body equations are very complicated for ${\rm N}\ge 5$ and a numerical solution of them is practically not feasible, one has to resort to certain models and approximations in order to solve the N-body problems with large N. One such model approach consists in describing the cluster-cluster interactions by effevtive two-body potentials, which reduces the number of particles to the number of clusters involved. At present we are concerned with constructing an effective potential for the nucleon interaction with

H and

He nuclei.

Collaboration: Prof. S. A. Sofianos (UNISA), Prof. S. Oryu (Tokyo)

Nonadiabatic treatment of the three-body systems with one light particle

Exploiting the ideas of the resonating group method of nuclear physics, we derived a system of differential equations for the wave function of three distinct particles. Despite the fact that this approach is not adiabatic, it suits the problems involving one very light particle. Its another advantage is the possibility to treat highly excited states like, for example, the antiprotonic-helium atomcule $\bar pe{\rm He}$ . Such states attracted recently much attention after the discovery of the delayed annihilation of antiprotons in helium medium.

Collaboration: Prof. S. A. Sofianos (UNISA)

Quantum econo-physics

I am trying to apply the time-dependent Shroedinger equation for describing evolution of the stock-price probability-density. In contrast to the traditional approach based on classical statistical physics, the quantum dynamics includes various resonance phenomena which may reflect financial turmoils and crashes. By locating position and widths of resonances, one could predict when such phenomena might occur. The Jost function method for locating quantum resonances, which I developed recently, could be very useful for this purpose.

Links to the other pages of this CV:
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