Accomplished research (Dr. S. Rakityansky)

Accomplished Research

My publications cover the following topics:

Theory of resonances.

Locating quantum resonances was always a difficult problem in quantum mechanics. It is well-known that resonances are associated with zeros of the Jost function in the complex momentum plane. Almost any textbook on the scattering theory has a chapter devoted to the Jost function, but none of them gives a practical recipe for its calculation. Thus one usually gets a feeling that Jost function is a pure mathematical entity, elegant and useful in formal theory, but impractical in computations. In practice, therefore, resonances are located by various very complicated expansion methods.
During last few years we developed an exact and practical method for direct calculation of the Jost function for all complex momenta of physical interest, including the spectral points corresponding to bound and resonant states. The method proved to be valid also for complex values of the angular momentum, which enables us to locate the Regge trajectories as well. It is shown, by using several examples, that highly accurate results can be obtained for extremely wide as well as for extremely narrow resonances with or without the presence of the Coulomb interaction and for noncentral potentials which couple states of different angular momenta. The method is also extended to multichannel problems, singular potentials, and to the class of few-body problems which can be treated within the hyperspherical approach. This extention enabled us to locate the subthreshold resonances in the three- and four-neutron systems, namely, E(nnn)=

(MeV) and E(nnnn)=

(MeV), which were unsuccessfully searched by other methods many times before.
Currently, I am developing a method based on the Jost functions, for locating quantum resonances in semiconductor nanostructures.

$\eta$ -meson physics.

The production of $\eta$ mesons and their collisions with nuclei have been studied experimentally and theoretically with increasing interest during the last years. To a large extent this is motivated by the fundamental questions of charge symmetry breaking, the breakdown of the Okubo-Zweig-Iizuka rule, and the possible restoration of chiral symmetry in a nuclear medium. Another relevant question concerns the possible formation of $\eta$ -nucleus quasibound states. Estimates obtained in the framework of the optical potential and Green's function methods put a lower bound on the atomic number

which is needed to bind an $\eta$ meson inside a nucleus, namely, $A\ge 12$ .
In our papers published during the last five years, we presented the first microscopic calculations concerning the low-energy scattering of $\eta$ -meson from

He, and

He nuclei. The few-body dynamics of these systems was treated in our calculations by employing the Finite-Rank Approximation and the exact Faddeev type equations. By locating the

-matrix poles in the complex momentum plane, we showed that even very light nuclei can bind the $\eta$ meson, i.e. the constraint $A\ge 12$ is too strong. The dismissal of this constraint boosted the activity around this problem. In several experimental and theoretical investigations which followed our publications, similar results were obtained. In the latest article [49] we predicted near-threshold $\eta$ -deuteron resonance which may explain the corresponding experimental results of Uppsala and Giessen-Mainz groups.

Nuclear astrophysics.

During a short period of cosmic history, between about 10 and 500 seconds after the Big Bang, the primordial abundances of light elements were formed via the

-chain fusion. A comparison of the predictions for these abundances with the corresponding astronomical data is one of the key tests of the Big Bang theory. In the standard model it is assumed that all the reactions forming the

-chain, are generated by various two-body nucleus-nucleus and electron-nucleus collisions. However, due to the high densities, some intermediate products of this chain can emerge from three-body initial states as well. The role of the three-body collisions was not yet estimated properly, but the three-body states have different selection rules and, therefore, in principle could significantly change the whole picture of the nucleosynthesis. This can be said not only about the processes in the early universe but also about burning of hydrogen in the main sequence stars.
We performed (for the first time) a microscopic analysis of several nuclear reactions not included into the standard model of the

-chain, such as $e+p+d\to {}^3{\rm He}+e$ and $e+{}^3{\rm He}+{}^4{\rm He}\to {}^7{\rm Be}+e$ . For the synthesis of

Be, for example, we found that at the earliest stages of the Big Bang nucleosynthesis, when the temperature was $\sim 3\times10^9\,{}^{\circ}$ K, the non-radiative (three-body) reaction was $\sim 5$ times faster than the radiative fusion ${}^3{\rm He}+{}^4{\rm He}\to {}^7{\rm Be}+\gamma$ . Our finding raises the question about the importance of other three-body reactions not included in the

-chain.

Nuclear fusion in molecules.

Nuclei, being confined in a molecule for a relatively long time, can penetrate through the Coulomb barrier and interact via strong forces at sub-keV energies which can never be achieved in collision experiments. Having performed microscopic analysis of several muonic molecules, we found that among all possible nucleus-nucleus reactions inside them there is a special class having a rather high probability of occurrence due to a correlation between the spectra of the nuclei involved, and this is applicable not only to muonic but to ordinary (electronic) molecules as well. In particular, if a compound nucleus has a narrow excited state close to the threshold energy (zero relative energy) of the fragments which constitute the molecule, then the probability of their fusion can be very high. Moreover, the smaller the gap between this excited state and the threshold energy, the faster nuclei penetrate through the barrier.
A very interesting example is ordinary water molecule. The threshold energy of the system $pp^{16}$ O coincides exactly (within experimental errors) with the energy of an excited state of the nucleus $^{18}$ Ne. Hence, the wave function of 18 nucleons in the molecule H

O, in addition to the clustered configuration $pp^{16}$ O, must have small admixture of the compound state $^{18}{\rm Ne}^*(1^-)$ . Investigating the muonic molecules, we found that such mixing could enhance rate of the fusion reaction in many orders of magnitude. Therefore, if excited to a rotational state with quantum numbers

, the water molecule H

O can spontaneously collapse via the nuclear reaction $pp^{16}{\rm O}\longrightarrow {}^{18}{\rm Ne}^*(1^-)$ , which means that water, in principle, can burn. In ordinary water, however, all the molecules are bound in clusters consisting of several dozens of them. Even in steam these clusters remain tightly bound and therefore individual molecules cannot rotate.

Accelerator physics.

The difficulties associated with the space charge of the particle beam in an accelerator, grow rapidly when the current carried by the beam increases. Dealing with an electron accelerator with the pulse current of 200A, we tried to keep the flow of electrons as close to laminar one as possible. To this end we designed a source of electrons (electron gun) with a special geometry and the optical system with minimal disturbance of the laminar flow. With beams of high intensity instabilities caused by its coherent oscillations significantly limit the length to which the beam can be transported through the optical system. We developed a new stochastic method for analyzing the tolerances within which this system may deviate from axial symmetry.

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