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Sergei P. Maydanyuk

Publications and source records attributed to Sergei P. Maydanyuk.

50 records · Page 3Linked to original sources
arXiv2006

Angular analysis of bremsstrahlung in alpha decay

A new quantum electrodynamical method of calculations of bremsstrahlung spectra in the $α$-decay of heavy nuclei taking into account the angle between the directions of $α$-particle motion (or its tunneling) and photon emission is presented. The angular bremsstrahlung spectra for $^{210}{Po}$ have been obtained for the first time. According to calculations, the bremsstrahlung in the $α$-decay of this nucleus depends extremely weakly on the angle. Taking into account nuclear forces, such dependence is not changed visibly. An analytical formula of the angular dependence of the bremsstrahlung spectra is proposed and gives its harmonic behavior. The extremal values of the angle, at which the bremsstrahlung has maximal and minimal values, has been found.

nucl-th↗
arXiv2006

Search of a general form of superpotential in hierarchy with discrete energy spectrum

A generalized definition of superpotential has proposed, which connects two one-dimensional potentials $V_{1}$ and $V_{2}$ with discrete energy spectra completely and where: 1) energy of factorization equals to arbitrary level of spectrum of $V_{1}$ and function of factorization is defined concerning bound state at this level, 2) energy of factorization equals to arbitrary energy and function of factorization is defined concerning unbound (or non-normalizable) state at this energy. It has shown, that for unknown superpotential such its definition follows from solution of Riccati equation at given $V_{1}$. Using arbitrary bound state in construction of superpotential, SUSY QM methods in detailed calculations of spectral characteristics have been coming to level of methods of inverse problem. So, if as starting $V_{1}$ to choose rectangular well with finite width and infinitely high walls, then we reconstruct by SUSY QM approach all pictures of deformation of this potential and its wave functions of lowest bound states, which were obtained early by methods of inverse problem. Dependence between parameters of deformation for methods of SUSY QM and inverse problem has found, analysis of behavior of wave functions and the potential under deformation has fulfilled, a classification has proposed for zero-points of potential, nodes of the deformed wave functions, points, where wave functions are not deformed, an analysis of angles of wave functions leaving from such points has fulfilled. Using unbound states at arbitrary energy of factorization, we obtain new types of deformations. So, using only one superpotential, one can join two potentials, which have real energy spectra with own bound states and without coincident levels.

hep-th↗
arXiv2005

SIP-potentials and self-similar potentials of Shabat and Spiridonov: space asymmetric deformation

An appropriateness of a space asymmetry of shape invariant potentials with scaling of parameters and potentials of Shabat and Spiridonov in calculation of their forms, wave functions and discrete energy spectra has proved and has demonstrated on a simple example. Parameters, defined space asymmetry, have found. A new type of a hyerarchy, in which superpotentials with neighbouring numbers are connected by space rotation relatively a point of origin of space coordinates, has proposed.

hep-th↗
arXiv2005

Invisible nuclear system

A consecutive formalism and analysis of exactly solvable radial reflectionless potentials with barriers, which in the spatial semiaxis of radial coordinate $r$ have one hole and one barrier, after which they fall down monotonously to zero with increasing of $r$, is presented. It has shown, that at their shape such potentials look qualitatively like radial scattering potentials in two-partial description of collision between particles and nuclei or radial decay potentials in the two-partial description of decay of compound spherical nuclear systems. An analysis shows, that the particle propagates without the smallest reflection and without change of an angle of motion (or tunneling) during its scattering inside the spherically symmetric field of the nucleus with such radial potential of interaction, i. e. the nuclear system with such interacting potential shows itself as invisible for the incident particle with any kinetic energy. An approach for construction of a hierarchy such reflectionless potentials is proposed, wave functions of the first potentials of this hierarchy are found.

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arXiv2005

New exactly solvable reflectionless potentials of Gamov's type

In paper SUSY-hierarchies of one-dimensional potentials with continuous energy spectra are studied. Use of such hierarchies for analysis of reflectionless potentials is substantiated from the physical point of view. An interdependence (based on Darboux transformations) between spectral characteristics of potentials-partners is determined, an uniqueness of its solution in result of use of boundary conditions is shown. A rule of construction of new reflectionless potentials on the basis of known one is corrected, its proof is proposed. At first time a general solution for a superpotential $W_{n+m}(x)$ with an arbitrary number n+m in the studied hierarchy on the basis of only one known partial solution for the superpotential $W_{n}(x)$ with the selected number n is found. A general solution of a hierarchy of inverse power (reflectionless) potentials is obtained. Such a hierarchy can be interesting as an example for solution of a known problem of search of general solutions of the hierarchies of different types (both in standard and parasupersymmetric quantum mechanics). A consequent statement and analysis of exactly solvable reflectionless potentials of Gamov's type, which at their shapes look qualitatively like scattering potentials in two-particle description of collisions between particles and nuclei or decay potentials in two-particle description of decay of compound spherical nuclear systems, are presented.

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arXiv2005

SUSY-hierarchy of one-dimensional reflectionless potentials

A class of one-dimensional reflectionless potentials, an absolute transparency of which is concerned with their belonging to one SUSY-hierarchy with a constant potential, is studied. An approach for determination of a general form of the reflectionless potential on the basis of construction of such a hierarchy by the recurrent method is proposed. A general form of interdependence between superpotentials with neighboring numbers of this hierarchy, opening a possibility to find new reflectionless potentials, have a simple analytical view and are expressed through finite number of elementary functions (unlike some reflectionless potentials, which are constructed on the basis of soliton solutions or are shape invariant in one or many steps with involving scaling of parameters, and are expressed through series), is obtained. An analysis of absolute transparency existence for the potential which has the inverse power dependence on space coordinate (and here tunneling is possible), i.e. which has the form $V(x) = \pm α/ |x-x_{0}|^{n}$ (where $α$ and $x_{0}$ are constants, $n$ is natural number), is fulfilled. It is shown that such a potential can be reflectionless at n = 2 only. A SUSY-hierarchy of the inverse power reflectionless potentials is constructed. Isospectral expansions of this hierarchy is analyzed.

hep-th↗
arXiv2004

Bremsstrahlung in alpha-decay: angular analysis of spectra

A quantum mechanical method of calculation of bremsstrahlung spectra in alpha-decay of heavy nuclei with taking into account an angle between directions of the alpha-particle motion and the photon emission is presented. Dependence between the bremsstrahlung spectrum and the angle value is obtained in a simple analytical form. The method can be used for a comparative analysis of experimental data, obtained at different angles.

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arXiv2004

One-dimensional inverse power reflectionless potentials

A condition, at which the one-dimensional inverse power potential becomes reflectionless during propagation through it of a plane wave, is obtained on the basis of SUSY QM methods. A scattering of a particle on spherically symmetric inverse power potential is analysed with taking into account of the reflectionless possibility.

quant-ph↗
arXiv2004

Method of multiple internal reflections in description of nuclear alpha-decay

A spatial-time method of description of alpha-decay of a nucleus is presented. The method is based on the quantum mechanical model of the alpha-decay of a compound nuclear system with the barrier. alpha-decay dynamics is described on the basis of multiple internal reflections of wave packets from boundaries of the decay barrier. The method allows to study this process in details at any time moment or point of space. According to the method, some time before the time moment of the nuclear decay the nucleus makes oscilations. In the calculations of the time duration of the alpha-decay of the compound nucleus we propose to take into account the time durations of these oscillations. The method of the multiple internal reflections allows to calculate the time of such oscillations before the alpha-decay and the total alpha-decay time.

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arXiv2004

Periodic systems in time: double-well potential

Time analysis of oscillations of a particle between wells in the one-dimensional double-well potential with infinite high outside walls, based on wave packet use and energy spectrum analysis, is presented. For the double-well potential of the form $x^{2}+1/x^{2}$ in the external regions, an exact analytical solution of the energy spectrum is found (by standard QM approach), an analysis of oscillation periodicity is fulfilled, an approach for exact analitical calculation of the oscillation period is proposed (for the first time for the double-well potential).

nucl-th↗
arXiv2004

The method of multiple internal reflections in a description of tunneling evolution of nonrelativistic particles and photons

A non-stationary method for tunneling description of non-relativistic particles and photons through a barrier on the basis of consideration of the multiple internal reflections of vawe packets in relation of barrier boundaries is presented. The method is described in details and proved in the case of the one-dimentional tunneling of the particle through the rectangular barrier. For problems of the tunneling of the particle through the spherically symmetric barrier and of the photon through the one-dimensional barrier the amplitudes of transmitted and reflected wave packets in relation to the barrier, times of the tunneling and the reflection are found using of the method. Hartman's and Fletcher's effect is analysed.

nucl-th↗
arXiv2004

Does Sub-Barrier Bremsstrahlung in alpha-decay of 210Po Exist?

A quantum mechanical model for the description of the alpha-decay of heavy nuclei with accompanying photons emission is presented. The model is based on a quantum mechanical one-particle model of alpha-decay through a decay barrier. The bremsstrahlung spectrum calculation employs multipole expansion of the vector potential of the Coulomb field of the daughter nucleus and takes into account the dependence on the angle between the directions of the alpha-particle propagation and the photon emission. Spectra of 210Po are obtained for the angles 25 and 90, and the best agreement with the experimental data in the 90 case in a comparison with other existing models is achieved. From the angular analysis, the model gives monotonic behavior of the bremsstrahlung spectrum for any value of the angle. We find that sub-barrier photon emission (i. e. bremsstrahlung photon emission during alpha-particle tunneling through decay barrier) exists but gives a small contribution to the total bremsstrahlung spectrum.

nucl-th↗
arXiv2004

Method of multiple internal reflections in description of tunneling evolution through barriers

A method of a non-stationary description of tunneling of a particle through the one-dimensional and spherically symmetric rectangular barriers on the basis of analisis of multiple internal reflections of wave packets in relation on the barrier boundaries, named as the Method of multiple internal reflections, is presented at the first time. For the one-dimensional problem the applicability of this method is proved, its specific features are analyzed. For the spherically symmetric problem the amplitudes of the transmitted and reflected wave packets, times of tunneling and reflection in relation to the barrier are calculated using this method. The effect of Hartman-Fletcher is analyzed.

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