arXiv subjects

Sergei P. Maydanyuk

Publications and source records attributed to Sergei P. Maydanyuk.

At least 37 records · Page 2Linked to original sources

arXiv2015

Can a many-nucleon structure be visible in bremsstrahlung emission during $α$ decay?

We analyze if the nucleon structure of the $α$ decaying nucleus can be visible in the experimental bremsstrahlung spectra of the emitted photons which accompany such a decay. We develop a new formalism of the bremsstrahlung model taking into account distribution of nucleons in the $α$ decaying nuclear system. We conclude the following: (1) After inclusion of the nucleon structure into the model the calculated bremsstrahlung spectrum is changed very slowly for a majority of the $α$ decaying nuclei. However, we have observed that visible changes really exist for the $^{106}{\rm Te}$ nucleus ($Q_α=4.29$ MeV, $T_{1/2}$=70 mks) even for the energy of the emitted photons up to 1 MeV. This nucleus is a good candidate for future experimental study of this task. (2) Inclusion of the nucleon structure into the model increases the bremsstrahlung probability of the emitted photons. (3) We find the following tendencies for obtaining the nuclei, which have bremsstrahlung spectra more sensitive to the nucleon structure: (a) direction to nuclei with smaller $Z$, (b) direction to nuclei with larger $Q_α$-values.

nucl-th↗

arXiv2015

Quantum design using a multiple internal reflections method in a study of fusion processes in the capture of alpha-particles by nuclei

A high precision method to determine fusion in the capture of $α$-particles by nuclei is presented. For $α$-capture by $^{40}{\rm Ca}$ and $^{44}{\rm Ca}$, such an approach gives (1) the parameters of the $α$--nucleus potential and (2) fusion probabilities. This method found new parametrization and fusion probabilities and decreased the error by $41.72$ times for $α+ ^{40}{\rm Ca}$ and $34.06$ times for $α+ ^{44}{\rm Ca}$ in a description of experimental data in comparison with existing results. We show that the sharp angular momentum cutoff proposed by Glas and Mosel is a rough approximation, Wong's formula and the Hill-Wheeler approach determine the penetrability of the barrier without a correct consideration of the barrier shape, and the WKB approach gives reduced fusion probabilities. Based on our fusion probability formula, we explain the difference between experimental cross-sections for $α+ ^{40}{\rm Ca}$ and $α+ ^{44}{\rm Ca}$, which is connected with the theory of coexistence of the spherical and deformed shapes in the ground state for nuclei near the neutron magic shell $N=20$. To provide deeper insight into the physics of nuclei with the new magic number $N=26$, the cross-section for $α+ ^{46}{\rm Ca}$ is predicted for future experimental tests. The role of nuclear deformations in calculations of the fusion probabilities is analyzed.

nucl-th↗

arXiv2015

New approach to determine proton-nucleus interactions from experimental bremsstrahlung data

A new approach is presented to determine the proton-nucleus interactions from the analysis of the accompanying photon bremsstrahlung. We study the scattering of $p + ^{208}{\rm Pb}$ at the proton incident energies of 140 and 145~MeV, and the scattering of $p + ^{12}{\rm C}$, $p + ^{58}{\rm Ni}$, $p + ^{107}{\rm Ag}$ and $p + ^{197}{\rm Au}$ at the proton incident energy of 190~MeV. The model determines contributions of the coherent emission (formed by an interaction between the scattering proton and nucleus as a whole without the internal many-nucleon structure), incoherent emission (formed by interactions between the scattering proton and nucleus with the internal many-nucleon structure), and transition between them in dependence on the photon energy. The radius-parameter of the proton-nucleus potential for these reactions is extracted from the experimental bremsstrahlung data analysis. We explain the hump-shaped plateau in the intermediate- and high-energy regions of the spectra by the essential presence of the incoherent emission, while at low energies the coherent emission predominates which produces the logarithmic shape spectrum. We provide our predictions (in absolute scale) for the angular distribution of the bremsstrahlung photons in order to test our model, results and analysis in further experiments.

nucl-th↗

arXiv2014

Quantum method of determination of penetrability in FRW model with radiation

In paper the closed Friedmann-Robertson-Walker model with quantization in presence of the positive cosmological constant, radiation and Chaplygin gas is studied. For analysis of tunneling probability for birth of an asymptotically deSitter, inflationary Universe as a function of the radiation energy a new definition of a "free" wave propagating inside strong fields is introduced. Vilenkin's tunneling boundary condition is corrected, penetrability and reflection are calculated in fully quantum stationary approach.

gr-qc↗

arXiv2014

Quantum dynamics of early Universe

In order to study quantum dynamics of the FRW-universe of closed type, definitions of velocity, Hubble function and duration of the evolved universe are introduced into cosmology. The proposed definitions are characterized by high stability of calculations and easy for use. The introduced characteristics are supported by calculations of wave function in the fully quantum (non-semiclassical) approach. We achieve high precision agreement between the classical and quantum calculations after the formation of Universe with classical spacetime (i.e. Big Bang). Such an agreement confirms efficiency of the proposed definitions, and classical-quantum correspondence allows to obtain quantum information before Big Bang, to study dynamics of evolution of universe in the first stage and later times.

gr-qc↗

arXiv2013

A fully quantum model of Big Bang

In the paper the closed Friedmann-Robertson-Walker model with quantization in the presence of the positive cosmological constant and radiation is studied. For analysis of tunneling probability for birth of an asymptotically deSitter, inflationary Universe as a function of the radiation energy a new definition of a "free" wave propagating inside strong fields is proposed. On such a basis, tunneling boundary condition is corrected, penetrability and reflection concerning to the barrier are calculated in fully quantum stationary approach. For the first time non-zero interference between the incident and reflected waves has been taken into account which turns out to play important role inside cosmological potentials and could be explained by non-locality of barriers in quantum mechanics. Inside whole region of energy of radiation the tunneling probability for the birth of the inflationary Universe is found to be close to its value obtained in semiclassical approach. The reflection from the barrier is determined for the first time (which is essentially differs on 1 at the energy of radiation close to the barrier height). The proposed method could be easily generalized on the cosmological models with the barriers of arbitrary shape, that has been demonstrated for the FRW-model with included Chaplygin gas. Result is stable for variations of the studied barriers, accuracy are found to be 11--18 digits for all coefficients and energies below the barrier height.

gr-qc↗

arXiv2013

Quantum dynamics of evolution of flat universe in the first stage

Process of formation of the universe with its further expansion in the first evolution stage is investigated in the framework of Friedmann-Robertson-Walker metrics on the basis of quantum model, where a new type of matter is introduced, which energy density is dependent on velocity of the expansion. It is shown that such an improvement of the model forms potential barrier for the flat universe at $k=0$ (in contrast with generalized Chaplygin gas model). Peculiarities of wave function are analyzed in details, which is calculated by fully quantum (non-semiclassic) approach, for the different barrier regions and stages of evolution. Resonant influence of the initial and boundary conditions on the barrier penetrability is shown (in contrast with Vilenkin and Hawking approaches). In order to perform a comparative analysis, how much quickly the universe is expanded by different models, new quantum definitions of velocity and Hubble function are introduced. These notions allow us to study dynamics of evolution of universe in quantum cosmology both in the first stage, and in later times.

gr-qc↗

arXiv2012

Model of the bremsstrahlung emission accompanying interactions between protons and nuclei from low up to intermediate energies: role of magnetic emission

A new model of the bremsstrahlung emission which accompanies proton decay and collisions of protons off nuclei in the energy region from the lowest up to intermediate, has been developed. This model includes spin formalism, potential approach for description of interaction between protons and nuclei, and operator of emission includes component of the magnetic emission (defined on the basis of Pauli equation). In the problem of the bremsstrahlung during the proton decay in the first time a role of the magnetic emission is studied using such a model. For the studied $^{146}{\rm Tm}$ nucleus it has been studied the following: (1) How much does the magnetic emission change the full bremsstrahlung spectrum? (2) At which angle is the magnetic emission the most intensive relatively electric one? (3) Is there some space region where the magnetic emission increases strongly relatively electric one? (4) How intensive is the magnetic emission in the tunneling region? (5) Which values has the probability at its maximum and at zero energy limit of the emitted photons? It is demonstrated that the model is able to describe enough well experimental data of the bremsstrahlung emission which accompanies collisions of protons off the $^{9}{\rm Be}$, $^{12}{\rm C}$ and $^{208}{\rm Pb}$ nuclei at the incident energy $T_{\rm lab}=140$ MeV (at the photon energy up to 120 MeV).

nucl-th↗

arXiv2011

Multipolar model of bremsstrahlung accompanying proton-decay of nuclei

Emission of bremsstrahlung photons accompanying proton decay of nuclei is studied. The new improved multipolar model describing such a process is presented. The angular formalism of calculations of the matrix elements is stated in details. The bremsstrahlung probabilities for the $^{157}{\rm Ta}$, $^{161}{\rm Re}$, $^{167}{\rm Ir}$ and $^{185}{\rm Bi}$ nuclei decaying from the $2s_{1/2}$ state, the $^{109}_{53}{\rm I}_{56}$ and $^{112}_{55}{\rm Cs}_{57}$ nuclei decaying from the $1d_{5/2}$ state, the $^{146}_{69}{\rm Tm}_{77}$ and $^{151}_{71}{\rm Lu}_{80}$ nuclei decaying from the $0h_{11/2}$ state are predicted. Such spectra have orders of values similar to the experimental data for the bremsstrahlung photons emitted during the $α$-decay. This indicates on real possibility to study bremsstrahlung photons during proton decay experimentally and perform further measurements.

nucl-th↗

arXiv2010

Resonant structure of space-time of early universe

A new fully quantum method describing penetration of packet from internal well outside with its tunneling through the barrier of arbitrary shape used in problems of quantum cosmology, is presented. The method allows to determine amplitudes of wave function, penetrability $T_{\rm bar}$ and reflection $R_{\rm bar}$ relatively the barrier (accuracy of the method: $|T_{\rm bar}+R_{\rm bar}-1| < 1 \cdot 10^{-15}$), coefficient of penetration (i.e. probability of the packet to penetrate from the internal well outside with its tunneling), coefficient of oscillations (describing oscillating behavior of the packet inside the internal well). Using the method, evolution of universe in the closed Friedmann--Robertson--Walker model with quantization in presence of positive cosmological constant, radiation and component of generalize Chaplygin gas is studied. It is established (for the first time): (1) oscillating dependence of the penetrability on localization of start of the packet; (2) presence of resonant values of energy of radiation $E_{\rm rad}$, at which the coefficient of penetration increases strongly. From analysis of these results it follows: (1) necessity to introduce initial condition into both non-stationary, and stationary quantum models; (2) presence of some definite values for the scale factor $a$, where start of expansion of universe is the most probable; (3) during expansion of universe in the initial stage its radius is changed not continuously, but passes consequently through definite discrete values and tends to continuous spectrum in latter time.

gr-qc↗

arXiv2010

Calculations of widths in the problem of decay by proton emission

We develop a new fully quantum method for determination of widths for nuclear decay by proton emission where multiple internal reflections of wave packet describing tunneling process inside proton--nucleus radial barrier are taken into account. Exact solutions for amplitudes of wave function, penetrability $T$ and reflection $R$ are found for $n$-step barrier (at arbitrary $n$) which approximates the realistic barrier. In contrast to semiclassical approach and two-potential approach, we establish by this method essential dependence of the penetrability on the starting point $R_{\rm form}$ in the internal well where proton starts to move outside (for example, for $^{157}_{73}{\rm Ta}$ the penetrability is changed up to 200 times; accuracy is $|T+R-1| < 1.5 \cdot 10^{-15}$). We impose a new condition: in the beginning of the proton decay the proton starts to move outside from minimum of the well. Such a condition provides minimal calculated half-life and gives stable basis for predictions. However, the half-lives calculated by such an approach turn out to be a little closer to experimental data in comparison with the semiclassical half-lives. Estimated influence of the external barrier region is up to 1.5 times for changed penetrability.

nucl-th↗

arXiv2010

A fully quantum method of determination of penetrability and reflection coefficients in quantum FRW model with radiation

In the paper the closed Friedmann--Robertson--Walker model with quantization in the presence of the positive cosmological constant and radiation is studied. For analysis of tunneling probability for birth of an asymptotically deSitter, inflationary Universe as a function of the radiation energy a new definition of a "free" wave propagating inside strong fields is proposed. On such a basis, tunneling boundary condition is corrected, penetrability and reflection concerning to the barrier are calculated in fully quantum stationary approach. For the first time non-zero interference between the incident and reflected waves has been taken into account which turns out to play important role inside cosmological potentials and could be explained by non-locality of barriers in quantum mechanics. Inside whole region of energy of radiation the tunneling probability for the birth of the inflationary Universe is found to be close to its value obtained in semiclassical approach. The reflection from the barrier is determined for the first time (which is essentially differs on 1 at the energy of radiation close to the barrier height). The proposed method could be easily generalized on the cosmological models with the barriers of arbitrary shape, that has been demonstrated for the FRW-model with included Chaplygin gas. Result is stable for variations of the studied barriers, accuracy are found to be 11--18 digits for all coefficients and energies below the barrier height.

gr-qc↗

arXiv2009

Angular bremsstrahlung during $α$-decay, emission from the internal region and unified formula of the bremsstrahlung probability

Model of angular bremsstrahlung of photons emitted during $α$-decay is presented. A special emphasis is given on development of unified formalism of matrix elements in the dipole and multipolar approaches. A probability of the emission of photons calculated on the basis of the multipole model without any normalization on experimental data (i. e. in absolute scale) is found at $90^{\circ}$ of the angle $\vartheta_{αγ}$ between directions of motion of the $α$-particle (with its tunneling under barrier) and emission of photons to be in a good agreement with the newest experimental data for the $^{210}{\rm Po}$, $^{214}{\rm Po}$, and $^{226}{\rm Ra}$ nuclei. The spectrum for $^{244}{\rm Cm}$ is found at $\vartheta_{αγ} = 25^{\circ}$ to be in satisfactory agreement with high limit of errors of experimental data of Japanese group. A comparative analysis for the spectra calculated for $^{210}{\rm Po}$ by the multipole and dipole approaches in the absolute scale and with normalization on experimental data is performed. The emission of photons from the internal well in the dipole approach is found to be not small while the multipolar approach does not show such a strong dependence. Distribution of the bremsstrahlung probability on the numbers of protons and nucleons of the $α$-decaying nucleus in selected region close to $^{210}{\rm Po}$ is obtained. An unified formula of the bremsstrahlung probability during the $α$-decay of arbitrary nucleus expressed directly through the $Q_α$-value and numbers $A_{p}$, $Z_{p}$ of nucleons and protons of this nucleus is proposed.

nucl-th↗

arXiv2009

On non-selfadjoint operators for observables in quantum mechanics and quantum field theory

Aim of this paper is to show the possible significance, and usefulness, of various non-selfadjoint operators for suitable Observables in non relativistic and relativistic quantum mechanics, and in quantum electrodynamics. More specifically, this work starts dealing with: (i) the maximal hermitian (but not selfadjoint) Time operator in non-relativistic quantum mechanics and in quantum electrodynamics; and with: (ii) the problem of the four-position and four-momentum operators, each one with its hermitian and anti-hermitian parts, for relativistic spin-zero particles. Afterwards, other physically important applications of non-selfadjoint (and even non-hermitian) operators are discussed: In particular, (iii) we reanalyze in detail the interesting possibility of associating quasi-hermitian Hamiltonians with (decaying) unstable states in nuclear physics. Finally, we briefly mention the cases of quantum dissipation, as well as of the nuclear optical potential. [PACS numbers: 03.65.Ta; 03.65.-w; 03.65.Pm; 03.70.+k; 03.65.Xp; 11.10.St; 11.10.-z; 11.90.+t; 02.00.00; 03.00.00; 24.10.Ht; 03.65.Yz; 21.60.-u; 11.10.Ef; 03.65.Fd. Keywords: time operator in quantum mechanics; space-time operator; time-"Hamiltonian"; non-selfadjoint operators; non-hermitian operators; bilinear operators; time operator for discrete energy spectra; time-energy uncertainty relations; unstable states; quasi-hermitian Hamiltonians; Klein-Gordon equation; quantum dissipation; nuclear optical model].

quant-ph↗

arXiv2008

Wave function of the Universe in the early stage of its evolution

In quantum cosmological models, constructed in the framework of Friedmann-Robertson-Walker metrics, a nucleation of the Universe with its further expansion is described as a tunneling transition through an effective barrier between regions with small and large values of the scale factor $a$ at non-zero (or zero) energy. The approach for describing this tunneling consists of constructing a wave function satisfying an appropriate boundary condition. There are various ways for defining the boundary condition that lead to different estimates of the barrier penetrability and the tunneling time. In order to describe the escape from the tunneling region as accurately as possible and to construct the total wave function on the basis of its two partial solutions unambiguously, we use the tunneling boundary condition that the total wave function must represent only the outgoing wave at the point of escape from the barrier, where the following definition for the wave is introduced: the wave is represented by the wave function whose modulus changes minimally under a variation of the scale factor $a$. We construct a new method for a direct non-semiclassical calculation of the total stationary wave function of the Universe, analyze the behavior of this wave function in the tunneling region, near the escape point and in the asymptotic region, and estimate the barrier penetrability. We observe oscillations of modulus of wave function in the external region starting from the turning point which decrease with increasing of $a$ and which are not shown in semiclassical calculations. The period of such an oscillation decreases uniformly with increasing $a$ and can be used as a fully quantum dynamical characteristic of the expansion of the Universe.

gr-qc↗

arXiv2008

Bremsstrahlung during $α$-decay: quantum multipolar model

In this paper the improved multipolar model of bremsstrahlung accompanied the $α$-decay is presented. The angular formalism of calculations of the matrix elements, being enough complicated component of the model, is stated in details. A new definition of the angular (differential) probability of the photon emission in the $α$-decay is proposed where direction of motion of the $α$-particle outside (with its tunneling inside barrier) is defined on the basis of angular distribution of its spacial wave function. In such approach, the model gives values of the angular probability of the photons emission in absolute scale, without its normalization on experimental data. Effectiveness of the proposed definition and accuracy of the spectra calculations of the bremsstrahlung spectra are analyzed in their comparison with experimental data for the $^{210}{\rm Po}$, $^{214}{\rm Po}$, $^{226}{\rm Ra}$ and $^{244}{\rm Cm}$ nuclei, and for some other nuclei predictions are performed (in absolute scale). With a purpose to find characteristics taking influence on the bremsstrahlung probability strongly, a dependence of the bremsstrahlung probability on effective charge of the decaying system is analyzed. As a natural result, as supposed type of decaying system the emission of proton from nucleus is studied, for which the effective charge is essentially larger in a comparison with $α$-decay. For some proton emitters estimations of the bremsstrahlung probability are obtained (at first time, in fully quantum approach). Also the bremsstrahlung in fission of the $^{252}{\rm Cf}$ nucleus is analyzed.

nucl-th↗

arXiv2008

Method of determination of the most probable coordinate of formation of $α$-particle in $α$-decay

Method of multiple internal reflections (method MIR) in description of $α$-decay of nucleus in the spherically symmetric approximation is presented in paper. In approach MIR the formalism of calculation of amplitudes of wave function, described moving of $α$-particle from the internal region outside with its tunneling through a realistic radial $α$-nucleus barrier of arbitrary shape, has been constructed at first time. The method MIR gives convergent values for the amplitudes of transmission and reflection, coefficients of penetrability and reflection, obtained in description of leaving of the $α$-particle relatively a potential with barrier in form of a number of rectangular steps (multi-steps potential), with tending this potential to the realistic $α$-nucleus one, and limit values of the amplitudes and coefficients are considered as exact concerning the realistic $α$-nucleus potential (without application of WKB approximation). In approach MIR a dependence of the penetrability coefficient and half-live on the location of the starting point, from where $α$-particle begins to move outside, is opened. From here, we define a radial coordinate of the most probable formation of the $α$-particle inside nucleus before its $α$-decay as such starting point, at moving of the $α$-particle from which outside the half-live, calculated by approach MIR, is maximally closed to its experimental value. For isotopes ${\rm Po}$ with different mass number $A$ we have obtained essentially closer values for half-live, calculated by such approach, to their experimental values in a comparison with half-lives obtained by approach WKB. This result is stable for all studied nuclei.

nucl-th↗

arXiv2007

Double complex SUSY-transformations: deformations of real potentials and their spectral characteristics

In paper approach of double complex SUSY-transformations with not coincident complex energies of transformation is developed, allowing to deform given real potential $V_{1}$ with obtaining exact solutions. The explicit solutions of the deformation of shape of the potential, its wave function at arbitrary energy, not coincident with energies of transformation, wave functions at the energies of transformation are obtained, condition of keeping of continuity of the solutions and isospectral condition are determined. Using a rectangular well of finite width with infinitely high walls as the starting $V_{1}$ with discrete energy spectrum, by the proposed approach new types of deformation of this potential with deformation of the energy spectrum as a whole have been obtained. The new potential contains the rectangular well as own partial case (with simultaneous transformation of the shape of this new potential, energy spectrum, wave functions of all bound states, wave function at arbitrary energy into corresponding characteristics of the rectangular well at needed choice of parameters). Using null potential as the starting $V_{1}$ with continuous energy spectrum, new form of reflectionless real potential has been constructed. This potential generalizes well-known reflectionless potential of the type $V_{\rm ref}(x) = A^{2}(1-2 {\rm sech}^{2}{Ax})$, allowing: to pull down tails of the potential $V_{\rm ref}$ in the asymptotic regions up to zero (with keeping of nonzero depth); to pull down continuously the depth of the hole; to displace arbitrary along axis $x$ the hole with its passing through zero; to create and to increase the second hole, transforming $V_{\rm ref}$ into double-well potential; to control continuously and simply the asymmetry of the shape of such reflectionless potential.

hep-th↗