Searcharxiv⌕ Search

arXiv subjects

M. I. Krivoruchenko

Publications and source records attributed to M. I. Krivoruchenko.

At least 19 recordsLinked to original sources
arXiv2026

Projection operator onto spin-S eigenspaces of total and orbital angular momenta

The Frobenius covariant is used to construct a projection operator onto the spin-S eigenspaces associated with the squares of the total and orbital angular momenta. The covariant admits two equivalent representations: as a polynomial in powers of the scalar product of the spin and orbital angular momentum operators, and as a finite expansion in terms of their respective polarization operators. A correspondence is established with Villars' angular momentum projection, used in nuclear structure studies.

nucl-th↗
arXiv2025

Electromagnetic nucleon form factors in the extended vector meson dominance model

An extended vector meson dominance model is developed to describe electromagnetic nucleon form factors. The model includes families of the $ρ$- and $ω$-mesons with the associated radial excitations. The free parameters of the model are determined using a global statistical analysis of experimental data on the electromagnetic nucleon form factors in space- and timelike regions of transferred momenta. The vector meson masses and widths are equal to their empirical values, while the residues of form factors at the poles corresponding to the ground states of the $ρ$- and $ω$-mesons are consistent with the findings of both the Frazer-Fulco unitarity relations and the Bonn potential for coupling constants of the $ρ$- and $ω$-mesons with nucleons. Theoretical constraints imposed on the model include the quark counting rules, the Okubo-Zweig-Iizuka rule, the scaling law of Sachs form factors at moderate momentum transfers, and the suppression of Sachs form factors near the nucleon-antinucleon threshold. A reasonable description of the nucleon form factors in the experimentally accessible range of transferred momenta, as well as the electric and magnetic nucleon radii and Zemach radii, is obtained.

hep-ph↗
arXiv2024

Exchange contribution to the variance of the excitation energy of the electron shell of the daughter atom in double-$β$ decay

The excitation of electron shell of a daughter atom in a neutrinoless double $β$-decay causes change in shape of the total energy peak of $β$ electrons at the end of the energy spectrum. The main parameters of the modified distribution are the average energy and variance of the excitation energy of the electron shell. We derive an expression for the variance taking into account exchange effects and make numerical estimates of the average excitation energy and variance based on the non-relativistic Roothaan-Hartree-Fock method and the relativistic Dirac-Hartree-Fock method implemented in the General Relativistic Atomic Structure Package (Grasp2018). Estimates are made for eleven isotopes, two-neutrino double-$β$ decay of which is observed experimentally. The results are determined by the first two negative moments of the electron radii in the parent atom. The values obtained for change in the peak shape can be used to parameterize the energy distribution of $β$ electrons, taking into account the excitation of the electron shell of the daughter atom.

hep-ph↗
arXiv2024

Eigenvectors in terms of reduced complements of minor determinants

Eigenvectors associated with non-degenerate eigenvalues are shown to correspond to columns of the adjugate of the characteristic matrix. Degenerate eigenvalues are associated with eigenvectors that correspond to reduced complement tensors of minor determinants of the characteristic matrix. These observations are corroborated by a description of the non-degenerate two-level system and the Dirac equation, which exhibits twofold spin degeneracy of energy eigenvalues. Trace identities for the reduced order-one complement tensor and the diagonal sum of minor determinants are also presented.

math-ph↗
arXiv2024

Neutrino Mass Matrix in Neutrino-Related Processes

Techniques are developed for constructing amplitudes of neutrino-related processes in terms of the neutrino mass matrix, with no reference to the neutrino mixing matrix. The amplitudes of neutrino oscillations in vacuum and medium, quasi-elastic neutrino scattering, $β$ decays and double-$β$ decays are considered. The proposed approach makes extensive use of Frobenius covariants within the framework of Sylvester's theorem on matrix functions. The in-medium dispersion laws are found in terms of elementary functions for three flavors of Majorana neutrinos as an application of the developed formalism. The in-medium dispersion laws for Dirac neutrinos can be determined in the general case by searching for the roots of a polynomial of degree 6. In the rest frame of baryon matter, the minimum energy of both Majorana and Dirac neutrinos is achieved at a finite neutrino momentum. In such cases, Dirac neutrinos occupy a hollow Fermi sphere at zero temperature and low densities. Fitting experimental data in terms of the neutrino mass matrix can provide better statistical accuracy in determining the neutrino mass matrix compared to methods using the neutrino mixing matrix at intermediate stages.

hep-ph↗
arXiv2023

Atomic electron shell excitations in double-$β$ decay

The problem of the transition of electron shells of atoms to excited states in the process of neutrinoless double-$β$ decay is investigated. This subject is crucial for modeling the energy spectrum of $β$-electrons, which is sensitive to the mass and Majorana nature of neutrinos. The dependence of the obtained results on the atomic number indicates the determining role of the Feinberg--Migdal effect in the electron shell excitations. We report the overlap amplitudes of the electron shells of the parent atom and the daughter ion for eleven atoms, the two-neutrino double-$β$ decay of which was observed experimentally. In around one-fourth of the cases where the structure of the electron shells is inherited from the parent atom, there is a transition to the ground state or the excited state with the lowest energy. The de-excitation of the daughter ion in the latter scenario is accompanied by the emission of photons in the ultraviolet range, which can serve as an auxiliary signature of double-$β$ decay. The average excitation energy of the electron shells ranges between 300 and 800 eV, with the variance ranging from $(1.7~\mathrm{keV})^2$ in calcium to $(14~\mathrm{keV})^2$ in uranium.

hep-ph↗
arXiv2023

Impact of electron shell excitations on the energy spectrum of $β$-electrons in neutrinoless double-$β$ decay

The electron shell of the daughter atoms often appears excited in the double-$β$ decays, which causes a change in the energy taken away by $β$-electrons. The average value and variance of the excitation energy of the electron shell of the daughter atom are calculated for the double-$β$ decay of germanium $_{32}^{76}\mathrm{Ge} \rightarrow _{34}^{76}\mathrm{Se}^*+2β^-(+~2\bar{ν_e})$ in both the Thomas--Fermi model and the relativistic Dirac--Hartree--Fock theory. Using the results obtained, a two-parameter model of the energy spectrum of $β$-electrons in the neutrinoless mode is constructed, taking into account reaction energy redistribution in the decay channels. The shift in total energy of $β$-electrons is found to be under 50 eV at a confidence level of 90%. The average excitation energy, on the other hand, is an order of magnitude higher and equal to $\sim 400$ eV, while the square root of the variance is equal to $\sim 2900$ eV, which is presumably explained by the contribution of the core electrons to the energy characteristics of the process. The probability is nearly saturated with excitations with a small amount of released energy, which is common for the outermost electrons. The distortion of the peak shape of the neutrinoless double-$β$ decay should be taken into consideration when analyzing data from detectors with a resolution of $\sim 100$ eV or higher.

hep-ph↗
arXiv2023

Gauge invariance of quantum electrodynamics of multi-electron atoms

The proof of gauge invariance of the quantum electrodynamics of photons and electrons does not apply directly to the quantum electrodynamics of photons, electrons, and nuclei because multi-electron atoms belong to the space of asymptotic states of the extended theory. We offer two possible ways to circumvent this problem and prove, using a fairly general model for the description of nucleon-nucleon interaction in nuclei, the gauge invariance of the masses and electromagnetic form factors of multi-electron atoms in all orders of perturbation theory.

hep-ph↗
arXiv2022

Long-range multiparticle interactions induced by neutrino exchange in neutron-star matter

Forces with a large radius of interaction can have a significant impact on the equation of state of matter. Low-mass neutrinos generate a long-range potential due to the exchange of neutrino pairs. We discuss a possible relationship between the neutrino masses, which determine the interaction radius of the neutrino-pair exchange potential, and the equation of state of neutron matter. Contrary to previous statements, the thermodynamic potential, when decomposed into the number of neutrino interactions, vanishes in any decomposition order, except for the interaction of two neutrons. In the one-loop approximation, long-range multiparticle neutrino interactions are stable in the infrared region for all neutrino masses and do not affect the equation of state of neutron matter or the stability of neutron stars.

nucl-th↗
arXiv2022

Observation of an ultra-low $Q$-value electron-capture channel decaying to $^{75}$As via high-precision mass measurement

A precise determination of the atomic mass of $^{75}$As has been performed utilizing the double Penning trap mass spectrometer, JYFLTRAP. The mass excess is measured to be -73035.519(42) keV/c$^2$, which is a factor of 21 more precise and 1.3(9) keV/c$^2$ lower than the adopted value in the newest Atomic Mass Evaluation (AME2020). This value has been used to determine the ground-state-to-ground-state electron-capture decay $Q$ value of $^{75}$Se and $β^-$ decay $Q$ value of $^{75}$Ge, which are derived to be 866.041(81) keV and 1178.561(65) keV, respectively. Using the nuclear energy-level data of 860.00(40) keV, 865.40(50) keV (final states of electron capture) and 1172.00(60) keV (final state of $β^-$ decay) for the excited states of $^{75}$As$^*$, we have determined the ground-state-to-excited-state $Q$ values for two transitions of $^{75}$Se $\rightarrow$ $^{75}$As$^*$ and one transition of $^{75}$Ge $\rightarrow$ $^{75}$As$^*$. The ground-state-to-excited-state $Q$ values are determined to be 6.04(41) keV, 0.64(51) keV and 6.56(60) keV, respectively, thus confirming that the three low $Q$-value transitions are all energetically valid and one of them is a possible candidate channel for antineutrino mass determination. Furthermore, the ground-state-to-excited-state $Q$ value of transition $^{75}$Se $\rightarrow$ $^{75}$As$^*$ (865.40(50) keV) is revealed to be ultra-low (< 1 keV) and the first-ever confirmed EC transition possessing an ultra-low $Q$ value from direct measurements.

nucl-ex↗
arXiv2022

High-precision electron-capture $Q$ value measurement of $^{111}$In for electron-neutrino mass determination

A precise determination of the ground state $^{111}$In ($9/2^+$) electron capture to ground state of $^{111}$Cd ($1/2^+$) $Q$ value has been performed utilizing the double Penning trap mass spectrometer, JYFLTRAP. A value of 857.63(17) keV was obtained, which is nearly a factor of 20 more precise than the value extracted from the Atomic Mass Evaluation 2020 (AME2020). The high-precision electron-capture $Q$ value measurement along with the nuclear energy level data of 866.60(6) keV, 864.8(3) keV, 855.6(10) keV, and 853.94(7) keV for $^{111}$Cd was used to determine whether the four states are energetically allowed for a potential ultra-low $Q$-value $β^{}$ decay or electron-capture decay. Our results confirm that the excited states of 866.60(6) keV with spin-parity ($J^π$) of 3/2$^{+}$ and 864.8(3) keV with $J^π$ = 3/2$^{+}$ are ruled out due to their deduced electron-capture $Q$ value being smaller than 0 keV at the level of around 20$σ$ and 50$σ$, respectively. Electron-capture decays to the excited states at 853.94(7) keV ($J^π$ = 7/2$^+$) and 855.6(10) keV ($J^π$ = 3/2$^+$), are energetically allowed with $Q$ values of 3.69(19) keV and 2.0(10) keV, respectively. The allowed decay transition $^{111}$In (9/2$^{+}$) $\rightarrow$ $^{111}$Cd (7/2$^{+}$), with a $Q$ value of 3.69(19) keV, is a potential a new candidate for neutrino-mass measurements by future EC experiments featuring new powerful detection technologies. The results show that the indium level $2p_{1/2}$ for this decay branch leads to a significant increase in the number of EC events in the energy region sensitive to the electron neutrino mass.

nucl-ex↗
arXiv2021

$^{159}$Dy electron-capture: a strong new candidate for neutrino mass determination

{ The ground-state to ground-state electron-capture $Q$ value of $^{159}$Dy ($3/2^-$) has been measured directly utilizing the double Penning trap mass spectrometer JYFLTRAP. A value of 364.73(19)~keV was obtained from a measurement of the cyclotron frequency ratio of the decay parent $^{159}$Dy and the decay daughter $^{159}$Tb ions using the novel phase-imaging ion-cyclotron resonance technique. The $Q$ values for allowed Gamow-Teller transition to $5/2^-$ and the third-forbidden unique transition to $11/2^+$ state with excitation energies of 363.5449(14)~keV and 362.050(40)~keV in $^{159}$Tb were determined to be 1.18(19) keV and 2.68(19) keV, respectively. The high-precision $Q$ value of transition $3/2^-\to 5/2^-$ from this work, revealing itself as the lowest electron-capture $Q$ value, is utilized to unambiguously characterise all the possible lines that are present in its electron capture spectrum. { We performed atomic many-body calculations for both transitions to determine electron-capture probabilities from various atomic orbitals, and found an order of magnitude enhancement in the event rates near the end-point of energy spectrum in the transition to the $5/2^-$ nuclear excited state, which can become very interesting once the experimental challenges of identifying decays into excited states are overcome. The transition to the $11/2^+$ state is strongly suppressed and found unsuitable for measuring the neutrino mass. These results show that the electron capture in the $^{159}$Dy atom, going to the $5/2^-$ state of the $^{159}$Tb nucleus, %\textcolor{red} {is a new candidate which may open the way to determine the electron-neutrino mass in the sub-eV region by studying EC. Further experimental feasibility studies, including coincidence measurements with realistic detectors, will be of great interest.} }

nucl-ex↗
arXiv2021

Quark condensate seesaw mechanism for neutrino mass

We study a mechanism of generation of Majorana neutrino mass due to spontaneous breaking of chiral symmetry (SBCS) accompanied by the formation of a quark condensate. The effect of the condensate is transmitted to the neutrino sector via Lepton-Number Violating (LNV) lepton-quark dimension-$7$ operators known in the literature as an origin of the neutrino-mass-independent mechanism of neutrinoless double-beta ($0 νββ$) decay. The smallness of neutrino masses is due to a large ratio between the LNV scale and the scale of the SBCS. This is a new realization of the seesaw mechanism, which we dub the Quark Condensate SeeSaw (QCSS). We examine the predictions of the QCSS for $0 νββ$-decay and neutrino mass spectrum. We will show that our model predicts the normal neutrino mass ordering and narrow ranges of the neutrino masses.

hep-ph↗
arXiv2020

Neutrinoless Double-Electron Capture

Double-beta processes play a key role in the exploration of neutrino and weak interaction properties, and in the searches for effects beyond the Standard Model. During the last half century many attempts were undertaken to search for double-beta decay with emission of two electrons, especially for its neutrinoless mode ($0\nu2β^-$), the latter being still not observed. Double-electron capture (2EC) was not in focus so far because of its in general lower transition probability. However, the rate of neutrinoless double-electron capture ($0\nu2$EC) can experience a resonance enhancement by many orders of magnitude in case the initial and final states are energetically degenerate. In the resonant case, the sensitivity of the $0\nu2$EC process can approach the sensitivity of the $0\nu2β^-$ decay in the search for the Majorana mass of neutrinos, right-handed currents, and other new physics. We present an overview of the main experimental and theoretical results obtained during the last decade in this field. The experimental part outlines search results of 2EC processes and measurements of the decay energies for possible resonant $0ν$2EC transitions. An unprecedented precision in the determination of decay energies with Penning traps has allowed one to refine the values of the degeneracy parameter for all previously known near-resonant decays and has reduced the rather large uncertainties in the estimate of the $0\nu2$EC half-lives. The theoretical part contains an updated analysis of the electron shell effects and an overview of the nuclear structure models, in which the nuclear matrix elements of the $0\nu2$EC decays are calculated. One can conclude that the decay probability of $0ν$2EC can experience a significant enhancement in several nuclides.

hep-ph↗
arXiv2020

A generalization of the Levinson theorem about the asymptotic value of the scattering phase shift

In quantum scattering theory, there exists a relationship between the difference in the scattering phase shifts at threshold and infinity and the number of bound states, which is established by the Levinson theorem. The presence of Castillejo, Dalitz and Dyson poles in the scattering amplitude, as well as Jaffe and Low primitives, corresponding to zeros of $D$ function on the unitary cut, modify the Levinson theorem. The asymptotic value of the scattering phase shift is shown to be determined by the number of bound states, the number of Castillejo, Dalitz and Dyson poles, and the number of primitives. Some consequences of the generalized theorem with respect to properties of nucleon-nucleon interactions are discussed.

hep-ph↗
arXiv2019

Overlap of electron shells in $β$ and double-$β$ decays

The $β$ and double-$β$ decay channels, which are not accompanied by excitation of the electron shells, are suppressed due to the nonorthogonality of the electron wave functions of the parent and daughter atoms. The effect is sensitive to the contribution of the outer electron shells. Since valence electrons participate in chemical bonding and collectivize in metals, the decay rates of the unstable nuclides are modified when they are embedded in a host material. Core electrons are less affected by the environment, and their overlap amplitudes are more stable. The suppression effect is estimated for $ β^- $ decay of $^{87}$Kr, electron capture in $^{163}$Ho, and $2β^-$ decays of $^{76}$Ge, $^{100}$Mo, $^{130}$Te, and $^{136}$Xe. The overlap amplitude of the electron shells enters the relationship between the half-life of neutrinoless $2β$ decay and the effective electron neutrino Majorana mass.

hep-ph↗
arXiv2018

Bound-state double-$β$ decay

We consider new modes of two-neutrino and neutrinoless double-$β$ decays in which one $β$ electron goes over to a continuous spectrum and the other occupies a vacant bound level of the daughter ion. We calculate the corresponding phase-space factors of the final states, estimate the partial decay rates, and derive the one- and two-electron energy spectra using relativistic many-electron wave functions of atoms provided by the multiconfiguration Dirac-Hartree-Fock package GRASP2K. While the bound-state neutrinoless double-$β$ decays are strongly suppressed, their two-neutrino counterparts can be observed in the next-generation double-$β$-decay experiments, most notably SuperNEMO.

hep-ph↗