Search

The Levinson theorem relates the difference of the phase shifts at the threshold and at infinity to the number of bound states. The theorem is modified in view of the fact that Castillejo–Dalitz–Dyson (CDD) poles and Jaffe–Low primitives corresponding to zeros of the $$D$$ function on the unitary cut are present in the scattering amplitude. It is shown that, in general, the difference of the phase shifts at the threshold and at infinity is determined by the number of bound states, the number of CDD poles, and the number of primitives. Some consequences of this theorem that concern the properties of the nucleon–nucleon interaction are discussed.

Preprint of paper published on PRL The ground-state to ground-state electron-capture Q value of 159Dy (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 159Dy and the decay daughter 159Tb 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 159Tb were determined to be 1.18(19) keV and 2.68(19) keV, respectively. The highprecision Q value of transition 3/2 − → 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 159Dy atom, going to the 5/2 − state of the 159Tb nucleus, 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.

The ground state to ground state electron-capture Q value of ^{159}Dy (3/2^{-}) has been measured directly using 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^{-}→5/2^{-} from this work, revealing itself as the lowest electron-capture Q value, is used to unambiguously characterize 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, is a new candidate that may open the way to determine the electron-neutrino mass in the sub-eV region by studying electron-capture. Further experimental feasibility studies, including coincidence measurements with realistic detectors, will be of great interest.

The problem of internal ionization in the beta decay of tritium due to the scattering of a β electron off a bound electron is discussed. The total probability of the process per a single decay event is calculated. The distributions over the momentum and the kinetic energy of a liberated electron are plotted. A correction to the β spectrum produced by internal ionization is determined. The identity of electrons is taken into account in all calculations. The results of calculations of the modified spectrum are of interest for the KATRIN experiment aimed at measuring the mass of an electron antineutrino. The high-luminosity source also makes it possible to search for keV-scale sterile neutrinos in the middle part of the β spectrum, where the internal ionization effect is significant.

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 ($0\nu2\beta^-$), 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 $0\nu2\beta^-$ 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 $0\nu$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 $0\nu$2EC can experience a significant enhancement in several nuclides., Comment: 68 pages, 14 tables, 19 figures, accepted for publication in Reviews of Modern Physics

The equation of state for neutron matter is derived in the framework of the Quark Compound Bag model, in which the nucleon–nucleon interaction is generated by the s-channel exchange of six-quark Jaffe–Low primitives.

The $\beta$ and double-$\beta$ 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 $ \beta^- $ decay of $^{87}$Kr, electron capture in $^{163}$Ho, and $2\beta^-$ 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 $2\beta$ decay and the effective electron neutrino Majorana mass., Comment: 7 pages, 2 figures, 2 tables; accepted for publication in EPJA

We study a possibility of generation of the neutrino masses by a quark condensate resulting from a spontaneous break-down of the chiral symmetry. The existence of exotic scalar interactions between Majorana neutrinos and quarks in vacuum as well as in nuclear medium gives rise to a Majorana mass matrix. We construct the Majorana mass matrix and set limits on coupling constants of the exotic scalar interactions based on experiments searching for the neutrinoless double-beta decay.We study a possibility of generation of the neutrino masses by a quark condensate resulting from a spontaneous break-down of the chiral symmetry. The existence of exotic scalar interactions between Majorana neutrinos and quarks in vacuum as well as in nuclear medium gives rise to a Majorana mass matrix. We construct the Majorana mass matrix and set limits on coupling constants of the exotic scalar interactions based on experiments searching for the neutrinoless double-beta decay.

We consider alternative 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.

We revisit the "interpolating formula" proposed in our previous publication. It allows one to calculate the neutrinoless double beta decay ($0\nu\beta\beta$-decay) half-life for arbitrary neutrino mass without involvement of the complicated results for nuclear matrix elements (NME) obtained within specific nuclear structure models. The formula derives from the finding that the value of a properly normalized ratio of the NMEs for the light and heavy neutrino mass mechanisms weakly depends on isotope. From this fact it follows, in particular, that the light and heavy neutrino mass mechanisms can hardly be distinguished in a model independent way searching for $0\nu\beta\beta$-decay of different nuclei. Here we show that this formula holds for all the known nuclear structure approaches. We give a mathematical justification of our results examining analytical properties of the NMEs. We also consider several simplified benchmark scenarios within left-right symmetric models and analyze the conditions for the dominance of the light or heavy neutrino mass mechanisms in $0\nu\beta\beta$-decay.

The general solution of hydrostatic equilibrium equations for a two-component fluid of ions and electrons without a local electroneutrality constraint is found in the framework of Newtonian gravity theory. In agreement with the Poincar\'e theorem on analyticity and in the context of Dyson's argument, the general solution is demonstrated to possess a fixed (essential) singularity in the gravitational constant $G$ at $ G = 0 $. The regular component of the general solution can be determined by perturbation theory in $G$ starting from a locally neutral solution. The non-perturbative component obtained using the method of Wentzel, Kramers and Brillouin is exponentially small in the inner layers of the star and grows rapidly in the outward direction. Near the surface of the star, both components are comparable in magnitude, and their non-linear interplay determines the properties of an electro- or ionosphere. The stellar charge varies within the limits of $- 0.1 $ to $150$ C per solar mass. The properties of electro- and ionospheres are exponentially sensitive to variations of the fluid densities in the central regions of the star. The general solutions of two exactly solvable stellar models without a local electroneutrality constraint are also presented., Comment: 20 pages, 5 figures, replaced with published version

The generalized Ward identity is derived for the vertex function of the weak vector current (VC) of nucleons within an effective theory with account of the isotopic symmetry breaking. The generalized Ward identity establishes a relationship between the form factor of the longitudinal weak VC component and the mass difference and the charge radii of an isotopic doublet on the mass shell. This relationship can be used to evaluate the form factors of both nucleons and nuclei with spin J = 1/2 and isospin I = 1/2. The reactions with large transferred momenta involving isotopic doublets, in which the mass splitting is maximized, offer the greatest promise for measuring the form factor. Numerical estimates of the form factor of the longitudinal weak VC component of a nucleon pair and eight nuclear isodoublets are presented.

We study a new mode of the neutrinoless and two-neutrino double-beta decays in which one of the electrons is emitted from the atom, while the other is directly produced in one of the available s1/2 or p1/2 subshells of the daughter ion. We calculate the phase-space factors, estimate the half-lives and derive the single-electron spectra for 0+ → 0+ ground-state nuclear transitions of the most relevant double-beta-decay isotopes: 48Ca, 76Ge, 82Se, 100Mo, 136Xe and 150Nd. The relativistic electron wave functions are evaluated at the nuclear radius by means of the multiconfiguration Dirac–Hartree–Fock package Grasp2K. We discuss the prospects for detecting these new modes in the tracking-and-calorimetry experiments NEMO-3 and SuperNEMO.

The determination of the absolute scale of the neutrino masses is one of the most challenging present questions in particle physics. The most stringent limit, $$m(\bar{\nu }_{\mathrm {e}})< 2$$ eV, was achieved for the electron anti-neutrino mass. Different approaches are followed to reach a sensitivity on neutrino masses in the sub-eV range. Among them, experiments exploring the beta decay or electron capture of suitable nuclides can provide information on the electron neutrino mass value. We present the electron capture $$^{163}$$ Ho experiment ECHo, which aims to investigate the electron neutrino mass in the sub-eV range by means of the analysis of the calorimetrically measured energy spectrum following electron capture in $$^{163}$$ Ho. A high precision and high statistics spectrum will be measured with arrays of metallic magnetic calorimeters. We discuss some of the essential aspects of ECHo to reach the proposed sensitivity: detector optimization and performance, multiplexed readout, $$^{163}$$ Ho source production and purification, as well as a precise theoretical and experimental parameterization of the calorimetric EC spectrum including in particular the value of $$Q_{\mathrm {EC}}$$ . We present preliminary results obtained with a first prototype of single channel detectors as well as a first 64-pixel chip with integrated micro-wave SQUID multiplexer, which will already allow to investigate $$m(\nu _{\mathrm {e}})$$ in the eV range.

The form factor f- of the longitudinal component of the weak vector current in pion β-decay is derived using the generalized Ward identity. The form factor is expressed through the pion mass difference and mean-square radii in the channels with angular momenta J = 1, 0 and isospins T = 1, 2.

The fundamental importance of searching for neutrinoless double-beta decay is widely recognized. Observation of the decay would tell us that the total lepton number is not conserved and that, consequently, neutrinos are massive Majorana fermions. The same statement could be made in the case of observing neutrinoless double-electron capture. We address the question of the sensitivity of the 0 ν e e decay to the effective mass of the Majorana neutrino. According to our estimates, in the case of 152Gd and 164Er the sensitivity can be comparable to the favored 0 ν β β decays of nuclei. The main uncertainty in the prediction of half-lives of the 0 ν e e decay stems from the lack of sufficient precision in measuring the mass difference between the parent and daughter atoms. More accurate measurements can be accomplished using the modern high-precision ion traps.

Phase transition from hadronic matter to quark-gluon matter is discussed for various regimes of temperature and baryon number density. For small and medium densities, the phase transition is accurately described in the framework of the Field Correlation Method, whereas at high density predictions are less certain and leave room for the phenomenological models. We study formation of multiquark states (MQS) at zero temperature and high density. Relevant MQS components of the nuclear matter can be described using a previously developed formalism of the quark compound bags (QCB). Partial-wave analysis of nucleon-nucleon scattering indicates the existence of 6QS which manifest themselves as poles of $P$-matrix. In the framework of the QCB model, we formulate a self-consistent system of coupled equations for the nucleon and 6QS propagators in nuclear matter and the G-matrix. The approach provides a link between high-density nuclear matter with the MQS components and the cumulative effect observed in reactions on the nuclei, which requires the admixture of MQS in the wave functions of nuclei kinematically. 6QS determine the natural scale of the density for a possible phase transition into the MQS phase of nuclear matter. Such a phase transition can lead to dynamic instability of newly born protoneutron stars and dramatically affect the dynamics of supernovae. Numerical simulations show that the phase transition may be a good remedy for the triggering supernova explosions in the spherically symmetric supernova models. A specific signature of the phase transition is an additional neutrino peak in the neutrino light curve. For a Galactic core-collapse supernova, such a peak could be resolved by the present neutrino detectors. The possibility of extracting the parameters of the phase of transition from observation of the neutrino signal is discussed also., Comment: 57 pages, 22 figures, 7 tables; RevTeX 4; submitted to Phys. Atom. Nucl

We consider new modes of two-neutrino and neutrinoless double-$\beta$ decays in which one $\beta$ 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-$\beta$ decays are strongly suppressed, their two-neutrino counterparts can be observed in the next-generation double-$\beta$-decay experiments, most notably SuperNEMO., Comment: 11 pages, 12 figures, 1 table; minor style corrections, accepted for publication in Phys. Rev. C

We discuss oscillations of two neutral atoms which proceed with the violation of lepton number. One of the neutral atoms is stable, the other one represents a quasistationary state subjected to electromagnetic deexcitation. The system of neutral atoms exhibits oscillations similar to those of the system of neutral kaons and neutron-antineutron oscillations in the nuclear medium. The underlying mechanism is a transition of two protons and two bound electrons to two neutrons p + p + eb− + eb− ↔ n + n. A signature of the oscillations might be an electromagnetic deexcitation of the involved unstable nucleus and atomic shell with the electron holes. A resonant enhancement of the neutrinoless double electron capture takes place when the atomic masses tend to be degenerate. Qualitative estimates show that in searches for lepton number violation oscillations of atoms might be a possible alternative to the conventional mechanism of the neutrinoless double β decay process with emission of two electrons.

Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an approximate scaling and heavy tails of the return distributions, long-ranged volatility-volatility correlations (volatility clustering) and return-volatility correlations (leverage effect). Free parameters of the model are fixed over the long term by fitting 100+ years of daily prices of the Dow Jones 30 Industrial Average. The multivariate probability density functions which we have constructed can be used for pricing derivative securities and risk management., Talk given by M. I. Krivoruchenko at the International Conference of Computational Methods in Sciences and Engineering 2003 (ICCMSE 2003), Kastoria, Greece, 12-16 September 2003; 16 pages, 4 Postscript figures, REVTeX. Extended abstract appeared in: Proceedings of the International Conference of Computational Methods in Sciences and Engineering 2003 (ICCMSE 2003), Ed. T.E. Simos (World Scientific Publishing Co., Singapore, 2003), pp. 323-326

The longitudinal form factors of the weak vector current of particles with spin $ J = 1/2 $ and isospin $ I = 1/2 $ are determined by the mass difference and the charge radii of members of the isotopic doublets. The most promising reactions to measure these form factors are the reactions with large momentum transfers involving the spin-1/2 isotopic doublets with a maximum mass splitting. Numerical estimates of longitudinal form factors are given for nucleons and eight nuclear spin-1/2 isotopic doublets., Comment: 6 pages. Talk given at the 10th MEDEX'15 meeting Matrix Elements for the Double-beta-decay Experiments, Prague, June 9-12, 2015

Dileptons represent a unique probe for nuclear matter under extreme conditions reached in heavy ion collisions. They allow the study of meson properties, like mass and decay width, at various density and temperature regimes. Up to now, in the Tubingen model for dilepton production, modification of meson properties in nuclear medium has been accounted for by allowing a density dependence of the mass (Brown-Rho scaling) together with an ad hoc dependence of the meson decay widths on the same variable. We use the extended vector meson dominance (eVMD) model to extract meson properties in nuclear matter by computing the in-medium meson spectral functions. Dilepton spectra for C+C at 1.0 and 2.0 AGeV are calculated and compared with previous results.

Systems under holonomic constraints are classified within the generalized Hamiltonian framework as second-class constraints systems. We show that each system of point particles with holonomic constraints has a hidden gauge symmetry which allows to quantize it in the original phase space as a first-class constraints system. The proposed method is illustrated with quantization of a point particle moving on an $n-1$-dimensional sphere $S^{n-1}$ as well as its field theory analog the O(n) nonlinear sigma model., Comment: 5 pages REVTeX, new references added

It is shown that the random-phase approximation (RPA) method with its nonlinear generalization, which was previously considered as approximation, reproduces the exact solutions of the Lipkin model. The nonlinear RPA is based on an equation nonlinear on eigenvectors and includes many-particle-many-hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number $N$ = 2 and, numerically, for $N$ = 20. This finding indicates that the nonlinear RPA is equivalent to the exact Schr\"{o}dinger equation, which opens up new possibilities for realistic calculations in many-body problems., Comment: 17 pages, 9 figures

We discuss a novel effect in neutrinoless double beta (0{\nu}{\beta}{\beta}) decay related with the fact that its underlying mechanisms take place in the nuclear matter environment. We study the neutrino exchange mechanism and demonstrate the possible impact of nuclear medium via Lepton Number Violating (LNV) 4-fermion interactions of neutrino with quarks from decaying nucleus. The net effect of these interactions is generation of an effective in-medium Majorana neutrino mass matrix. The enhanced rate of the 0{\nu}{\beta}{\beta}-decay can lead to the apparent incompatibility of observations of the 0{\nu}{\beta}{\beta}-decay with the value of the neutrino mass determined or restricted by the {\beta}-decay and cosmological data. The effective neutrino masses and mixing are calculated for the complete set of the relevant 4-fermion neutrino-quark operators. Using experimental data on the 0{\nu}{\beta}{\beta}-decay in combination with the {\beta}-decay and cosmological data we evaluate the characteristic scales of the LNV operators: {\Lambda} > 2.4 TeV., Comment: 5 pages REVTeX, accepted for publication in PRL

The production of d' dibaryons in heavy ion collisions due to the elementary process NN -> d' + pion is considered. The cross section NN -> d' + pion is estimated using the vacuum d' width = 0.5 MeV extracted from data on the double charge exchange reactions on nuclei. The d' production rate per single collision of heavy ions is estimated at an incident beam energy of 1 A GeV within the framework of the Quantum Molecular Dynamics transport model. We suggest to analyse the invariant mass spectrum of the NN + pion system in order to search for an abundance of events with the invariant mass of the d' dibaryon. The d' peak is found to exceed the statistical fluctuations of the background at a level of 6 standard deviations for 2 10^5 A central collisions of heavy ions with the atomic number A., 29 pages including 7 figures, REVTeX

The Green's functions are constructed and a one-loop calculation is given for the scalar and vector densities and for the equation of state of nuclear matter with a Bose condensate of dibaryons. This is the lowest approximation in the loop expansion of quantum hadrodynamics, sufficient to account for the presence of dibaryons not in the condensate in the heterophase nucleon-dibaryon matter. It leads to a finite effective nucleon mass and remains consistent with increasing the density., Comment: 14 pages, 1 figure

The effect of narrow dibaryon resonances on basic nuclear matter properties and on the structure of neutron stars is investigated in mean-field theory and in relativistic Hartree approximation. The existence of massive neutron stars imposes constraints on the coupling constants of the {omega} and {sigma} mesons with dibaryons. In the allowed region of the parameter space of the coupling constants, a Bose condensate of the light dibaryon candidates d{sub 1}(1920) and d{sup {prime}}(2060) is stable against compression. This proves the stability of the ground state of heterophase nuclear matter with a Bose condensate of light dibaryons. {copyright} {ital 1997} {ital The American Physical Society}

We investigate dense nuclear matter with a dibaryon Bose-Einstein condensate as a possible intermediate state before the quark-gluon phase transition. An exact analysis of this state of matter is presented in a one-dimensional model. The analysis is based on a reduction of the quantization rules for the N-body problem to N coupled algebraic transcendental equations. We observe that when the Fermi momentum approaches the resonance momentum, the one-particle distribution function increases near the Fermi surface. When the Fermi momentum is increased beyond the resonance momentum, the equation of state becomes softer. The observed behavior can be interpreted in terms of formation of a Bose-Einstein condensate of two-fermion resonances (dibaryons). In cold nuclear matter, it should occur if 2(m_N + epsilon_F) is greater or equal to m_D, where m_N and m_D are respectively the nucleon and dibaryon masses and epsilon_F is the nucleon Fermi energy.

The influence of nuclear matter on the properties of coherently produced resonances is discussed. It is shown that, in general, the mass distribution of resonance decay products has a two-component structure corresponding to decay outside and inside the nucleus. The first (narrow) component of the amplitude has a Breit-Wigner form determined by the vacuum values of mass and width of the resonance. The second (broad) component corresponds to interactions of the resonance with the nuclear medium. It can be also described by a Breit-Wigner shape with parameters depending e.g. on the nuclear density and on the cross section of the resonance-nucleon interaction. The resonance production is examined both at intermediate energies, where interactions with the nucleus can be considered as a series of successive local rescatterings, and at high energies, $E>E_{crit}$, where a change of interaction picture occurs. This change of mechanisms of the interactions with the nucleus is typical for the description within the Regge theory approach and is connected with the nonlocal nature of the reggeon interaction., 22 pages LaTeX, 1 Postscript file containing 7 figures; addition in beginning of Ch. 2; Nucl. Phys. A, to be published

A one-dimensional integral representation for isovector kaon form factor is constructed within the dispersion theory in terms of the pion form factor and the backwardπK-scattering amplitude. The normalization condition for isovector kaon form factor at zero momentum transfer gives a sum rule for theπK-scattering amplitude, with the use of which difference between thes-waveπK-scattering lengths in triplet and singlet isospin states is estimated to bea 0 3/2 - a 0 1/2 ≈μ− 1 whereμ is the pion mass. In agreement with the vector-meson-dominance model, deviations of the isovector kaon form factor from half of the pion form factor are found to be small.

The probability-generating function of the number of electron-positron pairs produced in a uniform electric field is constructed. The mean and variance of the numbers of pairs are calculated, and analytical expressions for the probability of low numbers of electron-positron pairs are given. A recursive formula is derived for evaluating the probability of any number of pairs. In electric fields of supercritical strength |eE| > ��m^2/ \ln 2, where e is the electron charge, E is the electric field, and m is the electron mass, a branch-point singularity of the probability-generating function penetrates the unit circle |z| = 1, which leads to the asymptotic divergence of the cumulative probability. This divergence indicates a failure of the continuum limit approximation. In the continuum limit and for any field strength, the positive definiteness of the probability is violated in the tail of the distribution. Analyticity, convergence, and positive definiteness are restored upon the summation over discrete levels of electrons in the normalization volume. Numerical examples illustrating the field strength dependence of the asymptotic behavior of the probability distribution are presented., 7 pages, REVTeX, 4 figures; new references added; a short version of this e-print has appeared in PRD

We provide an introduction to deformation quantisation and discuss the application of the formalism in solving the evolution problem for many-body systems in terms of semiclassical expansion. In any fixed order of expansion over the Planck's constant, the evolution problem can be reduced to a statistical-mechanics problem of calculating an ensemble of quantum characteristics in the phase space and their Jacobi fields. In comparison with the corresponding rules of classical statistical mechanics, the rules for computing the probabilities and time-dependent averages of observables are modified. The evolution equations represent a finite system of first-order ordinary differential equations for quantum trajectories in the phase space and the associated Jacobi fields. Quantum characteristics allow for the consistent inclusion of specific quantum effects, such as non-localities and coherence, in the description of the propagation of particles in the transport models. Since the late 1980s - early 1990s, when the first transport models were created for modeling heavy-ion collisions, computing power has increased by about five orders of magnitude. This dramatic rise in computing power makes it possible to include Jacobi fields in the collision dynamics, to extend beyond the classical treatment of phase-space trajectories, currently adopted in all of the transport models.

The theory of octupolar-excitation ion-cyclotron-resonance mass spectrometry is presented which predicts an increase of up to several orders of magnitude in resolving power under certain conditions. The new method has been applied for a direct Penning-trap mass-ratio determination of the $^{164}\mathrm{Er}\mathrm{\text{\ensuremath{-}}}^{164}\mathrm{Dy}$ mass doublet. $^{164}\mathrm{Er}$ is a candidate for the search for neutrinoless double-electron capture. However, the measured ${Q}_{ϵϵ}$ value of 25.07(12) keV results in a half-life of ${10}^{30}$ years for a 1 eV Majorana-neutrino mass.

Compound states manifest themselves as bound states, resonances, or primitives, and their character is determined by their interaction with the continuum. If the interaction experiences a perturbation, a compound state can change its manifestation. Phase analysis of nucleon-nucleon scattering indicates the existence of primitives in the 3S1, 1S0, and 3P0 channels. Electromagnetic interaction can shift primitives from the unitary cut, turning them into narrow resonances. We evaluate this effect on the 1S0 proton-proton scattering channel within the framework of the Simonov-Dyson model. We show that electromagnetic interaction turns a primitve with a mass of 2000 MeV into a dibaryon resonance of approximately the same mass and a width of 260 keV. Narrow resonances of a similar nature may occur in other nucleon-nucleon channels. Experimental confirmation of the existence of narrow resonances would have important implications for the theory of nucleon-nucleon interaction., Comment: 6 pages REVTeX, 2 eps figures; version to appear in PRC

The theory of octupolar-excitation ion-cyclotron-resonance mass spectrometry is presented which predicts an increase of up to several orders of magnitude in resolving power under certain conditions. The new method has been applied for a direct Penning-trap mass-ratio determination of the (164)Er-(164)Dy mass doublet. (164)Er is a candidate for the search for neutrinoless double-electron capture. However, the measured Q(ϵϵ) value of 25.07(12) keV results in a half-life of 10(30) years for a 1 eV Majorana-neutrino mass.

In the search for the nuclide with the largest probability for neutrinoless double-electron capture, we have determined the ${Q}_{ϵϵ}$ value between the ground states of $^{152}\mathrm{Gd}$ and $^{152}\mathrm{Sm}$ by Penning-trap mass-ratio measurements. The new ${Q}_{ϵϵ}$ value of 55.70(18) keV results in a half-life of ${10}^{26}\text{ }\text{ }\mathrm{yr}$ for a 1 eV neutrino mass. With this smallest half-life among known $0\ensuremath{\nu}ϵϵ$ transitions, $^{152}\mathrm{Gd}$ is a promising candidate for the search for neutrinoless double-electron capture.

The extended vector meson dominance model, which allows one to describe the electromagnetic form factors of nucleons obeying the asymptotic quark counting rule prescriptions and contains the minimal number of free parameters, is presented. We obtain a reasonable fit of form factors over the experimentally available spacelike region of momentum transfer and reasonable results in the timelike region.

Castillejo-Dalitz-Dyson (CDD) poles are known to be connected with bound states and resonances. We discuss a new type of CDD pole associated with primitives i.e., poles of the P matrix that correspond to zeros of the D function on the unitary cut. Low's scattering equation is generalized for amplitudes with primitives. The relationship between the CDD poles and the primitives is illustrated by a description of the S-wave nucleon-nucleon phase shifts., 5 pages REVTeX, 5 eps figures

Theories beyond the standard model include a number of new particles some of which might be light and weakly coupled to ordinary matter. Such particles affect equation of state of nuclear matter and can shift admissible masses of neutron stars to higher values. The internal structure of neutron stars is modified provided the ratio between coupling strength and mass squared of a weakly interacting light boson is above $g^2/\mu^2 \sim 25 ~\mathrm{GeV}^{-2}$. We provide limits on the couplings with the strange sector, which cannot be achieved from laboratory experiments analysis. When the couplings to the first family of quarks is considered the limits imposed by the neutron stars are not more stringent than the existing laboratory ones. The observations on neutron stars give evidence that equation of state of the $\beta$-equilibrated nuclear matter is stiffer than expected from many-body theory of nuclei and nuclear matter. A weakly interacting light vector boson coupled predominantly to the second family of the quarks can produce the required stiffening., Comment: 5 pages REVTeX, 2 pdf figures

The in-medium spectral functions of $\rho$ and $\omega$ mesons and the broadening of the nucleon resonances at finite baryon density are calculated self-consistently by combining a resonance dominance model for the vector meson production with an extended vector meson dominance model. The influence of the in-medium modifications of the vector meson properties on the dilepton spectrum in heavy-ion collisions is investigated. The dilepton spectrum is generated for the C+C reaction at 2.0$A$ GeV and compared with recent HADES Collaboration data. The collision dynamics is then described by the T\"ubingen relativistic quantum molecular dynamics transport model. We find that an iterative calculation of the vector meson spectral functions that takes into account the broadening of the nucleon resonances due to their increased in-medium decay branchings is convergent and provides a reasonable description of the experimental data in the mass region $0.45\leq M \leq 0.75$ GeV. On the other side, the theoretical calculations slightly underestimate the region $m_\pi\leq M \leq 0.4$ GeV. Popular in-medium scenarios such as a schematic collisional broadening and dropping vector mesons masses are discussed as well., Comment: v2: some references, comments and one Fig. added; accepted for publication in Phys. Rev. C

We report on a self-consistent calculation of the in-medium spectral functions of the rho and omega mesons at finite baryon density. The corresponding in-medium dilepton spectrum is generated and compared with HADES data. We find that an iterative calculation of the vector meson spectral functions provides a reasonable description of the experimental data., Comment: Talk given at International School of Nuclear Physics, 30th Course, "Heavy Ion Collisions from the Coulomb Barrier to the Quark Gluon Plasma", Erice, Italy, 16-24 Sep 2008

The phase-space paths introduced by Cheuk-Yin Wong in Phys. Rev.C25, 1460 (1982) and discussed recently in the literature can be used for calculation of evolution of the Wigner function to first order in the time increments only. The first-order solutions are helpful to determine the phase-space Green function in the framework of the phase-space path integral method., 2 pages, accepted to publication in PRC, section Comments

Contact $P$-wave interactions connected to the Larmor interaction of a magnetic dipole and Thomas spin precession in the filed of an electric quadrupole are described and their implications for spectroscopy of exotic $\Omega^{-}$-atoms are studied. In order to evaluate the magnitude of the contact $P$-wave interactions as compared to the conventional long-range interactions and the sensitivity of spectroscopic data to the $\Omega^{-}$-hyperon quadrupole moment, we consider $2P$ states of $\Omega ^{-}$ atoms formed with light stable nuclei with spins $I \geq 1/2$ and atomic numbers $Z \leq 10$. The energy level splitting caused by the contact interactions is 2-5 orders of magnitude smaller than the conventional long-range interactions. Strong decay widths of $p\Omega ^{-}$ atoms due to reactions $p\Omega^{-} \to \Lambda \Xi^{0}$ and $p\Omega^{-} \to \Sigma \Xi$, induced by $t$-channel kaon exchanges, are calculated. $\Omega ^{-}$ atoms formed with the light nuclei have strong widths 5-6 orders of magnitude higher than splitting caused by the contact interactions. The low-$L$ pattern in the energy spectra of intermediate- and high-$Z$ $\Omega ^{-}$ atoms thus cannot be observed. The $\Omega ^{-}$ quadrupole moment can be measured by observing $X$-rays from circular transitions between high-$L$ levels in $\Omega^{-}$ exotic atoms. The effect of strong interactions in $^{208}$Pb$\Omega ^{-}$ atoms is negligible starting from $L \sim 10$. The contact $P$-wave interactions exist in ordinary atoms and $\mu$-meson atoms., Comment: LaTeX 49 pages, 3 eps figures, replaced with published version

An introduction to physics of in-medium hadrons with special emphasis towards modification of vector meson properties in dense nuclear matter is given. We start from remarkable analogy between the in-medium behavior of atoms in gases and hadrons in nuclear matter. Modifications of vector meson widths and masses can be registered experimentally in heavy-ion collisions by detecting dilepton spectra from decays of nucleon resonances and light unflavored mesons including $\rho$- and $\omega$-mesons. Theoretical schemes for description of the in-medium hadrons are reviewed and recent experimental results of the NA60 and HADES collaborations on the dilepton production are discussed., Comment: 18 pages WS LaTeX, 9 eps figures. Lecture given at the 42-nd Predeal International Summer School in Nuclear Physics "Collective Motion and Phase Transitions in Nuclear Systems", 28 August - 9 September, Predeal, Romania