Bound-state beta-decay of a neutron in a strong magnetic field

The beta-decay of a neutron into a bound $(pe^-)$ state and an antineutrino in the presence of a strong uniform magnetic field ($B \gtrsim 10^{13}$ G) is considered. The beta-decay process is treated within the framework of the standard model of weak interactions. A Bethe-Salpeter formalism is employed for description of the bound $(pe^-)$ system in a strong magnetic field. For the field strengths $10^{13}$ G$\lesssim B \lesssim10^{18}$ G the estimate for the ratio of the bound-state decay rate $w_b$ and the usual (continuum-state) decay rate $w_c$ is derived. It is found that in such strong magnetic fields $w_b/w_c \sim 0.1-0.4$. This is in contrast to the field-free case, where $w_b/w_c \simeq 4.2 \times 10^{-6}$ [J. N. Bahcall, Phys. Rev. {\bf 124}, 495 (1961); L. L. Nemenov, Sov. J. Nucl. Phys. {\bf 15}, 582 (1972); X. Song, J. Phys. G: Nucl. Phys. {\bf 13}, 1023 (1987)]. The dependence of the ratio $w_b/w_c$ on the magnetic field strength $B$ exhibits a logarithmic-like behavior. The obtained results can be important for applications in astrophysics and cosmology.Comment: 22 pages (revtex4), 1 figure; v2: more detailed discussion on astrophysical applications in conclusion section, accepted for publication in Phys. Rev.

Relativistic theory of inverse beta-decay of polarized neutron in strong magnetic field

The relativistic theory of the inverse beta-decay of polarized neutron, $\nu _{e} + n \to p + e ^{-}$, in strong magnetic field is developed. For the proton wave function we use the exact solution of the Dirac equation in the magnetic filed that enables us to account exactly for effects of the proton momentum quantization in the magnetic field and also for the proton recoil motion. The effect of nucleons anomalous magnetic moments in strong magnetic fields is also discussed. We examine the cross section for different energies and directions of propagation of the initial neutrino accounting for neutrons polarization. It is shown that in the super-strong magnetic field the totally polarized neutron matter is transparent for neutrinos propagating antiparallel to the direction of polarization. The developed relativistic approach can be used for calculations of cross sections of the other URCA processes in strong magnetic fields.Comment: 41 pages in LaTex including 11 figures in PostScript, discussion on nucleons AMM interaction with magnetic field is adde

Upper and Lower Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems

In this paper we study a class of dynamical systems defined by Pfaffian maps. It is a sub-class of o-minimal dynamical systems which capture rich continuous dynamics and yet can be studied using finite bisimulations. The existence of finite bisimulations for o-minimal dynamical and hybrid systems has been shown by several authors; see e.g. Brihaye et al (2004), Davoren (1999), Lafferriere et al (2000). The next natural question to investigate is how the sizes of such bisimulations can be bounded. The first step in this direction was done by Korovina et al (2004) where a double exponential upper bound was shown for Pfaffian dynamical and hybrid systems. In the present paper we improve this bound to a single exponential upper bound. Moreover we show that this bound is tight in general, by exhibiting a parameterized class of systems on which the exponential bound is attained. The bounds provide a basis for designing efficient algorithms for computing bisimulations, solving reachability and motion planning problems

Black-hole concept of a point-like nucleus with supercritical charge

The Dirac equation for an electron in the central Coulomb field of a point-like nucleus with the charge greater than 137 is considered. This singular problem, to which the fall-down onto the centre is inherent, is addressed using a new approach, based on a black-hole concept of the singular centre and capable of producing cut-off-free results. To this end the Dirac equation is presented as a generalized eigenvalue boundary problem of a self-adjoint operator. The eigenfunctions make complete sets, orthogonal with a singular measure, and describe particles, asymptotically free and delta-function-normalizable both at infinity and near the singular centre $r=0$. The barrier transmission coefficient for these particles responsible for the effects of electron absorption and spontaneous electron-positron pair production is found analytically as a function of electron energy and charge of the nucleus. The singular threshold behaviour of the corresponding amplitudes substitutes for the resonance behaviour, typical of the conventional theory, which appeals to a finite-size nucleus.Comment: 22 pages, 5 figures, LATEX requires IOPAR

Recent Advances in Σ-definability over Continuous Data Types

The purpose of this paper is to survey our recent research in computability and definability over continuous data types such as the real numbers, real-valued functions and functionals. We investigate the expressive power and algorithmic properties of the language of Sigma-formulas intended to represent computability over the real numbers. In order to adequately represent computability we extend the reals by the structure of hereditarily finite sets. In this setting it is crucial to consider the real numbers without equality since the equality test is undecidable over the reals. We prove Engeler's Lemma for Sigma-definability over the reals without the equality test which relates Sigma-definability with definability in the constructive infinitary language L_{omega_1 omega}. Thus, a relation over the real numbers is Sigma-definable if and only if it is definable by a disjunction of a recursively enumerable set of quantifier free formulas. This result reveals computational aspects of Sigma-definability and also gives topological characterisation of Sigma-definable relations over the reals without the equality test. We also illustrate how computability over the real numbers can be expressed in the language of Sigma-formulas

Effect of exogenous factors on somatic health and autonomic nervous regulation in children and young people

Монографія присвячена аналізу впливу зовнішних чинників та особливостей способу життя на стан здоров’я, зміни автономної нервової регуляції та стан серцево-судинної системи, які здатні призводити до порушень стану здоров’я у дітей та юнацтва

Взаємозв’язки аліментарних та мікросоціальних факторів із захворюваністю дітей та молоді

In different age groups morbidity essentially depends on microsocial factors, nutritional and behavioral fisbits, preceding level of morbidity, but the significance of these factors varies with age. For the girls unbalance of a nutrition and reduced physical activity are more expressed in comparison with the young men. The observable gender morbidity differences, probably, are connected with differences in the indicated factors and with a different level of health generated in childhood and adolescent age.В різних вікових групах захворюваність істотно залежить від мікросоціальних чинників, аліментарних і поведінкових звичок, від попереднього рівня захворюваності, але значимість чинників змінюється з віком. У дівчат з’являються більш виражений, порівняно з хлопцями, дисбаланс харчування і знижена фізична активність. Міжстатеві відмінності в захворюваності, імовірно, пов'язані як із відмінностями в указаних чинниках, так і з різним рівнем здоров’я, сформованим ще в дитинстві та підлітковому віці