The Assessment of Light Environment with the First Generation Leds

The article describes experimental studies on the effectiveness of lighting installations (LI) with light-emitting diodes (LEDs). It is established that LED-based lighting does not cause a negative impact on the organ of vision and the human body as a whole. The changes in the functional parameters of the organ of sight, which occur during the visual performance has the corresponding limits of physiological fluctuations and are reversible. The integral indicators of the efficiency of LED-based lighting were estimated. The practical significance of the results was shown

Fermion with Three Mass Parameters

In the chapter, starting from a 20-component wave function in general Gel’fand-Yaglom approach a new wave equation for spin 1/2 fermion, which is characterized by three mass parameters, is derived. In absence of external field, three involved bispinors obey three separate Dirac-like equations with different masses M1, M2, M3. In presence of external electromagnetic fields or non-Euclidean background with nonvanishing Ricci scalar curvature, the main equation is not split into separated equations, instead a quite definite mixing of three Dirac-like equations arises. It is shown that a generalized equation for Majorana particle with three mass parameters exists as well, such a generalized Majorana equation is not split into three separated equations in curved space-time if the Ricci scalar of the space-time model does not vanish

Spin 1/2 Particle with Two Masses in External Magnetic Field

Equation for spin 1/2 particle with two mass states is investigated in presence of magnetic field. The problem reduces to a system of 4 linked 2-nd order differential equations. After diagonalization of the mixing term, separate equations for four different functions are derived, in which the spectral parameters coincide with the roots of a 4-th order polynomial. Solutions are constructed in terms of confluent hypergeometric functions; four series of energy spectrum are found. Numerical study of the spectra is performed. Physical energy levels for the two mass fermion differ from those for the ordinary Dirac fermion

РЕШЕНИЯ ФРОБЕНИУСА И АНАЛИЗ ТУННЕЛЬНОГО ЭФФЕКТА ДЛЯ ЧАСТИЦЫ СО СПИНОМ 1/2 В ПОЛЕ ШВАРЦШИЛЬДА

For a Dirac particle, the general mathematical study of the particle tunneling process through an effective potential barrier generated by the Schwarzschild black hole background is done. The study is based on the use of 8 Frobenius’ solutions of the related second-order differential equation with 3 regular and 2 irregular singularities of the rank 2. Solutions of the radial equations are constructed in explicit form, and the convergence of the involved power series is proved in the physical range f the variable (1, ). r∈ +∞ Results for the tunneling effect are significantly different for two situations: one when the particle falls on the barrier from the inside and another when the particle falls from the outside. The mathematical structure of the derived asymptotic relations is exact, however the analytical expressions for the involved convergent powers series are unknown, and a further study of penetration and reflection coefficients should be based on the numerical summation of the power series.Выполнено исследование эффекта туннелирования дираковских частиц через эффективный потенциальный барьер, порождаемый статической метрикой черной дыры Шварцшильда. Исследование основано на использовании решений Фробениуса возникающего дифференциального уравнения второго порядка с тремя регулярными особыми точками и двумя нерегулярными точками ранга 2. Решения радиального уравнения построены в явном виде, показана сходимость вовлеченных в них степенных рядов во всей физической области изменения переменной: от радиуса Шварцшильда до бесконечности. Результаты анализа процесса туннелирования существенно зависят от того, с какой стороны частицы падают на барьер: слева или справа от барьера. Математическая структура полученных асимптотических формул является точной, однако неизвестны аналитические выражения для сумм входящих в эти формулы степенных рядов. Эта часть исследования должна базироваться на численном суммировании рядов

Паулиевское приближение для векторной частицы с аномальным магнитным моментом во внешнем кулоновском поле

Herein, a spin 1 particle with anomalous magnetic moment in an external Coulomb field is studied. We start with the relativistic tensor system of the Proca type in Cartesian coordinates. In these equations the Γ parameter is present related to an additional characteristic of the particle. In the case of an external magnetic field, it is interpreted as an anomalous magnetic moment. In the presence of an external electric field, additional interaction terms are presented as well; moreover, the terms of the first and second orders in parameter Γ appear. The case of an external Coulomb field is considered in detail. In the nonrelativistic approximation a Pauli type equation is obtained. In the nonrelativistic equation the separation of the variables with the use of spherical vectors is realized. One separate 2-nd order differential equation is found, in which additional interaction terms are missing. Besides, we derive systems of two coupled 2-nd order equations wherein linear and quadratic in parameter Γ interaction terms are presented. Previously, another approach was developed for analyzing the vector particle with anomalous magnetic moment. It was based on the use of tetrad formalism and separation of the variables in the Duffin – Kemmer equation with the help of the Wigner function. The nonrelativistic approximation was performed directly in the system of radial equations. Besides, previously formal Frobenius type solutions for an arising 4-th order differential equation were constructed; however, physically interpretable energy spectra were not found. We have proved that the radial equations derived by different methods are the same up to a simple liner transformation over two radial functions. In this paper, we have obtained a simpler 4-th order equation, the construction of Frobenius solutions becomes technically easier, but physical energy spectra are not found either.Исследуется частица со спином 1 и аномальным магнитным моментом во внешнем кулоновском поле. Исходной является релятивистская тензорная система уравнений типа Прока в декартовой системе координат. В этих уравнениях присутствует параметр Γ, связанный с дополнительной характеристикой частицы. В случае внешнего магнитного поля он интерпретируется как аномальный магнитный момент. Дополнительные члены взаимодействия появляются также и при наличии электрического поля, причем в этом случае есть члены первого и второго порядков по параметру Γ. Детально рассматривается случай внешнего кулоновского поля. Проведена процедура нерелятивистского приближения, получено уравнение паулиевского типа. В нерелятивистском уравнении проведено разделение переменных с использованием аппарата шаровых векторов. Получено одно отдельное радиальное уравнение второго порядка, в котором дополнительные члены взаимодействия отсутствуют. Кроме того, выведена система двух связанных уравнений второго порядка, в них присутствуют линейные и квадратичные по параметру Γ дополнительные члены взаимодействия. Ранее был развит другой подход к анализу векторной частицы с аномальным магнитным моментом, основанный на использовании тетрадного формализма и разделении переменных в уравнении Даффина – Кеммера с применением функций Вигнера, после чего процедура нерелятивистского приближения была выполнена непосредственно в радиальной системе уравнений. Были построены в явном виде формальные решения Фробениуса возникающего уравнения 4-го порядка, однако физически интерпретируемых спектров получить не удалось. Показано, что полученные разными методами нерелятивистские радиальные уравнения совпадают с точностью до простого линейного преобразования над двумя функциями. В настоящей работе получено более простое уравнение 4-го порядка, при этом построение решений Фробениуса технически проще, но найти физически интерпретируемые спектры также не удается

ЧАСТИЦА СО СПИНОМ 1/2 И АНОМАЛЬНЫМ МАГНИТНЫМ МОМЕНТОМ В КУЛОНОВСКОМ ПОЛЕ

The Dirac equation for a spin 1/2 particle with anomalous magnetic moment in the applied Coulomb field is studied. The problem reduces to a second-order differential equation, in which the points x = 0,∞  are the irregular singular points of rank 2, and at the point x = 1 there is the regular singularity. The general structure of possible solutions of the equation is described, and the recurrent formulas for coefficients of relevant power series are derived. The case of an electrically neutral spin 1/2 particle with anomalous magnetic moment (neutron) is specified in detail; the problem reduces to a second-order differential equation with two irregular singular points x = 0,∞  of rank 2, which is referred the double confluent Heun equation. The qualitative analysis of the equations shows that the bound states for neutron in the Coulomb field can exist only for one definite sign of the anomalous magnetic moment. Исследовано уравнение Дирака для частицы со спином 1/2 и аномальным магнитным моментом во внешнем кулоновском поле. Задача приведена к дифференциальному уравнению второго порядка, в котором точки x =0 ,∞  являются нерегулярными особыми точками ранга 2, а в точке x = 1 имеется регулярная особенность. Описана общая структура решений уравнения, исследован характер зацепления коэффициентов в соответствующих степенных рядах. Выполнено ограничение к случаю электрически нейтральной частицы с аномальным магнитным моментом (нейтрону); задача сведена к более простому уравнению с двумя нерегулярными особыми точками x = 0,∞  ранга 2 (дважды вырожденному уравнению Гойна). Качественный анализ уравнений показывает, что связанные состояния для нейтрона в кулоновском поле могут существовать только при одном знаке величины аномального магнитного момента.

Скалярная частица со структурой Дарвина – Кокса во внешнем кулоновском поле

The generalized Klein – Fock – Gordon equation for a particle with the Darwin–Cox structure allowing for a charge distribution of a particle over a sphere of finite radius is studied with regard to the external Coulomb field. The separation of variables is carried out, the obtained radial equation is significantly more complicated than the equation in the case of ordinary particles, it has essentially singular points r = 0 of rank 3, r = ∞ of rank 2 and 4 regular singular points. In the case of a minimum orbital momentum l = 0, the structure of singularities is simplified: there are essentially singular points r = 0, r = ∞ of rank 2 and 4 regular singular points. Frobenius solutions of this equation are constructed and the structure of the 7-term recurrence relations for the coefficients of the arising power series is investigated. As an analytical quantization condition, the generalized transcendence requirement of solutions is used; it allows one to obtain a fourth-degree algebraic equation for energy levels. The equation has 4 sets of roots depending on the orbital moment l and the main quantum number k = 1,2,3,… . The numerical analysis shows that one of the sets of the roots 0 < εl,k < mc2 can be interpreted as those corresponding to certain bound states of the particle in the Coulomb field.Обобщенное уравнение Клейна – Фока – Гордона для частицы со структурой Дарвина – Кокса, учитывающее распределение заряда частицы по сфере конечного радиуса, исследуется с учетом внешнего кулоновского поля. Проведено разделение переменных, полученное радиальное уравнение сложнее уравнения в случае обычной частицы – оно имеет существенно особые точки r = 0 ранга 3, r = ∞ ранга 2 и 4 регулярные особые точки. В случае минимального орбитального момента l = 0 структура сингулярностей упрощается: есть существенно особые точки r = 0, r = ∞ ранга 2 и 4 регулярные особые точки. Построены решения Фробениуса этого уравнения, исследована структура рекуррентных соотношений для коэффициентов возникающего 7-членного степенного ряда. В качестве аналитического условия квантования используется обобщенное требование трансцендентности решений, которое позволяет получить алгебраическое уравнение 4-й степени для уровней энергии. Уравнение имеет 4 множества корней, зависящих от орбитального момента l и главного квантового числа k = 1,2,3,… . Численный анализ показывает, что одно из множеств корней 0 < εl,k < mc2 может интерпретироваться как отвечающее некоторым связанным состояниям частицы в кулоновском поле

Fermion with three mass parameters: general theory, interactions with external fields

In the paper, starting from Gel’fand-Yaglom approach a new 20-component wave equation for a spin ½ fermion, which is characterized by three mass parameters, is derived. On the base of 20-component wave function, three auxiliary bispinors are introduced, they in absence of external field for three bispinors obey to three separate Dirac-lice equations with different masses. It is shown that in presence of external fields, electromagnetic field and gravitational non-Euclidean background with nob-vanishing Ricci scalar curvature, the main equation is not split into separated equations, instead a quite definite mixing of three Dirac-lice equations arises. It is shown that a generalized equation for Majorana particle with three mass parameters exists as well, such a generalized Majorana equation is not split into three separated equations in curved background if Ricci scalar of space-time model does not vanish

Q fever in Bulgaria and Slovakia.

As a result of dramatic political and economic changes in the beginning of the 1990s, Q-fever epidemiology in Bulgaria has changed. The number of goats almost tripled; contact between goat owners (and their families) and goats, as well as goats and other animals, increased; consumption of raw goat milk and its products increased; and goats replaced cattle and sheep as the main source of human Coxiella burnetii infections. Hundreds of overt, serologically confirmed human cases of acute Q fever have occurred. Chronic forms of Q fever manifesting as endocarditis were also observed. In contrast, in Slovakia, Q fever does not pose a serious public health problem, and the chronic form of infection has not been found either in follow-ups of a Q-fever epidemic connected with goats imported from Bulgaria and other previous Q-fever outbreaks or in a serologic survey. Serologic diagnosis as well as control and prevention of Q fever are discussed

On describing bound states for a spin 1 particle in the external Coulomb field

The system of 10 radial equations, derived from the Duffin–Kemmer–Petiau equation for a spin 1 particle in the external Coulomb field, is studied. With the use of the space reflection operator, the whole system is split to independent subsystems, consisting of 4 and 6 equations, respectively. The most simple subsystem of 4 equations is solved in terms of hypergeometric functions, which gives the known energy spectrum. Also, the solutions and energy spectrum are found for the minimal value of the total angular momentum, j = 0. The second subsystem is expected to give the description of the other two series of bound states. With the use of the Lorentz generalized condition in presence of the Coulomb field, we prove that one of 6 radial function turns to be equal to zero. This simplifies the explicit form of the system of 6 equations, which contains only 5 unknown functions. Combining this system, we derive a new separated of 2-nd order system of differential equations for three radial functions. In particular, one of the equations turns out to be a rather simple one, and may be recognized as a confluent Heun equation. A series of bound states is constructed in terms of the so called transcendental confluent Heun functions, which provides us with solutions for the second class of bound states, with corresponding formula for energy levels. The subsystem of 6 equations, with no use of additional constraints due to the Lorentz condition, after excluding two non-differential relations reduces to the system of 1-st order differential equations for 4 functions fi, i = 1, 2, 3, 4. We derive the explicit form of a corresponding of 4-th order equation for each function. Among them, there are equations with two substantially different sets of singular points: 3 regular (or 2) and 2 irregular of rank 2. Any of these functions may be considered as a main one, and all remaining functions may be found in explicit form, in terms of the main one. From the four independent solutions of each 4-th order equation, only two solutions may be referred to series of bound states