A calorimeter is an object used for calorimetry, or the process of measuring the heat of chemical reactions or physical changes as well as heat capacity. Differential scanning calorimeters, isothermal micro calorimeters, titration calorimeters and accelerated rate calorimeters are among the most common types. A simple calorimeter just consists of a thermometer attached to a metal container full of water suspended above a combustion chamber, it is one of the measurement devices used in the study of thermodynamics and biochemistry. To find the enthalpy change per mole of a substance A in a reaction between two substances A and B, the substances are separately added to a calorimeter and the initial and final temperatures are noted. Multiplying the temperature change by the mass and specific heat capacities of the substances gives a value for the energy given off or absorbed during the reaction. Dividing the energy change by how many moles of A were present gives its enthalpy change of reaction.
Q = C v Where q is the amount of heat according to the change in temperature measured in joules and Cv is the heat capacity of the calorimeter, a value associated with each individual apparatus in units of energy per temperature. In 1761 Joseph Black introduced the idea of latent heat which lead to creation of the first ice-calorimeters. In 1780, Antoine Lavoisier used the heat from the guinea pig's respiration to melt snow surrounding his apparatus, showing that respiratory gas exchange is combustion, similar to a candle burning. Lavoisier dubbed this apparatus the calorimeter, based on both Latin roots. One of the first ice calorimeters was used in the winter of 1782 by Lavoisier and Pierre-Simon Laplace, which relied on the heat required to melt ice to water to measure the heat released from chemical reactions. An adiabatic calorimeter is a calorimeter used to examine a runaway reaction. Since the calorimeter runs in an adiabatic environment, any heat generated by the material sample under test causes the sample to increase in temperature, thus fueling the reaction.
No adiabatic calorimeter is adiabatic - some heat will be lost by the sample to the sample holder. A mathematical correction factor, known as the phi-factor, can be used to adjust the calorimetric result to account for these heat losses; the phi-factor is the ratio of the thermal mass of the sample and sample holder to the thermal mass of the sample alone. A reaction calorimeter is a calorimeter in which a chemical reaction is initiated within a closed insulated container. Reaction heats are measured and the total heat is obtained by integrating heatflow versus time; this is the standard used in industry to measure heats since industrial processes are engineered to run at constant temperatures. Reaction calorimetry can be used to determine maximum heat release rate for chemical process engineering and for tracking the global kinetics of reactions. There are four main methods for measuring the heat in reaction calorimeter: The cooling/heating jacket controls either the temperature of the process or the temperature of the jacket.
Heat is measured by monitoring the temperature difference between heat transfer fluid and the process fluid. In addition, fill volumes, specific heat, heat transfer coefficient have to be determined to arrive at a correct value, it is possible with this type of calorimeter to do reactions at reflux, although it is less accurate. The cooling/heating jacket controls the temperature of the process. Heat is measured by monitoring the heat lost by the heat transfer fluid. Power compensation uses a heater placed within the vessel to maintain a constant temperature; the energy supplied to this heater can be varied as reactions require and the calorimetry signal is purely derived from this electrical power. Constant flux calorimetry is derived from heat balance calorimetry and uses specialized control mechanisms to maintain a constant heat flow across the vessel wall. A bomb calorimeter is a type of constant-volume calorimeter used in measuring the heat of combustion of a particular reaction. Bomb calorimeters have to withstand the large pressure within the calorimeter as the reaction is being measured.
Electrical energy is used to ignite the fuel. When the air is escaping through the copper tube it will heat up the water outside the tube; the change in temperature of the water allows for calculating calorie content of the fuel. In more recent calorimeter designs, the whole bomb, pressurized with excess pure oxygen and containing a weighed mass of a sample and a small fixed amount of water, is submerged under a known volume of water before the charge is electrically ignited; the bomb, with the known mass of the sample and oxygen, form a closed system — no gases escape during the reaction. The weighed reactant put inside the steel container is ignited. Energy is released by the combustion and heat flow from this crosses the stainless steel wall, thus raising the temperature of the steel bomb, its contents, the surrounding water jacket; the temperature change in the water is accurately measured with a thermometer. This reading, along with a bomb factor (which is dependent on the heat capacity of t
The nuclear force is a force that acts between the protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nuclear force identically. Since protons have charge +1 e, they experience an electric force that tends to push them apart, but at short range the attractive nuclear force is strong enough to overcome the electromagnetic force; the nuclear force binds nucleons into atomic nuclei. The nuclear force is powerfully attractive between nucleons at distances of about 1 femtometre, but it decreases to insignificance at distances beyond about 2.5 fm. At distances less than 0.7 fm, the nuclear force becomes repulsive. This repulsive component is responsible for the physical size of nuclei, since the nucleons can come no closer than the force allows. By comparison, the size of an atom, measured in angstroms, is five orders of magnitude larger; the nuclear force is not simple, since it depends on the nucleon spins, has a tensor component, may depend on the relative momentum of the nucleons.
The strong nuclear force is one of the fundamental forces of nature. The nuclear force plays an essential role in storing energy, used in nuclear power and nuclear weapons. Work is required to bring charged protons together against their electric repulsion; this energy is stored when the protons and neutrons are bound together by the nuclear force to form a nucleus. The mass of a nucleus is less than the sum total of the individual masses of the protons and neutrons; the difference in masses is known as the mass defect, which can be expressed as an energy equivalent. Energy is released; this energy is the electromagnetic potential energy, released when the nuclear force no longer holds the charged nuclear fragments together. A quantitative description of the nuclear force relies on equations that are empirical; these equations model the internucleon potential energies, or potentials. The constants for the equations are phenomenological, that is, determined by fitting the equations to experimental data.
The internucleon potentials attempt to describe the properties of nucleon–nucleon interaction. Once determined, any given potential can be used in, e.g. the Schrödinger equation to determine the quantum mechanical properties of the nucleon system. The discovery of the neutron in 1932 revealed that atomic nuclei were made of protons and neutrons, held together by an attractive force. By 1935 the nuclear force was conceived to be transmitted by particles called mesons; this theoretical development included a description of the Yukawa potential, an early example of a nuclear potential. Mesons, predicted by theory, were discovered experimentally in 1947. By the 1970s, the quark model had been developed, by which the mesons and nucleons were viewed as composed of quarks and gluons. By this new model, the nuclear force, resulting from the exchange of mesons between neighboring nucleons, is a residual effect of the strong force. While the nuclear force is associated with nucleons, more this force is felt between hadrons, or particles composed of quarks.
At small separations between nucleons the force becomes repulsive, which keeps the nucleons at a certain average separation if they are of different types. This repulsion arises from the Pauli exclusion force for identical nucleons. A Pauli exclusion force occurs between quarks of the same type within nucleons, when the nucleons are different. At distances larger than 0.7 fm the force becomes attractive between spin-aligned nucleons, becoming maximal at a center–center distance of about 0.9 fm. Beyond this distance the force drops exponentially, until beyond about 2.0 fm separation, the force is negligible. Nucleons have a radius of about 0.8 fm. At short distances, the attractive nuclear force is stronger than the repulsive Coulomb force between protons. However, the Coulomb force between protons has a much greater range as it varies as the inverse square of the charge separation, Coulomb repulsion thus becomes the only significant force between protons when their separation exceeds about 2 to 2.5 fm.
The nuclear force has a spin-dependent component. The force is stronger for particles with their spins aligned than for those with their spins anti-aligned. If two particles are the same, such as two neutrons or two protons, the force is not enough to bind the particles, since the spin vectors of two particles of the same type must point in opposite directions when the particles are near each other and are in the same quantum state; this requirement for fermions stems from the Pauli exclusion principle. For fermion particles of different types, such as a proton and neutron, particles may be close to each other and have aligned spins without violating the Pauli exclusion principle, the nuclear force may bind them, since the nuclear force is much stronger for spin-aligned particles, but if the particles' spins are anti-aligned the nuclear force is too weak to bind them if they are of different types. The nuclear force has a tensor component which depends on the interaction between the nucleon spins and the angular momentum of the nucleons, leading to deformation from a simple spherical shape
In experimental and applied particle physics, nuclear physics, nuclear engineering, a particle detector known as a radiation detector, is a device used to detect, and/or identify ionizing particles, such as those produced by nuclear decay, cosmic radiation, or reactions in a particle accelerator. Detectors can measure the particle energy and other attributes such as momentum, charge, particle type, in addition to registering the presence of the particle. Many of the detectors invented and used so far are ionization detectors and scintillation detectors. Historical examples Bubble chamber Wilson cloud chamber Photographic plateDetectors for radiation protection The following types of particle detector are used for radiation protection, are commercially produced in large quantities for general use within the nuclear and environmental fields. Dosimeter Electroscope Gaseous ionization detector Geiger-Müller tube Ionization chamber Proportional counter Scintillation counter Semiconductor detectorCommonly used detectors for particle and nuclear physics Gaseous ionization detector Ionization chamber Proportional counter Multiwire proportional chamber Drift chamber Time projection chamber Geiger-Müller tube Spark chamber Solid-state detectors: Semiconductor detector and variants including CCDs Silicon Vertex Detector Solid-state nuclear track detector Cherenkov detector Ring-imaging Cherenkov detector Scintillation counter and associated photomultiplier, photodiode, or avalanche photodiode Lucas cell Time of flight detector Transition radiation detector Calorimeter Microchannel plate detector Neutron detector Modern detectors in particle physics combine several of the above elements in layers much like an onion.
Detectors designed for modern accelerators are huge, both in cost. The term counter is used instead of detector when the detector counts the particles but does not resolve its energy or ionization. Particle detectors can usually track ionizing radiation. If their main purpose is radiation measurement, they are called radiation detectors, but as photons are particles, the term particle detector is still correct. At CERN for the LHC CMS ATLAS ALICE LHCb for the LEP Aleph Delphi L3 Opal for the SPS The COMPASS Experiment Gargamelle NA61/SHINE At Fermilab for the Tevatron CDF D0 Mu2e At DESY for HERA H1 HERA-B HERMES ZEUS At BNL for the RHIC PHENIX Phobos STAR At SLAC for the PeP-II BaBar for the SLC SLD At Cornell for CESR CLEO CUSB At BINP for the VEPP-2M and VEPP-2000 ND SND CMD for the VEPP-4 KEDR Others MECO from UC Irvine For International Linear Collider CALICE Antarctic Muon And Neutrino Detector Array Cryogenic Dark Matter Search Super-Kamiokande Alpha Magnetic Spectrometer JEDI Counting efficiency List of particles Tail-pulse generator Jones, R. Clark.
"A New Classification System for Radiation Detectors". Journal of the Optical Society of America. 39: 327–341. Doi:10.1364/JOSA.39.000327. Jones, R. Clark. "Erratum: The Ultimate Sensitivity of Radiation Detectors". Journal of the Optical Society of America. 39: 343. Doi:10.1364/JOSA.39.000343. Jones, R. Clark. "Factors of Merit for Radiation Detectors". Journal of the Optical Society of America. 39: 344–356. Doi:10.1364/JOSA.39.000344. Filmstrips"Radiation detectors". H. M. Stone Productions, Schloat. Tarrytown, N. Y. Prentice-Hall Media, 1972. General InformationGrupen, C.. "Physics of Particle Detection". AIP Conference Proceedings, Instrumentation in Elementary Particle Physics, VIII. 536. Istanbul: Dordrecht, D. Reidel Publishing Co. pp. 3–34. ArXiv:physics/9906063. Doi:10.1063/1.1361756
Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force exhibits electromagnetic fields such as electric fields, magnetic fields, light, is one of the four fundamental interactions in nature; the other three fundamental interactions are the strong interaction, the weak interaction, gravitation. At high energy the weak force and electromagnetic force are unified as a single electroweak force. Electromagnetic phenomena are defined in terms of the electromagnetic force, sometimes called the Lorentz force, which includes both electricity and magnetism as different manifestations of the same phenomenon; the electromagnetic force plays a major role in determining the internal properties of most objects encountered in daily life. Ordinary matter takes its form as a result of intermolecular forces between individual atoms and molecules in matter, is a manifestation of the electromagnetic force.
Electrons are bound by the electromagnetic force to atomic nuclei, their orbital shapes and their influence on nearby atoms with their electrons is described by quantum mechanics. The electromagnetic force governs all chemical processes, which arise from interactions between the electrons of neighboring atoms. There are numerous mathematical descriptions of the electromagnetic field. In classical electrodynamics, electric fields are described as electric potential and electric current. In Faraday's law, magnetic fields are associated with electromagnetic induction and magnetism, Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents; the theoretical implications of electromagnetism the establishment of the speed of light based on properties of the "medium" of propagation, led to the development of special relativity by Albert Einstein in 1905. Electricity and magnetism were considered to be two separate forces; this view changed, with the publication of James Clerk Maxwell's 1873 A Treatise on Electricity and Magnetism in which the interactions of positive and negative charges were shown to be mediated by one force.
There are four main effects resulting from these interactions, all of which have been demonstrated by experiments: Electric charges attract or repel one another with a force inversely proportional to the square of the distance between them: unlike charges attract, like ones repel. Magnetic poles attract or repel one another in a manner similar to positive and negative charges and always exist as pairs: every north pole is yoked to a south pole. An electric current inside a wire creates a corresponding circumferential magnetic field outside the wire, its direction depends on the direction of the current in the wire. A current is induced in a loop of wire when it is moved toward or away from a magnetic field, or a magnet is moved towards or away from it. While preparing for an evening lecture on 21 April 1820, Hans Christian Ørsted made a surprising observation; as he was setting up his materials, he noticed a compass needle deflected away from magnetic north when the electric current from the battery he was using was switched on and off.
This deflection convinced him that magnetic fields radiate from all sides of a wire carrying an electric current, just as light and heat do, that it confirmed a direct relationship between electricity and magnetism. At the time of discovery, Ørsted did not suggest any satisfactory explanation of the phenomenon, nor did he try to represent the phenomenon in a mathematical framework. However, three months he began more intensive investigations. Soon thereafter he published his findings, proving that an electric current produces a magnetic field as it flows through a wire; the CGS unit of magnetic induction is named in honor of his contributions to the field of electromagnetism. His findings resulted in intensive research throughout the scientific community in electrodynamics, they influenced French physicist André-Marie Ampère's developments of a single mathematical form to represent the magnetic forces between current-carrying conductors. Ørsted's discovery represented a major step toward a unified concept of energy.
This unification, observed by Michael Faraday, extended by James Clerk Maxwell, reformulated by Oliver Heaviside and Heinrich Hertz, is one of the key accomplishments of 19th century mathematical physics. It has had far-reaching consequences, one of, the understanding of the nature of light. Unlike what was proposed by the electromagnetic theory of that time and other electromagnetic waves are at present seen as taking the form of quantized, self-propagating oscillatory electromagnetic field disturbances called photons. Different frequencies of oscillation give rise to the different forms of electromagnetic radiation, from radio waves at the lowest frequencies, to visible light at intermediate frequencies, to gamma rays at the highest frequencies. Ørsted was not the only person to examine the relationship between magnetism. In 1802, Gian Domenico Romagnosi, an Italian legal scholar, deflected a magnetic needle using a Voltaic pile; the factual setup of the experiment is not clear, so if current flew across the needle or not.
An account of the discovery was published in 1802 in an Italian newspaper, but it was overlooked by the contemporary scientific community, because Romagnosi did not belong to this community. An earlier, neglected, connec
Calorimetry is the science or act of measuring changes in state variables of a body for the purpose of deriving the heat transfer associated with changes of its state due, for example, to chemical reactions, physical changes, or phase transitions under specified constraints. Calorimetry is performed with a calorimeter; the word calorimetry is derived from the Latin word calor, meaning heat and the Greek word μέτρον, meaning measure. Scottish physician and scientist Joseph Black, the first to recognize the distinction between heat and temperature, is said to be the founder of the science of calorimetry. Indirect calorimetry calculates heat that living organisms produce by measuring either their production of carbon dioxide and nitrogen waste, or from their consumption of oxygen. Lavoisier noted in 1780 that heat production can be predicted from oxygen consumption this way, using multiple regression; the dynamic energy budget theory explains. Heat generated by living organisms may be measured by direct calorimetry, in which the entire organism is placed inside the calorimeter for the measurement.
A used modern instrument is the differential scanning calorimeter, a device which allows thermal data to be obtained on small amounts of material. It involves heating the sample at a controlled rate and recording the heat flow either into or from the specimen. Calorimetry requires that a reference material that changes temperature have known definite thermal constitutive properties; the classical rule, recognized by Clausius and by Kelvin, is that the pressure exerted by the calorimetric material is and determined by its temperature and volume. There are many materials that do not comply with this rule, for them, the present formula of classical calorimetry does not provide an adequate account. Here the classical rule is assumed to hold for the calorimetric material being used, the propositions are mathematically written: The thermal response of the calorimetric material is described by its pressure p as the value of its constitutive function p of just the volume V and the temperature T. All increments are here required to be small.
This calculation refers to a domain of volume and temperature of the body in which no phase change occurs, there is only one phase present. An important assumption here is continuity of property relations. A different analysis is needed for phase change When a small increment of heat is gained by a calorimetric body, with small increments, δ V of its volume, δ T of its temperature, the increment of heat, δ Q, gained by the body of calorimetric material, is given by δ Q = C T δ V + C V δ T where C T denotes the latent heat with respect to volume, of the calorimetric material at constant controlled temperature T; the surroundings' pressure on the material is instrumentally adjusted to impose a chosen volume change, with initial volume V. To determine this latent heat, the volume change is the independently instrumentally varied quantity; this latent heat is not one of the used ones, but is of theoretical or conceptual interest. C V denotes the heat capacity, of the calorimetric material at fixed constant volume V, while the pressure of the material is allowed to vary with initial temperature T.
The temperature is forced to change by exposure to a suitable heat bath. It is customary to write C V as C V, or more as C V; this latent heat is one of the two used ones. The latent heat with respect to volume is the heat required for unit increment in volume at constant temperature, it can be said to be'measured along an isotherm', the pressure the material exerts is allowed to vary according to its constitutive law p = p. For a given material, it can have a positive or negative sign or exceptionally it can be zero, this can depend on the temperature, as it does for water about 4 C; the concept of latent heat with respect to volume was first recognized by Joseph Black in 1762. The term'latent heat of expansion' is used; the latent heat with respect to
In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object. Energy is a conserved quantity; the SI unit of energy is the joule, the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton. Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object's position in a force field, the elastic energy stored by stretching solid objects, the chemical energy released when a fuel burns, the radiant energy carried by light, the thermal energy due to an object's temperature. Mass and energy are related. Due to mass–energy equivalence, any object that has mass when stationary has an equivalent amount of energy whose form is called rest energy, any additional energy acquired by the object above that rest energy will increase the object's total mass just as it increases its total energy. For example, after heating an object, its increase in energy could be measured as a small increase in mass, with a sensitive enough scale.
Living organisms require exergy to stay alive, such as the energy. Human civilization requires energy to function, which it gets from energy resources such as fossil fuels, nuclear fuel, or renewable energy; the processes of Earth's climate and ecosystem are driven by the radiant energy Earth receives from the sun and the geothermal energy contained within the earth. The total energy of a system can be subdivided and classified into potential energy, kinetic energy, or combinations of the two in various ways. Kinetic energy is determined by the movement of an object – or the composite motion of the components of an object – and potential energy reflects the potential of an object to have motion, is a function of the position of an object within a field or may be stored in the field itself. While these two categories are sufficient to describe all forms of energy, it is convenient to refer to particular combinations of potential and kinetic energy as its own form. For example, macroscopic mechanical energy is the sum of translational and rotational kinetic and potential energy in a system neglects the kinetic energy due to temperature, nuclear energy which combines utilize potentials from the nuclear force and the weak force), among others.
The word energy derives from the Ancient Greek: translit. Energeia, lit.'activity, operation', which appears for the first time in the work of Aristotle in the 4th century BC. In contrast to the modern definition, energeia was a qualitative philosophical concept, broad enough to include ideas such as happiness and pleasure. In the late 17th century, Gottfried Leibniz proposed the idea of the Latin: vis viva, or living force, which defined as the product of the mass of an object and its velocity squared. To account for slowing due to friction, Leibniz theorized that thermal energy consisted of the random motion of the constituent parts of matter, although it would be more than a century until this was accepted; the modern analog of this property, kinetic energy, differs from vis viva only by a factor of two. In 1807, Thomas Young was the first to use the term "energy" instead of vis viva, in its modern sense. Gustave-Gaspard Coriolis described "kinetic energy" in 1829 in its modern sense, in 1853, William Rankine coined the term "potential energy".
The law of conservation of energy was first postulated in the early 19th century, applies to any isolated system. It was argued for some years whether heat was a physical substance, dubbed the caloric, or a physical quantity, such as momentum. In 1845 James Prescott Joule discovered the generation of heat; these developments led to the theory of conservation of energy, formalized by William Thomson as the field of thermodynamics. Thermodynamics aided the rapid development of explanations of chemical processes by Rudolf Clausius, Josiah Willard Gibbs, Walther Nernst, it led to a mathematical formulation of the concept of entropy by Clausius and to the introduction of laws of radiant energy by Jožef Stefan. According to Noether's theorem, the conservation of energy is a consequence of the fact that the laws of physics do not change over time. Thus, since 1918, theorists have understood that the law of conservation of energy is the direct mathematical consequence of the translational symmetry of the quantity conjugate to energy, namely time.
In 1843, James Prescott Joule independently discovered the mechanical equivalent in a series of experiments. The most famous of them used the "Joule apparatus": a descending weight, attached to a string, caused rotation of a paddle immersed in water insulated from heat transfer, it showed that the gravitational potential energy lost by the weight in descending was equal to the internal energy gained by the water through friction with the paddle. In the International System of Units, the unit of energy is the joule, named after James Prescott Joule, it is a derived unit. It is equal to the energy expended in applying a force of one newton through a distance of one metre; however energy is expressed in many other units not part of the SI, such as ergs, British Thermal Units, kilowatt-hours and kilocalories, which require a conversion factor when expressed in SI units. The SI unit of energy rate is the watt, a joule per second. Thus, one joule is one watt-second, 3600 joules equal one wa
Total absorption spectroscopy
Total absorption spectroscopy is a measurement technique that allows the measurement of the gamma radiation emitted in the different nuclear gamma transitions that may take place in the daughter nucleus after its unstable parent has decayed by means of the beta decay process. This technique can be used for beta decay studies related to beta feeding measurements within the full decay energy window for nuclei far from stability, it is implemented with a special type of detector, the "total absorption spectrometer", made of a scintillator crystal that completely surrounds the activity to be measured, covering a solid angle of 4π. In an ideal case, it should be thick enough to have a peak efficiency close to 100%, in this way its total efficiency is very close to 100%, it should be blind to any other type of radiation. The gamma rays produced in the decay under study are collected by photomultipliers attached to the scintillator material; this technique may solve the problem of the Pandemonium effect.
There is a change in philosophy when measuring with a TAS. Instead of detecting the individual gamma rays, it will detect the gamma cascades emitted in the decay; the final energy spectrum will not be a collection of different energy peaks coming from the different transitions, but a collection of peaks situated at an energy, the sum of the different energies of all the gammas of the cascade emitted from each level. This means that the energy spectrum measured with a TAS will be in reality a spectrum of the levels of the nuclei, where each peak is a level populated in the decay. Since the efficiency of these detectors is close to 100%, it is possible to see the feeding to the high excitation levels that can not be seen by high-resolution detectors; this makes total absorption spectroscopy the best method to measure beta feedings and provide accurate beta intensity distributions for complex decay schemes. In an ideal case, the measured spectrum would be proportional to the beta feeding, but a real TAS has limited efficiency and resolution, the Iβ has to be extracted from the measured spectrum, which depends on the spectrometer response.
The analysis of TAS data is not simple: to obtain the strength from the measured data, a deconvolution process should be applied. The complex analysis of the data measured with the TAS can be reduced to the solution of a linear problem: d = Ri given that it relates the measured data with the feedings from which the beta intensity distribution Iβ can be obtained. R is the response matrix of the detector; the function R depends of the detector but of the particular level scheme, being measured. To be able to extract the value of i from the data d the equation has to be inverted; this can not be done because there is similar response to the feeding of adjacent levels when they are at high excitation energies where the level density is high. In other words, this is one of the so-called "ill-posed" problems, for which several sets of parameters can reproduce the same data set. To find i, the response has to be obtained for which the branching ratios and a precise simulation of the geometry of the detector are needed.
The higher the efficiency of the TAS used, the lower the dependence of the response on the branching ratios will be. It is possible to introduce the unknown branching ratios by hand from a plausible guess. A good guess can be calculated by means of the Statistical Model; the procedure to find the feedings is iterative: using the expectation-maximization algorithm to solve the inverse problem, Then the procedure to find the feedings is iterative: using the expectation-maximization algorithm to solve the inverse problem, the feedings are extracted. Repeating this procedure iteratively in a reduced number of steps, the data is reproduced; the best way to handle this problem is to keep a set of discrete levels at low excitation energies and a set of binned levels at high energies. The set at low energies can be taken from databases; the set at high energies does not overlap with the known part. At the end of this calculation, the whole region of levels inside the Q value window is binned. At this stage of the analysis it is important to know the internal conversion coefficients for the transitions connecting the known levels.
The internal conversion coefficient is defined as the number of de-excitations via e− emission over those via γ emission. If internal conversion takes place, the EM multipole fields of the nucleus do not result in the emission of a photon, the fields interact with the atomic electrons and cause one of the electrons to be emitted from the atom; the gamma that would be emitted after the beta decay is missed, the γ intensity decreases accordingly: IT = Iγ + Ie− = Iγ, so this phenomenon has to be taken into account in the calculation. The x rays will be contaminated with those coming from the electron conversion process; this is important in electron capture decay, as it can affect the results of any x-ray gated spectra if the internal c