Emission probability

The Co nucleus decays with a half-life of 5.27 years by /5 emission to the levels in Ni. These levels then deexcite to the ground state of Ni by the emission of one or more y-rays. The spins and parities of these levels are known from a variety of measurements and require that the two strong y-rays of 1173 and 1332 keV both have E2 character, although the 1173 y could contain some admixture of M3. However, from the theoretical lifetime shown ia Table 7, the E2 contribution is expected to have a much shorter half-life and therefore also to dominate ia this decay. Although the emission probabilities of the strong 1173- and 1332-keV y-rays are so nearly equal that the difference cannot be determined by a direct measurement, from measurements of other parameters of the decay it can be determined that the 1332 is the stronger. Specifically, measurements of the continuous electron spectmm from the j3 -decay have shown that there is a branch of 0.12% to the 1332-keV level. When this, the weak y-rays, the internal conversion, and the internal-pair formation are all taken iato account, the relative emission probabilities of the two strong y-rays can be determined very accurately, as shown ia Table 8. 

In a different example, traceability in the amount-of-substance analysis of natural potassium, thorium, and uranium by the method of passive gamma-ray spectrometry was demonstrated by Nir-El (1997). For an absolute quantitative determination, accurate values of two parameters were required (i) the emission probability of a gamma-ray in the decay of the respective indicator radionuclides, and (2) the detection efficiency of that gamma-ray. This work employed a number of CRMs in the critical calibration of the detection efficiency of the gamma-ray spectrometer and the establishment of precise emission probabilities. The latter results compared well with literature values and provided smaller uncertainties for several gamma-rays that were critical for the traceabUity claim. The amount-of-substance analytical results of the long lived naturally occurring radionucHdes K, Th, and... 

Crystal anapole moment is composed of the atomic magnetic moments which array in anapole structure [3]. It has the same intrinsic structure as Majorana neutrino [2], If we plant a p decay atom into this anapole lattice, the crystal anapole moment will couple to the nuclear anapole moment of the decaying nuclei. So the emitted electron will be given an additional pseudoscalar interaction by the presence of the crystal anapole moment. Then the emission probability will be increased. This is a similar process to that assumed by Zel dovich [1], The variation of the decay rate may be measured to tell whether the crystal anapole moment has an effect on the p decay or not. 

For example, let us consider a typical crystal anapole moment of MrnNiN [4], Its anapole moment can be adjusted by temperature. The p source 3H may be permeated into this lattice without destroying the crystal structure. When the temperature is higher than 266K, the atomic magnetic moments of Mn do not array in anapole structure. Then the crystal anapole moment is zero. The p emission probability of 3H is normal. Contributions from other electro-weak processes may be measured at this temperature. When the temperature is lower than 184 K, the atomic magnetic moments of Mn array in the anapole structure and the crystal present anapole moment to the 3H nuclei. Then the electron s emission rate of 3H will be increased. 

De-excitation of 99mTc has specific features. This nuclide decays with a half-life of 6 hours, but its half-life varies slightly according to environmental conditions [30] or chemical states [31,32], Moreover, the emission probabilities of characteristic X-rays just after the isomeric transition 99mTc — "Tc are influenced by environmental factors [33] which result in a change of the K/VKoc X-ray intensity ratio [34],... 

In a celebrated paper, Einstein (1917) analyzed the nature of atomic transitions in a radiation field and pointed out that, in order to satisfy the conditions of thermal equilibrium, one has to have not only a spontaneous transition probability per unit time A2i from an excited state 2 to a lower state 1 and an absorption probability BUJV from 1 to 2 , but also a stimulated emission probability B2iJv from state 2 to 1 . The latter can be more usefully thought of as negative absorption, which becomes dominant in masers and lasers.1 Relations between the coefficients are found by considering detailed balancing in thermal equilibrium... 

The emission spectrum of some PT and PBD polymer bilayer devices cannot be explained by a linear combination of emissions of the components. Thus, white emission of the PLEDs ITO/422/PBD/A1 showed Hof 0.3% at 7 V, and consisted of blue (410 nm), green (530 nm), and red-orange (620 nm) bands. Whereas the first and the last EL peaks are due to the EL from the PBD and the PT layers, respectively, the green emission probably originates from a transition between electronic states in the PBD layer and hole states in the polymer... 

Let N(j,Ni,N2, and Nj, be the equilibrium population densities of the states 0, 1,2, and 3, respectively (reached under continuous wave excitation intensity Iq), and let N = NQ + Ni+N2 + N3he the total density of optical absorbing centers. The up-converted luminescence intensity ho (corresponding to the transition 2 0) depends on both N2 and on the radiative emission probability of level 2, A2. This magnitude, which is dehned below, is proportional to the cross section a20 (called the emission cross section and equal to the absorption cross section ao2, as shown in Chapter 5). Thus we can write... 

In this section, we will study the absorption and emission probabilities for a single two-level atomic center that is illnminated by a monochromatic electromagnetic wave. 

Expression (5.14) shows that the absorption probability depends on both the incoming light intensity and the matrix element It is easy to see that /Lt,j = l/Lt = /x and so we can conclude that the absorption probability between two defined energy levels i and / is equal to the stimulated emission probability between levels / and i ... 

Using Equations (5.17) and (A4.2), the cross section can be written in terms of the spontaneous emission probability ... 

Purcell, E.M., 1946, Spontaneous emission probabilities at radio frequencies, Phys. Rev. 69 681. 

Many flames show perceptible spectra produced by chemo-luminescence, such as the diatomic molecules CH, C2 and CN in the blue-green cone of a Bunsen burner (7) also known from the absorption spectra of sun-spots and of red stars, and from the emission (probably fluorescence) of comet tails. 

The photoelectric cross-section o is defined as the one-electron transition probability per unit-time, with a unit incident photon flux per area and time unit from the state to the state T en of Eq. (2). If the direction of electron emission relative to the direction of photon propagation and polarization are specified, then the differential cross-section do/dQ can be defined, given the emission probability within a solid angle element dQ into which the electron emission occurs. Emission is dependent on the angular properties of T in and Wfin therefore, in photoelectron spectrometers for which an experimental set-up exists by which the angular distribution of emission can be scanned (ARPES, see Fig. 2), important information may be collected on the angular properties of the two states. In this case, recorded emission spectra show intensities which are determined by the differential cross-section do/dQ. The total cross-section a (which is important when most of the emission in all direction is collected), is... 

The procedure is to extract by deconvolution from the measured emission probabilities the surface density of occupied states for energies between the Fermi level and about 10 eV below that, and to predict the relative atomic positions from that information about the electronic structure of the surface for example, adsorbate-induced peaks will occur, that depend on the adsorbate and its position, as in UPS. This technique is primarily sensitive to the outermost atoms of the surface, in particular adsorbates, since the emitted electrons originate from those regions only. The difficulties in deconvoluting and interpreting the density-of-states information have limited the use of INS. 

From the principle of microscopic reversibility it may be inferred that what is probable in absorption should also be probable in emission. A high emission probability for (it, it ) state is predicted. The rate constant for emission is observed to be large for dipole allowed it it transitions. As a consequence, other deactivating processes cannot compete with the radiative process, and a high fluorescence efficiency for such a system is usually observed. 

Emission and absorption spectra are thus given by the same basic profile, J(co), commonly referred to as the spectral density, times some factors that depend on frequency. The exponential in Eq. 5.2 accounts for stimulated emission (see pp. 48ff.). The factor co of Eq. 5.2 is typical for absorption, just as the factor co3 is typical for the emission probability, Eq. 5.4, see also pp. 49ff. 

The semiclassical treatment just given has the defect of not predicting spontaneous emission. According to (3.13), if there is no outside perturbation, that is, if // (0 = 0, then dcm/dt = 0 for all m if the atom is in the nth stationary state at / = 0, it will persist in that state forever. However, experimentally we find that unperturbed atoms in excited states spontaneously radiate energy and drop to lower states. Quantum field theory does predict spontaneous emission. Since quantum field theory is beyond us, we shall use an argument given by Einstein in 1917 to find the spontaneous-emission probability. 

Similarly, the rate of stimulated emission from state m to n equals mu(vmn) where is another constant. The spontaneous emission probability is independent of the presence or absence of radiation. Hence the rate of spontaneous emission from m to n is Am nNm, where Am n is still another constant. 

Room temperature emission has been observed for a number of transition metal complexes. Examples include Rh111 ammines,53 [Pt(CN)4]2-,54 and some Cu1 phosphine complexes.55 An important class is that of the polypyridine complexes of Ru11 and related species.56 This last emission, probably from a 3CT state, is quite strong and its occurrence has made possible a number of detailed studies of electron transfer quenching reactions. 

It was relatively recently that heavy cluster emission was observed at a level enormously lower than these estimates. Even so, an additional twist in the process was discovered when the radiation from a 223Ra source was measured directly in a silicon surface barrier telescope. The emission of 14C was observed at the rate of 10-9 times the a-emission rate, and 12C was not observed. Thus, the very large neutron excess of the heavy elements favors the emission of neutron-rich light products. The fact that the emission probability is so much smaller than the simple barrier penetration estimate can be attributed to the very small probability... 

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