Electron Capture Rates Research Articles

Capture of outer orbital electrons

Theoretical electron capture rates are given for all electrons captured in unique second and third forbidden transitions. The M I/L I capture ratios and M subshell capture ratios are tabulated for 55 ≦ Z ≦ 90, and capture from the N,O, and P shells is estimated. The available experimental data on La 138 and Po 209 are re-interpreted in the light of these results, and M/L capture ratios are given as functions of transition energy for the low-energy captures Pt 193, Pb 202 and Pb 205. Comparative half-lives of unique second and third forbidden transitions are tabulated and discussed in connection with La 138 decay.

The capture of thermal electrons by gold centres in N-type germanium at 20°K

Measurements of the capture rate of thermal electrons at Au − and Au − centres at 20°K in n-type germanium yielded the values 2.6 × 10 −11 cm 3 sec −1 and 2.0 × 10 −12 cm 3 sec −1 for the singly and doubly charged centres respectively. The method of measurement involved observation of the escape of electrons previously driven into the centres by an electric field. An analysis of the trapping kinetics for the system—conduction band, donor level, and two gold levels—is given, but this is found to be inadequate to explain the variation of time-constant with photo-excitation level which is observed, and the existence of a further trapping level has to be postulated. The origin of this trap is unknown, but a rough estimate suggests that a trap density of about 10 12 cm −3 and a level about 0.03 eV below the conduction band would account for the results. Changes in the electron population of the gold levels occur at moderate-to-high excitation-levels, and it is found that quantitative results for the population shifts could be indirectly inferred from experiment. Evidence is found for the existence of a highly photosensitive surface strip, about ten Debye lengths thick, within the space-charge region of an accumulation layer. This strip is due to the complete filling of the gold level 0.20 eV from the conduction band by the additional electrons which form the space-charge so that only Au − centres are present.

Hot electrons and negative resistance at 20°K In n-type germanium containing Au − centres

Experimental results are presented of the variation with electric field of the capture rate of electrons at Au − centres in n-type germanium at 20°K. The capture rate per centre at low fields is about 2.0 × 10 −12 cm 3 sec −1 and at high fields about 3 × 10 −9 cm 3 sec −1, an increase by a factor of about 1 × 10 3. This is shown to be consistent with the assumption of a transition probability which depends on electron tunnelling through a Coulombic potential barrier, if the energy-loss part of the transition probability decreases with increasing electron energy. Evidence of a shallow trap, other than the compensating donor, is found which supports the interpretation of previous work. It is shown that the current density vs. field curve in the absence of an electrical domain exhibits a pronounced differential negative resistance. The steady state current in the presence of a domain is seen to take up a value above the minimum permissible value, the latter being predicted on the basis of a simple model of domain formation and the principle of least entropy production. The velocity at which the domain migrates towards the positive contact is measured as a function of illumination level and applied field. It is shown to vary in an approximately linear way with illumination level, but its absolute magnitude is lower by a factor of 10 2 than that expected on the basis of a simple model. The situation at high illumination levels is complicated by electron transfer from one gold level to the other and it is not considered in detail.

Dislocations as Traps for Holes in Germanium

AbstractA further development of the barrier model of recombination at dislocations is presented. It is shown that in spite of the tunnel effect, the barrier height is the main factor limiting the capture rate of electrons down to about 180 °K. Some features of photoconductivity in crystals with dislocations and their temperature‐dependences, are discussed (such as the lux‐ampere characteristics, and the relaxation of the photocurrent). It is shown how the density of dislocations and the position of the dislocation acceptor level can be estimated from experimental data.

Electron Capture in Stellar Interiors.

The reasons why nuclear electron-capture rates in stars depend on temperature and density are discussed, and some astrophysical applications of continuum electron-capture rates are reviewed. The modern theory of nuclear BETA decay is then used to calculate stellar-continuum electroncapture rates for transitions of an arbitrary degree of forbiddenness. The equations that are most useful for astrophysical applications are discussed in detail; particular emphasis is placed upon methods for predicting stellar rates that utilize, whenever possible, terrestrial measurements. Three examples are discussed that illustrate the use of the formulas given; the examples are: the electroncapture lifetime of a proton, the stellar BETA decay of Mo, and the effect of forbidden transitions on the abundances of elements in the iron peak. (auth)

Overlap and Exchange Effects in Beta Decay

The change in nuclear charge by one unit in beta decay causes initial and final atomic states to overlap imperfectly. The effect of this imperfect overlap on the shape of allowed electron and positron emission spectra is calculated. The calculated change in the spectrum shape can be simulated by including the average excitation energy of the final atom in the energy balance. The inhibition, due to imperfect atomic overlap, of electron-capture rates, as well as total electron and positron-emission rates, is also determined. In all known cases, imperfect atomic overlap increases beta-decay lifetimes by at most a few percent and usually by an amount less than a few tenths of one percent. Antisymmetrization between decay and bound atomic electrons, in conjunction with the change in nuclear charge, gives rise to exchange effects in electron emission and electron capture. Due to exchange terms, the usual allowed electron spectrum is multiplied by a quantity that is of the order of $1\ensuremath{-}2{Z}^{\ensuremath{-}1}$ for energies less than the binding energy of a $K$ electron in the initial atom. This exchange correction is negligible for higher energies of the emitted continuum electron. A simple approximate formula is derived that predicts the effect of exchange on $L$ to $K$ capture ratios; this formula predicts a 22% increase over the usual theoretical value for the $L$ to $K$ ratio of ${\mathrm{Ar}}^{37}$. The ${\mathrm{Ar}}^{37}$ prediction is in excellent agreement with recent experiments and with a more complicated calculation by Odiot and Daudel. Exchange effects change total electron emission and electron capture rates by at most a few percent.

Electron Capture and Nuclear Matrix Elements ofBe7

BS>The Be/sup 7/ electron capture rate from continuum orbits is calculated as a function of electron temperature and concentration, and the effect on the decay rate of the statistical distribution of electrons, the electron-nucleus Coulomb intetaction, relativistic and nuclear size corrections, the imperfect overlap between Initial and final atomic states, and electron screening in bound decay, is considered. Experimental information on Be/sup 7/ and Li/sup 7/ is analyzed to obtain accurate experimental Gamow-Teller matrix elements for both the ground- and excited-state transitions and compare these matrix elements with the predictions of some simple nuclear models. This comparison supports the conclusion that near the beginning of the 1p nuclear shell L-S coupling is better satisfied than j-j coupling. (auth)

Determination of the ϵK/β+ ratio and endpoint energy of internal bremsstrahlung due to the electron capture process in the non-unique second forbidden decay of Cl36

The 2/sup +/ yields 0/sup +/ nonunique second forbidden transition decay of Cl/sup 36/ into S/sup 36/ was examined for the presence of positron emission. From scintillation gamma -spectra obtained with a 50 mu C-source and previous determinations of the rate of electron capture, the epsilon /sub kappa // BETA /sup +/ ratio for the transiticn is calculated as (7.5 plus or minus 3.0) x 10/sup 2/. The uncorrected experimental bremsstrahlung spectrum and the Jauch-diagram with corrections are shown. (H.D.R.)

Formation ofFCenters in KCl by X Rays

Measurements have been made of the growth of the $F$ band in undeformed, deformed, and heat-treated KCl crystals at room temperature using 140-kvp x-ray irradiation. The growth curves were analyzed in terms of the initial concentration of negative-ion vacancies in the lattice before irradiation, rate of formation of new vacancies, rate of electron capture by the initial and by the new vacancies, and bleaching constants. These parameters were studied as a function of the intensity of irradiation. It appears that the new vacancies are generated at a rate proportional to the square of the intensity of irradiation and inversely proportional to the dislocation density. Deformation increases the concentration of initial vacancies near dislocations, while heat treatment increases the concentration of initial vacancies dispersed in the volume of the crystal. Since neither the jog mechanism nor the Varley mechanism can account for the observations, a new model is proposed which accounts for all the observed phenomena.

Disintegration Scheme ofZn65

Spectroscopic-coincidence techniques have been employed to re-examine the electron capture rate, branching ratio, and positron rate of ${\mathrm{Zn}}^{65}$. Decay by positron emission occurs to the extent of (1.70\ifmmode\pm\else\textpm\fi{}0.10)%. Electron capture to the excited state was found to be associated with (51.3\ifmmode\pm\else\textpm\fi{}3.0)% of the disintegrations, significantly higher than the (44-46)% reported in previous investigations.

Measurement of Absolute Electron Capture Rates with an Application to the Decay ofNi57

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