Internal-conversion Theory Research Articles

Effects of Non-Adiabatic Electromagnetic Vacuum Fluctuations on Internal Conversion.

To explore non-adiabatic effects caused by electromagnetic (EM) vacuum fluctuations in molecules, we develop a general theory of internal conversion (IC) in the framework of quantum electrodynamics and propose a new mechanism, "quantum electrodynamic internal conversion" (QED-IC). The theory allows us to compute the rates of the conventional IC and QED-IC processes at the first-principles level. Our simulations manifest that, under experimentally feasible weak light-matter coupling conditions, EM vacuum fluctuations can significantly affect IC rates by an order of magnitude. Moreover, our theory elucidates three key factors in the QED-IC mechanism: the effective mode volume, coupling-weighted normal mode alignment, and molecular rigidity. The theory successfully captures the nucleus-photon interaction in the factor "coupling-weighted normal mode alignment". In addition, we find that molecular rigidity plays a totally different role in conventional IC versus QED-IC rates. Our study provides applicable design principles for exploiting QED effects on IC processes.

Examination of the solution to the hyperfine structure “puzzle” in H-like and Li-like Bi209 ions

Some aspects of description of the Bohr-Weisskopf effect in hyperfine splitting of the H- and Li-like ions of 209Bi are considered by application of the surface and volume models of the nuclear currents. Extension of these models, used in internal conversion theory, to description of the HFS allows one to successfully describe the effect, without resorting to the specific differences. The latters are shown not to be needed at all. Moreover, they turn out to depend on the nuclear model even stronger than the HFS values themselves. Comparison of the calculated HFS values to experiment shows a satisfactory agreement. Both models provide equally good description of the effect. However, they result in different values of the retrieved rms radius of the nuclear magnetization. In this respect, situation resembles the proton radius puzzle. Prospects of future research are discussed.

Precise test of internal-conversion theory: αK measurements for transitions in nine nuclei spanning 45 ≤ Z ≤ 78

We have been testing the theory used to calculate internal-conversion coefficients (ICCs) by making a series of measurements of αK values with precision better than ±2%. So far we have measured E3 transitions in three nuclei, 103Rh, 111Cd and 134Cs; and M4 transitions in six nuclei, 119Sn, 125Te, 127Te, 137Ba, 193Ir and 197Pt. Together, these span a wide range of A and Z values. In all cases, the results strongly favor Dirac-Fock calculations in which the final-state electron wave function has been computed in an atomic field that includes the vacancy created by the internal-conversion process.

Precise measurement of αK for the 88.2-keV M4 transition in Te127 : Test of internal-conversion theory

We have measured the $K$-shell internal conversion coefficient, ${\ensuremath{\alpha}}_{K}$, for the 88.2-keV $M4$ transition from the 106-day isomer to the ground state in $^{127}\mathrm{Te}$ to be 484(6). When compared with Dirac-Fock calculations of ${\ensuremath{\alpha}}_{K}$, this result agrees well with the version of the theory that incorporates the effect of the $K$-shell atomic vacancy and disagrees with the one that does not. As a byproduct of this measurement, we have determined the $\ensuremath{\beta}$ branching from the isomer to be 2.14(3)%.

Test of internal-conversion theory with a measurement in 111Cd

We have measured the K -shell and total internal conversion coefficients for the 150.8-keV E 3 transition in 111 Cd: αK = 1.449(18) and αT = 2.217(26) respectively. The αK value agrees well with Dirac-Fock calculations, in which the effect of the K -shell atomic vacancy is included. It is consistent with our previous precise measurements of αK values, which cover a range of atomic numbers, and extends that range down to Z = 48. The αT measurement, however, disagrees by about two standard deviations from the calculated αT value, whether the atomic vacancy is included or not.

Further Test of Internal-conversion Theory with a Measurement in 119Sn

Precise measurements are being used to test theoretical K-shell internal conversion coefficients (ICCs): in particular, our program has focused on examining whether the atomic K-vacancy formed during the conversion process must be incorporated into the calculations. We report here a measurement on the 65.66-keV, M4 isomeric transition in 119Sn. Our preliminary result is αK=1610(27), which confirms the importance of including the vacancy in the ICC calculations.

Precise test of internal-conversion theory: Transitions measured in five nuclei spanning 50≤Z≤78

In a research program aimed at testing calculated internal-conversion coefficients (ICCs), we have made precise measurements of αK values for transitions in five nuclei, 197Pt, 193Ir, 137Ba, 134Cs and 119Sn, which span a wide range of A and Z values. In all cases, the results strongly favor calculations in which the final-state electron wave function has been computed using a potential that includes the atomic vacancy created by the internal-conversion process.

Theory of Excited State Decays and Optical Spectra: Application to Polyatomic Molecules

General formalism of absorption and emission spectra, and of radiative and nonradiative decay rates are derived using a thermal vibration correlation function formalism for the transition between two adiabatic electronic states in polyatomic molecules. Displacements, distortions, and Duschinsky rotation of potential energy surfaces are included within the framework of a multidimensional harmonic oscillator model. The Herzberg-Teller (HT) effect is also taken into account. This formalism gives a reliable description of the Q(x) spectral band of free-base porphyrin with weakly electric dipole-allowed transitions. For the strongly dipole-allowed transitions, e.g., S(1) --> S(0) and S(0) --> S(1) of linear polyacenes, anthracene, tetracene, and pentacene, the HT effect is found to enhance the radiative decay rates by approximately 10% compared to those without the HT effect. For nonradiative transition processes, a general formalism is presented to extend the application scope of the internal conversion theory by going beyond the promoting-mode approximation. Numerical calculations for the nonradiative S(1) --> S(0) decay rate of azulene well explain the origin of the violation of Kasha's rule. When coupled with first-principles density functional theory (DFT) calculations, the present approach appears to be an effective tool to obtain a quantitative description and detailed understanding of spectra and photophysical processes in polyatomic molecules.

Precise tests of internal-conversion theory

Using the 165.9-keV M1 transition in 139La as a calibrant, we have determined the K-shell internal conversion coefficients (ICCs) for the 127.5-keV E3 transition in 134Cs and the 661.7-keV M4 transition in 137Ba to 0.6% precision. Unlike previous less-precise measurements of these ICCs, which differed significantly from calculated values, our results agree well with calculations that include the atomic K-shell vacancy and disagree with those that exclude it. These results, which are consistent with what we also found for 193Ir, confirm our earlier conclusions but for different energies, multipolarities and atomic numbers.

Test of internal-conversion theory with measurements inCs134andBa137

We have measured the ratio of K-shell internal conversion coefficients, {alpha}{sub K}, for the 127.5-keV E3 transition in {sup 134}Cs and the 661.7-keV M4 transition in {sup 137}Ba. Previous measurements of these {alpha}{sub K} values led to a ratio that differed from calculated internal conversion coefficients. Our measured result, 30.01(15), disagrees with, but is a factor of three more precise than, the previous average of all experimental results. Our new result is consistent with calculations.

Test of internal-conversion theory with precise γ- and X-ray spectroscopy

Precise measurements of K-shell internal conversion coefficients (ICCs) are being used to determine the best method for calculating these coefficients. A recent result for the M4 transition from 193Ir m has been refined, demonstrating conclusively that the atomic vacancy created by the ejected electron must be properly accounted for in the calculation of ICCs. Measurements of additional cases are discussed.

Controversy and consensus: nuclear beta decay, 1911-1934

1 Prelude: Beta-Spectrum Research in the Pre-Nuclear Years, 1900-1911.- 1.1 Discovery and identification of the beta particle.- 1.2 The first experiments on the velocity distribution of beta particles.- 1.3 Absorption measurements question the inhomogeneity of the beta particles.- 1.4 The Hahn-Meitner vs. Wilson controversy.- 1.5 From unity to complexity: magnetic-deflection experiments, 1910-1911.- 2 The Origin of Beta Rays, and the Growing Complexity of Their Spectrum: The Rutherford Era, 1911-1919.- 2.1 Introduction.- 2.2 Rutherford's 1912 theory, and reactions to it.- 2.3 The beta particle as a nuclear constituent.- 2.4 An extreme complexity of beta line-spectra is brought to light: deflection experiments in the years 1911-1913.- 2.5 Continuity as well as lines: The composite beta spectrum.- 2.6 Rutherford's 1914 theory.- 2.7 The Bohr-Sommerfeld quantum conditions and the beta line-spectrum.- 2.8 Rutherford and the gamma rays.- 3 The Rise of a Controversy: Ellis, Meitner and Smekal Advance Different Beta-Spectrum Theories, 1920-1922.- 3.1 Introduction.- 3.2 Internal conversion, nuclear levels, and Ellis's interpretation of the beta line-spectrum.- 3.3 Analogy between alpha and beta emission, and Meitner's interpretation of the beta line-spectrum.- 3.4 Ellis's response to Meitner's hypothesis, and his interpretation of the continuous beta spectrum.- 3.5 Meitner replies to Ellis, and reveals her view on the continuous beta spectrum.- 3.6 The atom as a unity: Smekal joins the discussion, and is met with a sharp reaction.- 3.7 Two repetitions of the Chadwick experiment lead to contradictory conclusions.- 4 Secondary Effects and Order of Emission: Two Main Questions in the Controversy, 1923-1925.- 4.1 Introduction.- 4.2 Meitner investigates the beta spectrum of UX1 and takes it as further support for her view.- 4.3 Radiationless transitions: Rosseland suggests an explanation of the emission of primary, and some secondary, beta particles.- 4.4 The nuclear field and the Compton effect: Two possible reasons for the continuous beta spectrum.- 4.5 Ellis and Skinner reinvestigate the beta line-spectra of RaB and C, and serious problems arise.- 4.6 Beta first, gamma second, or is it the other way around?.- 5 The End of the Beginning: The Controversy Enters the Decisive Phase, 1925-1929.- 5.1 Introduction.- 5.2 Ellis adjusts his view on the emission process, but maintains his interpretation of the continuous spectrum.- 5.3 The number of emitted beta particles.- 5.4 Ellis and Wooster's tour de force: A determination of the heating effect of RaE.- 5.5 Continental reactions to Ellis and Wooster's experiment.- 5.6 Some concluding remarks about the controversy.- 6 From Anomaly to Explanation: The Continuous Beta Spectrum, 1929-1934.- 6.1 Introduction.- 6.2 Non-conservation of energy or a new particle? The first phase of the Bohr-Pauli dispute, 1929-1932.- 6.3 Other attempts at explaining the anomalous continuity.- 6.4 The question of upper limits in beta spectra, and the thorium C branching problem.- 6.5 The impact of the miraculous year: The second phase of the Bohr-Pauli dispute, 1932-1933.- 6.6 The two theories of beta decay.- 7 Towards a Theory of Internal Conversion: The Beta Line-Spectrum, 1927-1934.- 7.1 Introduction.- 7.2 Experimental evidence brings about a new view on the origin of gamma rays.- 7.3 The radiation hypothesis proves insufficient to explain internal conversion of gamma rays.- 7.4 A theory of internal conversion is developed.- Summary and Conclusion.- Name Index.

A unified theory of electron transfer and internal conversion based on solitary electronic states

A description of electron transfer processes is presented which makes use of the concept of solitary states for the construction of the initial and the final state wave functions. Even though this concept is closely related to an adiabatic description in the sense that it provides partial delocalization of these states it also assures localization for a symmetric donor–acceptor system. The theory can be applied to arbitrary values of the internal parameters characterizing the system, that is the electronic donor–acceptor coupling V, the free energy change ΔE, and the coupling of the electron to nuclear motions represented by a Stokes shift S. This way the theory of nonadiabatic electron transfer processes is put on equal footing with the theory of adiabatic transitions and even more interestingly the same concept unifies the common electron transfer theory and the theory of internal conversion processes if ‖ΔE‖ and (or) ‖V‖ exceed S. It is shown analytically how the results of the conventional treatments for adiabatic, nonadiabatic, and internal conversion processes fall out of this theory as special cases. It is further examplified how the system develops from the so-called normal regime with ‖ΔE‖<S into the inverted regime with ‖ΔE‖>S as function of ΔE for fixed parameters of V and S and as function of V for fixed parameters of ΔE and S.

The Electromagnetic Interaction in Nuclear Spectroscopy

W D Hamilton (ed) Amsterdam: North-Holland 1975 pp xi + 941 price Dfl 260, $108.50 The large volume on the electromagnetic interaction in nuclear spectroscopy contains separate chapters on the theory of gamma ray emission, the prediction of electromagnetic moments from macroscopic and microscopic models, Coulomb excitation, and the theory of internal conversion. Other chapters are concerned with experimental methods including Doppler shift timing techniques, delayed coincidence measurements, and methods of measuring gamma ray angular distributions and correlations.

Auto-Ionization ofH2near Threshold

The purpose of this paper is to show by a model calculation that the internal conversion theory may be used to obtain auto-ionization rates for $\ensuremath{\Delta}{\ensuremath{\nu}}_{\mathrm{if}}=1$ vibrational transitions in ${\mathrm{H}}_{2}$, within the right order of magnitude. Thus, the present calculation remedies the apparent inability of the model to predict desirable rates as calculated by previous authors. The results obtained compare fairly well with the experimental estimates of Chupka and Berkowitz, but are closer to the alternative theoretical calculations of Berry and Nielsen for $\ensuremath{\Delta}{\ensuremath{\nu}}_{\mathrm{if}}=1$. It explicitly shows the $\frac{1}{{n}^{3}}$ dependence of rates for increasing principal quantum numbers $n$, and follows the so-called propensity rule for vibrational transitions involved. Limitations and possible refinements of the present model are discussed, and the generalization for molecules other than ${\mathrm{H}}_{2}$ is indicated. Within the approximation of the model, it provides a simple formula from which rates may be easily estimated.

The effective screening parameters in the theory of internal conversion in the M shell of the atom

An investigation is conducted into the dependence of the effective screening parameters σ(σ = Z-Zeff) on Z, multipolarity, parity, and nuclear transition energy in the theory of internal conversion in the M shell of the atom, taking account of Thomas-Fermi-Dirac and Gashpar screening with semiempirical corrections.

Radiationless transitions and population inversions: Two examples of internal conversion

A theory of internal conversion between two displaced harmonic modes is shown to imply that the coupling strength increases with the initial excess vibrational energy. The same molecule (or collision pair) can exhibit both weak and strong coupling (i.e. both enhancement and retardation of the conversion probability by the initial vibrational energy).

The atomic screening in internal L-conversion calculations

Three different problems connected by the theory of internal conversion are discussed. (i) The influence of the atomic screening of the wave functions on the bound and free electrons as well as on the internal conversion coefficients is discussed. A semi-empirical procedure is suggested, which includes more or less correctly the screening effects in atomic calculations. (ii) The effective Coulomb field and its limits are discussed for the M-shell. (iii) New theoretical M/L total shell ratios of internal conversion are presented, where screening is taken into account. The semi-empirical rule that the total M/L shell ratios are about 0.3 up to a factor of two is verified numerically.

Penetration matrix elements and nuclear structure effects in Tl 201

The study of nuclear structure effects in internal conversion discussed in part (I) (preceding paper) has been extended to the neighbouring nucleus Tl 201. Gamma-gamma, electron-gamma and gamma-electron correlations have been measured. The following results have been obtained: A 2(946+907γ−330γ) = +0.72±0.04 , A 2(946+907γ−330 e) = +0.210±0.007 , A 2(361γ−330γ) = −0.20±0.08 , A 2(361γ−330 e) = −0.09±0.01 , A 2(361 e−330γ) = +0.001±0.004 , A 2(585γ−330 e) = +0.022±0.015 , A 2(585γ−361 e) = −0.013±0.008 . From coincidence and single counting rates the following conversion coefficients were determined: α K (330) = 0.113±0.008, α K (361) = 0.21±0.025, α K (585) = 0.06±0.01 . A decay scheme including 17 transitions and 9 excited states has been established. The angular correlations and conversion coefficients were used to determine the spins and parities for the first, second and fifth excited states as well as the multipolarities, characters and mixing ratios of the most intense transitions. The results have been analyzed in terms of nuclear structure effects in the conversion process. Our conclusions reached in part (I) have been confirmed, i.e. for the d 2 3 → d 2 3 M1 transition there is no evidence for nuclear structure effects in agreement with what is to be expected from the theory. For the strongly retarded l- forbidden d 2 3 → s 1 2 M1 transition the experimental data are in complete agreement with the theory for λ = +74±3, where λ is defined as the ratio of the penetration matrix element and the corresponding gamma ray matrix element. The value for the weighting factor C(Z, k) was taken to be 0.0274. the errors for λ given here do not include the uncertainty in the weighting factor which is supposed to be known to within ±10%. Thus the evidence for large nuclear structure effects in the internal conversion process found for the 279 keV transition in Tl 203 (cf. ref. 13) has been confirmed for the analogous 330 keV transition in Tl 203. The λ-values for these two transitions are in dose agreement. Corrections for static finite size effects in the E2 conversion process have been applied and as in the case of Tl 203 these corrections were found to be small. It is concluded that the present formulation of the theory of internal conversion, including nuclear structure dependent factors, is fully consistent with the experimental data. Experimentally determined penetration matrix elements provide new pieces of information about the nuclear structure. It is shown that in order to get a unique determination of the λ-parameter it is necessary to determine both the internal conversion coefficient and the electron-gamma angular correlation.

Directional Correlation Between Successive Internal-Conversion Electrons: II

A previous paper examined the directional correlation I(θ) between two conversion electrons in cascade, each electron being ejected, with energy much less than mc2, from an initial s-state, under the action of a pure electric multipole γ-transition, and I(θ) was shown to be completely determined by symmetry arguments alone in this case. In the present paper we consider the same problem for pure magnetic, and for mixed transitions. Here I(θ) usually appears as a weighted mixture of constituents I1(θ), I2(θ), etc., each of which is completely determined by symmetry arguments alone The weight factors, however, must be determined from standard internal-conversion theory.