Higher Multipole Transitions Research Articles

Resonance Energy Transfer in Arbitrary Media: Beyond the Point Dipole Approximation

In this work, we present a comprehensive theoretical and computational study of donor/acceptor resonance energy transfer (RET) beyond the dipole approximation, in arbitrary inhomogeneous and dispersive media. The theoretical method extends Forster theory for RET between particles (molecules or nanoparticles) to the case where higher multipole transitions in the donor and/or acceptor play a significant role in the energy transfer process. In our new formulation, the energy transfer matrix element is determined by a fully quantum electrodynamic expression, but its evaluation requires only classical electrodynamics calculations. By means of a time domain electrodynamical approach (TED), the matrix element evaluation involves the electric and magnetic fields generated by the donor and evaluated at the position of the acceptor, including fields associated with transition electric dipoles, electric quadrupoles, and magnetic dipoles in the donor, and the acceptor response to the electric and magnetic fields and ...

Energy levels and radiative data for Kr-like W38+ from MCDHF and RMBPT calculations

Energies, transition rates, line strengths and lifetimes have been computed for all levels of the 4p6 and 4p54d configurations of W38+ by using the multi-configuration Dirac–Hartree–Fock (MCDHF) method as well as relativistic many-body perturbation theory. We investigate systematically correlation, relativistic and quantum electro-dynamical (QED) effects of different properties, including excitation energies and transition rates. We demonstrate that it is important to include the core-valence correlation of rather deep subshells (including 3d and 3p) to reach close to spectroscopic accuracy for the transition energies. We also show that high-multipole transitions (E3, M2) are important for the lifetime of some metastable levels of 4p54d (). The present results are in good agreement with experiments and of considerably higher accuracy than those achieved in previous theoretical works.

Reactions onAr40involving solar neutrinos and neutrinos from core-collapsing supernovae

We calculated neutrino reactions on {sup 40}Ar for detecting core-collapsing supernovae (SNe) neutrinos. The nucleus was originally exploited to identify the solar neutrino emitted from {sup 8}B produced in pp chains on the Sun. With the higher energy neutrinos emitted from the core-collapsing SNe, contributions from higher multipole transitions, as well as from the Gamow-Teller and Fermi transitions, are shown to be important ingredients for understanding reactions induced by the SN neutrino. Moreover, higher excited states beyond a few states known in experiment diminish significantly the expected large difference between the cross sections of {nu}{sub e} and {nu}-bar{sub e} reactions on {sup 40}Ar, which difference is anticipated because of the large Qvalue in the {nu}-bar{sub e} reaction. The reduction is shown to lead to a difference between them of only a factor of 2.

Internal conversion coefficients of high multipole transitions: Experiment and theories

A compilation of the available experimental internal conversion coefficients (ICCs), α T, α K, α L, and ratios K/L and K/LM of high multipole ( L > 2) transitions for a number of elements in the range 21 ⩽ Z ⩽ 94 is presented. Our listing of experimental data includes 194 data sets on 110 E3 transitions, 10 data sets on 6 E4 transitions, 11 data sets on 7 E5 transitions, 38 data sets on 21 M3 transitions, and 132 data sets on 68 M4 transitions. Data with less than 10% experimental uncertainty have been selected for comparison with the theoretical values of Hager and Seltzer [R.S. Hager, E.C. Seltzer, Nucl. Data Tables A 4 (1968) 1], Rosel et al. [F. Rösel, H.M. Fries, K. Alder, H.C. Pauli, At. Data Nucl. Data Tables 21 (1978) 91], and BRICC. The relative percentage deviations (%Δ) have been calculated for each of the above theories and the averages ( % Δ ¯ ) are estimated. The Band et al. [I.M. Band, M.B. Trzhaskovskaya, C.W. Nestor Jr., P.O. Tikkanen, S. Raman, At. Data Nucl. Data Tables 81 (2002) 1] tables, using the BRICC interpolation code, are seen to give theoretical ICCs closest to experimental values.

Role of two-body operators in electromagnetic transitions

Effective electromagnetic transition operators pertinent to the model space in the shell model are formulated for many- j-shell configurations and in isospin formalism within the framework of the first-order perturbation theory. The correlated operators thus obtained consist of one-body and two-body transition operators, the former of which is considered to be the origin of effective charges, while the latter cannot be incorporated into the idea of effective charges. Electromagnetic transitions in the 1 f 7/2-shell nuclei are studied systematically by using the effective transition operators so generated. It is found that the two-body contributions are very important not only in the higher-multipole transitions but also in the E2 transitions, to the extent that the concept of effective charge breaks down, and they are indispensable in achieving reasonable agreement with experiment.

Two-body part of effective transition operators and higher-multipole transitions in the1f7/2-shell nuclei

E4, E6, and M5 transitions in the 1f{sub 7/2}-shell nuclei, for which anomalous effective charges are required to reproduce experiment, are discussed by using the effective transition operators which are calculated within the framework of the first-order perturbation theory. The correlated operators thus obtained consist of one-body and two-body transition operators, the former of which is considered to be the origin of effective charges, while the latter cannot be incorporated into the idea of effective charges. The two-body contributions are very important in those higher-multipole transitions, to the extent that the concept of effective charge breaks down, and they are found indispensable in achieving reasonable agreement with experiment. {copyright} {ital 1997} {ital The American Physical Society}

The 12C(n, p) 12B reaction at En = 98 MeV

Double-differential cross sections of the 12C(n, p) reaction have been measured at 98 MeV in the angular range 0°–33° for excitation energies up to 35 MeV. The spectra have been analysed in terms of multipole components, using peak fitting and decomposition techniques. The data have been compared with cross sections obtained in the distorted-wave Born approximation, using matrix elements from shell-model calculations. The unit cross section and the related strength of the spin-isospin part of the nucleon-nucleon interaction were determined from the extracted Gamow-Teller strength. Cross sections and fractions of strength exhausted by dipole and higher-multipole transitions were extracted and compared with data available in the literature.

150.8 keV, E3 transition in 111Cdm and comparison of experimental and theoretical high multipole order internal conversion coefficients.

/sup 111/Cd/sup m/ was excited by (..gamma..,..gamma..') reactions with bremsstrahlung of a 4.5 MeV linear electron accelerator, and the K and total internal conversion coefficients of the 150.8 keV, E3 transition were measured. The obtained values are ..cap alpha../sub K//sup 151/ = 1.29 +- 0.11, ..cap alpha../sub T//sup 151/ = 1.98 +- 0.05 (68% confidence level). These values deviate from the theory by more than 10%, but less strongly than was reported very recently. Several experimental internal conversion coefficient values of high multipole transitions with better than 5% accuracy are compared with the theory, and definite discrepancies are observed.

Positions of zeros in the multipole matrix elements of the point Coulomb field.

Minima in the photoionization cross sections (Cooper minima) are known to occur for all types of transitions in atoms, even for dipole transitions from the ground state. These minima are caused by zeros in the transition matrix elements which are, in turn, the result of a zero value for the radial integral of a particular energy. For transitions involving the point Coulomb field there are no zeros in the dipole matrix elements, but there are zeros in higher multipole transitions. The zeros in the quadrupole matrix elements involve transitions between low-angular-momentum bound states and free states with two more units of angular momentum. Zeros in octupole matrix elements fall into two categories. The first involves transitions between low-angular-momentum bound states and free states with three more units of angular momentum and the second involves transitions between all s and p states. In this paper the position (energy) of the zeros in the multipole matrix elements of the point Coulomb field are examined. Why the dipole matrix elements of hydrogen have no zeros and what causes the zeros in the higher-multipole matrix elements are then discussed.

Total-conversion coefficients of high multipole transitions in the decay of 1197ptm

The relative gamma intensities of the 53 keV, 130 keV, 279 keV and 346.5 keV transitions in the decay of197ptm are determined, by using a high-resolution HPGe system. The total-conversion coefficients of the 130 keV and 346.5 keV transitions are evaluated from the relative intensities as 29.4(50) and 7.7(4), respectively, in agreement with the theoretical values.

Trajectory, binding and relativistic effects in the K-shell ionization process investigated by particle-photon coincidences

The influence of the projectile trajectory on the K-shell ionization probability has been investigated by proton and deuteron impact on Ni and Ag by using particle-photon coincidence techniques. Good agreement with calculations in first order peturbation theory is obtained also at very large scattering angles, where higher multipole transitions and the recoil effect have an important influence on the ionization probability. The importance of the increased K-electron binding energy due to the influence of the projectile nuclear charge is demonstrated in the Ne on Ni and Cl on Pb collision systems. Even in the Cl on Pb collision system good agreement is obtained between the first order peturbation theory and experiment, if relativistic united-atom wave functions are used for the 1s electrons.

Nuclear Surface and Inelastic Proton Scattering

Comparisons of the electromagnetic and proton inelastic-scattering reduced transition probabilities for the even nickel isotopes are made. It is found that the values obtained for high multipole transitions in the inelastic scattering are extremely sensitive to the nuclear density distribution. This sensitivity is investigated for various phenomenological models of the nuclear density distribution.

Wide‐Angle Interference and Multipole Nature of Fluorescence and Phosphorescence of Organic Dyes

AbstractPart of a wave front radiated by an excited molecule interferes with the part of the same wave front reflected by a mirror. Thus in certain directions a strong luminescence is observed, while in others no emission of the same wavelength can be seen. This phenomenon of wide‐angle interference has been investigated for the case of monomolecular layers of organic dyes, which are kept in a fixed distance from an evaporated silver mirror. To circumvent the effects of refraction at the air‐monolayer interface the substrate carrying the layer system is immersed in a cylindrical cuvette filled with an aqueous solution of calcium thiocyanate. This solution is particularly well suited as immersion fluid for phosphorescence measurements, since its low solubility for oxygen coupled with an increased viscosity prevents the quenching of phosphorescence. A small wavelength range is selected by an interference filter and its intensity measured as a function of the angle with the normal on the mirror surface.The angular characteristics of the emission is an indicator for the nature of the transitions associated with fluorescence and phosphorescence. The well defined distance between the luminescing molecules in the monomolecular layer and the mirror permits a much higher precision compared with earlier investigations. While there is no doubt that the fluorescence is electrical dipole in nature, it might be possible that higher multipole transitions (e.g. magnetic dipole or electric quadrupole) participate in the phosphorescence emission. We have indeed found, that the phosphorescence from the triplet state of monomethin‐cyanines at room temperature is not a pure electrical dipole transition, but is partly electric quadrupole in nature.

THEORY OF TWO-PHOTON ABSORPTION

The two-photon absorption process is discussed using a density matrix formalism. The electromagnetic field is described by means of coherent states, a technique that permits a simple evaluation of the effect of coherence on the transition probability. It is concluded that the latter is the same for a coherent and an incoherent pulse of radiation. In the case of a stationary field containing many modes, the transition probability is nearly the same in the coherent and incoherent cases, whereas for a single mode the transition probability is twice as high for the incoherent field. These conclusions are independent of the multipole expansion of the interaction Hamiltonian and are valid for electric dipole and higher multipole transitions.

Excitation of isometric states in Rh 103 and In 115 by electrons

Yields for the production of the 57 m isomeric state of Rh 103 and for the 4.5 h state of In 115 were measured both for electrons and photons of energies between 7 and 18 MeV. The electrons were produced by the Stanford Mark II Linear Accelerator, and the irradiations were made with the “stacked foil” method. The sensitivity of the electron/photon yield ratio to the multipole character of the reaction was used to obtain information on the absorption process of γ-rays. The results of Rh 103 lie somewhat lower than, but approximately parallel to, the theoretical results expected for electric dipole absorption. This type of result has been observed previously where electric dipole absorption is the dominating mechanism. The results for In 115, on the contrary, are more than a factor of two higher than expected for dipole absorption, indicating that quadrupole or higher multipole transitions have a dominating role. In the course of the experiment we observed the reaction Rh 103 ( γ, 2p)Tc 101. The cross section for this reaction is about three orders of magnitude smaller than that for the (γ, γ′) reaction.

Effects of Radioactive Disintegrations on Inner Electrons of the Atom

The probability that nuclear emission of an alpha- or beta-particle causes ionization of a $K$ or $L$ electron of the atom is calculated by time-dependent perturbation theory using nonrelativistic Coulomb wave functions. Beta-emission (electron or positron) causes an ionization probability of $\frac{0.64}{{Z}^{2}}$ and $\frac{2.1}{{Z}^{2}}$ per beta in the $K$ and $L$ shells, respectively. (The $K$ shell result agrees with Migdal and Feinberg; the $L$ shell result disagrees with Migdal.) The use of nonrelativistic wave functions causes an appreciable underestimate in the ionization probability for $K$ electrons of heavy atoms. Screening corrections for the use of Coulomb wave functions would increase the ionization probabilities by a factor of 1.4 for $K$ electrons and by a factor of 3 or 4 for $L$ electrons. Migdal's result for dipole electronic transitions caused by nuclear alpha-decay are reduced by a factor 25 (for the case of ${\mathrm{Po}}^{210}$) because of nuclear recoil. Quadrupole matrix elements such as ${({r}^{\ensuremath{-}3})}_{1s,{n}^{\ensuremath{'}}d}$ are evaluated by a new method developed by H. A. Bethe. This method uses the Sommerfeld integral representation for the continuum ${n}^{\ensuremath{'}}d$ wave function. Quadrupole transitions are negligible for $K$ electrons, but are the predominant effect for $L$ electrons. The calculated ionization probabilities for ${\mathrm{Po}}^{210}$ are ${10}^{\ensuremath{-}7}$ and 1.1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ per alpha in the $K$ and $L$ shells, respectively. For alpha-decay, screening corrections and higher multipole transitions would both increase the ionization probability for $L$ electrons. Madansky and Rasetti's measurements of photons from RaE are consistent with our calculations, but Bruner's measurements on ${\mathrm{Sc}}^{44}$ are not. Grace's interpretation of $K$ x-rays from ${\mathrm{Po}}^{210}$ is consistent with the calculation of this paper, while Barber and Helm's interpretation is not. Rubinson and Bernstein find 8 times the $L$ x-ray yield from ${\mathrm{Po}}^{210}$ we have calculated for Coulomb wave functions.