Electric Quadrupole Transition Probabilities Research Articles

Comments on electric quadrupole transition probability in sodium and potassium sequences

Some theoretical electric quadrupole transition probabilities for 3 2 D−3 2 S and 4 2 D−4 2 S transitions in the sodium and potassium isoelectronic sequences have been published recently by Ali.( 1) Despite the apparent agreement in the case of neutral sodium between his results and the experimental values of Hertel and Ross( 2) we believe Ali's theoretical results to be substantially in error.

A simple relation involving the E2 transition probabilities of neighbouring doubly even nucleides

We consider, for doubly even nuclei, the excitation energy E 2 and the reduced electric quadrupole transition probability B(E2) between the ground state and first excited 2 + state. For a nucleus ( N, Z), the quantity [E 2 B(E2)] −1 is denoted by F( N, Z), and it is shown, on the basis of a microscopic model, that F(N, Z) + F(N + 2, Z + 2) − F(N, Z + 2) − F(N + 2, Z) ≈ 0 , excepting in certain specified regions. The consistency of the above difference equation is tested with the available experimental data. A few predictions of unmeasured B(E2) values are also made to illustrate the possible use of this approach.

High resolution study of the electron impact spectrum of zinc vapour at kinetic energies 50-150 eV and in the angular range 0 degrees -11 degrees

The generalized oscillator strength of the transition r1S to 41P in zinc has been measured at 150 eV incident electron kinetic energy and over an angular range 1.5 degrees to 11 degrees . These measurements have been placed on an absolute scale by normalizing to the optical oscillator strength. Absolute generalized oscillator strengths for other lines in the spectrum have been obtained by normalizing to the resonance line. The reduced matrix elements (41S//r2//51S) and (41S//r-2//61S) were found to be 6.1 au+or-+or-15% and 2.5 au+or-30% respectively), and the electric quadrupole transition probabilities AnO(41S to 41D) and AnO(41S to 51D) calculated to be 2287s-1+or-10% and 760 s-1+or-20% respectively.

Forbidden Emission Lines of MN i and fe II in the Spectra of Long-Period Variables Near Minimum Light.

view Abstract Citations (4) References (12) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Forbidden Emission Lines of Mn I and Fe II in the Spectra of Long-Period Variables Near Minimum Light. Nussbaumer, H. ; Swings, J. P. Abstract The behavior of the emission-line intensities of Mn I and [Mn I] in spectra of the long-period variable x Cygni is discussed. Departures from a statistical distribution of the metastable levels occur in the cases of neutral manganese and singly ionized iron, as seen from relative intensities of [Mn ii and [Fe iii lines in the spectra of several Mira variables near minimum light. The magnetic dipole and electric quadrupole transition probabilities are computed for the configurations 3d54s and 3d64s of Mn I. Publication: The Astrophysical Journal Pub Date: February 1972 DOI: 10.1086/151332 Bibcode: 1972ApJ...172..121N full text sources ADS | data products SIMBAD (6)

Electric quadrupole transition probability in sodium and potassium sequences

Electric quadrupole transition probabilities for 3 2 D-3 2 S and 4 2 D-4 2 S transitions in sodium and potassium sequences have been calculated within the frozen-core, Hartree-Fock approximation using experimental transition energies and assuming the L-S coupling scheme. Comparison is made with the experimental result for the sodium transition, and agreement is satisfactory. Results are tabulated for several members of both sequences.

Generalized oscillator strengths in the electron impact spectra of cadmium vapour

Studies of generalized oscillator strengths as a function of incident electron kinetic energy in the range 60-150 eV have been made for cadmium using a crossed beam high resolution electron energy loss spectrometer. Absolute generalized oscillator strengths have been derived by normalizing the resonance transition, 51S to 51P, to the optical oscillator strength at zero momentum change. The reduced matrix elements (51S//r2//61S) and (51S//r2//71S) were found to be 6.6 au+or-25% and 2.3 au+or-50% respectively, and the electric quadrupole transition probabilities A(51S to 51D) and A(51S to 61D) calculated as 2588 s-1+or-30% and 572 s-1+or-40% respectively.

Many-particle shell model calculation of electromagnetic transition rates and multipole moments in A = 30–34 nuclei

Many-particle shell model wavefunctions have been used to calculate magnetic dipole and electric quadrupole transition probabilities and moments as well as log ft values for even-parity states in the A = 30–34 region. The calculations were performed: (i) for bare-nucleon g factors and charges; (ii) for effective g factors and charges obtained from a least-squares fit to experimental data; (iii) for effective single-particle matrix elements obtained from an analogous fit. For the magnetic dipole transitions and moments it appeared necessary to perform separate fits for the A = 30–32 and 33–34 regions. The final best fits for strong transitions are excellent. The average deviation between theory and experiment with three effective single-particle matrix elements for M1 transitions and effective charges for E2 transitions is about 30 %, only slightly larger than the average experimental error. Show cases are 31Si and 33S where the calculated lifetimes, branching ratios and mixing ratios (including the sign) all agree with the measured values within the experimental error. Poor fits, however, are obtained for transitions involving 1 + states and, more generally, states for which the experimental and theoretical spectroscopic factors are in disagreement. Strong M1 transitions generally have a pronounced singe-particle character (with one contribution in the matrix element predominating), whereas all E2 transitions have a collective character (many small contributions).

Fe I] Lines: Their Transition Probabilities and Occurrences in Sunspots

Magnetic dipole and electric quadrupole transition probabilities have been calculated for all the transitions in the configurations 3d74s and 3d64s2 of Fe I. Configuration interaction has been included. A search with the Kitt Peak solar telescope has been made in sunspots for the lines corresponding to the strongest predicted transitions. Lines of the multiplets |${a}^{5}\,D-{a}^{3}\,P,{a}^{5}\,D-{b}^{2}\,F,\,\text{and}\,{a}^{5}\,D-{a}^{5}\,P$| have been tentatively identified. Their equivalent widths confirm the high solar iron abundance: log NFe = 7.5. The possible presence of [Fe I] lines in the absorption spectrum of Arcturus is also discussed.

Hartree-Fock Calculations of Coronal Forbidden Lines in the Argon i Iso-Electronic Sequence

view Abstract Citations (11) References (13) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Hartree-Fock Calculations of Coronal Forbidden Lines in the Argon i Iso-Electronic Sequence Wagner, William J. ; House, Lewis L. Abstract In the Argon i isoelectronic sequence it is highly likely that coronal forbidden visible transitions will be discovered occurring between levels of the lowest excited configuration 3p53d. Hartree-Fock calcula- tions of wavelengths and magnetic dipole and electric quadrupole transition probabilities have been made in the ions Cr vii to Cu xii. In these stages thirty-four forbidden lines are predicted having transition probabilities greater than 1 sec'. Due to large uncertainties inherent in state-of-the-art self-consistent field calculations, the predicted wavelengths have insufficient accuracy at present to allow a unique identification with coronal lines observed at eclipses Publication: The Astrophysical Journal Pub Date: February 1969 DOI: 10.1086/149900 Bibcode: 1969ApJ...155..677W full text sources ADS |

Electric quadrupole transition probabilities in even nuclei

The collective E2 transition rates between allowed positive-parity states of even nuclei are computed using the rotational component of the wave function as well as its β- and γ-part. In 65% (90) of 163 experimental intensity ratios compared with predicted values, agreement is found within a factor 2 (10). Axial asymmetry plays an important role to predict transition probabilities in the lanthanide region.

Electron collision cross sections and generalized oscillator strengths for potassium

A crossed-beam electron spectrometer using hemispherical electrostatic velocity analysers is described. Electron energy-loss spectra for K have been obtained at 41, 51, 68, 101 and 201 eV incident electron kinetic energies. The f-sum rule has been used to obtain generalized oscillator strengths and absolute differential cross sections for the transitions 4 2S -> 4 2P, 5 2S, 3 2D, 5 2P, 4 2F, 6 2P. The reduced matrix element (4 2Sparallelr2parallel5 2S) was found to be 54 A.U., and the electric quadrupole transition probability for 3 2D -> 4 2S found to be 5 × 102 s-1. A method is suggested for absolute calibration of atomic beams in crossed-beam experiments.

Inelastic scattering of alpha particles and deuterons on 185Re and 187Re

Collective states in 185Re and 187Re have been studied by inelastic scattering of 16.6 MeV alpha particles and 12.1 MeV deuterons. In both nuclei four members of the ground-state rotational band were observed. In addition, three members of the K = K 0 − 2 gamma-vibrational band together with the K = K 0 + 2 state were seen. The reduced electric quadrupole transition probabilities for the latter states were determined. The decoupling parameter a for the K = 1 2 + band is 0.39±0.04 ( 185 Re), 0.38±0.04 ( 187 Re) and the inertial parameter ℏ 2/2 I is 17.0±0.4 keV ( 185 Re), 18.9±0.4 keV ( 187 Re) . The observed angular dependence of the deuteron scattering cross section is discussed. An empirical relationship between the deuteron cross section and the B(E2) value has been derived.

Probabilities for Radiative and Nonradiative Decay ofEr3+in LaF3

The rates of radiative and nonradiative decay were determined for several excited states of ${\mathrm{Er}}^{3+}$ in La${\mathrm{F}}_{3}$ from calculated spontaneous emission probabilities and measured lifetimes. Electric-dipole, magnetic-dipole, and electric-quadrupole transition probabilities were evaluated using intermediate coupled states derived from computer diagonalization of the combined spin-orbit and electrostatic energy matrix. The required spin-orbit and Racah parameters for La${\mathrm{F}}_{3}$: ${\mathrm{Er}}^{3+}$ were obtained from a least-squares fit of experimental and theoretical energy levels. The probabilities for electric-dipole transitions were calculated using the theory of Judd and Ofelt; the phenomenological parameters needed in this approach were derived from measurements of integrated absorption coefficients. By comparing the total calculated radiative lifetimes and the observed lifetimes, the probabilities for nonradiative decay from nine different excited states were determined. The probability of nonradiative decay was found to be very dependent upon the proximity of lower energy levels, which for the levels investigated ranged from approximately 1600 to 6000 ${\mathrm{cm}}^{\ensuremath{-}1}$, and hence upon the number of phonons required to conserve energy. The rates of nonradiative transitions corresponding to the simultaneous emission of as many as five phonons were found to make significant contributions to the lifetimes of fluorescent states of rare earths in La${\mathrm{F}}_{3}$.

General asymmetric rotor level structure of some even nuclei

The quasi-adiabatic general asymmetric rotor model for nuclei was applied to the level structures of 56Fe, 96Mo, 106Pd, 110Cd, 132Xe, 148,152Sm, 154,156Gd, 182W, 186,188,190Os and 192Pt. The agreement of predicted levels with experimental data is satisfactory for nucleides at least 7% apart from magic numbers. The electric quadrupole transition probabilities are predicted within a factor 2(1.5) in 72% (53%) of the cases.

Evidence of Deformation inV51

The energy levels, static moments, and transition rates of ${\mathrm{V}}^{51}$ have been investigated using the strongcoupling symmetric-rotator model. Nilsson's energy levels and wave functions in the $1f\ensuremath{-}2p$ shell are recomputed for a well depth corresponding to $\ensuremath{\hbar}{\ensuremath{\omega}}_{0}=\frac{41}{{A}^{\frac{1}{3}}}$ MeV and for a spin-orbit strength $C=\ensuremath{-}0.26\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$ appropriate to the $1f\ensuremath{-}2p$ shell. The shell-model level ordering at zero deformation requires a well-flattening parameter $D=\ensuremath{-}0.035\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$. Band-head energies are not adjusted, but determined strictly from the appropriate summation over the occupied states. The final spectrum is obtained by diagonalizing the Coriolis coupling term with the rotational wave function based on the ten available single-particle or single-hole states in the $1f\ensuremath{-}2p$ shell. The same moment of inertia has been used for all bands and is determined from a least-squares fit to the experimental level scheme. Both for a deformation parameter $\ensuremath{\beta}=\ensuremath{-}0.32$ and for $\ensuremath{\beta}=0.20$, the calculated spectrum is in reasonable agreement with the experiment. The rotational bands are mixed to a high degree. As a consequence the band structure is destroyed and the lowest eigenvalue of the spectrum becomes $\frac{7}{2}$. The wave functions corresponding to the optimal deformation are used in predicting (a) the magnetic moment of the ground and the first excited state, (b) the ground-state quadrupole moment, and (c) the magnetic dipole and the electric quadrupole transition probabilities. The agreement with the experiment, especially for the oblate deformation, is good and is achieved without using an effective charge and an effective gyromagnetic ratio.

Empirical data concerning the electric quadrupole moments

Experimental data on the electric quadrupole transition probability of an even nucleus and the electric quadrupole moment of an odd-mass nucleus are collected and discussed. From the empirical magnitude of the moments it is suggested that the neutron-proton interaction plays an important role both in the spherical region and in the deformed one.

Collective vibrations of spheroidal even nuclei

An extension of the Inglis “cranking model”, in which we describe nuclear shape oscillations without the adiabatic approximation, is derived and applied to quadrupole vibrations of spheroidal nuclei, with special emphasis on γ vibrations. This method leads to a dispersion formula for the collective frequencies agreeing in form with the frequency formula given by the Sawada method. Collective γ-vibrational frequencies and electric quadrupole transition probabilities are theoretically estimated for rare earth and actinide isotopes and compared with experimental values. The numerical calculations involve use of Nilsson's single-particle eigenvalues and the asymptotic eigenfunctions, pairing correlations being taken into account by means of the method of Bardeen, Cooper and Schrieffer and of Bogolyubov.

Low excited states of O 16 (II)

The 0 + and 2 + excited states are treated by taking into account the excitation of two nucleons as well as the excitation of a single nucleon. A contact interaction of the Wigner type is used in estimating the particle hole energy. To start with, some of the components in the two-particle-two-hole configuration are separated out by a certain symmetry property. Among the possible components left, only the components which have a strong particle-hole energy are taken into account. The spurious states are separated out. The wave function thus obtained has still a free parameter left. Two sets of values are chosen for this parameter as examples. By using the wave functions thus fixed, the monopole transition probabilities and the two electric quadrupole transition probabilities of the 2 + excited state are calculated.

Branching Ratios and Magnetic Dipole Transition Probabilities in Odd-ARotational Nuclei

Branching ratios have been measured for gamma radiations from the second excited level in odd-$A$ rotational nuclei. The magnetic dipole transition probability for the first member of the cascade transition could thus be measured in terms of the known electric quadrupole transition probability for the crossover transition. Results are reported for ${\mathrm{Eu}}^{153}$, ${\mathrm{Gd}}^{155}$, ${\mathrm{Gd}}^{157}$, ${\mathrm{Er}}^{167}$, ${\mathrm{Yb}}^{173}$, ${\mathrm{Lu}}^{175}$, ${\mathrm{Hf}}^{177}$, and ${\mathrm{Ta}}^{181}$. Electric quadrupole transition probabilities could also be determined in some cases where mixing ratios $\frac{E2}{M1}$ were known. The $M1$ and $E2$ transition probabilities are compared with the corresponding quantities for the transition from the first excited state to the ground state. The ratios of $M1$ transition probabilities for the two transitions are in good agreement with the values predicted for collective rotational motion. The gyromagnetic ratios of the collective motion ${g}_{R}$ for odd-$Z$ nuclei are found to be consistently higher than the ${g}_{R}$ for odd-$N$ nuclei.

The uniform behaviour of electric quadrupole transition probabilities from first 2+ states in even-even nuclei

Although most nuclear spectroscopy as well as atomic hyperfine structure data do not deliver accurate information on nuclear axiality the ad-hoc assumption of symmetry about one axis found widespread use in nuclear model calculations. In the theoretical interpretation of nuclear properties as well as in the analysis of experimental data triaxiality was considered – if at all – only for some, often exotic, nuclides. A breaking of axial symmetry combined to a spin-independent moment of inertia results in a surprisingly simple heuristic triaxial parametrization of the yrast sequence in all heavy nuclei, including well deformed ones. No additional fit parameters are needed in detailed studies of the mass and charge dependence of the electric dipole strength in the range of and outside of giant dipole resonances. Allowing triaxiality also avoids the introduction of an arbitrary level density parameter ã to fit the accurate values observed in n-capture experiments and ã can be taken from nuclear matter studies. A combination of this value to the yrast energies no longer based on axiality and the related I(I+1) rule results in agreement to data independent of spin. And predictions for radiative neutron capture as derived on the basis of non-axiality are improved as well. The experimentally favoured broken axial symmetry is in accord to HFB and MC-shell model calculations already for nuclei in the valley of stability.