Quadrupole Transition Probabilities Research Articles

Electromagnetic transition rates in 100,101Pd using the Recoil Doppler Shift Technique

The quadrupole deformations for the low-lying states in the transitional nuclei 100,101Pd have been deduced through the measurement of their electric quadrupole transition probabilities using the Recoil Distance Doppler Shift Method. The nuclei were studied using a 268MeV 80Se beam impinging on a thin, self-supporting 24Mg target. States in 100Pd and 101Pd populated by the four and three neutron evaporation channels respectively, with reaction gamma-rays detected using the SPEEDY gamma-ray detection array. The recoiling nuclei were stopped in a copper foil and gamma-ray coincidence data taken at 10 separate target-stopper distances between 35μm and 750μm. The mean-lifetimes for the lowest lying 2+ (in 100Pd) and 15/2− (in 101Pd) states were measured to be 13.3(9)ps and 10.8(8)ps respectively. These data are compared with predictions from nuclear Total Routhian Surface calculations, which are found to agree with the experimentally deduced values to within 10%.

Microscopic analysis of shape mixing in low-lying states of proton-rich nuclei in the Se-Kr region

Using the five-dimensional quadrupole collective Hamiltonian, we study the oblate-prolate shape coexistence/mixing phenomena in the low-lying states of proton-rich nuclei in the A=70-90 region from a viewpoint of oblate-prolate symmetry and its breaking. To derive the collective Hamiltonian microscopically, we have developed a new method, on the basis of the adiabatic self-consistent collective coordinate method, for determining the collective potential, the vibrational and rotational inertial masses in it. By solving the collective Schrödinger equation, we calculate excitation spectra, spectroscopic quadrupole moments and electric quadrupole transition probabilities among the low-lying states. The result of the calculation clearly indicates the dominant role of the large-amplitude vibration in the triaxial shape degree of freedom. It also exhibits an interesting effect of rotation, which may be called 'rotational hindrance to the oblate-prolate shape mixing', that is, the growth of localization of the collective wave function in the (β, γ) deformation space assisted by the rotational motion.

Multiconfiguration Dirac-Fock results for forbidden transitions in the 2p 4 configuration

Abstract Relativistic configuration interaction calculations with the inclusion of the Breit interaction, quantum electrodynamics and finite nuclear mass corrections have been carried out in the extended optimal level scheme using multiconfiguration Dirac-Fock wavefunctions on the forbidden transition probabilities for the 2p 4 ground state configuration of the oxygen isoelectronic sequence for 8 ⩽ Z ⩽ 42. Electric quadrupole and magnetic dipole transition probabilities are reported for transitions between several of these levels. Our results are compared with those from other theories and experiments. Our energy levels are in better agreement with experiment than other theories.

Search for critical-point nuclei in terms of the sextic oscillator

The spherical to deformed $\ensuremath{\gamma}$-unstable shape transition in nuclei is discussed in terms of the sextic oscillator as a $\ensuremath{\gamma}$-independent potential in the Bohr Hamiltonian. The wave functions, energy eigenvalues, and electric quadrupole and monopole transition rates are calculated in closed analytical form for the lowest-lying energy levels. It is shown that the locus of critical points for the spherical to deformed $\ensuremath{\gamma}$-unstable shape phase transition corresponds to a parabola in the parameter space of the model. The ratios of energy eigenvalues and electromagnetic transition probabilities are constant along this parabola. It is thus possible to associate parameter-free benchmark values to the ratios of relevant observables at the critical point of the transition that can be compared to experimental data. In addition, systematic studies of the shape evolution in isotope chains can be performed within the model. As an application, the model parameters are fitted to the energy spectra of the chains of even-even Ru, Pd, and Cd isotopes and the electric quadrupole transition probabilities are calculated. It is found that $^{104}\mathrm{Ru}$, $^{102}\mathrm{Pd}$, and $^{106,108}\mathrm{Cd}$ nuclei, which are usually considered to be good candidates for the $E$(5) symmetry, lie rather close to the critical parabola that separates the spherical and deformed $\ensuremath{\gamma}$-unstable domains. The isotope $^{116}\mathrm{Cd}$ is proposed as a new candidate for a similar critical-point nucleus.

Polarization charges and electric quadrupole transitions of yrast terminating bands inTi44,46,48

The polarization charges in $^{44,46,48}\mathrm{Ti}$ are studied by the microscopic particle-vibration model and used to investigate the electric quadrupole transitions of the yrast terminating bands. The validity of the commonly used empirical effective charges in the $\mathit{pf}$ shell-model calculations is confirmed. The quadrupole transition probabilities $B(E2,I\ensuremath{\rightarrow}I\ensuremath{-}2)$ and electromagnetic moments are reasonably well reproduced compared with experimental results. It is found that a globally decreasing $B(E2)$ is accompanied with convergence of valence particles into the $1{f}_{7/2}$ shell when approaching the terminating states. The $I={6}^{+}$ state in $^{48}\mathrm{Ti}$ shows an exotic behavior with an irregularity of $B(E2)$ and sign change of electromagnetic moments, which is related to a neutron-dominant prolate shape.

IBM-1 calculations towards the neutron-rich nucleusZr106

The neutron-rich $N=66$ isotonic and $A=106$ isobaric chains, covering regions with varying types of collectivity, are interpreted in the framework of the interacting boson model. Level energies and electric quadrupole transition probabilities are compared with available experimental information. The calculations for the known nuclei in the two chains are extrapolated toward the neutron-rich nucleus $^{106}\mathrm{Zr}$.

Spectroscopy and reduced transition probabilities of negative parity bands up to band termination in 45Ti

The negative parity high spin states in 45Ti have been investigated with the interacting shell model including the full fp shell and the configuration dependent cranked Nilsson–Strutinsky approach. Generally, the shell model has successfully reproduced the energy levels of negative parity bands, especially has a good description of the signature inversion at 17/2−. The reduced electric quadrupole transition probabilities of high spin states are calculated by the two models and compared with the experimental results. Reasonable agreement between theories and experiment are obtained, while the shell model can give more fine structures. The large differences of elctromagnetic moments between the shell model calculation and observation call for more elaborate effective interaction and more active shells.

Persistent decoupling of valence neutrons toward the dripline: Study ofC20byγspectroscopy

The very neutron-rich nucleus $^{20}\mathrm{C}$ has been investigated by inelastic scattering on $^{208}\mathrm{Pb}$ and liquid hydrogen targets. Through distorted wave analysis, the reduced electric quadrupole transition probability $B(E2;{0}_{\mathrm{g}.\mathrm{s}.}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})l18.4$ (stat) ${e}^{2} {\mathrm{fm}}^{4}$ and the neutron transition probability ${M}_{n}^{2}=292\ifmmode\pm\else\textpm\fi{}52$ (stat) ${\mathrm{fm}}^{4}$ have been derived. A simple shell model calculation has shown a need for a factor of about 0.4 decrease of the normal polarization charges to elucidate the results. This is interpreted as a decoupling of the valence neutrons from the nuclear core in carbon isotopes heavier than $^{14}\mathrm{C}$.

Multiconfiguration Dirac-Hartree-Fock energy levels and transition probabilities for 3d5in Fe iv

Multiconfiguration Dirac-Hartree-Fock electric quadrupole (E2) and magnetic dipole (M1) transition probabilities are reported for transitions between levels of 3d 5 in [Fe iv]. The accuracy of the ab initio energy levels and the agreement in the length and velocity forms of the line strength for the E2 transitions are used as indicators of accuracy. The present E2 and Ml transition probabilities are compared with earlier Breit-Pauli results and other theories. An extensive set of transition probabilities with indicators of accuracy are reported in Appendices A and B. Recommended values of A(E2) + A(M1) are listed in Appendix C.

Electric quadrupole transitions of K-like ions (Z=22—42)

A fully relativistic multiconfiguration Dirac-Fock method with Breit and QED corrections is used to calculate the 4s 2S─3d 2D(Z=22—42)transition energy level separations, transition probabilities and oscillator strengths for the K-like ions. In the calculation, we have considered the significant Breit and QED corrections. The results are in good agreements with recent experimental data and other theoretical values. The results show that the electric quadrupole transition probabilities are in correspondence with these of E1 transitions and can not be ignored in the laser plasma of high temperature in ICF and MCF Fusion.

Branching ratios of radiative transitions in O VI

We study the branching ratios of the allowed and forbidden radiative transitions among the first few (9) fine structure levels of O VI using relativistic coupled-cluster theory. We find irregular patterns for a number of transitions within n-complexes with n ⩽ 4. We have used the existing values of the allowed electric dipole (E1) transition as a benchmark of our theory. Good agreement with the existing values establish accuracies of not only the theoretical method but the basis function as well. In general, the electric quadrupole (E2) transition probabilities are greater in magnitude than magnetic dipole (M1) transition probabilities, whereas for medium atomic transition frequencies they are of the same order of magnitude. On the other hand, if the transitions involved are in between two fine-structure components of the same term, then the M1 transition probability is more probable than that of E2. The results presented here in tabular and graphical form are compared with the available theoretical and observed data. Graphical analysis helps to understand the trends of electric and magnetic transitions for the decay channels presented here. Our calculated values of the lifetimes of the excited states are in very good agreement with the available results.

A Correspondence Between IBA-I and IBA-II Model and Electromagnetic Transitions of Some Erbium Isotopes

Since the lowest levels are symmetric under the interchange of neutrons and protons from calculations in the interacting boson approximation IBA-2 model, IBA-1 model space, in which neutron and proton degrees of freedom are not distinguished can be considered as a subspace of the IBA-2 model space. Using the microscopic background of the IBA-2 model, a correspondence can be established between IBA-1 and IBA-2 model space. Since the space of the IBA-1 model can be regarded as a subspace of the IBA-2 model there is a unique way to “Project” the operators of the IBA-2 model onto those of IBA-1. This projection can be carried out by using the Fspin formalism. In the IBA-2, the lowest states are indeed fully symmetric, the calculations with the help of this projection, we explore the energy levels and the electric quadrupole transition probabilities B(E2;Ii If) and -ray E2/M1 mixing ratios for selected transitions of 166-168Er .Owing to admixtures of non-fully-symmetric states in IBA-2, we renormalized the parameters (ε) and (κ).This is the first time we show that this projection can be applied to some heavier isotopes and the results obtained for 166-168Er isotopes are reasonably in good agreement with the previous experimental values.

Deformation parameters and transition probabilities for shears bands in Pb isotopes

Tilt angles, deformation parameters, angular momenta, and reduced magnetic dipole and electric quadrupole transition probabilities are calculated within the framework of the tilted-axis cranking model for shears bands in the neutron-deficient Pb isotopes $^{193}\mathrm{Pb}$ to $^{202}\mathrm{Pb}$. The self-consistently calculated quadrupole-deformation parameters for the various configurations lie around ${\ensuremath{\varepsilon}}_{2}=\ensuremath{-}0.1$, and the triaxiality is small. The tilt angle, i.e., the angle between the angular momentum and the nuclear symmetry axis, remains almost constant within each band, showing only a small increase toward higher angular momenta. The angular momentum increases mainly due to the shears effect, which is a step-by-step alignment of high-$j$ proton and neutron orbitals into the direction of the total angular momentum. Calculated and experimental $M1$ transition rates are in good agreement. They decrease with increasing spin within the bands as expected for the shears effect. The calculated $B(E2)$ values show only a weak spin dependence. However, the experimental $B(E2)$ values have large errors, and more accurate data are needed to decide between the present model and a recently suggested geometrical approach.

Magnetic quadrupole M2 2s2 1S0—2s2p3P2(Z=10—103) trangsions for Be-like ions

A full relativistic multi-configuration Dirac-Fock theory with quantum electrodynamical (QED) effect and Breit corrections is used to calculate the magnetic quadrupole M2 2s21S0—2s2p3P2(Z=10—103) transition energy level, transition probabilities and oscillator strengths for Be-like ions for the first time. The results with Breit and QED corrections included are in good agreements with current experimental data and other theoretical values. The results show that the magnetic quadrupole transition probabilities of highly ionized atoms are comparable with those of neutral atomic allowed transitions and cannot be ignored in the laser plasma of high temperatures in ICF and MCF fusions. The effect of the magnetic quadrupole transition of highly ionsized atoms should be considered in the calculation of dielectronic recombination process, opacity, free path and so on.

GRASP92: a package for large-scale relativistic atomic structure calculations

GRASP92: a package for large-scale relativistic atomic structure calculations

Some corrections to GRASP92

The GRASP92 package is a suite of programs for atomic structure calculations based on Dirac–Hartree–Fock theory. In this paper we report corrections that concern three issues. Corrections to a logical error are reported that affect extended optimal level (EOL) calculations important for correlation studies. The removal of a limitation on diagonal energy parameters is recommended for correlation orbitals. Another correction removes an error in the evaluation of one-electron matrix elements for tensors of rank greater than zero. This error affects electric quadrupole (E2) transition probabilities, off-diagonal hyperfine parameters, and quadrupole moments.

Some electromagnetic transition properties and mixing ratios of tellurium isotopes

IBM-2 calculation is presented for the low-lying states in the even-even 122-128Te core nucleus. We developed the projection by using the F-spin formalism from the operator of IBA-2 model over the operator of IBA-1 model space. With the help of this projection IBA-2 Hamitonian parameters are obtained and we explore the energy levels and the electric quadrupole transition probabilities B (E2;Ii ® If) and g-ray E2/M1 mixing ratios for selected transitions. It was found that the calculated positive parity low spin state energy spectra of the even-even 122-128Te isotopes agree quite well with the experimental data. Key words: Interacting boson model, the electric quadrupole transition probability, mixing ratios, Low spin states, PACS: 21.60. Fw, 23.20.Lv, 27.70. +q

Measurement ofE2transition strengths inMg32,34

The degree of collectivity in the neutron-rich nuclei {sup 32}Mg and {sup 34}Mg has been determined via intermediate-energy Coulomb excitation in inverse kinematics. Measured energies of the first excited 2{sup +} states and reduced electric quadrupole transition probabilities B(E2;0{sub g.s.}{sup +}{yields}2{sub 1}{sup +}) are presented for {sup 32}Mg and {sup 34}Mg. The results agree with previous measurements and confirm the placement of both nuclei within the ''island of inversion.''.

Quadrupole moments and transition probabilities B(E2) for light nuclei in the orthogonal-scheme basis with symmetric representations of the O(A − 1) group

Quadrupole moments and transition probabilities B(E2) for light nuclei in the orthogonal-scheme basis with symmetric representations of the O(A − 1) group

Coulomb-nuclear interference withLi6: Isospin character of the21+excitation inGe70,72,74

Ratios of $B(E2)$ to $B(IS2)$, that is, of the reduced quadrupole transition probabilities related, respectively, to charge and mass were extracted through Coulomb-nuclear interference (CNI) for the excitation of the ${2}_{1}^{+}$ states in $^{70,72,74}\mathrm{Ge}$, with a relative accuracy of less than 4%. For this purpose, the CNI angular distributions associated with the inelastic scattering of 28-MeV incident $^{6}\mathrm{Li}$ ions accelerated by the S\~ao Paulo Pelletron, and momentum analyzed by the Enge magnetic spectrograph were interpreted within the DWBA-DOMP approach (distorted wave approximation for the scattering process and deformed optical model for the structure representation) with global $^{6}\mathrm{Li}$ optical parameters. The present CNI results demonstrate an abrupt change in the $B(E2)/B(IS2)$ ratio for $^{74}\mathrm{Ge}$: although for $^{70,72}\mathrm{Ge}$, values of the order of 1.0 or slightly higher were obtained, this ratio is 0.66 (7) for $^{74}\mathrm{Ge}$. The heavier Ge isotope is thus one of the few nuclei that, so far, have been shown to present clear mixed symmetry components in their ground-state band.