Electric Monopole Transitions Research Articles

The LSU-Argonne conversion electron spectrometer: A new detector for the X-Array and SATURN decay station

A new conversion electron detector has been commissioned at the ATLAS/ CARIBU facility at Argonne National Laboratory. The LSU-Argonne Conversion Electron Spectrometer (LACES) is a LN2-cooled Si(Li) detector system designed to be incorporated into a decay station that comprises the dedicated HPGe clover array with a box geometry (X-Array) and the Scintillator and Tape Using Radioactive Nuclei (SATURN) device. This integration enables simultaneous measurements of conversion electrons and gamma-rays in decay experiments, yielding novel information on transition multipolarities, electric monopole transitions, and isomeric states that decay mostly via conversion electrons. A measurement of the energy resolution of LACES yielded 2.3-keV FWHM at 975 keV for electrons and 1.3-keV FWHM at 75 keV for X-rays. A detailed study of the absolute detection efficiency (at 5 mm from the source) was performed, where this quantity was determined experimentally in the range of electron transition energies between 25.5 keV and 1047.8 keV and subsequently simulated using the GEANT4 code. Measurement and simulations are found to be in excellent agreement. A precise characterization, for this type of detector system, of the absolute detection efficiency for such a wide energy range is reported for the first time.

Investigations of electric monopole transitions in medium-mass to heavy nuclei: Beyond mean field calculations with the Gogny force

Investigations of electric monopole transitions in medium-mass to heavy nuclei: Beyond mean field calculations with the Gogny force

Emergence of triaxiality in 74Se from electric monopole transition strengths

The structure of 74Se at low energy was investigated via spectroscopy of internal conversion electrons at the INFN Legnaro National Laboratories (LNL). A set of internal K-conversion coefficients and monopole transition strengths was measured. A large ρ2(E0;22+→21+)⋅103=210(130) value was deduced. This result, in addition to a low upper limit for the 03+→02+ electron transition, casts in doubt a simple interpretation of the 74Se low-lying structure, in particular the recently proposed spherical, vibrational character. New microscopic beyond-mean-field calculations generally agree with the experimental results and are capable of producing a large ρ2(E0;22+→21+) value, even if still a factor ≈7 smaller than the experiment. Triaxiality and a complex shape-coexistence and mixing scenario seem responsible for this unexpected experimental result.

Reassigning the shapes of the 0+ states in the 186Pb nucleus

Across the physics disciplines, the 186Pb nucleus is the only known system, where the two first excited states, together with the ground state, form a triplet of zero-spin states assigned with prolate, oblate and spherical shapes. Here we report on a precision measurement where the properties of collective transitions in 186Pb were determined in a simultaneous in-beam γ-ray and electron spectroscopy experiment employing the recoil-decay tagging technique. The feeding of the {0}_{2}^{+} state and the interband {2}_{2}^{+}to {2}_{1}^{+} transition have been observed. We also present direct measurement of the energies of the electric monopole transitions from the excited 0+ states to the 0+ ground state. In contrast to the earlier understanding, the obtained reduced transition probability B(E2;{2}_{1}^{+}to {0}_{2}^{+}) value of 190(80) W.u., the transitional quadrupole moment | {Q}_{t}({2}_{1}^{+}to {0}_{2}^{+})| =7.7(33) eb and intensity balance arguments provide evidence to reassign the {0}_{2}^{+} and {0}_{3}^{+} states with predominantly prolate and oblate shape, respectively. Our work demonstrates a step-up in experimental sensitivity and paves the way for systematic studies of electric monopole transitions in this region. These electric monopole transitions probe the nuclear volume in a unique manner and provide unexploited input for development of the next-generation energy density functional models.

Electric Monopole Transition from the Superdeformed Band in ^{40}Ca.

The electric monopole (E0) transition strength ρ^{2} for the transition connecting the third 0^{+} level, a "superdeformed" band head, to the "spherical" 0^{+} ground state in doubly magic ^{40}Ca is determined via e^{+}e^{-} pair-conversion spectroscopy. The measured value ρ^{2}(E0;0_{3}^{+}→0_{1}^{+})=2.3(5)×10^{-3} is the smallest ρ^{2}(E0;0^{+}→0^{+}) found in A<50 nuclei. In contrast, the E0 transition strength to the ground state observed from the second 0^{+} state, a band head of "normal" deformation, is an order of magnitude larger ρ^{2}(E0;0_{2}^{+}→0_{1}^{+})=25.9(16)×10^{-3}, which shows significant mixing between these two states. Large-scale shell-model (LSSM) calculations are performed to understand the microscopic structure of the excited states and the configuration mixing between them; experimental ρ^{2} values in ^{40}Ca and neighboring isotopes are well reproduced by the LSSM calculations. The unusually small ρ^{2}(E0;0_{3}^{+}→0_{1}^{+}) value is due to destructive interference in the mixing of shape-coexisting structures, which are based on several different multiparticle-multihole excitations. This observation goes beyond the usual treatment of E0 strengths, where two-state shape mixing cannot result in destructive interference.

Electric monopole transitions and structure of low-spin states in Pd106

Structures in the $^{106}\mathrm{Pd}$ nucleus have been studied in the $\mathrm{EC}/{\ensuremath{\beta}}^{+}$ decay of $^{106}\mathrm{Ag}$ at the INFN Legnaro National Laboratories using the Spes Low-energy Internal Conversion Electron Spectrometer (SLICES). The K-conversion coefficients and the electric monopole transition strengths, between low-lying ${2}^{+}$ and ${0}^{+}$ states, have been studied. These experimental data combined with the results from conversion electron measurement on $^{104}\mathrm{Pd}$ previously performed by the Florence spectroscopy group were compared with the theoretical values calculated in the framework of the interacting proton-neutron boson model. Good agreement between experimental and theoretical values is found when interpreting the ${0}_{3}^{+}$ level as an intruder state.

Extended analytical solutions of the Bohr Hamiltonian with the sextic oscillator

Low-lying collective quadrupole states in even–even nuclei are studied for the particular case of a γ-unstable potential within the Bohr Hamiltonian. In particular, the quasi-exactly solvable β-sextic potential is extended to cover the most relevant part of the low-lying spectra in nuclei. In previous papers (2004 Phys. Rev. C 69 014304, 2010 Phys Rev. C 81 044304), the same situation was solved for β-wavefunctions with up to one node (M = 0, 1), which are relevant for the first few low-lying states. Here, the model space is enlarged by including β-wavefunctions also with two nodes (M = 2), which generate many more states, in order to make it useful for actual fittings and more detailed checking of shape phase transitions between spherical and γ-unstable β-deformed shapes in nuclei. In addition to the energy eigenvalues and wavefunctions, closed analytical formulas are obtained for electric quadrupole and monopole transition probabilities too. The model is applied to the chains of even Ru and Pd isotopes to illustrate the transition between the spherical and deformed γ-unstable phases. These applications indicate that the optional extension of the model with a phenomenologic rotational term L ⋅ L is consistent with the experimental data.

Transitions probabilities B(E2), B(M1) and B(E0) in 130Ba isotope

Nuclear structure for even-even 130Ba isotope have been investigated. They examined carefully with IBM1 and IBM2. Low lying energy levels for even even positive parity states, reduced electric quadruple transitions probabilities B(E2), branching ratios, reduced magnetic dipole transitions probability B(M1), reduced electric monopole transitions probability B(E0), and mixing ratio X(E0/E2) have been studied.In the framework of IBM1 noted the competition between the two parameters (a 0 and a 2) in 130Ba isotope was the increases of a0 associated with decreases of a2 which mean that the γ-unstable features in IBM2 χπ and χν were (-1.3 and 0.7) which signified similarity with IBM1 expected.130Ba isotope described to be transitional nucleus, transitional between SU(3) and O(6) features.

Electric Monopole Transitions in Nd Nuclei within IBM-2

The monopole transitions of 144-154Nd isotopes have been investigated in this work within the interacting boson model-2 (IBM-2) framework. The low-lying energy levels, electric quadrupole transition probability rates B(E2), electric quadrupole moments for first excited states monopole transition matrix elements and the intensity ratio were calculated in this work. The results of IBM-2 have been compared with the available experimental data; we have obtained a reasonable agreement. Unfortunately, the experimental data available on E0 transitions are very rare.The electric transition probability rates of beta and gamma bands to ground state band were calculated are fairly good agreement with available experimental values. Concerning the electric transition rates properties in IBM-2, we find that all calculations trends is reproduced well reasonably. The effective charges for neutron bosons and proton bosons calculated within IBM-2 are depending on the IBM-2 symmetries, we get suitable values for which is a constant for all 144-154Nd isotopes because the number of proton bosons is constant. The effective charge for neutron bosons varies from isotope to another

Nuclear structure features in 72-80Se isotopes

Interacting boson model (IBM – 1 and IBM – 2) have been used to perform a whole studying for isotopes. The low lying positive party states, dynamic symmetries, mixed symmetry states MSS, reducing electric quadruple transition probabilities B(E2), branching ratio, quadruple momentum , reducing magnetic dipole transition probability B(M1), mixing ratio δ(E2/M1), reducing electric monopole transition probability B(E0), and X(E0/E2) ratio have been investigated. U(5) features are the dominant in with addition of a 2 small effect of parameter started from to isotopes, energy ratios show that isotopes as the nearest isotopes to typical vibrational limit while isotopes tend towards the rotational region that lied on U(5) - SU(3), leg of “Casten’s triangle”. Spin and party for many energy levels and electromagnetic transition probability are confirmed. The mixing symmetry states in isotopes are slowly increased with ζ2 while there is no clear effected in isotope. The calculated branching ratios B(E2), B(M1) mixing ratios δ(E2/M1), B(E0), and X(E0/E2) depend in comparisons with fewer available experimental data. The results are in acceptable agreement; to completed a perfect comparison, more experimental investigations are still needed to these nuclei. isotopes have small values of electric quadruple moment of state.

Monopole and dipole transitions of the cluster states of O18

On the basis of an extended antisymmetrized molecular dynamics calculation, we study the cluster structure and the of the 0+ and 1- states of 18O. We discuss that several different kinds of cluster states appear in the excitation spectrum, and their monopole and dipole transitions are interesting fingerprints of unique cluster structure. We show that the monopole/dipole transitions are enhanced for the 14C+alpha cluster states, while they are hindered for the molecular-orbit state. We also point out that the ratio of the electric and isoscalar monopole transition strengths gives a good hint for the structure of the excited states.

Benchmark calculations of electromagnetic sum rules with a symmetry-adapted basis and hyperspherical harmonics

We demonstrate the ability to calculate electromagnetic sum rules with the \textit{ab initio} symmetry-adapted no-core shell model. By implementing the Lanczos algorithm, we compute non-energy weighted, energy weighted, and inverse energy weighted sum rules for electric monopole, dipole, and quadrupole transitions in $^4$He using realistic interactions. We benchmark the results with the hyperspherical harmonics method and show agreement within $2\sigma$, where the uncertainties are estimated from the use of the many-body technique. We investigate the dependence of the results on three different interactions, including chiral potentials, and we report on the $^4$He electric dipole polarizability calculated in the SA-NCSM that reproduces the experimental data and earlier theoretical outcomes. We also detail a novel use of the Lawson procedure to remove the spurious center-of-mass contribution to the sum rules that arises from using laboratory-frame coordinates. We further show that this same technique can be applied in the Lorentz integral transform method, with a view toward studies of electromagnetic reactions for light through medium-mass nuclei.

Generalized oscillator strengths of the valence-shell excitations of argon studied by fast electron impact

The generalized oscillator strengths of the valence-shell excitations from the ground state to 3p5(4s, 4s′, 4p, 4p′, 3d, 3d′, 5p, 5p′, 5s, 4d) of argon have been determined at an incident electron energy of 1500 eV and an energy resolution of about 90 meV. The accuracy of the present generalized oscillator strengths is improved by the adopted relative flow technique. The comprehensive comparison of the present results with the previous experimental and theoretical ones shows that the first Born approximation is satisfied in the lower squared momentum transfer region for the electric dipole excitations, while the deviations from the prediction of the first Born approximation and the inelastic x-ray scattering measurements near the minimum and in the larger K2 region are obvious, which can be attributed to the failure of the first Born approximation in this K2 region. The invalidity of the first Born approximation has also been observed for the electric monopole transitions even at a high impact electron energy of 2500 eV.

Electron spectrometer for electric monopole (E0) transition studies in nuclei

The study of electric monopole (E0) transitions between two 0+ states is important because the monopole strength carries vital information about the nuclear structure due to its direct link with the mean squared charge radius r2 and quadrupole deformation parameter β. Therefore, the measurement of internal conversion electrons (ICE) or internal pair formation (IPF) is crucial for E0 transition studies. Transitions between 0+ states do not change angular momentum. Hence, single-photon emission is forbidden, but can decay by conversion electrons or pair formation and two-photon emission which is mostly negligible. In order to implement E0 studies at iThemba LABS, an electron spectrometer that uses a solenoidal magnetic field acting as a lens and a Si(Li) detector has been refurbished and characterized using calibration sources of ICE. Figures of merit have been extracted and compared with simulations. The spectrometer coupled with an array of LaBr3:Ce detectors and Low Energy Photon Spectrometers (LEPS) was successfully implemented for in-beam experiments. Measurements of internal conversion coefficients (ICC) and monopole strengths extracted from in-beam measurements of 72As, 72Ge, and 72Se are presented.

Evidence for shape coexistence in 52Cr through conversion-electron and pair-conversion spectroscopy

Electric monopole (E0) transitions are a highly sensitive probe of the charge distribution of an atomic nucleus. A large E0 transition strength (ρ2(E0)) is a clear indicator of nuclear shape coexistence. In the region between doubly magic 40Ca and 56Ni, E0 transitions have never been observed in the Ti or Cr isotopes, nor in the heavier iron isotopes (56,58Fe). We have performed the first measurements of the E0 transitions in 52Cr via conversion-electron and pair-conversion spectroscopy using the Super-e spectrometer at the Australian National University Heavy Ion Accelerator Facility. We present the first spectra obtained for 52Cr, including the first observation of the E0 transition from the first-excited 0+ state in 52Cr, in both electron-positron pairs and conversion-electron spectroscopy. The preliminary values for the E0 strength in the 1531keV 2+ → 2+ transition in 52Cr is ρ2(E0) × 103 = 470(190), and for the 1728-keV 23+ → 21+ transition, it is ρ2(E0) 103 = 1800(1200). The large E0 strengths observed are consistent with shape coexistence in this region. However, despite the relatively precise observation of the conversion-electron and electron-positron pair intensities, the E0 strengths have large uncertainties. More precise determinations of relevant spectroscopic quantities, such as the state lifetimes and transition mixing ratios for mixed M1 + E2 transitions, are needed to determine the E0 strength more precisely.

Energy levels, oscillator strengths, radiative transition probabilities, level lifetimes and electron-impact excitation rate coefficients for Ne-like Mo XXXIII

The energy levels, oscillator strengths, radiative decay rates, lifetimes, collision strengths, direct and resonance electron-impact excitation rate coefficients have been computed for the 257 fine-structure levels arising from 1s22s22p5nl and 1s22s2p6n′l′ configurations belonging to the Mo32+ ion with n≤7, l≤4 and n′≤5, l′≤4. The model-potential approach is used for the target ion structure calculations. Additionally, we employ the multiconfiguration Dirac–Hartree–Fock method to further assess the energy levels and transition probabilities. The collision strengths for the electron-impact direct excitation are computed within the relativistic distorted-wave approximation at 34, 135, 680, 1700, 5436, and 12,740 eV scattered electron energy values. We also perform collision calculations at 85, 175, and 450 keV electron energies using the plane-wave approximation and interpolate the reduced cross section within Fano plots, thus accounting for relativistic effects at asymptotic energies. This assures the convergence of Maxwellian integration for effective collision strengths calculation at electron temperatures up to 80 keV. The resonance contribution to the excitation rates is accounted for within the independent process isolated resonance approximation by including Na-like Mo31+ doubly excited autoionization states arising from the 1s227nln′l′ configurations with n≤7,l≤4,n′≤20,l′≤8. Contributions from high n′≥21 Rydberg states to the excitation rate coefficients are included by employing the n′−3 extrapolation law for radiative and autoionization decay rates. Radiative decay of resonances to lower autoionization states followed by autoionization cascade as well as radiative damping via core transitions are included in our model. The highest rate coefficients corresponding to ground state excitations are the 2p–3d allowed and 2p–3p electric monopole transitions, respectively. Intercombination and generally higher-order electric multipole transitions amount to lower excitation rate coefficients but are not to be neglected. Magnetic transitions are only relevant for low electron temperatures since both their direct and resonance contributions to excitation significantly decrease with increasing electron energy. Present results compare well with existing data from literature. The resonance contributions play an important role in the accuracy of rate coefficients, especially for weak forbidden transitions at low electron temperatures. These results may be useful in fusion related plasmas, astrophysics and fundamental physics.

E0 transition strengths in 110Pd

Internal conversion coefficients have been measured for transitions in 110Pd to allow the determination of electric monopole (E0) transition strengths. Excited states were populated through inelastic alpha scattering and the SPICE+TIGRESS detectors at TRIUMF-ISAC-II were used to detect the emitted gamma rays and internal conversion electrons. The E0 transition strengths are found to be small and are consistent with the expectation for transitions from a K = 2 band to the K = 0 ground-state band in the axial rotor model.

Microscopic method for E0 transition matrix elements

We present a microscopic model for electric monopole ($E0$) transition matrix elements by combining a configuration interaction model for orbital occupations with an energy-density functional model for the single-particle potential and radial wave functions. The configuration interaction model is used to constrain the orbital occupations for the diagonal and off-diagonal matrix elements. These are used in an energy-density functional calculation to obtain a self-consistent transition density. This density contains the valence contribution, as well as the polarization of the protons by the valence protons and neutrons. We show connections between $E0$ matrix elements and isomer and isotope shifts of the charge radius. The spin-orbit correction to the charge density is important in some cases. This model accounts for a large part of the data over a wide region of the nuclear chart. It also accounts for the shape of the observed electron scattering form factors. The results depend on the Skyrme parameters used for the energy-density functional and might be used to provide new constraints for them.

E0 transitions in 106Pd: Implications for shape coexistence

Level lifetimes in 106Pd were measured with the Doppler-shift attenuation method following inelastic neutron scattering, and electric monopole transition strengths between low-lying 2+ states were deduced. The large \( \rho^{2}\)(E0) values obtained provide evidence for shape coexistence, extending observation of such structures in the N = 60 isotones. Included in these results is the first determination of the E0 transition strength in the Pd nuclei between levels with K = 2 .

Shape coexistence and evolution inSr98

Shape coexistence between the strongly deformed ground state and the weakly deformed ${0}_{2}^{+}$ state in $^{98}\mathrm{Sr}$ has been a major topic of interest due to the energy difference of 215 keV, which is the smallest in all even-even nuclei. The electric monopole transition strength ${\ensuremath{\rho}}^{2}(E0)$ is an important quantity that can relate the deformation difference and the shape mixing between the two ${0}^{+}$ states, which are admixtures of the vibrational (S) and the rotational (D) states in a simple mixing model. In a $\ensuremath{\beta}$-decay spectroscopy experiment, the experimental ${\ensuremath{\rho}}^{2}(E0)$ was measured. A value of 0.053(5) is consistent with the previous measurement and was combined with known electric quadrupole transition strengths $B(E2)$ in calculations of a two-state mixing model. Based on a systematic study on neighboring Kr, Zr, and Mo isotopes, the mixing of the ${0}^{+}$ and ${2}^{+}$ states in $^{98}\mathrm{Sr}$ was determined to be 8.6% and 1.3%, respectively, corresponding to deformation parameters ${\ensuremath{\beta}}_{\text{D}}=0.38(1)$ and ${\ensuremath{\beta}}_{\text{S}}=\ensuremath{-}0.23(2)$. These parameters reproduce experimental transition strengths well except for the ${4}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+}$ transition, which suggests a smaller D-band deformation for $J\ensuremath{\ge}4$.