Non-yrast States Research Articles

Suppressed electric quadrupole collectivity in 49Ti

Single-step Coulomb excitation of 46,48,49,50Ti is presented. A complete set of E2 matrix elements for the quintuplet of states in 49Ti, centred on the 2+ core excitation, was measured for the first time. A total of nine E2 matrix elements are reported, four of which were previously unknown. 2249Ti27 shows a 20% quenching in electric quadrupole transition strength as compared to its semi-magic 2250Ti28 neighbour. This 20% quenching, while empirically unprecedented, can be explained with a remarkably simple two-state mixing model, which is also consistent with other ground-state properties such as the magnetic dipole moment and electric quadrupole moment. A connection to nucleon transfer data and the quenching of single-particle strength is also demonstrated. The simplicity of the 49Ti-50Ti pair (i.e., approximate single-j0f7/2 valence space and isolation of yrast states from non-yrast states) provides a unique opportunity to disentangle otherwise competing effects in the ground-state properties of atomic nuclei, the emergence of collectivity, and the role of proton-neutron interactions.

Systematic shell-model study of structure and isomeric states in 204–213Bi isotopes

In this work, we have performed systematic shell-model (SM) calculations for Bi isotopes with A = 204–213 using KHH7B and KHM3Y effective interactions. We have reported yrast and non-yrast SM states corresponding to the available experimental data. From the comparison with the experimental data, we could assign spin and parity of several unconfirmed states. We have also calculated electromagnetic properties and compared them with the available experimental data and predicted where experimental data are not available. This study also includes a detailed discussion of multiple isomeric states based on computed SM configurations and their respective half-lives.

Weighted variation after projection method for low-lying nonyrast states* *Supported by the National Natural Science Foundation of China (11975314), the Key Laboratory of Nuclear Data foundation (JCKY2022201C158), and the Continuous Basic Scientific Research Project (WDJC-2019-13, BJ20002501)

We propose a simple algorithm to further improve the previous variation after projection (VAP) wave functions for low-lying nonyrast states. We attach a weight factor to each calculated energy; then, the sum of these weighted energies is minimized. It turns out that a low-lying nonyrast VAP wave function can be further optimized when the weight factor for the corresponding energy is far larger than the other ones. Based on the improved WVAP wave functions, the energy-variance extrapolation method is applied to estimate the exact shell model energies. The calculated results for nuclei in the and model spaces clearly show that the extrapolated energies for all the calculated states are very close to the exact shell model ones within keV.

New collective structures in Au179 and their implications for the triaxial deformation of the Pt178 core

The extremely neutron-deficient isotope Au179 has been studied by a combination of in-beam γ-ray and isomeric-decay spectroscopy. For in-beam spectroscopy, the recoil-isomer tagging technique was employed, using the known 3/2−, T1/2=328 ns isomer. A new rotational band, associated with the unfavored signature band of the 1h9/2⊕2f7/2 proton-intruder configuration, was revealed. A previously unknown, high-spin isomeric state with an excitation energy of 1743(17) keV and T1/2=2.16(8)µs was discovered. Five decay paths were identified, some of them feeding previously unknown non-yrast excited states, associated with the 1i13/2 proton-intruder configuration. Calculations based on the particle-plus-triaxial-rotor model were performed to interpret the data. On the basis of these calculations, the new 1h9/2⊕2f7/2 rotational band is interpreted as due to triaxial deformation of the underlying configuration with β2≈0.26 and γ≈27∘. Observed non-yrast states of the positive-parity 1i13/2 intruder configuration are interpreted as due to triaxial deformation with β2≈0.26 and γ≈20∘.5 MoreReceived 9 May 2022Accepted 21 November 2022DOI:https://doi.org/10.1103/PhysRevC.106.064324©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsIsomer decaysLifetimes & widthsNuclear structure & decaysProperties150 ≤ A ≤ 189Nuclear Physics

Coulomb excitation of Rn222

The nature of quadrupole and octupole collectivity in Rn222 was investigated by determining the electric-quadrupole (E2) and octupole (E3) matrix elements using subbarrier, multistep Coulomb excitation. The radioactive Rn222 beam, accelerated to 4.23 MeV/u, was provided by the HIE-ISOLDE facility at CERN. Data were collected in the Miniball γ-ray spectrometer following the bombardment of two targets, Sn120 and Ni60. Transition E2 matrix elements within the ground-state and octupole bands were measured up to 10ℏ and the results were consistent with a constant intrinsic electric-quadrupole moment, 518(11)efm2. The values of the intrinsic electric-octupole moment for the 0+→3− and 2+→5− transitions were found to be respectively 2360−210+300efm3 and 2300−500+300efm3 while a smaller value, 1200−900+500efm3, was found for the 2+→1− transition. In addition, four excited non-yrast states were identified in this work via γ−γ coincidences.6 MoreReceived 10 December 2021Accepted 8 February 2022DOI:https://doi.org/10.1103/PhysRevC.105.024323Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectromagnetic transitionsNuclear structure & decaysPropertiesA ≥ 220Nuclear Physics

γ -ray spectroscopy of low-lying yrast and non-yrast states in neutron-rich Kr94,95,96

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Low-Energy Coulomb Excitation for the Shell Model

Low-energy Coulomb excitation is capable of providing unique information on static electromagnetic moments of short-lived excited nuclear states, including non-yrast states. The process selectively populates low-lying collective states and is, therefore, ideally suited to study phenomena such as shape coexistence and the development of exotic deformation (triaxial or octupole shapes). Historically, these experiments were restricted to stable isotopes. However, the advent of new facilities providing intense beams of short-lived radioactive species has opened the possibility to apply this powerful technique to a much wider range of nuclei. The paper discusses the observables that can be measured in a Coulomb-excitation experiment and their relation to the nuclear structure parameters with an emphasis on the nuclear shape. Recent examples of Coulomb-excitation studies that provided outcomes relevant for the Shell Model are also presented.

Nuclear structure of Te isotopes beyond neutron magic number N=82

Newly observed decay schemes of the nuclei Sb137 and Sb138 are reported. The neutron-rich Sb isotopes were produced by the in-flight fragmentation of a U238 primary beam with an energy of 345 MeV/nucleon. Several new excited states of Te137 with tentatively assigned spin-parities of (5/2−), (9/2−), and (7/2) have been established which play an important role in the evolution of neutron levels beyond N=82. The study of the β decay of Sb138 led to a considerable extension of the level scheme of Te138 including the identification of several nonyrast states. The structure of Te137 and Te138 is discussed on the basis of large-scale shell-model calculations performed using two different effective interactions.

Quasi- γ band in Te114

The low-lying non-yrast states in $^{114}$Te have been investigated using the Indian National Gamma Array through the fusion-evaporation reaction $^{112}$Sn($^{4}$He, 2n) at a beam energy of 37 MeV. Eight new $\gamma$-transitions have been placed in the level scheme to establish the quasi-$\gamma$ band in this nucleus. Spin and parity of several excited states have been assigned from the present spectroscopy measurements. The comparison of experimental results on the observed bands with the Interacting Boson Model (IBM) and Triaxial Projected Shell Model (TPSM) confirming the existence of the quasi-$\gamma$ band structure in the $^{114}$Te nucleus.

New level scheme and shell model description of Rn212

Level structures of Rn212 have been studied by in-beam γ-ray spectroscopic methods using the Bi209(Li6,3n)Rn212 reaction at beam energies of 28, 30, and 34 MeV. A number of new nonyrast states based on πh9/24 and πh9/23f7/2 configurations have been identified. A 3(−) collective state is also proposed at 2121 keV, which is most likely formed by mixing the octupole vibration with the 3− member of the πh9/23i13/2 multiplet. The level scheme is compared with large-scale shell model calculations and discussed in terms of excitations of valence protons and without contributions from the Pb208 core. An overall excellent agreement is obtained for states that can be described in this model space.

Shape coexistence and multiparticle-multihole structures in Cd110,112

From detailed spectroscopy of Cd-110 and Cd-112 following the beta(+)/EC decay of In-110,In-112 and the beta(-) decay of Ag-112, the presence of very weak decay branches from nonyrast states is revealed. In Cd-112, 2(5)(+) -> 0(4)(+) and 4(6)(+) -> 2(5)(+) transitions are observed that yield B(E2; 2(5)(+) -> 0(4)(+)) = 34 +/- 15 W.u. and B(E2; 4(6)(+) -> 2(5)(+)) = 77 +/- 30 W.u., respectively, clearly indicating a collective structure. In 110Cd, a weak decay branch from the 4(6)(+) level to the 2(5)(+) level is observed, and from a lifetime measurement following the (n, n gamma' reaction, B(E2; 4(6)(+) -> 2(5)(+)) = 55 +/- 14 W.u. is determined. A new branch is also observed for the decay of the 6(4)(+) level to the 4(6)(+) state, indicating that the sequence 2(5)(+), 4(6)(+), and 6(4)(+) forms part of a collective structure. The presence of 3(3)(+) and 5(2)(+) levels spaced between the previous sequence is highly suggestive of a gamma band built on the 0(2)(+) shape-coexisting intruder state. The 0(4)(+) levels in Cd-110,Cd-112,Cd-114 have preferred decays to the lowest 2(+) members of the intruder bands, and for 114Cd a previous measurement had established an enhanced B(E2; 0(4)(+) -> 2(3)(+)). The energy systematics of the 0(2)(+), 0(3)(+), and 0(4)(+) levels all display the characteristic parabolic-shaped pattern, suggesting that they are built on multiparticle-multihole proton excitations. The results are compared with beyond-mean-field calculations that reproduce qualitatively the observed levels and their decays and suggest that the 0(1)(+), 0(2)(+), 0(3)(+), and 0(4)(+) levels and the excited states built on them possess different deformations.

High spin states of Zr isotopes around A = 80 mass region — A study on cold and hot rotating nuclei

High spin structure of Zr isotopes, in particular, around [Formula: see text] has been studied in yrast and nonyrast regions. Spin dependence of shapes for the yrast levels are investigated by employing Cranked Hartree–Fock–Bogoliubov (CHFB) theory using a [Formula: see text] model interaction and the calculations are in good accord with the experimental data. The nonyrast states are treated by incorporating temperature degree of freedom using the statistical theory (ST). Highly deformed prolate shapes dominate the nonrotating proton rich region at low temperatures (T) with coexisting oblate and prolate shapes in [Formula: see text]Zr. Hot rotating nuclei show highest deformation around [Formula: see text] among all the other Zr isotopes even at high temperatures. [Formula: see text]Zr exhibits interesting structural transitions, hence studied in detail in yrast and non yrast regions. Triaxiality predominates in both yrast and nearly yrast (low temperature) regions at low spins with transition to elongated shapes at mid spin values 30–38[Formula: see text] to highly deformed oblate shapes at higher spins. CHFB predicts a strong backbending effect at 32[Formula: see text] and 40[Formula: see text]. A shape coexistence between the rare shape phase of noncollective prolate and oblate is reported in [Formula: see text]Zr at low temperature and [Formula: see text]. Prolate shape phase disappears with increasing temperature and spin but the nucleus remains highly deformed (with [Formula: see text] at spin [Formula: see text]40[Formula: see text]) even at high temperatures of the order of 3–3.5[Formula: see text]MeV, hence a very promising candidate for GDR probes of nuclear shapes.

Multiple Shape Coexistence in ^{110,112}Cd.

From detailed spectroscopy of ^{110}Cd and ^{112}Cd following the β^{+}/electron-capture decay of ^{110,112}In and the β^{-} decay of ^{112}Ag, very weak decay branches from nonyrast states are observed. The transition rates determined from the measured branching ratios and level lifetimes obtained with the Doppler-shift attenuation method following inelastic neutron scattering reveal collective enhancements that are suggestive of a series of rotational bands. In ^{110}Cd, a γ band built on the shape-coexisting intruder configuration is suggested. For ^{112}Cd, the 2^{+} and 3^{+} intruder γ-band members are suggested, the 0_{3}^{+} band is extended to spin 4^{+}, and the 0_{4}^{+} band is identified. The results are interpreted using beyond-mean-field calculations employing the symmetry conserving configuration mixing method with the Gogny D1S energy density functional and with the suggestion that the Cd isotopes exhibit multiple shape coexistence.

Shape coexistence in the neutron-deficient lead region: A systematic study of lifetimes in the even-even Hg188–200 with the GRIFFIN spectrometer at TRIUMF

Lifetimes of $2^+_1$ and $4^+_1$ states, as well as some negative-parity and non-yrast states, in $^{188-200}$Hg were measured using $\gamma-\gamma$ electronic fast timing techniques with the LaBr$_3$(Ce) detector array of the GRIFFIN spectrometer. The excited states were populated in the $\epsilon/\beta^+$-decay of $J^\pi =7^+/2^-$ $^{188-200}$Tl produced at the TRIUMF-ISAC facility. The deduced B(E2) values are compared to different interacting boson model predictions. The precision achieved in this work over previous ones allows for a meaningful comparison with the different theoretical models of these transitional Hg isotopes, which confirms the onset of state mixing in $^{190}$Hg.

Electromagnetic properties of low-lying states in neutron-deficient Hg isotopes: Coulomb excitation of 182Hg, 184Hg, 186Hg and 188Hg

.The neutron-deficient mercury isotopes serve as a classical example of shape coexistence, whereby at low energy near-degenerate nuclear states characterized by different shapes appear. The electromagnetic structure of even-mass 182-188 Hg isotopes was studied using safe-energy Coulomb excitation of neutron-deficient mercury beams delivered by the REX-ISOLDE facility at CERN. The population of 0^{+}_{1,2}, 2^{+}_{1,2} and 4^{+}_{1} states was observed in all nuclei under study. Reduced E2 matrix elements coupling populated yrast and non-yrast states were extracted, including their relative signs. These are a sensitive probe of shape coexistence and may be used to validate nuclear models. The experimental results are discussed in terms of mixing of two different configurations and are compared with three different model calculations: the Beyond Mean Field model, the Interacting Boson Model with configuration mixing and the General Bohr Hamiltonian. Partial agreement with experiment was observed, hinting to missing ingredients in the theoretical descriptions.

New Results on Excited States in the one-particle one-hole nucleus 56Co measured with MINIBALL detectors

The non-yrast states of the odd-odd nucleus 56Co have been investigated by studying the γ-rays induced in the predominantly fusion-evaporation reaction 56Fe(p,n γ)56Co at an incident energy of 10 MeV. The γ-rays were measured in-beam with four high-resolution MINIBALL-triple germanium (Ge) detectors. The experiment provided excellent data in γ-γ coincidences. The complex level scheme of 56Co was constructed mainly based on the analysis of these γ-γ coincidences. The angular distributions of the γ-rays were also analysed and allowed us to assign spin-parity values to most of the excited states in this nucleus. Despite the extensive work previously done studying the 56Co nucleus, the analysis presented in this work has resulted in a large improvement in the knowledge of its structure.

Quadrupole phonons in the cadmium isotopes

A key question concerning the spherical-vibrator attributes of states in Cadmium isotopes is addressed by means of a boson Hamiltonian encompassing U(5) partial dynamical symmetry. The U(5) symmetry is preserved in a segment of the spectrum and is broken in particular non-yrast states, and the resulting mixing with the intruder states is small. The vibrational character is thus maintained in the majority of low-lying normal states, as observed in $^{110}$Cd.

New yrast and non-yrast states in I136 and medium-spin structure of I136 and Xe136 : Roles of the proton d5/2 and the neutron h9/2 orbitals beyond Sn132

In this article we report on the observation of new yrast and non-yrast states in $^{136}\mathrm{I}$, populated in the prompt-$\ensuremath{\gamma}$ spectroscopy EXILL campaign at the ILL using both $^{235}\mathrm{U}$(n,f) and $^{241}\mathrm{Pu}$(n,f) reactions. We propose an extension of the level scheme and interpretation of the new spectroscopic results in comparison to state-of-the-art shell-model calculations. We discuss the role of the proton ${d}_{5/2}$ orbital in the structure of this nucleus with $Z=53$ and the energy split between the $\ensuremath{\pi}{d}_{5/2}\phantom{\rule{0.28em}{0ex}}\text{and}\phantom{\rule{0.28em}{0ex}}\ensuremath{\pi}{g}_{7/2}$ orbitals. We also provide a complete overview of all experimental information about this nucleus and include new data from $^{252}\mathrm{Cf},^{248}\mathrm{Cm}$ fission and $\ensuremath{\beta}$ decay of $^{136}\mathrm{Te}$ to $^{136}\mathrm{I}$. We give a new interpretation of $^{136}\mathrm{I}$ and its decay to $^{136}\mathrm{Xe}$ in terms of the influence of the neutron ${h}_{9/2}$ orbital and the Gamow-Teller strength for $N=83$.

New algorithm in the variation after projection calculations for non-yrast nuclear states

We present a novel and simple algorithm in the variation after projection (VAP) approach for the non-yrast nuclear states. It is for the first time that the yrast state and non-yrast states can be varied on the same footing. The orthogonality among the calculated states is automatically fulfilled by solving the Hill-Wheeler equation. This avoids the complexity of the frequently used Gram-Schmidt orthogonalization, as adopted by the excited VAMPIR method. Thanks to the Cauchy's interlacing theorem in the matrix theory, the sum of the calculated lowest projected energies with the same quantum numbers can be safely minimized. Once such minimization is converged, all the calculated energies and the corresponding states can be obtained, simultaneously. The present VAP calculations are performed with time-odd Hartree-Fock Slater determinants. It is shown that the calculated VAP energies (both yrast and non-yrast) are very close to the corresponding ones from the full shell model calculations. It looks the present algorithm is not limited to the VAP, but should be universal, i.e., one can do the variation with different forms of the many-body wavefunctions to calculate the excited states in different quantum many-body systems.

Partial dynamical symmetry and the vibrational structure of Cd isotopes

The recently reported deviations of selected non-yrast states in 110Cd from the expected sphericalvibrator behaviour, is addressed by means of an Hamiltonian with U(5) partial dynamical symmetry. The latter preserves the U(5) symmetry in a segment of the spectrum and breaks it in other states. The effect of intruder states is treated in the framework of the interacting boson model with configuration mixing.