E2 Transition Research Articles

ηc2(D21) and its electromagnetic decays

The spin-singlet state ηc2(D21) has not been discovered in experiment and it is the only missing low-excited D-wave charmonium, so in this paper, we like to study its properties. Using the Bethe-Salpeter equation method, we obtain its mass as 3828.2 MeV and its electromagnetic decay widths as Γ[ηc2(1D)→hc(1P)γ]=284 keV, Γ[ηc2(1D)→J/ψγ]=1.04 keV, Γ[ηc2(1D)→ψ(2S)γ]=3.08 eV, and Γ[ηc2(1D)→ψ(3770)γ]=0.143 keV. Considering the strong decay widths are estimated to be Γ(ηc2(1D)→ηcππ)=144 keV and Γ(ηc2(1D)→gg)=46.1 keV, we obtain the total decay width of 475 keV for ηc2(1D), and point out that the full width is very sensitive to the mass Mηc2. In our calculation, the emphasis is put on the relativistic corrections. Our results show that ηc2→hcγ is the nonrelativistic E1 transition dominated E1+M2+E3 decay, and ηc2→ψγ is the M1+E2+M3+E4 decay but the relativistic E2 transition contributes the most. Published by the American Physical Society 2024

Magnetization-current-induced E1 transition in the d+t→α+n+γ reaction

The d−t collisions have a minor reaction branch, of the order of 10−5, involving γ emission from the incident state with the spin of 3/2+ to the final 3/2− and 1/2− states of the α−n system. Standard E1 treatment of such a transition results in zero cross sections because of the spin conservation rule. For this reason, the first theoretical work on d+t→α+n+γ [], described the E1 transition as coming from the high-energy d-wave spin-1/2 state of the α−n partition of He5, coupled to the d−t component by tensor interaction. However, the exact E1 operator contains a contribution from the usually neglected magnetization current, represented by the nucleon spin operators, which can allow the E1 d+t→α+n+γ transition to occur without passing via the d-wave spin-1/2 α−n channel. The present paper studies the magnetization-current-induced E1 transition using several potential models of the d−t interaction. It was found that the strength of this transition depends strongly on the choice of the d−t interaction model. With the optical folding potential, correctly capturing the deuteron extended structure, this contribution is suppressed by three orders of magnitude, thus validating its neglect in the previous work. Published by the American Physical Society 2024

Asymptotic normalization coefficients for α+C12 synthesis and the S factor for C12(α,γ)O16 radiative capture

: The C12(α,γ)O16 reaction, determining the survival of carbon in red giants, is of interest for nuclear reaction theory and nuclear astrophysics. A specific feature of the O16 nuclear structure is the presence of two subthreshold bound states, (6.92 MeV, 2+) and (7.12 MeV, 1−), that dominate the behavior of the low-energy S factor. The strength of these subthreshold states is determined by their asymptotic normalization coefficients (ANCs), which need to be known with high accuracy. : The objective of this research is to examine how the subthreshold and ground-state ANCs impact the low-energy S factor, especially at the key astrophysical energy of 300keV. The S factors are calculated within the framework of the R-matrix method using the code. Our total S factor takes into account the E1 and E2 transitions to the ground state of O16 including the interference of the subthreshold and higher resonances, which also interfere with the corresponding direct captures, and cascade radiative captures to the ground state of O16 through four subthreshold states: 02+,3−,2+, and 1−. To evaluate the impact of subthreshold ANCs on the low-energy S factor, we employ two sets of the ANCs. The first selection, which offers higher ANC values, is attained through the extrapolation process [Blokhintsev , ]. The set with low ANC values was employed by deBoer []. A detailed comparison of the S factors at the most effective astrophysical energy of 300 keV is provided, along with an investigation into how the ground-state ANC affects this S factor. : The contribution to the total E1 and E2S factors from the corresponding subthreshold resonances at 300keV are (71–74)% and (102–103)%, respectively. The correlation of the uncertainties of the subthreshold ANCs with the E1 and E2S(300keV) factors is found. The E1 transition of the subthreshold resonance 1− does not depend on the ground-state ANC but interferes constructively with a broad (9.585MeV;1−) resonance giving (for the present subthreshold ANC) an additional 26% contribution to the total E1S(300keV) factor. Interference of the E2 transition through the subthreshold resonance 2+ with direct capture is almost negligible for small ground-state ANC of 58fm−1/2. However, its interference with direct capture for higher ground-state ANC of 337fm−1/2 is significant and destructive, contributing −27%. The low-energy SE2(300keV) factor experiences a smaller increase when both subthfreshold and the ground-state ANCs rise together due to their anticorrelation, compared to when only the subthreshold ANCs increase.Published by the American Physical Society2024

Core excitation in 92Mo up to high-spin

Abstract An in-beam gamma-ray spectroscopy study of the even-even nucleus 92Mo
has been carried out using the 30Si + 65Cu, 18O + 80Se reactions at beam energies of
120 and 99 MeV, respectively. Angular distribution from oriented state ratio (RADO)
and linear polarization (Δasym) measurements have fixed most of the tentatively
assigned spin-parity of the high energy levels. A large-scale shell-model calculation
using the GWBXG interaction has been carried out to understand the configuration
and structure of both positive and negative parity states up to the highest observed
spin. The high-spin states primarily originate from the coupling of excited proton and
neutron-core structures in an almost stretched manner. The systematics of energy
required for forming a neutron particle-hole pair excitation, νg9/2→νd5/2, is discussed.
Lifetime of few high-spin states have been measured using DSAM. Additionally, a
qualitative argument is proposed to explain the comparatively strong E1 transition
feeding the 7310.9-keV level.

Hard-scattering approach to strongly hindered electric dipole transitions between heavy quarkonia

The conventional wisdom in dealing with electromagnetic transition between heavy quarkonia is the multipole expansion, when the emitted photon has a typical energy of order quarkonium binding energy. Nevertheless, in the case when the energy carried by the photon is of order typical heavy quark momentum, the multipole expansion doctrine is expected to break down. In this work, we apply the “hard-scattering” approach originally developed to tackle the strongly hindered magnetic dipole (M1) transition [Y. Jia , ] to the strongly hindered electric dipole (E1) transition between heavy quarkonia. We derive the factorization formula for the strongly hindered E1 transition rates at the lowest order in velocity and αs in the context of the nonrelativistic QCD, and conduct a detailed numerical comparison with the standard predictions for various bottomonia and charmonia E1 transition processes. Published by the American Physical Society 2024

On the low-energy electromagnetic dipole modes in 151,153,155Sm Nuclei

The recently observed low-energy magnetic dipole (M1) and electric dipole (E1) excitations in deformed 151,153,155Sm are theoretically analysed. Rotational Invariant (RI-) and Translational-Galilean Invariant (TGI-) Quasiparticle Nuclear Model (QPNM) are used in the calculation of M1 and E1 properties, respectively. Both theories consider monopole pairing between nucleons, and the deformed Woods-Saxon potential is used as the mean-field potential. Pyatov's symmetry restoration procedure is applied in these models to eliminate the spurious modes from the intrinsic nuclear excitations. Model calculations show that although E1 transitions dominate the low-energy dipole spectra of 151,153,155Sm, many low-lying M1 transitions exist in these nuclei. It is shown that the most significant contribution to E1 and M1 excitation comes from ΔK=±1 transitions. The theory satisfactorily reproduces the gross features of low-lying dipole modes determined from the Oslo Method analysis of the experimental spectra.

Magnetic dipole contribution to the γ spectrum from d−t collisions

One in about a few 105 sub-Coulomb d−t collisions is accompanied by the emission of a γ photon. The γ spectrum from these collisions is dominated by a 16.7 MeV peak, corresponding to the population of the p-wave 3/2− α−n ground-state resonance in the E1 transition from an intermediate d-wave α−n state, corresponding to the He5 excited state around 16.7 MeV. The strength of this spectrum at the large γ-energy endpoint decreases fast both due to kinematic factors and due to centrifugal repulsion between neutron and α particle at near-zero relative energies. However, no centrifugal repulsion would occur if s-wave α−n states were populated in a magnetic dipole transition. Therefore, one can expect that close to the γ-spectrum endpoint around 17.5 MeV the M1 transition could dominate, leading to additional counts in experimental spectra which could be easily misinterpreted as a background. This work presents calculations of the M1 contribution to the d+t→α+n+γ cross section caused both by convection and magnetization currents. While the first contribution was found to be negligible, the one from magnetization depends strongly on the choice of the model for the d−t channel scattering wave function. Using d−t interaction models from the literature, represented either by a gaussian of by a square well, resulted in unrealistically strong M1 contribution. Withoptical folding potential constructed in the present work, correctly representing the sizes of deuteron and triton, the M1 contribution near the endpoint is reduced to about 2% of the 16.7-MeV E1 peak. Arguments in favor of more detailed calculations, that could potentially change this number, are put forward. Published by the American Physical Society 2024

Second order Rayleigh–Schrödinger perturbation theory for the Grasp2018 package: Core–core correlations

GRASP package is based on the relativistic configuration interaction in which accurate calculations, accounting for valence, valence–valence, core–valence, core and core–core electron correlations, often rely on massive CSF expansions. This paper presents a further development of the method based on the second-order perturbation theory for finding the most important CSFs that have the greatest influence on the core–valence, core and core–core correlations. This method is based on a combination of the relativistic configuration interaction method and the stationary second-order Rayleigh–Schrödinger many-body perturbation theory in an irreducible tensorial form [G. Gaigalas, P. Rynkun, and L. Kitovienė, Second-order Rayleigh–Schrödinger perturbation theory for the GRASP2018 package: Core–valence correlations, Lith. J. Phys. 64(1), 20–39 (2024), https://doi.org/10.3952/physics.2024.64.1.3, and G. Gaigalas, P. Rynkun, and L. Kitovienė, Second-order Rayleigh–Schrödinger perturbation theory for the GRASP2018 package: Core correlations, Lith. J. Phys. 64(2), 73–81 (2024), https://doi.org/10.3952/physics.2024.64.2.1]. In this extension, the perturbation theory takes into account electron core–valence, core and core–core correlations, where an atom or ion has any number of valence electrons, for calculation of energy spectra and other properties. Meanwhile, the rest of the correlations are taken into account in a traditional way. This allows a significant reduction of the space of the configuration state function for complex atoms and ions. We also demonstrate how this method works for calculations of the energy structure and E1 transition properties of Fe XV ion.

Direct observation of E0 transitions in 188Pb through in-beam spectroscopy

Competing configurations, assigned with three different shapes, are mixed at low angular momentum in the neutron-deficient 188Pb nucleus. Here, we present a simultaneous conversion electron and γ-ray in-beam spectroscopic precision measurement employing the sage spectrometer. The level energy of the first excited state, 02+, has been determined at 591(1)keV through direct measurement of conversion electrons. By using the intensity of the observed 02+→01+ transition to the ground state, the feeding of the 02+ state has been determined for the first time, which suggests the 02+ state is the head of the predominantly prolate band. The compositions of the 42+→41+ and 22+→21+ inter-band transitions have been determined, indicating configuration mixing between the bands.

Ab initio calculations of anomalous seniority breaking in the πg9/2 shell for the N = 50 isotones

We performed ab initio valence-space in-medium similarity renormalization group (VS-IMSRG) calculations based on chiral two-nucleon and three-nucleon interactions to investigate the anomalous seniority breaking in the neutron number N=50 isotones: 92Mo, 94Ru, 96Pd, and 98Cd. Our calculations well reproduced the measured low-lying spectra and electromagnetic E2 transitions in these nuclei, supporting partial seniority conservation in the first πg9/2 shell. Recent experiments have revealed that, compared to the symmetric patterns predicted under the conserved seniority symmetry, the 41+→21+E2 transition strength in 94Ru is significantly enhanced and that in 96Pd is suppressed. In contrast, the 61+→41+ and 81+→61+ transitions exhibit the opposite trend. We found that this anomalous asymmetry is sensitive to subtle seniority breaking effects, providing a stringent test for state-of-the-art nucleon-nucleon interactions and nuclear models. We analyzed the anomalous asymmetry using VS-IMSRG calculations across various valence spaces. Our ab initio results suggest that core excitations of both proton and neutron across the Z=50 shell are ascribed to the observed anomalous seniority breaking in the N=50 isotones.

Octupole correlations in stable nucleus 153Eu within reflection-asymmetric particle rotor model

Abstract The observed low-lying K=5/2± positive- and negative-parity bands in the stable nucleus 153Eu are investigated by the reflection-asymmetric triaxial particle rotor model. The experimental energy spectra, the energy staggering parameters, as well as the intraband E2 and M1 transition probabilities are well reproduced. It is found that the calculated interband B(E1) values depend sensitively on the octupole deformation parameter β30, although the energy spectra and intraband E2 and M1 transitions can be reproduced without the octupole degree of freedom. The observed enhanced E1 transition probabilities can be reproduced with β30=0.05. The detailed analysis of the intrinsic wave functions shows these nearly degenerate positive- and negative-parity bands are built on two individual proton configurations, i.e., dominated by πg9/2[Ω=5/2] and πh11/2[Ω=5/2], respectively, which differs from the parity doublet bands built on a single parity-mixed configuration.

Collectivity at the prolate-oblate transition: The [formula omitted] lifetime of 190W

The neutron-rich rare isotope 190W is discussed as a candidate for a prolate-oblate transitional nucleus with maximum γ-softness. The collectivity of this isotope is assessed for the first time by the measurement of the reduced E2 transition probability of its first 2+ state to the ground state. The experiment employed the FAst TIming Array (FATIMA), comprised of 36 LaBr3(Ce) scintillators, which was part of the DESPEC setup at GSI, Darmstadt. The 41+ and 21+ states of 190W were populated subsequently to the decay of its 127(12) μs isomeric Jπ=10− state. The mean lifetime of the 21+ state was determined to be τ=274(28) ps, which corresponds to a B(E2;21+→01+) value of 95(10) W.u. The results motivated a revision of previous calculations within an energy-density functional-based interacting boson model-2 approach, yielding E2 transition properties and spectroscopic quadrupole moments for tungsten isotopes. From comparison to theory, the new data suggest that 190W is at the transition from prolate to oblate structure along the W isotopic chain, which had previously been discussed as a nuclear shape-phase transition.

Role of the short-distance interaction in e+e−→γX(3872)

In this study, we analyze the cross-section data from the e+e−→γJ/ψω process to explore both short-distance and long-distance interactions for the radiative transition Y(4200)→γX(3872). We investigate the short-distance effects through the E1 transition among the cc¯ components, and the long-distance effects via hadronic loop diagrams. Our numerical analysis reveals that short-distance interactions play a significantly larger role in the radiative transition than that of the long-distance interactions. This finding underscores the importance of the compact cc¯ components in both the initial and the final states for accurately understanding the cross-section σ[e+e−→γJ/ψω]. Furthermore, with the help of relative branch ratio R we estimate the Γ[Y(4200)→γX(3872)] implied in the experimental study. Finally, we also discuss the possible existence of the ψ(4040) signal within the cross-section data. Published by the American Physical Society 2024

First Exploration of Monopole-Driven Shell Evolution above the N=126 Shell Closure: New Millisecond Isomers in ^{213}Tl and ^{215}Tl.

Isomer spectroscopy of heavy neutron-rich nuclei beyond the N=126 closed shell has been performed for the first time at the Radioactive Isotope Beam Factory of the RIKEN Nishina Center. New millisecond isomers have been identified at low excitation energies, 985.3(19)keV in ^{213}Tl and 874(5)keV in ^{215}Tl. The measured half-lives of 1.34(5)ms in ^{213}Tl and 3.0(3)ms in ^{215}Tl suggest spins and parities 11/2^{-} with the single proton-hole configuration πh_{11/2} as leading component. They are populated via E1 transitions by the decay of higher-lying isomeric states with proposed spin and parity 17/2^{+}, interpreted as arising from a single πs_{1/2} proton hole coupled to the 8^{+} seniority isomer in the ^{A+1}Pb cores. The lowering of the 11/2^{-} states is ascribed to an increase of the πh_{11/2} proton effective single-particle energy as the second νg_{9/2} orbital is filled by neutrons, owing to a significant reduction of the proton-neutron monopole interaction between the πh_{11/2} and νg_{9/2} orbitals. The new ms isomers provide the first experimental observation of shell evolution in the almost unexplored N>126 nuclear region below doubly magic ^{208}Pb.

Direct Observation of Competing M1 and M3 Transitions in ^{10}B.

Excited states in ^{10}B were populated with the ^{10}B(p,p^{'}γ)^{10}B^{*} reaction at 8.5MeV and their γ decay was investigated via coincidence γ-ray spectroscopy. The emitted γ rays were measured using large-volume LaBr_{3}:Ce and CeBr_{3} detectors placed in anti-Compton shields. This allowed the observation of weak γ-ray transitions, such as the M3 transition between the J^{π},T=0^{+},1 isobaric analog state (IAS) and the J^{π},T=3^{+},0 ground state and the E2 transition between the J^{π},T=2_{1}^{+},0 state and the IAS, i.e., performing measurements of branching ratios at the level of λ≥10^{-4}. For the first time in ^{10}B, the competing M1 and M3 transitions from the decay of the IAS have been observed in a γ spectroscopy experiment. The experimental results are compared with abinitio no-core shell model calculation using the newest version of the local position-space chiral N^{3}LO nucleon-nucleon interaction. The calculations reproduce correctly the ordering of the bound states in ^{10}B, and are in reasonable agreement with the observed branching ratios and reduced transition probabilities.

First observation of excited states in 120La and its impact on the shape evolution in the A ≈ 120 mass region

Excited states have been observed for the first time in the very neutron-deficient odd-odd nucleus 57120La63. The observed γ rays have been assigned based on coincidences with lanthanum X rays measured with the JUROGAM 3 array and with A=120 fusion-evaporation residues measured with the MARA separator. The observed γ rays form a rotational band which decays to the ground state via a cascade of four low-energy transitions. Based on the systematic comparisons with the heavier odd-odd La isotopes we assign spin-parity 4+ to the ground state and a πh11/2⊗νh11/2 configuration to the rotational band. The nuclear shape has been investigated by the cranked Nilsson-Strutinsky model. Two quasiparticle plus triaxial rotor model calculations including the np interaction nicely reproduce the spin of the inversion between the even- and odd-spin cascades of E2 transitions, giving credit to the np interaction as an important parameter responsible for the mechanism inducing the inversion. The position of the Fermi levels, in particular for neutrons, also has a strong impact on the observed inversion in the chain of lanthanum nuclei.

Intertwined quantum phase transitions in the zirconium and niobium isotopes

Nuclei in the A ≈ 100 region exhibit intricate shape-evolution and configuration crossing signatures. Exploring both even–even and their adjacent odd-mass nuclei gives further insight on the emergence of deformation and shape-phase transitions. We employ the algebraic frameworks of the interacting boson model with configuration mixing and the new interacting boson-fermion model with configuration mixing in order to investigate the even–even zirconium with neutron number 52–70 (40Zr) and odd-mass niobium (41Nb) isotopes with 52–62. We compare between the evolution in energy levels, configuration and symmetry content of the wave functions, two neutron separation energies and E2 transition rates, alongside comparison with the experimental data. The comparisons between the two chains of isotopes denote the occurrence of two types of QPTs, a crossing of normal and intruder configurations (named Type II QPT), and a shape-evolution of the intruder configuration (named Type I QPT). The latter QPT begins from spherical shape to axially deformed rotor in the Zr isotopes and from weak to strong coupling scenario in the Nb isotopes. This occurrence, named intertwined quantum phase transitions (IQPTs), in the even–even Zr chain is thus demonstrated to persists when coupling a proton to the boson core for the odd-mass Nb chain, even as deformation increases.

The shape of the Tz = +1 nucleus 94Pd and the role of proton-neutron interactions on the structure of its excited states

Reduced transition probabilities have been extracted between excited, yrast states in the N=Z+2 nucleus 94Pd. The transitions of interest were observed following decays of the Iπ=14+, Ex=2129-keV isomeric state, which was populated following the projectile fragmentation of a 124Xe primary beam at the GSI Helmholtzzentrum für Schwerionenforschung accelerator facility as part of FAIR Phase-0. Experimental information regarding the reduced E2 transition strengths for the decays of the yrast 8+ and 6+ states was determined following isomer-delayed Eγ1−Eγ2−△T2,1 coincidence method, using the LaBr3(Ce)-based FATIMA fast-timing coincidence gamma-ray array, which allowed direct determination of lifetimes of states in 94Pd using the Generalized Centroid Difference (GCD) method. The experimental value for the half-life of the yrast 8+ state of 755(106) ps results in a reduced transition probability of B(E2:8→+6+) = 205−25+34 e2fm4, which enables a precise verification of shell-model calculations for this unique system, lying directly between the N=Z line and the N=50 neutron shell closure. The determined B(E2) value provides an insight into the purity of (g9/2)n configurations in competition with admixtures from excitations between the (lower) N=3pf and (higher) N=4gds orbitals for the first time. The results indicate weak collectivity expected for near-zero quadrupole deformation and an increasing importance of the T=0 proton-neutron interaction at N=48.

171Yb+ optical clock with 2.2×10−18 systematic uncertainty and absolute frequency measurements

A full evaluation of the uncertainty budget for the ytterbium ion optical clock at the National Physical Laboratory (NPL) was performed on the electric octupole (E3) 2S1/2→2F7/2 transition. The total systematic frequency shift was measured with a fractional standard systematic uncertainty of 2.2×10−18 . Furthermore, the absolute frequency of the E3 transition of the 171Yb+ ion was measured between 2019 and 2023 via a link to International Atomic Time (TAI) and against the local caesium fountain NPL-CsF2. The absolute frequencies were measured with fractional standard uncertainties between 3.7×10−16 and 1.1×10−15 , and all were in agreement with the 2021 BIPM recommended frequency.

Compositional dependence of direct transition energies in SixGe1−x−ySny alloys lattice-matched to Ge/GaAs

SixGe1−x−ySny ternary alloys are a candidate material system for use in solar cells and other optoelectronic devices. We report on the direct transition energies and structural properties of Ge-rich SixGe1−x−ySny alloys with six different compositions (up to 10% Si and 3% Sn), lattice-matched to Ge or GaAs substrates. The direct interband transitions occurring at energies between 0.9 and 5.0 eV were investigated using spectroscopic ellipsometry, and the resulting data were used to obtain the dielectric functions of the SixGe1−x−ySny layer by fitting a multilayer model. Values for the E0, E1, Δ1, E0′, and E2 transition energies were then found by identifying critical points in the dielectric functions. Structurally, the composition of the samples was measured using energy-dispersive x-ray measurements. The lattice constants predicted from these compositions are in good agreement with reciprocal space maps obtained through x-ray diffraction. The results confirm that a 1 eV absorption edge due to direct interband transitions can be achieved using relatively low Si and Sn fractions (<10% and <3%, respectively), although the bandgap remains indirect and at lower energies. The higher-energy critical points show smaller shifts relative to Ge and match results previously observed or predicted in the literature.