Low-lying Negative Parity States Research Articles

The interplay of single-particle and collective motions in the low-lying states of $$_\Lambda ^{21}$$ with quadrupole-octupole correlations

The beyond mean-field approach for low-lying hypernuclear states is extended by mixing the configurations associated with both single-particle and quadrupole-octupole collective excitations within the generator coordinate method based on a covariant density functional theory. The method is demonstrated in the application to the low-lying states of $$_\Lambda ^{21}$$ , where the configurations with the Λ hyperon occupying the first (Λs) and second (Λp) lowest-energy states are considered. The results indicate that the positive-parity states are dominated by the α + 12C + α + Λs structure. In contrast, the low-lying negative-parity states are dominated by a strong admixture of α +16O + Λs structure and α + 12C + α + Λp structure due to the inclusion of octupole correlations. As a result, the low-lying negative-parity states become much lower than what is expected from the previous studies without the mixing, and the electric multipole transition strengths are significantly quenched.

Effect of configuration mixing on quadrupole and octupole collective states of transitional nuclei

A model is presented that simultaneously describes shape coexistence and quadrupole and octupole collective excitations within a theoretical framework based on the nuclear density functional theory and the interacting boson model. An optimal interacting-boson Hamiltonian that incorporates the configuration mixing between normal and intruder states, as well as the octupole degrees of freedom, is identified by means of self-consistent mean-field calculations using a universal energy density functional and a pairing interaction, with constraints on the triaxial quadrupole and the axially-symmetric quadrupole and octupole shape degrees of freedom. An illustrative application to the transitional nuclei $^{72}$Ge, $^{74}$Se, $^{74}$Kr, and $^{76}$Kr shows that the inclusion of the intruder states and the configuration mixing significantly lower the energy levels of the excited $0^+$ states, and that the predicted low-lying positive-parity states are characterized by the strong admixture of nearly spherical, weakly deformed oblate, and strongly deformed prolate shapes. The low-lying negative-parity states are shown to be dominated by the deformed intruder configurations.

First observation of the π0h11/2⊗ν0h9/2 partner orbital configuration in the odd-odd I138 nucleus

The β-decay scheme of Te138 and the level structure of I138 is reported for the first time. The experiment was performed at the Radioactive Isotope Beam Factory of RIKEN, as one of the EUROBALL-RIKEN Cluster Array campaigns. Secondary radioactive ions, including Te138 and Sb138, were produced by the in-flight fission of a U238 beam with the energy of 345 MeV per nucleon. From the β decay of Te138, the level scheme of I138 was supplemented with new spin and parity assignments, such as the low-lying negative-parity states and a positive-parity 1+ state. This 1+ state can be interpreted as being associated with the π0h11/2⊗ν0h9/2 partner orbital configuration populated by the Gamow-Teller transition between a neutron in the 0h9/2 orbital and a proton in the 0h11/2 orbital. Details of the structure of I138 are discussed in terms of the proton-neutron interactions and Gamow-Teller transition strength within the theoretical context of shell-model calculations.Received 5 December 2021Accepted 16 March 2022DOI:https://doi.org/10.1103/PhysRevC.105.034334©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBeta decayNuclear structure & decaysProperties90 ≤ A ≤ 149TechniquesRadiation detectorsRadioactive beamsShell modelSpectrometers & spectroscopic techniquesNuclear Physics

Observation of multiphonon transverse wobbling in 133Ba

The low-lying negative parity states in the 133Ba nucleus have been investigated using the 124Sn(13C, 4nγ)133Ba reaction at Elab = 48 MeV. With the addition of new γ-transitions, nω=0,1,2 wobbling bands were identified in this nucleus. The angular correlations and linear polarization measurements have been performed to confirm the spin and parity of the states. Predominant E2 character was obtained for the inter-linking ΔI=1 transitions between the successive phonon (Δnω=1) wobbling bands. The transverse nature of the wobbling bands is concluded on the basis of observed decreasing behavior of the wobbling frequency with increasing spin. The quasiparticle triaxial rotor model calculations are found to be in agreement with the experimentally determined wobbling frequency and the transition probability ratios. This letter reports the first observation of transverse wobbling mode associated with a hole-like quasiparticle.

Lifetimes and structures of low-lying negative-parity states of Po209

The $5/{2}_{1}^{\ensuremath{-}}$, $9/{2}_{1}^{\ensuremath{-}}$, and $11/{2}_{1}^{\ensuremath{-}}$ states in $^{209}\mathrm{Po}$ were populated in the $\ensuremath{\beta}$ decay of $^{209}\mathrm{At}$ and their lifetimes measured using the electronic $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ fast timing technique. The lifetime of the $9/{2}_{1}^{\ensuremath{-}}$ state is measured for first time. The lifetime of the $5/{2}_{1}^{\ensuremath{-}}$ is measured to be shorter than the value adopted in the literature while the lifetime of the $11/{2}_{1}^{\ensuremath{-}}$ state agrees well with the previous measurement. In order to get deeper insight into the structure of the states, a shell-model calculation was carried out adopting a microscopic effective interaction derived from the realistic CD-Bonn potential. The comparison between theoretical and experimental data for the low-lying negative-parity states of $^{209}\mathrm{Po}$ supports the reliability of the predicted wave functions, which are found to be dominated by the coupling of a neutron hole to the yrast states of $^{210}\mathrm{Po}$. However, it also points to the important role played by minor wave-function components in describing the reduced electromagnetic strengths, suggesting the need of additional configuration mixing for achieving a better quantitative agreement.

Coriolis coupling effects in proton-pickup spectroscopic factors from B12

Spectroscopic factors to low-lying negative-parity states in $^{11}$Be extracted from the $^{12}$B($d$,$^3$He)$^{11}$Be proton-removal reaction are interpreted within the rotational model. Earlier predictions of the $p$-wave proton removal strengths in the strong coupling limit of the Nilsson model underestimated the spectroscopic factors to the $3/2^-_1$ and $5/2^-_1$ states and suggested that deviations in the $1^+$ ground state of the odd-odd $^{12}$B due to Coriolis coupling should be further explored. In this work we use the Particle Rotor Model to take into account these effects and obtain a good description of the level scheme in $^{11}$B, with a moderate $K$-mixing of the proton Nilsson levels [110]1/2 and [101]3/2. This mixing, present in the $1^+$ bandhead of $^{12}$B, is key to explaining the proton pickup data.

Nuclear shape phase transition in even-even 158−168Hf isotopes

The interacting sdf-boson-approximation model is adopted to describe the low-lying positive and negative parity states in even-even 158−168Hf isotopes. The negative parity states are described using the sdf-IBM model by adding the L = 3 f-bosons nucleon pairs to the standard sd-boson model space. To determine the deformation of the nuclear structure of these isotopes the potential energy surfaces are calculated as functions of the deformation parameters. The reduced transition probabilities B(E2) in N = 94 are compared to the critical point symmetry X(5) predictions. In this chain, the sdf-boson interacting parameters are investigated and plotted against a number of neutrons. The shape phase transition from spherical 158Hf to well-deformed 168Hf nuclei is observed.

Microscopic structure of the low-lying negative-parity states in the proton-neutron symplectic model

The proton-neutron symplectic shell-model approach is applied to the description of the microscopic structure of the low-lying negative-parity states of the and bands in 154Sm and 238U without the introduction of additional degrees of freedom that are inherent to other approaches to odd-parity nuclear states. A good description of the energy levels of the two bands under consideration, as well as the reproduction of some energy splitting quantities which are usually introduced in the literature as a measure of the octupole correlations, is obtained for these two nuclei. Additionally, the low-energy B(E1) transition strengths between the states of the ground band and band for the two nuclei are calculated in the extended proton-neutron symplectic model and compared with experiment. The results obtained reproduce well the experimental data for the two nuclei under consideration without the use of an effective charge, which could be considered as a significant achievement of the present approach.

Experimental study of the low-lying negative-parity states in Be11 using the B12(d,He3)Be11 reaction

Low-lying negative-parity states in $^{11}\mathrm{Be}$ having dominant $p$-wave neutron configurations were studied using the $^{12}\mathrm{B}(d,^{3}\mathrm{He})\phantom{\rule{0.16em}{0ex}}^{11}\mathrm{Be}$ proton-removal reaction in inverse kinematics. The $1/{2}_{1}^{\ensuremath{-}}$ state at 0.32 MeV, the $3/{2}_{1}^{\ensuremath{-}}$ state at 2.56 MeV, and one or both of the states including the $5/{2}_{1}^{\ensuremath{-}}$ level at 3.89 MeV and the $3/{2}_{2}^{\ensuremath{-}}$ level at 3.96 MeV were populated in the present reaction. Spectroscopic factors were determined from the differential cross sections using a distorted wave Born approximation method. The $p$-wave proton removal strengths were well described by the shell model calculations while the Nilsson model calculation underestimates the spectroscopic factors for the higher excited states. Results from both variational Monte Carlo and no-core shell-model calculations were also compared with the experimental observations.

Structure of the low-lying positive and negative parity states in even–even 144−154Nd isotopes

The low-lying positive and negative parity states of even–even [Formula: see text]Nd isotopes are studied using the interacting boson model (IBM). The negative parity states are involved within the IBM model by adding a single angular momentum ([Formula: see text]) boson with intrinsic negative parity [Formula: see text]-boson to [Formula: see text] and [Formula: see text]-bosons model space. For these nuclei, the potential energy surfaces [Formula: see text], transition probability [Formula: see text], [Formula: see text] and [Formula: see text] are calculated. Phase transition from the [Formula: see text] limit to the [Formula: see text] limit is observed in the chain and the critical point has been determined for [Formula: see text]Nd isotope. It is found that the calculated positive and negative parity energy spectra of Nd-isotopes agree well with the experimental data.

Microscopic structure of the low-lying negative-parity states inSm154

The proton-neutron symplectic model with Sp(12,$R$) dynamical algebra is applied to the description of the microscopic structure of the low-lying negative-parity states of the ${K}^{\ensuremath{\pi}}={0}_{1}^{\ensuremath{-}}$ and ${K}^{\ensuremath{\pi}}={1}_{1}^{\ensuremath{-}}$ bands in $^{154}\mathrm{Sm}$ without the introduction of additional degrees of freedom that are inherent to other approaches to odd-parity nuclear states. For this purpose, the model Hamiltonian is diagonalized in a U(6)-coupled basis, restricted to state space spanned by the fully symmetric U(6) irreps of the lowest odd irreducible representation of Sp(12,$R$). In this way, the positive- and negative-parity collective bands are treated on equal footing within the framework of the microscopic symplectic-based shell-model scheme. A good description of the energy levels of the two bands under consideration, as well as the reproduction of some energy splitting quantities which are usually introduced in the literature as a measure of the octupole correlations, is obtained. The microscopic structure of low-lying collective states with negative-parity in $^{154}\mathrm{Sm}$ shows that practically there are no admixtures from the higher shells and hence the presence of a very good U(6) dynamical symmetry. Additionally, the structure of the collective states under consideration shows also the presence of a good SU(3) quasidynamical symmetry.

Search for excited states in O25

Theoretical calculations suggest the presence of low-lying excited states in $^{25}$O. Previous experimental searches by means of proton knockout on $^{26}$F produced no evidence for such excitations. We search for excited states in $^{25}$O using the ${ {}^{24}\text{O} (d,p) {}^{25}\text{O} }$ reaction. The theoretical analysis of excited states in unbound $^{25,27}$O is based on the configuration interaction approach that accounts for couplings to the scattering continuum. We use invariant-mass spectroscopy to measure neutron-unbound states in $^{25}$O. For the theoretical approach, we use the complex-energy Gamow Shell Model and Density Matrix Renormalization Group method with a finite-range two-body interaction optimized to the bound states and resonances of $^{23-26}$O, assuming a core of $^{22}$O. We predict energies, decay widths, and asymptotic normalization coefficients. Our calculations in a large $spdf$ space predict several low-lying excited states in $^{25}$O of positive and negative parity, and we obtain an experimental limit on the relative cross section of a possible ${ {J}^{\pi} = {1/2}^{+} }$ state with respect to the ground-state of $^{25}$O at $\sigma_{1/2+}/\sigma_{g.s.} = 0.25_{-0.25}^{+1.0}$. We also discuss how the observation of negative parity states in $^{25}$O could guide the search for the low-lying negative parity states in $^{27}$O. Previous experiments based on the proton knockout of $^{26}$F suffered from the low cross sections for the population of excited states in $^{25}$O because of low spectroscopic factors. In this respect, neutron transfer reactions carry more promise.

Spectroscopic factors in the N=20 island of inversion: The Nilsson strong-coupling limit

Spectroscopic factors, extracted from one-neutron knockout and Coulomb dissociation reactions, for transitions from the ground state of $^{33}\mathrm{Mg}$ to the ground-state rotational band in $^{32}\mathrm{Mg}$, and from $^{32}\mathrm{Mg}$ to low-lying negative-parity states in $^{31}\mathrm{Mg}$, are interpreted within the rotational model. Associating the ground state of $^{33}\mathrm{Mg}$ and the negative-parity states in $^{31}\mathrm{Mg}$ with the $\frac{3}{2}[321]$ Nilsson level, the strong coupling limit gives simple expressions that relate the amplitudes (${C}_{j\ensuremath{\ell}}$) of this wave function with the measured cross sections and derived spectroscopic factors (${S}_{j\ensuremath{\ell}}$). To obtain a consistent agreement with the data within this framework, we find that one requires a modified $\frac{3}{2}[321]$ wave function with an increased contribution from the spherical $2{p}_{3/2}$ orbit as compared to a standard Nilsson calculation. This is consistent with the findings of large-scale shell model calculations and can be traced to weak binding effects that lower the energy of low-$\ensuremath{\ell}$ orbitals.

Transition from vibrational to rotational character in low-lying states of hypernuclei

In order to clarify the nature of hypernuclear low-lying states, we carry out a comprehensive study for the structure of $^{144-154}_{~~~~~~~~\Lambda}$Sm-hypernuclei, which exhibit a transition from vibrational to rotational characters as the neutron number increases. To this end, we employ a microscopic particle-core coupling scheme based on a covariant density functional theory. We find that the positive-parity ground-state band in the hypernuclei shares a similar structure to that of the corresponding core nucleus. That is, regardless of whether the core nucleus is spherical or deformed, each hypernuclear state is dominated by the single configuration of the $\Lambda$ particle in the $s_{1/2}$ state ($\Lambda s_{1/2}$) coupled to one core state of the ground band. In contrast, the low-lying negative-parity states mainly consist of $\Lambda p_{1/2}$ and $\Lambda p_{3/2}$ configurations coupled to plural nuclear core states. We show that, while the mixing amplitude between these configurations is negligibly small in spherical and weakly-deformed nuclei, it strongly increases as the core nucleus undergoes a transition to a well-deformed shape, being consistent with the Nilsson wave functions. We demonstrate that the structure of these negative-parity states with spin $I$ can be well understood based on the $LS$ coupling scheme, with the total orbital angular momentum of $L=[I\otimes 1]$ and the spin angular momentum of $S=1/2$.

Simultaneous description of low-lying positive and negative parity states in spd, sdf and spdf interacting boson model

In order to investigate negative parity states, it is necessary to consider negative parity-bosons additionally to the usual [Formula: see text]- and [Formula: see text]-bosons. The dipole and octupole degrees of freedom are essential to describe the observed low-lying collective states with negative parity. An extended interacting boson model (IBM) that describes pairing interactions among s, p, d and f-boson based on affine [Formula: see text] Lie algebra in the quantum phase transition (QPT) field, such as spd-IBM, sdf-IBM and spdf-IBM, is composed based on algebraic structure. In this paper, a solvable extended transitional Hamiltonian based on affine [Formula: see text] Lie algebra is proposed to describe low-lying positive and negative parity states between the spherical and deformed gamma-unstable shape. Three model of new algebraic solution for even–even nuclei are introduced. Numerical extraction to low-lying energy levels and transition rates within the control parameters of this evaluated Hamiltonian are presented for various [Formula: see text] values. We reproduced the positive and negative parity states and our calculations suggest that the results of spdf-IBM are better than spd-IBM and sdf-IBM in this literature. By reproducing the experimental results, the method based on signature of the phase transition such as level crossing in the lowest excited states is used to provide a better description of Ru isotopes in this transitional region.

Shell evolution approaching the N= 20 island of inversion: Structure of 26Na

The levels in 26Na with single particle character have been observed for the first time using the d(25Na,p gamma) reaction at 5 MeV/nucleon. The measured excitation energies and the deduced spectroscopic factors are in good overall agreement with (0+1) hbar-omega shell model calculations performed in a complete spsdfp basis and incorporating a reduction in the N=20 gap. Notably, the 1p3/2 neutron configuration was found to play an enhanced role in the structure of the low-lying negative parity states in 26Na, compared to the isotone 28Al. Thus, the lowering of the 1p3/2 orbital relative to the 0f7/2 occurring in the neighbouring Z=10 and 12 nuclei -- 25,27Ne and 27,29Mg -- is seen also to occur at Z=11 and further strengthens the constraints on the modelling of the transition into the island of inversion.

Spectrum of heavy baryons in the quark model

Single- and double- heavy baryons are studied in the constituent quark model. The model Hamiltonian is chosen as a standard one with two exceptions : (1) The color-Coulomb term depend on quark masses, and (2) an antisymmetric $LS$ force is introduced. Model parameters are fixed by the strange baryon spectra, $\Lambda$ and $\Sigma$ baryons. The masses of the observed charmed and bottomed baryons are, then, fairly well reproduced. Our focus is on the low-lying negative-parity states, in which the heavy baryons show specific excitation modes reflecting the mass differences of heavy and light quarks. By changing quark masses from the SU(3) limit to the strange quark mass, further to the charm and bottom quark masses, we demonstrate that the spectra change from the SU(3) symmetry patterns to the heavy quark symmetry ones.

Multipole modes in deformed nuclei within the finite amplitude method

Background: To access selected excited states of nuclei, within the framework of nuclear density functional theory, the quasiparticle random phase approximation (QRPA) is commonly used. Purpose: We present a computationally efficient, fully self-consistent framework to compute the QRPA transition strength function of an arbitrary multipole operator in axially-deformed superfluid nuclei. Methods: The method is based on the finite amplitude method (FAM) QRPA, allowing fast iterative solution of QRPA equations. A numerical implementation of the FAM-QRPA solver module has been carried out for deformed nuclei. Results: The practical feasibility of the deformed FAM module has been demonstrated. In particular, we calculate the quadrupole and octupole strength in a heavy deformed nucleus $^{240}$Pu, without any truncations in the quasiparticle space. To demonstrate the capability to calculate individual QRPA modes, we also compute low-lying negative-parity collective states in $^{154}$Sm. Conclusions: The new FAM implementation enables calculations of the QRPA strength function throughout the nuclear landscape. This will facilitate global surveys of multipole modes and beta decays, and will open new avenues for constraining the nuclear energy density functional.

Low-lying intruder and tensor-driven structures inAs82revealed byβdecay at a new movable-tape-based experimental setup

The $\ensuremath{\beta}$ decay of $^{82}\mathrm{Ge}$ was re-investigated using the newly commissioned tape station BEDO at the electron-driven ISOL (isotope separation on line) facility ALTO operated by the Institut de Physique Nucl\'eaire, Orsay. The original motivation of this work was focused on the sudden occurrence in the light $N=49$ odd-odd isotonic chain of a large number of $J\ensuremath{\le}1$ states (positive or negative parity) in $^{80}\mathrm{Ga}$ by providing a reliable intermediate example, viz., $^{82}\mathrm{As}$. The extension of the $^{82}\mathrm{As}$ level scheme towards higher energies from the present work has revealed three potential ${1}^{+}$ states above the already known one at 1092 keV. In addition our data allow ruling out the hypothesis that the 843 keV level could be a ${1}^{+}$ state. A detailed analysis of the level scheme using both an empirical core-particle coupling model and a fully microscopic treatment within a Skyrme-QRPA (quasiparticle random-phase approximation) approach using the finite-rank separable approximation was performed. From this analysis two conclusions can be drawn: (i) the presence of a large number of low-lying low-spin negative parity states is due to intruder states stemming from above the $N=50$ shell closure, and (ii) the sudden increase, from $^{82}\mathrm{As}$ to $^{80}\mathrm{Ga}$, of the number of low-lying ${1}^{+}$ states and the corresponding Gamow-Teller fragmentation are naturally reproduced by the inclusion of tensor correlations and couplings to 2p-2h excitations.

Quadrupole-octupole coupled states inCd112populated in theCd111(d⃗,p)reaction

States in $^{112}\mathrm{Cd}$ have been studied with the $^{111}\mathrm{Cd}(\stackrel{P\vec}{d},p)^{12}\mathrm{Cd}$ reaction using 22 MeV polarized deuterons. The protons from the reaction were momentum analyzed with a Q3D magnetic spectrograph, and spectra have been recorded with a position-sensitive detector located on the focal plane. Angular distributions of cross sections and analyzing powers have been constructed for the low-lying negative-parity states observed, including the ${3}^{\ensuremath{-}},\phantom{\rule{0.16em}{0ex}}{4}^{\ensuremath{-}}$, and ${5}^{\ensuremath{-}}$ members of the previously assigned quadrupole-octupole quintuplet. The ${5}^{\ensuremath{-}}$ member at 2373-keV possess the second largest spectroscopic strength observed, and is reassigned as having the ${s}_{\frac{1}{2}}\ensuremath{\bigotimes}{h}_{\frac{11}{2}}$ two-quasineutron configuration as the dominate component of its wave function.