Low-lying Positive Parity States Research Articles

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.

Investigation of Mixed Symmetry States in 170-178Yb isotopes

low-lying positive parity states, dynamic symmetries, mixed symmetry states (MSS), reducing electric quadrupole transition probabilities B(E2), branching ratio, reducing magnetic dipole transition probabilities B(M1), and mixing ratios δ(E2/M1) for 170-178Yb have been investigated by applied IBM-1 and IBM-2 program package. The software package IBM-1 and IBMT computer code for IBM-1 and Neutron Proton Boson NPBOS and Neutron Proton Boson Electromagnetic NPBEM software package have been used. The Ytterbium nuclei with the (170 − 178) mass number considered as rotational nuclei after applying the first and second interacting boson model with studying dynamic symmetry and energy ratios , and that approximated to (3.33,7 and 12). The reducing transition probability for electric quadruple B(E2) and branching ratios that state the small values of the ratios R′ and R″ as having rotational characteristics. A study of the mixed symmetry state of these nuclei shows that the lower energy mixing level is the first 1+ level, which distinguishes the rotational determination nuclei. The energy levels values for the states have a clear mixed symmetry state (MSS) directly proportional with Majorana parameters ζ2, while , and , tend to be approximately more conservative.

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.

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.

U(6) quasi-dynamical symmetry in 238U

The proton-neutron symplectic model with Sp(12,R) dynamical algebra is applied for the simultaneous description of the microscopic structure of the low-lying positive-parity states of the lowest ground, β and γ bands in U238. For this purpose, the model Hamiltonian is diagonalized in a U(6)-coupled basis, restricted to the state space spanned by the fully symmetric U(6) irreps. A good description of the energy levels of the three bands under consideration, as well as the enhanced intraband B(E2) transition strengths between the states of the ground band is obtained without the use of an effective charge. The results obtained show small admixtures from the higher major shells and a highly coherent mixing of different U(6) irreps which is manifested by the presence of a good U(6) quasi-dynamical symmetry in the microscopic structure of the collective states under consideration.

Structure of the low-lying positive parity states in the proton-neutron symplectic model

The proton-neutron symplectic model with Sp(12, R) dynamical symmetry is applied for the simultaneous description of the microscopic structure of the low-lying states of the ground state, γ and β bands in 166Er. For this purpose, the model Hamiltonian is diagonalized in the space of stretched states by exploiting the SUp(3) ⊗ SUn(3) symmetry-adapted basis. The theoretical predictions are compared with experiment and some other microscopic collective models, like the one-component Sp(6, R) symplectic and pseudo-SU(3) models. A good description of the energy levels of the three bands under consideration, as well as the enhanced intraband B(E2) transition strengths between the states of the ground and γ bands is obtained without the use of effective charges. The results show the presence of a good SU(3) dynamical symmetry. It is also shown that, in contrast to the Sp(6, R) case, the lowest excited bands, e.g., the β and γ bands, naturally appear together with the ground state band within a single Sp(12, R) irreducible representation.

Deformed shell model study of event rates for WIMP-73Ge scattering

The event detection rates for the Weakly Interacting Massive Particles (WIMP) (a dark matter candidate) are calculated with [Formula: see text]Ge as the detector. The calculations are performed within the deformed shell model (DSM) based on Hartree–Fock states. First, the energy levels and magnetic moment for the ground state and two low-lying positive parity states for this nucleus are calculated and compared with experiment. The agreement is quite satisfactory. Then the nuclear wave functions are used to investigate the elastic and inelastic scattering of WIMP from [Formula: see text]Ge; inelastic scattering, especially for the [Formula: see text] transition, is studied for the first time. The nuclear structure factors which are independent of supersymmetric model are also calculated as a function of WIMP mass. The event rates are calculated for a given set of nucleonic current parameters. The calculation shows that [Formula: see text]Ge is a good detector for detecting dark matter.

Proton and neutron pair correlations in 10B

We developed an extension of the antisymmetrized molecular dynamics in which we perform energy variation after the projection to isospin eigenstates. In our first application of this method to 10B, we found that low-lying positive-parity states() have a spatially correlated pn pair and 2α structure.

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.

Algebraic approach to the structure of the low-lying states inA≈100Ru isotopes

The structure of the low-lying states in the odd- and even-mass $A\ensuremath{\approx}100$ Ru isotopes is studied in the framework of two algebraic models. The even-mass Ru nuclei are first described within the interacting boson model 1 (IBM-1). The output of these calculations was then used to calculate the odd-$A$ isotopes within the interacting boson-fermion model 1 (IBFM-1), where a coupling of the odd neutron to the even-even core is considered. The level energies and transition probabilities calculated in the present work are tested against the experimental data. One-nucleon transfer spectroscopic factors as well as electromagnetic moments were also calculated for the odd-$A$ Ru and compared to the experimental values. The transitional character of the isotopes is studied. Most of the low-lying positive-parity states in the odd-$A$ Ru nuclei below 2 MeV are interpreted on the basis of $\ensuremath{\nu}{d}_{5/2}$ and $\ensuremath{\nu}{g}_{7/2}$ configurations. The role of the $\ensuremath{\nu}{s}_{1/2}$ orbital in the nuclear structure of the odd-mass Ru nuclei at low energies is also studied. The negative-parity states are interpreted as $\ensuremath{\nu}{h}_{11/2}$ excitations coupled to the core. The evolution of the IBM-1 and IBFM-1 parameters is discussed.

High-spin Structure of $^{87}$Sr and $^{87}$Zr Nuclei: Shell-model Interpretation

In the present work we report a comprehensive analysis of shell model results for high-spin states of $^{87}$Sr and $^{87}$Zr for recently available experimental data within the full $f_{5/2}pg_{9/2}$ model space using JUN45 and jj44b effective interactions developed for this model space. In this work we have compared the energy levels, electromagnetic transition probabilities, quadrupole and magnetic moments with available experimental data. We have confirmed structure of high-spin states of these two nuclei which were tentatively assigned in the recent experimental work. In the case of $^{87}$Sr, for positive parity states up to $\sim$ 7.5 MeV, both interactions predict very good agreement with experimental data, while negative parity states are slightly suppressed in jj44b calculation.For the $^{87}$Zr nucleus, the jj44b interaction predicts higher energies for the negative parity states beyond $J \geq 27/2^{-}$. The configuration, which have one hole in $\nu g_{9/2}$ orbital, is responsible for generating the states in $^{87}$Sr. In the case of $^{87}$Zr, low-lying positive parity states come with the configuration having three holes in the $\nu g_{9/2}$, while the odd-parity states have configuration $\nu (f_{5/2}^{-1}g_{9/2}^{-2})$.

Ab initio calculations for Be-isotopes with JISP16

We present recent results from no-core configuration interaction calculations for 8Be, 10Be, and 12Be using the phenomenological two-body interaction JISP16. We calculate the binding energies of the ground state and the excitation energies of the low-lying positive-parity states. We discuss the contributions from the proton and neutron intrinsic spin and orbital motion to the total spin for several states, and use this to identify states which may be dominated by α-cluster configurations. In addition, we also calculate other observables such as dipole and quadrupole moments, as well as transition rates for select E2 transitions.

Electromagnetic transition strengths in52109Te

Lifetime measurements have been made in the neutron-deficient nucleus ${}^{109}$Te using the coincident recoil distance Doppler-shift method. The experimental $B(E2)$ values have been compared with state-of-the-art shell-model calculations using the monopole-corrected realistic charge-dependent Bonn nucleon-nucleon potential. Lifetimes in the $\ensuremath{\nu}{h}_{11/2}$ band are consistent with an interpretation based on the deformation driving properties of a single valence neutron outside of the even-even tellurium core and highlight the unexpected presence of collective behavior as the $N=50$ shell closure is approached. Lifetime measurements for the low-lying positive-parity states also appear to correlate well with shell-model calculations. In addition, a comparison with the proton-unbound nucleus ${}^{109}$I suggests that the presence of a single decoupled valence proton affects the total measured $B(E2)$ strengths in a manner that is not currently well understood.

Projected shell model study for neutron-rich, odd-odd Mn isotopes

Odd-odd nuclei are good candidates for probing possible structure changes away from the valley of stability. By using the projected shell model in which deformed Nilsson single-particle states are taken to build the model basis, we study band properties in odd-odd Mn ($Z=25$) isotopes with neutron number $N=33,35$, and 37. With the help of model analysis, we interpret the low-lying positive-parity states in these nuclei in terms of their intrinsic structures. Our study on high-spin negative-parity states explores the important role of the neutron ${g}_{9/2}$ orbit in this mass region.

Low-lying spectroscopy of a few even-even silicon isotopes investigated with the multiparticle-multihole Gogny energy density functional

A multiconfiguration microscopic method has been applied with the Gogny effective interaction to the calculation of low-lying positive-parity states in even-even ${}^{26\ensuremath{-}32}$Si isotopes. The aim of the study is to compare the results of this approach with those of a standard method of generator coordinate method (GCM) type and to get insight into the predictive power of multiconfiguration methods employed with effective nucleon-nucleon force tailored to mean-field calculations. It is found that the multiconfiguration approach leads to an excellent description of the low-lying spectroscopy of ${}^{26}$Si, ${}^{28}$Si, and ${}^{32}$Si, but gives a systematic energy shift in ${}^{30}$Si. A careful analysis of this phenomenon shows that this discrepancy originates from too large proton-neutron matrix elements supplied by the Gogny interaction at the level of the approximate resolution of the multiparticle-multihole configuration mixing method done in the present study. These proton-neutron matrix elements enter in the definition of both single-particle orbital energies and coupling matrix elements. Finally, a statistical analysis of highly excited configurations in ${}^{28}$Si is performed, revealing exponential convergence in agreement with previous work in the context of the shell model approach. This latter result provides strong arguments toward an implicit treatment of highly excited configurations.

A new cluster model interpretation of the anomalous lifetime of 14C

A new cluster model solution to the long-standing nuclear structure problem of describing the anomalously long lifetime of 14C is presented. Related beta-decay data for 14O to states in 14N, gamma-decay data between low-lying positive parity states in 14N and the elastic and inelastic magnetic dipole electron scattering from 14N data are all shown to be very accurately described by the model. The shapes of the beta spectra for the A = 14 system are also well reproduced by the model. The model invokes four-nucleon tetrahedral symmetric spatial correlations arising from three- and four-nucleon interactions, which yields a high degree of SU(4) singlet structure for the clusters and a tetrahedral intrinsic shape for the doubly magic 16O ground state. The large quadrupole moment of the 14N ground state is obtained here for the first time and arises because of the almost 100% d-wave deuteron-like-hole cluster structure inherent in the model.

Levels above the19/2−isomer inCu71: Persistence of theN=40neutron shell gap

Two prompt $\ensuremath{\gamma}$ rays of energies 2020 and 554 keV were observed in coincidence with delayed transitions depopulating the ${19/2}^{\ensuremath{-}}$ isomer in the $Z=29$, $N=42$ $^{71}\mathrm{Cu}$ nucleus. The newly identified transitions are proposed to deexcite the 4776- and 5330-keV levels above the ${19/2}^{\ensuremath{-}}$ isomer. Based on the comparison with the low-lying positive-parity states observed in the $Z=42$, $N=50$ $^{92}\mathrm{Mo}$ nucleus, spin and parity ${23/2}^{\ensuremath{-}}$ are proposed for the 4776-keV level in $^{71}\mathrm{Cu}$. The high-energy, 2020-keV transition is interpreted as arising from the breaking of the $N=40$ neutron core. Shell-model calculations with a $^{56}\mathrm{Ni}$ core reproduce the $(23/{2}^{\ensuremath{-}})\ensuremath{\rightarrow}(19/{2}^{\ensuremath{-}})$ gap well, suggesting that the ${23/2}^{\ensuremath{-}}$ state is dominated by $\ensuremath{\pi}{p}_{3/2}\ensuremath{\nu}((\mathit{fp}){}^{10}({g}_{9/2}){}^{4})$ configurations. The present result constitutes further evidence supporting the view that the $N=40$ subshell closure persists in $^{71}\mathrm{Cu}$, herewith challenging recent suggestions that the coupling of two or more proton or neutron quasiparticles induces a large polarization of the $^{68}\mathrm{Ni}$ core.

Spin-parity measurements in the neutron-rich N ∼ 20 34P and 36S nuclei

Yrast and near-yrast energy levels in the neutron-rich N ∼ 20 nuclei 34P, 36S were populated using transfer/deep-inelastic processes following the 34S + 115In reaction at an incident energy of 140MeV. The use of a multi-clover array has facilitated polarization measurements of the observed γ-rays and necessitated some changes in the previously known level scheme. The observation of the negative-parity levels in these nuclei on the periphery of the “island of inversion” is indicative of the influence of the intruder orbitals on the level structure at low spins. Shell-model calculations indicate that the inclusion of the orbitals from the upper pf shell is important even for the low-lying positive-parity states.

β decay ofS40,42andCl43

Results from the study of the \ensuremath{\beta} decays of $^{40,42}\mathrm{S}$ and $^{43}\mathrm{Cl}$, produced in the fragmentation of a 70-MeV/nucleon $^{48}\mathrm{Ca}$ beam, are presented. The half-lives for $^{42}\mathrm{S}$ and $^{43}\mathrm{Cl}$ have been measured to be $1.03\ifmmode\pm\else\textpm\fi{}0.03$ s and $3.13\ifmmode\pm\else\textpm\fi{}0.09$ s, respectively. On the basis of \ensuremath{\gamma}-ray singles and $\ensuremath{\gamma}\ensuremath{\gamma}$ coincidence data, decay schemes for each of these decays have been established. Only subtle changes in low-energy nuclear structure, including switching of the order of the ${2}^{\ensuremath{-}}$ and ${3}^{\ensuremath{-}}$ states in the odd-odd Cl isotopes, were observed when passing the midpoint of the $\ensuremath{\nu}{f}_{7/2}$ subshell. These results agree well with previous shell-model calculations using restricted model spaces suggesting that deformation and shell-breaking effects in the midshell region are small. However, excitations across the $N=20$ shell gap are important to explain the low-lying positive parity states.

Unique features of structure in an odd-protonN≈ZnucleusAs69

We apply a large-scale shell model to the study of proton-rich odd-mass nuclei with $N \approx Z$. Calculations predict unexpected structure in the $^{69}$As nucleus for which a detailed experiment was recently performed. In this odd-proton nucleus, one neutron competes with one proton for occupying the high-$j$ intruder orbit $g_{9/2}$ in the $9/2_1^+$ state and almost solely occupies the $g_{9/2}$ orbit in other low-lying positive-parity states. The T=0, J=9 one-proton-one-neutron alignment takes place in the negative-parity states with medium-high spins. A unique coexistence of two lowest bands with positive and negative signs of spectroscopic quadrupole moments is predicted.