high-K States Research Articles

Fission hindrances in transfermium nuclei

Very heavy nuclei owe their stability against spontaneous fission to quantum shell effects, which depend on the local density of single-particle states. The height but also the width and the structure of the barrier in multi-dimensional deformation space determine the fission half-lives. Other effects come into play, such as the conservation of quantum numbers and superfluidity or stiffness of the system in the fission process. This is why odd nuclei have longer fission partial half-lives with respect to their even neighbours and also why multi-quasi-particle states, such as high-K states, are thought to be more stable against fission than the ground state. We will report here on two different fission studies carried out with the GABRIELA detector array at the focal plane of the recoil separator SHELS. The first study concerns the fission properties of 253Rf, the most neutron deficient Rf isotope known to date. The second study focusses on a new measurement of the fission hindrance of the known 8- isomer in 254No.

Fission-stability of high-K states in superheavy nuclei

Fission is the one of the primary radioactive decay modes for the heaviest nuclei and ultimately determines the existence of the heaviest elements on a macroscopic time scale, e.g., ge 10^{-14} s. The present experimental data on the decay properties of the heaviest nuclei with proton numbers 102–118 and/or of neutron numbers up to 177 show that fission occurs occasionally. This confirms that shell structure plays an essential role for their stability against fission. The shell effect on fission manifests in both collective and single-particle ways, which can experimentally be studied in decays of even–even, odd-A and odd–odd nuclei. At the same time, high-K states formed in couplings of quasiparticles are also known to be stable against fission. However, detailed knowledge and theoretical descriptions on a retardation effect/strength of high-K quantum number on fission are still scarce. In the present work, fission from high-K states are discussed and described within the semi-empirical approach. Fission half-lives are calculated for various high-K states, which have been theoretically predicted to exist in Fm-Rf (Z = 100–104) and Hs-Ds (Z = 108–112). The results are found to be in line with the available experimental findings, and also leading to different intriguing predictions, e.g., high-K states in superheavy nuclei tend to be more stable against fission compared to their ground states.

First observation of high-K isomeric states in $$^{249}$$Md and $$^{251}$$Md

Decay spectroscopy of the odd-proton nuclei $^{249}$Md and $^{251}$Md has been performed. High-$K$ isomeric states were identified for the first time in these two nuclei through the measurement of their electromagnetic decay. An isomeric state with a half-life of $2.8(5)$ ms and an excitation energy $\geq 910$ keV was found in $^{249}$Md. In $^{251}$Md, an isomeric state with a half-life of $1.4(3)$ s and an excitation energy $\geq 844$ keV was found. Similarly to the neighbouring $^{255}$Lr, these two isomeric states are interpreted as 3 quasi-particle high-$K$ states and compared to new theoretical calculations. Excited nuclear configurations were calculated within two scenarios: via blocking nuclear states located in proximity to the Fermi surface or/and using the quasiparticle Bardeen-Cooper-Schrieffer method. Relevant states were selected on the basis of the microscopic-macroscopic model with a deformed Woods-Saxon potential. The most probable candidates for the configurations of $K$-isomeric states in Md nuclei are proposed.

Metastable States of ^{92,94}Se: Identification of an Oblate K Isomer of ^{94}Se and the Ground-State Shape Transition between N=58 and 60.

Here we present new information on the shape evolution of the very neutron-rich ^{92,94}Se nuclei from an isomer-decay spectroscopy experiment at the Radioactive Isotope Beam Factory at RIKEN. High-resolution germanium detectors were used to identify delayed γ rays emitted following the decay of their isomers. New transitions are reported extending the previously known level schemes. The isomeric levels are interpreted as originating from high-K quasineutron states with an oblate deformation of β∼0.25, with the high-K state in ^{94}Se being metastable and K hindered. Following this, ^{94}Se is the lowest-mass neutron-rich nucleus known to date with such a substantial K hindrance. Furthermore, it is the first observation of an oblate K isomer in a deformed nucleus. This opens up the possibility for a new region of K isomers at low Z and at oblate deformation, involving the same neutron orbitals as the prolate orbitals within the classic Z∼72 deformed hafnium region. From an interpretation of the level scheme guided by theoretical calculations, an oblate deformation is also suggested for the ^{94}Se_{60} ground-state band.

K isomerism in Rf255 and total kinetic energy measurements for spontaneous fission of Rf255,256,258

Spontaneous fission properties of the isotopes $^{255}\mathrm{Rf}$, $^{256}\mathrm{Rf}$, and $^{258}\mathrm{Rf}$ produced in the reactions $^{50}\mathrm{Ti}+^{207}\mathrm{Pb}$, $^{50}\mathrm{Ti}+^{208}\mathrm{Pb}$, and $^{50}\mathrm{Ti}+^{209}\mathrm{Bi}$ were studied. The method of time and position correlations was used to identify spontaneous fission events. The correction to the energy deficit in measured total kinetic energy (TKE) determined on the basis of a study of $^{252}\mathrm{No}$ was applied to evaluate the $\overline{\mathrm{TKE}}$ of investigated rutherfordium isotopes. A signature which we assigned tentatively to bimodal fission was observed in TKE distributions of $^{255}\mathrm{Rf}$ and $^{256}\mathrm{Rf}$. Two new high-K isomeric states in $^{255}\mathrm{Rf}$ were identified by ER-CE-(CE)-$\ensuremath{\alpha}$/SF correlation search, with half-lives of ${38}_{\ensuremath{-}7}^{+12}$ and ${15}_{\ensuremath{-}4}^{+6}$ $\ensuremath{\mu}\mathrm{s}$ at excitation energies 1150--1450 and 900--1200 keV, respectively. Including those metastable states a tentative partial level scheme was proposed.

Prediction of high-K isomeric states in transactinide nuclei close to N=162

Transactinide nuclei around neutron number N=162 display axially deformed equilibrium shapes. In the present study we are particularly interested in the occurrence of high-K isomers in the axially deformed isotopes of Rf (Z=104), Sg (Z=106), Hs (Z=108), and Ds (Z=110), with neutron number N=160-166 and the effect of the N=162 closure on the structure and distribution of two-quasiparticle (2qp) states. The evolution of high-K isomers is analyzed in a self-consistent axially symmetric relativistic Hartree-Bogoliubov calculation using the blocking approximation with time-reversal symmetry breaking.

High-K Isomers in Light Superheavy Nuclei by PNC-CSM method

The high-K isomeric states in light superheavy nuclei around A = 250 mass region are investigated by the Cranked Shell Model (CSM) with pairing treated by a Particle-Number Conserving (PNC) method. With including the higher-order deformation ε6, both of the high–K multi-particle state energies and the rotational bands in 254No and N = 150 isotone are reproduced well. The isomeric state energies and the microscopic mechanism of kinematic moment of inertia variations versus rotational frequency are discussed. The irregularity of the two-neutron Kπ = 8- state band at ħω ≈ 0:17 in 252No is caused by the configuration mixing with the two-proton Kπ = 8- band. .

Systematic study of multi-quasiparticleK-isomeric bands in tungsten isotopes by the extended projected shell model

Background: The interplay between collective and single-particle degrees of freedom is an important structure aspect to study. The nuclei in theA ≈ 180 mass region are often denoted as good examples to study such problems because these nuclei are known to exhibit many rotational bands based on multi-quasiparticle K isomers. Purpose: A large set of high-quality experimental data on high-K isomeric states in the A ≈ 180 mass region has accumulated. A systematic description of them is a theoretical challenge as it requires a method going beyond the usual mean field with multi-quasiparticle configurations built in the shell-model basis. The K-isomer data provide an ideal testing ground for theoretical models. Method: The recently extended projected shell model (PSM) by the Pfaffian method is employed with a sufficiently large configuration space including up to 10 quasiparticles. The restoration of rotational symmetry which is broken in the deformed mean field is obtained by means of angular-momentum projection. With axial symmetry in the basis deformation, each multi-quasiparticle state, classified by a K quantum number, represents the major component of a rotational K band. Shell-model diagonalization in such a projected basis defines the K mixing, which is the key ingredient of the present method. Results: Quasiparticle structure and rotational properties of high-K isomers in even-even neutron-rich 174−186W isotopes are described. The rotational evolution of the yrast and near-yrast bands is discussed with successive band crossings. Multi-quasiparticle K isomers and associated rotational bands in each W isotope are studied with detailed quasiparticle configurations given. Electromagnetic transition properties are also studied and the calculated B(E2), B(M1), and g-factors are compared with experiment if data exist. Conclusions: Many nuclei of the A ≈ 180 mass region exhibit properties of an axially symmetric shape and K is approximately a good quantum number. For such nuclei, the extended PSM assuming an axially symmetric basis but including K mixing through diagonalization of the two-body Hamiltonian is an appropriate method to study multi-quasiparticle K isomers and K violations in these states. For special examples where one finds highly K-forbidden transitions the present model needs to be further improved.

Configurations and decay hindrances of high- K states in Hf180

Multi-quasiparticle high-K states, several of which are isomeric, were observed in Hf-180 with the Gammasphere array. We determined the lifetimes in the ns-μs range using centroid-shift and decay measurements within a mu s coincidence time window. The configurations of high-K states involve two and four quasiparticles, with states up to Kπ = (18-) established. High-K excitations are found to be progressively more favored with increasing excitation energy. The K quantum number is quite robust up to the highest spins observed, as evidenced by the large values of the reduced hindrance for isomeric decays. Furthermore, rotational bands built on three high-K states are identified, and the measured branching ratios in these sequences enable the assignment of underlying configurations. Multi-quasiparticle calculations using the Lipkin-Nogami approach for pairing, with blocking included, reproduce the observed high-K energies quite well.

Searching for high-K isomers in the proton-rich A ∼ 80 mass region**Supported by National Key Basic Research Program of China (2013CB834402) and National Natural Science Foundation of China (11235001, 11320101004 and 11575007)

Configuration-constrained potential-energy-surface calculations have been performed to investigate the K isomerism in the proton-rich A ∼ 80 mass region. An abundance of high-K states are predicted. These high-K states arise from two and four-quasi-particle excitations, with Kπ = 8+ and Kπ = 16+, respectively. Their excitation energies are comparatively low, making them good candidates for long-lived isomers. Since most nuclei under study are prolate spheroids in their ground states, the oblate shapes of the predicted high-K states may indicate a combination of K isomerism and shape isomerism.

Octupole deformations in high-Kisomeric states of heavy and superheavy nuclei

We study the effects of quadrupole-octupole deformations on the energy and magnetic properties of high-K isomeric states in even-even heavy and superheavy nuclei. The neutron two-quasiparticle (2qp) isomeric energies and magnetic dipole moments are calculated within a deformed shell model with the Bardeen-Cooper- Schrieffer (BCS) pairing interaction over a wide range of quadrupole and octupole deformations. We found that in most cases the magnetic moments exhibit a pronounced sensitivity to the octupole deformation, while the 2qp energies indicate regions of nuclei in which the presence of high-K isomeric states may be associated with the presence of octupole softness or even with octupole deformation. In the present work we also examine the influence of the BCS pairing strength on the energy of the blocked isomer configuration. We show that the formation of 2qp energy minima in the space of quadrupole-octupole and eventually higher multipolarity deformations is a subtle effect depending on nuclear pairing correlations.

Multi-quasiparticle high-K isomeric states in deformed nuclei

In the past years, we have made many theoretical investigations on multi-quasiparticle high- K isomeric states. A deformation-pairing-configuration self-consistent calculation has been developed by calculating a configuration-constrained multi-quasiparticle potential energy surface (PES). The specific single-particle orbits that define the high- K configuration are identified and tracked (adiabatically blocked) by calculating the average Nilsson numbers. The deformed Woods-Saxon potential was taken to give single-particle orbits. The configuration-constrained PES takes into account the shape polarization effect. Such calculations give good results on excitation energies, deformations and other structure information about multi-quasiparticle high- K isomeric states. Many different mass regions have been investigated.

Candidates for long-lived high-Kground states in superheavy nuclei

On the basis of systematic calculations for 1364 heavy and superheavy nuclei, including odd-systems, we have found a few candidates for high-K ground states in superheavy nuclei. The macroscopic-microscopic model based on the deformed Woods-Saxon single particle potential which we use offers a reasonable description of SH systems, including known: nuclear masses, $Q_{\alpha}$-values, fission barriers, ground state deformations, super- and hyper-deformed minima in the heaviest nuclei. %For odd and odd-odd systems, both ways of including pairing correlations, % blocking and the quasi-particle method, have been applied. Exceptionally untypical high-K intruder contents of the g.s. found for some nuclei accompanied by a sizable excitation of the parent configuration in daughter suggest a dramatic hindrance of the $\alpha$-decay. Multidimensional hyper-cube configuration - constrained calculations of the Potential Energy Surfaces (PES's) for one especially promising candidate, $^{272}$ Mt, shows a $\backsimeq$ 6 MeV increase in the fission barrier above the configuration- unconstrained barrier. There is a possibility, that one such high-K ground- or low-lying state may be the longest lived superheavy isotope.

Influence of the octupole mode on nuclear high-K isomeric properties

The influence of quadrupole–octupole deformations on the energy and magnetic properties of high-K isomeric states in even–even actinide (U, Pu, Cm, Fm, No), rare-earth (Nd, Sm and Gd), and superheavy ( nuclei is examined within a deformed shell model with pairing interaction. The neutron two-quasiparticle (2qp) isomeric energies and magnetic dipole moments are calculated over a wide range in the plane of quadrupole and octupole deformations. In most cases the magnetic moments exhibit a pronounced sensitivity to the octupole deformation. At the same time, the calculations outline three different groups of nuclei: with pronounced, shallow, and missing minima in the 2qp energy surfaces with respect to the octupole deformation. The result indicates regions of nuclei with octupole softness as well as with possible octupole deformation in the high-K isomeric states. These findings show the need for further theoretical analysis as well as of detailed experimental measurements of magnetic moments in heavy deformed nuclei.

Magnetic properties ofHf177andHf180in the strong-coupling deformed model

This paper reports NMR measurements of the magnetic dipole moments of two high-K isomers, the 37/2$^-$, 51.4 m, 2740 keV state in $^{\rm 177}$Hf and the 8$^-$, 5.5 h, 1142 keV state in $^{\rm 180}$Hf by the method of on-line nuclear orientation. Also included are results on the angular distributions of gamma transitions in the decay of the $^{\rm 177}$Hf isotope. These yield high precision E2/M1 multipole mixing ratios for transitions in bands built on the 23/2$^+$, 1.1 s, isomer at 1315 keV and on the 9/2$^+$, 0.663 ns, isomer at 321 keV. The new results are discussed in the light of the recently reported finding of systematic dependence of the behavior of the g$_{\rm R}$ parameter upon the quasi-proton and quasi-neutron make up of high-K isomeric states in this region.

Oblate Superdeformed High-K States in Superheavy Nuclei

Configuration-constrained calculations of potential-energy surfaces for 292122 show the occurrence of multiquasiparticle high-K isomeric state at oblate super deformation. Such state could play a unique role in superheavy nuclei, with possible long life time from enhanced difficulty in fission due to additional barrier at oblate deformation, retardation in α decay due to unpaired nucleons, and hindrance in γ-ray transition due to K forbiddenness.

Decay of the high-Kisomeric state to a rotational band in257Rf

The 257Rf isotope has been populated via the 208Pb(50Ti, n) fusion-evaporation reaction and delayed gamma-ray and electron decay spectroscopy has been performed. The existence of a high-K isomeric state in 257Rf has been confirmed. The isomeric state decays into a rotational band based on the 11/2(-)[725] excitation, which was observed up to spin of (23/2(-)). Three multipolarity-E1 gamma transitions depopulating the isomeric state have been observed, which fixes the spin for that state to (21/2(+)). This assignment agrees with theoretical predictions calculated with the microscopic-macroscopic approach, which suggest the isomeric state to be formed by coupling an unpaired 11/2(-)[725] quasineutron to the (1/2(-)[521] circle times 9/2(+)[624])(5)- two-quasiproton state. The same two-quasiproton excitation is possible for the lowest isomer in 256Rf. (Less)

Isomers and excitation modes in the gamma-soft nucleus 192Os

New spectroscopic results for high-spin states in 192Os populated in deep-inelastic reactions include the identification of a 2-ns, 12+ isomeric state at 2865 keV and a 295-ns, 20+ state at 4580 keV and their associated ΔJ=2 sequences. The structures are interpreted as manifestations of maximal rotation alignment within the neutron i13/2 and proton h11/2 shells at oblate deformation. Rotational band members based on the long-lived, Kπ=10− isomer are also identified for the first time. Configuration-constrained, potential-energy-surface calculations predict that other prolate multi-quasiparticle high-K states should exist at low energy.

Particle-number conserving analysis for the 2-quasiparticle and high-K multi-quasiparticle states in doubly-odd 174,176Lu

Two-quasiparticle bands and low-lying excited high-K four-, six-, and eight-quasiparticle bands in the doubly-odd174,176 Lu are analyzed by using the cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method, in which the blocking effects are taken into account exactly. The proton and neutron Nilsson level schemes for174,176, Lu are taken from the adjacent odd-A Lu and Hf isotopes, which are adopted to reproduce the experimental bandhead energies of the one-quasiproton and one-quasineutron bands of these odd-A Lu and Hf nuclei, respectively. Once the quasiparticle configurations are determined, the experimental bandhead energies and the moments of inertia of these two- and multi-quasiparticle bands are well reproduced by PNC-CSM calculations. The Coriolis mixing of the low-K (K=|Ω1−Ω2|) two-quasiparticle band of the Gallagher-Moszkowski doublet with one nucleon in the Ω=1/2 orbital is analyzed.

Competition between collective oblate rotation and non-collective prolate K isomerism in neutron-rich tungsten isotopes

Recent experiments open up the possibility to investigate oblate rotation-aligned states and prolate high-K isomers in neutron-rich tungsten isotopes. In the present work, we perform the projected-shell-model calculations for A ∼ 190 tungsten nuclei. The 190W results are compared with experimental data. The observed 8+ isomer is assigned as a two-quasiproton Kπ = 8+ configuration. Low-lying high-K four-quasiparticle states are predicted. Of particular interest is the prediction of the Kπ = 20+ state in 190,192W, which may form a long-lived spin trap. In competition with the prolate high-K states, rotational alignment leads to near-yrast collective oblate rotation.