Two-quasiparticle States Research Articles

Identification of a possible proton two-quasiparticle band inSm158

High-spin states in neutron-rich $^{158}\mathrm{Sm}$ have been reinvestigated by measuring the prompt $\ensuremath{\gamma}$ rays emitted in the spontaneous fission of $^{252}\mathrm{Cf}$. A new negative-parity band has been established up to spin 12. By comparison with the theoretical calculations, a two-quasiparticle state with $\ensuremath{\pi}5/2[532]$ $\ensuremath{\bigotimes}$ $\ensuremath{\pi}5/2[413]$ configuration has been proposed for the band head. The systematics of the two-quasiparticle states and bands in this region are discussed.

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One- and two-quasiparticle states are studied in the complex energy plane. It is found that the pairing interaction does not change the character of the complex state. If a normal state is a physically meaningful resonance, then it will remain as such throughout the shell and if it is unphysical it will also remain as such throughout the shell. An important consequence of this is that it justifies the use of bound representations to evaluate many-body systems within the shell-model in cases where the single-particle states are narrow resonances. The character of two-quasiparticle states may oscillate between meaningful resonances and unphysical complex excitations as the number of particles increases.

High-spin level structure of the doubly odd nucleus104Ag

The high-spin level structure of the doubly odd nucleus ${}^{104}$Ag has been investigated via the ${}^{97}$Mo(${}^{11}$B, 4n)${}^{104}$Ag reaction at a beam energy of 50 MeV. The newly established level scheme includes lower-lying two-quasiparticle states and several higher-lying bands. Two positive-parity bands associated with the $\ensuremath{\pi}{g}_{9/2}^{\ensuremath{-}1}\ensuremath{\bigotimes}\ensuremath{\nu}{d}_{5/2}$ and $\ensuremath{\pi}{g}_{9/2}^{\ensuremath{-}1}\ensuremath{\bigotimes}\ensuremath{\nu}{g}_{7/2}$ configurations are extended significantly. Based on the comparison with the analogous structures in neighboring nuclei and the features of nuclear chirality, the negative parity bands are suggested as candidate chiral doublet bands with the $\ensuremath{\pi}{g}_{9/2}^{\ensuremath{-}1}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}$ configuration.

Role of the quasiparticle structure in α-decays of superheavy nuclei

The one-quasiparticle structures of nuclei in the α-decay chains of 287114 and 293116 are studied using a modified two-center shell model. Two-quasiparticle states are revealed in the α-decay chain of even-even nuclei 286,288114. The calculated values for Qα are compared to the available experimental data. The termination of the α-decay chains by spontaneous fission is analyzed.

Magnetic moments of K isomers as indicators of octupole collectivity

The relation between the quadrupole-octupole deformation and the structure of high-K isomers in heavy even-even nuclei is studied through a reflection asymmetric deformed shell model including a BCS procedure with constant pairing interaction. Two-quasiparticle states with K π = 4−, 5−, 6−, 6+ and 7− are considered in the region of actinide nuclei (U, Pu and Cm) and rare-earth nuclei (Nd, Sm and Gd). The behaviour of two-quasiparticle energies and magnetic dipole moments of these configurations is examined over a wide range in the plane of quadrupole and octupole deformations (β 2 and β 3. In all considered actinide nuclei, the calculations show that there is pronounced sensitivity of the magnetic moments to the octupole deformation. In the rare-earth nuclei, the calculations for 154, 156Gd show stronger sensitivity of the magnetic moment to the octupole deformation than in the other considered cases.

Microscopic and nonadiabatic Schrödinger equation derived from the generator coordinate method based on zero- and two-quasiparticle states

A new approach called the Schr\"odinger Collective Intrinsic Model (SCIM) has been developed to achieve a microscopic description of the coupling between collective and intrinsic excitations. The derivation of the SCIM proceeds in two steps. The first step is based on a generalization of the symmetric moment expansion of the equations derived in the framework of the Generator Coordinate Method (GCM), when both Hartree-Fock-Bogoliubov (HFB) states and two-quasi-particle excitations are taken into account as basis states. The second step consists in reducing the generalized Hill and Wheeler equation to a simpler form to extract a Schr\"odinger-like equation. The validity of the approach is discussed by means of results obtained for the overlap kernel between HFB states and two-quasi-particle excitations at different deformations.

Structure of some low lying two-quasiparticle and collective states in nuclei with Z ∼ 100 considered in the quasiparticle phonon model

The excitation energies and the structure of the low lying states with Kπ = 8−, 0−, 1−, 2−, 3+ are calculated based on the quasiparticle phonon model. The results of calculations demonstrate agreement with the existing experimental data and also give information which can be used for planning the experiments.

Isomeric states in heavy nuclei

The one- and two-quasiparticle states in heavy nuclei are treated. The change of one-quasiparticle states in isotone chain seems to be rather smooth. Two-quasiparticle states in nuclei of alpha-decay chain of (270)Ds are discussed.

High-K isomers as probes of octupole collectivity in heavy nuclei

The influence of the octupole deformation on the structure of high-K isomeric states in the region of heavy even–even actinide nuclei is studied through a reflection asymmetric deformed shell model (DSM). Two-quasiparticle states with high-K values are constructed by taking into account the pairing effect through a DSM+BCS procedure with constant pairing interaction. The behaviour of two-quasiparticle energies and magnetic dipole moments of Kπ=6+, 6− and 8− configurations, applicable to mass numbers in the range A=234–252, was examined over a wide range of quadrupole and octupole deformations. A pronounced sensitivity of the magnetic moments to the octupole deformation is found. The result suggests a possibly important role for high-K isomers in determining the degree of octupole deformation in heavy actinide nuclei.

Low-lying levels of 188Re nucleus from γγ-coincidence measurements

Low–high and low–low energy γγ-coincidences, following the Re 187 ( n , γ ) Re 188 reaction with thermal neutrons, have been measured. Spectra have been recorded in the energy range from 50 to 2600 keV, and from 4500 to 6500 keV. The earlier known 188Re level scheme is corrected and extended up to ∼800 keV excitation energy and 62 levels by including 20 new levels. For 11 levels, the earlier interpretation has been changed. The complete level scheme is presented for up to ∼400 keV energy and spins ⩽5. Core plus two-quasiparticles model calculations have been performed. Some 188Re two-quasiparticle states display features indicating the nuclear shape phase transition from axial-deformation to γ-soft form.

Two-quasiparticle K-isomeric states in strongly deformed neutron-rich Nd and Sm isotopes: a projected shell-model analysis

Motivated by recent spectroscopy data from fission experiments, we apply the projected shell model to study systematically the structure of strongly deformed, neutron-rich, even–even Nd and Sm isotopes with neutron number from 94 to 100. We perform calculations for rotational bands up to spin I = 20 and analyze the band structure of low-lying states with quasiparticle excitations, with emphasis given to rotational bands based on various negative-parity two-quasiparticle (2-qp) isomers. Experimentally known isomers in these isotopes are described well. The calculations further predict proton 2-qp bands based on a 5− and a 7− isomer and neutron 2-qp bands based on a 4− and an 8− isomer. The properties for the yrast line are discussed, and quantities to test the predictions are suggested for future experiment.

High-spin isomers in some of the heaviest nuclei: Spectra, decays, and population

The isotopic dependence of two-quasiparticle isomeric states in Fm and No is treated for future experiments. The population of the isomeric states in evaporation residues is considered. In several even isotopes of Rf, Sg, Hs, and Ds, the $K$ isomers and their decay modes are predicted. An $\ensuremath{\alpha}$-decay chain through the isomeric states of superheavy nuclei is demonstrated for the first time and proposed for the experimental verification.

Two-fermion–four-boson description ofHg198within theUν(6/12)⊗Uπ(6/4)extended nuclear structure supersymmetry

Using the U{sub {nu}}(6/12) x U{sub {pi}}(6/4) extended supersymmetry, we constructed the energy spectrum and electromagnetic transition properties of the supermultiplet member {sup 198}Hg with two proton fermions coupled to a neutron boson core. Consistency between the supersymmetric interacting boson fermion fermion approximation (IBFFA) description and the F-spin symmetric interacting boson approximation (IBA-2) description is shown for this two-fermion-N-boson multiplet member. The data of a {gamma}{gamma} angular correlation experiment using the HORUS cube {gamma}-ray spectrometer--determining new multipole mixing ratios, level spins, {gamma} transitions, and energy states--shows quite a good agreement, also for the low-energy part of the spectrum, when comparing theoretical predictions and experimental data. This is contrary to the usual assumption that a two-fermion-N-boson constellation should describe just the excited two-quasiparticle states.

Two-quasiparticle states inBk250studied by decay scheme and transfer reaction spectroscopy

Two-quasiparticle states in $^{250}\mathrm{Bk}$ were investigated with decay scheme studies and the single-neutron transfer reaction $^{249}\mathrm{Bk}$($d,p$)$^{250}\mathrm{Bk}$. Mass-separated sources of $^{254}\mathrm{Es}$ were used for \ensuremath{\alpha} singles and $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidence measurements. These studies, plus previous studies of ${}^{254}{\mathrm{Es}}^{m}$ \ensuremath{\alpha} decay and the $^{249}\mathrm{Bk}$($n,\ensuremath{\gamma}$) reaction, provide spins and parities of the observed levels. The transfer reaction $^{249}\mathrm{Bk}$($d,p$)$^{250}\mathrm{Bk}$ was used to deduce neutron single-particle components of the observed bands. Six pairs of singlet and triplet states, formed by the coupling of proton and neutron one-quasiparticle states, were identified. The splitting energies between the triplet and singlet states were found to be in agreement with previous calculations.

High-spin isomeric structures in exotic odd-odd nuclei: Exploration of the proton drip line and beyond

We investigate the role of two-quasiparticle isomeric states along the proton drip line, using configuration-constrained potential-energy-surface calculations. In contrast to even-even nuclei, odd-odd nuclei can have coexisting low-lying two-quasiparticle states. The low excitation energy and high angular momentum can lead to long-lived isomers. Also, because of the hindrance by spin selection, the probabilities of beta and proton decays from high-spin isomers can be reduced significantly. The present calculations reproduce reasonably well the available data for observed isomers in such nuclei. Unobserved high-spin isomers are predicted, which could be useful for future experimental studies of exotic nuclei at and beyond the proton drip line.

Isomeric and two-quasiparticle states in the neutron-excess odd-odd nucleus 134Sb

Detailed theoretical calculations of the properties of the neutron-excess odd-odd nucleus 134Sb are performed by using different theoretical approaches. A comprehensive comparison with the recent experimental data is performed; this comparison suggests the presence of isomeric states among the low-lying levels of this nucleus. These states are the twins of the corresponding levels of the odd-odd nucleus 210Bi that is situated near the stability line. The obtained results manifest the similarity of nuclear structure in the region of the “remote” doubly magic nucleus 132Sn and in the region of the classical stable doubly magic nucleus 208Pb.

One- and two-quasiparticle states in the complex energy plane

One- and two-quasiparticle states are studied in the complex energy plane. It is found that the pairing interaction does not change the character of the complex state. If a normal state is a physically meaningful resonance, then it will remain as such throughout the shell and if it is unphysical it will also remain as such throughout the shell. An important consequence of this is that it justifies the use of bound representations to evaluate many-body systems within the shell-model in cases where the single-particle states are narrow resonances. The character of two-quasiparticle states may oscillate between meaningful resonances and unphysical complex excitations as the number of particles increases.

Nuclear stucture studies of transfermium nuclei

The study of deformed nuclei in the region of 254No provides an indirect method to access the single-particle orbitals which are of relevance in determining the location of the next closed proton and neutron closed shells above 208Pb. Several of these orbitals are strongly down-sloping and are close to the Fermi surface in the deformed region. These nuclei are some of the heaviest for which detailed spectroscopy can be performed. Initial in-beam measurements in the region focussed on γ-ray spectroscopy of even-even nuclei (e.g. 252,254No, 250Fm), while more recently attention has switched to odd-mass nuclei such as 253No, 251Md and 255Lr, the latter being the heaviest nucleus so far studied in-beam. Non-yrast and isomeric states have recently been observed in 252,254No and 250Fm through the use of both in-beam and focal plane decay spectroscopy. Such experiments have yielded data which can be used to determine the excitation energies and configurations of two-quasiparticle states in the region, providing a stringent test for current nuclear structure models. An overview of the most recent results and the experimental techniques used is presented. Perspectives for the development of new devices for further studies in this region are also discussed.

Pairing-induced spatially extended coherence of low-lying vibrational excitations unique in neutron drip line nuclei

Continuum effects for pairing correlations and low-frequency vibrational excitations in nuclei close to the neutron drip line are investigated within the framework of quasiparticle random phase approximation (QRPA) based on the coordinate space Hartree–Fock–Bogoliubov (HFB) method. Quasiparticle states with small orbital angular momentum ℓ, that suffer a significant change of the spatial structure by pairing correlations, bring about the spatially extended structure of the pairing density that leads to the enhancement of the pairing energy. The similar mechanism in two-quasiparticle states also causes the strong transition strength of low-frequency vibrational excitations.

Two-quasiparticle K-isomers and pairing strengths in the neutron-rich isotopes 174Er and 172Er

Isomeric two-quasiparticle states have been identified in the neutron-rich isotopes 172Er and 174Er using multi-nucleon transfer reactions with 136Xe beams incident on various targets, and γ-ray spectroscopy with Gammasphere. A candidate for the Kπ=6+ two-quasineutron state in 172Er is found at 1500 keV. In 174Er, a nuclide whose level scheme was previously unknown, a long-lived isomer is identified at 1112 keV decaying via an inhibited E1 transition and revealing the yrast sequence of 174Er. This isomer is proposed to be a Kπ=8− two-quasineutron state, defining a sequence in the N=106 isotones extending from the well-deformed neutron-rich isotope 174Er to the neutron-deficient isotope 188Pb, where the presence of the isomer signifies a prolate minimum in an otherwise spherical well. Configuration-constrained potential-energy surface calculations are used to predict the excitation energies of the 6+ and 8− intrinsic states and as a basis for extracting the pairing force strength, Gn, in the N=104 and N=106 isotones.