Intruder Orbitals Research Articles

Microscopic derivation of the octupole magic numbers from symmetry considerations

The valence shells of medium mass and heavy nuclei consist of the normal and the intruder parity orbitals; therefore the Shell Model SU(3) symmetry of Elliott cannot have a straightforward application on them. The proxy-SU(3) can be applied instead, since it uses a unitary transformation, meant to act on the intruder orbitals to alter their parity and transform them to their proxy orbitals. The inverse unitary operator transforms the proxy orbitals back to the intruder ones. The highest weight proxy-SU(3) irreducible representations (irreps) allows one to determine the corresponding number of occupied intruder orbitals. In this way we obtain the so-called ‘octupole magic numbers’ 32, 56, 90, 134 and 194 without any parameter. Moreover, the proxy (unitary) mapping and its inverse transformation make the proxy space eligible for the calculation of observables associated with octupole deformation and the relevant treatment of mixed parity states. The implemented study validates the proxy-SU(3) approach with respect to the octupole deformation and suggests its full applicability in the corresponding mass regions.

Fast rotation of nuclei with extreme isospin in the vicinity of neutron and proton drip lines

The analysis of the present understanding of collective rotation in very neutron-rich nuclei is presented. It is shown that collective rotation can lead to the increase of stability of rotational states with increasing spin. The detailed investigation of rotational excitations in very proton-rich nuclei confirms this conclusion and indicates that experimental studies of such features are more feasible in the nuclei near proton drip line. They also show that rotational bands which are proton quasi-bound at zero or low spins can be transformed into proton bound ones at high spin by collective rotation of nuclear systems. This is due to strong Coriolis interaction which acts on high-j or strongly mixed M orbitals and drives the highest in energy occupied single-particle states into negative energy domain. These physical mechanisms lead to a substantial extension of the nuclear landscape beyond the spin zero proton drip line. In addition, a new phenomenon of the formation of giant proton halos in rotating nuclei emerges: it is triggered by the occupation of strongly mixed M intruder orbitals.

Further monopole effects in neutron-rich Sb isotopes* *Research at ZSTU is supported by the National Natural Science Foundation of China (U2267205). Research at IMP is supported by the National Natural Science Foundation of China (U2032211, 12075287). Research at SJTU is supported by the China and Germany Postdoctoral Exchange Fellowship Program 2019 from the office of China Postdoctoral Council (20191024)

The level spectra of neutron-rich Sb isotopes have been investigated within a shell-model space containing cross-shell excitations and the intruder orbit . High-spin levels (27/2 ) and (29/2 ) in Sb are taken over by the monopole effect induced by orbit . The ground state and excited levels in Sb are well improved by considering the monopole correction between neutron orbits and . The energy shrinking of the first excited state 5/2 in Sb isotopes is explained by the shift due to the attractive monopole interaction when increasingly more neutrons occupy orbit . The ground state of Sb is predicted as 5/2 owing to the shrinking of the 5/2 states in Sb isotopes that causes ground state inversion when N = 88. Further monopole effects extend the applicable range of the present Hamiltonian to nuclei with more neutrons above the N = 82 shell. This Hamiltonian will be public, and researchers are encouraged to contact the authors.

Investigation of the level spectra of nuclei in the northeast region of doubly magic 40Ca with intruder orbit $$g_{9/2}$$

Investigation of the level spectra of nuclei in the northeast region of doubly magic 40Ca with intruder orbit $$g_{9/2}$$

Enlarged deformation region in neutron-rich Zr isotopes promoted by the second intruder orbit

Enlarged deformation region in neutron-rich Zr isotopes promoted by the second intruder orbit

Investigation of the high-spin yrast band structure of Pu236–246 isotopes

The available data on some actinide nuclei point to certain significant features of the rotational yrast band and other excited bands. The rotational properties of plutonium isotopes ($^{236--346}\mathrm{Pu}$) were studied via projected shell model (PSM). Calculations are based on the Hamiltonian of the PSM which includes the formed part of a single particle, the $Q\ensuremath{-}Q$ force, and the residual interaction of monopole and quadrupole pairings. The results of the calculated energy levels of the yrast band are then compared with available experimental data and a good agreement has been found. The crossing between two-quasiparticle (2qp) excited bands and the ground state band (g band) in the high-spin regions has been analyzed in terms of band diagrams. The upbendings observed in the kinematic moments of inertia (${j}^{(1)}$ MOI) curves for $^{236--346}\mathrm{Pu}$ isotopes are due to the effect of two aligning nucleons that occupy excited bands and the $\ensuremath{\nu}({j}_{15/2}$), $\ensuremath{\pi}({i}_{13/2}$) high-$j$ intruder orbits. The PSM successfully reproduces the observed upbending in ${j}^{(1)}$ as well as the upturning and downturning in ${j}^{(2)}$. For the $^{240}\mathrm{Pu}$ isotope, the PSM predicts a simultaneous alignment of neutrons ${\ensuremath{\nu}}^{2} [1/2,\ensuremath{-}7/2] {K}^{\ensuremath{\pi}}$ = ${4}^{+}$ and protons ${\ensuremath{\pi}}^{2} [\ensuremath{-}3/2,5/2] {K}^{\ensuremath{\pi}}$ = ${1}^{+}$ bands cross the g band at spin $I=22$. We expect it to be mainly responsible for the disagreement at $I=22$. Furthermore, electric quadrupole transition probabilities $B(E2)$ and the gyromagnetic factor ($g$ factor) for the yrast band energy levels are also studied.

Monopole effects and spin-trap structures in neutron-rich Te isotopes

A new Hamiltonian is established for the particle nuclei near $^{132}\mathrm{Sn}$ by including both core excitations and neutron intruder orbit ${i}_{13/2}$. In this Hamiltonian, the two-body force strengths and monopole terms are determined by the data in $^{133}\mathrm{Sn}$, $^{134}\mathrm{Sn}$, $^{133}\mathrm{Sb},^{134}\mathrm{Sb}$, $^{134}\mathrm{Te}$, $^{135}\mathrm{Te}$, and $^{135}\mathrm{I}$. According to this interaction, the level spectra and electromagnetic transitions are described well in the model space including six proton orbits ($0{g}_{9/2},0{g}_{7/2},1{d}_{5/2},1{d}_{3/2},2{s}_{1/2},0{h}_{11/2}$), and eight neutron orbits ($1{d}_{3/2},0{h}_{11/2},1{f}_{7/2},2{p}_{3/2},2{p}_{1/2},0{h}_{9/2},1{f}_{5/2},0{i}_{13/2}$). This work shows that the neutron intruder orbit ${i}_{13/2}$ is necessary to describe particle nuclei near $^{132}\mathrm{Sn}$. The configuration including orbit ${i}_{13/2}$ forms a spin-trap structure and wins the competition of the lowest states at level $13/{2}^{+}$ in $^{137,139}\mathrm{Te}$. Spin-trap structures are also existed in levels ${2}^{\ensuremath{-}}$ and ${9}^{\ensuremath{-}}$ in $^{136,138}\mathrm{Te}$. Due to the decay block by spin-trap structures, these states are predicted as good isomers.

Large enhancement of total reaction cross sections at the edge of the island of inversion in Ti, Cr, and Fe isotopes

A systematic analysis of nuclear deformation is made for neutron-rich Ti, Cr, and Fe isotopes to explore the nuclear structure in the island of inversion near N = 40, where strong nuclear deformation is predicted. The nuclear ground states are obtained by the Skyrme Hartree-Fock method in three-dimensional coordinate space, which properly describes any nuclear shape. Three types of Skyrme interactions are employed to generate various deformed states in its isotopic chain. We find that in the island of inversion the occupation of highly elongated intruder orbits induces not only large quadrupole deformation but also large hexadecapole deformation. This appears as a sizable enhancement of the nuclear matter radius, showing the characteristic shell effect of the density profile near the nuclear surface. We show that the edge of the island of inversion, where the intruder orbit starts being occupied, can be determined by measuring the enhancement of the total reaction cross section at high incident energy. The possibility of constraining the hexadecapole deformation by a measurement of the total reaction cross sections is discussed.

Identification of excited states in Te5552107

Excited states in the extremely neutron-deficient nucleus Te107 have been identified from two separate experiments using the recoil-decay tagging technique. Two connected structures were observed on the basis of γγ-coincidence relations and tentatively assigned as built on the mixed-parentage νg7/2d5/2 and νh11/2 intruder configurations. The observed structures were compared with large-scale shell-model calculations and total Routhian surface calculations. Collective behavior was discovered to persist in the νh11/2 band of Te107 which highlights the shape-polarizing effect of a single valence neutron occupying the h11/2 intruder orbit as the N=50 shell closure is approached.1 MoreReceived 31 August 2021Accepted 22 November 2021DOI:https://doi.org/10.1103/PhysRevC.104.064305Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsElectromagnetic transitionsEnergy levels & level densitiesNuclear structure & decaysProperties90 ≤ A ≤ 149Nuclear Physics

Quasi-SU(3) coupling of ( 1h11/2,2f7/2 ) across the N=82 shell gap: Enhanced E2 collectivity and shape evolution in Nd isotopes

The essence of the quasi-SU(3) coupling scheme suggested by Zuker et al. is that the high-$j$ intruder orbit alone is insufficient to induce required large collectivity, and it is necessary for the high-$j$ orbit to correlate through the quadrupole interaction with another higher-lying orbit with $\mathrm{\ensuremath{\Delta}}j=2$. To extend this idea to the medium-heavy mass region, we investigate the systematics of energy levels and $B(E2)$ values for Sn, Te, Xe, Ba, Ce, Nd, and Sm isotopes by applying the recently proposed realistic PMMU shell model. The calculations are performed by using the projected Hartree-Fock-Bogolyubov plus generator coordinate method in the model space of ($1{g}_{9/2},1{g}_{7/2},2{d}_{5/2},2{d}_{3/2},3{s}_{1/2},1{h}_{11/2}$). The calculations describe well the experimental data over a wide range of nuclei. However, it is found that, in some nuclei close to the neutron midshell, $^{124,126}\mathrm{Ce}$, $^{130,132}\mathrm{Nd}$, and $^{134}\mathrm{Sm}$, the calculated $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})$ values underestimate the data considerably. This problem can be resolved by inclusion of the $2{f}_{7/2}$ orbit into the model space, which, with $1{h}_{11/2}$, forms a quasi-SU(3) coupling scheme. It is shown that the $QQ$ interaction between the SU(3)-partner $1{h}_{11/2}\text{\ensuremath{-}}2{f}_{7/2}$ is a driving force for enhanced $E2$ collectivity in the above nuclei and is responsible for the shape evolution in Nd isotopes. In addition, the participation of the $2{f}_{7/2}$ orbit in the model space favors prolate shape in the ground state of $N\ensuremath{\le}76$ isotopes, thus subverting the oblate result from the same calculation but without $2{f}_{7/2}$.

Connecting the proxy-SU(3) symmetry to the shell model

Proxy-SU(3) symmetry is an approximation scheme extending the Elliott SU(3) algebra of the sd shell to heavier shells. When introduced in 2017, the approximation had been justified by calculations carried out within the Nilsson model. Recently our group managed to map the cartesian basis of the Elliott SU(3) model onto the spherical shell model basis, proving that the proxy-SU(3) approximation corresponds to the replacement of the intruder orbitals by their de Shalit-Goldhaber partners, paving the way for using the proxy-SU(3) approximation in shell model calculations. The connection between the proxy-SU(3) scheme and the spherical shell model has also been worked out in the original framework of the Nilsson model, with identical results.

Alternating-parity bands of U236,238 and Pu238,240 in a particle-number-conserving method based on the cranked shell model

The particle-number-conserving (PNC) method in the framework of cranked shell model (CSM) is developed to deal with the reflection-asymmetric nuclear system by applying the ${S}_{x}$ symmetry. Based on an octupole-deformed Nilsson potential, the alternating-parity bands in $^{236,238}\mathrm{U}$ and $^{238,240}\mathrm{Pu}$ are investigated. The experimental kinematic moments of inertia (MoI) and the angular momentum alignments of all studied bands are reproduced well in the PNC-CSM calculations. The striking difference of rotational behaviors between U and Pu isotopes can be linked to the strength of octupole correlations. The upbendings of the alternating-parity bands in $^{236,238}\mathrm{U}$ are due to the alignments of pairs of nucleons occupying $\ensuremath{\nu}{g}_{9/2}, \ensuremath{\pi}{f}_{7/2}$ orbitals and $\ensuremath{\nu}{j}_{15/2}, \ensuremath{\pi}{i}_{13/2}$ high-$j$ intruder orbitals. In particular, the interference terms of nucleon occupying the octupole-correlation pairs of ${\ensuremath{\nu}}^{2}{j}_{15/2}{g}_{9/2}$ and of ${\ensuremath{\pi}}^{2}{i}_{13/2}{f}_{7/2}$ give a very important contribution to the suddenly gained alignments.

Highly deformed bands in Nd nuclei: New results and consistent interpretation within the cranked Nilsson-Strutinsky formalism

Three new highly-deformed (HD) bands are identified in Nd136 and the highly deformed band of Nd137 is extended at higher spin by four transitions, revealing a band crossing associated with the occupation of the second νi13/2 intruder orbital. Extended cranked Nilsson-Strutinsky calculations are performed for all HD bands observed in Nd134, Nd136, and Nd137, achieving for the first time a consistent interpretation of all HD bands in the Nd nuclei. The new interpretation has significant consequences, like the change of parity of the yrast HD bands of Nd134 and Nd136, and the involvement of two negative-parity neutron intruder orbitals in the configurations of most HD bands. The present experimental results and their theoretical interpretation represent an important step forward in the understanding of the second-minimum excitations in the Nd nuclei.

Structure of Mg28 and influence of the neutron pf shell

Gamma-ray spectroscopy and lifetime measurements using the Doppler shift attenuation method (DSAM) were performed on the nucleus $^{28}\mathrm{Mg}$ near the $N=20$ ``island of inversion,'' which was populated using a $^{12}\mathrm{C}(^{18}\mathrm{O},2\mathrm{p})^{28}\mathrm{Mg}$ fusion-evaporation reaction to investigate the impact of shell evolution on its high-lying structure. Three new levels were identified at 7203(3), 7747(2), and 7929.3(12) keV along with several new gamma rays. A newly extracted $B(E2;{4}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})$ of 42(7) ${e}^{2}{\mathrm{fm}}^{4}$ indicates reduced collectivity in the yrast band at high spin, consistent with ab initio symmetry adapted no-core shell model (SA-NCSM) calculations. At high excitation energy, evidence for the population of intruder orbitals was obtained through identification of negative parity levels $[{I}^{\ensuremath{\pi}}={(0,4)}^{\ensuremath{-}}$, ${(4,5)}^{\ensuremath{-}}]$. Calculations using the SDPF-MU interaction indicate that these levels arise from single neutron excitation to the $pf$ shell and provides evidence for the lowering of these intruder orbitals approaching the island of inversion.

The impact of the intruder orbitals on the structure of neutron-rich Ag isotopes

The low-lying high-spin yrast band structure of neutron-rich 113,118–121Ag has been established for the first time using prompt γ-ray spectroscopy of isotopically identified fission fragments produced in the 9Be(238U, fγ) fusion- and transfer-induced fission processes. The newly obtained level energies follow the systematics of the neighboring isotopes. The sequences of levels exhibit an energy inheritance from states in the corresponding Cd core. A striking constancy of a large signature splitting in odd-A Ag throughout the long chain of isotopes with 50<N<82 and a signature inversion in even-A Ag isotopes, which are indications of triaxiality, were evidenced. These observed features were reproduced by large-scale shell-model calculations with a spherical basis for the first time in the Ag isotopic chain, revealing microscopically their complex nature with severely broken seniority ordering. The essential features of the observed signature splitting were further examined in the light of simplified, two-orbital shell-model calculations including only two intruder orbitals πg9/2 and νh11/2 from two consecutive shells above Z=50 and N=82 for protons and neutrons respectively, resulting in the πg9/2−3×νh11/2m configurations. The newly established bands were understood as fairly pure, built mainly on unique-parity intruder configurations and coupled to the basic states of the Cd core.

Post-Newtonian evolution of massive black hole triplets in galactic nuclei – I. Numerical implementation and tests

Massive black-hole binaries (MBHBs) are thought to be the main source of gravitational waves (GWs) in the low-frequency domain surveyed by ongoing and forthcoming Pulsar Timing Array campaigns and future space-borne missions, such as {\it eLISA}. However, many low-redshift MBHBs in realistic astrophysical environments may not reach separations small enough to allow significant GW emission, but rather stall on (sub)pc-scale orbits. This "last-parsec problem" can be eased by the appearance of a third massive black hole (MBH) -- the "intruder" -- whose action can force, under certain conditions, the inner MBHB on a very eccentric orbit, hence allowing intense GW emission eventually leading to coalescence. A detailed assessment of the process, ultimately driven by the induced Kozai-Lidov oscillations of the MBHB orbit, requires a general relativistic treatment and the inclusion of external factors, such as the Newtonian precession of the intruder orbit in the galactic potential and its hardening by scattering off background stars. In order to tackle this problem, we developed a three-body Post-Newtonian (PN) code framed in a realistic galactic potential, including both non-dissipative 1PN and 2PN terms, and dissipative terms such as 2.5PN effects, orbital hardening of the outer binary, and the effect of the dynamical friction on the early stages of the intruder dynamics. In this first paper of a series devoted at studing the dynamics of MBH triplets from a cosmological perspective, we describe, test and validate our code.

Properties of superdeformed bands in A ∼ 190 region within the framework of three parameters nuclear softness model

The three parameters nuclear softness model (NS3) have been applied to eleven superdeformed (SD) bands of A ≈190 mass region namely: 191Hg(SD2,SD3), 192Hg(SD1), 194Hg(SD1,SD2), 193Tl(SD1,SD2), 194Tl(SD1,SD3, SD5) and 194Pb(SD1). The level spins and the model parameters are determined by fitting the electric quadrupole transition energies Eγ with the experimental ones, by using a computer simulated search program. Rotational frequencies ħω, kinematic J(1) and dynamic J(2)moments of inertia and the quadrupole deformation parameter β2 have been calculated. In all cases of our selected SD bands the results obtained are in good agreement with experimental ones. J(2) reveal a steady increase with ħω, this can be attributed to the successive alignment of πi13/2 (N = 6) and υj15/2 (N = 7) intruder orbitals in the presence of dynamical pairing correlations. The presence of ΔI = 2 staggering in the two SD bands 1,2 of 194Hg and in the three SD bands 1,3,5 of 194Tl have been investigated by calculating the staggering parameter which represent the fourth order derivative of the gamma-ray transition energies. Also the ΔI = 1 staggering in SD bands of odd nuclei has been investigated in the signature partner pairs 191Hg (SD2, SD3) and 193Tl (SD1, SD2). The yrast SD bands in the isotones 194Pb and 192Hg have almost identical transition energies which implies that their J(2) are also identical. This indicates that either the two occupied 5/2+[642] protons have a very weak influence on Eγ and J(2).

Rotation and alignment of high-jorbitals in transfermium nuclei

The structure of nuclei with $Z\sim100$ is investigated systematically by the Cranked Shell Model (CSM) with pairing correlations treated by a Particle-Number Conserving (PNC) method. In the PNC method, the particle number is conserved and the Pauli blocking effects are taken into account exactly. By fitting the experimental single-particle spectra in these nuclei, a new set of Nilsson parameters ($\kappa$ and $\mu$) is proposed. The experimental kinematic moments of inertia and the band-head energies are reproduced quite well by the PNC-CSM calculations. The band crossing, the effects of high-$j$ intruder orbitals and deformation are discussed in detail.

Pseudospin symmetry in single-particle resonances in spherical square wells

The pseudospin symmetry (PSS) has been studied extensively for bound states. Recently we justified rigorously that the PSS in single particle resonant states is exactly conserved when the attractive scalar and repulsive vector potentials of the Dirac Hamiltonian have the same magnitude but opposite sign [PRL 109, 072501 (2012)]. To understand more deeply the PSS, we focus on several issues related to the exact conservation and breaking mechanism of the PSS in single particle resonances. In particular, we are interested in how the energy and width splittings of PS partners depend on the depth of the scalar and vector potentials. We investigate the asymptotic behaviors of radial Dirac wave functions. Spherical square well potentials are employed in which the PSS breaking part in the Jost function can be well isolated. By examining the zeros of Jost functions corresponding to small components of the radial Dirac wave functions, general properties of the PSS are analyzed. By examining the Jost function, the occurrence of intruder orbitals is explained and it is possible to trace continuously the PSS partners from the PSS limit to the case with a finite potential depth. The dependence of the PSS in resonances as well as in bound states on the potential depth is investigated systematically. We find a threshold effect in the energy splitting and an anomaly in the width splitting of pseudospin partners when the depth of the single particle potential varies from zero to a finite value. The conservation and the breaking of the PSS in resonant states and bound states share some similar properties. The appearance of intruder states can be explained by examining the zeros of Jost functions. Origins of the threshold effect in the energy splitting and the anomaly in the width splitting of PS partners, together with many other problems, are still open and should be further investigated.

Nuclear Data Sheets for [formula omitted

Nuclear spectroscopic information for the known nuclides of mass 31 (F, Ne, Na, Mg, Al, Si, P, S, Cl, Ar) has been evaluated. A useful source of many of the Adopted Levels for 31P and 31S is presented in Endtʼs evaluations (1998En04,1990En08,1978En02,1973EnVA), however all the adopted properties of levels and gamma rays have been re-evaluated in this work. The data sets for reactions and decays, including all available gamma–ray data, are based mostly on the original literature.The 31Mg nuclide is a prime candidate for the study of ‘island-of-inversion’ as its ground state and first excited state can only be explained by intruder orbitals in a deformed shell-model approach. 31S is of importance in astrophysics rp-process as a possible ‘bottleneck’ nuclide. There are no data available for excited states in 31F, 31Ne and 31Ar. No gamma transitions are known in 31Cl. For 31Na, only one excited state is known. The radioactive decay characteristics of 31F and 31Ne isotopes have not yet been investigated. The 31S and 31Mg nuclei are currently being pursued intensively by various experimental groups, including recent work by Nuclear Astrophysics group at McMaster, the results of which will soon become available.