Intruder Orbitals Research Articles

Coulomb Energy Difference as a Probe of Isospin-Symmetry Breaking in the Upperfp-Shell Nuclei

The anomaly in Coulomb energy differences (CEDs) between the isospin T=1 states in the odd-odd N=Z nucleus 70Br and the analogue states in its even-even partner 70Se has remained a puzzle. This is a direct manifestation of isospin-symmetry breaking in effective nuclear interactions. Here, we perform large-scale shell-model calculations for nuclei with A=66 to 78 using the new filter diagonalization method based on the Sakurai-Sugiura algorithm. The calculations reproduce well the experimental CED. The observed negative CED for A=70 are accounted for by the cross-shell neutron excitations from the fp shell to the g(9/2) intruder orbit with the enhanced electromagnetic spin-orbit contribution at this special nucleon number.

Understanding the different rotational behaviors of252No and254No

Total Routhian surface calculations have been performed to investigate rapidly rotating transfermium nuclei, the heaviest nuclei accessible by detailed spectroscopy experiments. The observed fast alignment in $^{252}$No and slow alignment in $^{254}$No are well reproduced by the calculations incorporating high-order deformations. The different rotational behaviors of $^{252}$No and $^{254}$No can be understood for the first time in terms of $\beta_6$ deformation that decreases the energies of the $\nu j_{15/2}$ intruder orbitals below the N=152 gap. Our investigations reveal the importance of high-order deformation in describing not only the multi-quasiparticle states but also the rotational spectra, both providing probes of the single-particle structure concerning the expected doubly-magic superheavy nuclei.

Triaxial superdeformed bands in odd–odd [formula omitted] isotopes

The triaxial superdeformed rotational bands in the odd–odd Lu 160 ∼ 168 isotopes are investigated by performing the configuration dependent three-dimensional total routhian surface calculations. About fifty low lying triaxial superdeformed bands have been found for these odd–odd nuclei within the excitation energy of 3 MeV above the normal deformed yrast bands. The calculated equilibrium elongation, triaxial and hexadecapole deformations for these triaxial superdeformed bands are close to the values of ε 2 ∼ 0.4 , γ ∼ 20 ° and ε 4 ∼ 0.03 , respectively. The configurations of calculated triaxial superdeformed bands have been assigned based on the total routhian surface calculations and the analysis of quasiparticle routhians in the rotating frame. The observed yrast triaxial superdeformed band of 164Lu, where the linking transitions between superdeformed and normal deformed states are measured, have been reproduced by the present calculation in the relative energy to the normal deformed band. We show that the stability of superdeformed triaxial shapes in the odd–odd Lu isotopes is similar to that presented in odd–even Lu nuclei, and thus the wobbling excitations could be expected to occur in odd–odd Lu isotopes. The deformation driving effect of the proton high-j low-K orbit play an important role in the formation of the triaxial superdeformed states in both odd–odd and odd–even Lu isotopes, while the shell effect is a fundamental factor for the triaxial superdeformed shapes. The shell gaps and the positions of the deformation driving intruder orbits which are responsible for the triaxial superdeformed minima have been localized, particularly, the neutron N = 94 gap and the position of the proton [ 660 ] 1 / 2 orbit in the deformed single particle diagram provide the basis for a microscopic understanding of the observed triaxial superdeformed bands in the mass region.

Onset of collectivity in neutron-rich Fe isotopes: Toward a new island of inversion?

The lifetimes of the first excited 2+ states in 62Fe and 64Fe have been measured for the first time using the recoil‐distance Doppler shift technique, at GANIL. A 238U beam of 6.5 AMeV impinged on 64Ni target, and the target like products were slowed down by a degrader foil positioned at micrometer distance downstream of the target and identified in the VAMOS spectrometer on an event‐by‐event basis. The lifetimes were then determined from the intensities of the degraded and fully Doppler shifted components of the 2+→0+ transition detected in EXOGAM detectors positioned at backward angles.The resulting lifetimes show a steep increase of the B(E2) values of the first excited 2+ state from 62Fe to 64Fe. A comparison with shell model calculations shows that the onset of collectivity is related to the occupation of neutron intruder orbitals. The large B(E2) value for 64Fe is only reproduced if the valence space includes both the neutron g9/2 and d5/2 orbitals. The transition from spherical 68Ni to more proton‐...

Extracting single-particle information for the superheavy mass region by studying excited structure in transfermium nuclei

Recent experimental advances have made it possible to study spectroscopy in very heavy nuclei. We show that from the excited high-spin structure of transfermium isotopes, one may gain useful information on single-particle states for the superheavy mass region, which is the key to locating the anticipated ‘island of stability’. In this work, we employ the Projected Shell Model for Cf, Fm, and No isotopes to study rotation alignment of the particles that occupy particular high- j intruder orbitals.

Higher Tamm-Dankoff approximation for rotational nuclear states

Within the Higher Tamm Dancoff Approximation (HTDA), single particle states associated with a mean field of the Hartree-Fock type are used into shell model like calculations. Recently, this approach has been used for ground state calculations in magic nuclei and in the N = Z mass region, as well as to study properties of some important isomeric states. The Cranking version of this formalism (Cr. HTDA) represents an attempt to reproduce rotational bands up to high spins in heavy nuclei. In this context, through the use of the mean field part of HTDA, many deformation and rotation effects (as intruder orbitals and effects of the time reversal symmetry breaking) are included in the configuration space. This work discusses the Cr. HTDA results obtained for two Pb isotopes (in order to test the approach), when using up to 2 particles – 2 holes excitations and provides tests for enlargement of the configuration space by 4 particle – 4 holes excitations. It is focused on the configuration space properties, improvement of truncation schemes, computational problems and saturation behavior of some physical quantities.

Competition in rotation-alignment between high-jneutrons and protons in transfermium nuclei

The study of rotation-alignment of quasiparticles probes sensitively the properties of high-$j$ intruder orbits. The distribution of very-high-$j$ orbits, which are consequences of the fundamental spin-orbit interaction, links with the important question of single-particle levels in superheavy nuclei. With the deformed single-particle states generated by the standard Nilsson potential, we perform Projected Shell Model calculations for transfermium nuclei where detailed spectroscopy experiments are currently possible. Specifically, we study the systematical behavior of rotation-alignment and associated band-crossing phenomenon in Cf, Fm, and No isotopes. Neutrons and protons from the high-$j$ orbits are found to compete strongly in rotation-alignment, which gives rise to testable effects. Observation of these effects will provide direct information on the single-particle states in the heaviest nuclear mass region.

Possible existence of triaxial superdeformation in 172,174,176W

Two-dimensional total routhian surface (TRS) calculations are carried out to determine the triaxial superdeformation (TSD) of the even-even nucleus W, and the result indicates that TSD state exists with deformation parameters ∊2 = 0.42 and γ = 34.7°. In the same way, the total routhian surfaces for the nuclei W are also calculated. It shows that the neutron shell correction energy plays a key role in the formation of TSD nuclei 172,174,176W, while the high j intruder orbitals and rotational energy are also crucial in the formation mechanism.

Proton Orbital [541]1/2 and Backbending in 178W

The microscopic mechanism of nine experimentally observed bands in 178W is investigated using the particle-number conserving method of the cranked shell model with monopole and quadrupole paring interactions. The experimental results, including the moments of inertia and angular momentum alignments of nine bands in 178W, are reproduced well by the particle-number conserving calculations, in which no free parameter is involved. Calculations demonstrate that occurrence of sharp backbending comes mainly from the contribution of high-j intruder orbitals νi13/2 or πh11/2 and their interference effect with orbitals near the Fermi surface. The ω variation of the occupation probability of each cranked orbital and the contribution to moment of inertia from each cranked orbital are analyzed.

Further research on high-spin structure in 161Lu

The two-dimensional total routhian surface (TRS) calculations were performed to probe into the triaxial superdeformed characteristics of a strongly populated band X2 in 161Lu. This band was identified as a triaxial superdeformed band by using our TRS method. We also got its formation mechanics, i.e. the neutron-shell correction energy plays a crucial role, while the rotating energy and the deformation-driving effect of high j intruder orbit i13/2 also play an additional role.

Nuclear shapes of highly deformed bands inHf171,172and neighboring Hf isotopes

A Gammasphere experiment was carried out to search for triaxial strongly deformed (TSD) structures in $^{171,172}\mathrm{Hf}$ and the wobbling mode, a unique signature of nuclei with stable triaxiality. Three strongly deformed bands in $^{172}\mathrm{Hf}$ and one in $^{171}\mathrm{Hf}$ were identified through $^{48}\mathrm{Ca}$($^{128}\mathrm{Te}$, xn) reactions. Linking transitions were established for the band in $^{171}\mathrm{Hf}$ and, consequently, its excitation energies and spins (up to $111/2\ensuremath{\hbar}$) were firmly established. However, none of the $^{172}\mathrm{Hf}$ sequences were linked to known structures. Experimental evidence of triaxiality was not observed in these bands. The new bands are compared with other known strongly deformed bands in neighboring Hf isotopes. Theoretical investigations within various models have been performed. Cranking calculations with the Ultimate Cranker code suggest that the band in $^{171}\mathrm{Hf}$ and two previously proposed TSD candidates in $^{170}\mathrm{Hf}$ and $^{175}\mathrm{Hf}$ are built on proton $({i}_{13/2}{h}_{9/2})$ configurations, associated with near-prolate shapes and deformations enhanced with respect to the normal deformed bands. Cranked relativistic mean-field calculations suggest that band 2 in $^{175}\mathrm{Hf}$ has most likely a near-prolate superdeformed shape involving the $\ensuremath{\pi}{i}_{13/2}\ensuremath{\bigotimes}\ensuremath{\nu}{j}_{15/2}$ high-$j$ intruder orbitals. It is quite likely that the bands in $^{172}\mathrm{Hf}$ are similar in character to this band.

Yrast structure ofFe64

The level structure of the $N=38$ isotone $^{64}\mathrm{Fe}$ was studied with the $^{64}\mathrm{Ni}$ + $^{238}\mathrm{U}$ reaction at 430 MeV. Several new levels were identified and compared to shell model calculations. Results show no evidence for deformation in the ground state, but a possible contribution from intruder orbitals at higher energy and spin.

A simple model for doublet bands in doubly odd nuclei

Nuclear structure of doublet bands in doubly odd nuclei with mass A ∼ 130 is investigated within the framework of a simple model where the even-even core couples with a neutron and a proton in intruder orbitals through a quadrupole-quadrupole interaction. The model reproduces quite well the energy levels of doublet bands and electromagnetic transitions. The staggering of the ratios B(M1;I → I - 1)/B(E2;I → I - 2) of the yrast bands turns out to be described by the chopsticks-like motion of two angular momenta of the unpaired neutron and the unpaired proton when they are weakly coupled with the core.-1

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.

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.

The intruder orbitals in superdeformed bands and alignment additivity of odd–odd nuclei in the [formula omitted] region

The particle-number conserving (PNC) method for treating the cranked shell model with monopole and quadrupole pairing correlations is used to study the superdeformed (SD) bands observed in odd–odd nuclei in the A ∼ 190 mass region. Spins are assigned to the levels in these bands. The microscopic mechanism of the ℏω evolution of the dynamic moment of inertia J ( 2 ) for these SD bands are analyzed. In particular, the major roles of the j 15 / 2 neutron and i 13 / 2 proton orbitals played in the SD bands are investigated in detail by contributions to J ( 2 ) from each cranked orbital and interference terms between two cranked orbitals. Additivity in the A ∼ 190 mass region is investigated. The experimental evidence for additivity of alignments in 192Tl can be reproduced by our calculations.

Structure of isomeric states in 66As and 67As

Strong residual correlations between neutrons and protons in N ≈ Z systems can lead to unusual structure. Using the spherical shell model, we show that a low-excitation shape isomer can occur in the odd–odd N = Z nucleus 66As. This extends the picture of shape coexistence beyond even–even nuclei. Furthermore, it is demonstrated that in 66As and in the N = Z + 1 nucleus 67As, a new type of isomer, which we term j-isomer, can be formed. The underlying mechanism for the isomerism formation is structure change in the isomeric states, which involves either an alignment of a neutron–proton pair from the high- j intruder orbitals, or a simultaneous occupation of these neutron and proton high- j orbitals.

Microscopic Mechanism of Large Fluctuation in Odd-Even Differences in Momentsof Inertia for Actinide Nuclei

The experimental large fluctuation in odd-even differences in moments ofinertia of deformed actinide nuclei is investigated using the particle-numberconserving (PNC) method for treating the cranked shell model with monopole andquadrupole pairing interactions. PNC calculations show that the large odd-evendifference in moments of inertia mainly comes from the interferencecontributions j(μν) from particles in high j intruder orbitals μand ν quite near the Fermi surface, which have no counterpart in the BCSformalism. The effective monopole and quadrupole pairing interaction strengthsare determined to fit the experimental odd-even differences in bindingenergies and bandhead moments of inertia. The experimental results for thevariation of moments of inertia with rotational frequency ω arereproduced well by the PNC calculation. The nearly identical experimentalmoments of inertia between 236U(gsb) and 238U(gsb) at lowfrequencies ℏω⩽0.20 MeV are also reproduced quite well.

Highly deformed Bands inHf175

Two high-spin regularly spaced rotational bands with large dynamical moments of inertia have been identified in Hf-175 with the Gammasphere spectrometer. These new bands are very similar to the previously identified superdeformed bands in the hafnium nuclei. However, the new bands in Hf-175 have been linked into the known level scheme and thereby provide the first firm spin assignments for these structures in this region. In order to understand the new bands, theoretical calculations have been performed based on the ULTIMATE CRANKER code. The new bands in Hf-175 are deduced to be built upon highly deformed structures. No experimental evidence for triaxiality was established and this work suggests that the structure of the so-called triaxial superdeformed bands in the Hf nuclei may be quite different from those identified in the lighter mass Lu nuclei. Since the two highly deformed bands in Hf-175 are associated with different deformations, this work also identifies the role of the intruder orbits in polarizing the nuclear shape.

SU(3) model description of Be isotopes

Experimental data on light nuclei close to dripline suggests that as the nucleon number asymmetry increases, the shell structure from stability line is not preserved. In contrast with spherical shell model, Elliott's SU(3) model, uses a deformed multi-nucleon basis to describe nuclear states. The SU(3) symmetry is a strong feature of 1p shell nuclei, where symmetry breaking spin-orbit force is rather weak. We have calculated the binding energies and low-lying energy spectra of Be isotopes (A=6 to A=14), within the framework of Elliott's SU(3) model, with special emphasis on effects due to the presence of intruder orbit 1S1/2 in the region. The model space includes SU(3) basis states that maximize the quadrupole-quadrupole interaction (-chiQ.Q). An extended model space includes, in addition, a set of 2p-2h excitations, with excited nucleons occupying lowest energy SU(3) states in harmonic oscillator shell N=2. Group theoretical methods have been used to classify the states and calculate the nuclear interaction matrix elements. Good angular momentum states are projected out from intrinsic deformed SU(3) states by using standard angular momentum projection techniques. The interaction used contains the monopole-monopole, quadrupole-quadrupole and isospin dependent terms. Interaction parameters are fixed so as to reproduce the binding of 4 nucleons in N=1 orbit for the N=Z isotope-8Be in ground state and first excited 2+ state, along with the known systematics of single neutron separation energies for Be isotopes. The calculated energy espectra are compared with available experimental data. The calculated excitation energies of intruder states in 8Be and 10Be, are discussed in the light of available experimental evidence and theoretical results from shell model as well as deformed oscillator model calculations of Fayache et al..