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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Persistence of the Z = 28 shell gap in A = 75 isobars: Identification of a possible ( 1 / 2 – ) μ s isomer in Co 75 and β decay to Ni 75

Here, the evolution of shell structure around doubly magic exotic nuclei is of great interest in nuclear physics and astrophysics. In the ‘southwest’ region of 78 Ni, the development of deformation might trigger a major shift in our understanding of explosive nucleosynthesis. To this end, new spectroscopic information on key close-lying nuclei is very valuable. We intend to measure the isomeric and β decay of 75 Co, with one-proton and two-neutron holes relative to 78Ni, to access new nuclear structure information in 75 Co and its β-decay daughters 75 Ni and 74 Ni. The nucleus 75 Co is produced in relativistic in-flight fission reactions of 238 U at the Radioactive Ion Beam Factory in the RIKEN Nishina Center. Its isomeric and β decay are studied exploiting the BigRIPS and EURICA setups. We obtain partial β-decay spectra for 75 Ni and 74 Ni, and report a new isomeric transition in 75 Co. The energy [E γ = 1914(2)keV] and half-life [t 1/2 = 13(6) μs] of the delayed γ ray lend support for the existence of a J π = (1/2 – ) isomeric state at 1914(2) keV. A comparison with PFSDG-U shell-model calculations provides a good account for the observed states in 75 Ni, but the first calculated 1/2 – level in 75 Co, a prolate K = 1/2 state, is predicted about 1 MeV below the observed (1/2 – ) level. The spherical-like structure of the lowest-lying excited states in 75 Ni is proved. In the case of 75 Co, the results suggest that the dominance of the spherical configurations over the deformed ones might be stronger than expected below 78 Ni. Further experimental efforts to discern the nature of the J π = (1/2 – ) isomer are necessary.

59 ≤ A ≤ 89↗
DOE OSTI2022

Identification of excited states in Bi 188 and Po 188

The neutron-deficient 188 Bi and 188 Po isotopes have been studied by γ-ray spectroscopy using the recoil-decay tagging technique with the Argonne Gas-Filled Analyzer. A new 0.25(5)-μs isomeric state and a prompt cascade formed by 319-, 366-, and 462-keV γ rays have been established on top of the (10¯) α -decaying isomer in 188 Bi. The first excited (2 + ) state in 188 Po was identified, its excitation energy of 242(2) keV continues the nearly constant trend for the first 2 + states in 190, 192,194 Po. Here, the state is most likely a member of a prolate rotational band built on the ground state, albeit mixing with other coexisting configurations cannot be excluded. The new results obtained in the present work provide new information to shape coexistence in bismuth and polonium isotopes near the neutron midshell at N = 104 . In this mass region, a reduction in the prompt γ-ray yield obtained with recoil decay tagging was observed for a few nuclides, and the possible reasons are presented.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Total absorption spectroscopy of two isomers in 70 Cu influencing nucleosynthesis signatures

Isomers have long been known to be important for astrophysical nucleosynthesis processes, yet they are often neglected in network calculations due to computational limitations or lack of data. "Astromers" are astrophysically metastable nuclear states that can greatly impact nucleosynthesis pathways. In this work we show that astromers further impact the time-dependent electromagnetic signal during heavy element nucleosynthesis. In an experiment performed at the National Superconducting Cyclotron Laboratory, three 𝛽-decaying states of 70 Cu (6 − ground state, and two isomeric states: 3 − and 1 + ) were produced. 𝛽-feeding values were extracted from experimental spectra and compared to shell-model and QRPA+PVC calculations. Here, average 𝛾-ray energies from the 𝛽-decay events were incorporated into simulations of heavy element nucleosynthesis and were found to exhibit different energy release profiles over time, which may impact, in aggregate, time-dependent observable signals.

59 ≤ A ≤ 89↗
DOE OSTI2022

237 Np Mössbauer Isomer Shifts: A Lesson About the Balance of Static and Dynamic Electron Correlation in Heavy Element Complexes

A large set of neptunium compounds with different oxidation states (III to VII) was assembled to study the Mössbauer isomer shift by wave function calculations and better understand covalency in f-elements complexes. The contact density approach was used to calculate the isomer shift using complete active space self-consistent field (CASSCF) multiconfiguration wave functions, as well as matrix product states [from Density Matrix Renormalization Group (DMRG) algorithms] for large active spaces. Dynamic correlation effects for the isomer shifts were treated via CASPT2 energy derivatives with respect to the nuclear radius. The CASSCF calculations appear to produce different orbital overlocalization errors for low and high Np oxidation states. For compounds with low Np oxidation numbers, the errors can be attributed to the overlocalization of the 5f orbitals. For the compounds with high Np oxidation numbers, the main errors arise from an overlocalization of ligand orbitals and concomitant to weak donation bonding. Attempts to mitigate the overlocalization errors with large active spaces using DMRG were only partially successful, showing that explicit treatment of dynamic correlation is necessary for accurate predictions of Mössbauer isomer shifts. The CASPT2 calculations perform very satisfactorily. For a subset of Np compounds, both static and dynamic correlation effects were substantial. Furthermore, a rational active space selection based on orbital entanglement diagrams proved beneficial for determining the optimal reference wave function.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Nanosecond isomers and the evolution of collectivity in stable, even- A Hg isotopes

Isomeric states and associated collective structures have been studied up to high spin in 198,200,202 Hg using multinucleon transfer reactions and the Gammasphere array. A coupled rotational band, with possible four-quasiparticle character, is established in 198 Hg. Sequences built on two-quasiparticle, positive- and negative-parity levels are assigned to 202 Hg. New isomers in 202 Hg with I π = (7 – ) and (9 – ), and T 1/2 = 10.4(4) ns and 1.4(3) ns, respectively, have been identified. A half-life of 1.0(3) ns is established for the I π = 12 + state in 200 Hg. B(E2) values deduced from isomeric transitions in Hg isotopes indicate that, while collectivity near the ground state gradually diminishes from N = 112 to N = 124, it is found to increase for the 12 + and 9 – states up to N = 118, followed by a reduction for higher neutron numbers. Calculations using the ultimate cranker code provide insight into the variation of deformation with spin and allow for an understanding of observed band crossings. As a result, the evolution of collectivity with spin, and along the isotopic chain, is described.

190 ≤ A ≤ 219↗
DOE OSTI2022

Theoretical Evaluation of Metal–Ligand Bonding in Neptunium Compounds in Relation to 237 Np Mössbauer Spectroscopy

The 237 Np Mössbauer isomer shift and quadrupole splitting (QS) are powerful probes for the metal–ligand bonding of neptunium, a 5f-element of vital importance in the nuclear fuel cycle. A large set of Np compounds with different oxidation states (III) to (VII) is studied to investigate, by first-principles calculations, isomer shifts and the QS trends in relation to the Np oxidation state. Natural Bond Orbital analysis reveals that in addition to donation bonding to the 5f shell, participation of the 6d and 7s neptunium shells in covalent (donation) bonding substantially impacts the isomer shifts. The isomer shift cannot be interpreted solely by the 5f shell electron count. The isomer shift for Np(II) compounds is estimated to be in the range of 31–34 mm/s, less positive than for Np(III) compounds. For the QS, density functional calculations fail to reproduce the quadrupole splitting for some Np(VI) ionic solids. A multiconfigurational wave function approach reproduces the observed QS trends. The calculations give a semiquantitative interpretation of the trends for Np oxidation states (V) to (VII). Furthermore, the contrasting QS for standard and “reverse” neptunyl(VI), at the opposite extremes of the observed QS scale, arises predominantly from the different crystal environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Laser-based conversion electron Mössbauer spectroscopy of 229 ThO 2

The exceptionally low-energy 229 Th nuclear isomeric state is expected to provide several new and powerful applications, including the construction of a robust and portable solid-state nuclear clock, perhaps contributing to a redefinition of the second, exploration of nuclear superradiance and tests of fundamental physics. Further, analogous to the capabilities of traditional Mössbauer spectroscopy, the sensitivity of the nucleus to its environment can be used to realize laser Mössbauer spectroscopy and, with it, new types of strain and temperature sensors and a new probe of the solid-state environment, all with excellent sensitivity. However, current models for examining the nuclear transition in a solid require the use of a high-bandgap, vacuum ultraviolet (VUV) transmissive host, severely limiting the applicability of these techniques. Here we report the first, to the authors’ knowledge, demonstration of laser-induced conversion electron Mössbauer spectroscopy (CEMS) of the 229 Th isomer in a thin ThO 2 sample whose bandgap (approximately 6 eV) is considerably smaller than the nuclear isomeric state energy (8.4 eV). Unlike fluorescence spectroscopy of the 229 Th isomeric transition, this technique is compatible with materials whose bandgap is less than the nuclear transition energy, opening a wider class of systems to study and the potential of a conversion-electron-based nuclear clock.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Improved Cumulative Fission Yield Measurements with Fission Spectrum Neutrons on 238U

Two isotopically-characterized targets of high-purity (99.961±0.002%) 238U metal and a neutron dosimetry package were exposed to a pulsed neutron irradiation using the Godiva IV critical assembly at the National Criticality Experiments Research Center to measure the integral fission product yields produced in a Watt fission neutron-energy spectrum. Following irradiation, the fissioned targets were counted with two broad energy germanium detectors. Estimates of the total fissions for each target were made using measurements of well-known fission products. The total number of fissions in each target were then used to measure the fission yields of 33 fission products, 18 of which are published as new measurements. Twelve of the 18 isotopes were in agreement with ENDF/B- VIII.0 using the zeta test and treating ENDF/B-VIII.0 as the true mean: 84mBr, 93Y, 94Y, 104Tc, 134I, 135I, 138Xe, 141Ba, 142Ba, 142La, 146Ce, and 149Nd. The ENDF/B-VIII.0 fission yield for 139Ba was only slightly outside of 1-s relative to the uncertainty measured in this work. Uncertainties for 5 fission product yields were markedly improved over those reported in ENDF/B-VIII.0: 128Sn, 129Sb, 130gSb, 131mTe, and 133I. The fission yields measured for 128Sn, 131mTe, and 133I were in good agreement with the ENDF/B-VIII.0 predicted fission yields. However, fission yields measurements of the isotopes 129Sb, and 130gSb deviated from the ENDF/B-VIII.0 value. Both of these isotopes reside near the doubly magic nuclear shell closures of 50 protons and 82 neutrons. These fission yields may be suppressed because of the odd-odd nuclear structure of 130gSb and the odd-even structure of 129Sb and isomer splitting. Comparisons to other recent work and a brief review with citations are included to support this conclusion.

Fission Yields↗
DOE OSTI2025

Nuclear excitation functions for medical isotope production: Targeted radionuclide therapy via nat IR$(d, x)$ 193m Pt

193m Pt is an Auger emitting radionuclide which may have therapeutic potential, particularly when labeled to the chemotherapeutic drug cisplatin. One challenge to broader explorations of its clinical potential is the need for production routes with high specific activity. As part of a larger campaign to address gaps in reaction data for emerging medical radionuclides, this work seeks to characterize the nat Ir(d,x) reactions as a potential production pathway for 193m Pt. A stacked target irradiation, consisting of natural iridium, iron, nickel, and copper foils, was performed using a 33 MeV deuteron beam at the Lawrence Berkeley National Laboratory 88-Inch Cyclotron. This measurement, along with previous experimental data, suggests an energy window between 11 to 18 MeV to maximize the production and radiopurity of 193m Pt. This experiment has yielded cross sections for 43 channels of deuteron-induced reactions from threshold to 30 MeV, including the first experimental results of nat Ir(d,x) 188m1+g,190m1+g Ir (cumulative), nat Ni(d,x) 56,57,58 m,58g Co (independent), nat Cu(d,x) 61 Co (cumulative) and nat Fe(d,x) 53 Fe, 48 V (cumulative). The results were compared with literature data, the TENDL-2023 database, and default theoretical calculations from the TALYS-2.04, CoH-3.6.0, EMPIRE 3.2.3, and ALICE-2020 reaction modeling codes. Here, this work presents another example of the lack of predictive capabilities for this set of modern nuclear-reaction modeling codes, and highlights the unsatisfactory modeling of experimental cross sections. Experimental data are important to improve the codes in general, and new experimental results can be used to improve the models. Finally, this measurement has revealed the need for an updated evaluation of the nat Cu(d,x) 63 Zn deuteron monitor reaction.

193mPt↗
DOE OSTI2023

Microsecond Isomer at the N = 20 Island of Shape Inversion Observed at FRIB

Excited-state spectroscopy from the first experiment at the Facility for Rare Isotope Beams (FRIB) is reported. A 24(2)-μs isomer was observed with the FRIB Decay Station initiator (FDSi) through a cascade of 224- and 401-keV γ rays in coincidence with 32 Na nuclei. This is the only known microsecond isomer (1 μs ≤T 1/2 <1 ms) in the region. This nucleus is at the heart of the N=20 island of shape inversion and is at the crossroads of the spherical shell-model, deformed shell-model, and ab initio theories. It can be represented as the coupling of a proton hole and neutron particle to 32 Mg, 32 Mg+π -1 +ν +1 . This odd-odd coupling and isomer formation provides a sensitive measure of the underlying shape degrees of freedom of 32 Mg, where the onset of spherical-to-deformed shape inversion begins with a low-lying deformed 2 + state at 885 keV and a low-lying shape-coexisting 0$^+_2$ state at 1058 keV. Here, we suggest two possible explanations for the 625-keV isomer in 32 Na: a 6 - spherical shape isomer that decays by E2 or a 0 + deformed spin isomer that decays by M2. The present results and calculations are most consistent with the latter, indicating that the low-lying states are dominated by deformation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

{beta}- and {gamma}-spectroscopy study of {sup 119}Pd and {sup 119}Ag

Neutron-rich Pd-119 nuclei were produced in fission of natural uranium, induced by 25-MeV protons. Fission fragments swiftly extracted with the Ion Guide Isotope Separation On-Line method were mass separated using a dipole magnet and a Penning trap, providing mono-isotopic samples of Pd-119. Their beta(-) decay was measured with gamma gamma- and beta gamma-spectroscopy methods using low-energy germanium detectors and a thin plastic scintillator. Two distinct nuclear-level structures were observed in Ag-119, based on the 1/2(-) and 7/2(+) isomers reported previously. The beta(-)decay work was complemented by a prompt-gamma study of levels in Ag-119 populated in spontaneous fission of (252)cf, performed using the Gammasphere array of germanium detectors. Contrary to previous suggestions, our data show that the 1/2(-) isomer is located below the 7/2(+) isomer and is proposed as a new ground state of Ag-119 with the 7/2(+) isomer excitation energy determined to be 33.4 keV. Our data indicate that there are two beta unstable isomers in Pd-119, a proposed ground state of Pd-119 with tentative spin 1/2(-) or 3/2(+) and a half-life of 0.88 s and the other one about 350 keV above, having spin (11/2(-)) and a half-life of 0.85 s. The higher-energy isomer probably decays to the 1/2(-) or 3/2(+) ground state via a gamma cascade comprising 18.7-219.8-X-keV transitions. The unobserved isomeric transition with energy X approximate to 100 keV probably has an E3 multipolarity. Its hindrance factor is significantly lower than for analogous E3 isomeric transitions in lighter Pd isotopes, suggesting an oblate deformation of levels in Pd-119. Oblate configurations in Ag-119 are discussed also.

Kurpeta, J↗
DOE OSTI2021

Theoretical Prediction and Interpretation of 237 Np Mössbauer Isomer Shifts

Different theoretical approaches for the calculation of 237 Np Mössbauer isomer shifts are investigated. The traditional contact density route is compared to a previously proposed alternative approach that uses energy derivatives with respect to the nuclear radius. Both approaches yield similar results as long as suitable basis sets augmented with large exponents and relativistic methods are used. Density functional theory (DFT) calculations do not show a strong dependency of the 237 Np isomer shift on the chosen functional. Wavefunction calculations show that dynamic electron correlation can be important when covalent bonding influences the isomer shift. Effects from spin–orbit coupling are small. The isomer shifts of ionic solids and Np(III) organometallic complexes are largely governed by the oxidation state of Np. Isomer shifts of organometallic Np(IV) complexes are strongly affected by donation bonding. Furthermore, detailed analysis of the wavefunction results with different active spaces demonstrates that correlation among the outer core Np and occupied ligand frontier orbitals contributes significantly to isomer shifts of Np(IV) compounds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Experimental and computational investigation of the bond energy of thorium dicarbonyl cation and theoretical elucidation of its isomerization mechanism to the thermodynamically most stable isomer, thorium oxide ketenylidene cation, OTh + CCO

Collision-induced dissociation (CID) of [Th,2C,2O] + with Xe is performed using a guided ion beam tandem mass spectrometer (GIBMS). The only products observed are ThCO + and Th + by sequential loss of CO ligands. The experimental findings and theoretical calculations support that the structure of [Th,2C,2O] + is the bent homoleptic thorium dicarbonyl cation, Th + (CO) 2 , having quartet spin, which is both thermodynamically and kinetically stable enough in the gas phase to be observed in our GIBMS instrument. Analysis of the kinetic energy-dependent cross sections for this CID reaction yields the first experimental determination of the bond dissociation energy (BDE) of (CO)Th + –CO at 0 K as 1.05 ± 0.09 eV. A theoretical BDE calculated at the CCSD(T) level with cc-pVXZ (X = T and Q) basis sets and a complete basis set (CBS) extrapolation is in very good agreement with the experimental result. Although the doublet spin bent thorium oxide ketenylidene cation, OTh + CCO, is calculated to be the most thermodynamically stable structure, it is not observed in our experiment where [Th,2C,2O] + is formed by association of Th + and CO in a direct current discharge flow tube (DC/FT) ion source. Potential energy profiles of both quartet and doublet spin are constructed to elucidate the isomerization mechanism of Th + (CO) 2 to OTh + CCO. The failure to observe OTh + CCO is attributed to a barrier associated with C–C bond formation, which makes OTh + CCO kinetically inaccessible under our experimental conditions. Furthermore, chemical bonding patterns in low-lying states of linear and bent Th + (CO) 2 and OTh + CCO isomers are also investigated.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Universal Effective Charges in the 𝑠⁢𝑑 and 𝑓⁡𝑝 Shells

The 247-keV state in 54 Sc, populated in the 𝛽 decay of 54 Ca, is reported here as a nanosecond isomer with a half-life of 26.0(22) ns. The state is interpreted as the 1 + member of the 𝜋⁢𝑓 7/2 ⊗ 𝜈⁢𝑓 5/2 spin-coupled multiplet, which decays to the 3 + ,𝜋⁢𝑓 7/2 ⊗ 𝜈⁢𝑝 1/2 ground state. The new half-life corresponds to a pure 𝐸⁢2 transition with a strength of 1.93(16) W.u., providing the most precise, unambiguous 𝐵⁡(𝐸⁢2) value in the neutron-rich 𝑓⁡𝑝 region to date for a nucleus with valence protons above 𝑍 = 20. Notably, it is roughly 4 times larger than the 𝐵⁡(𝐸⁢2;1/2 − → 5/2 − ) value in 55 Ca. The results, as compared to semiempirical and ab initio shell-model calculations, indicate (1) a weak 𝑁 = 34 subshell gap relative to 𝑁 = 32, (2) a large 𝐸⁢2 enhancement in Sc as compared to Ca due to 1⁢𝑝 − 1⁢ℎ proton excitations across 𝑍 = 28, and (3) empirical effective proton and neutron charges 𝑒 𝜋 = 1.30⁢(8)⁢𝑒 and 𝑒 𝜈 = 0.452⁢(7)⁢𝑒, respectively, that are in contrast to reports of 𝑒 𝜋 ≈1.1–1.15⁢𝑒 and 𝑒 𝜈 ≈ 0.6–0.8⁢𝑒 for 𝑓⁡𝑝-shell nuclei near 𝑁 = 𝑍. Here, we demonstrate that these reports are erroneous and that, in fact, a universal set of effective charges can be used across the 𝑠⁢𝑑 and 𝑓⁡𝑝 shells.

Beta decay↗
DOE OSTI2026

Environment-imposed selection rules for nuclear-spin conversion of H 2 in molecular crystals

Nuclear-spin conversion in molecular hydrogen is governed by strict symmetry rules that typically require magnetic fields or catalytic surfaces to break. Here we demonstrate that the intrinsic tensor composition of a non-magnetic molecular crystal field can impose and relax these rules without external fields. High-resolution infrared spectra of H 2 in crystalline CO 2 reveal large rank-2 (quadrupolar) crystal-field splittings of the 𝑚 sublevels, while nuclear-spin conversion occurs only through 𝛥𝑚 = 0 channels. Replacing CO 2 with polar N 2 O introduces rank-1 (dipole) components that partially open 𝛥⁢𝑚 ≠ 0 pathways, while incorporation of paramagnetic NO 2 fully lifts the restriction. Furthermore, these results establish a direct correspondence between crystal-field tensor rank and nuclear-spin dynamics, introducing a general symmetry-based framework for designing and controlling spin-isomer populations and quantum-state connectivity in molecular solids.

McLane, Nathan [University of Maryland, College Pa↗
DOE OSTI2024

Improving Fission Products at CARIBU: Near Field Detection (Q1/FY24 Quarterly Progress Report)

The article on “Direct Mass Measurements to Inform the Behavior for 128mSb in Nucleosynthesis Environments” by Daniel Hoff et al., recently published in Physical Review Letters. The results of the work are a combination of an extraordinary work on precision mass measurements performed with the Canadian Penning Trap at ANL (the most precise mass measurement of the ground state and the isomeric state in 128Sb performed to date), and an extensive nucleosynthesis theory calculation that include isomers performed by the theorists at LANL.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Prompt-delayed γ-ray spectroscopy of neutron-rich 119.121 In isotopes

The Z = 50 shell closure, near N = 82, is unique in the sense that it is the only shell closure with the spin-orbit partner orbitals, π g 9 / 2 and π g 7 / 2 , enclosing the magic gap. The interaction of the proton hole/particle in the above-mentioned orbitals with neutrons in the νh 11/2 orbital is an important prerequisite to the understanding of the nuclear structure near N = 82 and the νπ interaction. To explore the structural similarity between the high-spin isomeric states in In ( Z = 49), Sn ( Z = 50), and Sb ( Z = 51) isotopes from a microscopic point of view. In addition, to understand the role of a proton hole or particle in the spin-orbit partner orbitals, π g 9 / 2 and π g 7 / 2 , respectively, with neutron holes in the ν h 11 / 2 orbital on these aforementioned isomers. The fusion and transfer induced fission reaction Be 9 ( U 238 , f ) with 6.2 MeV/u beam energy, using a unique setup consisting of AGATA, VAMOS++, and EXOGAM detectors, was used to populate through the fission process and study the neutron-rich In 119 , 121 isotopes. This setup enabled the prompt-delayed γ -ray spectroscopy of isotopes in the time range of 100 ns – 200 μ s . In the odd- A In 119 , 121 isotopes, indications of a short half-life 19/2 - isomeric state, in addition to the previously known 25/2 + isomeric state, were observed from the present data. Further, new prompt transitions above the 25/2 + isomer in In 121 were identified along with reevaluation of its half-life. The experimental data were compared with the theoretical results obtained in the framework of large-scale shell-model calculations in a restricted model space. Furthermore, the ( π g 9 / 2 ν h 11 / 2 ; I | H ^ | π g 9 / 2 ν h 11 / 2 ; I ) two-body matrix elements of residual interaction were modified to explain the excitation energies and the B ( E 2) transition probabilities in the neutron-rich In isotopes. The (i) decreasing trend of E (29/2 + ) - E (25/2 + ) in odd-In (with dominant configuration π g 9 / 2 - 1 ν h 11 / 2 - 2 and maximum aligned spin of 29/2 + ) and (ii) increasing trend of E (27/2 + ) - E (23/2 + ) in odd-Sb (with dominant configuration π g 7 / 2 + 1 ν h 11 / 2 - 2 and maximum aligned spin of 27/2 + ) with increasing neutron number could be understood as a consequence of hole-hole and particle-hole interactions, respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗