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At least 451 records · Page 25
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DOE OSTI2021

SU(3)-guided realistic nucleon-nucleon interactions for large-scale calculations

We examine nucleon-nucleon realistic interactions, based on their SU(3) decomposition to SU(3)-symmetric components. We find that many of these interaction components are negligible, which, in turn, allows us to identify a subset of physically relevant components that are sufficient to describe the structure of low-lying states in 12C and related observables, such as excitation energies, electric quadrupole transitions, and rms radii. Here, we find that paring down the interaction by half or more yields results that practically coincide with the corresponding ab initio calculations with the full interaction. In addition, we show that while various realistic interactions differ in their SU(3) decomposition, their renormalized effective counterparts exhibit a striking similarity and composition that can be linked to dominant nuclear features such as deformation, pairing, clustering, and spin-orbit effect.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Quadrupole collectivity in the neutron-rich sulfur isotopes 38,40,42,44 S

Electromagnetic transition strengths in the even-even neutron-rich sulfur isotopes 38,40,42,44 S were measured using intermediate-energy Coulomb excitation at the National Superconducting Cyclotron Laboratory. By utilizing the sensitivity of the experimental technique to E2 excitations from the ground state, the evolution of the pattern of B(E2) strengths to several low-lying 2 + states was investigated at Z = 16 from near stability to the N = 28 island of inversion. The experimental results allowed a detailed comparison with predictions from shell-model calculations using the SDPF-MU Hamiltonian, which was designed to describe collectivity in this region of the nuclear chart. While the shell-model calculations succeeded in modeling transition strengths at N = 22, 24, 26, the experimental B(E2; $0$ $^{+}_{1}$ → $2$ $^{+}_{1}$) at N = 28 was smaller than the predicted value by about a factor of 2, similar to previous observations for chlorine and argon isotopes around N = 28. The dependence of this overprediction by theory on the choice of effective charges was explored.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Nuclear charge densities in spherical and deformed nuclei: Toward precise calculations of charge radii

Precise measurements of atomic transitions affected by electron-nucleus hyperfine interactions offer sensitivity to explore basic properties of the atomic nucleus and study fundamental symmetries, including the search for new physics beyond the standard model of particle physics. Specifically, such measurements, augmented by atomic and nuclear calculations, will enable extraction of the higher-order radial moments of the charge-density distribution in spherical and deformed nuclei. The new data impose higher precision requirements on a theoretical description. The nuclear charge density is composed of the proton point distribution folded with the nucleonic charge distributions. The latter induce subtle relativistic corrections due to the coupling of nucleon magnetic moments with the nuclear spin-orbit density. Additional corrections come from the effect of center-of-mass projection. We assess the precision of nuclear charge density calculations by studying the behavior of relativistic and center-of-mass motion corrections to the second and fourth charge radial moments. Special attention has been paid to the magnetic spin-orbit density associated with the local variations of the spin-orbit current. The calculations for semimagic and open-shell nuclei are performed in the framework of self-consistent mean-field theory using quantified energy density functionals and density-dependent pairing forces. We used the general expression for the spin-orbit form factor that is valid for spherical and deformed nuclei. We studied the impact of various correction terms on the charge radii, fourth radial moments, diffraction radii, and surface thickness of spherical and deformed nuclei. The spin-orbit corrections to charge radial moments and surface thickness show strong shell fluctuations which can make an appreciable effect when aiming at high-precision predictions of isotopic shifts. The inclusion of relativistic and center-of-mass corrections impacts the quality of energy density functionals optimized to charge radii data. To establish reliable constraints on the existence of new forces from isotope shift measurements, precise calculations of nuclear charge densities of deformed nuclei are needed. The proper inclusion of the spin-orbit charge density and other correction terms is essential when aiming at extraction of subtle effects which become particularly visible in isotopic trends. It is also important when developing high-quality nuclear energy density functionals optimized using heterogeneous datasets involving absolute charge radii, differential charge radii, and charge form factor properties deduced from electron-scattering data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Nuclear spin features relevant to ab initio nucleon-nucleus elastic scattering

Effective interactions for elastic nucleon-nucleus scattering from first principles require the use of the same nucleon-nucleon interaction in the structure and reaction calculations, as well as a consistent treatment of the relevant operators at each order. Previous work using these interactions has shown good agreement with available data. Here, we study the physical relevance of one of these operators, which involves the spin of the struck nucleon, and examine the interpretation of this quantity in a nuclear structure context. Using the framework of the spectator expansion and the underlying framework of the no-core shell model, we calculate and examine spin-projected, one-body momentum distributions required for effective nucleon-nucleus interactions in $J=0$ nuclear states. The calculated spin-projected, one-body momentum distributions for $^4$He, $^6$He, and $^8$He display characteristic behavior based on the occupation of protons and neutrons in single particle levels, with more nucleons of one type yielding momentum distributions with larger values. Additionally, we find this quantity is strongly correlated to the magnetic moment of the $2^+$ excited state in the ground state rotational band for each nucleus considered. In conclusion, we find that spin-projected, one-body momentum distributions can probe the spin content of a $J=0$ wave function. This feature may allow future ab initio nucleon-nucleus scattering studies to inform spin properties of the underlying nucleon-nucleon interactions. The observed correlation to the magnetic moment of excited states illustrates a previously unknown connection between reaction observables such as the analyzing power and structure observables like the magnetic moment.

6 ≤ A ≤ 19↗
DOE OSTI2021

Extracting the number of short-range correlated nucleon pairs from inclusive electron scattering data

The extraction of the relative abundances of short-range correlated (SRC) nucleon pairs from inclusive electron scattering is studied using the generalized contact formalism (GCF) with several nuclear interaction models. GCF calculations can reproduce the observed scaling of the cross-section ratios for nuclei relative to deuterium at high xB and large Q 2 , a 2 =(σ A /A)/(σ d /2). In the nonrelativistic instant-form formulation, the calculation is very sensitive to the model parameters and only reproduces the data using parameters that are inconsistent with ab initio many-body calculations. Using a light-cone GCF formulation significantly decreases this sensitivity and improves the agreement with ab initio calculations. The ratio of similar mass isotopes, such as 40 Ca and 48 Ca, should be sensitive to the nuclear asymmetry dependence of SRCs, but is found to also be sensitive to low-energy nuclear structure. Thus the empirical association of SRC pair abundances with the measured a2 values is only accurate to about 20%. Finally, improving this will require cross-section calculations that reproduce the data while properly accounting for both nuclear structure and relativistic effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Exploring the role of high- j configurations in collective observables through the Coulomb excitation of 106 Cd

In this work, the shape and collectivity of 106 Cd was investigated via a sub-barrier-energy Coulomb excitation experiment performed at the NSCL ReA3 facility using the JANUS setup. Transition matrix elements between low-lying states were found to agree with adopted values, and information on the shape and collectivity of higher-lying states was extracted for the first time. Locally-optimized large-scale shell-model calculations were found to describe well the B(E2) transition strengths but failed to reproduce the spectroscopic quadrupole moments Q s . An analysis of the E2 rotational invariants and the normalized quadrupole moment q s indicates that this may be due to a significant degree of triaxiality in 106 Cd which is not captured by the present shell-model calculations. Analogous calculations for the Fe isotopes (two protons below the Z = 28 magic number) reveal the critical role of high-j neutron configurations for the description of quadrupole moments in the heavy Fe and Cd isotopes (two protons below magic Z = 50), but this effect is insufficient to explain the shape of 106 Cd, posing a puzzle for the understanding of nuclear structure towards N = 50.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Cross-shell excitations in Ca 46 studied with fusion reactions induced by a reaccelerated rare isotope beam

Discovering unexplored high-spin states in neutron-rich nuclei can open up a new direction to study band structure and the associated shell structure in isospin-asymmetric many-body systems. However, experimental reach has so far been limited to neutron-deficient or stable nuclei which are preferentially produced in fusion reactions used in such studies. Here in this paper, we report the first γ-ray spectroscopy with fusion reactions using a reaccelerated rare-isotope beam of 45 K performed at the ReA3 facility of the National Superconducting Cyclotron Laboratory. Using particle and γ-ray coincidence techniques, three new higher-lying states around 6 MeV and five new γ-ray transitions were identified for 46 Ca, suggesting three independent band structures formed from different particle-hole configurations. The rotational-like band built on the 0$^+_2$ state is established up to the tentatively assigned 6$^+_2$ state. New results are compared to large-scale shell model calculations, confirming the validity of the effective interaction describing particle-hole excitations across the Z=20 and N=28 shell gaps in the vicinity of doubly-magic 48 Ca.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

In-beam γ-ray spectroscopy of 37–42 P

The level schemes of the neutron-rich 37-42 P isotopes are investigated via in-beam gamma-ray spectroscopy following the fragmentation of a 45 Cl projectile beam at intermediate beam energies. Information on gamma-gamma coincidence relationships complemented by comparisons to shell-model calculations in the sd-pf model space were used to construct excitation level schemes for these neutron-rich nuclei. For the odd-mass 37,39 P isotopes, a level scheme is presented that appears essentially complete at low energies and exhausts the states predicted by the SDPF-MU shell-model Hamiltonian. In conclusion, simple Nilsson configurations are proposed for the low-lying excited states of 38,39,40,41 P from an analysis of the E2 transition matrix elements and moments calculated within the shell model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Role of quadrupole deformation and continuum effects in the “island of inversion” nuclei 28,29,31 F

The peculiar properties of nuclei in the so-called “island of inversion” around Z = 10 and N = 20 are the focus of current nuclear physics research. Recent studies showed that 28 F has a negative-parity ground state and thus lies within the southern shore of the island of inversion, and 29 F presents a halo structure in its ground state, but it is unclear which effects, such as deformation, shell evolution due to tensor forces, or couplings to the continuum, lead to this situation. Here, we investigate the role of quadrupole deformation and continuum effects on the single-particle structure of 28,29,31 F from a relativistic mean-field approach and show how both phenomena can lead to a negative-parity ground state in 28 F and halo structures in 29,31 F. We solve the Dirac equation in the complex-momentum (Berggren) representation for a potential with quadrupole deformation at the first order obtained from relativistic mean-field calculations using the NL3 interaction and calculate the continuum level densities using the Green’s function method. We extract single-particle energies and widths from the continuum level densities to construct the Nilsson diagrams of 28,29,31 F in the continuum and analyze the evolution of both the widths and occupation probabilities of relevant Nilsson orbitals in 28 F and find that some amount of prolate deformation must be present. In addition, we calculate the density distributions for bound Nilsson orbitals near the Fermi surface in 29,31 F and reveal that, for a quadrupole deformation 0.3 ≤ β 2 ≤ 0.45 (prolate), characteristic halo tails appear at large distances. Using the relativistic mean-field approach in the complex-momentum representation with the Green’s function method, we demonstrate that in neutron-rich fluorine isotopes, while in the spherical case the pf shells are already inverted and close to the neutron emission threshold, a small amount of quadrupole deformation can dramatically reduce the gap between positive- and negative-parity states and increase the role of continuum states, ultimately leading to the negative parity in the ground state of 28 F and the halo structures in 29,31 F.

20 ≤ A ≤ 38↗
DOE OSTI2021

Structure of rotational bands in 109 Rh

Rotational bands in 109 Rh are investigated in a simple model and in the interacting boson-fermion model. We have developed a solvable extended transitional Hamiltonian by adding a two-configuration mixing term. Results suggest that 109 Rh is a good candidate for triaxiality and shape coexistence. Mixing between 3/2 + states with K = 1/2 and 3/2 is found to be weak, as evidenced by the E2 strengths.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

From noise to information: The transfer function formalism for uncertainty quantification in reconstructing the nuclear density

The neutron distribution of neutron-rich nuclei provides critical information on the structure of finite nuclei and neutron stars. Parity violating experiments—such as PREX and CREX—provide a clean and largely model-independent determination of neutron densities. Such experiments, however, are challenging and expensive, which is why sound statistical arguments are required to maximize the information gained. We introduce a new framework, the “transfer function formalism,” aimed at uncertainty quantification, model selection, and experimental design in the context of neutron densities. The transfer functions (TFs) are built analytically by expressing the linear response of the objective function (e.g., χ2) to small perturbations of the data. Using the TF formalism, we are able to analyze the expected overall uncertainty—quantified in terms of bias and variance—of the mean square radius and interior density of 48 Ca and 208 Pb. Using relativistic mean field models as a proxy for the weak-charge density—and assuming that a total of five measurements could be performed on the weak form factor of 48 Ca and 208 Pb—we identify the optimal models and experimental locations that minimize the uncertainty in the extraction of the radius and interior density. We also explore the use of the TF formalism to understand the influence of prior distributions for the model parameters, as well as the optimization of model hyperparameters not constrained by the data. Here,we establish how the choice of experimental locations and the model that is used can have a significant impact on the final uncertainties of the extracted quantities of interest. For challenging experiments such as CREX and PREX, a proper quantification of such uncertainties is critical. We have demonstrated how the TF formalism provides several advantages for this type of analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Nucleon-pair approximation for nuclei from spherical to deformed regions

Here we model low-lying states of atomic nuclei in the nucleon-pair approximation of the shell model, using three approaches to select collective nucleon pairs: the generalized seniority scheme, the conjugate gradient method, and the Hartree-Fock approach. We find the collective pairs obtained from the generalized seniority scheme provide a good description for nearly spherical nuclei, and those from the conjugate gradient method or the Hartree-Fock approach work well for transitional and deformed nuclei. Our NPA calculations using collective pairs with angular momenta 0, 2, and 4 (denoted by S D G pairs) reproduce the nuclear shape evolution in the N = 26 isotones, Ca 46 , Ti 48 , Cr 50 , and Fe 52 , and yield good agreement with full configuration-interaction calculations of low-lying states in medium-heavy transitional and deformed nuclei: Ti 44 – 48 , Cr 48 , Cr 50 , Fe 52 , Zn 60 – 64 , Ge 64 , 66 , Mo 84 , and Xe 108 – 112 . Finally, using the S D G I -pair approximation we describe low-lying states of Ba 112 , 114 , cases difficult to reach by conventional configuration-interaction methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Lifetime measurements in the even-even Cd 102 – 108 isotopes

The heaviest T z = 0 doubly-magic nucleus, Sn 100 , and the neighboring nuclei offer unique opportunities to investigate the properties of nuclear interaction. For instance, the structure of light-Sn nuclei has been shown to be affected by the delicate balance between nuclear-interaction components, such as pairing and quadrupole correlations. From Cd to Te, many common features and phenomena have been observed experimentally along the isotopic chains, leading to theoretical studies devoted to a more general and comprehensive study of the region. In this context, having only two proton holes in the Z = 50 shell, the Cd isotopes are expected to present properties similar to those found in the Sn isotopic chain. The aim of this work was to measure lifetimes of excited states in neutron-deficient nuclei in the vicinity of Sn 100 . Here, the neutron-deficient nuclei in the N ≈ Z ≈ 50 region were populated using a multinucleon transfer reaction with a Cd 106 beam and a Mo 92 target. The beamlike products were identified by the VAMOS + + spectrometer, while the γ rays were detected using the AGATA array. Lifetimes of excited states were determined using the recoil distance Doppler-shift method, employing the Cologne differential plunger. Lifetimes of low-lying states were measured in the even-mass Cd 102 – 108 isotopes. In particular, multiple states with excitation energy up to ≈ 3 MeV, belonging to various bands, were populated in Cd 106 via inelastic scattering. The transition strengths corresponding to the measured lifetimes were compared with those resulting from state-of-the-art beyond-mean-field calculations using the symmetry-conserving configuration-mixing approach. Conclusions: Despite the similarities in the electromagnetic properties of the low-lying states, there is a fundamental structural difference between the ground-state bands in the Z = 48 and Z = 50 isotopes. The comparison between experimental and theoretical results revealed a rotational character of the Cd nuclei, which have prolate-deformed ground states with β 2 ≈ 0.2 . At this deformation Z = 48 becomes a closed-shell configuration, which is favored with respect to the spherical one.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Shapes, softness, and nonyrast collectivity in 186 W

Nonyrast, excited states in neutron-rich 186 W were populated via inelastic-scattering reactions using beams of 136 Xe nuclei accelerated to 725 and 800 MeV. Levels populated in the reactions were investigated via particle-γ coincidence techniques using the Gammasphere array of high-purity germanium detectors and the compact heavy-ion counter, CHICO2. The K π = 2 + (γ ), K π = 0 + and K π = 2 – (octupole) rotational side bands were extended to spins 14h¯, 12h¯, and 13h¯, respectively. A staggering pattern observed in the energies of levels in the K π = 2 + band was found to be consistent with a potential that gets softer to vibration in the γ degree of freedom with increasing spin. Furthermore, the odd-even staggering of states in the K π = 2 – band was found to exhibit a phase opposite to that seen in the γ band; an effect most probably associated with Coriolis coupling to other, unobserved octupole vibrational bands in 186 W.

150 ≤ A ≤ 189↗
DOE OSTI2021

Semiclassical shell-structure micro-macroscopic approach for the level density

Level density ρ(E,A) is derived for a one-component nucleon system with a given energy E and particle number A within the mean-field semiclassical periodic-orbit theory beyond the saddle-point method of the Fermi gas model. We obtain ρ∝I ν (S)/S ν , with I ν (S) being the modified Bessel function of the entropy S. Within the micro-macro-canonical approximation (MMA), for a small thermal excitation energy U, with respect to rotational excitations E rot , one obtains ν = 3/2 for ρ(E,A). In the case of excitation energy U larger than E rot but smaller than the neutron separation energy, one finds a larger value of ν = 5/2. A role of the fixed spin variables for rotating nuclei is discussed. The MMA level density ρ reaches the well-known grand-canonical ensemble limit (Fermi gas asymptote) for large S related to large excitation energies, and also reaches the finite micro-canonical limit for small combinatorial entropy S at low excitation energies (the constant “temperature” model). Fitting the ρ(E,A) of the MMA to the experimental data for low excitation energies, taking into account shell and, qualitatively, pairing effects, one obtains for the inverse level density parameter K a value which differs essentially from that parameter derived from data on neutron resonances.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Investigation of the ground-state spin inversion in the neutron-rich Cl 47 , 49 isotopes

A first γ -ray study of Cl 47 , 49 spectroscopy was performed at the Radioactive Isotope Beam Factory with Ar 50 projectiles at 217 MeV/nucleon, impinging on the liquid hydrogen target of the MINOS device. Prompt deexcitation γ rays were measured with the NaI(Tl) array DALI2 + . Through the one-proton knockout reaction Ar 50 ( p , 2 p ) , a spin assignment could be determined for the low-lying states of Cl 49 from the momentum distribution obtained with the SAMURAI spectrometer. A spin-parity J π = 3 / 2 + is deduced for the ground state of Cl 49 , similar to the recently studied N = 32 isotope K 51 . The evolution of the energy difference E ( 1 / 2 1 + ) - E ( 3 / 2 1 + ) is compared to state-of-the-art theoretical predictions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Neutron occupancies and single-particle energies across the stable tin isotopes

The occupancies and vacancies of the valence neutron orbitals across the stable tin isotopic chain from 112 ≤ A ≤ 124 have been determined. These were inferred from the cross sections of neutron adding and -removing reactions. In each case, the reactions were chosen to have good angular momentum matching for transfer to the low- and high-` orbitals present in this valence space. Here, these new data are compared to older systematic studies. The effective single-neutron energies are determined by combining information from energy centroids determined from the adding and removing reactions. Two of the five orbitals are nearly degenerate, below N = 64, and approximately two MeV more bound than the other three, which are also degenerate.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗