Medium-mass Nuclei Research Articles

Few-nucleon and many-nucleon systems with semilocal coordinate-space regularized chiral nucleon-nucleon forces

We employ a variety of ab initio methods including Faddeev-Yakubovsky equations, No-Core Configuration Interaction Approach, Coupled-Cluster Theory and In-Medium Similarity Renormalization Group to perform a comprehensive analysis of the nucleon-deuteron elastic and breakup reactions and selected properties of light and medium-mass nuclei up to 48Ca using the recently constructed semilocal coordinate-space regularized chiral nucleon-nucleon potentials. We compare the results with those based on selected phenomenological and chiral EFT two-nucleon potentials, discuss the convergence pattern of the chiral expansion and estimate the achievable theoretical accuracy at various chiral orders using the novel approach to quantify truncation errors of the chiral expansion without relying on cutoff variation. We also address the robustness of this method and explore alternative ways to estimate the theoretical uncertainty from the truncation of the chiral expansion.

Nuclear Structure from the In-Medium Similarity Renormalization Group

Efforts to describe nuclear structure and dynamics from first principles have advanced significantly in recent years. Exact methods for light nuclei are now able to include continuum degrees of freedom and treat structure and reactions on the same footing, and multiple approximate, computationally efficient many-body methods have been developed that can be routinely applied for medium-mass nuclei. This has made it possible to confront modern nuclear interactions from Chiral Effective Field Theory, that are rooted in Quantum Chromodynamics with a wealth of experimental data.Here, we discuss one of these efficient new many-body methods, the In-Medium Similarity Renormalization Group (IMSRG), and its applications in modern nuclear structure theory. The IMSRG evolves the nuclear many-body Hamiltonian in second-quantized form through continuous unitary transformations that can be implemented with polynomial computational effort. Through suitably chosen generators, we drive the matrix representation of the Hamiltonian in configuration space to specific shapes, e.g., to implement a decoupling of low-and high-energy scales, or to extract energy eigenvalues for a given nucleus.We present selected results from Multireference IMSRG (MR-IMSRG) calculations of open-shell nuclei, as well as proof-of-principle applications for intrinsically deformed medium-mass nuclei. We discuss the successes and prospects of merging the (MR-)IMSRG with many-body methods ranging from Configuration Interaction to the Density Matrix Renormalization Group, with the goal of achieving an efficient simultaneous description of dynamic and static correlationsin atomic nuclei.

Auxiliary field diffusion Monte Carlo calculations of light and medium-mass nuclei with local chiral interactions

Quantum Monte Carlo methods have recently been employed to study properties of nuclei and infinite matter using local chiral effective field theory interactions. In this work, we present a detailed description of the auxiliary field diffusion Monte Carlo algorithm for nuclei in combination with local chiral two- and three-nucleon interactions up to next-to-next-to-leading order. We show results for the binding energy, charge radius, charge form factor, and Coulomb sum rule in nuclei with $3\le A\le16$. Particular attention is devoted to the effect of different operator structures in the three-body force for different cutoffs. The outcomes suggest that local chiral interactions fit to few-body observables give a very good description of the ground-state properties of nuclei up to $^{16}$O, with the exception of one fit for the softer cutoff which predicts overbinding in larger nuclei.

Ab initio optical potentials and nucleon scattering on medium mass nuclei

We show first results for the elastic scattering of neutrons off oxygen and calcium isotopes obtained from ab initio optical potentials. The potential is derived using self–consistent Green’s function theory (SCGF) with the saturating chiral interaction NNLOsat. Calculations are compared to available scattering data and show that it is possible to reproduce low energy scattering observables in medium mass nuclei from first principles.

Electromagnetic reactions from coupled-cluster theory

We review recent results for electromagnetic reactions and related sum rules in light and medium-mass nuclei obtained from coupled-cluster theory. In particular, we highlight our recent computations of the photodisintegration cross section of 40Ca and of the electric dipole polarizability for oxygen and calcium isotopes. We also provide new results for the Coulomb sum rule for 4He and 16O. For 4He we perform a thorough comparison of coupled-cluster theory with exact hyperspherical harmonics.

Spectroscopy ofSc50andab initiocalculations ofB(M3)strengths

The GRIFFIN spectrometer at TRIUMF-ISAC has been used to study excited states and transitions in $^{50}$Sc following the $\beta$-decay of $^{50}$Ca. Branching ratios were determined from the measured $\gamma$-ray intensities, and angular correlations of $\gamma$ rays have been used to firmly assign the spins of excited states. The presence of an isomeric state that decays by an $M3$ transition with a $B(M3)$ strength of 13.6(7)\,W.u. has been confirmed. We compare with the first {\it ab initio} calculations of $B(M3$) strengths in light and medium-mass nuclei from the valence-space in-medium similarity renormalization group approach, using consistently derived effective Hamiltonians and $M3$ operator. The experimental data are well reproduced for isoscalar $M3$ transitions when using bare $g$-factors, but the strength of isovector $M3$ transitions are found to be underestimated by an order of magnitude.

Ab initio electromagnetic observables with the in-medium similarity renormalization group

We present the formalism for consistently transforming transition operators within the in-medium similarity renormalization group framework. We implement the operator transformation in both the equations-of-motion and valence-space variants, and present first results for electromagnetic transitions and moments in medium-mass nuclei using consistently-evolved operators, including the induced two-body parts. These results are compared to experimental values, and--where possible--the results of no-core shell model calculations using the same input chiral interaction. We find good agreement between the equations-of-motion and valence space approaches. Magnetic dipole observables are generally in reasonable agreement with experiment, while the more collective electric quadrupole and octupole observables are significantly underpredicted, often by over an order of magnitude, indicating missing physics at the present level of truncation.

Central depression in nucleonic densities: Trend analysis in the nuclear density functional theory approach

Central depression of nucleonic density, i.e., a reduction of density in the nuclear interior, has been attributed to many factors. E.g., bubble structures in superheavy (SH) nuclei are believed to be due to the electrostatic repulsion. In light nuclei, the mechanism has been discussed in terms of shell effects associated with occupations of s-orbits. The objective of this work is to reveal mechanisms behind the formation of central depression in nucleonic densities in light and heavy nuclei. We introduce several measures of the internal nucleonic density. Through the statistical analysis, we study the information content of these measures with respect to nuclear matter properties. We apply nuclear density functional theory with Skyrme functionals. Using the statistical tools of linear least square regression, we inspect correlations between various measures of central depression and model parameters, including nuclear matter properties. We study bivariate correlations with selected quantities as well as multiple correlations with groups of parameters. Detailed correlation analysis is carried out for $^{34}$Si for which a bubble structure has been reported recently, $^{48}$Ca, and N=82, 126, and 184 isotonic chains. We show that the central depression in medium-mass nuclei is very sensitive to shell effects, whereas for SH systems it is firmly driven by the electrostatic repulsion. An appreciable semi-bubble structure in proton density is predicted for $^{294}$Og, which is currently the heaviest nucleus known experimentally. Our correlation analysis reveals that the central density indicators in nuclei below $^{208}$Pb carry little information on parameters of nuclear matter; they are predominantly driven by shell structure. On the other hand, in the SH nuclei there exists a clear relationship between the central nucleonic density and symmetry energy.

Structural effects of Na34 in the Na33(n,γ)Na34 radiative capture reaction

The path towards the production of \textit{r}-process seed nuclei follows a course where the neutron-rich light and medium mass nuclei play a crucial role. The neutron capture rates for these exotic nuclei could dominate over their $\alpha$-capture rates, thereby enhancing their abundances at or near the drip line. We calculate the radiative neutron capture cross-section for the $^{33}$Na(n,$\gamma)^{34}$Na reaction via the Coulomb dissociation of $^{34}$Na as it undergoes elastic breakup on $^{208}$Pb when directed at a beam energy of 100 MeV/u using the entirely quantum mechanical theory of finite range distorted wave Born approximation upgraded to incorporate deformation effects. The non-resonant one neutron radiative capture cross-section for $^{33}$Na(n,$\gamma)^{34}$Na is calculated and is found to increase with increasing deformation of $^{34}$Na. An analytic scrutiny of the capture cross-section with neutron separation energy as a parameter is also done at different energy ranges. The calculated reaction rate is compared with the rate of the $^{33}$Na($\alpha$,n)$^{36}$Al reaction (deduced from the Hauser-Feshbach theory), and is found to be significantly higher below a temperature of $T_9 = 2$. Further, at the equilibrium temperature of $T_9 = 0.62$, the rate for the neutron capture had a small but non-negligible dependence on the structural parameters of $^{34}$Na. In addition, this neutron capture rate exceeded that of the $\alpha$-capture reaction by orders of magnitude, indicating that the $\alpha$-process should not break the (n,$\gamma$) \textit{r-}process path at the $^{33}$Na isotope, thus, effectively pushing the abundance of sodium isotopes towards the neutron drip line.

N/Z effect on reaction mechanisms cross sections in the 78Kr +40Ca and 86Kr +48Ca collisions at 10 AMeV

Nuclear reactions between medium-mass nuclei at low energy are characterized by the competition between binary and evaporation process in the compound nucleus de-excitation. A study of the influence of the neutron richness of the entrance channel on the decay paths of the compound nuclei formed in the 78Kr +40Ca and 86Kr +48Ca at 10 MeV/A is presented. The experiment has been performed at Laboratori Nazionali del Sud by using the CHIMERA 4π multidetector for charged particles. The Kinematical characteristics of the two reactions support the conclusion of a production via long lived system. Besides the results relative to the n-poor system are compared to those obtained at GANIL, performed at 5.5 AMeV, in order to study the energy influence.

Pre-equilibrium emission and clustering in medium-mass nuclei: 46Ti from 16O + 30Si, 18O + 28Si, 19F + 27Al

The study of nuclear cluster states bound by valence neutrons is a field of recent large interest. In particular, it is interesting to study the pre-formation of α-clusters in α-conjugate nuclei and the dynamical condensation of clusters during nuclear reactions. The NUCL-EX collaboration (INFN, Italy) is carrying out a research campaign studying pre-equilibrium emission of light charged particles and cluster properties of light and medium-mass nuclei. For this purpose, a comparative study of the three nuclear reactions: 16O + 30Si, 18O + 28Si and 19F + 27Al, has been recently carried out using the GARFIELD+RCo 4π setup. After a general introduction on the experimental campaign, the preliminary results for the three systems are presented.

Calculations of the β-decay half-lives of neutron-deficient nuclei**Supported by National Nature Science Foundation of China (11535004, 11375086, 11120101005, 11175085 and 11235001), 973 Nation Major State Basic Research and Development of China (2013CB834400) and Science and Technology Development Fund of Macau (020/2014/A1 and 039/2013/A2)

In this work, β+/EC decays of some medium-mass nuclei are investigated within the extended quasiparticle random-phase approximation (QRPA), where neutron-neutron, proton-proton and neutron-proton (np) pairing correlations are taken into consideration in the specialized Hartree-Fock-Bogoliubov (HFB) transformation. In addition to the pairing interaction, the Brückner G-matrix obtained with the charge-dependent Bonn nucleon-nucleon force is used for the residual particle-particle and particle-hole interactions. Calculations are performed for even-even proton-rich isotopes ranging from Z=24 to Z=34. It is found that the np pairing interaction plays a significant role in β-decay for some nuclei far from stability. Compared with other theoretical calculations, our calculations show good agreement with the available experimental data. Predictions of β-decay half-lives for some very neutron-deficient nuclei are made for reference.

Electron scattering and reactions from exotic nuclei

The SCRIT and FAIR/ELISe experiments are the first to attempt to measure directly electron scattering form factors from nuclei far from stability. This will give direct information for the (one-body) charge densities of those systems, about which there is little information available. The SCRIT experiment will be taking data for medium-mass exotic nuclei, while the electron-ion collider at ELISe, when constructed, will be able to measure form factors for a wide range of exotic nuclei, as available from the radioactive ion beams produced by the FAIR experiment. Other facilities are now being proposed, which will also consider electron scattering from exotic nuclei at higher energies, to study short-range correlations in exclusive reactions. This review will consider all available information concerning the current status (largely theoretical) of electron scattering from exotic nuclei and, where possible, complement such information with equivalent information concerning the neutron densities of those exotic systems, as obtained from intermediate energy proton scattering. The issue of long- and short-range correlations will be discussed, and whether extending such studies to the exotic sector will elicit new information.

Ultrahigh energy cosmic ray nuclei from remnants of dead quasars

We re-examine the possibility of ultrahigh energy cosmic rays being accelerated in nearby dormant quasars. We particularize our study to heavy nuclei to accommodate the spectrum and nuclear composition recently reported by the Pierre Auger Collaboration. Particle acceleration is driven by the Blandford–Znajek mechanism, which wires the dormant spinning black holes as Faraday unipolar dynamos. We demonstrate that energy losses are dominated by photonuclear interactions on the ambient photon fields. We argue that the local dark fossils of the past quasar activity can be classified on the basis of how source parameters (mass of the central engine and photon background surrounding the accelerator) impact the photonuclear interaction. In this classification it is possible to distinguish two unequivocal type of sources: those in which nuclei are completely photodisintegrated before escaping the acceleration region and those in which photopion production is the major energy damping mechanism. We further argue that the secondary nucleons from the photodisintegrated nuclei (which have a steep spectral index at injection) can populate the energy region below “the ankle” feature in the cosmic ray spectrum, whereas heavy and medium mass nuclei (with a harder spectral index) populate the energy region beyond “the ankle”, all the way to the high energy end of the spectrum. In addition, we show that five potential quasar remnants from our cosmic backyard correlate with the hot-spot observed by the Telescope Array.

Exotic neutron-rich medium-mass nuclei with realistic nuclear forces

We present the first application of the newly developed EKK theory of the effective nucleon-nucleon interaction to shell-model studies of exotic nuclei, including those where conventional approaches with fitted interactions encounter difficulties. This EKK theory enables us to derive the interaction suitable for several major shells ($sd$+$pf$ in this work). By using such an effective interaction obtained from the Entem-Machleidt QCD-based $\chi\mathrm{N}^3\mathrm{LO}$ interaction and the Fujita-Miyazawa three-body force, the energies, E2 properties and spectroscopic factors of low-lying states of neutron-rich Ne, Mg and Si isotopes are nicely described, as the first shell-model description of the "island of inversion" without fit of the interaction. The long-standing question as to how particle-hole excitations occur across the $sd$-$pf$ magic gap is clarified with distinct differences from the conventional approaches. The shell evolution is shown to appear similarly to earlier studies.

Nucleus-Dependent Valence-Space Approach to Nuclear Structure.

We present a nucleus-dependent valence-space approach for calculating ground and excited states of nuclei, which generalizes the shell-model in-medium similarity renormalization group to an ensemble reference with fractionally filled orbitals. Because the ensemble is used only as a reference, and not to represent physical states, no symmetry restoration is required. This allows us to capture three-nucleon (3N) forces among valence nucleons with a valence-space Hamiltonian specifically targeted to each nucleus of interest. Predicted ground-state energies from carbon through nickel agree with results of other large-space abinitio methods, generally to the 1% level. In addition, we show that this new approach is required in order to obtain convergence for nuclei in the upper p and sd shells. Finally, we address the 1^{+}/3^{+} inversion problem in ^{22}Na and ^{46}V. This approach extends the reach of abinitio nuclear structure calculations to essentially all light- and medium-mass nuclei.

Ab Initio Optical Potentials and Nucleon Scattering on Medium Mass Nuclei

We show the first results for the elastic scattering of neutrons off oxygen and calcium isotopes obtained from ab initio optical potentials. The potential is derived using self consistent Green's function theory (SCGF) with the saturating chiral interaction NNLO$_{\textrm{sat}}$. Our calculations are compared to available scattering data and show that it is possible to reproduce low energy scattering observables in medium mass nuclei from first principles.

Clustering in light nuclei and their effects on fusion and pre – equilibrium processes.

The study of nuclear cluster states bound by valence neutrons is a field of recent large interest. In particular, it is important to study the pre-formation of α -clusters in α -conjugate nuclei and the dynamical condensation of clusters during nuclear reactions [1–5]. The NUCL–EX collaboration has recently initiated an experimental campaign of exclusive measurements of fusion–evaporation reactions with light nuclei as interacting partners. In collisions involving light systems, the low expected multiplicity of fragments increases the probability of achieving a quasi-complete reconstruction of the event. In particular the formation and decay modes of an excited 24 Mg system have been studied through two different reactions, 12 C (95 MeV)+ 12 C and 14 N (80.7 MeV)+ 10 B, which have been used to produce fused systems with nearly the same mass and excitation energy (~60 MeV). In particular, even the de-excitation of the Hoyle state in 12 C have been studied, both in peripheral (projectiles de-excitation) and in central collisions (six α-particles channel). Moreover, a research campaign studying pre-equilibrium emission of light charged particles and cluster properties of light and medium-mass nuclei has been carried out. For this purpose, a comparative study of the three nuclear systems 18 O+28 Si, 16 O+30 Si and 19 F+27 Al has been recently studied using the GARFIELD+RCo 4π setup [6]. The experimental data are compared with the predictions of simulated events generated with the statistical models (GEMINI++ and HFl) and through dynamical models like Stochastic Mean Field (SMF) and Antisymmetrized Molecular Dynamics (AMD) and filtered with a software replica of our apparatus in order to take into account the experimental conditions.

Study of breakup and transfer of weakly bound nucleus 6Li to explore the low energy reaction dynamics

Investigation of the breakup and transfer effect of weakly bound nuclei on the fusion process has been an interesting research topic in the past several years. However, owing to the low intensities of the presently available radioactive ion beam (RIB), it is difficult to clearly explore the reaction mechanisms of nuclear systems with unstable nuclei. In comparison with RIB, the beam intensities of stable weakly bound nuclei such as 6,7 Li and 9 Be, which have significant breakup probability, are orders of magnitude higher. Precise fusion measurements have already been performed with those stable weakly bound nuclei, and the effect of breakup of those nuclei on the fusion process has been extensively studied. Those nuclei indicated large production cross sections for particles other than the α + x breakup. The particles are originated from non-capture breakup (NCBU), incomplete fusion (ICF) and transfer processes. However, the conclusion of reaction dynamics was not clear and has the contradiction.In our previous experiments we have performed 6 Li+96 Zr and 154 Sm at HI-13 Tandem accelerator of China Institute of Atomic Energy (CIAE) by using HPGe array. It is shown that there is a small complete fusion (CF) suppression on medium-mass target nucleus 96 Zr different from about 35% suppression on heavier target nucleus 154 Sm at near-barrier energies. It seems that the CF suppression factor depends on the charge of target nuclei. We also observed one neutron transfer process. However, the experimental data are scarce for medium-mass target nuclei.In order to have a proper understanding of the influence of breakup and transfer of weakly bound projectiles on the fusion process, we performed the 6 Li+89 Y experiment with incident energies of 22 MeV and 34 MeV on Galileo array in cooperation with Si-ball EUCLIDES at Legnaro National Laboratory (LNL) in Italy. Using particle-particle and particle-γ coincidences, the different reaction mechanisms can be clearly explored.

Application of an extended random-phase approximation to giant resonances in light-, medium-, and heavy-mass nuclei

We present results of the time blocking approximation (TBA) on giant resonances in light, medium and heavy mass nuclei. The TBA is an extension of the widely used random-phase approximation (RPA) adding complex configurations by coupling to phonon excitations. A new method for handling the single-particle continuum is developed and applied in the present calculations. We investigate in detail the dependence of the numerical results on the size of the single particle space and the number of phonons as well as on nuclear matter properties. Our approach is self-consistent, based on an energy-density functional of Skyrme type where we used seven different parameter sets. The numerical results are compared with experimental data.