Proton-neutron pairing and like-nucleon pairing are two different facets of atomic nuclear configurations. While like-nucleon pair condensates manifest their superfluidic nature in semimagic nuclei, it is not absolutely clear if there exists a T = 0 proton-neutron pair condensate phase in N = Z nuclei. With an explicit formalism of general pair condensate with good particle numbers, we optimize proton-neutron pair condensates for all N = Z nuclei between 16O and 100Sn, given shell model effective interactions. As comparison, we also optimize like-nucleon pair condensates for their semimagic isotones. Shannon entanglement entropy is a measurement of mixing among pair configurations, and can signal intrinsic phase transition. It turns out the like-nucleon pair condensates for semimagic nuclei have large entropies signaling an entangled phase, but the proton-neutron pair condensates end up not far from a Hartree-Fock solution with small entropy. With artificial pairing interaction strengths, we show that the general proton-neutron pair condensate can transit from an entangled T = 1 phase to an entangled T = 0 phase, i.e., pairing phase transition driven by external parameters. In the T = 0 limit, the proton-neutron pair condensate optimized for 24Mg turns out to be a purely T = 0 P-pair condensate with large entanglement entropy, although such cases may occur in cold atom systems, unlikely in atomic nuclei.

Sum rules are a useful characterization of transition strength functions for atomic nuclei. Unlike the Ikeda sum rule for single Gamow–Teller transitions, as a result of SU(4) breaking, double Gamow–Teller transition sum rules depend upon the detailed many-body wavefunctions. In order to systematically investigate the double Gamow–Teller (DGT) transition sum rules, we approximate the shell-model ground state with nucleon-pair condensates, with angular-momentum projection after variation, and use expectation values to compute the 2β− and 2β+ sum rules. For even–even nuclei in the 1s0d and 1p0f valence spaces, we quantitatively estimate the model-dependent fractions of the DGT sum rules, and analyze the importance of the double isospin analog state to the DGT strength function, relative to SU(4) predictions.

A Bayesian neural network (BNN) is developed to predict the 1st excitation energy of odd-odd nuclei. Aside from the proton number and neutron number, we introduce two empirical physical quantities into the input layer. delta = [( - 1)(N) + (- 1)(Z) ] /2 is introduced to distinguish even-even, odd-odd and odd-A nuclei; and the so-called Casten factor P equivalent to v(p)v(n)/ v(p)+v(n) is introduced to stand for collectivity. The BNN is trained with an experimental dataset of the 1st excitation energy for 434 odd-odd, 649 even-even and 1050 odd-A nuclei. After training, the BNN predicts the 1st excitation energy of odd-odd nuclei with a rms of 0.21 MeV. Examples of Dy, Gd, Eu and Cs isotopes are also shown. The BNN results show moderate predictive ability, in comparison with results from the projected Hartree-Fock method.

We investigate nuclear shape coexistence for a wide range of even-even nuclides. By varying general pair condensates, which include Slater determinants as a limit but also allow for arbitrary pairing channels, we frequently find multiple coexisting minima and often more than two. This is consistent with recent experimental results. In order to measure general pairwise correlations beyond a simple Slater determinant, we introduce a novel entropy-like measure, which is smallest midshell and largest near shell closures; this is consistent with a picture of pairing-like behavior dominating near closed shells and deformation midshell. After surveying nuclides spanning from the sd shell to nuclides between magic numbers 50 and 82, we focus on the six lightest nuclei with shape coexistence. Angular-momentum projected variational pair condensate (PVPC) calculations identify band structures, including two newly proposed coexisting bands in 26Si/Mg and 24Si/Ne. The PVPC results agree well with data, providing robust experimental support for the pervasiveness of coexistence in these light nuclei.

Over the past decade, the collective rotation of atomic nuclei in the heavy mass region has emerged as an important area of interest within nuclear structure studies, particularly within the theoretical framework of the nuclear shell model. This field of research has profound implications for understanding the intricate dynamics and interactions within atomic nuclei. Despite the remarkable advances in modern computing techniques that have expanded the applicability of large-scale shell model calculations, the configuration space required to accurately study rotational nuclei in the heavy mass region remains prohibitively large, surpassing the current computational capabilities. This limitation is a critical obstacle to further progress in the field, emphasizing the need for innovative computational and theoretical strategies. To address this challenge, nucleon pair truncation has been introduced as an effective strategy for truncating the configuration space within the shell model. This truncation scheme has been successfully employed in numerous studies, accurately describing the properties of low-lying states in nearly spherical and transitional nuclei. However, the application of pair truncation methods to rotational nuclei presents significant difficulties, necessitating the development of novel theoretical frameworks. The focus of this review is on two such frameworks recently developed within the shell model. The first framework involves the nucleon pair approximation, which utilizes nucleon pairs of specific angular momentum as the fundamental building blocks. This approach significantly reduces the configuration space while retaining the essential physics of collective rotation. The second framework revolves around the projection of intrinsic nucleon pair states, a process that involves constructing "intrinsic" states within the shell model space and subsequently projecting them onto states of good angular momentum. These innovative frameworks open up new avenues for research, providing a more comprehensive understanding of the nucleon pairing mechanism in multi-nucleon systems, particularly in the SU(3) rotational limit. This review further examines the theoretical explanations provided by these pairing theories for several key phenomena observed in rotational nuclei, including the role of nuclear pairing and configuration mixing between different intrinsic states in nuclear shape evolution, the shape coexistence, as well as the backbending phenomenon in rotational bands. The novel methods presented in this review offer exciting new opportunities for studying rotational nuclei in the heavy mass region within the shell model. These methods not only provide valuable insights into the complex structure and behavior of atomic nuclei but also contribute to the ongoing efforts to unify the shell model and collective models within a common theoretical framework. The potential of these methods extends beyond the current research, offering a promising path towards a more comprehensive understanding of nuclear structures, such as nuclear shape-phase transition, subshell effects, octupole deformations, nuclear properties of neutron-rich nuclei and nuclei near the drip lines, resonance state physics, and predictions for superheavy nuclei.

In this study, we investigate the robustness of pair structures for nuclear yrast states, that is, whether the structures of relevant collective pairs as building blocks of different yrast states are the same. We focus on deformed and transitional nuclei and study the yrast states of Si, Cr, and Xe, whose experimental values are 2.60, 2.40, and 2.16, respectively, using the nucleon-pair approximation (NPA) and shell-model effective interactions. For each yrast state, we consider optimized pair structures to be those providing the energy minimum for this state. To find the minimum, many full NPA calculations are performed with varying pair structures, and the numerical optimization procedure of the conjugate gradient method is implemented. Our results suggest that optimized pair structures remain the same for all states within a rotational band of a deformed nucleus. Our results also suggest that after backbending, that is, changing of the intrinsic state, the structure of the S pair, which is essential to build the monopole pairing correlation, remains approximately unchanged, whereas the structures of the non-S pairs, which are essential to build the quadrupole correlation, change significantly.

Background: Computationally tractable models of atomic nuclei is a long-time goal of nuclear structure physics. A flexible framework which easily includes excited states and many-body correlations is the configuration-interaction shell model (SM), but the exponential growth of the basis means one needs an efficient truncation scheme, ideally one that includes both deformation and pairing correlations. Purpose: We propose an efficient truncation scheme of the SM: starting from a pair condensate variationally defined by Hartree-Fock single-particle states and the particle-number conserved Bardeen-Cooper-Schrieffer (NBCS) approximation, we carry out projection of states with good angular momentum. Methods: After generating Hartree-Fock single-particle states with Kramers degeneracy in a SM space, we optimize the pair amplitudes in the NBCS by minimizing the energy, and then use linear algebra projection (LAP) of states with good angular momentum. Both NBCS and LAP are computationally fast. Results: Our calculations yield good agreement with full configuration-interaction SM calculations for low-lying states of transitional and rotational nuclei with axially symmetric and triaxial deformation in medium- and heavy-mass regions: $^{44,46,48}$Ti, $^{48,50}$Cr, $^{52}$Fe, $^{60,62,64}$Zn, $^{66,68}$Ge, $^{68}$Se, and $^{108,110}$Xe. We predict low-lying states of $^{112-114}\textrm{Ba}$ and $^{116-120}\textrm{Ce}$, nuclei difficult to reach by large-scale SM calculations. Conclusions: Both pair correlation and the configuration mixing between different intrinsic states play a key role in reproducing collectivity and shape coexistence, demonstrating the utility of this truncation scheme of the SM to study transitional and deformed nuclei.

Atomic nuclei exhibit deformation, pairing correlations, and rotational symmetries. To meet these competing demands in a computationally tractable formalism, we revisit the use of general pair condensates with good particle number as a trial wave function for even-even nuclei. After minimizing the energy of the condensate, allowing for general triaxial deformations, we project out states with good angular momentum with a fast projection technique. To show applicability, we present example calculations from pair condensates in several model spaces and compare against angular-momentum projected Hartree-Fock and full configuration-interaction shell-model calculations. This approach successfully generates spherical, vibrational, and rotational spectra, demonstrating potential for modeling medium- to heavy-mass nuclei.

In this paper, we propose an approach to nucleon-pair approximation (NPA) with m-scheme bases, in which the collective nucleon pairs are represented in terms of antisymmetric matrices, and commutations between nucleon pairs are given using a matrix multiplication that avoids angular-momentum couplings and recouplings. Therefore the present approach significantly simplifies the NPA computation. Furthermore, it is formulated on the same footing with and without isospin.

Electromagnetic and weak transitions tell us a great deal about the structure of atomic nuclei. Yet modeling transitions can be difficult: it is often easier to compute the ground state, if only as an approximation, than excited states. One alternative is through transition sum rules, in particular the non-energy-weighted and energy-weighted sum rules, which can be computed as expectation values of operators. We investigate by computing sum rules for a variety of nuclei, comparing the numerically exact full configuration-interaction shell model, as a reference, to Hartree-Fock, projected Hartree-Fock, and the nucleon pair approximation. These approximations yield reasonable agreement, which we explain by prior work on the systematics of transition moments.

An important characterization of electromagnetic and weak transitions in atomic nuclei are sum rules. We focus on the non-energy-weighted sum rule (NEWSR), or total strength, and the energy-weighted sum rule (EWSR); the ratio of the EWSR to the NEWSR is the centroid or average energy of transition strengths from an nuclear initial state to all allowed final states. These sum rules can be expressed as expectation values of operators, in the case of the EWSR a double commutator. While most prior applications of the double-commutator have been to special cases, we derive general formulas for matrix elements of both operators in a shell model framework (occupation space), given the input matrix elements for the nuclear Hamiltonian and for the transition operator. With these new formulas, we easily evaluate centroids of transition strength functions, with no need to calculate daughter states. We apply this simple tool to a number of nuclides, and demonstrate the sum rules follow smooth secular behavior as a function of initial energy, as well as compare the electric dipole (E1) sum rule against the famous Thomas-Reiche-Kuhn version. We also find surprising systematic behaviors for ground state electric quadrupole (E2) centroids in the $sd$-shell.

Tunable synthesis of bimetallic AuxAg1-x alloyed nanoparticles and in situ monitoring of their plasmonic responses is presented. This is a new conceptual approach based on green and energy efficient, reactive, and highly-non-equilibrium microplasma chemistry.

The suffering from organ dysfunction due to damaged or diseased tissue/bone has been globally on the rise. Current treatment strategies for non-union bone defects include: the use of autografts, allografts, synthetic grafts and free vascularized fibular grafts. Bone tissue engineering has emerged as an alternative for fracture repair to satisfy the current unmet need of bone grafts and to alleviate the problems associated with autografts and allografts. The technology offers the possibility to induce new functional bone regeneration using synergistic combination of functional biomaterials (scaffolds), cells, and growth factors. Bone scaffolds are typically made of porous biodegradable materials that provide the mechanical support during repair and regeneration of damaged or diseased bone. Significant progress has been made towards scaffold materials for structural support, desired osteogenesis and angiogenesis abilities. Thanks for innovative scaffolds fabrication technologies, bioresorbable scaffolds with controlled porosity and tailored properties are possible today. Despite the presence of different bone scaffold fabrication methods, pore size, shape and interconnectivity have not yet been fully controlled in most of the methods. Moreover, scaffolds with tailored porosity for specific defects are still difficult to manufacture. Nevertheless, such scaffolds can be designed and fabricated using three dimensional (3D) printing approaches. 3D printing technology, as an advanced tissue scaffold fabrication method, offers the opportunity to produce complex geometries with distinct advantages. The technology has been used for the production of various types of bodily constructs such as blood vessels, vascular networks, bones, cartilages, exoskeletons, eyeglasses, cell cultures, tissues, organs and novel drug delivery devices. This review focuses on 3D printed scaffolds and their application in bone repair and regeneration. In addition, different classes of biomaterials commonly employed for the fabrication of 3D nano scaffolds for bone tissue engineering application so far are briefly discussed.

Atmospheric-pressure microplasma-assisted electrochemistry was used to synthesize Ag nanoparticles (NPs) for plasmonic applications. It is shown that the size and dispersion of the nanoparticles can be controlled by variation of the microplasma-assisted electrochemical process parameters such as electrolyte concentration and temperature. Moreover, Ag NP synthesis is also achieved in the absence of a stabilizer, with additional control over the dispersion and NP formation possible. As the microplasma directly reduces Ag ions in solution, the incorporation of toxic reducing agents into the electrolytic solution is unnecessary, making this an environmentally friendly fabrication technique with strong potential for the design and growth of plasmonic nanostructures for a variety of applications. These experiments therefore link microplasma-assisted electrochemical synthesis parameters with plasmonic characteristics.

Flight simulation activities contributing to development of the V-22 Osprey’s externally slung load carriage capabilities are discussed. Configuration of the simulator, use of visual cues to indicate load motion to the pilot, the unique Lagrangian approach taken to mathematically model coupled load/aircraft dynamics and nonlinear elastic sling effects in real-time, and scope of piloted evaluations are described. Use of flight simulation as an exploratory tool to evaluate the unique capability of tiltrotor aircraft to carry external loads in high speed airplane mode flight is described. The role of piloted simulation in design of the V-22 external load autojettison system is also discussed. Interfaces between simulation activities and flight test planning and execution are chronicled from the standpoint of documenting the utility of simulation as a tool that can reduce flight test expenditures and risk. Correlation of simulation results with available flight test data is presented. Use of simulation to augment flight test results with the goal of providing generic flight envelopes applicable to the wide variety of loads to be carried by the V-22 is also illustrated.