The quantum-mechanical nuclear-shell structure determines the stability and limits of the existence of the heaviest nuclides with large proton numbers Z ≳ 100 (refs. 1-3). Shell effects also affect the sizes and shapes of atomic nuclei, as shown by laser spectroscopy studies in lighter nuclides4. However, experimental information on the charge radii and the nuclear moments of the heavy actinide elements, which link the heaviest naturally abundant nuclides with artificially produced superheavy elements, is sparse5. Here we present laser spectroscopy measurements along the fermium (Z = 100) isotopic chain and an extension of data in the nobelium isotopic chain (Z = 102) across a key region. Multiple production schemes and different advanced techniques were applied to determine the isotope shifts in atomic transitions, from which changes in the nuclear mean-square charge radii were extracted. A range of nuclear models based on energy density functionals reproduce well the observed smooth evolution of the nuclear size. Both the remarkable consistency of model prediction and the similarity of predictions for different isotopes suggest a transition to a regime in which shell effects have a diminished effect on the size compared with lighter nuclei.

Project scheduling is an important management task in many companies across different industries. Generally, projects require resources, such as personnel or funds, whose availabilities are limited, giving rise to the challenging problem of resource-constrained project scheduling. In this paper, we consider the scheduling of a project consisting of precedence-related activities that require time and two types of resources for execution: storage resources representing, e.g., the project budget; and renewable resources representing, e.g., personnel or equipment. Storage resources are consumed by activities at their start or produced upon their completion, while renewable resources are allocated to activities at their start and released upon their completion. The resource-constrained project scheduling problem with consumption and production of resources (RCPSP-CPR) consists of determining a minimum-makespan schedule such that all precedence relations are respected, the demand for each renewable resource never exceeds its capacity, and the stock level of each storage resource never falls below a prescribed minimum. Due to the consideration of storage resources, the feasibility variant of this problem is NP-complete. We propose a novel compact mixed-integer linear programming (MILP) model based on a novel type of sequencing variables. These variables enable us to identify which activities are processed in parallel and whether a sequencing of activities is necessary to respect the resource capacities. Our computational results indicate that our novel model significantly outperforms state-of-the-art MILP models for all considered scarcity settings of the storage resources. Additionally, our results indicate a superior performance for instances of the well-known resource-constrained project scheduling problem (RCPSP).

We report on high-resolution laser spectroscopy studies on 249-253Cf with spectral linewidths in the order of 100 MHz carried out at the RISIKO mass separator at Mainz University. In total three atomic ground-state transitions were investigated and the hyperfine parameters for the odd-A isotopes and isotope shift for all examined isotopes have been determined from the measured spectra. The isotope shift measurements allowed tracking of changes in mean-squared charge radii across the deformed nuclear shell closure at N = 152, whereby shape discontinuities were not observed. Experimental hyperfine coupling constants of the atomic ground state were combined with relativistic many-body atomic calculations to extract the nuclear magnetic-dipole moment of 249Cf with improved precision to mu I(249Cf) = -0.395(17 )mu N, whereas mu I(251Cf) = -0.571(24 )mu N and mu I(253Cf) = -0.731(35 )mu N were derived for the first time. Additionally, the spectroscopic quadrupole moments QS(249Cf) = 6.27(33) eb and QS(253Cf) = 5.53(51) eb were extracted.

Electric vehicles (EVs) have the potential to reduce carbon emissions and significantly improve urban air quality. However, the current lack of charging infrastructure poses a major challenge for EV drivers. Therefore, building new charging stations is essential for the mass adoption of EVs. We address the location and capacity planning problem for EV charging stations under uncertainty. The locations of EVs with an uncertain driving range and uncertain charging demand are given, as well as locations at which charging stations can be established. The problem is to determine the locations and capacities of the charging stations such that the cost of establishing stations and building charging capacities plus the fictitious cost of assigning vehicles to stations are minimized and the stations' capacities and the vehicles' driving ranges are respected. We formulate the problem as a two-stage mixed-integer linear programming (MILP) model and present a branch-and-Benders-cut (BBC) solution algorithm. We present computational results for a case study comprising 1,079 demand nodes in Pennsylvania, indicating the superior performance of the BBC algorithm.

The resource-constrained project scheduling problem describes a situation in which the duration of a project must be minimized by choosing a start time for each project activity subject to given precedence constraints and resource capacities. Various mixed-integer programming models exist for this problem. Approaches that extend these models to enhance their performance are often formulation-specific or cannot be easily integrated with the original model, which limits their practical applicability. We suggest a model extension based on auxiliary variables and redundant con-straints that describe workload limitations for certain subsets of the planning horizon. We apply our approach to three state-of-the-art models from the literature. A computational evaluation demonstrates that the extension is beneficial to all three models tested.

The execution of a project is often distributed among multiple sites. The planning of such a project includes selecting a specific site for the execution of each of the project’s activities and allocating the available resource units to the execution of these activities over time. While some resource units are available at a certain site only, others can be moved across sites. Given the spatial distance between sites, transportation times arise if a resource unit must be transported from one site to another or if the output of an activity must be transported to another site. This planning problem has been introduced in recent literature as the multi-site resource-constrained project scheduling problem. We present a continuous-time model and devise a matheuristic for this planning problem. The continuous-time model uses, among others, binary variables to impose a sequence between activities assigned to the same resource units. In the matheuristic, the binary restrictions on these variables are initially relaxed and iteratively restored for the subset of activities scheduled in the current iteration. We compare the performance of the continuous-time model and the matheuristic to the performance of a discrete-time model and several metaheuristics from the literature using two sets of test instances from the literature. Both the continuous-time model and the matheuristic derive on average superior solutions in shorter average running times than the reference approaches.

We report on the investigation of the atomic structure of curium ( $$Z=96$$ ) by resonance ionization spectroscopy. Three different excited energy levels were populated from the $$5f^{7}6d7s^{2}\,^{9}D^{o}_{2}$$ ground state as first excitation steps. Wide-range scans were performed for the search of second excitation steps around the literature value of the ionization potential. These spectra were analyzed to identify Rydberg levels and auto-ionizing resonances. The ionization potential was consistently determined as 48330.68(16) $$\hbox {cm} ^{-1}$$ through the evaluation of Rydberg convergences and the complementary approach of DC electric field ionization by evaluating the ionization threshold according to the saddle point model. The new result deviates by 6.7 $$\hbox {cm} ^{-1}$$ from the literature value of 48324(2) $$\hbox {cm} ^{-1}$$ by Köhler et al. [15] and is about one order of magnitude more precise.

Excited atomic states of neutral einsteinium were investigated by resonant laser ionization using 10 pg (2 x 1010 atoms) of 254Es. Ten transitions from the 5 f 117s2 4Io15/2 ground state to even-parity states were investigated in detail, via studies of lifetimes and further excitation steps into higher-lying odd-parity states below and above the first ionization potential. This led to the identification of 37 previously unknown odd-parity energy levels in the region between 37 000 and 42 500 cm-1 and a number of autoionizing states, which ensure a high ion yield in resonant ionization. Rydberg states were identified and the corresponding Rydberg series converging either to the ionic ground or an excited state were analyzed to determine the first ionization potential of einsteinium to a value of EIP= 51 364.58(14)stat(50)sys cm-1, improving the previous result by a factor of four.

The atomic structure of californium is probed by two-step resonance ionization spectroscopy. Using samples with a total amount of about 2×1010 Cf atoms (ca. 8.3 pg), ground-state transitions as well as transitions to high-lying Rydberg states and auto-ionizing states above the ionization potential are investigated and the lifetimes of various atomic levels are measured. These investigations lead to the identification of efficient ionization schemes, important for trace analysis and nuclear structure investigations. Most of the measurements are conducted on 250Cf. In addition, the isotope shift of the isotopic chain 249−252Cf is measured for one transition. The identification and analysis of Rydberg series enables the determination of the first ionization potential of californium to EIP=50,666.76(5)cm−1. This is about a factor of 20 more precise than the current literature value.

Abstract The formation of carbonyl complexes using atom-at-a-time quantities of short-lived transition metals from fusion and fission reactions was reported in 2012. Numerous studies focussing on this chemical system, which is also applicable for the superheavy elements followed. We report on a novel two-chamber approach for the synthesis of such complexes that allows spatial decoupling of thermalization and gas-phase carbonyl complex synthesis. Neutron induced fission on 235U and spontaneous fission of 248Cm were employed for the production of the fission products. These were stopped inside a gas volume behind the target and flushed with an inert-gas flow into a second chamber. This was flushed with carbon monoxide to allow the gas-phase synthesis of carbonyl complexes. Parameter studies of the transfer from the first into the second chamber as well as on the carbonyl complex formation and transport processes have been performed. High overall efficiencies of more than 50% were reached rendering this approach interesting for studies of superheavy elements. Our results show that carbonyl complex formation of thermalized fission products is a single-atom reaction, and not a hot-atom reaction.

We deal with the following application of the cardinality-constrained covering traveling salesperson problem. A company offers the valuation of real-estate properties, which includes an on-site visit by a contractor. Each contractor visits several properties during a tour, which must comprise not less than a minimum and not more than a maximum number of visits and must not exceed a prescribed length. Given a set of properties, the planning problem is to determine the respective tours such that the total relevant cost of all tours is minimized; for each tour, this cost consists of some fixed costs plus some variable costs proportional to the total distance of the tour. We propose a novel order-first split-second approach which at first devises a giant tour, then splits this tour into feasible tours, and eventually tries to improve these tours individually. Our computational results for a set of test instances from the literature indicate that the proposed approach runs much faster than the reference approaches and devises good feasible solutions; for the largest instances, the proposed approach even outperforms the reference approaches.

Resonance ionization mass spectroscopy has proven to be a very efficient and selective method for the spatially resolved ultratrace determination of actinide contaminations, and the analysis of specific element and isotopic distributions on surfaces and environment particles. We report on the identification of highly element-selective optical excitation schemes identified for this purpose, with a particular focus on the precise determination of the isobaric ratios of 235U to 239Pu as well as 243Am to 241Pu. The chosen two-step ionization schemes were characterized with respect to their element selectivity on synthetic multi-element actinide mixtures, with an element ratio Pu : Am : U of 1 : 10 : 104, a composition which is typical, e.g., for spent nuclear reactor fuels.

In the multi-mode resource-constrained project scheduling problem, a set of precedence-related project activities and, for each activity, a set of alternative execution modes are given. Each activity requires some time and some scarce resources during execution; these requirements depend on the selected execution mode. Sought is a project schedule, i.e, a start time and an execution mode for each activity, such that the project makespan is minimized. In the literature, besides a large variety of specific solution approaches, several Mixed-Integer Linear Programming (MILP) models have been proposed for this problem. We present two novel MILP models that are based on mode-selection, resource-assignment and sequencing variables; we enhance the performance of the models by eliminating some symmetric solutions from the search space and by adding some redundant sequencing constraints for pairs and for triples of activities that cannot be processed in parallel. In a comparison with reference models from the literature, it turned out that the advantages of the novel models are a simple structure, an enhanced flexibility, and a superior performance when the range of the activities' durations is relatively large.

Abstract Resonance ionization mass spectrometry is an efficient tool to detect minute amounts of long-lived radio-isotopes in environmental samples. Applying resonant excitation and ionization with pulsed laser radiation within a hot cavity atomizer enables the sensitive detection and precise quantification of long-lived actinide isotopes. Due to the inherently element selective ionization process, this method ensures ultimate suppression of contaminations from other elements and molecules. The characterization of in-source resonance ionization of the actinide elements U, Th, Np, and Am using a compact quadrupole mass spectrometer (QMS) setup are discussed.

Enhanced index tracking is an emerging strategy for investing money in the stock market and is aimed at achieving outperformance over a given benchmark index while achieving a low tracking error. We consider the problem of rebalancing a portfolio for an enhanced index tracking strategy subject to various real-life constraints, including a lower bound and an upper bound on the expected tracking error. To solve this problem, we propose a three-phase approach consisting of preprocessing, optimization, and learning. In a computational experiment, we applied this approach to rebalance a given portfolio on a monthly basis over a time horizon of 10 years; the data for the S&P 500 benchmark index were provided by the investment company Principal Global Investors. Our approach generated portfolios that were provably close to optimality for all monthly rebalancing decisions. Over the entire horizon of 10 years, the portfolios devised by our approach yielded cumulative returns higher than the S&P 500 index after transaction costs with a moderate tracking error.

We study the complex combinatorial optimization problem to schedule the activities of a single project with the objective to complete the project within the shortest-possible amount of time such that the limited resource capacities as well as the prescribed precedence relations between pairs of the activities are taken into account. In addition to various specific solution algorithms, the related literature proposes several Mixed-Integer Linear Programming (MILP) models, but these models remain complex to solve even for small-sized instances. We present a novel approach based on an MILP model in which the resource-capacity constraints are formulated for all inclusion-minimal sets of activities which, due to the limited capacities of the resources, cannot be processed simultaneously. We propose to remove these constraints from the model and iteratively add those constraints back which are violated in the solutions obtained. For a set of test instances from the literature, our computational results indicate that with respect to both, the deviation of the project duration obtained from the lower bound devised from the critical-path length and the number of instances solved to optimality, the novel lazy-constraints approach outperforms ten state-of-the-art MILP models.

The execution of a project is nowadays often distributed among multiple sites. While some resource units are available at a certain site only, other resource units can be moved across the sites. The problem considered here consists of scheduling a single projects' activities which are interrelated by given precedence relationships of the completion-start type, require various renewable resource types during execution, and can be executed at the different sites of the project, such that the project makespan is minimized; transportation times must be taken into account if a resource unit is moved between two sites, or if two activities interrelated by a precedence relationship are executed at different sites. We present a continuous-time formulation of this problem as a mixed-binary linear program. In an experiment based on a set of 480 instances, we compared the performance of this novel formulation with a discrete-time formulation, which is the only formulation known from the literature; it turned out that when using the novel continuous-time formulation, considerably more instances can be solved to feasibility and to optimality, respectively.