The half-life of ${}^{37}\mathrm{K}$ has been measured to be $1.23651\left(94\right)\mathrm{s}$, a value nearly an order of magnitude more precise than the best previously reported. The ${\beta }^{+}$ decay of ${}^{37}\mathrm{K}$ occurs mainly via a superallowed branch to the ground state of its $T=1/2$ mirror, ${}^{37}\mathrm{Ar}$. This transition has been used recently, together with similar transitions from four other nuclei, as a method for determining $V_{ud}$, but the precision of its $ft$ value was limited by the relatively large half-life uncertainty. Our result corrects that situation. Another motivation for improving the $ft$ value was to determine the standard-model prediction for the $\beta$-decay correlation parameters, which will be compared to those currently being measured by the TRINAT Collaboration at TRIUMF. The new $ft$ value, $4605\left(8\right)\mathrm{s}$, is now limited in precision by the $97.99\left(14\right)\%$ ground-state branching ratio.

The production of the prompt charmed mesons $D^0$, $D^{+}$, and $D^{*+}$ relative to the reaction plane was measured in Pb-Pb collisions at a center-of-mass energy per nucleon-nucleon collision of $\sqrt{s_{\mathrm{NN}}}=2.76\mathrm{TeV}$ with the ALICE detector at the CERN Large Hadron Collider. $D$ mesons were reconstructed via their hadronic decays at central rapidity in the transverse-momentum ($p_{\mathrm{T}}$) interval 2–16 $\mathrm{GeV}/c$. The azimuthal anisotropy is quantified in terms of the second coefficient $v_2$ in a Fourier expansion of the $D$-meson azimuthal distribution and in terms of the nuclear modification factor $R_{\mathrm{AA}}$, measured in the direction of the reaction plane and orthogonal to it. The $v_2$ coefficient was measured with three different methods and in three centrality classes in the interval 0%–50%. A positive $v_2$ is observed in midcentral collisions (30%–50% centrality class), with a mean value of $0.{204}_{-0.036}^{+0.099}$ (tot. unc.) in the interval $2<p_{\mathrm{T}}<6\mathrm{GeV}/c$, which decreases towards more central collisions (10%–30% and 0%–10% classes). The positive $v_2$ is also reflected in the nuclear modification factor, which shows a stronger suppression in the direction orthogonal to the reaction plane for midcentral collisions. The measurements are compared to theoretical calculations of charm-quark transport and energy loss in high-density strongly interacting matter at high temperature. The models that include substantial elastic interactions with an expanding medium provide a good description of the observed anisotropy. However, they are challenged to simultaneously describe the strong suppression of high-$p_{\mathrm{T}}$ yield of $D$ mesons in central collisions and their azimuthal anisotropy in noncentral collisions.

Background: The hexadecapole deformation ${\beta }_4$ is usually difficult to determine experimentally, especially its sign. The rapidly accumulated knowledge of ${\beta }_2$ inspires the desire of ${\beta }_4$ for radioactive nuclei, but the current low-quality beam is a severe experimental challenge. Therefore, a simple but sensitive method to extract ${\beta }_4$ in such a condition is urgently called for.

Purpose: To study the feasibility of extracting ${\beta }_4$ from the lower-energy backward quasi-elastic (QEL) scattering.

Methods: The QEL scattering at sub-barrier energy region is sensitive to the coupled-channels (CC) effect and consequently may be used to extract ${\beta }_4$. The QEL scattering excitation functions for ${}^{16}\mathrm{O}+{}^{152}\mathrm{Sm}$,${}^{170}\mathrm{Er}$, and ${}^{174}\mathrm{Yb}$ were measured at a backward angle with small energy intervals at energies near the Coulomb barrier. Experimental fusion barrier distributions were also derived. The lower-energy data were analyzed to extract ${\beta }_4$ with the help of the CC calculations.

Results: The obtained ${\beta }_4$ agrees with the available results reasonably well.

Conclusions: We have demonstrated that the QEL scattering at sub-barrier energies provides a feasible and sensitive method to extract the value of ${\beta }_4$, which is essentially meaningful for the radioactive nucleus because of its low beam intensity.

The Brussels-Montreal Skyrme functionals have been successful in describing properties of both finite nuclei and infinite homogeneous nuclear matter. In their latest version, these functionals have been equipped with two extra density-dependent terms in order to reproduce simultaneously ground state properties of nuclei and infinite nuclear matter properties while avoiding at the same time the arising of ferromagnetic instabilities. In the present article, we extend our previous results of the linear response theory to include such extra terms at both zero and finite temperature in pure neutron matter. The resulting formalism is then applied to derive the neutrino mean free path. The predictions from the Brussels-Montreal Skyrme functionals are compared with ab initio methods.

Background: Complex many-body systems, such as triaxial and reflection-asymmetric nuclei, weakly bound halo states, cluster configurations, nuclear fragments produced in heavy-ion fusion reactions, cold Fermi gases, and pasta phases in neutron star crust, are all characterized by large sizes and complex topologies in which many geometrical symmetries characteristic of ground-state configurations are broken. A tool of choice to study such complex forms of matter is an adaptive multi-resolution wavelet analysis. This method has generated much excitement since it provides a common framework linking many diversified methodologies across different fields, including signal processing, data compression, harmonic analysis and operator theory, fractals, and quantum field theory.

Purpose: To describe complex superfluid many-fermion systems, we introduce an adaptive pseudospectral method for solving self-consistent equations of nuclear density functional theory in three dimensions, without symmetry restrictions.

Methods: The numerical method is based on the multi-resolution and computational harmonic analysis techniques with a multi-wavelet basis. The application of state-of-the-art parallel programming techniques include sophisticated object-oriented templates which parse the high-level code into distributed parallel tasks with a multi-thread task queue scheduler for each multi-core node. The internode communications are asynchronous. The algorithm is variational and is capable of solving coupled complex-geometric systems of equations adaptively, with functional and boundary constraints, in a finite spatial domain of very large size, limited by existing parallel computer memory. For smooth functions, user-defined finite precision is guaranteed.

Results: The new adaptive multi-resolution Hartree-Fock-Bogoliubov (HFB) solver madness-hfb is benchmarked against a two-dimensional coordinate-space solver hfb-ax that is based on the $B$-spline technique and a three-dimensional solver hfodd that is based on the harmonic-oscillator basis expansion. Several examples are considered, including the self-consistent HFB problem for spin-polarized trapped cold fermions and the Skyrme-Hartree-Fock ($+\text{BCS}$) problem for triaxial deformed nuclei.

Conclusions: The new madness-hfb framework has many attractive features when applied to nuclear and atomic problems involving many-particle superfluid systems. Of particular interest are weakly bound nuclear configurations close to particle drip lines, strongly elongated and dinuclear configurations such as those present in fission and heavy-ion fusion, and exotic pasta phases that appear in neutron star crust.

The shape transition in the neutron-rich Os isotopes is studied by investigating the neutron-rich ${}^{196}\text{Os}$ nucleus through in-beam $\gamma$-ray spectroscopy using a two-proton transfer reaction from a ${}^{198}\text{Pt}$ target to a ${}^{82}\text{Se}$ beam. The beam-like recoils were detected and identified with the large-acceptance magnetic spectrometer PRISMA, and the coincident $\gamma$ rays were measured with the advanced gamma tracking array (AGATA) demonstrator. The de-excitation of the low-lying levels of the yrast-band of ${}^{196}\text{Os}$ were identified for the first time. The results are compared with state-of-the-art beyond-mean-field calculations, performed for the even-even ${}^{188-198}\mathrm{Os}$ isotopes. The new results suggest a smooth transition in the Os isotopes from a more axial rotational behavior towards predominately vibrational nuclei through triaxial configurations. An almost perfect $\gamma$-unstable/triaxial rotor yrast band is predicted for ${}^{196}\text{Os}$ which is in agreement with the experimentally measured excited states.

Background: The numerical solution of few-body scattering problems with realistic interactions is a difficult problem that normally must be solved on powerful supercomputers, taking a lot of computer time. This strongly limits the possibility of accurate treatments for many important few-particle problems in different branches of quantum physics.

Purpose: To develop a new general highly effective approach for the practical solution of few-body scattering equations that can be implemented on a graphics processing unit.

Methods: The general approach is realized in three steps: (i) the reformulation of the scattering equations using a convenient analytical form for the channel resolvent operator, (ii) a complete few-body continuum discretization and projection of all operators and wave functions onto an $L_2$ basis constructed from stationary wave packets, and (iii) the ultrafast solution of the resulting matrix equations using a graphics processor.

Results: The whole approach is illustrated by a calculation of the neutron-deuteron elastic scattering cross section below and above the three-body breakup threshold with a realistic $NN$ potential that is performed on a standard PC using a graphics processor with an extremely short runtime.

Conclusions: The general technique proposed in this paper opens a new way for a fast practical solution of quantum few-body scattering problems in both nonrelativistic and relativistic formulations in hadronic, nuclear, and atomic physics.

The reaction $\pi N\to \pi \pi N$ is studied at tree level up to next-to-leading order in the framework of manifestly covariant baryon chiral perturbation theory with explicit $\Delta \left(1232\right)$ degrees of freedom. Using total cross-section data to determine the relevant low-energy constants, predictions are made for various differential as well as total cross sections at higher energies. A detailed comparison of results based on the heavy-baryon and relativistic formulations of chiral perturbation theory with and without explicit $\Delta$ degrees of freedom is given.

Background: A model-independent formulation of weakly interacting massive particle (WIMP)-nucleon scattering was recently developed in Galilean-invariant effective field theory.

Purpose: Here we complete the embedding of this effective interaction in the nucleus, constructing the most general elastic nuclear cross section as a factorized product of WIMP and nuclear response functions. This form explicitly defines what can and cannot be learned about the low-energy constants of the effective theory—and consequently about candidate ultraviolet theories of dark matter—from elastic scattering experiments.

Results: We identify those interactions that cannot be reliably treated in a spin-independent/spin-dependent (SI/SD) formulation: For derivative- or velocity-dependent couplings, the SI/SD formulation generally mischaracterizes the relevant nuclear operator and its multipolarity (e.g., scalar or vector) and greatly underestimates experimental sensitivities. This can lead to apparent conflicts between experiments when, in fact, none may exist. The new nuclear responses appearing in the factorized cross section are related to familiar electroweak nuclear operators such as angular momentum $\vec{l}\left(i\right)$ and the spin-orbit coupling $\vec{\sigma }\left(i\right)·\vec{l}\left(i\right)$.

Conclusions: To unambiguously interpret experiments and to extract all of the available information on the particle physics of dark matter, experimentalists will need to (1) do a sufficient number of experiments with nuclear targets having the requisite sensitivities to the various operators and (2) analyze the results in a formalism that does not arbitrarily limit the candidate operators. In an appendix we describe a code that is available to help interested readers implement such an analysis.

Background: Weak interactions between quarks induce a parity-violating (PV) component in the nucleon-nucleon potential, whose effects are currently being studied in a number of experiments involving few-nucleon systems. In the present work, we reconsider the derivation of this PV component within a chiral effective field theory ($\chi$EFT) framework.

Purpose: The objectives of the present work are twofold. The first is to perform a detailed analysis of the PV nucleon-nucleon potential up to next-to-next-to-leading (N2LO) order in the chiral expansion, in particular, by determining the number of independent low-energy constants (LECs) at N2LO. The second objective is to investigate PV effects in a number of few-nucleon observables, including the $\vec{p}$-$p$ longitudinal asymmetry, the neutron spin rotation in $\vec{n}$-$p$ and $\vec{n}$-$d$ scattering, and the longitudinal asymmetry in the ${}^3$He${(\vec{n},p)}^3$H charge-exchange reaction.

Methods: The $\chi$EFT PV potential includes one-pion-exchange, two-pion-exchange, and contact terms as well as $1/M$ ($M$ being the nucleon mass) nonstatic corrections. Dimensional regularization is used to renormalize pion loops. The wave functions for the $A=2$–4 nuclei are obtained by using strong two- and three-body potentials also derived, for consistency, from $\chi$EFT. In the case of the $A=3$–4 systems, the wave functions are computed by expanding on a hyperspherical harmonics functions basis.

Results: We find that the PV potential at N2LO depends on six LECs: the pion-nucleon PV coupling constant $h_{\pi }^1$ and five parameters multiplying contact interactions. An estimate for the range of values of the various LECs is provided by using available experimental data, and these values are used to obtain predictions for the other PV observables.

Conclusions: The $\chi$EFT approach provides a very satisfactory framework to analyze PV effects in few-nucleon systems.

The ability to accurately compute the series of coefficients $v_n$ characterizing the momentum space anisotropies of particle production in ultrarelativistic heavy-ion collisions as a function of centrality is widely regarded as a triumph of fluid dynamics as the description of the bulk matter evolution. A key ingredient to fluid dynamical modeling is, however, the initial spatial distribution of matter as created by a not yet completely understood equilibration process. A measurement directly sensitive to this initial state geometry is therefore of high value for constraining models of pre-equilibrium dynamics. Recently, it has been shown that such a measurement is indeed possible in terms of the event-by-event probability distribution of the normalized $v_n$ distribution as a function of centrality, which is to high accuracy independent of the details of the subsequent fluid dynamical evolution and hence directly reflects the primary distribution of spatial eccentricities. We present a study of this observable using a variety of Glauber-based models and argue that the experimental data place very tight constraints on the initial distribution of matter and rule out all simple Glauber-based models.

In reviewing the data that has accumulated about light nuclei, we find that the binding energy plays a critical role in describing the variation in energy of $s$ states relative to other states. The behavior of states with zero angular momentum within a few MeV of threshold is qualitatively different from that of neutron states with any other $\ell$ value or of any proton state. This observation is explored for simple Woods-Saxon potentials and is remarkably successful in describing a wealth of experimental data for nuclei with neutron numbers between 5 and 10. The lingering of neutron $s$ states just below threshold is associated with the increases in radii of the neutron density distributions, the neutron halos, and leads to speculations about possible halos in heavier nuclei.

Background: The ${}_{38}^{88}\text{Sr}$ and ${}_{40}^{90}\text{Zr}$ nuclei have been utilized as closed cores for large-scale shell-model calculations in the $28\le Z\le 50$ region around the $N=50$ shell. Measurements of magnetic moments for nuclei in this region would provide microscopic information about the use of ${}^{88}$Sr and ${}^{90}$Zr as stable closed-core nuclei. While the $g$ factors of the 2${}_1^{+}$ states in the stable Sr isotopes have been previously measured, experimental $g$ factors for the radioactive ${}^{82,90}$Sr have not been obtained to date.

Purpose: The purpose was to measure the $g$ factors of the 2${}_1^{+}$ and 4${}_1^{+}$ states in the unstable ${}^{82}$Sr and ${}^{90}$Sr nuclei in order to extend the systematics along the Sr isotopic chain. A comparison of the structure of the $N=52$ isotopes ${}^{90}$Sr and ${}^{92}$Zr will shed light on the relative robustness of proton subshell closures at $Z=38$ and $Z=40$.

Methods: The pickup reaction of $\alpha$ particles in inverse kinematics together with the transient field technique were applied to beams of ${}^{78}$Kr and ${}^{86}$Kr at the Cyclotron Institute of Texas A&M University.

Results: The values $g{(}^{82}\mathrm{Sr};2_1^{+})=+0.44\left(19\right)$, $g{(}^{82}\mathrm{Sr};4_1^{+})=+0.53\left(39\right)$, $g{(}^{90}\mathrm{Sr};2_1^{+})=-0.12\left(11\right)$, and $g{(}^{90}\mathrm{Sr};4_1^{+})=-0.02\left(17\right)$ were measured for the first time. Simultaneously, the $g$ factors of the low-lying states in the Coulomb-excited beam projectiles were remeasured. The $g\left(4_1^{+}\right)$ = +1.03(14) in ${}^{86}$Kr was also measured for the first time.

Conclusions: For ${}^{82}$Sr both $g$ factors are in agreement with the collective value $Z/A$ expected for nuclei in the middle of a major shell. The $g$ factors in ${}^{90}$Sr are negative but smaller than in the isotone ${}^{92}$Zr. The results also indicate that ${}^{88}$Sr is a proton-soft core nucleus and perhaps even softer than ${}^{90}$Zr.

We apply stochastic hydrodynamics to the study of charge-density fluctuations in QCD matter undergoing Bjorken expansion. We find that the charge-density correlations are given by a time integral over the history of the system, with the dominant contribution coming from the QCD crossover region where the change of susceptibility per entropy, $\chi T/s$, is most significant. We study the rapidity and azimuthal angle dependence of the resulting charge balance function using a simple analytic model of heavy-ion collision evolution. Our results are in agreement with experimental measurements, indicating that hydrodynamic fluctuations contribute significantly to the measured charge correlations in high-energy heavy-ion collisions. The sensitivity of the balance function to the value of the charge diffusion coefficient $D$ allows us to estimate the typical value of this coefficient in the crossover region to be rather small, of the order of ${\left(2\pi T\right)}^{-1}$, characteristic of a strongly coupled plasma.

The $\mathrm{UCN}\tau$ experiment is designed to measure the lifetime ${\tau }_n$ of the free neutron by trapping ultracold neutrons (UCN) in a magneto-gravitational trap. An asymmetric bowl-shaped NdFeB magnet Halbach array confines low-field-seeking UCN within the apparatus, and a set of electromagnetic coils in a toroidal geometry provides a background “holding” field to eliminate depolarization-induced UCN loss caused by magnetic field nodes. We present a measurement of the storage time ${\tau }_{\text{store}}$ of the trap by storing UCN for various times and counting the survivors. The data are consistent with a single exponential decay, and we find ${\tau }_{\text{store}}=860\pm 19$ s, within $1\sigma$ of current global averages for ${\tau }_n$. The storage time with the holding field deactivated is found to be ${\tau }_{\text{store}}=470\pm 160$ s; this decreased storage time is due to the loss of UCN, which undergo Majorana spin flips while being stored. We discuss plans to increase the statistical sensitivity of the measurement and investigate potential systematic effects.

The hot QCD matter produced in any heavy ion collision with a nonzero impact parameter is produced within a strong magnetic field. We study the imprint that these fields leave on the azimuthal distributions and correlations of the produced charged hadrons. The magnetic field is time dependent and the medium is expanding, which leads to the induction of charged currents owing to the combination of Faraday and Hall effects. We find that these currents result in a charge-dependent directed flow $v_1$ that is odd in rapidity and odd under charge exchange. It can be detected by measuring correlations between the directed flow of charged hadrons at different rapidities, $\langle v_1^{\pm }\left(y_1\right)v_1^{\pm }\left(y_2\right)\rangle$.

Background: Much less is known about neutron structure than that of the proton due to the absence of free neutron targets. Neutron information is usually extracted from data on nuclear targets such as deuterium, requiring corrections for nuclear binding and nucleon off-shell effects. These corrections are model dependent and have significant uncertainties, especially for large values of the Bjorken scaling variable $x$. As a consequence, the same data can lead to different conclusions, for example, about the behavior of the $d$ quark distribution in the proton at large $x$.

Purpose: The Barely Off-shell Nucleon Structure experiment at Jefferson Lab measured the inelastic electron-deuteron scattering cross section, tagging spectator protons in coincidence with the scattered electrons. This method reduces nuclear binding uncertainties significantly and has allowed for the first time a (nearly) model-independent extraction of the neutron structure function $F_2(x,Q^2)$ in the resonance and deep-inelastic regions.

Method: A novel compact radial time projection chamber was built to detect protons with momentum between 70 and 150 MeV$/c$ and over a nearly $4\pi$ angular range. For the extraction of the free-neutron structure function $F_2^n$, spectator protons at backward angles ($>{100}^{\circ }$ relative to the momentum transfer) and with momenta below 100 MeV$/c$ were selected, ensuring that the scattering took place on a nearly free neutron. The scattered electrons were detected with Jefferson Lab's CLAS spectrometer, with data taken at beam energies near 2, 4, and 5 GeV.

Results: The extracted neutron structure function $F_2^n$ and its ratio to the inclusive deuteron structure function $F_2^d$ are presented in both the resonance and the deep-inelastic regions for momentum transfer squared $Q^2$ between 0.7 and 5 GeV${}^2/c^2$, invariant mass $W$ between 1 and 2.7 GeV$/c^2$, and Bjorken $x$ between 0.25 and 0.6 (in the deep-inelastic scattering region). The dependence of the semi-inclusive cross section on the spectator proton momentum and angle is investigated, and tests of the spectator mechanism for different kinematics are performed.

Conclusions: Our data set on the structure function ratio $F_2^n/F_2^d$ can be used to study neutron resonance excitations, test quark-hadron duality in the neutron, develop more precise parametrizations of structure functions, and investigate binding effects (including possible mechanisms for the nuclear EMC effect) and provide a first glimpse of the asymptotic behavior of $d/u$ at $x\to 1$.

Background: Quasi dynamical symmetry (QDS) and partial dynamical symmetry (PDS) play an important role in the understanding of complex systems. Up to now these symmetry concepts have been considered to be unrelated.

Purpose: The goal of this paper is to establish a link between PDS and QDS and find an empirical manifestation.

Methods: Quantum number fluctuations and the intrinsic state formalism are used within the framework of the interacting boson model of nuclei.

Results: A previously unrecognized region of the parameter space of the interacting boson model that has both O(6) PDS (purity) and SU(3) QDS (coherence) in the ground band is established. Many rare-earth nuclei approximately satisfying both symmetry requirements are identified.

Conclusions: PDS is more abundant than previously recognized and can lead to a QDS of an incompatible symmetry.

Background: Heavy-flavor modification in relativistic $p\left(d\right)+A$ collisions are sensitive to different kinds of strong-interaction physics ranging from modifications of the nuclear wave function to initial- and final-state energy loss. Modifications to single heavy-flavor particles and their decay leptons at midrapidity and forward rapidity are well established at the Relativistic Heavy Ion Collider (RHIC).

Purpose: This paper presents measurements of azimuthal correlations of electron-muon pairs produced from heavy-flavor decays, primarily $c\overline{c}$, in $\sqrt{s_{{}_{NN}}}=200$ GeV $p+p$ and $d+\mathrm{Au}$ collision using the PHENIX detector at RHIC. The electrons are measured at midrapidity while the muons in the pair are measured at forward rapidity, defined as the direction of the deuteron beam, in order to utilize the deuteron to probe low-$x$ partons in the gold nucleus.

Methods: This analysis uses the central spectrometer arms for electron identification and forward spectrometer arms for muon identification. Azimuthal correlations are built in all sign combinations for $e\text{−}\mu$ pairs. Subtracting the like-sign yield from the unlike-sign yield removes the correlations from light flavor decays and conversions.

Results: Comparing the $p+p$ results with several different Monte Carlo event generators, we find the results are consistent with a total charm cross section ${\sigma }_{c\overline{c}}=538\pm 46$ (stat) $\pm$ 197 (data syst) $\pm$ 174 (model syst) $\mu$b. These generators also indicate that the back-to-back peak at $\Delta \varphi =\pi$ is dominantly from the leading-order contributions (gluon fusion), while higher-order processes (flavor excitation and gluon splitting) contribute to the yield at all $\Delta \varphi$. We observe a suppression in the pair yield per collision in $d+\mathrm{Au}$. We find the pair yield suppression factor for $2.7<\Delta \varphi <3.2$ rad is $J_{dA}=0.433\pm 0.087$ (stat) $\pm$ 0.135 (syst).

Conclusions: The $e\text{−}\mu$ pairs result from partons at $x_{\mathrm{Au}}\sim {10}^{-2}$ at $Q^2=10$ GeV/$c^2$ at the edge of the shadowing region. The pair suppression indicates modification to $c\overline{c}$ pairs for these kinematics in the cold nuclear medium at RHIC.

In the present work we were able to synthesize and measure with high accuracy the production cross sections of more than 190 heavy neutron-rich nuclei by the in-flight fragmentation of relativistic ${}^{208}$Pb projectiles, 26 of which were produced for the first time. This work has shown that the $N=126$ region far below the doubly magic ${}^{208}$Pb has become accessible experimentally and represents a step further towards the study of heavy neutron-rich nuclei approaching the r-process waiting point at $A=195$.