We present continuum and lattice calculations for elastic scattering between a fermion and a bound dimer in the shallow binding limit. For the lattice calculation we use the finite-volume method of Lüscher. We take into account topological finite-volume corrections to the dimer binding energy which depend on the momentum of the dimer. After subtracting these effects, we find from the lattice calculation $\kappa a_{fd}=1.174\left(9\right)$ and $\kappa r_{fd}=-0.029\left(13\right)$. These results agree well with the continuum values $\kappa a_{fd}=1.17907\left(1\right)$ and $\kappa r_{fd}=-0.0383\left(3\right)$ obtained from the STM equation. We discuss applications to cold atomic Fermi gases, deuteron-neutron scattering in the spin-quartet channel, and lattice calculations of scattering for nuclei and hadronic molecules at finite volume.

Deformed shell structures in nuclear mean-field potentials are systematically investigated as functions of deformation and surface diffuseness. As the mean-field model to investigate nuclear shell structures in a wide range of mass numbers, we propose the radial power-law potential model, $V\propto r^{\alpha }$, which enables a simple semiclassical analysis by the use of its scaling property. We find that remarkable shell structures emerge at certain combinations of deformation and diffuseness parameters, and they are closely related to the periodic-orbit bifurcations. In particular, significant roles of the “bridge orbit bifurcations” for normal and superdeformed shell structures are pointed out. It is shown that the prolate-oblate asymmetry in deformed shell structures is clearly understood from the contribution of the bridge orbit to the semiclassical level density. The roles of bridge orbit bifurcations in the emergence of superdeformed shell structures are also discussed.

In this paper we present a new formalism to implement the nuclear particle-vibration coupling (PVC) model. The key issue is the proper treatment of the continuum that is allowed by the coordinate space representation. Our formalism, based on the use of zero-range interactions such as the Skyrme forces, is microscopic and fully self-consistent. We apply it to the case of neutron single-particle states in ${}^{40}$Ca, ${}^{208}$Pb, and ${}^{24}$O. The first two cases are meant to illustrate the comparison with the usual (i.e., discrete) PVC model. However, we stress that the present approach allows one to calculate properly the effect of PVC on resonant states. We compare our results with those from experiments in which the particle transfer in the continuum region has been attempted. The latter case, namely ${}^{24}$O, is chosen as an example of a weakly-bound system. Such a nucleus, being double magic and not displaying collective low-lying vibrational excitations, is characterized by quite pure neutron single-particle states around the Fermi surface.

Background: The $g$ factors and lifetimes of the 2${}_1^{+}$ states in the stable, proton-rich Sn isotopes have been measured, but there is scant information on neutron-rich Sn isotopes.

Purpose: Measurement of the $g$ factor and the lifetime of the 2${}_1^{+}$ state at 1.141 MeV in neutron-rich ${}^{126}$Sn ($T_{1/2}=2.3\times {10}^{5}y$).

Method: Coulomb excitation in inverse kinematics together with the transient field and the Doppler shift attenuation techniques were applied to a radioactive beam of ${}^{126}$Sn at the Holifield Radioactive Ion Beam Facility.

Results: $g\left(2_1^{+}\right)=-0.25\left(21\right)$ and $\tau \left(2_1^{+}\right)=1.5\left(2\right)$ ps were obtained.

Conclusions: The data are compared to large-scale shell-model and quasiparticle random-phase calculations. Neutrons in the $h_{11/2}$ and $d_{3/2}$ orbitals play an important role in the structure of the 2${}_1^{+}$ state of ${}^{126}$Sn. Challenges, limitations, and implications for such experiments at future rare isotope beam facilities are discussed.

The ${}^{12}$C excitation energy spectra populated in both proton and $\alpha$-particle inelastic scattering measurements are examined. The data indicate the existence of a 2${}^{+}$ state at $E_x=9.75$(0.15) MeV with a width of 750(150) keV. It is believed that this state corresponds to the 2${}^{+}$ excitation of the 7.65 MeV, 0${}^{+}$, Hoyle state, which acts as the main path by which carbon is synthesized in stars. A simultaneous $R$-matrix analysis of the two sets of data indicates that the 2${}^{+}$ state possesses a very large $\alpha$-reduced width, approaching the Wigner limit. This would indicate that the state is associated with a highly clustered structure. The potential geometric arrangements of the clusters is discussed.

Background: Time-reversal-invariance violation, or equivalently $CP$ violation, may explain the observed cosmological baryon asymmetry as well as indicate physics beyond the Standard Model. In the decay of polarized neutrons, the triple correlation $D\langle {\vec{J}}_n\rangle /J_n·({\vec{\beta }}_e\times {\widehat{p}}_{\nu })$ is a parity-even, time-reversal-odd observable that is uniquely sensitive to the relative phase of the axial-vector amplitude with respect to the vector amplitude. The triple correlation is also sensitive to possible contributions from scalar and tensor amplitudes. Final-state effects contribute to $D$ at the level of 10${}^{-5}$ and can be calculated with a precision of 1$\%$ or better.

Purpose: We have improved the sensitivity to $T$-odd, $P$-even interactions in nuclear $\beta$ decay.

Methods: We measured proton-electron coincidences from decays of longitudinally polarized neutrons with a highly symmetric detector array designed to cancel the time-reversal-even, parity-odd Standard-Model contributions to polarized neutron decay. Over 300 million proton-electron coincidence events were used to extract $D$ and study systematic effects in a blind analysis.

Results: We find $D=[-0.94\pm 1.89\left(\mathrm{stat}\right)\pm 0.97\left(\mathrm{sys}\right)]\times {10}^{-4}$. This differs from the result of our recent paper [Phys. Rev. Lett. 107, 102301 (2011)] due to refinement of corrections for background and backscattering.

Conclusions: This is the most sensitive measurement of $D$ in nuclear $\beta$ decay. Our result can be interpreted as a measurement of the phase of the ratio of the axial-vector and vector coupling constants ($C_A/C_V=\left|\lambda \right|e^{i{\phi }_{AV}}$) with ${\phi }_{AV}=180.{012}^{\circ }\pm 0.{028}^{\circ }$ (68$\%$ confidence level). This result can also be used to constrain time-reversal-violating scalar and tensor interactions that arise in certain extensions to the Standard Model such as leptoquarks.

Background: Astrophysical models studying the origin of the neutron-deficient $p$ nuclides require knowledge of proton capture cross sections at low energy. The production site of the $p$ nuclei is still under discussion but a firm basis of nuclear reaction rates is required to address the astrophysical uncertainties. Data at astrophysically relevant interaction energies are scarce. Problems with the prediction of charged particle capture cross sections at low energy were found in the comparisons between previous data and calculations in the Hauser-Feshbach statistical model of compound reactions.

Purpose: A measurement of ${}^{74}$Ge($p,\gamma$)${}^{75}$As at low proton energies, inside the astrophysically relevant energy region, is important in several respects. The reaction is directly important because it is a bottleneck in the reaction flow which produces the lightest $p$ nucleus ${}^{74}$Se. It is also an important addition to the data set required to test reaction-rate predictions and to allow an improvement in the global $p+\text{nucleus}$ optical potential required in such calculations.

Method: An in-beam experiment was performed, making it possible to measure in the range $2.1\le E_p\le 3.7\mathrm{MeV}$, which is for the most part inside the astrophysically relevant energy window. Angular distributions of the $\gamma$-ray transitions were measured with high-purity germanium detectors at eight angles relative to the beam axis. In addition to the total cross sections, partial cross sections for the direct population of 12 levels were determined.

Results: The resulting cross sections were compared to Hauser-Feshbach calculations using the code smaragd. Only a constant renormalization factor of the calculated proton widths allowed a good reproduction of both total and partial cross sections. The accuracy of the calculation made it possible to check the spin assignment of some states in ${}^{75}$As. In the case of the 1075-keV state, a double state with spins and parities of 3/2${}^{-}$ and 5/2${}^{-}$ is needed to explain the experimental partial cross sections. A change in parity from 5/2${}^{+}$ to 5/2${}^{-}$ is required for the state at 401 keV. Furthermore, in the case of ${}^{74}$Ge, studying the combination of total and partial cross sections made it possible to test the $\gamma$ width, which is essential in the calculation of the astrophysical ${}^{74}$As($n,\gamma$)${}^{75}$As rate.

Conclusions: Between data and statistical model prediction a factor of about two was found. Nevertheless, the improved astrophysical reaction rate of ${}^{74}$Ge($p,\gamma$) (and its reverse reaction) is only 28$\%$ larger than the previous standard rate. The prediction of the ${}^{74}$As($n,\gamma$)${}^{75}$As rate (and its reverse) was confirmed, the newly calculated rate differs only by a few percent from the previous prediction. The in-beam method with high-efficiency detectors proved to be a powerful tool for studies in nuclear astrophysics and nuclear structure.

The quantum phase transitional behavior of an alternative characterization of the spherical to axially deformed shape-phase transition in the interacting boson model is explored. Specifically, the usual SU(3) quadrupole-quadrupole interaction is replaced by an O(6) cubic interaction, and the transitional behaviors of the low-lying energy levels, eigenstates, isomer shifts, $E$2 transition rates, and expectation values of shape variables across the entire transitional region are all examined within this context. A comparison with outcomes of the usual U(5)-SU(3) transitional description shows that the spherical to axially deformed shape-phase transition can also be described within this alternative context, especially near the critical point. However, with the O(6) cubic interaction the transition is considerably smoother than for the U(5)-SU(3) case, but with the nuclear shape less well defined, even in the axially deformed limit. It is also shown that the new scheme seems better than the usual U(5)-SU(3) scheme in describing the low-lying spectrum of ${}^{152}$Sm with X(5) critical point symmetry.

The transition helicity amplitudes from the proton ground state to the $P_{11}\left(1440\right)$ and $D_{13}\left(1520\right)$ excited states (${\gamma }_{v}p{N}^{*}$ electrocouplings) were determined from the analysis of nine independent one-fold differential ${\pi }^{+}{\pi }^{-}p$ electroproduction cross sections off a proton target, taken with CLAS at photon virtualities of $0.25<Q^2<0.60$ GeV${}^2$. The phenomenological reaction model was employed for separation of the resonant and nonresonant contributions to the final state. The $P_{11}\left(1440\right)$ and $D_{13}\left(1520\right)$ electrocouplings were obtained from the resonant amplitudes parametrized within the framework of a unitarized Breit-Wigner ansatz. They are consistent with results obtained in the previous CLAS analyses of the ${\pi }^{+}n$ and ${\pi }^{0}p$ channels. The successful description of a large body of data in dominant meson-electroproduction channels off protons with the same ${\gamma }_{v}p{N}^{*}$ electrocouplings offers clear evidence for the reliable extraction of these fundamental quantities from meson-electroproduction data. This analysis also led to the determination of the long-awaited hadronic branching ratios for the $D_{13}\left(1520\right)$ decay into $\Delta \pi$ (24$\%$–32$\%$) and $N\rho$ (8$\%$–17$\%$).

Background: The neutrinoproduction of photons and pions from nucleons and nuclei is relevant to the background analysis in neutrino-oscillation experiments [for example, the MiniBooNE; MiniBooNE Collaboration, A. A. Aquilar-Arevalo et al., Phys. Rev. Lett. 100, 032301 (2008)]. The production from nucleons and incoherent production with $E_{\nu }⩽0.5\mathrm{GeV}$ have been studied in B. D. Serot and X. Zhang, Phys. Rev. C 86, 015501 (2012); and X. Zhang and B. D. Serot, Phys. Rev. C 86, 035502 (2012).

Purpose: Study coherent productions with $E_{\nu }⩽0.5\mathrm{GeV}$. Also address the contributions of two contact terms in neutral current (NC) photon production that are partially related to the proposed anomalous $\omega \left(\rho \right)$, $Z$ boson, and photon interactions.

Methods: We work in the framework of a Lorentz-covariant effective field theory (EFT), which contains nucleons, pions, the $\Delta$ (1232) ($\Delta$s), isoscalar scalar ($\sigma$) and vector ($\omega$) fields, and isovector vector ($\rho$) fields, and incorporates a nonlinear realization of (approximate) $\mathrm{SU}{\left(2\right)}_{\mathrm{L}}\otimes \mathrm{SU}{\left(2\right)}_{\mathrm{R}}$ chiral symmetry. A revised version of the so-called “optimal approximation” is applied, where one-nucleon interaction amplitude is factorized out and the medium-modifications and pion wave function distortion are included. The calculation is tested against the coherent pion photoproduction data.

Results: The computation shows an agreement with the pion photoproduction data, although precisely determining the $\Delta$ modification is entangled with one mentioned contact term. The uncertainty in the $\Delta$ modification leads to uncertainties in both pion and photon neutrinoproductions. In addition, the contact term plays a significant role in NC photon production.

Conclusions: First, the contact term increases NC photon production by $\sim 10\%$ assuming a reasonable range of the contact coupling, which however seems not significant enough to explain the MiniBooNE excess. A high energy computation is needed to gain a firm conclusion and will be presented elsewhere. Second, the behavior of coherent neutrinoproductions computed here is significantly different from the expectation at high energy by ignoring the vector current contribution.

The dynamical cluster-decay model (DCM), using the well-known pocket formula of Blocki et al. [Ann. Phys. (NY) 105, 427 (1977)] for nuclear proximity potential, is extended to the use of various other nuclear proximity potentials with effects of deformations included up to hexadecapole (${\beta }_4$) and “compact” orientations taken for both coplanar ($\Phi =0$) and non-coplanar ($\Phi \ne 0$) configurations of nuclei for the first time. The other nuclear proximity potentials used are those derived from the Skyrme-energy-density-formalism-based semiclassical extended Thomas Fermi method under frozen density approximation for a compound nucleus, using SIII and GSkI Skyrme forces. This is in addition to extending the Blocki et al. interaction to “compact” and non-coplanar nuclei. Application of the method is made to the study of the decay of the hot and rotating compound nucleus ${}^{164}$Yb${}^{*}$, formed in the heavy-ion reaction ${}^{64}\mathrm{Ni}+{}^{100}\mathrm{Mo}$ at both below- and above-barrier energies. For the best fitted measured evaporation residue cross-sections, consisting of $x$ neutrons ($x=1–4$), the interesting result of including the $\Phi$ degree of freedom is to increase the neck-length parameter of the model which results in the decrease of reaction time as well as the “barrier-lowering” parameter responsible for fusion hindrance effect. In other words, the fusion hindrance effect, a built-in property of DCM, though different for different nuclear interactions, reduces for the non-coplanar nuclei, and this reduction is more at higher center-of-mass energies. In the case of fusion-fission, only the cascade cross sections are available, which, when fitted simultaneously to another neck-length parameter, result in different components of a fusion-fission cross section for different nuclear interactions, including also the possibility of quasifission at the highest energy and the symmetric fission alone, that is, no intermediate-mass fragments, etc. The non-coplanar degree of freedom also plays an important role in changing the constituents of the fusion-fission cross section significantly, say, from intermediate and heavy-mass fragments plus the symmetric fission to simply the intermediate-mass fragments plus near-symmetric fission. This situation calls for the data for fusion-fission cross sections.

We report on a new cross-section measurement for the ${}^3$He($\alpha$, $\gamma$)${}^7$Be reaction at three medium energies of $E_{\mathrm{c}.\mathrm{m}.}$ between 1 and 3 MeV. The interest stems from the significant role played by the reaction in calculating an accurate solar neutrino flux and the primordial ${}^7$Li abundance. The energy dependence of the astrophysical $S_{34}$ factor observed in the present work, especially above 1 MeV, highlights the need to constrain theories in order to obtain a precise extrapolated value for $S_{34}\left(0\right)$. In this context, a comparison with the recent theoretical work in a fully microscopic fermionic molecular dynamics approach and a few other representative calculations emphasize the need for further experimental as well as theoretical work to resolve the existing conflicts.

Background: Neutrino-nucleus quasi-elastic scattering is crucial to interpret the neutrino oscillation results in long baseline neutrino experiments. There are rather large uncertainties in the cross section, due to insufficient knowledge on the role of two-body weak currents.

Purpose: Determine the role of two-body weak currents in neutrino-deuteron quasi-elastic scattering up to GeV energies.

Methods: Calculate cross sections for inclusive neutrino scattering off deuteron induced by neutral and charge-changing weak currents, from threshold up to GeV energies, using the Argonne $v_{18}$ potential and consistent nuclear electroweak currents with one- and two-body terms.

Results: Two-body contributions are found to be small, and increase the cross sections obtained with one-body currents by less than 10$\%$ over the whole range of energies. Total cross sections obtained by describing the final two-nucleon states with plane waves differ negligibly, for neutrino energies $\gtrsim$ MeV, from those in which interaction effects in these states are fully accounted for. The sensitivity of the calculated cross sections to different models for the two-nucleon potential and/or two-body terms in the weak current is found to be weak. Comparing cross sections to those obtained in a naive model in which the deuteron is taken to consist of a free proton and neutron at rest, nuclear structure effects are illustrated to be non-negligible.

Conclusion: Contributions of two-body currents in neutrino-deuteron quasi-elastic scattering up to GeV are found to be smaller than 10$\%$. Finally, it should be stressed that the results reported in this work do not include pion production channels.

We investigate the existence of weakly coupled gaslike states comprised of three $\alpha$ particles around an ${}^{16}$O core in ${}^{28}$Si. We calculate the excited states in ${}^{28}$Si using the multiconfiguration mixing method based on the ${}^{16}$O+3$\alpha$ cluster model. We also include the ${}^{16}$O+${}^{12}$C and ${}^{24}$Mg+$\alpha$ basis wave functions prepared by the generator coordinate method. To identify the gaslike states, we calculate the isoscalar monopole transition strengths and the overlap of the obtained states with the geometrical cluster wave function and the Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function. The results show that the obtained fourth and twelfth states significantly overlap with the THSR wave function. These two states clearly coexist with the ${}^{16}$O+${}^{12}$C cluster states, emerging at similar energies. The calculated isoscalar monopole strengths between those two states are significantly large, indicating that the states are members of the excitation mode. Furthermore, the calculated root-mean-square radii for these states also suggest that a layer of gaslike three $\alpha$ particles could exist around the surface of the ${}^{16}$O core, which can be described as a “two-dimensional gas” in the intermediate state before the Hoyle-like three-$\alpha$ states emerge.

Theoretical description of reactions in general, and the theory for $(d,p)$ reactions, in particular, needs to advance into the future. Here deuteron-stripping processes off a target nucleus consisting of $A$ nucleons are treated within the framework of the few-body integral equations theory. The generalized Faddeev equations in the Alt-Grassberger-Sandhas (AGS) form, which take into account the target excitations, with realistic optical potentials provide the most advanced and complete description of the deuteron stripping. The main problem in practical application of such equations is the screening of the Coulomb potential, which works only for light nuclei. In this paper we present a formulation of the Faddeev equations in the AGS form taking into account the target excitations with explicit inclusion of the Coulomb interaction. By projecting the $(A+2)$-body operators onto target states, matrix three-body integral equations are derived, which allow for the incorporation of the excited states of the target nucleons. Using the explicit equations for the partial Coulomb scattering wave functions in the momentum space we present the AGS equations in the Coulomb distorted wave representation without screening procedure. We also use the explicit expression for the off-shell two-body Coulomb scattering $T$ matrix, which is needed to calculate the effective potentials in the AGS equations. The integrals containing the off-shell Coulomb $T$ matrix are regularized to make the obtained equations suitable for calculations. For $NN$ and nucleon-target nuclear interactions we assume the separable potentials what significantly simplifies solution of the AGS equations.

The dipole strength distribution of ${}^{76}$Se has been investigated via photon scattering in the energy region below 9 MeV utilizing bremsstrahlung produced at the S-DALINAC facility at the TU Darmstadt. About 0.20(1)% of the classical $E1$ sum rule is exhausted by observed $J=1$ states of justifiably assumed negative parity. An extrapolation of the GDR below 9 MeV suggests that considerable strength may remain unobserved due to background, finite detector resolution, and fragmentation. The observed strength thus represents a lower limit. Candidates for the $2_{1,ms}^{+}$ state and a fragment of the $1_s^{+}c$ mixed-symmetry states are presented.

We report on a quantitative study of the evolution of the nuclear shell structure, in particular, effective single-particle energies (ESPEs), based on the spin-tensor decomposition of an effective two-body shell-model interaction. While the global trend of the ESPEs is mainly due to the central term of the effective interaction, variations of shell gaps invoke various components of the in-medium NN force. From a detailed analysis of a well-fitted realistic interaction in the $sdpf$ shell-model space, two most important contributions for the evolution of the $N=20$ and $N=28$ shell gaps are confirmed to be the central term and the tensor term. The role of the latter is dominant to explain the energy shift of spin-orbit partners. Spin-tensor analysis of microscopic effective interactions in $sd$, $pf$, and $gds$ shell-model spaces, contrasted with that of the phenomenologically adjusted ones, shows no evidence of amplification of the tensor component contribution; however, it points toward the neglect of three-body forces in the present microscopic interactions.

Near yrast states in ${}^{89}$Zr were investigated up to high spin using the fusion evaporation reaction ${}^{80}$Se(${}^{13}$C, 4$n$) at an incident beam energy of 50 MeV. Excited levels of ${}^{89}$Zr have been observed up to $\sim$10 MeV excitation energy and spin $\sim$37/2$\hslash$ using the prompt gamma spectroscopy technique with the Indian National Gamma Array (INGA). The angular distribution, directional correlation, and polarization measurements were carried out to assign the spin and parity of the newly reported states. The structures of both the positive and negative parity states up to highest spin observed in the present experiment have been compared with shell-model calculations using two recently developed residual interactions, JUN45 and jj44b. The role of proton excitations from $p_{3/2}$ and $f_{5/2}$ orbitals to the $g_{9/2}$ orbital for the higher spin states has been discussed.

Background: The nucleon-nucleus dispersive optical model (DOM) has been successful in providing good fits to scattering data and in making valuable predictions for bound-state properties in single- and double-closed shell nuclei. However, the generalizability of the DOM remains an ongoing issue.

Purpose: We investigate the DOM in the continuum and bound-state regions of the open-shell, self-conjugate nuclei ${}^{28}$Si and ${}^{32}$S. We collect new differential cross section and analyzing power data for elastic scattering at incident neutron energies between 8.0 and 18.9 MeV.

Methods: The measurements were conducted using a pulsed deuteron beam, the ${}^2$He($d$,$n$)${}^3$He source reaction, and time-of-flight techniques. All data were corrected for finite-geometry effects. Phenomenological DOM potentials were tailored to fit the differential and total cross section data, and then extrapolated to the bound-state regions. The DOM bound-state predictions were then compared to experimental data available for single-particle energies, occupation probabilities, root-mean-square radii, and spectroscopic factors.

Results: The DOM bound-state predictions are in only fair agreement with experimental data and with USD shell-model predictions. Similar results are found after converting our neutron DOMs into proton DOMs. We investigate the separate effects of the dispersive surface and volume potential components on occupation probability and find that the volume component leads to a uniform depletion of the hole states, while the surface component acts mainly to deplete the valence orbitals. We compare these results to those of a variational multiparticle multihole configuration mixing (mp-mh CM) calculation using the Gogny D1S effective force.

Conclusions: We find that the phenomenological DOM, which was originally designed for spherical nuclei, show certain deficiencies when applied to open-shell nuclei and suggest possible avenues of improvement. We also find that the predictions of occupation probability by the DOM using the dispersive surface component are similar to those by the mp-mh CM. This lends support to the interpretation that the surface absorption in the optical model originates from particle-vibration couplings, that is, long-range correlations.

We present additions to the MARTINI event generator for examining heavy quarks and quarkonia in heavy-ion collisions. All stages of a heavy-ion collision affect the observables associated with heavy quarks: the initial phase space of the heavy quarks are sampled with pythia8.1, the heavy quarks are evolved using Langevin dynamics and a 3+1-dimensional hydrodynamical description of the heavy-ion collision, and are fragmented and hadronized using a modified version of the color evaporation model that takes into account nontrivial evolution in position space, as well as the possibility of recombinant quarkonium production in heavy-ion collisions. We use this to re-examine the production of quarkonium at the Relativistic Heavy Ion Collider (RHIC), and anticipating vertex detection we predict yields of $B_c$ mesons at RHIC and the Large Hadron Collider.