The energy of a free gas of neutrons and protons is well known to be approximately isospin parabolic with a negligibly small quartic term of only $0.45$ MeV at the saturation density of nuclear matter ${\rho }_0=0.16{\mathrm{fm}}^{-3}$. Using an isospin-dependent single-nucleon momentum distribution including a high (low) momentum tail (depletion) with its shape parameters constrained by recent high-energy electron scattering and medium-energy nuclear photodisintegration experiments as well as the state-of-the-art calculations of the deuteron wave function and the equation of state of pure neutron matter near the unitary limit within several modern microscopic many-body theories, we show for the first time that the kinetic energy of interacting nucleons in neutron-rich nucleonic matter has a significant quartic term of $7.18\pm 2.52$ MeV. Such a large quartic term has broad ramifications in determining the equation of state of neutron-rich nucleonic matter using observables of nuclear reactions and neutron stars.

The nonmesonic weak decay of double-$\mathrm{\Lambda }$ hypernuclei is studied within a microscopic diagrammatic approach. In addition to the nucleon-induced mechanism, $\mathrm{\Lambda }N\to nN$ and $\mathrm{\Lambda }NN\to nNN$, widely studied in single-$\mathrm{\Lambda }$ hypernuclei, additional hyperon-induced mechanisms, $\mathrm{\Lambda }\mathrm{\Lambda }\to \mathrm{\Lambda }n$, $\mathrm{\Lambda }\mathrm{\Lambda }\to {\mathrm{\Sigma }}^{0}n$, and $\mathrm{\Lambda }\mathrm{\Lambda }\to {\mathrm{\Sigma }}^{-}p$, are accessible in double-$\mathrm{\Lambda }$ hypernuclei and are investigated here. As in previous works on single-$\mathrm{\Lambda }$ hypernuclei, we adopt a nuclear matter formalism extended to finite nuclei via the local density approximation and a one-meson exchange weak transition potential (including the ground-state pseudoscalar and vector octets mesons) supplemented by correlated and uncorrelated two-pion-exchange contributions. The weak decay rates are evaluated for hypernuclei in the region of the experimentally accessible light hypernuclei ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^{10}\mathrm{Be}$ and ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^{13}\mathrm{B}$. Our predictions are compared with a few previous evaluations. The rate for the $\mathrm{\Lambda }\mathrm{\Lambda }\to \mathrm{\Lambda }n$ decay is dominated by $K$-, $K^{*}$-, and $\eta$-exchange and turns out to be about 2.5% of the free $\mathrm{\Lambda }$ decay rate, ${\mathrm{\Gamma }}_{\mathrm{\Lambda }}^{\mathrm{free}}$, while the total rate for the $\mathrm{\Lambda }\mathrm{\Lambda }\to {\mathrm{\Sigma }}^{0}n$ and $\mathrm{\Lambda }\mathrm{\Lambda }\to {\mathrm{\Sigma }}^{-}p$ decays, dominated by $\pi$-exchange, amounts to about 0.25% of ${\mathrm{\Gamma }}_{\mathrm{\Lambda }}^{\mathrm{free}}$. The experimental measurement of these decays would be essential for the beginning of a systematic study of the nonmesonic decay of strangeness $-2$ hypernuclei. This field of research could also shed light on the possible existence and nature of the $H$ dibaryon.

Background: The relativistic Hartree-Fock-Bogoliubov (RHFB) theory has recently been developed and it provides a unified and highly predictive description of both nuclear mean-field and pairing correlations. Ground-state properties of finite nuclei can accurately be reproduced without neglecting exchange (Fock) contributions.

Purpose: Finite-temperature RHFB (FT-RHFB) theory has not yet been developed, leaving yet unknown its predictions for phase transitions and thermal excitations in both stable and weakly bound nuclei.

Method: FT-RHFB equations are solved in a Dirac Woods-Saxon (DWS) basis considering two kinds of pairing interactions: finite or zero range. Such a model is appropriate for describing stable as well as loosely bound nuclei since the basis states have correct asymptotic behavior for large spatial distributions.

Results: Systematic FT-RH(F)B calculations are performed for several semimagic isotopic/isotonic chains comparing the predictions of a large number of Lagrangians, among which are PKA1, PKO1, and DD-ME2. It is found that the critical temperature for a pairing transition generally follows the rule $T_c=0.60\mathrm{\Delta }\left(0\right)$ for a finite-range pairing force and $T_c=0.57\mathrm{\Delta }\left(0\right)$ for a contact pairing force, where $\mathrm{\Delta }\left(0\right)$ is the pairing gap at zero temperature. Two types of pairing persistence are analyzed: type I pairing persistence occurs in closed subshell nuclei while type II pairing persistence can occur in loosely bound nuclei strongly coupled to the continuum states.

Conclusions: This FT-RHFB calculation shows very interesting features of the pairing correlations at finite temperature and in finite systems such as pairing re-entrance and pairing persistence.

Within the quantum diffusion approach, the capture process of a projectile nucleus by a target nucleus is studied at bombarding energies above and below the Coulomb barrier. The entrance channel effects on the partial and total capture cross sections and the mean angular momentum of the captured system are studied in the reactions leading to ${}^{156,160}\mathrm{Er}$, ${}^{170}\mathrm{Hf}$, ${}^{200}\mathrm{Pb}$, ${}^{216}\mathrm{Ra}$, and ${}^{220}\mathrm{Th}$ compound nuclei.

We analyze the accumulation of ultracold neutrons (UCNs) in a superfluid-helium converter vessel surrounded by a magnetic multipole reflector. We solved the spin-dependent rate equation, employing formulas valid for adiabatic spin transport of trapped UCNs in mechanical equilibrium. Results for saturation UCN densities are obtained in dependence of order and strength of the multipolar field. The addition of magnetic storage to neutron optical potentials can increase the density and energy of the low-field-seeking UCNs produced and serves to mitigate the effects of wall losses on the source performance. It also can provide a highly polarized sample of UCNs without need to polarize the neutron beam incident on the converter. This work was performed in preparation of the UCN source project SuperSUN at the Institut Laue–Langevin.

The center of the predicted island of stability of superheavy nuclei (SHN) has not yet been observed experimentally. Many theories are being developed to understand the synthesizing mechanism of superheavy nuclei. However, all of them have to use some basic nuclear data. Three data tables, FRDM1995 [P. Möller et al., At. Data Nucl. Data Tables 59, 185 (1995)], KTUY2005 [H. Koura et al., Prog. Theor. Phys. 113, 305 (2005)], and WS2010 [Ning Wang et al., Phys. Rev. C 82, 044304 (2010)], are used to investigate the SHN production. Based on the dinuclear system concept, the evaporation residue cross sections of SHN for $Z$=112–118 are calculated for the ${}^{48}\mathrm{Ca}$-induced hot fusion reactions. It turns out that unlike the predictions made with the KTUY2005 and WS2010 data, the magic numbers $Z$=114 and $N$=184 predicted with the FRDM1995 data do not contradict the experimental data obtained so far.

The updated data for the ground-state-to-ground-state $\alpha$-transition half-lives in 401 nuclei and the $\alpha$-capture cross sections of ${}^{40}\mathrm{Ca},{}^{44}\mathrm{Ca},{}^{59}\mathrm{Co},{}^{208}\mathrm{Pb},$ and ${}^{209}\mathrm{Bi}$ are well described in the framework of the unified model for $\alpha$ decay and $\alpha$ capture. The updated values of the $\alpha$-decay half-lives, the binding energies of nuclei, the spins of parent and daughter nuclei, and the surface deformation parameters are used for the reevaluation of the model parameters. The data for the ground-state-to-ground-state $\alpha$-decay half-lives are also well described by the empirical relationships.

Shell-model calculations of $B\left(E2\right)$'s and quadrupole moments in the even-even nuclei in the $g_{9/2}$ shell region below ${}^{100}\mathrm{Sn}$ are hampered by the fact that the inclusion of the $g_{7/2}$ configuration will lead to model spaces that are too large to handle. Understanding the impact of specific orbit wave functions in large-scale shell-model (LSSM) calculations helps to shed light on the validity of the results that are obtained. We therefore examine lighter nuclei in the beginning of the $fp$ region where one can normally include all the orbitals, $f_{7/2},p_{3/2},p_{1/2}$, and $f_{5/2}$, for both protons and neutrons. We perform such calculations but then take a step back and exclude the $f_{5/2}$ orbital. By comparing the results of the two calculations we can hope to get insight into the importance of the missing spin-orbital partner in other regions.

Excitation functions for $\gamma$ production associated with the neutron inelastic scattering and the $(n, 2n)$ reactions on ${}^{206}\mathrm{Pb}$ were measured from threshold up to 18 MeV for about 40 transitions. Two independent measurements were performed using different samples and acquisition systems to check consistency of the results. The neutron flux was determined with a ${}^{235}\mathrm{U}$ fission chamber and a procedure that were validated against a fluence standard. For incident energy higher than the threshold for the first excited level and up to 3.5 MeV, estimates are provided for the total inelastic and level cross sections by combining the present $\gamma$ production cross sections with the level and decay data of ${}^{206}\mathrm{Pb}$ reported in the literature. The uncertainty common to all incident energies is 3.0% allowing overall uncertainties from 3.3% to 30% depending on transition and neutron energy. The present data agree well with earlier work, but significantly expand the experimental database while comparisons with model calculations using the talys reaction code show good agreement over the full energy range.

The ${}^{17}\text{O}(p,\alpha ){}^{14}\text{N}$ and ${}^{17}\text{O}(p,\gamma ){}^{18}\text{F}$ reactions are of paramount importance for the nucleosynthesis in a number of stellar sites, including red giants (RGs), asymptotic giant branch (AGB) stars, massive stars, and classical novae. In particular, they govern the destruction of ${}^{17}\text{O}$ and the formation of the short-lived radioisotope ${}^{18}\text{F}$, which is of special interest for $\gamma$-ray astronomy. At temperatures typical of the above-mentioned astrophysical scenario, $T=0.01$–0.1 GK for RG, AGB, and massive stars and $T=0.1$–0.4 GK for a classical nova explosion, the ${}^{17}\text{O}(p,\alpha ){}^{14}\text{N}$ reaction cross section is dominated by two resonances: one at about $E_R^{cm}=65$ keV above the ${}^{18}\text{F}$ proton threshold energy, corresponding to the $E_X=5.673$ MeV level in ${}^{18}\text{F}$, and another one at $E_R^{cm}=183$ keV $(E_X=5.786$ MeV). We report on the indirect study of the ${}^{17}\text{O}(p,\alpha ){}^{14}\text{N}$ reaction via the Trojan Horse method by applying the approach recently developed for extracting the strength of narrow resonance at ultralow energies. The mean value of the strengths obtained in the two measurements was calculated and compared with the direct data available in literature. This value was used as input parameter for reaction-rate determination and its comparison with the result of the direct measurement is also discussed in the light of the electron screening effect.

The decay widths of the $d^{*}\to d{\pi }^0{\pi }^0$ and $d^{*}\to d{\pi }^{+}{\pi }^{-}$ processes are explicitly calculated in terms of our chiral quark model. By using the experimental ratios of cross sections between various decay channels, the partial widths of the $d^{*}\to pn{\pi }^0{\pi }^0,d^{*}\to pn{\pi }^{+}{\pi }^{-},d^{*}\to pp{\pi }^0{\pi }^{-}$, and $d^{*}\to nn{\pi }^{+}{\pi }^0$ channels are also extracted. Further including the estimated partial width for the $d^{*}\to pn$ process, the total width of the $d^{*}$ resonance is obtained. In the first step of the practical calculation, the effect of the dynamical structure on the width of $d^{*}$ is studied in the single $\mathrm{\Delta }\mathrm{\Delta }$ channel approximation. It is found that the width is reduced by a few tens of MeV, in comparison with the one obtained by considering the effect of the kinematics only. This presents the importance of such an effect from the dynamical structure. However, the obtained width with the single $\mathrm{\Delta }\mathrm{\Delta }$ channel wave function is still too large to explain the data. It implies that the $d^{*}$ resonance will not consist of the $\mathrm{\Delta }\mathrm{\Delta }$ structure only, and instead there should be enough room for other structures such as the hidden-color (CC) component. Thus, in the second step, the width of $d^{*}$ is further evaluated by using a wave function obtained in the coupled $\mathrm{\Delta }\mathrm{\Delta }$ and CC channel calculation in the framework of the resonating group method (RGM). It is shown that the resultant total width for $d^{*}$ is about 69 MeV, which is compatible with the experimental observation of about 75 MeV and justifies our assertion that the $d^{*}$ resonance is a hexaquark-dominated exotic state.

High-spin states of the semimagic nucleus ${}^{141}\mathrm{Pr}$ have been investigated by in-beam $\gamma$-spectroscopic techniques using the fusion-evaporation ${}^{138}\mathrm{Ba}({}^7\mathrm{Li},4n)$ reaction at a beam energy of 38 MeV. The level scheme of ${}^{141}\mathrm{Pr}$ has been extended up to $\sim 6.2$ MeV in excitation energy and $35/2 \hslash$ in spin. A total of 14 new levels and 30 new transitions have been assigned to ${}^{141}\mathrm{Pr}$ on the basis of $\gamma \text{−}\gamma$ coincidence information. The observed level structures are discussed in light of the available experimental data and shell model calculations with the oxbash code. According to the calculations, most of the observed levels of ${}^{141}\mathrm{Pr}$ are from the proton excitations above the $Z=50$ shell. Possible evidence for the neutron excitations across the $N=82$ gap in ${}^{141}\mathrm{Pr}$ is also discussed and compared with other $N=82$ isotones.

Background: Ab initio many-body methods have been developed over the past 10 yr to address closed-shell nuclei up to mass $A\approx 130$ on the basis of realistic two- and three-nucleon interactions. A current frontier relates to the extension of those many-body methods to the description of open-shell nuclei. Several routes to address open-shell nuclei are currently under investigation, including ideas that exploit spontaneous symmetry breaking.

Purpose: Singly open-shell nuclei can be efficiently described via the sole breaking of U(1) gauge symmetry associated with particle-number conservation as a way to account for their superfluid character. While this route was recently followed within the framework of self-consistent Green's function theory, the goal of the present work is to formulate a similar extension within the framework of coupled cluster theory.

Methods: We formulate and apply Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-state wave function of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the ground-state energy and the cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes three-nucleon forces at the normal-ordered two-body level. The first BCC code is implemented in $m$ scheme, which will permit the treatment of doubly open-shell nuclei via the further breaking of SU(2) symmetry associated with angular momentum conservation.

Results: Proof-of-principle calculations in an $N_{\text{max}}=6$ spherical harmonic oscillator basis for ${}^{16,18}\mathrm{O}$ and ${}^{18}\mathrm{Ne}$ in the BCCD approximation are in good agreement with standard coupled cluster results with the same chiral two-nucleon interaction, while ${}^{20}\mathrm{O}$ and ${}^{20}\mathrm{Mg}$ display underbinding relative to experiment. The breaking of U(1) symmetry, monitored by computing the variance associated with the particle-number operator, is relatively constant for all five nuclei, in both the Hartree-Fock-Bogoliubov and BCCD approximations.

Conclusions: The newly developed many-body formalism increases the potential span of ab initio calculations based on single-reference coupled cluster techniques tremendously, i.e., potentially to reach several hundred additional midmass nuclei. The new formalism offers a wealth of potential applications and further extensions dedicated to the description of ground and excited states of open-shell nuclei. Short-term goals include the implementation of three-nucleon forces at the normal-ordered two-body level. Midterm extensions include the approximate treatment of triples corrections and the development of the equation-of-motion methodology to treat both excited states and odd nuclei. Long-term extensions include exact restoration of U(1) and SU(2) symmetries.

Previous measurements of a quadrupole component of azimuth correlations denoted by symbol $v_2$ have been interpreted to represent elliptic flow, a hydrodynamic phenomenon conjectured to play a major role in noncentral nucleus-nucleus collisions. $v_2$ measurements provide the main support for conclusions that a “perfect liquid” is formed in heavy-ion collisions at the Relativistic Heavy Ion Collider. However, conventional $v_2$ methods based on one-dimensional (1D) azimuth correlations give inconsistent results and may include a jet contribution. In some cases the data trends appear to be inconsistent with hydrodynamic interpretations. In this study we distinguish several components of 2D angular correlations and isolate a nonjet (NJ) azimuth quadrupole denoted by $v_2\left\{\text{2D}\right\}$. We establish systematic variations of the NJ quadrupole on $y_t$, centrality, and collision energy. We adopt transverse-rapidity $y_t$ as both a velocity measure and a logarithmic alternative to transverse momentum $p_t$. Based on NJ-quadrupole trends, we derive a completely factorized universal parametrization of quantity $v_2\left\{\text{2D}\right\}(y_t,b,\sqrt{s_{NN}})$ which describes the centrality, $y_t$, and energy dependence. From $y_t$-differential $v_2\left(y_t\right)$ data we isolate a quadrupole spectrum and infer a quadrupole source boost having unexpected properties. NJ quadrupole $v_2$ trends obtained with 2D model fits are remarkably simple. The centrality trend appears to be uncorrelated with a sharp transition in jet-related structure that may indicate rapid change of Au-Au medium properties. The lack of correspondence suggests that the NJ quadrupole may be insensitive to such a medium. Several quadrupole trends have interesting implications for hydro interpretations.

To study the Gamow-Teller (GT) transitions from the $T_z=+1$ nucleus ${}^{42}\text{Ca}$ to the $T_z=0$ nucleus ${}^{42}\text{Sc}$, where $T_z$ is the $z$ component of isospin $T$, we performed a ($p,n$)-type $({}^3\text{He},t)$ charge-exchange reaction at 140 MeV/nucleon and scattering angles around $0^{\circ }$. With an energy resolution of 29 keV, states excited by GT transitions (GT states) could be studied accurately. The reduced GT transition strengths $B\left(\text{GT}\right)$ were derived up to the excitation energy of 13 MeV, assuming the proportionality between the cross sections at $0^{\circ }$ and $B\left(\text{GT}\right)$ values. The main part of the observed GT transition strength is concentrated in the lowest 0.611-MeV, $J^{\pi }=1^{+}$ GT state. All the other states at higher energies are weakly excited. Shell-model calculations could reproduce the gross feature of the experimental $B\left(\text{GT}\right)$ distribution, and random-phase-approximation calculations including an attractive isoscalar interaction showed that the 0.611-MeV state has a collective nature. It was found that this state has all of the properties of a “low-energy super-Gamow-Teller state.” It is expected that low-lying $J^{\pi }=1^{+}$ GT states have $T=0$ in the $T_z=0$ nucleus ${}^{42}\text{Sc}$. However, $T=1$ states are situated in a higher energy region. Assuming an isospin-analogous structure in $A=42$ isobars, analogous $T=1, 1^{+}$ states are also expected in ${}^{42}\text{Ca}$. Comparing the ${}^{42}\text{Ca}({}^3\text{He},t){}^{42}\text{Sc}$ and ${}^{42}\text{Ca}(p,p^{\prime })$ spectra measured at $0^{\circ }$, candidates for $T=1$ GT states could be found in the $10–12-\mathrm{MeV}$ region of ${}^{42}\text{Sc}$. They were all weakly excited. The mass dependence of the GT strength distributions in Sc isotopes is also discussed.

The $\beta$ decay of ${}^{82}\mathrm{Ge}$ was re-investigated using the newly commissioned tape station BEDO at the electron-driven ISOL (isotope separation on line) facility ALTO operated by the Institut de Physique Nucléaire, Orsay. The original motivation of this work was focused on the sudden occurrence in the light $N=49$ odd-odd isotonic chain of a large number of $J\le 1$ states (positive or negative parity) in ${}^{80}\mathrm{Ga}$ by providing a reliable intermediate example, viz., ${}^{82}\mathrm{As}$. The extension of the ${}^{82}\mathrm{As}$ level scheme towards higher energies from the present work has revealed three potential $1^{+}$ states above the already known one at 1092 keV. In addition our data allow ruling out the hypothesis that the 843 keV level could be a $1^{+}$ state. A detailed analysis of the level scheme using both an empirical core-particle coupling model and a fully microscopic treatment within a Skyrme-QRPA (quasiparticle random-phase approximation) approach using the finite-rank separable approximation was performed. From this analysis two conclusions can be drawn: (i) the presence of a large number of low-lying low-spin negative parity states is due to intruder states stemming from above the $N=50$ shell closure, and (ii) the sudden increase, from ${}^{82}\mathrm{As}$ to ${}^{80}\mathrm{Ga}$, of the number of low-lying $1^{+}$ states and the corresponding Gamow-Teller fragmentation are naturally reproduced by the inclusion of tensor correlations and couplings to 2p-2h excitations.

We analyze the role of maximally aligned isoscalar pairs in heavy $N=Z$ nuclei by employing a formalism of quartets. Quartets are superpositions of two neutrons and two protons coupled to total isospin $T=0$ and given $J$. The study is focused on the contribution of spin-aligned pairs carrying the angular momentum $J=9$ to the structure of ${}^{96}\mathrm{Cd}$ and ${}^{92}\mathrm{Pd}$. We show that the role played by the $J=9$ pairs is quite sensitive to the model space and, in particular, it decreases considerably by passing from the simple $0g_{9/2}$ space to the more complete $1p_{1/2},1p_{3/2},0f_{5/2},0g_{9/2}$ space. In the latter case the description of these nuclei in terms of only spin-aligned $J=9$ pairs turns out to be unsatisfactory while an important contribution, particularly in the ground state, is seen to arise from isovector $J=0$ and isoscalar $J=1$ pairs. Thus, contrary to previous studies, we find no compelling evidence of a spin-aligned pairing phase in ${}^{92}\mathrm{Pd}$.

The spatial structures of the chiral symmetry $\text{breaking}\left(\chi \mathrm{SB}\right)-\text{quark}-\mathrm{antiquark}\left(q\overline{q}\right)$ pair and two-color $\text{superconducting(2SC)}-\text{quark}-\mathrm{quark}\left(qq\right)$, $\text{antiquark}-\mathrm{antiquark}\left(\overline{q}\overline{q}\right)$, and $\text{hole}-\mathrm{hole}\left(hh\right)$ pairs are investigated. At low density, it is found that the $q\overline{q}$ pair is well localized with average bond length of the order $1\mathrm{fm}$. It is then suggested that the pions, which are excitations arising from flavor-space phase fluctuations, exhibit the spatial structure of the underlying $q\overline{q}$-paired ground state. At intermediate density where the quarks form a 2SC state, it is found that the $qq$ and $hh$ pairs are extended and oscillating in real space while the $\overline{q}\overline{q}$ pair remains well localized.

The two fragments produced in fission reactions induced by ${}^{208}\mathrm{Pb}$ projectiles impinging on a liquid hydrogen target at $500A\mathrm{MeV}$ have been fully identified in coincidence. The experiment was performed at GSI Darmstadt, where the combined use of the inverse kinematics technique with an efficient detection setup permitted one to detect and to fully identify the fission fragments in a range from $Z=27$ to $Z=52$. The corresponding isotopic cross sections and velocities of the fission fragments were measured with high accuracy. The results are compared to state-of-the-art model calculations that reproduce the measured observables. Correlations between the two fragments were used to assess the role of charge polarization and the excitation energy gained by the nascent fragments using the neutron excess of the final fragments. The analysis of the average velocities of the fission fragments allowed us to parametrize the distance between the two fission fragments at scission as a function of the size of the fissioning system.