The neutron-rich nucleus ${}^{112}$Rh has been reinvestigated by examining the prompt $\gamma$ rays emitted in the spontaneous fission of ${}^{252}$Cf with the Gammasphere detector array. A new side band was built in ${}^{112}$Rh. Total Routhian surface calculations have been performed and confirm the role of triaxiality in the negative-parity structure of ${}^{112}$Rh.

Based on the stochastic Langevin equation coupled with a statistical decay model, we study the effects of deformation on the accuracy of extracting saddle-to-scission friction ($\beta$) by analyzing prescission neutron yields measured in heavy compound nuclei ${}^{248}$Fm, ${}^{252}$Fm, ${}^{256}$Fm, and ${}^{251}$Es. It is shown that accounting for the effect can appreciably reduce the value of $\beta$ needed to fit data, and a friction value of (11–$13)\times {10}^{21}$ s${}^{-1}$ is obtained. Furthermore, we find that at low energy the sensitivity of light charged particles (LCPs) to $\beta$ almost disappears, but the sensitive dependence of neutrons and LCPs on friction is substantially enhanced with increasing excitation energy. Our findings suggest that to obtain precise information of saddle-to-scission nuclear dissipation with particle emission, besides taking into account deformation effects in theoretical calculations, in experiments it is best to populate heavy fissioning systems with high energy.

We apply the functional renormalization group to few-nucleon systems. Our starting point is a local effective action that includes three- and four-nucleon interactions, expressed in terms of nucleon and two-nucleon boson fields. The evolution of the coupling constants in this action is described by a renormalization group flow. We derive these flow equations both in the limit of exact Wigner SU(4) symmetry and in the realistic case of broken symmetry. In the symmetric limit we find that the renormalization flow equations decouple and can be combined into two sets, one of which matches the known results for bosons, and the other result matches the one for a single flavor of spin $1/2$ fermions. The equations show universal features in the unitary limit, which is obtained when the two-body scattering length tends to infinity. We calculate the spin-quartet neutron-deuteron scattering length and the deuteron-deuteron scattering lengths in the spin-singlet and spin-quintet channels.

We formulated the $\Lambda \left(1405\right)$ (abbreviated as ${\Lambda }^{*}$) $\to {\left(\Sigma \pi \right)}^0$ invariant-mass spectra produced in $p+p\to p+{\Lambda }^{*}+K^{+}$ reactions, in which both the incident channel for a quasibound $K^{-}p$ state and its decay process to ${\left(\Sigma \pi \right)}^0$ were taken into account realistically. We calculated $M\left(\Sigma \pi \right)$ spectral shapes for various theoretical models for ${\Lambda }^{*}$. These asymmetric and skewed shapes were then compared with recent experimental data of HADES, yielding $M\left({\Lambda }^{*}\right)={1405}_{-9}^{+11}$ MeV/$c^2$ and $\Gamma =62\pm 10$ MeV, where the interference effects of the $\overline{K}N$-$\Sigma \pi$ resonance with the $I=0$ and 1 $\Sigma \pi$ continuum are considered. The nearly isotropic proton distribution observed in DISTO and HADES is ascribed to a short collision length in the production of ${\Lambda }^{*}$, which justifies the high sticking mechanism of ${\Lambda }^{*}$ and the participating proton into $K^{-}pp$.

QCD sum rules using polynomial kernels are used to evaluate the strong part of the proton-neutron mass difference $\delta M_{np}$ in a model independent fashion. The result for the mass difference turns out to depend sensitively on the value of the four-quark condensate $\langle {\left(\overline{q}q\right)}^2\rangle$ and reproduces the experimental value of $\delta M_{np}$ for $\langle {\left(\overline{q}q\right)}^2\rangle \sim 2{\langle \overline{q}q\rangle }^2$.

We study the properties of the nuclear rotational excitations with hypothetical tetrahedral symmetry by employing the microscopic mean-field and residual-interaction Hamiltonians with angular-momentum and parity projection method; we focus on the deformed nuclei with tetrahedral doubly closed shell configurations. We find that for pure tetrahedral deformation the obtained excitation patterns satisfy the characteristic features predicted by group-representation theory applied to the tetrahedral symmetry group. We find that a gradual transition from the approximately linear to the characteristic rigid-rotor, parabolic energy-vs.-spin dependence occurs as a function of the tetrahedral deformation parameter. The form of this transition is compared with the similar well-known transition in the case of quadrupole deformation.

Neutrinoless double-$\beta$ decay is of fundamental importance for determining the neutrino mass. Although double electron decay is the most promising mode, in very recent years interest in double positron decay, positron emitting electron capture, and double electron capture has been renewed. We present here results of a calculation of nuclear matrix elements for neutrinoless double-${\beta }^{+}$ decay and positron emitting electron capture within the framework of the microscopic interacting boson model (IBM-2) for ${}^{58}$Ni, ${}^{64}$Zn, ${}^{78}$Kr, ${}^{96}$Ru, ${}^{106}$Cd, ${}^{124}$Xe, ${}^{130}$Ba, and ${}^{136}$Ce decay. By combining these with a calculation of phase space factors we calculate expected half-lives.

The question of isospin-symmetry breaking in nuclei of the $sd$ shell is addressed. We propose a new global parametrization of the isospin-nonconserving shell-model Hamiltonian which accurately describes experimentally known isobaric mass splittings. The isospin-symmetry violating part of the Hamiltonian consists of the Coulomb interaction and effective charge-dependent forces of nuclear origin. Particular attention has been paid to the effect of the short-range correlations. The behavior of $b$ and $c$ coefficients of the isobaric-mass-multiplet equation (IMME) is explored in detail. In particular, a high-precision numerical description of the staggering effect is proposed and contribution of the charge-dependent forces to the nuclear pairing is discussed. The Hamiltonian is applied to the study of the IMME beyond a quadratic form in the $A=32$ quintet, as well as to calculation of nuclear structure corrections to superallowed $0^{+}\to 0^{+}$ Fermi $\beta$ decay and to amplitudes of Fermi transitions to nonanalog states in $sd$-shell nuclei.

Background: Neutron-deficient krypton isotopes are of particular interest due to the coexistence of oblate and prolate shapes in low-lying states and the transition of the ground state from one dominate shape to another as a function of neutron number. Moreover, the onset of large $E2$ transition strength around ${}^{76}$Kr indicates the erosion of the $N=40$ subshell gap.

Purpose: A detailed interpretation of these phenomena in neutron-deficient Kr isotopes requires the use of a method going beyond a mean-field approach that permits the determination of spectra and transition probabilities. The aim of this work is to provide a systematic calculation of low-lying states in the even-even ${}^{68–86}$Kr isotopes and to understand the shape coexistence phenomenon and the onset of large collectivity around $N=40$ from beyond relativistic mean-field studies.

Method: The starting point of our method is a set of relativistic mean-field plus BCS wave functions generated with a constraint on triaxial deformations $(\beta ,\gamma )$. The excitation energies and electric multipole transition strengths of low-lying states are calculated by solving a five-dimensional collective Hamiltonian (5DCH) with parameters determined by the mean-field wave functions. To examine the role of triaxiality, a configuration mixing of both particle-number- and angular-momentum-projected axially deformed states is also carried out within the exact generator coordinate method based on the same energy density functional.

Results: The energy surfaces, the excitation energies of $0_2^{+}$, $2_1^{+}$, and $2_2^{+}$ states, as well as the $E0$ and $E2$ transition strengths are compared with the results of similar 5DCH calculations but with parameters determined by the nonrelativistic mean-field wave functions, as well as with the available data. The results show a picture of oblate-triaxial-prolate shape transition. Coexistence of low-lying excited $0^{+}$ states is found to be a common feature in the neutron-deficient Kr isotopes. The underlying mechanism responsible for the shape coexistence is discussed.

Conclusions: The main features of the low-spin spectra and the systematics of excitation energies and transition strengths in the neutron-deficient Kr isotopes are reproduced very well. The effects of dynamic correlations and triaxiality turn out to have important influences on the balance between the competing oblate and prolate states. An exact treatment of configuration mixing of particle-number- and angular-momentum-projected triaxial states is highly demanded to pin down these effects.

In this work we present an analysis of the yields of fission fragments induced by bremsstrahlung photons with endpoint energies of 50 and 3500 MeV on ${}^{232}$Th and ${}^{238}$U targets using the simulation code crisp. A multimodal fission option was added to this code and an extension of the calculation to the properties of the fission products is presented. By dividing the fissioning nuclei according to their fissionability, an approach is introduced which accounts for the contribution of symmetric and asymmetric fission. By adopting this procedure, it was possible to calculate the main parameters for the fission-fragment charge distribution such as the most-probable charge for a given fission product mass chain and its corresponding width parameter. Also, it was possible to reproduce features of fragment mass distribution and evaluate the fissility of fissioning nuclei for photon-induced fission of ${}^{232}$Th and ${}^{238}$U.

The discrete variable representation (DVR) basis is nearly optimal for numerically representing wave functions in nuclear physics: Suitable problems enjoy exponential convergence, yet the Hamiltonian remains sparse. We show that one can often use smaller basis sets than with the traditional harmonic oscillator basis, and still benefit from the simple analytic properties of the DVR bases which require no overlap integrals, simply permit using various Jacobi coordinates, and admit straightforward analyses of the ultraviolet and infrared convergence properties.

Background: Neutron-rich nuclei with protons in the $fp$ shell show an onset of collectivity around $N=40$. Spectroscopic information is required to understand the underlying mechanism and to determine the relevant terms of the nucleon-nucleon interaction that are responsible for the evolution of the shell structure in this mass region.

Methods: We report on the lifetime measurement of the first 2${}^{+}$ and 4${}^{+}$ states in ${}^{70,72,74}$Zn and the first 6${}^{+}$ state in ${}^{72}$Zn using the recoil distance Doppler shift method. The experiment was carried out at the INFN Laboratory of Legnaro with the AGATA demonstrator, first phase of the Advanced Gamma Tracking Array of highly segmented, high-purity germanium detectors coupled to the PRISMA magnetic spectrometer. The excited states of the nuclei of interest were populated in the deep inelastic scattering of a ${}^{76}$Ge beam impinging on a ${}^{238}$U target.

Results: The maximum of collectivity along the chain of Zn isotopes is observed for ${}^{72}$Zn at $N=42$. An unexpectedly long lifetime of 20${}_{-5.2}^{+1.8}$ ps was measured for the 4${}^{+}$ state in ${}^{74}$Zn.

Conclusions: Our results lead to small values of the $B(E2;4_1^{+}\to 2_1^{+})/B(E2;2_1^{+}\to 0_1^{+})$ ratio for ${}^{72,74}$Zn, suggesting a significant noncollective contribution to these excitations. These experimental results are not reproduced by state-of-the-art microscopic models and call for lifetime measurements beyond the first 2${}^{+}$ state in heavy zinc and nickel isotopes.

Background: Heavy atomic nuclei are often described using the Hartree-Fock-Bogoliubov (HFB) method. In principle, this approach takes into account Pauli effects and pairing correlations while other correlation effects are mimicked through the use of effective density-dependent interactions.

Purpose: Investigate the influence of higher-order correlation effects on nuclear binding energies using Skyrme's effective interaction.

Methods: A cutoff in relative momenta is introduced to remove ultraviolet divergencies caused by the zero-range character of the interaction. Corrections to binding energies are then calculated using the quasiparticle-random-phase approximation and second-order many-body perturbation theory.

Result: Contributions to the correlation energies are evaluated for several isotopic chains and an attempt is made to disentangle which parts give rise to fluctuations that may be difficult to incorporate on the HFB level. The dependence of the results on the cutoff is also investigated.

Conclusions: The improved interaction allows explicit summations of perturbation series, which is useful for the description of some nuclear observables. However, refits of the interaction parameters are needed to obtain more quantitative results.

Cascades of $\gamma$-ray transitions in ${}^{112}$Cd and ${}^{114}$Cd have been studied in a neutron-capture experiment at the Los Alamos Neutron Science Center using a highly segmented and highly efficient $\gamma$-ray calorimeter—Detector for Advanced Neutron Capture Experiments. Intensity distributions of two-, three-, and multifold coincidence $\gamma$-ray transitions de-exciting resonances with known angular momenta and terminating at the ground state and at the first excited levels have been obtained. The results are compared with statistical-model calculations using the code dicebox for the two theoretical models of electric-dipole photon-strength functions, the standard Lorentzian and the model of Kadmenskii, Markushev, and Furman. It has been found that a combination of the two models reproduces the data best. Adding resonance structures, such as the scissors mode and the pygmy resonance, to the photon-strength function do not improve the description of the $\gamma$-ray spectra.

We present a strategy to extract the position of the two $\Lambda \left(1405\right)$ poles from experimental photoproduction data measured recently at different energies in the $\gamma p\to K^{+}{\pi }^0{\Sigma }^0$ reaction at Jefferson Laboratory. By means of a chiral dynamics motivated potential with free parameters, we solve the Bethe-Salpeter equation in the coupled channels $\overline{K}N$ and $\pi \Sigma$ in isospin $I=0$ and parametrize the amplitude for the photonuclear reaction in terms of a linear combination of the $\pi \Sigma \to \pi \Sigma$ and $\overline{K}N\to \pi \Sigma$ scattering amplitudes in $I=0$, with a different linear combination for each energy. Good fits to the data are obtained with some sets of parameters, by means of which one can also predict the cross section for the $K^{-}p\to {\pi }^0{\Sigma }^0$ reaction. These later results help us decide among the possible solutions. The result is that the different solutions lead to two poles similar to those found in the chiral unitary approach. With the best result we find the two $\Lambda \left(1405\right)$ poles at $1385-68i\text{MeV}$ and $1419-22i\text{MeV}$.

A comment on the paper by Deepika Choudhury et al. [Phys. Rev. C 82, 061308(R) (2010)].

The structure of ${}^{10}$Be was studied via resonant $\alpha$-particle scattering of a neutron-rich ${}^6$He beam. A time projection chamber, PAT-TPC, was operated in an active-target mode to provide a gaseous ${}^4$He target and trace the beam and reaction products traversing its active tracking volume. This significantly lowered the detection threshold of reaction products at low energies. Elastic scattering, inelastic scattering to the ${}^6$He 2${}^{+}$ state, and the ${}^6$He($\alpha$, 2$n$)${}^8$Be reaction were measured below an energy of 6 MeV in the center-of-mass frame. Continuous spectra of excitation functions and angular distributions were obtained from unambiguously-identified recoiling $\alpha$ particles for the elastic and inelastic channels. While a resonance of the 4${}^{+}$ state at 10.15 MeV in ${}^{10}$Be previously reported was confirmed, no other resonances were identified in the elastic channel over the measured energy region. The results are in line with antisymmetric molecular dynamics calculations that predict the limits of $\alpha$ clustering in high-spin states due to a spin-orbit force.

Using the well-established wave function of ${}^{12}$Be(g.s.), I have estimated the cross-section ratio for the reaction ${}^{12}$Be(p,t) populating the ground-state and first excited 0${}^{+}$ state of ${}^{10}$Be. I find that the excited-state to ground-state ratio is small for any reasonable value of configuration mixing in ${}^{10}$Be.

Relativistic dissipative fluid dynamics is a common tool to describe the space-time evolution of the strongly interacting matter created in ultrarelativistic heavy-ion collisions. For a proper comparison to experimental data, fluid-dynamical calculations have to be performed on an event-by-event basis. Therefore, fluid dynamics should be able to reproduce, not only the event-averaged momentum anisotropies, $\langle v_n\rangle$, but also their distributions. In this paper, we investigate the event-by-event distributions of the initial-state and momentum anisotropies ${\epsilon }_n$ and $v_n$, and their correlations. We demonstrate that the event-by-event distributions of relative $v_n$ fluctuations are almost equal to the event-by-event distributions of corresponding ${\epsilon }_n$ fluctuations, allowing experimental determination of the relative anisotropy fluctuations of the initial state. Furthermore, the correlation $c(v_2,v_4)$ turns out to be sensitive to the viscosity of the fluid providing an additional constraint to the properties of the strongly interacting matter.