Relativistic energy density functionals (REDF) provide a complete and accurate global description of nuclear structure phenomena. A modern semiempirical functional, adjusted to the nuclear matter equation of state and to empirical masses of deformed nuclei, is applied to studies of shapes of superheavy nuclei. The theoretical framework is tested in a comparison of calculated masses, quadrupole deformations, and potential energy barriers to available data on actinide isotopes. Self-consistent mean-field calculations predict a variety of spherical, axial, and triaxial shapes of long-lived superheavy nuclei, and their $\alpha$-decay energies and half-lives are compared to data. A microscopic, REDF-based, quadrupole collective Hamiltonian model is used to study the effect of explicit treatment of collective correlations in the calculation of $Q_{\alpha }$ values and half-lives.

We study the Li isotopes systematically in terms of the tensor-optimized shell model (TOSM) by using a bare nucleon-nucleon interaction as the AV8${}^{\prime }$ interaction. The short-range correlation is treated in the unitary correlation operator method (UCOM). Using the TOSM + UCOM approach, we investigate the role of the tensor force on each spectrum of the Li isotopes. It is found that the tensor force produces quite a characteristic effect on various states in each spectrum and those spectra are affected considerably by the tensor force. The energy difference between the spin-orbit partner, the $p_{1/2}$ and $p_{3/2}$ orbits of the last neutron, in ${}^5$Li is caused by opposite roles of the tensor correlation. In ${}^6$Li, the spin-triplet state in the $LS$ coupling configuration is favored energetically by the tensor force in comparison with $jj$ coupling shell-model states. In ${}^{7,8,9}$Li, the low-lying states containing extra neutrons in the $p_{3/2}$ orbit are favored energetically due to the large tensor contribution to allow the excitation from the $0s$, orbit to the $p_{1/2}$ orbit by the tensor force. Those three nuclei show the $jj$ coupling character in their ground states which is different from ${}^6$Li.

Background: Shape phase transitions in finite quantal systems are very interesting phenomena of general physical interest. There is a very restricted number of the examples of nuclei demonstrating this phenomenon.

Purpose: Based on experimental excitation spectra, there is a second order phase transition in the alternating parity bands of some actinide nuclei.

Method: The mathematical techniques of supersymmetric quantum mechanics, two-center octupole wave functions ansatz, and the Landau theory of phase transitions are used to analyze the experimental data on alternating parity bands.

Results: The potential energy of the octupole collective motion is determined and analyzed for all observed values of the angular momentum of the alternating parity band states in ${}^{232}$Th, ${}^{238}$U, and ${}^{240}$Pu.

Conclusion: It is shown that as a function of increasing angular momentum there is a second order phase transition from the octupole-nondeformed to the octupole-deformed shape in the considered nuclei.

Excited states up to $J^{\pi }={11}^{-}$ at 10 296 keV and $J^{\pi }={10}^{+}$ at 10 707 keV have been populated in the odd-odd ${}^{36}$Cl nucleus using the ${}^{24}\text{Mg}{(}^{14}\text{N},2p)$ fusion-evaporation reaction at $E_{\text{lab}}=31$ MeV. Twenty new states and 62 new $\gamma$ transitions have been identified by employing $\gamma$-$\gamma$ and $\gamma$-$\gamma$-$\gamma$ coincidences. Lifetimes have been investigated by the Doppler shift attenuation method. The experimental data have been compared with the results of large-scale shell-model calculations performed using different effective interactions and model spaces allowing particle-hole excitations across the $N=Z=20$ shell gap.

Neutrino-nucleus coherent elastic scattering provides a theoretically appealing way to measure the neutron part of nuclear form factors. Using an expansion of form factors into moments, we show that neutrinos from stopped pions can probe not only the second moment of the form factor (the neutron radius) but also the fourth moment. Using simple Monte Carlo techniques for argon, germanium, and xenon detectors of 3.5 tonnes, 1.5 tonnes, and 300 kg, respectively, we show that the neutron radii can be found with an uncertainty of a few percent when near a neutrino flux of $3\times {10}^7$ neutrinos/(cm${}^2$ s). If the normalization of the neutrino flux is known independently, one can determine the moments accurately enough to discriminate among the predictions of various nuclear energy functionals.

A systematic study on α-decay fine structure of odd-odd nuclei in the region 83 ≤ $Z$ ≤ 101 has been done using the recently proposed Coulomb and proximity potential model for deformed nuclei (CPPMDN). The computed partial half-lives, total half-lives, and branching ratios are compared with the experimental data and they are in good agreement. We have modified the assault frequency and redetermined the half-lives and they show better agreement with the experimental value. Using the new assault frequency, the standard deviations for the half-life and branching ratio are found to be 0.997 and 1.07, respectively, and this implies that CPPMDN is apt for α-decay fine-structure study for an entire range of nuclei.

We discuss opportunities that may arise from subjecting high-multiplicity events in relativistic heavy ion collisions to an analysis similar to the one used in cosmology for the study of fluctuations of the cosmic microwave background (CMB). To this end, we discuss examples of how pertinent features of heavy ion collisions including global characteristics, signatures of collective flow, and event-wise fluctuations are visually represented in a Mollweide projection commonly used in CMB analysis, and how they are statistically analyzed in an expansion over spherical harmonic functions. If applied to the characterization of purely azimuthal dependent phenomena such as collective flow, the expansion coefficients of spherical harmonics are seen to contain redundancies compared to the set of harmonic flow coefficients commonly used in heavy ion collisions. Our exploratory study indicates, however, that these redundancies may offer novel opportunities for a detailed characterization of those event-wise fluctuations that remain after subtraction of the dominant collective flow signatures. By construction, the proposed approach allows also for the characterization of more complex collective phenomena like higher-order flow and other sources of fluctuations, and it may be extended to the characterization of phenomena of noncollective origin such as jets.

We investigate the possible thermodynamic instability in a warm and dense nuclear medium ($T⩽50$ MeV and ${\rho }_0⩽{\rho }_B⩽3{\rho }_0$) where a phase transition from nucleonic matter to resonance-dominated $\Delta$ matter can take place. The analysis is performed by requiring the global conservation of baryon and electric charge numbers in the framework of a relativistic equation of state. Similarly to the liquid-gas phase transition, we show that the nucleon-$\Delta$ matter phase transition is characterized by both mechanical instability (fluctuations on the baryon density) and by chemical-diffusive instability (fluctuations on the charge concentration) in asymmetric nuclear matter. We then perform an investigation and a comparative study on the different nature of such instabilities and phase transitions.

The dependence of the differential cross section and polarization observables in the $\overline{p}+p\to {\pi }^0+e^{+}+e^{-}$ reaction on the polarizations of the proton target and antiproton beam (the produced electron may be unpolarized or longitudinally polarized) have been derived in a general form using hadron electromagnetic current conservation and $P$-parity invariance of the hadron electromagnetic interaction. The analysis was done for the case of an exclusive experimental setup where the produced electron and pion are detected in coincidence. The explicit dependence of all polarization observables on two, from five, kinematic variables (the azimuthal angle $\varphi$ and the virtual-photon parameter $\epsilon$) have been obtained assuming one-photon exchange. The application to the particular case of a mechanism which contains information on time-like proton form factors in the unphysical region is considered in the Born approximation.

A systematic investigation of the inclusive cross sections for single-nucleon knockout reactions from $p$-shell nuclei has been performed. A total of seven reactions were studied for projectiles with masses between $A=7$ and 10, having a wide range of nucleon separation energies. Results were obtained for a range of incident beam energies and targets. These differences were found to have a minimal impact on the deduced cross sections. Experimental results were compared to theoretical predictions based on variational Monte Carlo (VMC) nuclear structure calculations, whose radial overlap functions and neutron and proton densities were included in the reaction description. These results are compared with the conventional model, developed for heavier nuclei, that uses shell-model and Hartree-Fock structure inputs. The VMC-based calculations agreed with the experimental data for several reactions where deeply bound nucleons are removed but does not describe some of the more weakly bound nucleon removal cases with comparable accuracy.

The spherical-to-prolate shape transition in neutron-rich Cr isotopes from $N=34$ to 42 is studied by solving the collective Schrödinger equation for the five-dimensional quadrupole collective Hamiltonian. The collective potential and inertial functions are microscopically derived with use of the constrained Hartree-Fock-Bogoliubov plus local quasiparticle random-phase approximation method. Nature of the quadrupole collectivity of low-lying states is discussed by evaluating excitation spectra and electric quadrupole moments and transition strengths. The result of calculation indicates that Cr isotopes around ${}^{64}$Cr are prolately deformed but still possess transitional character; large-amplitude shape fluctuations dominate in their low-lying states.

We calculate the gluon dissociation cross section in an anisotropic quark gluon plasma expected to be formed in relativistic nucleus-nucleus collisions. It is shown that the thermally weighted cross section of gluon dissociation undergoes modification in anisotropic plasma, affecting the $J/\psi$ survival probability. The dependence of the cross section on the direction of propagation of the charmonium with respect to the anisotropy axis is presented. Survival probability of $J/\psi$ in two different space-time models of anisotropic quark gluon plasma (AQGP) has been calculated. It is shown that, depending upon the initial conditions [corresponding to Relativistic Heavy Ion Collider (RHIC) energies], the survival probability in AQGP differs from that in isotropic QGP both in the central as well as forward rapidity regions. For initial conditions relevant for Large Hadron Collider (LHC) energies, a marginal difference between the the two space-time models has been observed with given initial conditions.

A new approach for solving the Bethe ansatz (Gaudin-Richardson) equations of the standard pairing problem is established based on the Heine-Stieltjes correspondence. For $k$ pairs of valence nucleons on $n$ different single-particle levels, it is found that solutions of the Bethe ansatz equations can be obtained from one $(k+1)\times (k+1)$ and one $(n-1)\times (k+1)$ matrices, which are associated with the extended Heine-Stieltjes and Van Vleck polynomials, respectively. Since the coefficients in these polynomials are free from divergence with variations in contrast to the original Bethe ansatz equations, the approach provides an efficient and systematic way to solve the problem, which by extension, can also be used to solve a large class of Gaudin-type quantum many-body problems, including an efficient angular momentum projection method for multiparticle systems.

The excitation of Gamow-Teller (GT) and isovector spin monopole (IVSM) $J^{\pi }=1^{+}$ modes in ${}^{116}$In by ($p,n$) and ($n,p$) charge-exchange reactions on ${}^{116}$Cd and on ${}^{116}$Sn, respectively, is studied within the framework of the quasiparticle random-phase approximation. The calculations have been performed both for schematic and realistic model situations. It appears that the calculated admixture of the IVSM and Gamow-Teller (GT) $J^{\pi }=1^{+}$ excitations is negligible and that the contribution to the strength above 20 MeV of excitation energy, in ${}^{116}$In, is due to the IVSM ($\sigma r^2{t}^{\pm }$) mode. This result is compared with the recent experimental work that reported a large amount of both ($p,n$) and ($n,p$) strength beyond 10 MeV of excitation energy in ${}^{116}$In. This measured excess strength has led to speculations about its importance for the double beta decay rate of ${}^{116}$Cd.

Pseudoscalar mesons can be produced and studied in high-energy electron-nucleus scattering. We review and extend our previous theoretical analysis of meson production in the nuclear Coulomb field. The $P\to \gamma \gamma$ decay rates are most directly determined for mesons produced in the double-Coulomb region where both photons are nearly real, and provided the hadronic-background contributions remain small. The larger the mass of the meson the higher the electron energy needed to assure such favorable conditions.

The relationship between the volume and the surface energy coefficients in the liquid drop $A^{-1/3}$ expansion of nuclear masses is discussed. The volume and surface coefficients share the same physical origin and their physical connection is used to extend the expansion with a curvature term. A possible generalization of the Wigner term is also suggested. This connection between coefficients is used to fit the experimental nuclear masses. The excellent fit obtained with a smaller number of parameters validates the assumed physical connections and the usefulness of the curvature term.

Under the assumption of isospin symmetry, $T_z=\pm 3/2\to \pm 1/2$ Gamow-Teller (GT) transitions in an isobar quartet with a mass $A$ are analogous, where $T_z=(1/2)(N-Z)$ is the $z$ component of the isospin $T$. We studied the $T_z=+3/2\to +1/2$ GT transitions by the ${}^{37}$Cl(${}^3\mathrm{He},t$)${}^{37}$Ar reaction at an incoming beam energy of $E_{\mathrm{beam}}=140$ MeV/nucleon with an energy resolution of $\Delta E=30$ keV. The distribution of the GT strength was obtained up to an excitation energy ($E_x$) of 14.2 MeV. This distribution was compared with that of the $T_z=-2/3\to -1/2$ transitions studied in ${}^{37}$Ca $\beta$ decay up to $E_x=8.6$ MeV. Although the overall distributions were similar, details of the fine structure were not necessarily reproduced. The experimental results were compared with a shell-model (SM) calculation using the USD interaction and the effective GT operator that compensates for the effect of limited model space. Although the overall distribution was reproduced by the SM calculation, the fragmentation of states was not reproduced. Neutrino cross sections were derived for the ${}^8$B solar-neutrino source.

We study dissipation and relaxation processes within the time-dependent Hartree-Fock approach using the Wigner distribution function. On the technical side we present a geometrically unrestricted framework which allows us to calculate the full six-dimensional Wigner distribution function. With the removal of geometrical constraints, we are now able to extend our previous phase-space analysis of heavy-ion collisions in the reaction plane to unrestricted mean-field simulations of nuclear matter on a three-dimensional Cartesian lattice. From the physical point of view we provide a quantitative analysis on the stopping power in TDHF. This is linked to the effect of transparency. For the medium-heavy ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ system we examine the impact of different parametrizations of the Skyrme force, energy-dependence, and the significance of extra time-odd terms in the Skyrme functional.

Average N(γ,$X$)${}^7$Be, O(γ,$X$)${}^7$Be, and C(γ,$X$)${}^7$Be cross sections of the natural composition of target isotopes in an energy range from threshold to 90 MeV are measured. By using cross sections of the photoproduction of ${}^7$Be and a simulation of the nuclear-electromagnetic cascade in the atmosphere, the contribution from the photonuclear mechanism into the production of a cosmogenic ${}^7$Be radionuclide in the Earth's atmosphere is investigated. It is shown that the contribution from the photonuclear channel into the production of cosmogenic ${}^7$Be is to be taken into account in processes of the accumulation and transfer of ${}^7$Be in the ground layer.

Background: Fission-fragment mass distributions are asymmetric in the fission of typical actinide nuclei for nucleon number $A$ in the range $228⋦A⋦258$ and proton number $Z$ in the range $90⋦Z⋦100$. For somewhat lighter systems it has been observed that fission mass distributions are usually symmetric. However, a recent experiment showed that fission of ${}^{180}$Hg following electron capture on ${}^{180}$Tl is asymmetric.

Purpose: We calculate potential-energy surfaces for a typical actinide nucleus and for 12 even isotopes in the range ${}^{178}$Hg–${}^{200}$Hg, to investigate the similarities and differences of actinide compared to mercury potential surfaces and to what extent fission-fragment properties, in particular shell structure, relate to the structure of the static potential-energy surfaces.

Methods: Potential-energy surfaces are calculated in the macroscopic-microscopic approach as functions of five shape coordinates for more than five million shapes. The structure of the surfaces is investigated by the use of an immersion technique.

Results: We determine properties of minima, saddle points, valleys, and ridges between valleys in the five-dimensional shape-coordinate space. Along the mercury isotope chain the barrier heights and the ridge heights and their persistence with elongation vary significantly and show no obvious connection to possible fragment shell structure, in contrast to the actinide region, where there is a deep asymmetric valley extending from the saddle point to scission.

Conclusions: The mechanism of asymmetric fission must be very different in the lighter proton-rich mercury isotopes compared to the actinide region and is apparently unrelated to fragment shell structure. Isotopes lighter than ${}^{192}$Hg have the saddle point shielded from a deep symmetric valley by a significant ridge. The ridge vanishes for the heavier Hg isotopes, for which we would expect a qualitatively different asymmetry of the fragments.