The rotational bands in nuclei with $Z\approx 100$ are investigated systematically by using a cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method, in which the blocking effects are taken into account exactly. By fitting the experimental single-particle spectra in these nuclei, a new set of Nilsson parameters ($\kappa$ and $\mu$) and deformation parameters (${\varepsilon }_2$ and ${\varepsilon }_4$) are proposed. The experimental kinematic moments of inertia for the rotational bands in even-even, odd-$A$, and odd-odd nuclei, and the band-head energies of the one-quasiparticle bands in odd-$A$ nuclei, are reproduced quite well by the PNC-CSM calculations. By analyzing the $\omega$ dependence of the occupation probability of each cranked Nilsson orbital near the Fermi surface and the contributions of valence orbitals in each major shell to the angular momentum alignment, the upbending mechanism in this region is understood clearly.

The “island of stability” of superheavy nuclei due to shell effects is explored and the $\alpha$-decay half-lives of these nuclei are predicted. The calculations of the binding energies within a new macroscopic-microscopic model (MMM) are performed and compared with the experimental data for heavy nuclei from Md to the $Z=118$ element. The agreement is excellent. The data confirm that the ${}^{270}$Hs is a deformed double submagic nucleus beyond ${}^{208}$Pb. The features of $\alpha$-decay energies and one-proton-separation energies from the MMM reveal that the next double magic nucleus after ${}^{270}$Hs should be ${}^{298}$114. The potential energy surfaces calculated within the constrained relativistic mean-field (CRMF) theory show that the ${}^{270}$Hs is a deformed double magic nucleus, but ${}^{298}$114 is a spherical double magic nucleus. The $\alpha$-decay half-lives are determined using a generalized liquid drop model (GLDM) with the $Q_{\alpha }$ from the MMM for Hs and $Z=114$ isotopes, respectively.

We calculate the exclusive cross section of the process ${\pi }^{+}d\to \eta pp$ in the energy region $T_{\pi }\approx 775$ MeV in order to study the effect of the $\eta N\to \eta N$ final-state interaction in the region of the $N\left(1535\right)S_{11}$ resonance. Our model includes first- and second-order diagrams involving $\pi N\to \pi N$, $\pi N\to \eta N$, $\eta N\to \eta N$, and $NN\to NN$ interactions. The sensitivity of the cross section to different parametrizations of the less-known $\eta N$ final-state interaction is studied.

Neutron and proton odd-even mass differences are systematically studied with Hartree-Fock $\left(\mathit{HF}\right)+\mathrm{BCS}$ calculations with Skyrme interactions and an isospin-dependent contact pairing interaction. The strength of pairing interactions is determined to reproduce empirical odd-even mass differences in a wide region of the mass table. By using the optimal parameter sets for proton and neutrons, we perform global $\left(\mathit{HF}\right)+\mathrm{BCS}$ calculations with Skyrme interactions and an isospin-dependent contact pairing interaction. The strength of pairing interactions is determined to reproduce empirical odd-even mass differences in a wide region of the mass table. By using the optimal parameter sets for proton and neutrons, we perform global $\mathit{HF}+\mathrm{BCS}$ calculations of nuclei and compare them with experimental data. The importance of the isospin dependence of the pairing interaction is singled out for odd-even mass differences in medium and heavy isotopes. Proton and neutron radii are studied systematically using the same model.

The quenching of the $N=20$ shell gap in neutron-rich nuclei is investigated by studying the single-particle structure of ${}^{27}$Ne via neutron transfer using a ${}^{26}$Ne beam. Two low-lying negative-parity intruder states have been observed, the lowest of which is identified as $J^{\pi }=3/2^{-}$, confirming earlier speculations. A level identified as 7/2${}^{-}$ is observed higher in energy than the 3/2${}^{-}$, contrary to the ordering at $\beta$-stability and at an energy significantly different from the predictions of previous shell-model calculations. The measured energies and deduced spectroscopic factors are well reproduced in full (0,1)-$\hslash \omega$ $0s$-$0p$-$0d$-$1s$-$0f$-$1p$ calculations in which there is a significant ad hoc reduction ($\sim 0.7$ MeV) in the $N=20$ shell gap.

The in-pseudoscalar-meson condensate can be represented through the pseudoscalar meson's scalar form factor at zero-momentum transfer. With the aid of a mass formula for scalar mesons, revealed herein, the analog is shown to be true for in-scalar-meson condensates. The concept is readily extended to all hadrons so that, via the zero-momentum-transfer value of any hadron's scalar form factor, one can readily extract the value for a quark condensate in that hadron which is a measure of dynamical chiral symmetry breaking.

Primary $\gamma$-ray spectra for a wide excitation-energy range have been extracted for ${}^{44}$Ti from particle-$\gamma$ coincidence data of the ${}^{46}$Ti($p,t\gamma$)${}^{44}$Ti reaction. These spectra reveal information on the $\gamma$-decay pattern of the nucleus and may be used to extract the level density and radiative strength function applying the Oslo method. Models of the level density and radiative strength function are used as input for cross-section calculations of the ${}^{40}$Ca($\alpha ,\gamma$)${}^{44}$Ti reaction. Acceptable models should reproduce data on the ${}^{40}$Ca($\alpha ,\gamma$)${}^{44}$Ti reaction cross section as well as the measured primary $\gamma$-ray spectra. This is only achieved when a coherent normalization of the slope of the level density and radiative strength function is performed. Thus, the overall shape of the experimental primary $\gamma$-ray spectra puts a constraint on the input models for the rate calculations.

The structure of the weakly bound ${}_9^{26}$F${}_{17}$ odd-odd nucleus, produced from ${}^{27,28}$Na nuclei, has been investigated at GANIL by means of the in-beam $\gamma$-ray spectroscopy technique. A single $\gamma$-line is observed at 657(7) keV in ${}_9^{26}$F which has been ascribed to the decay of the excited $J=2^{+}$ state to the $J=1^{+}$ ground state. The possible presence of intruder negative parity states in ${}^{26}$F is also discussed.

In general relativity, there is a maximum mass allowed for neutron stars that, if exceeded, entails collapse into a black hole. Its precise value depends on details of the nuclear matter equation of state, a subject where much progress has been accomplished thanks to low energy effective theories. The discovery of a two-solar-mass neutron star, near that maximum mass, when analyzed with modern equations of state, implies that Newton's gravitational constant in the star cannot exceed its value on Earth by more than 12$\%$ at the 95$\%$ confidence level. This significantly extends the gravitational field intensity at which the constant has been constrained at the 10$\%$ level.

Thermal and isospin composition effects on the heat capacity of infinite nuclear matter are studied within the binodal coexistence region of the nuclear phase diagram. Assuming the independent conservation of both proton and neutron densities, a second-order phase transition is expected, leading to a discontinuous behavior of the heat capacity. This discontinuity is analyzed for the full range of the thermodynamical variables consistent with the equilibrium coexistence of phases. Two different effective models of the nuclear interaction are examined in the mean-field approximation: the nonrelativistic Skyrme force and the covariant QHD formulation. We found qualitative agreement between both descriptions. The discontinuity in the specific heat per particle is finite and decreases with both the density of particles and the isospin asymmetry. As a byproduct, the latent heat for isospin-symmetric matter is considered.

The shell structure of heavy nuclei with $Z>104$, which can be produced in the actinide-based complete fusion reactions, is studied with a modified two-center shell model. Using the microscopic-macroscopic approach, the mass excesses and $Q_{\alpha }$-values are calculated and compared with available experimental data. The predicted properties of superheavy nuclei show that the next doubly magic nucleus beyond ${}^{208}$Pb is at $Z\ge 120$. It is shown that the production cross sections of new superheavy nuclei decisively depend on the position of proton shell closure.

We reconsider a method based on dispersion theory that allows one to extract the scattering length of any two-baryon system from corresponding final-state interactions in production reactions. The application of the method to baryon-baryon systems with strangeness $S=-2$ and $S=-3$ systems is discussed. Theoretical uncertainties due to the presence of inelastic channels with near-by thresholds are examined for the specific situation of the reaction $K^{-}d\to K^0\Lambda \Lambda$ and the coupling of $\Lambda \Lambda$ to the $\Xi N$ channel. The possibility to disentangle spin-triplet and spin-singlet scattering lengths by means of various polarization measurements is demonstrated for several production reactions in $K^{-}d$ and $\gamma d$ scattering. Employing the method to available data on the $\Lambda \Lambda$ invariant mass from the reaction ${}^{12}C(K^{-},K^{+}\Lambda \Lambda X)$, a ${}^1{S}_0$ scattering length of $a_{\Lambda \Lambda }=-1.2\pm 0.6$ fm is deduced.

The dynamical cluster decay model (DCM) is applied in reference to recent data on ${}^{78,82}\mathrm{Kr}+{}^{40}$Ca reactions at a bombarding energy of 5.5 MeV/nucleon. For the nuclear systems ${}^{118,122}$Ba${}^{*}$, experimental data for the complete charge spectrum are also available along with evaporation residue and fission cross sections. Within the DCM approach, we are able to fit the total fission and evaporation residue cross sections for spherical choice of nuclei by simultaneously fitting the neck length parameter. The effect of different level density parameters is also studied. Results of DCM calculations are compared with busco-, gemini-, and DNS-based calculations. All the models use the maximum angular momentum ${\ell }_{\max }$ as the fitting parameter, which in the DCM is fixed via the neck-length parameter ($\Delta R$) for the penetrability $P\to 1$. Also, the role of a nonzero pairing strength ($\delta >0$) is seen, using $\delta \left(T\right)$ in $V_{\mathrm{LDM}}$ as a fitting parameter, say, to Li data. The effect of different proximity potentials is also studied. Finally, some noncompound nucleus contribution is shown to be operating in the context of the reactions under study. The $N$/$Z$ dependence of decay fragments is also studied for Ba isotopes with $A=114$–126.

Background: Thick-target-induced nucleon-adding transfer reactions onto energetic rare-isotope beams are an emerging spectroscopic tool. Their sensitivity to single-particle structure complements one-nucleon removal reaction capabilities in the quest to reveal the evolution of nuclear shell structure in very exotic nuclei. Purpose: Our purpose is to add intermediate-energy, carbon-target-induced one-proton pickup reactions to the arsenal of $\gamma$-ray-tagged direct reactions applicable in the regime of low beam intensities and to apply these for the first time to $fp$-shell nuclei. Methods: Inclusive and partial cross sections were measured for the ${}^{12}\mathrm{C}({}^{48}\mathrm{Cr},{}^{49}\mathrm{Mn}+\gamma )$X and ${}^{12}\mathrm{C}({}^{50}\mathrm{Fe},{}^{51}\mathrm{Co}+\gamma )$X proton pickup reactions at 56.7 and 61.2 MeV/nucleon, respectively, using coincident particle-$\gamma$ spectroscopy at the National Superconducting Cyclotron Laboratory. The results are compared to reaction theory calculations using $fp$-shell-model nuclear structure input. For comparison with our previous work, the same reactions were measured on ${}^9$Be targets. Results: The measured partial cross sections confirm the specific population pattern predicted by theory, with pickup into high-$\ell$ orbitals being strongly favored, driven by linear and angular momentum matching. Conclusion: Carbon-target-induced pickup reactions are well suited, in the regime of modest beam intensity, to study the evolution of nuclear structure, with specific sensitivities that are well described by theory.

The mass distributions of the fission fragments were measured in reactions induced by ${}^{48}$Ti beams on ${}^{144,154}$Sm, ${}^{162}$Dy, ${}^{174}$Yb, ${}^{186}$W, ${}^{192}$Os, ${}^{196}$Pt, ${}^{200}$Hg, and ${}^{208}$Pb targets at near-barrier energies. The systematic tendencies of the mass widths have been explored. For the reactions with the lighter or spherical target nuclei, the mass widths increase with increasing bombarding energy, a behavior expected for fusion-fission. For the heavier and statically deformed nuclei, the mass widths increase rapidly as energies fall close to and below the capture barriers. Well above the barrier energies, the mass widths and estimated minimum quasifission contributions increase smoothly with increasing fissility of the composite nucleus. The observed behavior is a complex function of the fissility, deformation, and energy with respect to the capture barrier. Comparisons with dynamical quasifission model calculations for these reactions will be a good test of models of fusion in heavy-element formation reactions.

Starting with a confining linear Lorentz scalar potential $V_s$ and a Lorentz vector potential $V_v$, which is also linearly rising but has in addition a color-Coulomb attraction piece $-{\alpha }_s/r$, we solve the Dirac equation for the ground-state $c$- and $u$-quark wave functions. Then, convolving $V_v$ with the $u$-quark density, we find that the Coulomb attraction almost completely washes out, making an essentially linear ${\overline{V}}_v$ for the $c$ quark. A similar convolution using the $c$-quark density also leads to an essentially linear ${\tilde{V}}_v$ for the $u$ quark. For bound $\overline{c}$-$c$ charmonia, where one must solve using a reduced mass for the $c$ quarks, we again find by convolution an essentially linear ${\widehat{V}}_v$. Thus, the relativistic quark model is consistent with the absence of a color-Coulomb attraction in the charmed-meson mass spectrum. To see if this near-linearity of $V_v$ provides a reasonable model for the bound $\overline{c}$-$c$ charmonium states, we then solve the radial Dirac equations for $V_s$ and $V_v$, both with and without a color-Coulomb attraction at shorter distances. We present and compare the predictions of their masses for the two models. We find that a strictly linear $V_v$ provides about as good a fit to the charmonia masses as the one with a color-Coulomb attraction, despite having one less parameter.

I demonstrate that the $B$($E$2) value in ${}^{32}$Mg can be understood with a model in which both the ground and 2${}^{+}$ first-excited states are predominantly of $sd$-shell character.

The geometrical mapping of algebraic nuclear cluster models is investigated within the coherent state formalism. Two models are considered: the semimicroscopic algebraic cluster model (SACM) and the phenomenological algebraic cluster model (PACM), which is a special limit of the SACM. The SACM strictly observes the Pauli exclusion principle while the PACM does not. The discussion of the SACM is adapted to the coherent state formalism by introducing the new SO(3) dynamical symmetry limit and third-order interaction terms in the Hamiltonian. The potential energy surface is constructed in both models and it is found that the effects of the Pauli principle can be simulated by higher-order interaction terms in the PACM. The present study is also meant to serve as a starting point for investigating phase transitions in the two algebraic cluster models.

Based on the results of a previous paper (Paper I), by performing the geometrical mapping via coherent states, phase transitions are investigated and compared within two algebraic cluster models. The difference between the semimicroscopic algebraic cluster model (SACM) and the phenomenological algebraic cluster model (PACM) is that the former strictly observes the Pauli exclusion principle between the nucleons of the individual clusters, while the latter ignores it. From the technical point of view the SACM is more involved mathematically, while the formalism of the PACM is closer to that of other algebraic models with different physical content. First- and second-order phase transitions are identified in both models, while in the SACM a critical line also appears. Analytical results are complemented with numerical studies on $\alpha$-cluster states of the ${}^{20}$Ne and ${}^{24}$Mg nuclei.