Measurements of the $N=28$ isotones ${}^{42}\mathrm{Si}$, ${}^{43}\mathrm{P}$, and ${}^{44}\mathrm{S}$ using one- and two-proton knockout reactions from the radioactive beam nuclei ${}^{44}\mathrm{S}$ and ${}^{46}\mathrm{Ar}$ are reported. The knockout reaction cross sections for populating ${}^{42}\mathrm{Si}$ and ${}^{43}\mathrm{P}$ and a 184 keV γ-ray observed in ${}^{43}\mathrm{P}$ establish that the $d_{3/2}$ and $s_{1/2}$ proton orbits are nearly degenerate in these nuclei and that there is a substantial $Z=14$ subshell closure separating these two orbits from the $d_{5/2}$ orbit. The increase in the inclusive two-proton knockout cross section from ${}^{42}\mathrm{Si}$ to ${}^{44}\mathrm{S}$ demonstrates the importance of the availability of valence protons for determining the cross section. New calculations of the two-proton knockout reactions that include diffractive effects are presented. In addition, it is proposed that a search for the $d_{5/2}$ proton strength in ${}^{43}\mathrm{P}$ via a higher statistics one-proton knockout experiment could help determine the size of the $Z=14$ closure.

Motivated by the observed regularity in the energy spectra and the structure of the shell model wave functions for the levels of ${}^{137}\mathrm{Te}$ and ${}^{137}\mathrm{I}$, a few weakly and moderately deformed neutron-rich odd-$A$ nuclei above the doubly magic nucleus ${}^{132}\mathrm{Sn}$ were studied using the particle rotor model (PRM). The calculated energy spectra and branching ratios agree reasonably well with the most recent experimental data. In a few cases ambiguity in level ordering was resolved and spin-parities were assigned to the levels. Observed octupole correlation in some of these nuclei is discussed in the light of the present results.

We derive new Hamiltonians for the $\mathit{sd}$ shell, USDA and USDB, based on a renormalized $G$ matrix with linear combinations of two-body matrix elements adjusted to fit a complete set of data for experimental binding energies and excitation energies for the $\mathit{sd}$-shell nuclei. These Hamiltonians provide a new level of precision for realistic $\mathit{sd}$-shell wave functions for applications to nuclear structure and nuclear astrophysics.

Excited states have been observed for the first time in the very neutron-deficient, odd-odd nucleus, ${}_{55}^{116}{\mathrm{Cs}}_{61}$. The assignment to ${}^{116}\mathrm{Cs}$ has been made by the detection of γ rays in coincidence with evaporated charged particles and with evaporation residues. The observed states form a rotational band which has been assigned to the $\nu (h_{11/2})\hspace{1em}\otimes \hspace{1em}\pi (h_{11/2})$ configuration. Tentative spin assignments have been made on the basis of systematic comparisons with neighboring cesium isotopes. A low-spin signature inversion is observed in the band at a rotational frequency of about 0.23 MeV$/\hslash$. The observed signature inversions in the odd-odd ${}^{116-126}\mathrm{Cs}$ isotopes have been compared with the results of extended total Routhian surface calculations, in which signature inversion arises as a consequence of quadrupole-pairing correlations and triaxial deformation. As previously shown for some of the odd-odd $A\simeq 120$ isotopes, the calculations reproduce the signature inversions reasonably well.

A dripline nucleus ${}^{22}\mathrm{C}$ is studied in a Borromean three-body model of ${}^{20}\mathrm{C}+n+n$. The valence neutrons, interacting via a realistic potential, are constrained to be orthogonal to the occupied orbits in ${}^{20}\mathrm{C}$. We obtain ample results supporting that ${}^{22}\mathrm{C}$ is an ideal $s$-wave two-neutron halo nucleus: The ground state is bound by 390–570 keV, the root mean square neutron and proton radii are 4.0 and 2.4 fm, and the two neutrons are predominantly in $(s_{1/2}){}^2$ orbits. The binding mechanism of ${}^{22}\mathrm{C}$ is discussed. One- and two-body density distributions elucidate the halo character as well as the correlated motion of the neutrons. The reaction cross sections of ${}^{22}\mathrm{C}+{}^{12}\mathrm{C}$ collisions are predicted.

The nearest neighbor spacing distribution of levels of deformed even-even nuclei classified according to their quadrupole deformation parameter is investigated. The results suggest that oblate deformed nuclei have more regular spectra than prolate nuclei.

The level structure of ${}^{83}\mathrm{Se}$ was studied via prompt γ-ray spectroscopy of fragments following the fission of the compound nucleus ${}^{226}\mathrm{Th}$ formed in the ${}^{18}\mathrm{O}$ (91 MeV) + ${}^{208}\mathrm{Pb}$ fusion-evaporation reaction. The first four high-spin states above the ${9/2}^{+}$ ground state were established. The coupling of the neutron hole in the $g_{9/2}$ orbital to the yrast states in the ${}^{84}\mathrm{Se}$ core can account for these states. The experimentally observed high-spin states are compared with predictions of shell-model calculations.

The quadrupole moment of the $8^{+}$ yrast state in ${}^{84}\mathrm{Kr}$ was measured using the level-mixing spectroscopy technique to be $Q=$ 36(4) $e$ fm${}^2$. The result is compared with predictions of the shell model using common sets of effective charges. The comparison of experimental quadrupole moments with calculated values for 8${}^{+}$ states in Kr, Sr and Zr isotopes with $N=$ 48, 50 and for $9/2^{+}$ states in isotopes with $N=$ 47, 49 suggests a modification of the effective charges used in this region.

The ratio of the proton's electric to magnetic form factor, $G_E/G_M$, can be extracted in elastic electron-proton scattering by measuring cross sections, beam-target asymmetry, or recoil polarization. Separate determinations of $G_E/G_M$ by cross sections and recoil polarization observables disagree for $Q^2>1$ (GeV/$c){}^2$. Measurement by a third technique might uncover an unknown systematic error in either of the previous measurements. The beam-target asymmetry has been measured for elastic electron-proton scattering at $Q^2$ = 1.51 (GeV/$c){}^2$ for target spin orientation aligned perpendicular to the beam momentum direction. This is the largest $Q^2$ at which $G_E/G_M$ has been determined by a beam-target asymmetry experiment. The result, $\mu G_E/G_M=0.884\pm 0.027\pm 0.029$, is compared to previous world data.

We propose the no-recoil approximation, which is valid for heavy systems, for a double folding nucleus-nucleus potential. With this approximation, the nonlocal knock-on exchange contribution becomes a local form. We discuss the applicability of this approximation for elastic scattering of the ${}^6\mathrm{Li}$ $+{}^{40}\mathrm{Ca}$ system. We find that, for this and heavier systems , the no-recoil approximation works as good as another widely used local approximation that employs a local plane wave for the relative motion between the colliding nuclei. We also compare the results of the no-recoil calculations with those of the zero-range approximation often used to handle the knock-on exchange effect.

A search for isomeric states was performed in the nucleus ${}_{60}^{140}{\mathrm{Nd}}_{80}$ using in-beam γ-ray spectroscopy and the ${}^{126}\mathrm{Te}$(${}^{18}\mathrm{O}$,$4n$) reaction. Prompt and delayed γ-ray coincidences were measured with the AFRODITE spectrometer using the pulsed beam delivered by the Separated Sector Cyclotron of iThemba LABS. One new isomer was identified, with spin-parity $I^{\pi }={20}^{+}$ and lifetime $T_{1/2}\ge 400$ ns, at an excitation energy $E_x=7430$ keV. The lifetime of the ${10}^{+}$ isomer at $E_x=3619$ keV was determined to be 32.9(1.8) ns, confirming the previously reported value. The configuration of the $I^{\pi }={20}^{+}$ isomer is assigned based on configuration-dependent cranked Nilsson-Strutinsky (CNS) calculations as a state $\pi (d_{5/2}{g}_{7/2}{)}_{{10}^{+}}^{-4}\otimes \nu (h_{11/2}^{-2}){}_{{10}^{+}}$, with the spin vectors of the six holes in the ${}_{64}^{146}{\mathrm{Gd}}_{82}$ core fully aligned.

Highly excited resonance states lying above the $t+t$ threshold in ${}^6\mathrm{He}$ are theoretically studied by the $t+t$ microscopic two-cluster model. The $t+t$ two-body scattering problem is solved by the microscopic $R$-matrix method in order to localize resonance states. Excited states of ${}^6\mathrm{Be}$ and ${}^6\mathrm{Li}$ (both $T=1$ and 0) are as well studied within the consistent two-cluster models. We have employed four different effective nucleon-nucleon interactions in order to check the sensitivity to our results and we have obtained fairly consistent results in every interaction. In positive parity states, our model gives deeply bound states which are well-known low-lying $\alpha +n+n$ three-body states and these states are obtained through the overlap between the $t+t$ and $\alpha +n+n$ configurations at smaller cluster relative distance. Similar bound states are found in the $T=0$ state in ${}^6\mathrm{Li}$. In negative parity states, our calculation shows broad $0^{-}$ and $2^{-}$ $P$-wave resonances just above the $t+t$ threshold and in addition three $F$-wave resonances of $2^{-}$, $3^{-}$, and $4^{-}$ at higher energies with broader widths. Our calculations show that the noncentral term of the effective nucleon-nucleon interaction plays an important role for these broad resonance states. $T=0$ states of ${}^6\mathrm{Li}$ show single broad resonances in $P$- and $F$-waves, respectively, and their positions are very close to those of $T=1$ resonances.

The parameter independent (up to overall scale factors) predictions of the X(5)-${\beta }^2$, X(5)-${\beta }^4$, and X(3) models, which are variants of the X(5) critical point symmetry developed within the framework of the geometric collective model, are compared to two-parameter calculations in the framework of the interacting boson approximation (IBA) model. The results show that these geometric models coincide with IBA parameters consistent with the shape/phase-transition region of the IBA for boson numbers of physical interest (close to 10). Nuclei within the rare-earth region and select Os and Pt isotopes are identified as good examples of X(3), X(5)-${\beta }^2$, and X(5)-${\beta }^4$ behavior.

A new shell model Hamiltonian for $p$-shell nuclei which properly takes into account important roles of spin-isospin interactions is used to obtain cross sections of neutrino-${}^{12}\mathrm{C}$ reactions induced by decay-at-rest neutrinos as well as supernova neutrinos. Branching ratios to various decay channels are calculated by the Hauser-Feshbach theory. Neutrino-${}^4\mathrm{He}$ reactions are also investigated by using recent shell model Hamiltonians. The reaction cross sections are found to be enhanced for both ${}^{12}\mathrm{C}$ and ${}^4\mathrm{He}$ compared with previous calculations. As an interesting consequence of this, a possible enhancement of the production yields of light elements, ${}^7\mathrm{Li}$ and ${}^{11}\mathrm{B}$, during supernova explosions is pointed out.

The inclusive cross sections for 38 different reaction products produced in the interaction of ${}^{48}\mathrm{Ca}$, ${}^{40}\mathrm{S}$, and ${}^{42}\mathrm{S}$ beams around 100 MeV/nucleon with a liquid deuterium target are reported. The cross sections for the ${}^{48}\mathrm{Ca}$ +${}^2\mathrm{H}$ products are compared to those with ${}^{48}\mathrm{Ca}$ incident on the commonly used fragmentation targets ${}^9\mathrm{Be}$ and ${}^{181}\mathrm{Ta}$ and also to global calculations for fragmentation reaction cross sections based on the EPAX parameterization. The sizes of the measured reaction cross sections for the deuterium target were comparable to those of the cross sections measured on the heavier targets, indicating that nucleon removal from a deuterium target can be carried out for single- and multiple-nucleon knockout reaction studies. It was also found that the charge exchange cross sections were large enough that it should be possible to obtain nuclear structure information from these reactions.

We demonstrate the occurrence of canonical suppression associated with the conservation of a U(1) charge in current transport models. For this study a pion gas is simulated within two different transport approaches by incorporating inelastic and volume-limited collisions $\pi \pi \leftrightarrow K\overline{K}$ for the production of kaon pairs. Both descriptions can dynamically account for the suppression in the yields of rare strange particles in a limited box, being in full accordance with a canonical statistical description.

The density functional theory of nuclear structure provides a many-particle wave function that is useful for static properties, but an extension of the theory is necessary to describe correlation effects or other dynamic properties. We propose a procedure to extend the theory by mapping the properties of a self-consistent mean-field theory onto an effective shell-model Hamiltonian with quadrupole-quadrupole interaction. In this initial study, we consider the $\mathit{sd}$-shell nuclei ${}^{20}\mathrm{Ne}$, ${}^{24}\mathrm{Mg}$, ${}^{28}\mathrm{Si}$, and ${}^{36}\mathrm{Ar}$. The method is first tested with the USD shell-model Hamiltonian, using its mean-field approximation to construct an effective Hamiltonian and partially recover correlation effects. We find that more than half of the correlation energy is due to the quadrupole interaction. We then follow a similar procedure but using the SLy4 Skyrme energy functional as our starting point and truncating the space to the spherical $\mathit{sd}$ shell. The constructed shell-model Hamiltonian is found to satisfy minimal consistency requirements to reproduce the properties of the mean-field solution. The quadrupolar correlation energies computed with the mapped Hamiltonian are reasonable compared with those computed by other methods. The method also provides a well-defined renormalization of the quadrupole operator in the shell-model space, the “effective charge” of the phenomenological shell model.

This study is focused on probing the incompressibility of nuclear matter. Calculations are employed in the framework of the superasymmetric fission model of $\alpha$ decay for 182 radioactive nuclei, including the recently produced isotopes of superheavy elements, to probe nuclear incompressibility and its isospin dependence through the use of an effective density-dependent nucleon-nucleon force. The microscopic $\alpha$-daughter nuclear interaction potential is calculated by double folding the density distributions of both $\alpha$ and daughter nuclei with a realistic effective density-dependent M3Y force that is modified to consider the effect of incompressibility in the case of total overlapped densities inside the barrier. The microscopic Coulomb potential is calculated by folding the charge density distributions of the two interacting nuclei. The minimum angular momentum transfer required for the spin-parity conservation is considered. The half-lives of the different $\alpha$ decays have been calculated within the WKB approximation. The obtained values for nuclear matter incompressibility range between 205 and 255 MeV for the most studied cases which have an isospin asymmetry range of $\delta =0.033$ to 0.228. For the same isospin asymmetry, the incompressibility values of the even($N)$-even($Z)$ nuclei are found to be the highest, while those of the odd-odd nuclei are the lowest. The estimated symmetric nuclear matter incompressibility deduced from the results obtained for different asymmetric nuclei is $K_0(\delta =0)=241.28$ MeV.

Inelastic proton scattering via isobaric analog resonances allows derivation of rather complete information about neutron particle-hole states. We applied this method to the doubly-magic nucleus ${}^{208}\mathrm{Pb}$ by measuring angular distributions of the reaction ${}^{208}\mathrm{Pb}$($p,p^{\text{'}}$) on top of the isobaric analog resonances in ${}^{209}\mathrm{Bi}$ with the Q3D magnetic spectrograph at München. We identify the six states of the $i_{11/2}{f}_{5/2}$ multiplet and the four states of the $i_{11/2}{p}_{3/2}$ multiplet in the energy range $4.6\mathrm{MeV}<E_x<5.3$ MeV. Firm spin assignments for the 10 states are given, most of them new. Additional measurements of the reaction ${}^{207}\mathrm{Pb}$($d,p$) confirm the assignments. A new state at $E_x=5239$ keV has a dominant proton particle-hole structure with spin $4^{-}$.