High-spin states in ${}^{165}$Er have been studied experimentally using the ${}^{160}$Gd(${}^9$Be, 4$n$) reaction at beam energies of 42 and 45 MeV. The previously known bands based on the $5/2^{+}\left[642\right]$, $5/2^{-}\left[523\right]$, and $11/2^{-}\left[505\right]$ configurations are extended to $(49/2^{+})$, $(45/2^{-})$, and $(31/2^{-})$ states, respectively. The rotational bands in ${}^{165}$Er generally show gradual alignment processes, indicating strong band interactions associated with the $i_{13/2}$ neutron alignments. The band properties are compared with those in the neighboring nuclei and discussed within the framework of the cranked shell model.

The consequences of the spontaneous breaking of rotational symmetry are investigated in a field theory model for deformed nuclei, based on simple separable interactions. The crucial role of the Ward-Takahashi identities in describing the rotational states is emphasized. We show explicitly how the rotor picture emerges from the isoscalar Goldstone modes and how the two-rotor model emerges from the isovector scissors modes. As an application of the formalism, we discuss the $M1$ sum rules in deformed nuclei and make the connection to empirical information.

The shapes of light normal nuclei and $\Lambda$ hypernuclei are investigated in the $(\beta ,\gamma )$ deformation plane by using a newly developed constrained relativistic mean field (RMF) model. As examples, the results of some C, Mg, and Si nuclei are presented and discussed in details. We found that for normal nuclei the present RMF calculations and previous Skyrme-Hartree-Fock models predict similar trends of the shape evolution with the neutron number increasing. But some quantitative aspects from these two approaches, such as the depth of the minimum and the softness in the $\gamma$ direction, differ a lot for several nuclei. For $\Lambda$ hypernuclei, in most cases, the addition of a $\Lambda$ hyperon alters slightly the location of the ground state minimum toward the direction of smaller $\beta$ and softer $\gamma$ in the potential energy surface $E\sim (\beta ,\gamma )$. There are three exceptions, namely, ${}_{\Lambda }^{13}$C, ${}_{\Lambda }^{23}$C, and ${}_{\Lambda }^{31}$Si in which the polarization effect of the additional $\Lambda$ is so strong that the shapes of these three hypernuclei are drastically different from their corresponding core nuclei.

We performed at ISOLDE the spectroscopy of the decay of the $8^{-}$ isomer in ${}^{136}$Cs by $\gamma$ and conversion-electron detection. For the first time the excitation energy of the isomer and the multipolarity of its decay have been measured. The half-life of the isomeric state was remeasured to $T_{1/2}=17.5\left(2\right)$ s. This isomer decays via a very slow 518-keV $E3$ transition to the ground state. In addition to this, a much weaker decay branch via a 413-keV $M4$ and a subsequent 105-keV $E2$ transition has been found. Thus we have found a new level at 105 keV with spin $4^{+}$ between the isomeric and the ground state. The results are discussed in comparison to shell-model calculations.

The high-spin structure of the neutron-rich ${}^{204}$Tl isotope has been studied up to a 11.2-MeV excitation energy and a $I=30$ spin range using the deep-inelastic heavy-ion $\gamma$-spectroscopy method with reactions of ${}^{48}$Ca on thick ${}^{208}$Pb and ${}^{238}$U targets. The established structure of yrast levels involves four isomeric states up to $I^{\pi }={22}^{-}$, the highest spin state available for the maximally aligned four valence holes. The observations are interpreted and quantitatively confirmed by shell-model calculations. The rates of the identified M2 and E3 isomeric decays are discussed and a striking analogy is found for the yrast level structures and $\gamma$ decays observed in the ${18}^{+}$ to ${22}^{-}$ and $45/2^{-}$ to $53/2^{+}$ spin ranges in ${}^{204}$Tl and ${}^{203}$Hg, respectively. In the highest spin part of the scheme, two prominently populated yrast states are tentatively identified as the $3^{-}$ ${}^{208}$Pb core excitation built on the ${22}^{-}$ and ${20}^{+}$ maximally aligned four-hole states. Their energies are reproduced well by using energy shifts observed in experiments for the ${}^{208}$Pb core octupole excitation coupled to simpler intrinsic structures.

The role of configuration mixing in the Pt region is investigated. For this chain of isotopes, the nature of the ground state changes smoothly, being spherical around mass $A~174$ and $A~192$ and deformed around the midshell $N=104$ region. This has a dramatic effect on the systematics of the energy spectra as compared to the systematics in the Pb and Hg nuclei. Interacting boson model with configuration mixing calculations are presented for gyromagnetic factors, $\alpha$-decay hindrance factors, and isotope shifts. The necessity of incorporating intruder configurations to obtain an accurate description of the latter properties becomes evident.

Scissors modes were predicted in the framework of the two-rotor model. This model has an intrinsic harmonic spectrum, so that the level above the scissors mode, the first overtone, has excitation energy twice that of the scissors mode. Because the latter is of the order of 3 MeV in the rare-earth region, the energy of the overtone is below threshold for nucleon emission, and its width should remain small enough for the overtone to be observable. We find that ${B\left(E2\right)\uparrow }_{\text{overtone}}=\frac{1}{64{\theta }_0^2}{B\left(E2\right)\uparrow }_{\text{scissors}}$, where ${\theta }_0$ is the zero-point oscillation amplitude, which in the rare-earth region is of order ${10}^{-1}$.

We investigate the spatial extension of weakly bound Ne and C isotopes by taking into account the pairing correlation with the Hartree-Fock-Bogoliubov (HFB) method and a three-body model, respectively. We show that the odd-even staggering in the reaction cross sections of ${}^{30,31,32}$Ne and ${}^{14,15,16}$C are successfully reproduced, and thus the staggering can be attributed to the pairing anti-halo effect. A correlation between a one-neutron separation energy and the anti-halo effect is demonstrated for $s$ and $p$ waves using the HFB wave functions.

Fast-timing measurements were performed in the region of the medium-mass ${}^{103,105,107}\mathrm{Cd}$ isotopes, produced in fusion evaporation reactions. Results on new and reevaluated half-lives are analyzed within a systematic study of transition rates. The $7/2_1^{+}$ states in ${}^{103,105,107}\mathrm{Cd}$ are interpreted as arising from a single-particle excitation. The $9/2^{+}$ states configuration assignment is based on the observed decay branches.

New $\gamma$ transitions have been identified in argon isotopes in ${}^{40}$Ar + ${}^{208}$Pb multiple transfer reactions by exploiting, in a fragment-$\gamma$ measurement, the new generation of magnetic spectrometers based on trajectory reconstruction coupled to large $\gamma$ arrays. The coupling of single-particle degrees of freedom to nuclear vibration quanta was discussed. The interpretation of the newly observed states within a particle-phonon coupling picture was used to consistently follow, via their excitation energies, the evolution of collectivity in odd Ar isotopes. The proposed level schemes are supported by the results of $sd$-$pf$ shell-model calculations, which have been also employed to evaluate the strength functions of the populated states.

An extension of the Interacting Boson Model that includes the cubic ${(\widehat{Q}\times \widehat{Q}\times \widehat{Q})}^{\left(0\right)}$ term is proposed. The potential energy surface for the cubic quadrupole interaction is explicitly calculated within the coherent state formalism using the complete ($\chi -$dependent) expression for the quadrupole operator. The $Q$-cubic term is found to depend on the asymmetry deformation parameter $\gamma$ as a linear combination of $\cos \left(3\gamma \right)$ and ${\cos }^2\left(3\gamma \right)$ terms, thereby allowing for triaxiality. The phase diagram of the model in the large $N$ limit is explored: The orders of the phase transition surfaces that define the phase diagram are described, and the possible nuclear equilibrium shapes are established. It is found that for this particular Hamiltonian, contrary to expectations, there is only a very tiny region of triaxiality, and that the transition from prolate to oblate shapes is so fast that, in most cases, the onset of triaxiality might go unnoticed.

In this paper, nuclear reaction cross sections for 24 fission-like fragments ($30⩽Z⩽60$) have been measured for the 6.5 MeV/A ${}^{16}\mathrm{O}+{}^{181}$Ta system. The recoil-catcher activation technique was employed followed by off-line $\gamma$ spectroscopy. The isotopic yield distributions for yttrium and indium isotopes have been obtained from the experimental data. The variance of the presently measured isotopic yield distributions have been found to be in agreement with the literature values. However, the variance of the mass distribution of fission residues has found to be narrower as compared to other relatively heavier systems. A self-consistent approach to determining the isobaric charge dispersion parameters has been adopted. The measured fission cross sections at 97 and 100 MeV are satisfactorily described by a statistical model code. An attempt has been made to explain the production cross sections of intermediate mass residues in the fission of heavy residues populated via complete and/or incomplete fusion processes.

We study dynamical effects in proton breakup from a weakly bound state in an exotic nucleus on a heavy target. The Coulomb interactions between the proton and the core and between the proton and the target are treated to all orders, including also the full multipole expansion of the Coulomb potential. The dynamics of proton nuclear and Coulomb breakup is compared to that of an equivalent neutron of higher binding energy in order to elucidate the differences with the well-understood neutron breakup mechanism. A number of experimentally measurable observables such as parallel momentum distributions, proton angular distributions, and total breakup cross sections are calculated. With respect to nuclear breakup it is found that a proton behaves exactly as a neutron of higher binding energy. The extra “effective energy” is caused by the combined core-target Coulomb barrier. In Coulomb breakup we distinguish the effect of the core-target Coulomb potential (called the recoil effect), with respect to which the proton behaves, again, as a more bound neutron, from the direct proton-target Coulomb potential. The latter gives cross sections about an order of magnitude larger than the recoil term. The two effects give rise to complicated interferences in the parallel momentum distributions. They are instead easily separable in the proton angular distributions, which are therefore suggested as a very useful observable for future experimental studies.

We describe how various hadronic cascade models, which are implemented in the geant4 toolkit, describe proton and charged pion transverse momentum spectra from $p$ $+$ Cu and Pb collisions at 3, 8, and 15 GeV/$c$, recently measured in the hadron production (HARP) experiment at CERN. The Binary, ultrarelativistic quantum molecular dynamics (UrQMD) and modified FRITIOF (FTF) hadronic cascade models are chosen for investigation. The first two models are based on limited (Binary) and branched (UrQMD) binary scattering between cascade particles which can be either a baryon or meson, in the three-dimensional space of the nucleus, while the latter (FTF) considers collective interactions between nucleons only, on the plane of impact parameter. It is found that the slow ($p_T⩽0.3$ GeV/$c$) proton spectra are quite sensitive to the different treatments of cascade pictures, while the fast ($p_T>0.3$ GeV/$c$) proton spectra are not strongly affected by the differences between the FTF and UrQMD models. It is also shown that the UrQMD and FTF combined with Binary (FTFB) models could reproduce both proton and charged pion spectra from $p$ $+$ Cu and Pb collisions at 3, 8, and 15 GeV/$c$ with the same accuracy.

In this paper, our goal is to make a simultaneous analysis of the high- and low-$P_T$ parts of the charged-hadron $P_T$ spectrum measured by the ALICE collaboration [K. Aamodt et al. (ALICE Collaboration), Phys. Lett. B 696, 30 (2011)] in central Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV at the Large Hadron Collider (LHC), based on models which have been successfully applied and constrained in Au-Au collisions at the Relativistic Heavy Ion Collider (RHIC). For the hydrodynamical modeling with which we obtain the low-$P_T$ spectrum, we have computed the initial conditions based on perturbative QCD (pQCD) minijet production and saturation. The sensitivity of the obtained charged-hadron $P_T$ spectrum on the hydrodynamic model parameters is studied. For the high-$P_T$ part, we apply a number of parton-medium interaction models, which are tuned to describe the nuclear suppression factor $R_{AA}$ measured at RHIC in central Au-Au collisions at $\sqrt{s_{NN}}=200$ GeV. We find that the higher kinematic reach of the LHC, manifest in the hardening of the pQCD parton spectral slope, is in principle very efficient in discriminating the various models. However, due to the uncertainties in the $p$-$p$ baseline, none of the tested models can be firmly ruled out with the present ALICE data. Comparison with the LHC data in this approach shows that the combined hydrodynamic and pQCD + jet quenching components can reproduce the data well in the whole measured $P_T$ range.

In the present work the sensitivity of calculated $\beta \beta$-decay amplitudes to a realistic residual interaction is analyzed in the framework of the approach of O. A. Rumyantsev and M. H. Urin, Phys. Lett. B 443, 51 (1998). and V. A. Rodin, M. H. Urin, and A. Faessler, Nucl. Phys. A 747, 297 (2005). Both the Gamow-Teller (GT) and Fermi (F) matrix elements $M^{2\nu }$ for two-neutrino $\beta \beta$ decay ($2\nu \beta \beta$ decay), along with the monopole transition contributions to the total matrix elements $M^{0\nu }$ of neutrinoless $\beta \beta$ decay ($0\nu \beta \beta$ decay), are calculated within the quasiparticle random-phase approximation (QRPA). In the aforementioned approach decompositions of $M^{2\nu }$ and $M^{0\nu }$ can be obtained in terms of the corresponding energy-weighted sum rules $S$. It is shown that in most of the cases almost the whole dependence of $M^{2\nu }$ and $M^{0\nu }$ on the particle-particle (p-p) renormalization parameter $g_{\mathrm{pp}}$ is accounted for by the $g_{\mathrm{pp}}$ dependence of the corresponding sum rules $S$. General expressions relating $S$ to a realistic residual particle-particle interaction are derived, which show a pronounced sensitivity of $S$ to the singlet-channel interaction in the case of F transitions and to the triplet-channel interaction in the case of GT transitions. Thus, the sensitivity of $M^{2\nu }$ and $M^{0\nu }$ to the SU(4)-symmetry-breaking part of the p-p residual interaction is dictated by the generic structure of the $\beta \beta$-decay amplitudes. Therefore, a choice of this part in a particular calculation needs a special caution. Finally, a better isospin-consistent way of renormalization of a realistic residual p-p interaction to use in QRPA calculations is suggested.

A new value for the hyperfine magnetic field of copper impurities in iron is obtained by combining resonance frequencies from experiments involving $\beta$-NMR on oriented nuclei on ${}^{59}\mathrm{Cu}$, ${}^{69}\mathrm{Cu}$, and ${}^{71}\mathrm{Cu}$ with magnetic moment values from collinear laser spectroscopy measurements on these isotopes. The resulting value, i.e., $B_{\mathrm{hf}}(\mathrm{CuFe})\mathrm{\hspace{0.5em}}=\mathrm{\hspace{0.5em}}-21.794$(10) T, is in agreement with the value adopted until now but is an order of magnitude more precise. It is consistent with predictions from ab initio calculations. Comparing the hyperfine field values obtained for the individual isotopes, the hyperfine anomalies in Fe were determined to be ${}^{59}{\Delta }^{69}=0.15$(9)$\%$ and ${}^{71}{\Delta }^{69}=0.07$(11)$\%$.

Quasielastic excitation function measurement has been carried out for the ${}^4$He $+$ ${}^{232}$Th system at ${\theta }_{\text{lab}}={160}^{\circ }$ with respect to the beam direction, to obtain a representation of the fusion-barrier distribution. Using the present data along with previously measured barrier distribution results on ${}^{12}$C, ${}^{16}$O, and ${}^{19}$F $+$ ${}^{232}$Th systems, a systematic analysis has been carried out to investigate the role of target and/or projectile structures on fusion-barrier distribution. It is observed that for ${}^4$He, ${}^{12}$C, and ${}^{16}$O $+$ ${}^{232}$Th reactions, the couplings due to target states only are required in coupled-channel fusion calculations to explain the experimental data, whereas for the ${}^{19}$F $+$ ${}^{232}$Th system along with the coupling of target states, inelastic states of ${}^{19}$F are also required to explain the experimental results on fusion-barrier distribution. The width of the barrier distribution shows interesting transition behavior when plotted with respect to the target-projectile charge product for the above systems.

A semi-microscopic model for nucleon pairing in nuclei is presented starting from the ab initio BCS gap equation with the Argonne v${}_{18}$ force and the self-consistent energy density functional method basis characterized by the bare nucleon mass. The BCS theory is formulated in terms of the model space $S_0$ with the effective pairing interaction calculated from the first principles in the subsidiary space $S^{\prime }$. This effective interaction is supplemented with a small phenomenological addendum containing one phenomenological parameter, universal for all medium and heavy atomic nuclei. We consider the latter as a phenomenological way to take into account approximately both the many-body corrections to the BCS theory and the effective mass effects. For protons, the Coulomb interaction is introduced directly. Calculations made for several isotopic and isotonic chains of semi-magic nuclei are compared with empirical gap values derived from odd-even mass differences. The average disagreement is of the order of $0.1\text{--}0.2$MeV. The role of the self-consistent basis is analyzed.