[Background] The $\alpha$-cluster model was successful for describing spectroscopic properties of light nuclei near the shell closures. Evidences of the $\alpha$-cluster structure in ${}^{94}\mathrm{Mo}$ were shown, motivating the search for the same structure in other intermediate mass nuclei. [Purpose] The systematic analysis of the $\alpha$-cluster structure in ${}^{94}\mathrm{Mo}$ and four even-even neighboring nuclei. [Method] The $\alpha$-cluster model with the local potential approach. [Results] A good general description of the experimental ground state bands is obtained with only one variable parameter. It is shown that the employed $\alpha +\text{core}$ potential is weakly dependent on the angular momentum $L$ and such dependence may be described satisfactorily by a simple $L$-dependent factor for the five nuclei. The radial parameter of the $\alpha +\text{core}$ potential reveals a linear trend in relation to the total nuclear radius and the sum of the $\alpha$-cluster and core radii. The calculated $B\left(E2\right)$ transition rates reproduce correctly the order of magnitude of almost all experimental data without the use of effective charges. The rms intercluster separations and reduced $\alpha$ widths obtained for the ground state bands point to a reduction of the $\alpha$-cluster intensity with the increasing spin. Negative parity bands are calculated and compared to available experimental levels. The volume integral per nucleon pair and rms radii were calculated for the studied $\alpha +\text{core}$ potentials, revealing a similarity with the real parts of the optical potentials used to describe the $\alpha +{}^{90}\mathrm{Zr}$ and $\alpha +{}^{92}\mathrm{Mo}$ elastic scattering at several energies. [Conclusions] This work strongly indicates the presence of similar $\alpha +\text{core}$ structures for the $N=52$ even-even nuclei of the Mo region.

The low-lying positive- and negative-parity states in ${}^{168}\mathrm{Yb}$ have been investigated by means of the $(\alpha ,2\mathrm{n}\gamma )$ fusion evaporation reaction. Using the coincidence method, the level scheme was corrected and extended up to 3 MeV, for both the positive- and negative-parity states. Using the new branching ratios determined in the present experiment, the $K$ quantum number was proposed for two negative-parity bands by direct comparison with the Alaga rule. Like in some other nuclei, one negative-parity band was established, decaying predominantly to the $\gamma$-vibrational band. In a second experiment, the lifetimes of the low-lying excited states up to $J^{\pi }=6^{+}$ in the ground-state band were measured by using the in-beam fast-timing method with the Bucharest mixed high-purity germanium (HPGe) and ${\mathrm{LaBr}}_3$:Ce detector array using the triple-$\gamma$ coincidence method. Reduced $E2$ transition probabilities were extracted from the measured lifetimes and compared with the corresponding observables in neighboring isotopes, showing a smooth behavior with increasing mass. The positive- and negative-parity states as well as $E1$ and $E2$ transition probability ratios revealed by these experiments are compared with the interacting boson model in the $sd$ and $spdf$ boson space, and with the confined beta-soft rotor model, and are found to be in good agreement.

We analyze the sensitivity of $\beta$-decay rates in ${}^{78}\mathrm{Ni}$ and ${}^{100,132}\mathrm{Sn}$ to a correction term in Skyrme energy-density functionals (EDFs) which modifies the radial shape of the nucleon effective mass. This correction is added on top of several Skyrme parametrizations which are selected from their effective mass properties and predictions about the stability properties of ${}^{132}\mathrm{Sn}$. The impact of the correction on high-energy collective modes is shown to be moderate. From the comparison of the effects induced by the surface-peaked effective mass in the three doubly magic nuclei, it is found that ${}^{132}\mathrm{Sn}$ is largely impacted by the correction, while ${}^{78}\mathrm{Ni}$ and ${}^{100}\mathrm{Sn}$ are only moderately affected. We conclude that $\beta$-decay rates in these nuclei can be used as a test of different parts of the nuclear EDF: ${}^{78}\mathrm{Ni}$ and ${}^{100}\mathrm{Sn}$ are mostly sensitive to the particle-hole interaction through the $B\left(\text{GT}\right)$ values, while ${}^{132}\mathrm{Sn}$ is sensitive to the radial shape of the effective mass. Possible improvements of these different parts could therefore be better constrained in the future.

I study the effect of nuclear equation of state on the $r$-mode instability of a rotating neutron star. I consider the case where the crust of the neutron star is perfectly rigid and I employ the related theory introduced by Lindblom et al. [Phys. Rev. D 62, 084030 (2000)]. The gravitational and the viscous time scales, the critical angular velocity, and the critical temperature are evaluated by employing a phenomenological nuclear model for the neutron-star matter. The predicted equations of state for the $\beta$-stable nuclear matter are parameterized by varying the slope $L$ of the symmetry energy at saturation density on the interval $72.5\mathrm{MeV}\le L\le 110\mathrm{MeV}$. The effects of the density dependence of the nuclear symmetry energy on $r$-mode instability properties and the time evolution of the angular velocity are presented and analyzed. A comparison of theoretical predictions with observed neutron stars in low-mass x-ray binaries and millisecond radio pulsars is also performed and analyzed. I estimate that it may be possible to impose constraints on the nuclear equation of state by a suitable treatment of observations and theoretical predictions of the rotational frequency and spin-down rate evolution of known neutron stars.

We develop our previous study of the transition to deconfined quark phase in neutron stars, including the interaction in the quark equation of state to the leading order in the perturbative expansion within the confinement density-dependent mass model. Using the Gibbs conditions the hadron-quark mixed phase is constructed matching the latter with the hadron equation of state derived from the microscopic Brueckner-Hartree-Fock approximation. The influence of quark interaction parameters on threshold properties and phase diagram of dense neutron star matter are discussed in detail. We find that the leading-order quark interaction expands the density range of the mixed phase, pushing forward the disappearance of the hadron phase. Moreover, since the equation of state could turn out to be stiffer, a high-mass hybrid star is possible with mixed-phase core with typical parameter sets.

Excited states in the neutron-deficient nuclei ${}_{75}^{163}{\mathrm{Re}}_{88}$ and ${}_{75}^{165}{\mathrm{Re}}_{90}$ were populated in the ${}^{106}{\mathrm{Cd}(}^{60}\mathrm{Ni},p2n\gamma )$ and ${}^{92}{\mathrm{Mo}(}^{78}\mathrm{Kr}$, $3p2n\gamma )$ fusion-evaporation reactions at bombarding energies of 270 and 380 MeV, respectively. γ rays were detected at the target position using the JUROGAM spectrometer while recoiling ions were separated in-flight by the RITU gas-filled recoil separator and implanted in the GREAT spectrometer. The energy level schemes for ${}^{163}\mathrm{Re}$ and ${}^{165}\mathrm{Re}$ were identified using recoil-decay correlation techniques. At low spin, the yrast bands of these isotopes consist of signature partner bands based on a single $\pi h_{11/2}$ quasiproton configuration. The bands display large energy splitting consistent with the soft triaxial shape typical of transitional nuclei above $N=82$. The configurations of the excited states are proposed within the framework of the cranked shell model.

Background: The standard kinematic method for determining neutrino mass from the $\beta$ decay of tritium or other isotope is to measure the shape of the electron spectrum near the endpoint. A similar distortion of the “visible energy” remaining after electron capture is caused by neutrino mass. There has been a resurgence of interest in using this method with ${}^{163}\mathrm{Ho}$, driven by technological advances in microcalorimetry. Recent theoretical analyses offer reassurance that there are no significant theoretical uncertainties.

Purpose: The theoretical analyses consider only single vacancy states in the daughter ${}^{163}\mathrm{Dy}$ atom. It is necessary to consider configurations with more than one vacancy that can be populated owing to the change in nuclear charge.

Method: The shakeup and shake-off theory of Carlson and Nestor is used as a basis for estimating the population of double-vacancy states.

Results: A spectrum of satellites associated with each primary vacancy created by electron capture is presented.

Conclusions: The theory of the calorimetric spectrum is more complicated than has been described heretofore. There are numerous shakeup and shake-off satellites present across the spectrum, and some may be very near the endpoint. The spectrum shape is presently not understood well enough to permit a sensitive determination of the neutrino mass in this way.

A previous study of nuclear matter in a chiral nucleon-meson model is extended to isospin-asymmetric matter. Fluctuations beyond mean-field approximation are treated in the framework of the functional renormalization group. The nuclear liquid-gas phase transition is investigated in detail as a function of the proton fraction in asymmetric matter. The equations of state at zero temperature of both symmetric nuclear matter and pure neutron matter are found to be in good agreement with realistic many-body computations. We also study the density dependence of the pion mass in the medium. The question of chiral symmetry restoration in neutron matter is addressed; we find a stabilization of the phase with spontaneously broken chiral symmetry once fluctuations are included. Finally, neutron-star matter including $\beta$ equilibrium is discussed. The model satisfies the constraints imposed by the existence of two-solar mass neutron stars.

The three-nucleon bound and scattering equations are solved in momentum space for a coupled-channels Hamiltonian. The Hamiltonian couples the purely nucleonic sector of Hilbert space with a sector in which one nucleon is excited to a $\Delta$ isobar. The interaction consists of irreducible two-baryon and irreducible three-baryon potentials. The calculation keeps only the purely nucleonic one among the irreducible three-baryon potentials. The coupled-channels two-baryon potential yields additional reducible contributions to the three-nucleon force. The Coulomb interaction between the two protons is included using the method of screening and renormalization. Three-nucleon force effects on the bound-state energies and on observables of elastic nucleon-deuteron scattering and breakup are studied.

The excited states of the ${}^{20}\mathrm{Ne}$ nucleus from the ground state to $E_x$ = 25 MeV were investigated with the ${}^{22}\mathrm{Ne}$($p,t$)${}^{20}\mathrm{Ne}$ reaction at a beam energy of $E_p$ = 60 MeV using the QDD magnetic spectrometer at iThemba LABS. Narrow, low-spin $J^{\pi }=0^{+},1^{-}$, and $2^{+}$ states have been observed for the first time at high-excitation energies in ${}^{20}\mathrm{Ne}$, namely at $E_x$ = 17.67, 18.84, 20.59, 21.16, 21.80, and 22.5 MeV. Shell-model and coupled reaction channel calculations were performed to determine the nature of the newly observed states. Candidates for $T$ = 2 states are proposed at 3.86(5), 4.43(5) MeV and 5.07(5) MeV above the lowest $0^{+},T$ = 2 state at $E_x=16.73$ MeV. Two of these $T$ = 2 candidates appear to result from core excitations in the $0p$ shell. The state at $E_x$ = 22.5 MeV, which could not be interpreted by the shell-model calculations, is a tentative candidate for the 5-$\alpha$ cluster state.

We show that the correlations of the quasiparticle random-phase approximation (QRPA) significantly reduce the nuclear matrix element (NME) of neutrinoless $\text{double}-\beta$ decay by a new mechanism in the calculation for ${}^{150}\mathrm{Nd}\to {}^{150}\mathrm{Sm}$. This effect is due mainly to the normalization factors of the QRPA ground states included in the overlap of intermediate states, to which the QRPA states based on the initial and final ground states are applied. These normalization factors arise according to the definition of the QRPA ground state as the vacuum of quasibosons. Our NME is close to those of other groups in spite of this new reduction effect because we do not use the proton-neutron pairing interaction that is usually used for reproducing the experimental NME of the two-neutrino $\text{double}-\beta$ ($2\nu \beta \beta$) decay, without those normalization factors, and reduces the NME appreciably. Our method can reproduce the experimental $2\nu \beta \beta$ NME for ${}^{150}\mathrm{Nd}\to {}^{150}\mathrm{Sm}$ with the quenching axial-vector current coupling without approaching the breaking point of the QRPA. The consistency of QRPA approaches taking different virtual paths under the closure approximation is also discussed, and an extension of the QRPA ground state is proposed.

We formulate the Gamow shell model (GSM) in coupled-channel (CC) representation for the description of proton/neutron radiative capture reactions and present the first application of this new formalism for the calculation of cross sections in mirror reactions ${}^7\mathrm{Be}(p,\gamma ){}^8\mathrm{B}$ and ${}^7\mathrm{Li}{(n,\gamma )}^8\mathrm{Li}$. The GSM-CC formalism is applied to a translationally invariant Hamiltonian with an effective finite-range two-body interaction. Reactions channels are built by GSM wave functions for the ground state $3/2^{-}$ and the first excited state $1/2^{-}$ of ${}^7\mathrm{Be}$/${}^7\mathrm{Li}$ and the proton/neutron wave function expanded in different partial waves.

Background: Astrophysical reaction rates, which are mostly derived from theoretical cross sections, are necessary input to nuclear reaction network simulations for studying the origin of $p$ nuclei. Past experiments have found a considerable difference between theoretical and experimental cross sections in some cases, especially for ($\alpha ,\gamma$) reactions at low energy. Therefore, it is important to experimentally test theoretical cross section predictions at low, astrophysically relevant energies.

Purpose: The aim is to measure reaction cross sections of ${}^{107}\mathrm{Ag}\left(\alpha ,\gamma \right){}^{111}\mathrm{In}$ and ${}^{107}\mathrm{Ag}\left(\alpha ,n\right){}^{110}\mathrm{In}$ at low energies in order to extend the experimental database for astrophysical reactions involving $\alpha$ particles towards lower mass numbers. Reaction rate predictions are very sensitive to the optical model parameters and this introduces a large uncertainty into theoretical rates involving $\alpha$ particles at low energy. We have also used Hauser-Feshbach statistical model calculations to study the origin of possible discrepancies between prediction and data.

Method: An activation technique has been used to measure the reaction cross sections at effective center of mass energies between 7.79 MeV and 12.50 MeV. Isomeric and ground state cross sections of the ($\alpha ,n$) reaction were determined separately.

Results: The measured cross sections were found to be lower than theoretical predictions for the ($\alpha ,\gamma$) reaction. Varying the calculated averaged widths in the Hauser-Feshbach model, it became evident that the data for the ($\alpha ,\gamma$) and ($\alpha ,n$) reactions can only be simultaneously reproduced when rescaling the ratio of $\gamma$ to neutron width and using an energy-dependent imaginary part in the optical $\alpha$ + ${}^{107}\mathrm{Ag}$ potential.

Conclusions: The new data extend the range of measured charged-particle cross sections for astrophysical applications to lower mass numbers and lower energies. The modifications in the model predictions required to reproduce the present data are fully consistent with what was found in previous investigations. Thus, our results confirm the previously suggested energy-dependent modification of the optical $\alpha$+nucleus potential.

The quantum mechanical effects are investigated on the half-life of $\alpha$ decay. To this aim the penetration probability in $\alpha$ decay of spherical isotopes of ${}^{146}\mathrm{Sm},{}^{148}\mathrm{Sm},{}^{148}\mathrm{Gd}$, and ${}^{224}\mathrm{Ra}$ is calculated by employing coupled channel formalism by considering the effects of surface vibrations in the daughter nucleus; the obtained results are compared with those calculated by the semiclassical WKB approximation using two versions of the proximity potential. It is shown that by including low-lying excitation states the results are modified, in better agreement with experimental data.

Background: The nucleosynthesis of the neutron-deficient $p$ nuclei remains an open question in nuclear astrophysics. Beside uncertainties on the astrophysical side, the nuclear-physics input parameters entering Hauser-Feshbach calculations for the nucleosynthesis of the $p$ nuclei must be put on a firm basis.

Purpose: An extended database of experimental data is needed to address uncertainties of the nuclear-physics input parameters for Hauser-Feshbach calculations. Especially $\alpha$ + nucleus optical model potentials at low energies are not well known. The in-beam technique with an array of high-purity germanium (HPGe) detectors was successfully applied to the measurement of absolute cross sections of an $(\alpha ,\gamma )$ reaction on a heavy nucleus at sub-Coulomb energies.

Method: The total and partial cross-section values were measured by means of in-beam $\gamma$-ray spectroscopy. For this purpose, the absolute reaction yield was measured using the HPGe detector array HORUS at the FN tandem accelerator at the University of Cologne. Total and partial cross sections were measured at four different $\alpha$-particle energies from $E_{\alpha }=10.5\mathrm{MeV}$ to $E_{\alpha }=12\mathrm{MeV}$.

Results: The measured total cross-section values are in excellent agreement with previous results obtained with the activation technique, which proves the validity of the applied method. With the present measurement, the discrepancy between two older data sets is removed. The experimental data was compared to Hauser-Feshbach calculations using the nuclear reaction code talys. With a modification of the semi-microscopic $\alpha$ + nucleus optical model potential OMP 3, the measured cross-section values are reproduced well. Moreover, partial cross sections could be measured for the first time for an $(\alpha ,\gamma )$ reaction.

Conclusions: A modified version of the semimicroscopic $\alpha$ + nucleus optical model potential OMP3, as well as modified proton and $\gamma$ widths, are needed in order to obtain a good agreement between experimental data and theory. It is found that a model using a local modification of the nuclear-physics input parameters simultaneously reproduces total cross sections of the ${}^{112}\mathrm{Sn}(\alpha ,\gamma )$ and ${}^{112}\mathrm{Sn}(\alpha ,p)$ reactions. The measurement of partial cross sections turns out to be very important in this case in order to apply the correct $\gamma$-ray strength function in the Hauser-Feshbach calculations. The model also reproduces cross-section values of $\alpha$-induced reactions on ${}^{106}\mathrm{Cd}$, as well as of $(\alpha ,n)$ reactions on ${}^{115,116}\text{Sn}$, hinting at a more global character of the obtained nuclear-physics input.

Accurate knowledge about the neutron skin thickness $\Delta R_{np}$ in ${}^{208}\mathrm{Pb}$ has far-reaching implications for different communities of nuclear physics and astrophysics. Yet, the novel lead radius experiment (PREX) did not yield any stringent constraint on $\Delta R_{np}$ recently. We employ a more practicable strategy to probe the neutron skin thickness of ${}^{208}\mathrm{Pb}$ based on a high linear correlation between the $\Delta R_{np}$ and $J-a_{\text{sym}}$, where $J$ and $a_{\text{sym}}$ are the symmetry energy (coefficient) of nuclear matter at saturation density and of ${}^{208}\mathrm{Pb}$. An accurate $J-a_{\text{sym}}$ thus places a strong constraint on the $\Delta R_{np}$. Compared with the parity-violating asymmetry $A_{\text{PV}}$ in the PREX, the reliably experimental information on the $J-a_{\text{sym}}$ is much more easily available thanks to the wealth of measured data on nuclear masses and decay energies. The density dependence of the symmetry energy is also well constrained with the $J-a_{\text{sym}}$. Finally, with a “tomoscan” method, we find that one just needs to measure the nucleon densities in ${}^{208}\mathrm{Pb}$ starting from $R_m=7.61\pm 0.04$ fm to obtain the $\Delta R_{np}$ in hadron scattering experiments, regardless of its interior profile being hampered by strong absorption.

An extension of the time-dependent Hartree-Fock-Bogoliubov theory (ETDHFB) which includes higher-order effects such as screening of the pairing correlation is proposed. ETDHFB is applied to a pairing model and a fermion system trapped in a harmonic potential to test its feasibility by comparison with exact solutions. With the use of perturbative expressions for the pairing tensor and the two-body density matrix derived from ETDHFB, the screening effect is investigated for atomic fermion systems and isotopes of tin nuclei. It is found that the screening effect on the pairing correlation is not significant.