Background: The observation of the superdeformed (SD) bands in ${}^{60,62}\mathrm{Zn}$ indicates that the particle number 30 is a magic particle number, where two- and four-neutron single particles are considered to be promoted to the intruder $1g_{9/2}$ shell. However, the SD-yrast band in ${}^{62}\mathrm{Zn}$ is assigned negative parity.

Purpose: I investigate various SD configurations in the rapidly rotating ${}^{60,62}\mathrm{Zn}$ and ${}^{64}\mathrm{Ge}$, and attempt elucidating the different roles of the energy gaps at particle numbers 30 and 32.

Method: I employ a nuclear energy-density functional method: the configuration-constrained cranked Skyrme-Kohn-Sham approach is used to describe the rotational bands near the yrast line.

Results: The negative-parity SD bands appear higher in energy than the positive-parity SD-yrast band in ${}^{60}\mathrm{Zn}$ by about 4 MeV, which is indicative of the SD doubly magic nucleus. However, the energy gap in ${}^{64}\mathrm{Ge}$ is smaller $\approx 2–3$ MeV, though the quadrupole deformation of the SD states in ${}^{64}\mathrm{Ge}$ is greater than that of ${}^{60}\mathrm{Zn}$. The present calculation predicts the occurrence of the hyperdeformed state in ${}^{60}\mathrm{Zn}$ and ${}^{64}\mathrm{Ge}$ at a high rotational frequency $\approx 2.0\mathrm{MeV}/\hslash$ due to the occupation of the $h_{11/2}$ shell.

Conclusions: An SD-shell gap at particle number 30 and 32 appears at different deformations and the energy gap at particle number 32 is low, which make the SD structures of ${}^{62}\mathrm{Zn}$ unique, where the negative-parity SD states appear lower in energy than the positive-parity one.

Background: Isomeric states in atomic nuclei are a sensitive probe of their underlying microscopic structure and can be used to study the evolution of shell structure far from stability. Recent studies have identified and provided detailed spectroscopy of isomers in neutron-rich nuclei with $Z=28\text{−}50$. Isomeric states in the odd-odd gallium isotopes have been reported for all gallium isotopes from $A=72$ to $A=80$ with the exception of ${}^{76}\mathrm{Ga}$.

Purpose: The purpose of this experiment was to observe short-lived isomeric states in the vicinity of ${}^{78}\mathrm{Ni}$.

Methods: In-beam fragmentation of a ${}^{86}\mathrm{Kr}$ primary beam at the National Superconducting Cyclotron Laboratory produced radioactive ions which were delivered to and deposited in a $\mathrm{Ce}{\mathrm{Br}}_3$ scintillator coupled to a position-sensitive photomultiplier tube. Beta-delayed $\gamma$ rays were measured by ancillary HPGe clover and $\mathrm{La}{\mathrm{Br}}_3$ detectors which surrounded the implantation detector.

Results: The previously observed $J^{\pi }=1^{+}$, 199-keV level in ${}^{76}\mathrm{Ga}$, populated following the $\beta$ decay of ${}^{76}\mathrm{Zn}$, was identified as isomeric with a half-life of $34{\left(1\right)}_{\text{stat.}}{\left(8\right)}_{\text{sys.}}\mathrm{ns}$. Shell-model calculations suggest this state is formed by the coupling of protons in negative-parity configurations to $1/2^{-}$ neutron configurations. Transition strengths assuming a ground-state spin of $J=2$ and $J=3$ were determined from the experimental data.

The spectroscopy of ${}^{11}\mathrm{C}$ has been investigated by the resonant scattering of ${}^{10}\mathrm{B}+p$ with the thick target inverse kinematic method. The ${}^1\mathrm{H}({}^{10}\mathrm{B},p){}^{10}\mathrm{B}$ reaction was measured at ${\theta }_{\mathrm{c}.\mathrm{m}.}={180}^{\circ }, {170}^{\circ }, {160}^{\circ }, {150}^{\circ }$, and ${140}^{\circ }$ using a 35.93 MeV ${}^{10}\mathrm{B}$ beam. Resonances in ${}^{11}\mathrm{C}$ between the excitation energy of 9.6 and 11.8 MeV are observed. The excitation functions are compared with previous data using thin target direct kinematics measurements. A multichannel $R$-matrix calculation under the kinematics assumption of resonant elastic scattering is performed and the resonant parameters, such as the resonant energy $E_x$, the spin-parity $J^{\pi }$, and the proton-decay partial width ${\mathrm{\Gamma }}_p$ are extracted.

To explore the optimum conditions for producing new neutron-rich isotopes in the range $92\le Z\le 100$ by multinucleon transfer reactions, ${}^{86}\mathrm{Kr}+{}^{248}\mathrm{Cm}, {}^{129}\mathrm{Xe}+{}^{248}\mathrm{Cm}, {}^{132}\mathrm{Xe}+{}^{248}\mathrm{Cm}, {}^{136}\mathrm{Xe}+{}^{248}\mathrm{Cm}$ and ${}^{238}\mathrm{U}+{}^{248}\mathrm{Cm}$ systems with bombarding energies around their respective Coulomb barriers are investigated within an improved dinuclear system (DNS) model, combined with the statistical gemini$++$ model. The calculated production cross sections are in a good agreement with experimental data. It is found that, compared with projectiles ${}^{86}\mathrm{Kr}$ and ${}^{136}\mathrm{Xe}$, the projectile ${}^{238}\mathrm{U}$ can produce larger cross sections of neutron-rich nuclei of interest by bombarding the actinide target ${}^{248}\mathrm{Cm}$. Actinide projectile-target combination seems to be encouraging for the production of neutron-rich isotopes with $92\le Z\le 100$.

In the present work, we systematically study the effect of ultra-intense laser fields on proton radioactivity of deformed proton emitters with the state-of-the-art Gaussian laser and the latest evaluated nuclear properties table. The calculated results indicate that ultra-intense laser fields affect the proton radioactivity half-life by changing the proton radioactivity penetration probability to some small but finite extent, and the ${}^{108}\mathrm{I}$ is the most sensitive parent nuclei to the strong laser pulse. Moreover, we found that the released energy of proton radioactivity is negatively related to the rate of change of the proton radioactivity penetration probability. Finally, we investigate the effect of the asymmetric chirp-laser pulse on the average rate of change in proton radioactivity penetration probability. It is shown that the rational use of positive chirp is equivalent to increasing the laser intensity by two orders of magnitude.

To describe the yrast states in weakly bound nuclei, I directly solve the coordinate-space cranked Skyrme-Hartree-Fock-Bogoliubov equation on a three-dimensional lattice with the continuum states discretized in a box. After the numerical demonstration for the ground-state band in a medium-mass nucleus, I apply the newly developed method to neutron-rich even-$N$ Mg isotopes. I find that the appearance of the significantly low $I^{\pi }=2^{+}$ state in ${}^{40}\mathrm{Mg}$ is mainly due to the suppression of pairing. The calculation predicts that the $2^{+}$ state in ${}^{42}\mathrm{Mg}$ appears as high in energy as in ${}^{34–38}\mathrm{Mg}$ whereas the triaxial deformation is enhanced in nonzero spin states. The present numerical framework offers a practical approach for investigating the near yrast states systematically and revealing structures unique in drip-line nuclei.

Background: To calculate excited states in quantum many-body systems, multiconfiguration mixing has often been employed. However, it remains unclear how to choose important Slater determinants from a huge model space.

Purpose: We propose an efficient method as the replica exchange Monte Carlo (RXMC) method to sample important Slater determinants and optimize and analyze the results obtained. As an application, we investigate the ground and excited states of ${}^{12}\mathrm{C}$ based on the Bloch-Brink $\alpha$ cluster model and show the detailed structure of the obtained states.

Methods: The RXMC method enables us to efficiently sample Slater determinants following the Boltzmann distribution on the multidimensional potential-energy surface (PES) under a given model space. To analyze the excited states obtained, we embed sampled basis functions onto the PES calculated with the $\beta \text{−}\gamma$ constraint method and discuss the main component in each state.

Results: The RXMC method efficiently performs the samplings with a temperature parameter of $T_L=2.5$ MeV in ${}^{12}\mathrm{C}$. We obtain the gas-like state with a wide density distribution in the tail part in the second $0^{+}$ state. We also obtain the linear-chain-like states with the bending and stretching vibrational modes in the third and fourth $0^{+}$ states, respectively. In the fifth $0^{+}$ state, the main component of the basis functions contains expanded equilateral-triangle configurations.

Conclusions: The second $0^{+}$ gas-like state emerges at the local minimum in the PES, which is the beginning of the valley structure connected to the linear-chain breakup channel. The third and fourth linear-chain-like states emerge in this valley structure. We conclude that the RXMC method is a powerful method to calculate the excited states of nuclei, which would be applied to much more complicated nuclear fission dynamics in heavier nuclei.

The puzzle of finding consistent nuclear configurations to explain both the decay probabilities and moments of the ${9/2}^{-}, 8^{+}$, and ${21/2}^{-}$ isomers in and around the $N=126$ closed shell has been approached in the generalized seniority scheme. Though $h_{9/2}$ is the dominant orbital near Fermi energy, the role of configuration mixing from the surrounding $f_{7/2}$ and $i_{13/2}$ orbitals is found to be very important for the consistent explanation of all the isomeric properties such as the $B\left(E2\right)$ rates, $Q\mathrm{moments},$ and $g\mathrm{factors}$. The structural behavior of the closed shell $N=126$ isotonic isomers turns out to be very similar to that of the $N=124$ and $N=128$ isotonic isomers, which have two neutron holes and two neutron particles, respectively. This is due to the pairing symmetries of nuclear many-body Hamiltonian. As confirmation, the microscopic shell model occupancies are also calculated for these isomers in the $N=126$ chain which support the generalized seniority results. Additional arguments using the systematics of odd-proton ${9/2}^{-}$ states in Tl ($Z=81$), Bi ($Z=83$), At ($Z=85$), and Fr ($Z=87$) isotopes are also presented.

This work aims to study the various thermal characteristics of nuclei in view of the saturation and critical behavior of infinite nuclear matter. The free energy of a nucleus is parametrized using the density and temperature-dependent liquid-drop model, and interaction among nucleons is worked out within the effective relativistic mean-field theory (E-RMF). The effective mass ($m^{*}$) and critical temperature of infinite symmetric nuclear matter ($T_c$) of a given E-RMF parameter force play a seminal role in the estimation of thermal properties. Larger $m^{*}$ and $T_c$ of the E-RMF set estimate larger excitation energy, level density, and limiting temperature $\left(T_l\right)$ for a given nucleus. The limiting temperature of a nucleus also depends on the behavior of the nuclear gas surrounding the nucleus, making the equation of state (EoS) at subsaturation densities an important input. A stiff EoS in the subsaturation region estimates a higher pressure of the nuclear gas, making it less stable. Since $T_c$ plays an important part in these calculations, we perform a Pearson correlation statistical study of twenty E-RMF parameter sets, satisfying the relevant constraint on the EoS. Effective mass seems to govern the thermal characteristics of infinite as well as finite nuclear matter in the framework of E-RMF theory.

Background: The projectile fragmentation is associated with the liquid-gas phase transition in the finite nuclear system. Recent experimental data and calculations by the statistical multifragmentation model indicated that the higher-order fluctuations of the largest fragment charge exhibit the signatures of the second-order phase transition [PLB809(2020)135763]. However, these higher-order fluctuations calculated by the dynamical model are still not reported.

Purpose: This work is proposed to investigate dynamically this signature and emphasize the nonequilibrium effect.

Methods: The isospin-dependent quantum molecular dynamics (IQMD) model is used to study the nonequilibrium thermalization and fragmentation in the ${}^{124}\mathrm{Sn} + {}^{120}\mathrm{Sn}$ collisions at 600 MeV/nucleon. The minimum spanning tree algorithm is applied to distinguish the hot projectile-like system during the dynamics evolution.

Results: The fluctuations of the largest fragment charge $Z_{\max }$ up to the fourth order by the IQMD model reproduce the experimental data. The pseudocritical point indicated by zero of skewness (third-order fluctuation) together with minimum of kurtosis excess (fourth-order fluctuation) is found at impact parameter $b=8.7$ fm, where the multifragmentation and nucleon evaporation are well balanced. Two observables are defined to describe the asymmetry of temperature and density in the projectile-like system. The nonequilibrium of the projectile-like system is verified by the distributions of these two observables. By comparing the distributions of the largest fragment charge for the equilibrium and nonequilibrium systems, it is found that the nonequilibrium of the hot projectile-like system influences the competitive relation between the multifragmentation and nucleon evaporation.

Conclusions: It is proposed that the nonequilibrium effect should be considered when study the pseudocritical point from the projectile fragmentation.

We extend the kinetic theory of $D$ mesons to accommodate thermal and off-shell effects due to the medium modification of the heavy-meson spectral functions. From the Kadanoff-Baym approach we derive the off-shell Fokker-Planck equation which encodes the heavy-flavor transport coefficients. We analyze the thermal width (damping rate) of $D$ mesons due to their scattering off light mesons, focusing on new in-medium effects: off-shell corrections, inelastic channels, and the contribution of the Landau cut. We obtain that the latter effect (absent for vacuum scattering amplitudes) brings sizable corrections at moderate temperatures. We discuss how the heavy-flavor transport coefficients, like the drag and diffusion coefficients, are modified in matter. We find that the $D$-meson spatial diffusion coefficient matches smoothly to the latest results of lattice-QCD calculations and Bayesian analyses at higher temperatures.

$\mathrm{{\rm Y}}$ and ${\eta }_b$ nuclear bound-state energies are calculated for various nuclei, neglecting any possible effects of the widths. Essential input for the calculations, namely, the medium-modified $B$ and $B^{*}$ meson masses, as well as the density distributions in nuclei, are calculated within the quark-meson coupling (QMC) model. The attractive potentials for the $\mathrm{{\rm Y}}$ and ${\eta }_b$ mesons in nuclei are calculated from the mass shifts of these mesons in nuclear matter in the local density approximation. These potentials originate from the in-medium enhanced $BB$ and $B{B}^{*}$ loops in their respective self-energy. After an extensive analysis we conclude that our results suggest that the $\mathrm{{\rm Y}}$ and ${\eta }_b$ mesons should form bound states with all the nuclei considered.

We show that high-$p_{\perp }{R}_{\mathrm{AA}}$ and $v_2$ are sensitive to the early expansion dynamics, and that the high-$p_{\perp }$ observables prefer delayed onset of energy loss and transverse expansion. To calculate high-$p_{\perp }{R}_{\mathrm{AA}}$ and $v_2$, we employ our newly developed DREENA-A framework, which combines state-of-the-art dynamical energy loss model with (3$+$1)-dimensional hydrodynamical simulations. The model applies to both light and heavy flavor, and we predict a larger sensitivity of heavy flavor observables to the onset of transverse expansion. This presents the first time when bulk QGP behavior has been constrained by high-$p_{\perp }$ observables and related theory, i.e., by so-called QGP tomography.

The angular momentum of a primary excited compound nucleus produced in multinucleon transfer reaction is an important quantity to evaluate cross sections to synthesize neutron-rich heavy-element nuclei as well as for surrogate reaction studies. The mechanism is, however, not enough understood due to the lack of detailed experimental data. In the present study, we determined the angular momentum of primary excited nuclei, ${}^{237,238,239}\mathrm{Np}, {}^{238,239,240}\mathrm{Pu}$, and ${}^{239,240,241}\mathrm{Am}$, produced in the multinucleon transfer channels of the ${}^{18}\mathrm{O}+{}^{237}\mathrm{Np}$ reaction. With this aim, angular distributions of fission fragments with respect to the axis perpendicular to the reaction plane were measured for each compound nucleus. The distributions show an anisotropy exhibiting an enhanced yield on the reaction plane. They are well reproduced by a saddle-point model, from which the average angular momentum is derived in the model framework. The angular momentum increases with the compound-nucleus mass, thus the number of nucleons exchanged, but shows a saturating trend toward heavier compound nuclei. These results are the first ones to point to the dependence of the angular momentum on the transfer channels.

We present a study of two-nucleon scattering in chiral effective field theory with a finite cutoff to next-to-leading order in the chiral expansion. In the proposed scheme, the contributions of the lowest-order interaction to the scattering amplitude are summed up to an arbitrary order, while the corrections beyond leading order are iterated only once. We consider a general form of the regulator for the leading-order potential including local and nonlocal structures. The main objective of the paper is to address formal aspects of renormalizability within the considered scheme. In particular, we provide a rigorous proof, valid to all orders in the iterations of the leading-order potential, that power-counting breaking terms originating from the integration regions with momenta of the order of the cutoff can be absorbed into the renormalization of the low energy constants of the leading contact interactions. We also demonstrate that the cutoff dependence of the scattering amplitude can be reduced by perturbatively subtracting the regulator artifacts at next-to-leading order. The obtained numerical results for phase shifts in $P$ and higher partial waves confirm the applicability of our scheme for nucleon-nucleon scattering.

Background: The Hoyle state is the archetypal $\alpha$-cluster state which mediates the $3\alpha$ reaction to produce ${}^{12}\mathrm{C}$ and is of great interest for both nuclear structure and astrophysics. Recent theoretical calculations predict a breathing-mode excitation of the Hoyle state at $E_x\approx 9$ MeV. Its observation is hindered by the presence of multiple broad states and potential interference effects. An analysis with Gaussian line shapes of measurements at the Research Center for Nuclear Physics (Osaka University) with the Grand Raiden spectrometer suggested that additional strength was needed at $E_x\approx 9$ MeV to reproduce the data; this analysis did not account for the well-known threshold effects observed in ${}^{12}\mathrm{C}$. Nevertheless, various theoretical studies have since concluded that this additional strength corresponds to the predicted breathing-mode excitation of the Hoyle state. To meaningfully identify a new source of monopole strength in this astrophysically significant region, a more appropriate phenomenological analysis which accounts for penetrability and interference effects must be used to determine whether the data can be explained with previously established states.

Purpose: We aim to investigate the monopole strength in the astrophysically important excitation-energy region of ${}^{12}\mathrm{C}$ between $E_x=7$ and 13 MeV to determine whether the previously established sources of monopole strength are able to reproduce the data.

Method: The ${}^{12}\mathrm{C}(\alpha ,{\alpha }^{\prime }){}^{12}\mathrm{C}$ and ${}^{14}\mathrm{C}(p,t){}^{12}\mathrm{C}$ reactions, which are expected to exhibit contrasting selectivity towards different monopole excitations, were employed at various detection angles and beam energies to populate states in ${}^{12}\mathrm{C}$. The inclusive excitation-energy spectra were simultaneously analyzed with multilevel, multichannel line shapes. Various scenarios with different sources of monopole strength and interference effects were considered to determine whether the ghost of the Hoyle state and the previously established broad $0_3^{+}$ state at $E_x\approx 10$ MeV are able to reproduce the observed monopole strength.

Results: Clear evidence was found for excess monopole strength at $E_x\approx 9$ MeV, particularly in the ${}^{12}\mathrm{C}(\alpha ,{\alpha }^{\prime }){}^{12}\mathrm{C}$ reaction at $0^{\circ }$. This additional strength cannot be reproduced by the previously established monopole states between $E_x=7$ and 13 MeV. Coincident charged-particle decay data suggest that the strength at $E_x\approx 9$ MeV is dominantly monopole, with no evidence of a $J>0$ contribution.

Conclusions: The data support a new source of monopole strength at $E_x\approx 9$ MeV, which cannot be described with a phenomenological parametrization of all previously established states. An additional $0^{+}$ state at $E_x\approx 9$ MeV yielded a significantly improved fit of the data and is a clear candidate for the predicted breathing-mode excitation of the Hoyle state. Alternatively, the results may suggest that a more sophisticated, physically motivated parametrization of the astrophysically important monopole strengths in ${}^{12}\mathrm{C}$ is required.

Background: As the result of synthesis of nuclei with large proton numbers a new region of investigations of the structure of nuclei has been discovered. Due to the recent significant increase in the yield of superheavy nuclei their gamma-spectroscopic studies became possible.

Purpose: To predict the excitation energies of the $2_1^{+}$ states of nuclei with $Z\ge 100$.

Method: The microscopic variant of the Grodzins relation derived based on the geometrical collective model and a microscopic approach to description of the low-energy nuclear structure is applied.

Results: The excitation energies of the $2_1^{+}$ states of the even-even nuclei from ${}^{256}\mathrm{Fm}$ to ${}_{120}{}^{296}\mathrm{X}$ which differ from each other in the number of $\alpha$ particles are predicted.

Conclusion: It is shown that at the beginning of the chain of the studied nuclei the excitation energies of the $2_1^{+}$ states do not exceed 100 keV. Then $E\left(2_1^{+}\right)$ sharply increases with $A$ and reaches maximum value of $400\text{–}500$ keV in ${}^{284}\mathrm{Fl}$ or ${}^{292}\mathrm{Og}$.

In order to efficiently describe nucleon orbits around a heavy core nucleus, we propose locally peaked Gaussians orthogonalized to the occupied bound states in the core. We show the advantage of those functions in both numerical stability and fast convergence by taking examples of touchstone calcium isotopes ${}^{62,72}\mathrm{Ca}$ in ${}^{60,70}\mathrm{Ca}+n+n$ three-body models. Both weakly bound configurations and continuum coupling effect are taken into account. We evaluate the neutron radii and the occupation probabilities of two-neutron configurations not only for the ground state but also for some particle-bound excited states by varying the strength of the core-neutron interaction. The emergence of the halo structure in the ground state depends on the energy difference between $2s_{1/2}$ and $0g_{9/2}$ orbits. Two-neutron [consisting of ${\left(s_{1/2}\right)}^2$ configuration] and one-neutron [consisting of $\left(g_{9/2}{s}_{1/2}\right)$ configuration] halo structures of ${}^{62}\mathrm{Ca}$ can coexist in narrow energy spacing provided that both of $2s_{1/2}$ and $0g_{9/2}$ orbits are almost degenerate and barely bound. The ground-state structure of ${}^{72}\mathrm{Ca}$ is likely to be a two-neutron halo, although its emergence depends on the position of the $2s_{1/2}$ level.

Background: In highly deformed nuclei, there is a noticeable coupling of the isoscalar giant monopole resonance (ISGMR) and the $K=0$ component of the isoscalar giant quadrupole resonance (ISGQR), which results in a double peak structure of the isoscalar monopole (IS0) strength (a narrow low-energy deformation-induced peak and a main broad ISGMR part). The energy of the narrow low-lying IS0 peak is sensitive to both the incompressibility modulus $K_{\infty }$ and the coupling between IS0 and isoscalar quadrupole (IS2) strength.

Purpose: This study aims to investigate the two-peaked structure of the ISGMR in the prolate ${}^{24}\mathrm{Mg}$ and oblate ${}^{28}\mathrm{Si}$ nuclei and identify among a variety of energy density functionals based on Skyrme parametrizations the one which best describes the experimental data. This will allow for conclusions regarding the nuclear incompressibility. Because of the strong IS0/IS2 coupling, the deformation splitting of the ISGQR will also be analyzed.

Methods: The ISGMR was excited in ${}^{24}\mathrm{Mg}$ and ${}^{28}\mathrm{Si}$ using $\alpha$-particle inelastic scattering measurements acquired with an $E_{\alpha }=196$ MeV beam at scattering angles ${\theta }_{\text{Lab}}=0^{\circ }$ and $4^{\circ }$. The $\mathrm{K}600$ magnetic spectrometer at iThemba LABS was used to detect and momentum analyze the inelastically scattered $\alpha$ particles. An experimental energy resolution of $\approx 70$ keV (FWHM) was attained, revealing fine structure in the excitation-energy region of the ISGMR. The IS0 strength distributions in the nuclei studied were obtained with the difference-of-spectra (DoS) technique. The theoretical comparison is based on the quasiparticle random-phase approximation (QRPA) with a representative set of Skyrme forces.

Results: IS0 strength distributions for ${}^{24}\mathrm{Mg}$ and ${}^{28}\mathrm{Si}$ are extracted and compared to previously published results from experiments with a lower energy resolution. With some exceptions, a reasonable agreement is obtained. The IS0 strength is found to be separated into a narrow structure at about $13–14$ MeV in ${}^{24}\mathrm{Mg}$, $17–19$ MeV in ${}^{28}\mathrm{Si}$, and a broad structure at $19–26$ MeV in both nuclei. The data are compared with QRPA results. The results of the calculated characteristics of IS0 states demonstrate the strong IS0/IS2 coupling in strongly prolate ${}^{24}\mathrm{Mg}$ and oblate ${}^{28}\mathrm{Si}$. The narrow IS0 peaks are shown to arise due to the deformation-induced IS0/IS2 coupling and strong collective effects. The cluster features of the narrow IS0 peak at $13.87\mathrm{MeV}$ in ${}^{24}\mathrm{Mg}$ are also discussed. The best description of the IS0 data is obtained using the Skyrme force ${\mathrm{SkP}}^{\delta }$ with an associated low nuclear incompressibility $K_{\infty }=202\mathrm{MeV}$ allowing for both the energy of the peak and integral IS0 strength in ${}^{24}\mathrm{Mg}$ and ${}^{28}\mathrm{Si}$ to be reproduced. The features of the ISGQR in these nuclei are also investigated. An anomalous deformation splitting of the ISGQR in oblate ${}^{28}\mathrm{Si}$ is found. The observed structure of ISGQR in ${}^{24}\mathrm{Mg}$ is described.

Conclusions: The ISGMR and ISGQR in light deformed nuclei are coupled and thus need to be described simultaneously. Only such a description is relevant and consistent. The deformation-induced narrow IS0 peaks can serve as an additional sensitive measure of the nuclear incompressibility.

With the framework of the KIDS (Korea-IBS-Daegu-SKKU) density functional model, the isoscalar and isovector effective masses of nucleons and the effect of symmetry energy in nuclear medium are investigated in inclusive $(e,e^{\prime })$ reactions in the quasielastic region. The effective masses are varied in the range $(0.7–1.0)M$ with free nucleon mass $M$, and the symmetry energy is varied within the uncertainty allowed by nuclear data and neutron star observation. The wave functions of nucleons inside the target nucleus are generated by solving the Hartree-Fock equation with adjustment of the equation of state, binding energy, and radius of various stable nuclei, and the effective masses of nucleons in the KIDS model. With the obtained wave functions, we calculate the differential cross section for the inclusive $(e,e^{\prime })$ reaction and compare the theoretical results with Bates, Saclay, and SLAC experimental data. Our model describes better the experimental data at SLAC-type high incident electron energy than those measured from Bates and Saclay. The influence of the effective mass and symmetry energy on the longitudinal cross section appears to be precise.