We present a set of formulas to extract the ratio $F_L(x,Q^2)/F_2(x,Q^2)$ and $R(x,Q^2)$ from the proton structure function parameterized in the next-to-next-to-leading order of the perturbation theory at low $x$ values. The behavior of these ratios is considered with respect to the power-law behavior of the proton structure function. The results are compared with experimental data and the color dipole model bounds. These ratios are in good agreement with the Hadron Electron Ring Accelerator (HERA) data throughout the fixed value of the invariant mass. The behavior of these ratios controlled by the nonlinear corrections at low values of $Q^2$. These results and comparisons with HERA data demonstrate that the suggested method for the ratio of structure functions can be applied in analyses of the Large Hadron Collider and Future Circular Collider projects.

The multichannel cluster model (MCCM) is generalized to investigate the effect of nuclear collective vibrations on the $\alpha$-decay fine structure. Vibrational excitations up to two-phonon states are taken into account and coupled-channels calculations are performed for vibrational Rn, Ra, Th, and U isotopes. Without introducing any additional adjustable parameter, the calculated $\alpha$-decay branching ratios to various vibrational states show good agreement with the experimental data. In particular, it is shown that the $\alpha$-decay fine structure is strongly correlated with vibrational excitations, offering an alternative tool to explore the phonon states in daughter nuclei. Despite the $N=126$ shell closure, the calculated $\alpha$-decay half-lives are also found to be in good agreement with the experimental data. A unified description of the $\alpha$-decay fine structure has been achieved by the MCCM for both rotational and vibrational nuclei.

Tiwari et al. have identified an annual modulation of the $\gamma$-ray flux at the Soudan Underground Laboratory which is strongly correlated to the radon concentration. The $\gamma$-ray flux results from $\left(\alpha ,\gamma \right)$ reactions which are induced by the $\alpha$ activity of radon and its daughters. Unfortunately, the quantitative analysis of the $\gamma$-ray flux is based on unrealistic $\left(\alpha ,\gamma \right)$ cross sections, and thus the calculated $\gamma$-ray fluxes are not reliable.

Annual modulation of $\gamma$ rays from $\left(\alpha ,\gamma \right)$ reactions induced by the $\alpha$ activity of radon and its daughters was reported by Tiwari, Zhang, Mei, and Cushman (TZMC). While Mohr does not contest the measurements themselves, he has commented that unrealistic $\left(\alpha ,\gamma \right)$ cross sections were used in the analysis of the $\gamma$-ray flux, and thus the $\gamma$-ray fluxes calculated by TZMC are not reliable. We demonstrate that the $\left(\alpha ,\gamma \right)$ cross sections obtained from talys include the energy-broadened cross sections for discrete states in the high-energy tail of the spectra, which are required in order to compare with the angle-integrated and double-differential spectra obtained from a liquid scintillator detector with an energy resolution of only $\approx 15\%$. A comparison with varying “elwidth” shows that cross sections indeed are reliable within the energy region (4 to 10 MeV) reported by TZMC, especially for the dominant contribution, which is the aluminum wall of the detector. Any differences in the $\left(\alpha ,\gamma \right)$ cross sections for ${}^{16}\mathrm{O}$ at the level detailed by Mohr will have negligible effect on the final flux.

The excited states in the transitional nucleus ${}^{131}\mathrm{Xe}$ have been populated by using $\alpha$-induced fusion-evaporation reaction and the de-exciting $\gamma$ rays were detected with the Compton suppressed clover detector setup of the Indian National Gamma Array coupled to digital data acquisition system. The existing level structure of ${}^{131}\mathrm{Xe}$ has been significantly extended with the observation and placement of 72 new $\gamma$-ray transitions. The use of light-ion ($\alpha$) beam helped to identify several new band structures in ${}^{131}\mathrm{Xe}$ with different quasiparticle (qp) configurations. The multipolarities of the observed $\gamma$ rays have been determined on the basis of the directional correlation from oriented states ratio and polarization asymmetry measurements. The yrast negative-parity band has been confirmed up to ${35/2}^{-}$ spin and the highly nonyrast signature partner of this band has been identified for the first time. The positive-parity band, based on the ${3/2}^{+}$ ground state, has been extended up to ${23/2}^{+}$ with the observation of a signature inversion, which signifies a pair of particle alignment around the spin of 15/2 $\hslash$. A dipole band, consisting of $M1$ transitions has been identified and assigned a 5-qp configuration. A new band structure built on a 3-qp ${23/2}^{+}$ state has been observed with a large signature splitting. A comparison in the isotopic and isotonic chains reveals the transitional nature of the $N=77$ nuclei. Total Routhian surface calculations have been performed to understand the structure of ${}^{131}\mathrm{Xe}$ associated with different configurations.

Background: The chart of the nuclides is limited by particle drip lines beyond which nuclear stability to proton or neutron emission is lost. Predicting the range of particle-bound isotopes poses an appreciable challenge for nuclear theory as it involves extreme extrapolations of nuclear masses well beyond the regions where experimental information is available. Still, quantified extrapolations are crucial for a wide variety of applications, including the modeling of stellar nucleosynthesis.

Purpose: We use microscopic nuclear global mass models, current mass data, and Bayesian methodology to provide quantified predictions of proton and neutron separation energies as well as Bayesian probabilities of existence throughout the nuclear landscape all the way to the particle drip lines.

Methods: We apply nuclear density-functional theory with several energy density functionals. We also consider two global mass models often used in astrophysical nucleosynthesis simulations. To account for uncertainties, Bayesian Gaussian processes are trained on the separation-energy residuals for each individual model, and the resulting predictions are combined via Bayesian model averaging. This framework allows to account for systematic and statistical uncertainties and propagate them to extrapolative predictions.

Results: We establish and characterize the drip-line regions where the probability that the nucleus is particle bound decreases from 1 to 0. In these regions, we provide quantified predictions for one- and two-nucleon separation energies. According to our Bayesian model averaging analysis, 7759 nuclei with $Z\le 119$ have a probability of existence $\ge 0.5$.

Conclusions: The extrapolation results obtained in this study will be put through stringent tests when new experimental information on existence and masses of exotic nuclei becomes available. In this respect, the quantified landscape of nuclear existence obtained in this study should be viewed as a dynamical prediction that will be fine-tuned when new experimental information and improved global mass models become available.

The study of the heavy-ion reactions at the near- and sub-barrier regimes gives immense information about the nuclear structure and the involved reaction dynamics. It has been observed that a slight difference in the nuclear structure may lead to a significant change in the sub-barrier fusion excitation functions. The studies of different trends of excitation functions below the Coulomb barrier region due to dissimilar structures of the nuclei, which are involved in the reaction, are available in literature. To understand the role of different structures and dynamics involved in such reactions, an investigation of ${}^{48}\mathrm{Ti}$-induced reactions on ${}^{58}\mathrm{Fe}$ and ${}^{58}\mathrm{Ni}$ forming ${}^{106}\mathrm{Cd}^{*}$ and ${}^{106}\mathrm{Sn}^{*}$ compound nuclei (CN), respectively, has been made at similar $E_{\mathrm{c}.\mathrm{m}.}/V_b$ values within the framework of the dynamical cluster decay model (DCM). The difference in the structure between the nuclei is quite notable with ${}^{58}\mathrm{Ni}$ and ${}^{106}\mathrm{Sn}^{*}$ having a proton shell closure ($Z=28$ and 50, respectively). Within the DCM, the experimental fusion evaporation cross sections are reproduced using deformed configurations effects included up to quadruple deformations (${\beta }_{2i}$) for two nuclei having optimum orientations ${\theta }^{\mathrm{opt}.}$. The fusion evaporation data at near- and sub-barriers has been explained through the calculated enhanced $\mathrm{\Sigma }{P}_0$ values of the decaying channels in the case of ${}^{106}\mathrm{Cd}^{*}$ in comparison to ${}^{106}\mathrm{Sn}^{*}$. Moreover, it is observed that the quantum tunneling of the fragments is less hindered in the case of ${}^{106}\mathrm{Cd}^{*}$ as compared to ${}^{106}\mathrm{Sn}^{*}$ at the lower values of $E_{\mathrm{c}.\mathrm{m}.}/V_b$, i.e., having less barrier modification ($\mathrm{\Delta }{V}_B$) in the case of the former. The role of magicity has been further explored with the plotted values of the ratio of fusion cross sections (${\sigma }_{\mathrm{fus}}$) of CN ${}^{106}\mathrm{Sn}^{*}$ and ${}^{112}\mathrm{Xe}^{*}$ (formed in the reaction with both the projectile ${}^{58}\mathrm{Ni}$ and target ${}^{54}\mathrm{Fe}$ having proton and neutron magicity, respectively) with respect to ${}^{106}\mathrm{Cd}^{*}$, which are highly suppressed in the case of the latter in comparison to the former, particularly, below the Coulomb barrier.

Background: Previous theoretical work has found that the effective mass of the nucleon influences the excitation energy of the isoscalar giant quadrupole resonance (ISGQR).

Purpose: The present paper presents an attempt to constrain the effective mass splitting by using the isospin dependence of the ISGQR energies.

Methods: Using the macroscopic Langevin equation (LE), the ISGQR energies are calculated from the particle density and kinetic energy density of the nucleus in the ground state, obtained from either the Thomas-Fermi (TF) approach or the Skyrme Hartree-Fock-Bogolyubov (SHFB) model.

Results: It is found that the calculations of the ISGQR energies by the SHFB+LE model agree with, or are even better than, the results by other approaches when applying the Skyrme functional Sly4. The values of the isoscalar and isovector effective masses are optimized by fitting the data for the ISGQR energies for a mass region from 28 to 238. The root-mean-squared deviation of the best fit to the data measured after the year 2000 is 0.22 MeV by the TF+LE model and 0.30 MeV by the SHFB+LE model. The extracted isoscalar effective mass is $0.70<m_s^{*}/m<0.73$. With respect to the isovector effective mass $m_v^{*}$, the constrained value is about half of the isoscalar effective mass $m_s^{*}$.

Conclusions: The present work supports the statement that, in neutron-rich matter, the effective mass of the neutron is definitely larger than that of the proton.

The high-accuracy $\varphi$-meson photoproduction data from the CLAS experiment in Hall B of Jefferson Laboratory allow us to determine the near-threshold total cross section of the $\gamma p\to \varphi p$ reaction and use it for evaluating the $\varphi p$ scattering length ${\alpha }_{\varphi p}$. These data result in an absolute value of $|{\alpha }_{\varphi p}|=(0.063\pm 0.010)$ fm, which is smaller than the typical hadron size. A comparative analysis of ${\alpha }_{\varphi p}$ with the previously determined scattering lengths for $\omega p$ and $J/\psi p$ from the A2 and GlueX experiments is performed.

The differential cross section for the ${}^1\mathrm{H}(d,pp)n$ breakup reaction at deuteron beam energy of 340 MeV has been measured with the use of the WASA detector at COSY-Jülich. The set of proton-proton coincidences registered at the Forward Detector has been analyzed on a dense grid of kinematic variables, giving in total around 5600 data points. The cross-section data are compared to theoretical predictions based on the state-of-the-art nucleon-nucleon potentials, combined with a three-nucleon force or the Coulomb interaction or carried out in a relativistic regime.

The ${}^{10}\mathrm{B}+{}^{197}\mathrm{Au}$ reaction has been investigated through cross-section measurements for different channels, such as quasielastic and elastic scattering, inelastic excitation of low-lying ${}^{197}\mathrm{Au}$ states, and one-neutron pickup and one-proton stripping transfer reactions. Experimental angular distributions were obtained for 20 bombardment energies around the Coulomb barrier: $38\le E_{lab}\le 61\mathrm{MeV}$. Coupled reaction channels calculations have been performed in the context of the double-folding São Paulo potential, and details of the data analysis are discussed along the paper. In general, the theoretical calculations provide a satisfactory description of the data.

Background: A newly identified drip-line nucleus ${}^{31}\mathrm{F}$ offers a unique opportunity to study the two-neutron ($2n$) correlation at the east shore of the island of inversion where the $N=28$ shell closure is lost.

Purpose: We aim to present the first three-body theoretical results for the radius and total reaction cross sections of ${}^{31}\mathrm{F}$. This will further help to investigate how the pairing and the breakdown of the $N=28$ shell closure influence the formation of the $2n$-halo structure and the antihalo effect in this mass region.

Methods: A ${}^{29}\mathrm{F}+n+n$ three-body system is described by the cluster orbital shell model, and its total reaction cross section is calculated by the Glauber theory.

Results: Our three-body calculations predict 3.48–3.70 fm for the root-mean-square radius of ${}^{31}\mathrm{F}$, which corresponds to the total reaction cross section of 1530 (1410) to 1640 (1500) mb for a carbon target at 240 (900) MeV/nucleon. The binding mechanism and halo formation in ${}^{31}\mathrm{F}$ are discussed.

Conclusions: The present study suggests a novel antihalo effect in this mass region: When the pairing overcomes the energy gap between the $p_{3/2}$ and $f_{7/2}$ orbits, the inversion of the occupation number of these orbits takes place, and it diminishes the $2n$-halo structure.

The quality of the recent GlueX $J/\psi$ photoproduction data from Hall D at Jefferson Laboratory and the proximity of the data to the energy threshold, gives access to a variety of interesting physics aspects. As an example, an estimation of the $J/\psi$-nucleon scattering length ${\alpha }_{J/\psi p}$ is provided within the vector meson dominance model. It results in $|{\alpha }_{J/\psi p}|=(3.08\pm 0.55\left(\mathrm{stat}.\right)\pm 0.42\left(\mathrm{syst}.\right))$ mfm which is much smaller than a typical size of a hadron.

We investigate the influence of a monochromatic strong laser electromagnetic field on $\alpha$ clustering and emission, by analyzing the Fourier components of the time-dependent $\alpha$-core realistic potential in the Henneberger representation. It turns out that the resulting potential becomes deformed and the static component is by far dominant beyond the nuclear surface where the $\alpha$ cluster is formed, while higher Fourier terms are important in the internal region, where the $\alpha$-particle probability is hindered by the Pauli principle. This fact, combined with the observation that an $\alpha$ cluster lives much longer before its emission than the laser period, allows us the use of the stationary coupled channels approach in the system of coordinates given by the laser beam direction. We predict that the angular distribution of emitted $\alpha$ particles becomes anisotropic due to the deformation of the $\alpha$-core potential induced by the laser field, even for the spherical emitter ${}^{212}\mathrm{Po}$.

The relativistic and nonrelativistic finite temperature proton-neutron quasiparticle random phase approximation (FT-PNQRPA) methods are developed to study the interplay of the pairing and temperature effects on the Gamow-Teller excitations in open-shell nuclei, as well as to explore the model dependence of the results by using two rather different frameworks for effective nuclear interactions. The Skyrme-type functional SkM* is employed in the nonrelativistic framework, while the density-dependent meson-exchange interaction DD-ME2 is implemented in the relativistic approach. Both the isoscalar and isovector pairing interactions are taken into account within the FT-PNQRPA. Model calculations show that below the critical temperatures the Gamow-Teller excitations display a sensitivity to both the finite temperature and pairing effects, and this demonstrates the necessity for implementing both in the theoretical framework. The established FT-PNQRPA opens perspectives for the future complete and consistent description of astrophysically relevant weak interaction processes in nuclei at finite temperature such as $\beta$ decays, electron capture, and neutrino-nucleus reactions.

From detailed spectroscopy of ${}^{110}\mathrm{Cd}$ and ${}^{112}\mathrm{Cd}$ following the ${\beta }^{+}/\mathrm{EC}$ decay of ${}^{110,112}\mathrm{In}$ and the ${\beta }^{-}$ decay of ${}^{112}\mathrm{Ag}$, the presence of very weak decay branches from nonyrast states is revealed. In ${}^{112}\mathrm{Cd}$, $2_5^{+}\to 0_4^{+}$ and $4_6^{+}\to 2_5^{+}$ transitions are observed that yield $B(E2;2_5^{+}\to 0_4^{+})=34\pm 15$ W.u. and $B(E2;4_6^{+}\to 2_5^{+})=77\pm 30$ W.u., respectively, clearly indicating a collective structure. In ${}^{110}\mathrm{Cd}$, a weak decay branch from the $4_6^{+}$ level to the $2_5^{+}$ level is observed, and from a lifetime measurement following the $(n,n^{\prime }\gamma )$ reaction, $B(E2;4_6^{+}\to 2_5^{+})=55\pm 14$ W.u. is determined. A new branch is also observed for the decay of the $6_4^{+}$ level to the $4_6^{+}$ state, indicating that the sequence $2_5^{+}$, $4_6^{+}$, and $6_4^{+}$ forms part of a collective structure. The presence of $3_3^{+}$ and $5_2^{+}$ levels spaced between the previous sequence is highly suggestive of a $\gamma$ band built on the $0_2^{+}$ shape-coexisting intruder state. The $0_4^{+}$ levels in ${}^{110,112,114}\mathrm{Cd}$ have preferred decays to the lowest $2^{+}$ members of the intruder bands, and for ${}^{114}\mathrm{Cd}$ a previous measurement had established an enhanced $B(E2;0_4^{+}\to 2_3^{+})$. The energy systematics of the $0_2^{+}$, $0_3^{+}$, and $0_4^{+}$ levels all display the characteristic parabolic-shaped pattern, suggesting that they are built on multiparticle-multihole proton excitations. The results are compared with beyond-mean-field calculations that reproduce qualitatively the observed levels and their decays and suggest that the $0_1^{+}$, $0_2^{+}$, $0_3^{+}$, and $0_4^{+}$ levels and the excited states built on them possess different deformations.

A nonlocal dispersive optical model analysis is carried out for neutrons and protons in ${}^{208}\mathrm{Pb}$. Elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, neutron and proton numbers, the charge distribution, and the binding energy are fitted to extract the neutron and proton self-energies both above and below the Fermi energy. From the single-particle propagator derived from these self-energies, we determine the charge and matter distributions in ${}^{208}\mathrm{Pb}$. The predicted spectroscopic factors are consistent with results from the $(e,e^{\prime }p)$ reaction and inelastic-electron-scattering data to very high-spin states. Sensible results for the high-momentum content of neutrons and protons are obtained, with protons appearing more correlated, in agreement with experiment and ab initio calculations of asymmetric matter. A neutron skin of $0.25\pm 0.05\mathrm{fm}$ is deduced. An analysis of several nuclei leads to the conclusion that finite-size effects play a nonnegligible role in the formation of the neutron skin in finite nuclei.

We investigate how the drag coefficient $A$ and $\widehat{q}$, the transverse momentum transfer by unit length, of charm quarks are modified if the quark-gluon plasma (QGP) is not in complete thermal equilibrium using the dynamical quasiparticle model (DQPM), which reproduces both, the equation-of-state of the QGP and the spatial diffusion coefficient of heavy quarks as predicted by lattice quantum chromodynamics calculations. We study three cases: (i) the QGP has an anisotropic momentum distribution of the partons, which leads to an anisotropic pressure; (ii) the QGP partons have higher or lower kinetic energies as compared to the thermal expectation value; and (iii) the QGP partons have larger or smaller pole masses of their spectral function as compared to the pole mass from the DQPM at the QGP temperature. In the last two cases we adjust the number density of partons to obtain the same energy density as in an equilibrated QGP. We find that each non-equilibrium scenario affects $A$ and $\widehat{q}$ of charm quarks in a different way. The modifications in our scenarios are of the order 20–30% at temperatures relevant for heavy-ion reactions. These modifications have to be considered if one wants to determine these coefficients by comparing heavy-ion data with theoretical predictions from viscous hydrodynamics or Langevin equations.