I have calculated spectroscopic factors connecting three $d$ resonances in ${}^{13}\mathrm{Be}$ to the three lowest states of ${}^{12}\mathrm{Be}$. Combined with single-particle widths computed in a potential model, I have estimated the widths expected for the various decays. Comparing measured and calculated widths suggests that the resonance near 1 MeV is not $5/2^{+}$ and that the one just above 2 MeV is the lowest $5/2^{+}$ resonance.

The shell structure of low-lying neutron resonance levels in axially symmetric quadrupole-deformed potentials is discussed, which seems analogous to that of weakly bound neutrons. As numerical examples, nuclei slightly outside the neutron drip line, ${}_{12}{}^{39}\mathrm{Mg}_{27}$ and ${}_6{}^{21}\mathrm{C}_{15}$, are studied. For the lowest resonance I obtain $I^{\pi }={\mathrm{\Omega }}^{\pi }=5/2^{-}$ for ${}^{39}\mathrm{Mg}$ which is likely to be prolately deformed, while $I^{\pi }={\mathrm{\Omega }}^{\pi }=1/2^{+}$ may be assigned to the nucleus ${}^{21}\mathrm{C}$ which may be oblately deformed. Consequently, ${}^{21}\mathrm{C}$ will not be observed as a recognizable resonance state, in agreement with the experimental information.

Based on a generalized relativistic mean-field model, $\alpha$ clustering on the surface of Sn was recently predicted to vary systematically as a function of isotopic mass. Existing experimental information from $\left(d,{}^6\mathrm{Li}\right)$ cluster pickup is now used to verify the predicted trend. The extent of the anticipated validity of such a comparison between the experimental results and the theoretical formulation is evaluated and discussed in the present paper.

The spectral degeneracies emerging in the critical region of the interacting boson model are systematically investigated. The results indicate that the level crossings in the transitions from the U(5) to the SU(3) quasidynamical symmetry can induce the approximate spectral degeneracies along the first-order transitional line for large boson number $N$. The remnants of these types of degeneracies in finite-$N$ systems have been preliminarily identified from the low-lying spectra of ${}^{150}\mathrm{Nd}$. In addition, the similar approximate degeneracies emerging in the phase transition between the U(5) and SO(6) quasidynamical symmetries are parallel emphasized and those in other critical models are also mentioned.

We performed a $\gamma$-particle coincidence experiment for the ${}^{60}\text{Ni}+{}^{116}\text{Sn}$ system to investigate whether the population of the two-neutron pickup channel leading to ${}^{62}\text{Ni}$ is mainly concentrated in the ground-state transition, as has been found in a previous work [D. Montanari et al., Phys. Rev. Lett. 113, 052501 (2014)]. The experiment has been performed by employing the PRISMA magnetic spectrometer coupled to the Advanced Gamma Tracking Array (AGATA) demonstrator. The strength distribution of excited states corresponding to the inelastic, one- and two-neutron transfer channels has been extracted. We found that in the two-neutron transfer channel the strength to excited states corresponds to a fraction (less than 24%) of the total, consistent with the previously obtained results that the $2n$ channel is dominated by the ground-state to ground-state transition.

We investigate ratios of the elastic scattering cross section to Rutherford cross section, $P_{\mathrm{E}}$, and angular distributions of breakup cross section by using an optical model which exploits various long-range dynamic polarization potentials as well as short-range nuclear bare potentials for the ${}^{11}\text{Be}$ projectile. From these simultaneous analyses, we extract a large radius of a halo projectile from the experimental data for $P_{\mathrm{E}}$ and the angular distribution of the breakup cross section of the ${}^{11}\text{Be}+{}^{64}\text{Zn}$ and ${}^{11}\text{Be}+{}^{120}\text{Sn}$ systems. It results from the fact that a large radius for the long-range nuclear potential is more reasonable for properly explaining these data simultaneously. The extracted reduced interaction radius turns out to be $r_0=3.18\sim 3.61$ fm for ${}^{11}\text{Be}$ nucleus, which is larger than the conventional value of $r_0=1.1\sim 1.5$ fm used in the standard radius form $R=r_0{A}^{1/3}$. Furthermore, the larger radius as well as the normalization constant $N$ is shown to be important for understanding Coulomb dipole strength distribution.

Using the standard Lagrangian of gluons and a model of dual superconductor for magnetic monopoles, I calculate the number densities of the gluons and monopoles produced by the decay of background color electric $E$ and magnetic $B$ fields (glasma). It turns out that gluons are dominant decay products when the initial values of the gauge fields are large such that $gE=gB>{\left(0.5\text{GeV}\right)}^2$, while they are suppressed and monopoles are dominant decay products when the initial values are small such that $gE=gB<{\left(0.4\text{GeV}\right)}^2$. The feature of the gluon dominance at large $gE=gB$ and the monopole dominance at small $gE=gB$ is similar to that of thermalized quark gluon monopole plasmas proposed recently, if one identifies $\sqrt{gE}=\sqrt{gB}$ as temperatures of the plasmas. The identification is suggested by the fact that the energy densities of the gluons and monopoles are proportional to the initial values ${\left(gB\right)}^2={\left(gE\right)}^2$, while the energy densities of the plasmas are proportional to $T^4$. The feature of the gluon dominance in the glasmas with large saturation momenta was derived in classical statistical field theories, while the feature of the monopole dominance was not yet derived. Although the model of the monopoles is phenomenological, my analysis suggests that the monopoles play important roles in the decay of the glasmas with small saturation momenta, to which classical statistical field theories are not applicable.

Background: The proton charge radius extracted from recent muonic hydrogen Lamb shift measurements is significantly smaller than that extracted from atomic hydrogen and electron scattering measurements. The discrepancy has become known as the proton radius puzzle.

Purpose: In an attempt to understand the discrepancy, we review high-precision electron scattering results from Mainz, Jefferson Lab, Saskatoon, and Stanford.

Methods: We make use of stepwise regression techniques using the $F$ test as well as the Akaike information criterion to systematically determine the predictive variables to use for a given set and range of electron scattering data as well as to provide multivariate error estimates.

Results: Starting with the precision, low four-momentum transfer $\left(Q^2\right)$ data from Mainz (1980) and Saskatoon (1974), we find that a stepwise regression of the Maclaurin series using the $F$ test as well as the Akaike information criterion justify using a linear extrapolation which yields a value for the proton radius that is consistent with the result obtained from muonic hydrogen measurements. Applying the same Maclaurin series and statistical criteria to the 2014 Rosenbluth results on $G_E$ from Mainz, we again find that the stepwise regression tends to favor a radius consistent with the muonic hydrogen radius but produces results that are extremely sensitive to the range of data included in the fit. Making use of the high-$Q^2$ data on $G_E$ to select functions which extrapolate to high $Q^2$, we find that a Padé $\left(N=M=1\right)$ statistical model works remarkably well, as does a dipole function with a 0.84 fm radius, $G_E\left(Q^2\right)={(1+Q^2/0.66{\mathrm{GeV}}^2)}^{-2}$.

Conclusions: Rigorous applications of stepwise regression techniques and multivariate error estimates result in the extraction of a proton charge radius that is consistent with the muonic hydrogen result of 0.84 fm; either from linear extrapolation of the extremely-low-$Q^2$ data or by use of the Padé approximant for extrapolation using a larger range of data. Thus, based on a purely statistical analysis of electron scattering data, we conclude that the electron scattering results and the muonic hydrogen results are consistent. It is the atomic hydrogen results that are the outliers.

It is demonstrated how the use of all existing experimental information on electric and magnetic nucleon form factors, described by the unitary and analytic (U&A) nucleon electromagnetic structure model in spacelike and timelike regions simultaneously, can provide numerical values of $f^F,f^D,\text{and}{f}^S$ coupling constants in SU(3) invariant interaction Lagrangian of the vector-meson nonet with $1/2^{+}$ octet baryons. The latter, together with universal vector-meson coupling constants $f_V$, play an essential role in a prediction of $1/2^{+}$ octet hyperon electromagnetic form factor behaviors.

The $\gamma p\to {\pi }^{0}p$ reaction was studied at laboratory photon energies from 425 to 1445 MeV with a transversely polarized target and a longitudinally polarized beam. The beam-target asymmetry $F$ was measured for the first time and new high precision data for the target asymmetry $T$ were obtained. The experiment was performed at the photon tagging facility of the Mainz Microtron (MAMI) using the Crystal Ball and TAPS photon spectrometers. The polarized cross sections were expanded in terms of associated Legendre functions and compared to recent predictions from several partial-wave analyses. The impact of the new data on our understanding of the underlying partial-wave amplitudes and baryon resonance contributions is discussed.

In their recent study Neelam, Shubhchintak, and Chatterjee have claimed that “it would certainly be useful to perform a Coulomb dissociation experiment to find the low-energy capture cross section for the reaction” ${}^{15}\mathrm{N}$($n,\gamma$)${}^{16}\mathrm{N}$. However, it is obvious that a Coulomb dissociation experiment cannot constrain this capture cross section because the dominating branchings of the capture reaction lead to excited states in ${}^{16}\mathrm{N}$, which do not contribute in a Coulomb dissociation experiment. An estimate of the total ${}^{15}\mathrm{N}$($n,\gamma$)${}^{16}\mathrm{N}$ cross section from Coulomb dissociation of ${}^{16}\mathrm{N}$ requires a precise knowledge of the $\gamma$-ray branchings in the capture reaction. Surprisingly, the calculation of Neelam, Shubhchintak, and Chatterjee predicts a strongly energy-dependent ground-state branching of the order of 0.05% to 0.6% at energies between 100 and 500 keV, which is almost 2 orders of magnitude below calculations in the direct capture model. Additionally, this calculation of Neelam, Shubhchintak, and Chatterjee deviates significantly from the expected energy dependence for $p$-wave capture.

We analyze the $\alpha \text{−}{}^{12}\mathrm{C}$ inelastic scattering to the $0_2{}^{+}$ state of ${}^{12}\mathrm{C}$, the Hoyle state, in a fully microscopic framework. With no free adjustable parameter, the inelastic cross sections at forward angles are well reproduced by the microscopic reaction calculation using the transition density of ${}^{12}\mathrm{C}$ obtained by the resonating group method and the nucleon-nucleon $g$ matrix interaction developed by the Melbourne group. It is thus shown that the monopole transition strength obtained by the structural calculation is consistent with that extracted from the reaction observable, suggesting no missing monopole strength of the Hoyle state.

It was recently found that the formation probabilities of $\alpha$ particles in Te isotopes are larger than the corresponding probabilities in Po isotopes. We have done a full microscopic calculation within the framework of the multistep shell model to analyze in detail the formation probabilities and subsequent decays of $\alpha$ particles from ${}^{212}\mathrm{Po}$ and ${}^{104}\mathrm{Te}$. We have also calculated the spectra of these two decaying nuclei and found that the tentatively assigned spin $\left({18}^{+}\right)$ at 2.922 MeV in ${}^{212}\mathrm{Po}$ (National Nuclear Data Center, www.nndc.bnl.gov) is predicted to be a state ${16}^{+}$. We also present for the first time the full energy spectrum of ${}^{104}\mathrm{Te}$. The evaluated formation amplitudes in both nuclei show that in ${}^{104}\mathrm{Te}$ there is indeed a superallowed $\alpha$-decay transition.

Background: In recent years, the study of triaxiality in the low-lying states of atomic nuclei with transition character or shape coexistence has been of great interest. Previous studies indicate that the neutron-rich nuclei in the $A\sim 100$ mass region with $Z\sim 40,N\sim 60$ serve as good grounds for examining the role of triaxiality in nuclear low-lying states.

Purpose: The aim of this work is to provide a microscopic study of low-lying states for nuclei in the $A\sim 100$ mass regions and to examine in detail the role of triaxiality in the shape-coexistence phenomena and the variation of shape with the isospin and spin values at the beyond mean-field level.

Method: The starting point of our method is a set of relativistic mean-field plus BCS wave functions generated with a constraint on triaxial deformations $(\beta ,\gamma )$. The excitation energies and electric multipole transition strengths of low-lying states are calculated by solving a five-dimensional collective Hamiltonian (5DCH) with parameters determined by the mean-field wave functions.

Results: The low-lying states of Mo isotopes and of $N=60$ isotones in the $A\sim 100$ mass region are calculated. The results indicate that triaxiality is essential to reproduce the data of excitation energies and electric quadrupole transition strengths in low-lying states and plays an important role in the shape evolution as a function of nucleon number. However, the decrease of nuclear collectivity with the increase of angular momentum in neutron-rich Mo isotopes has not been reproduced.

Conclusions: The evolution of nuclear collectivity in the low-lying states of neutron-rich nuclei in the $A\sim 100$ mass region as a function of nucleon number is governed by the novel triaxial structure. However, the mechanism that governs the variation of nuclear shape with spin in Mo isotopes remains unclear and deserves further investigation by taking into account the effects other than the collective motions.

Detailed spectroscopic information on the $N\sim 82$ nuclei is necessary to benchmark shell-model calculations in the region. The nuclear structure above long-lived isomers in ${}^{134}\mathrm{Xe}$ is investigated after multinucleon transfer (MNT) and actinide fission. Xenon-134 was populated as (i) a transfer product in ${}^{136}\text{Xe}+{}^{238}\text{U}$ and ${}^{136}\text{Xe}+{}^{208}\text{Pb}$ MNT reactions and (ii) as a fission product in the ${}^{136}\text{Xe}+{}^{238}\text{U}$ reaction employing the high-resolution Advanced Gamma Tracking Array (AGATA). Trajectory reconstruction has been applied for the complete identification of beamlike transfer products with the magnetic spectrometer PRISMA. The ${}^{136}\text{Xe}+{}^{198}\text{Pt}$ MNT reaction was studied with the $\gamma$-ray spectrometer GAMMASPHERE in combination with the gas detector array Compact Heavy Ion Counter (CHICO). Several high-spin states in ${}^{134}\mathrm{Xe}$ on top of the two long-lived isomers are discovered based on $\gamma \gamma$-coincidence relationships and information on the $\gamma$-ray angular distributions as well as excitation energies from the total kinetic energy loss and fission fragments. The revised level scheme of ${}^{134}\mathrm{Xe}$ is extended up to an excitation energy of 5.832 MeV with tentative spin-parity assignments up to ${16}^{+}$. Previous assignments of states above the $7^{-}$ isomer are revised. Latest shell-model calculations employing two different effective interactions reproduce the experimental findings and support the new spin and parity assignments.

Background: The ratio method has been proposed as a means to remove the reaction model dependence in the study of halo nuclei.

Purpose: Originally it was developed for higher energies, but given the potential interest in applying the method at lower energy, in this work we explore its validity at 20 MeV/nucleon.

Method: The ratio method takes the ratio of the breakup angular distribution and the summed angular distribution (which includes elastic, inelastic, and breakup) and uses this observable to constrain the features of the original halo wave function. In this work we use the continuum discretized coupled channel method and the Coulomb-corrected dynamical eikonal approximation for the study.

Results: We study the reactions of ${}^{11}\mathrm{Be}$ on ${}^{12}\mathrm{C},{}^{40}\mathrm{Ca}$, and ${}^{208}\mathrm{Pb}$ at 20 MeV/nucleon. We compare the various theoretical descriptions and explore the dependence of our result on the core-target interaction.

Conclusions: Our study demonstrates that the ratio method is valid at these lower beam energies.

Background: Couplings with various reaction channels are known to enhance sub-barrier fusion cross sections by several orders in magnitude. However, a few open questions still remain. For example, the influence of higher order static deformations on sub-barrier fusion cross sections is yet to be comprehensively understood.

Purpose: We study the role of hexadecapole nuclear deformation effect on sub-barrier fusion cross sections. Also, this work aims to extract hexadecapole deformation $\left({\beta }_4\right)$ in nuclei in the lanthanide region.

Method: The evaporation residue (ER) excitation functions for ${}^{16}\mathrm{O}+{}^{174,176}\mathrm{Yb}$ were measured at laboratory beam energies $\left(E_{\mathrm{lab}}\right)$ in the range of 64.6–103.6 MeV. Measurements were carried out by employing the recoil mass spectrometer Heavy Ion Reaction Analyzer (HIRA) at IUAC, New Delhi. Fusion barrier distributions (BDs) were extracted from data. Results from the experiment were subjected to coupled-channels analysis, in which ${\beta }_4$ was varied as a free parameter.

Results: Experimental fusion cross sections at energies below the barrier expectedly showed strong enhancement compared to the predictions from the one-dimensional barrier penetration model. Data were satisfactorily reproduced after inclusion of negative ${\beta }_4$ for both the targets in the coupled-channels calculation.

Conclusions: The significant role of hexadecapole deformation was observed in the sub-barrier fusion of ${}^{16}\mathrm{O}+{}^{174,176}\mathrm{Yb}$. The proposed value of ${\beta }_4$ reproduced the measured fusion excitation function reasonably well. The BDs from these data were also extracted but no definitive conclusions could be drawn from them.

Low-lying states of even-even and odd-mass ruthenium isotopes with mass numbers from 95 to 102, including level schemes, electric quadrupole and magnetic dipole moments, and $E2$ transition rates, are studied within the framework of the nucleon pair approximation (NPA) of the shell model, by using the phenomenological pairing plus quadrupole interactions. Good agreement is obtained between the calculated results and experimental data. The interesting behaviors of $g\left(J_1^{+}\right)$ factors versus nuclear spin $J$ (and mass number $A$) in even-even ${}^{96–102}\mathrm{Ru}$ nuclei are analyzed. The dominant configurations of yrast low-lying states in odd-mass ${}^{95–101}\mathrm{Ru}$ isotopes are discussed in the collective nucleon-pair subspace. The calculated electric quadrupole moments and magnetic moments of low-lying states, many of which have not yet been measured for these nuclei, are useful for future studies.

Ternary fission in $(n,f)$ reactions was studied with polarized neutrons for the isotopes ${}^{233,235}\mathrm{U}$ and ${}^{239,241}\mathrm{Pu}$. A cold longitudinally polarized neutron beam was available at the High Flux Reactor of the Institut Laue-Langevin in Grenoble, France. The beam was hitting the fissile targets mounted at the center of a reaction chamber. Detectors for fission fragments and ternary particles were installed in a plane perpendicular to the beam. In earlier work it was discovered that the angular correlations between neutron spin and the momenta of fragments and ternary particles were very different for ${}^{233}\mathrm{U}$ or ${}^{235}\mathrm{U}$. These correlations could now be shown to be simultaneously present in all of the above major actinides though with different weights. For one of the correlations it was observed that up to scission the compound nucleus is rotating with the axis of rotation parallel to the neutron beam polarization. Entrained by the fragments also the trajectories of ternary particles are turned away albeit by a smaller angle. The difference in turning angles becomes observable upon reversing the sense of rotation by flipping neutron spin. All turning angles are smaller than $1^{\circ }$. The phenomenon was called the ROT effect. As a distinct second phenomenon it was found that for fission induced by polarized neutrons an asymmetry in the emission probability of ternary particles relative to a plane formed by fragment momentum and neutron spin appears. The asymmetry is attributed to the Coriolis force present in the nucleus while it is rotating up to scission. The size of the asymmetry is typically ${10}^{-3}$. This asymmetry was termed the TRI effect. The interpretation of both effects is based on the transition state model. Both effects are shown to be steered by the properties of the collective $(J,K)$ transition states which are specific for any of the reactions studied. The study of asymmetries of ternary particle emission in fission induced by slow polarized neutrons provides a new method for the spectroscopy of transition states $(J,K)$ near the fission barrier. Implications of collective rotation on fragment angular momenta are discussed.