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One-phonon states of vibrational nuclei with mixed proton–neutron symmetry have been observed throughout the nuclear chart besides the mass A ≈ 200 region. Very recently, it has been proposed that the 2 2 + state of 212Po is of isovector nature. This nucleus has two valence protons and two valence neutrons outside the doubly-magic 208Pb nucleus. The stable isotope 204Hg, featuring two valence-proton and valence-neutron holes, with respect to 208Pb, is the particle-hole mirror of 212Po. In order to compare the properties of low-lying isovector excitations in these particle-hole mirror nuclei, we have studied 204Hg by using the projectile Coulomb-excitation technique. The measured absolute B ( M 1 ; 2 2 + → 2 1 + ) strength of 0.20 ( 2 ) μ N 2 indicates that the 2 2 + level of 204Hg is at least the main fragment of the 2 1 , m s + state. For the first time in this mass region, both lowest-lying, one-quadrupole phonon excitations are established together with the complete set of their decay strengths. This allows for a microscopic description of their structures, achieved in the framework of the Quasi-particle Phonon Model.

We present a detailed comparison of shell model calculations with inverse kinematic transfer reaction data, obtained using a radioactive beam. Experimentally extracted spectroscopic factors from the $$^{26}\hbox {Al}(d,p)^{27}\hbox {Al}$$26Al(d,p)27Al reaction for both even and odd parity states are found to be exceptionally well reproduced by the shell model and a high level of consistency is observed between bound isobaric analog states in $$^{27}\hbox {Al}$$27Al and $$^{27}\hbox {Si}$$27Si, populated via (d, p) and (d, n) transfer, respectively. Furthermore, an evaluation of key resonances in the astrophysical $$^{26}\hbox {Al}(p,\gamma )^{27}\hbox {Si}$$26Al(p,γ)27Si reaction indicates that shell model calculations provide relatively accurate predictions for the existence of strong resonances and mirror nucleus comparisons appear to hold exceptionally well for proton-unbound levels. Consequently, we expect that the utilization of both techniques will likely be a very effective tool in the investigation of stellar processes outside the current reach of experiment.

Background: Weakly bound and unbound nuclei close to particle drip lines are laboratories of new nuclear structure physics at the extremes of neutron/proton excess. The comprehensive description of these systems requires an open quantum system framework that is capable of treating resonant and nonresonant many-body states on equal footing. Purpose: In this work, we construct the minimal complex-energy configuration interaction approach to describe binding energies and spectra of selected 5 $\leq$ A $\leq$ 11 nuclei. Method: We employ the complex-energy Gamow shell model (GSM) assuming a rigid $^4$He core. The effective Hamiltonian, consisting of a core-nucleon Woods-Saxon potential and a simplified version of the Furutani-Horiuchi-Tamagaki interaction with the mass-dependent scaling, is optimized in the sp space. To diagonalize the Hamiltonian matrix, we employ the Davidson method and the Density Matrix Renormalization Group technique. Results: Our optimized GSM Hamiltonian offers a good reproduction of binding energies and spectra with the root-mean-square (rms) deviation from experiment of 160 keV. Since the model performs well when used to predict known excitations that have not been included in the fit, it can serve as a reliable tool to describe poorly known states. A case in point is our prediction for the pair of unbound mirror nuclei $^{10}$Li-$^{10}$N in which a huge Thomas-Ehrman shift dramatically alters the pattern of low-energy excitations. Conclusion: The new model will enable comprehensive studies of structure and reactions aspects of light drip-line nuclei., Comment: 11 pages, 3 figures

The electromagnetic effects of the finite size of the nucleon are implemented self-consistently on top of the Skyrme Hartree-Fock calculation, where the electric form factors of both protons and neutrons are considered. Furthermore, the vacuum polarization and the electromagnetic spin-orbit interaction are taken into account. The self-consistent finite-size effects give a different Coulomb potential from the conventional one and affect the neutrons as well. The contribution of the finite-size effects to the total energy reaches $ 7 \, \mathrm{MeV} $ in $ {}^{208} \mathrm{Pb} $. The vacuum polarization and the electromagnetic spin-orbit interaction are also non-negligible, especially in the heavy nuclei. These effects provide a comparable contribution of the total energy to that of the isospin symmetry-breaking terms of the nuclear interaction. The mirror nuclei mass difference in $ {}^{48} \mathrm{Ca} $--$ {}^{48} \mathrm{Ni} $ is also studied, and its value is improved by approximately one order of magnitude., 13 pages, 1 figure, 5 tables

Experimental above-barrier fusion cross-sections for $^{17}$F + $^{12}$C are compared to the fusion excitation functions for $^{16,18}$O, $^{19}$F, and $^{20}$Ne ions on a carbon target. In comparing the different systems both the differing static size of the incident ions and changes in fusion barrier are accounted for by examining the reduced fusion cross-section. Remaining trends of the fusion cross-section above the barrier which reflect the sensitive interplay of the sd protons and neutrons are observed. The experimental data are also compared to both a widely-used analytical model of near-barrier fusion, as well as a time-dependent Hartree-Fock model. Both models fail to describe the trends observed., Comment: 6 pages, 5 figures

The structures of the first \(1/2^+\) unbound states of \(A=9\) mirror nuclei are studied in the complex scaled \(\alpha +\alpha +N\) three-body model. The results indicate that the \(1/2^+\) state of \(^9\)Be is a virtual state of the s-wave neutron around the \(^8\)Be (\(\alpha -\alpha \)) cluster. But the corresponding analog \(^9\)B\((1/2^+)\) state is predicted as a resonant state due to the Coulomb barrier.

The MARATHON experiment ran at Jefferson Laboratory in 2018, measuring deep inelastic scattering of 10.6 GeV electrons from the proton (p), deuterium (D), tritium ( 3H), and helium-3 ( 3He). MARATHON's experimental observables are cross section ratios, most notably 3H/ 3He. This ratio of mirror nuclei is used for a novel extraction of the nucleon structure function ratio $$F^n_2$$ /$$F^p_2$$ with minimal nuclear corrections. Determining leading-order $$F^n_2$$ /$$F^p_2$$ at high x provides important constrains on the ratio of nucleon valence quark distributions d/u. The ratios 3H/D and 3He/D allow a determination of the EMC effect in the lightest nuclei sensitive to possible isospin dependence of nuclear effects. Lastly, the D/p ratio allows a comparison of the MARATHON experiment to SLAC measurements, and provides data to which the A = 3 ratios can be renormalized. The MARATHON results provide new constraints on d/u. Additionally, the results emphasize the importance of higher-order effects in extracting $$F^n_2$$ /$$F^p_2$$ from DIS measurements, and can help constrain said effects. In the renormalization scheme applied in the MARATHON analysis, no significant isospin dependence of the EMC effect is observed.

Background: The advent of radioactive ion beams has helped considerably to explore exotic decay modes like proton radioactivity in extremely proton-rich nuclei lying on or beyond the proton drip line. Recently, an experimental study was reported on the structural properties of proton-rich nucleus $^{11}\mathrm{O}$. Interestingly, $^{11}\mathrm{O}$ is the mirror nucleus of the widely studied $2n$ halo system $^{11}\mathrm{Li}$. In addition, $^{11}\mathrm{O}$ formed in the experiment was identified through its decay by $2p$ emission. A similar kind of interdependence between neutron halo and its mirror counterpart for $2p$ emission was reported [Charity, Elson, Komarov, Sobotka, Manfredi, and Shane, J. Phys.: Conf. Series 420, 012073 (2013)].Purpose: To study and analyze whether the mirror nuclei of known $1n$/$2n$ halo systems are $1p$/$2p$ emitters.Method: The preference for the mirror nuclei of $1n$/$2n$ halo systems for $1p$/$2p$ emission over the other ($2p$/$1p$ emission) is studied by $Q$-value systematics and potential energy minimization using a cluster-core model. The half-lives of the mirror nuclei of neutron halo systems were determined using a recently proposed empirical formula [Sreeja and Balasubramaniam, Eur. Phys. J. A 54, 106 (2018); Sreeja and Balasubramaniam, Eur. Phys. J. A 55, 33 (2019)].Results: Among the mirror nuclei of $1n$ halo systems, $^{11}\mathrm{N}$ (the mirror of $^{11}\mathrm{Be}$) and $^{15}\mathrm{F}$ (the mirror of $^{15}\mathrm{C}$) were found to have a preference for $1p$ emission over $2p$ emission by $Q$-value systematics. The potential energy surface analysis supported the result where both $^{11}\mathrm{N}$ and $^{15}\mathrm{F}$ were found to be ground-state $1p$ emitters. The trend got changed with an increase in angular momentum where the minimum in potential shifted from $1p$ to $2p$ cluster. Moreover, the half-life calculation matches with the result obtained from $Q$-value systematics.Conclusion: For the $2n$ halo systems, all the studies made indicate that the respective mirror nuclei have a preference for $2p$ emission. A similar conclusion cannot be drawn for the mirror nuclei of $1n$ halo systems except for $^{11}\mathrm{N}$ and $^{15}\mathrm{F}$, which were found to be ground-state $1p$ emitters. All the remaining mirror nuclei of $1n$ halo systems prefers $2p$ emission as favorable decay mode than the expected $1p$ emission. The empirical formula can be used as a good tool to evaluate half-life values of proton emitters provided the $Q$ values are known with desirable accuracy.

In this paper we report two simple relations of masses between corresponding mirror nuclei, the first of which is based on the regularity of empirical neutron-proton interactions, and the second of which is based on the regularity of the one-nucleon separation energy. We demonstrate that, for $N\ensuremath{\ge}10$, the empirical neutron-proton interaction of given nucleus with neutron number $N\ensuremath{-}1$ and proton number $Z$ (we use the convention that $N=Z$ in this paper), or abbreviated by the $(N\ensuremath{-}1,Z)$ nucleus, equals the neutron-proton interaction of its corresponding mirror nucleus, i.e., the $(N,Z\ensuremath{-}1)$ nucleus; we also demonstrate that one-proton separation energy ${S}_{p}$ and one-neutron separation energy ${S}_{n}$ of the $(N\ensuremath{-}k,Z)$ nucleus ($k=1,2,3,4$) equals one-neutron separation energy ${S}_{n}$ and one-proton separation energy ${S}_{p}$, respectively, of the $(N,Z\ensuremath{-}k)$ nucleus, after a simple correction of Coulomb energy and proton-neutron mass difference are considered. Numerical experiments show that these correlations provide us with a remarkably accurate approach to predict masses and separation energies of some proton-rich nuclei with neutron numbers from 10--46. Our predicted masses of proton-rich nuclei are tabulated as a Supplemental Material of this paper.

Angle-integrated cross-section measurements of the $^{56}$Ni(d,n) and (d,p) stripping reactions have been performed to determine the single-particle strengths of low-lying excited states in the mirror nuclei pair $^{57}$Cu-$^{57}$Ni situated adjacent to the doubly magic nucleus $^{56}$Ni. The reactions were studied in inverse kinematics utilizing a beam of radioactive $^{56}$Ni ions in conjunction with the GRETINA $\gamma$-array. Spectroscopic factors are compared with new shell-model calculations using a full $pf$ model space with the GPFX1A Hamiltonian for the isospin-conserving strong interaction plus Coulomb and charge-dependent Hamiltonians. These results were used to set new constraints on the $^{56}$Ni(p,$\gamma$)$^{57}$Cu reaction rate for explosive burning conditions in x-ray bursts, where $^{56}$Ni represents a key waiting point in the astrophysical rp-process., Comment: Final version accepted and published. 5 pages, 2 figures

We report on high-precision ${Q}_{\mathrm{EC}}$ values of the $^{21}\mathrm{Na}\ensuremath{\rightarrow}^{21}\mathrm{Ne}$ and $^{23}\mathrm{Mg}\ensuremath{\rightarrow}^{23}\mathrm{Na}$ mirror $\ensuremath{\beta}$ transitions from mass measurements with ISOLTRAP at the CERN ISOLDE facility. A precision of $\ensuremath{\delta}m/m=9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ and $\ensuremath{\delta}m/m=1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ was reached for the masses of $^{21}\mathrm{Na}$ and $^{23}\mathrm{Mg}$, respectively. We reduce the uncertainty of the ${Q}_{\mathrm{EC}}$ values by a factor of 5, making them the most precise experimental input data for the calculation of the corrected $\mathcal{F}t$ value of these mixed Fermi and Gamow-Teller transitions. For the $^{21}\mathrm{Na}\ensuremath{\rightarrow}^{21}\mathrm{Ne}\phantom{\rule{4pt}{0ex}}{Q}_{\mathrm{EC}}$ value, a $2.3\ensuremath{\sigma}$ deviation from the literature ${Q}_{\mathrm{EC}}$ value was found.

We report on the observation of excited states in the neutron-deficient phosphorus isotopes $^{26,27,28}\mathrm{P}$ via in-beam $\ensuremath{\gamma}$-ray spectroscopy with both high-efficiency and high-resolution detector arrays. In $^{26}\mathrm{P}$, a previously unobserved level has been identified at 244(3) keV, two new measurements of the astrophysically important $3/{2}^{+}$ resonance in $^{27}\mathrm{P}$ have been performed, $\ensuremath{\gamma}$ decays have been assigned to the proton-unbound levels at 2216 and 2483 keV in $^{28}\mathrm{P}$, and the $\ensuremath{\gamma}$-ray line-shape method has been used to make the first determination of the lifetimes of the two lowest-lying excited states in $^{28}\mathrm{P}$. The expected Thomas-Ehrman shifts were calculated and applied to levels in the mirror nuclei. The resulting level energies from this procedure were then compared with the energies of known states in $^{26,27,28}\mathrm{P}$.

I develop a microscopic three-cluster model for exotic light nuclei. I use the hyperspherical formalism, associated with the Generator Coordinate Method. This model is well adapted to halo nuclei, since the long-range part of the radial wave functions is accurately reproduced. The core wave functions are described in the shell model, including excited states. This technique provides large bases, expressed in terms of projected Slater determinants. Matrix elements involve seven-dimension integrals, and therefore require long calculation times. I apply the model to 11Li, 14Be, 15B, and 17N described by two neutrons surrounding a 9Li, 12Be, 13B and 15N core, respectively. The 17Ne (as 15O+p+p) and 15Ne (as 13O+p+p) mirror nuclei are briefly discussed. I present the spectra and some spectroscopic properties, such as r.m.s. radii or E2 transition probabilities. I also analyze the importance of core excitations., Comment: Accepted for publication in Phys. Rev. C

We present a high-resolution in-beam γ-ray spectroscopy study of excited states in the mirror nuclei 55Co and 56Ni following one-nucleon knockout from a projectile beam of 56Ni. The newly determined partial cross sections and the γ-decay properties of excited states provide a test of state-of-the-art nuclear structure models and probe mirror symmetry in unique ways. The new experimental data are compared to large-scale shell-model calculations in the full pf space and including charge-dependent contributions. A mirror asymmetry for the partial cross sections leading to the two lowest 3/2− states in the A = 55 mirror pair was identified as well as a significant difference in the E1 decays from the 1/21+ state to the same two 3/2− states. The mirror asymmetry in the partial cross sections cannot be reconciled with the present shell-model picture or small mixing introduced in a two-state model. The observed mirror asymmetry in the E decay pattern, however, points at stronger mixing between the two lowest 3/2− states in 55Co than in its mirror 55Ni.

Background: The recent observation of the unbound nucleus $^{11}\mathrm{O}$ offers the unique possibility to study how the structure and dynamics of two-proton ($2p$) decay is affected by the removal of one neutron from $^{12}\mathrm{O}$, and provides important information on the Thomas-Ehrman effect in the mirror pairs $_{8}^{11}\mathrm{O}_{3}\text{\ensuremath{-}}_{3}^{11}\mathrm{Li}_{8}$ and $_{8}^{12}\mathrm{O}_{4}\text{\ensuremath{-}}_{4}^{12}\mathrm{Be}_{8}$, which involve the $2p$ emitters $^{11}\mathrm{O}$ and $^{12}\mathrm{O}$.Purpose: We investigate how continuum effects impact the structure and decay properties of $^{11}\mathrm{O}$ and $^{12}\mathrm{O}$, and their mirror partners.Methods: We solve the three-body core-nucleon-nucleon problem using the Gamow coupled-channel (GCC) method. The GCC Hamiltonian employs a realistic finite-range valence nucleon-nucleon interaction and the deformed cores of $^{9,10}\mathrm{C}$, $^{9}\mathrm{Li}$, and $^{10}\mathrm{Be}$.Results: We calculate the energy spectra and decay widths of $^{11}\mathrm{O}$ and $^{12}\mathrm{O}$ as well as those of their mirror nuclei. In particular, we investigate the dynamics of the $2p$ decay in the ground state of $^{12}\mathrm{O}$ by analyzing the evolution of the $2p$ configuration of the emitted protons as well as their angular correlations in the coordinate space. We also show how the analytic structure of the resonant states of $^{10}\mathrm{Li}$ and $^{10}\mathrm{N}$ impacts the low-lying states of $^{11}\mathrm{Li}$ and $^{11}\mathrm{O}$.Conclusions: We demonstrate that, in both nuclei $^{11}\mathrm{O}$ and $^{12}\mathrm{O}$, there is a competition between direct and ``democratic'' $2p$ ground-state emission. The broad structure observed in $^{11}\mathrm{O}$ is consistent with four broad resonances, with the predicted $3/{2}_{1}^{\ensuremath{-}}$ ground state strongly influenced by the broad threshold resonant state in $^{10}\mathrm{N}$, which is an isobaric analog of the antibound (or virtual) state in $^{10}\mathrm{Li}$.

The Tz=−32 nucleus 21Mg has been studied by Coulomb excitation on 196Pt and 110Pd targets. A 205.6(1)-keV γ-ray transition resulting from the Coulomb excitation of the 52+ ground state to the first excited 12+ state in 21Mg was observed for the first time. Coulomb excitation cross-section measurements with both targets and a measurement of the half-life of the 12+ state yield an adopted value of B(E2;52+→12+)=13.3(4) W.u. A new excited state at 1672(1) keV with tentative 92+ assignment was also identified in 21Mg. This work demonstrates a large difference in the B(E2;52+→12+) value between T=32, A=21 mirror nuclei. The difference is investigated in the shell-model framework employing both isospin conserving and breaking USD interactions and using modern ab initio nuclear structure calculations, which have recently become applicable in the sd shell. (Less)

The Beta-decay Paul Trap (BPT) at Argonne National Laboratory has proven to be an extremely effective tool for high-precision tests of the Standard Model via measurements of the β − ν correlation in mass-8 isotopes. Using four double-sided silicon strip detectors (DSSDs) backed by plastic scintillators and surrounding the ions confined by the BPT, the kinematics of the decays of the mirror nuclei lithium-8 and boron-8 are overdetermined when all charged decay products are measured. The most stringent low-energy limit on an intrinsic tensor current in the weak interaction was set using the BPT in 2015 (Sternberg, M.G., et al., Phys. Rev. Lett. 115, 182501 2015) utilizing trapped lithium-8. Since then, similar data for boron-8 and higher statistics data for lithium-8 have been collected and are currently being analyzed. With the elimination of radio-frequency (RF) pickup from the DSSDs and a detailed investigation of experimental systematic errors, the uncertainty is now dominated by the contribution from recoil-order terms in the decay rate. Our eventual goal is to limit tensor currents in the weak interaction with relative precision at or below 0.1%.

18 pags., 7 figs., 2 tabs., The neutron skin of nuclei is an important fundamental property, but its accurate measurement faces many challenges. Inspired by charge symmetry of nuclear forces, the neutron skin of a neutron-rich nucleus is related to the difference between the charge radii of the corresponding mirror nuclei. We investigate this relation within the framework of the Hartree-Fock-Bogoliubov method with Skyrme interactions. Predictions for proton skins are also made for several mirror pairs in the middle mass range. For the first time the correlation between the thickness of the neutron skin and the characteristics related with the density dependence of the nuclear symmetry energy is investigated simultaneously for nuclei and their corresponding mirror partners. As an example, the Ni isotopic chain with mass number A=48−60 is considered. These quantities are calculated within the coherent density fluctuation model using Brueckner and Skyrme energy-density functionals for isospin asymmetric nuclear matter with two Skyrme-type effective interactions, SkM* and SLy4. Results are also presented for the symmetry energy as a function of A for a family of mirror pairs from selected chains of nuclei with Z=20, N=14, and N=50. The evolution curves show a similar behavior crossing at the N=Z nucleus in each chain and a smooth growing deviation when N≠Z starts. Comparison of our results for the radii and skins with those from the calculations based on high-precision chiral forces is made., M.K.G., A.N.A., and D.N.K. are grateful for the support of the Bulgarian National Science Fund under Contract No. KP-06-N38/1. P.S. acknowledges support from Ministerio de Ciencia, Innovación y Universidades MCIU/AEI/FEDER, UE (Spain) under Contract No. PGC2018-093636-B-I00

The angular distribution of the nucleon elastic scattering on the lightest mirror nuclei 3H and 3He at incident energies of 6 and 9[Formula: see text]MeV has been analyzed. A new set of phenomenological optical potential parameters has been obtained. A comparison of differential cross-sections has been performed for both elastic scatterings of neutron and proton on the mirror nuclei. The contribution of individual volume, surface, and spin-orbit terms in the optical model potential for the projectiles at different energies was studied. The predicted elastic angular distributions results compared well with the experimental data.

In this study, starting from the nuclear binding energy, we studied the empirical formula of the Coulomb energy systematically. Beginning with the simplest empirical formula, we added the Coulomb exchange term, pairing correlation, and shell correction, to calculate the Coulomb energy more precisely. In addition, we investigated the Coulomb displacement energy of widely used mass models. The discrepancies between the calculation results and experimental data might be caused by the missing of the isospin breaking terms of strong interactions in theory. By investigating these discrepancies, we found that the results obtained by microscopic theories presented a distinctive systematical behavior. Thus, these theories can be improved by including isospin breaking terms. However, in the results obtained by phenomenological models, the systematical behavior is unclear. This occurs because it is difficult for the information of the microscopic nuclear structure to be absorbed into the parameters of phenomenological models.

We investigate how the Coulomb interaction affects the energy $E$ and width $\Gamma$ of resonance states in mirror nuclei. We employ a three-cluster microscopic model to determine position of resonance states in two- and three-body continua. Two parameters are introduced to quantify effects of the Coulomb interactions. As the energy and width of the corresponding resonance states of mirror nuclei are displayed on an $E$-$\Gamma$ plane, these parameters determine a rotation and a dilatation. With the help of these parameters we found resonance states with strong, small and medium effects of the Coulomb interaction. We also found two different scenarios of the motion of resonance states due to the Coulomb interaction. The first standard (major) scenario represent resonance states with the larger energy and larger width than their counterparts have. The second rear scenario includes resonance states with the larger energy but smaller width., Comment: 55 pages, 22 figures, two new paragraphs are added and typos are corrected, submitted to Nucl. Phys . A