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Artículo escrito por un elevado número de autores, solo se referencian el que aparece en primer lugar, el nombre del grupo de colaboración, si le hubiere, y los autores pertenecientes a la UAM, Detailed spectroscopy of the neutron-deficient nucleus Ca36 was obtained up to 9 MeV using the Ca37(p,d)Ca36 and the Ca38(p,t)Ca36 transfer reactions. The radioactive nuclei, produced by the LISE spectrometer at GANIL, interacted with the protons of the liquid hydrogen target CRYPTA, to produce light ejectiles (the deuteron d or triton t) that were detected in the MUST2 detector array, in coincidence with the heavy residues identified by a zero-degree detection system. Our main findings are (i) a similar shift in energy for the 11+ and 21+ states by about -250 keV, as compared with the mirror nucleus S36; (ii) the discovery of an intruder 02+ state at 2.83(13) MeV, which appears below the first 2+ state, in contradiction with the situation in S36; and (iii) a tentative 03+ state at 4.83(17) MeV, proposed to exhibit a bubble structure with two neutron vacancies in the 2s1/2 orbit. The inversion between the 02+ and 21+ states is due to the large mirror energy difference (MED) of -516(130) keV for the former. This feature is reproduced by shell model calculations, using the sd-pf valence space, predicting an almost pure intruder nature for the 02+ state, with two protons (neutrons) being excited across the Z=20 magic closure in Ca36 (S36). This mirror system has the largest MEDs ever observed, if one excludes the few cases induced by the effect of the continuum

The elegant concept of isospin symmetry is of fundamental importance in nuclear and elementary particle physics. As a β-decay process changes an up quark to a down quark or vice versa , studies of nuclei with exchanged numbers of neutrons and protons, known as mirror nuclei, can be a powerful means to probe isospin symmetry breaking. A series of β-decay experiments of sd-shell nuclei near the proton drip line produced by projectile fragmentation were performed at the Radioactive Ion Beam Line of the Heavy Ion Research Facility in Lanzhou (HIRFL-RIBLL1) using a silicon array with a high detection efficiency and a low detection threshold. The secondary ions were identified by the combination of Δ E -TOF and magnetic rigidity ( Bρ ) in which the time of flight (TOF) was measured by two plastic scintillators at the second and fourth focal planes of the RIBLL1 and the energy loss (Δ E ) was measured by two silicon detectors in the front of the silicon array. Double-sided silicon strip detectors (DSSDs) in the center of the array served to measure the residual energies of secondary ions on an event-by-event basis and study their decay properties with an implantation-decay correlation. Several quadrant silicon detectors (QSDs) placed behind DSSDs were used for anticoincidences of the penetrating fragments and light particles coming along with the beam, and measurements of β particles and high-energy protons. The β-delayed proton peaks with known energies and their corresponding absolute intensities were used for the energy and detection efficiency calibrations of the DSSDs. The system allows us to measure protons with energies down to about 200 keV without obvious β background in the proton spectrum and was successful to measure the energies, time, and positions of implanted ions and decay protons efficiently, supporting researchers to study the decay properties of nuclei towards the proton drip line. The β-decay data, together with the large-scale shell-model calculations, allows detailed investigations on the mirror-nuclei systems resulting in the systematic study of isospin symmetry breaking in the sd-shell nuclear region. It was found that the mirror asymmetry parameters become larger due to the smaller separation energies while approaching the proton drip line for the extremely proton-rich sulfur nuclei 27,28,29S and the Coulomb forces and other isospin-symmetry nonconserving forces acting between protons would lead to extended proton wave functions and cause mirror asymmetries. The properties of 22Si β-decay for the transitions to the low-lying states of 22Al were measured, and the reduced transition probabilities were determined. Comparing with the data on the β-decay of the mirror nucleus 22O, we found a mirror asymmetry of δ =209(96)% in the transition to the first 1+ excited state of the respective daughters. This is by far the largest value of δ observed in the low-lying states. Shell-model calculations with isospin-nonconserving forces, including the T =1, J =2, 3 interactions related to the s1/2 orbit that introduces explicitly the isospin-symmetry breaking force and describes the loosely bound nature of the wave functions of the s1/2 orbit, can reproduce the observed data well and demonstrate that this dramatically large mirror asymmetry is attributed to the significant proton occupation and loosely bound nature of the wave functions of the s1/2 orbit, which suggests that 22Al is a proton-halo nucleus.

The isobaric analog states with isospin T = 1 in triplet of the A = 14 nuclei: 14C, 14N, and 14O, are studied. The signs of a neutron halo in the 1− (6.09 MeV) state of 14C have been revealed earlier by two groups. We confirm this result and study isobaric analog 1− states of neighboring 14N and 14O nuclei. The differential cross sections for the 14C(α, α)14C* (6.09 MeV, 1−) inelastic scattering, the 13C(3He, d)14N* (8.06 MeV, 1−), and the 14N(3He, t)14O* (5.17 MeV, 1−) reactions are analyzed by two methods: the modified diffraction method and the method of asymptotic normalization coefficients. The rms radii for all three mirror nuclei in the studied 1− states are found almost the same: (2.7 ± 0.1) fm for 14C, (2.67 ± 0.07) fm for 14N, and (2.6 ± 0.2) fm for 14O. The signs of the proton halo in the 1− state of 14N are identified for the first time.

Fully self-consistent framework for isobaric-analog resonances is presented. The chains of parent neutron-rich Ca, Ni, Sn nuclei around the neutron shells at $$N=20$$ , $$28$$ , $$34$$ , $$50$$ , $$82$$ , as well as the nuclei on the neutron-deficient side of these chains are treated in the Density Functional plus Continuum Quasi particle Random Phase Approximation (DF $$+$$ CQRPA). The recently established new Fayans functional DF3-f is applied for calculations in long isotopic chains including non-magic nuclei with pairing in both neutron and proton sectors. A comparison with the relativistic QRPA and SAMi $$+$$ RPA shows a robust performance and flexibility of the DF $$+$$ CQRPA. Constraining the strength of exchange Coulomb contribution from the binding energy splitting of the doublets and triplets of the mirror nuclei allows for better description of the IAR energies.

Conservation laws are deeply related to any symmetry present in a physical system1,2. Analogously to electrons in atoms exhibiting spin symmetries3, it is possible to consider neutrons and protons in the atomic nucleus as projections of a single fermion with an isobaric spin (isospin) of t = 1/2 (ref. 4). Every nuclear state is thus characterized by a total isobaric spin T and a projection Tz—two quantities that are largely conserved in nuclear reactions and decays5,6. A mirror symmetry emerges from this isobaric-spin formalism: nuclei with exchanged numbers of neutrons and protons, known as mirror nuclei, should have an identical set of states7, including their ground state, labelled by their total angular momentum J and parity π. Here we report evidence of mirror-symmetry violation in bound nuclear ground states within the mirror partners strontium-73 and bromine-73. We find that a J π = 5/2− spin assignment is needed to explain the proton-emission pattern observed from the T = 3/2 isobaric-analogue state in rubidium-73, which is identical to the ground state of strontium-73. Therefore the ground state of strontium-73 must differ from its J π = 1/2− mirror bromine-73. This observation offers insights into charge-symmetry-breaking forces acting in atomic nuclei. Observations of the decay of 73Sr, when compared to its mirror nucleus 73Br, indicate that the spin assignment of their ground states differ, demonstrating mirror-symmetry violation.

The unitary scheme model with bases corresponding to the number of quanta of excitations 3 ≤ N ≤ 11 was used to construct the ground and excited state wave functions of the four mirror nuclei with A = 7 ; namely, the nuclei 7He, 7Li, 7Be, and 7B. The binding energies, spectra, and root mean square radii of these nuclei were calculated. The nuclear supermultiplet model was then applied to calculate the nuclear magnetic dipole moments of the four nuclei and the ft-value of the allowed β-decay during the electron capture in the transmutation of 7Be into 7Li. The calculations were performed using the GPT and the Av8’ nucleon–nucleon interactions along with the Urbana IX three-body interaction. Variations of the different characteristics of the four nuclei with respect to the number of quanta excitations N and the oscillator parameter ℏω were also calculated. Excellent convergences between the calculated values and the corresponding experimental values were obtained.

5 pags., 4 figs., Excited states in Zn were populated following one-neutron removal from a Zn beam impinging on a Be target at intermediate energies in an experiment conducted at the Radioactive Isotope Beam Factory at RIKEN. Three γ rays were observed and tentatively assigned to the 6→4→2→0 yrast sequence. This turns Zn into the heaviest T=−2 nucleus in which excited states are known. The excitation-energy differences between these levels and the isobaric analogue states in the T=+2 mirror partner, Fe, are compared with large-scale shell-model calculations considering the full pf valence space and various isospin-breaking contributions. This comparison, together with an analysis of the mirror energy differences in the A=58, T=±1 pair Zn and Ni, provides valuable information with respect to the size of the monopole radial and the isovector multipole isospin-breaking terms in the region above doubly-magic Ni., We thank the RIKEN Nishina Center accelerator staff and the BigRIPS team for providing excellent beams to the experiment. This work was supported by the Spanish Ministerio de Ciencia e Inno- vación under contracts FPA2017-84756-C4-2-P, PGC-2018-94583, and SEV-2016-0597, the Swedish Research Council (Vetenskap- srådet, VR 2016-3969), and the UK Science and Technology Facil- ities Council (STFC) under grants ST/L005727/1 and ST/P003885/1. FB is supported by the RIKEN Special Postdoctoral Researcher Pro- gram

A sequence of excited states has been established for the first time in the proton-rich nucleus 48Fe (Z=26, N=22). The technique of mirrored (i.e. analogue) one-nucleon knockout reactions was applied, in which the T z = ±2 mirror pair, 48Fe/48Ti were populated via one-neutron/one-proton knockout from the secondary beams 49Fe/49V, respectively. The analogue properties of the reactions were used to help establish the new level scheme of 48Fe. The inclusive and exclusive cross sections were determined for the populated states. Large differences between the cross sections for the two mirrored reactions were observed and have been interpreted in terms of different degrees of binding of the mirror nuclei and in the context of the recent observations of suppression of spectroscopic strength as a function of nuclear binding, for knockout reactions on light solid targets. Mirror energy differences (MED) have been determined between the analogue T = 2 states and compared with the shell model predictions. MED for this mirror pair, due to their location in the shell, are especially sensitive to excitations out of the f 7 / 2 shell, and present a stringent test of the shell-model prescription.

We study many-body resonances in the neuron-rich $^{8}\mathrm{He}$ and the mirror proton-rich $^{8}\mathrm{C}$ using the $^{4}\mathrm{He}+N+N+N+N$ five-body model with the isospin $T=2$ system. Resonances are described with the complex energy eigenvalues as the Gamow states using the complex scaling method. In $^{8}\mathrm{He}$, we obtain five states in which four states are resonances, and in $^{8}\mathrm{C}$ all five states are resonances. We discuss the isospin-symmetry breaking dynamically induced by the Coulomb interaction in the energy spectra and decay widths of the resonances in two mirror nuclei. We predict the resonance energies and decay widths for the future experiments. We also investigate the configurations of valence nucleons above $^{4}\mathrm{He}$ in two nuclei with the $jj$ coupling scheme, and all the states dominantly have the $p$-shell configurations. From the configuration mixing, $^{8}\mathrm{He}$ and $^{8}\mathrm{C}$ give the similar results, which indicates the good symmetry in two nuclei.

In this paper, we study the 9B and 9Be mirror nuclei with shell and cluster models. The modified Eckart plus Coulomb repulsive potentials are selected to describe the interaction between particles. By solving the Schrödinger equation, the exact solution of this equation is obtained by the parametric Nikiforov–Uvarov (PNU) method. The eigenvalues and wave function are calculated for 9B and 9Be. Our results are compared with experimental results, as well as results from other papers, and are in good agreement.

The energy density functional proposed earlier by Fayans and his coauthors is modified in such a way as to apply it in fully self-consistent calculations of isobaric analog resonances (IAR) in nuclei featuring pairing. The continuum quasiparticle random-phase approximation is used. Limits on the parameters of screening of exchange Coulomb interaction are deduced from a systematic analysis of binding energies of isobaric doublets and transition energies for isobaric triplets in mirror nuclei. A comparison with experimental data shows that the IAR energies for neutron-rich tin and lead isotopes involving fully developed pairing are described better on the basis of the new functional DF3-f than on the basis of self-consistent calculations performed with the DC3$$\ast$$ relativistic functional or with the SAMi Skyrme functional. The DF3-f functional is applied to calculating the properties of IARs in ruthenium, palladium, and cadmium isotopes featuring pairing in both neutron and proton subsystems, as well as to calculating similar properties in the chain of $$N=82$$ isotones.

It is well-known that the charge-violating interaction is usually underestimated in nuclear many-body approaches. In the framework of the Skyrme–Hartree–Fock (SHF) method, the effective two-body charge-symmetry breaking (CSB) and charge-independent breaking (CIB) interactions in nuclear medium based on Brueckner theory are included, then we constrain the effective Coulomb interaction in turn with the help of experimental Coulomb displacement energy (CDE), i.e., the binding-energy difference between mirror nuclei. Accordingly, we introduce a new (effective) Coulomb coupling constant e 0 2 = e 2 ( 1 + a exc Z − 2 / 3 ) to replace the original one e 2 between protons (note that the original coupling constant just applies to point-like charge), where Z is proton number. This effective coupling constant e 0 2 is phenomenologically embodying the effects of many complicated corrections beyond mean-field method or even nuclear structure physics such as core polarization, nucleon finite size and vacuum polarization. With e 0 2 = e 2 ( 1 + 0.45 Z − 2 / 3 ) for SLy4 interaction, the experimental CDE for T = 1 / 2 , 1 , 3 / 2 , 2 isobaric multiplets, together with the excitation energy of isobaric analog states for heavy nuclei such as 208Pb, can be rather well reproduced, indicating the validity of such a treatment. Moreover, the c coefficients in the isobaric multiplet mass equation for isobaric quartets are computed, and the results based on Coulomb force turns out to be around 10%–15% lower than the experimental ones persistently, just as the Nolen–Schiffer anomaly. Yet, the introduction of both the CIB effect and the e 0 2 systematically improves the agreement with experimental data substantially.

In this paper we study mass relations of mirror nuclei in terms of Coulomb energies calculated by the microscopic relativistic continuum Hartree-Bogoliubov theory. An additional term corresponding to the Nolen-Schiffer anomaly is assumed to take the same form as the well-known empirical formula. The resultant root-mean-square deviations of these mass relations are typically less than 100 keV. Based on these relations, 61 unknown proton-rich nuclear masses are predicted for $18\ensuremath{\leqslant}A\ensuremath{\leqslant}87$ with positive two-proton separation energies and are tabulated in the Supplemental Material of this paper.

We studied the proton-rich T_{z}=-1 nucleus ^{70}Kr through inelastic scattering at intermediate energies in order to extract the reduced transition probability, B(E2;0^{+}→2^{+}). Comparison with the other members of the A=70 isospin triplet, ^{70}Br and ^{70}Se, studied in the same experiment, shows a 3σ deviation from the expected linearity of the electromagnetic matrix elements as a function of T_{z}. At present, no established nuclear structure theory can describe this observed deviation quantitatively. This is the first violation of isospin symmetry at this level observed in the transition matrix elements. A heuristic approach may explain the anomaly by a shape change between the mirror nuclei ^{70}Kr and ^{70}Se contrary to the model predictions.