For mirror nuclei with masses A=42-95, the effects of isospin-nonconserving nuclear forces are studied with the nuclear shell model using the Coulomb displacement energy and triplet displacement energy as probes. It is shown that the characteristic behavior of the displacement energies can be well reproduced if the isovector and isotensor nuclear interactions with J=0 and T=1 are introduced into the f(7/2) shell. These forces, with their strengths being found consistent with the nucleon-nucleon scattering data, tend to modify nuclear binding energies near the N=Z line. At present, no evidence is found that these forces are needed for the upper fp shell. Theoretical one- and two-proton separation energies are predicted accordingly, and locations of the proton drip line are thereby suggested.

Mirror energy differences (MED) and triplet energy differences (TED) in the T = 1 analogue states are important probes of isospin-symmetry breaking. Inspired by the recent spectroscopic data of 66 Se, we investigate these quantities for A = 66 − 78 nuclei with large-scale shell-model calculations. For the first time, we find clear evidences suggesting that the isospin nonconserving (INC) nuclear force has a significant effect for the upper f p shell region. Detailed analysis shows that in addition to the INC force, the electromagnetic spin-orbit interaction plays an important role for the large, negative MED in A = 66 and 70 and the multipole Coulomb term contributes to the negative TED in all the T = 1 triplet nuclei. The INC force and its strength needed to reproduce the experimental data are compared with those from the G-matrix calculation using the modern charge-dependent nucleon-nucleon forces.PACS numbers: 21.10. Sf, 21.30.Fe, 21.60.Cs, 27.50.+e The impact of the Wigner's elegant concept, the isospin symmetry [1], is maximal near the N = Z line where nuclei have equal numbers of neutrons and protons. Breaking of this symmetry is generally attributed to the Coulomb and isospinnonconserving (INC) nuclear forces. To study the isospinsymmetry breaking, information for nuclei with N < Z is of particular interest but these nuclei are not easy to access experimentally. By comparison of nuclear masses [2] and detailed spectroscopic information [3] for nuclei having same isospin, T , one can study the isospin-related phenomena to explore the origin of the symmetry breaking.Measurable quantities have been suggested to probe the isospin-symmetry breaking. Mirror energy differences (MED), which are the differences between excitation energies of the T = 1 isobaric analogue states (IAS), are regarded as measures of the charge-symmetry breaking. On the other hand, triplet energy differences (TED) among the triplet T = 1 nuclei are used to indicate the charge-independence breaking. MED were extensively studied for the f 7/2 -shell nuclei up to high spins (see Ref.[4] for review). TED were discussed for the A = 46 [5,6], A = 50 [7], and A = 54 [8, 9] triplet nuclei. These studies have suggested that the INC nuclear interaction in the f 7/2 shell plays an important role in the explanation for the observed MED and TED [4,10]. In the upper sd shell, however, studies showed [11] that important contributions to the symmetry breaking come from the multipole Coulomb term and the electromagnetic spin-orbit interaction, but not from the INC nuclear interaction. Little has been explored for the upper f p-shell above the N = Z = 28 shell closure, and our knowledge on the isospin-symmetry breaking in the mass-70 region is presently very limited.Recent advances in experiment have made it possible to collect very exotic spectroscopic data. In the past few years, experimental information on mirror nuclei of the upper f p-shell above the doubly-magic nucleus 56 Ni became available. The MED in the A ∼ 60 mass region were discussed [12,...

Experimentally observed heaviest N Ϸ Z nuclei, Ru isotopes, are investigated by the shell model on a spherical basis with the extended P + QQ Hamiltonian. The energy levels of all the Ru isotopes can be explained by the shell model with a single set of force parameters. The calculations indicate an enhancement of quadrupole correlations in the N = Z nucleus 88 Ru as compared with the other Ru isotopes, but the observed moments of inertia seem to require much more enhancement of quadrupole correlations in 88 Ru. It is discussed that the particle alignment takes place at 8 + in 90 Ru but is delayed in 88 Ru till 16 + where the simultaneous alignments of proton and neutron pairs take place. The calculations present interesting predictions for 89 Ru that the ground state is the 1 / 2 − state and there are three ⌬J = 2 bands with different particle alignments including the T =0 p-n pair alignment.

The anomaly in Coulomb energy differences (CED) between the isospin T = 1 states in the odd-odd N = Z nucleus 70 Br and the analogue states in its even-even partner 70 Se has remained a puzzle. This is a direct manifestation of isospin-symmetry breaking in effective nuclear interactions. Here, we perform large-scale shell-model calculations for nuclei with A = 66 − 78 using the new filter diagonalization method based on the Sakurai-Sugiura algorithm. The calculations reproduce well the experimental CED. The observed negative CED for A = 70 are accounted for by the cross-shell neutron excitations from the f p-shell to the g 9/2 intruder orbit with the enhanced electromagnetic spin-orbit contribution at this special nucleon number.PACS numbers: 21.10. Sf, 21.30.Fe, 21.60.Cs, 27.50.+e Isospin is a fundamental concept in nuclear and particle physics. The isospin symmetry was introduced under the assumption of charge independence of the nuclear force [1]. Historically, the study of this symmetry led directly to the discovery and understanding of quarks. However, it is well known that this symmetry is only approximate because of the existence of the Coulomb interaction and isospin-breaking interactions among nucleons, leading to small differences, for example, in the binding energy of mirror-pair nuclei and in the excitation energy of the same spin, J, between isobaric analogue states (IAS) of the same isospin, T .A nucleus is a quantum many-body system with finite size, which generally shows two unique features in structure: the shell effect with the presence of strong spin-orbit interaction [2] and the nuclear deformation associated with collective motion [3]. To properly describe these aspects in the framework of nuclear shell models, effective interactions must be involved. Thus the effects of isospin-symmetry breaking can manifest themselves through structure changes in the vicinity of the N = Z line, providing information on the T z -dependence of the effective interactions. The effects have been extensively studied for nuclei in the upper sd-and the lower f p-shell regions (see Ref.[4] for review), where a remarkable agreement between experimental mirror energy differences (MED) and shell-model calculations has been found, allowing a clear identification of the origin of isospin-symmetry breaking in effective nuclear interactions. The Coulomb energy difference (CED), defined byis often regarded as a measure of isospin-symmetry breaking in effective nuclear interactions which include the Coulomb force [5,6]. In Eq. (1) ture changes along the N = Z line [7] and the phenomenon of shape coexistence [8][9][10] are known. Being pushed down to the lower shell by the spin-orbit interaction [2], the g 9/2 intruder orbit and its interplay with the f p-shell orbits play a key role in the overall structure. However, the influence of these structure changes on CED has not been explored. In Fig. 1, we show the experimental CED for nuclei with mass numbers A = 42 to 78, together with the very recent data of the 4 + 1 an...

The extended pairing plus QQ interaction with the J-independent isoscalar protonneutron force as an average monopole field, which has succeeded in describing collective yrast states of N ≈ Z even-A nuclei, is improved. The improvement is accomplished by adding small monopole terms (relevant to spectroscopy) to the average monopole field (indispensable to the binding energy). This modification extends the applicability of the interaction to nuclei with N ≈ 28 such as 48 Ca, and moreover improves energy levels of noncollective states. The modified interaction successfully describes not only even-A but also odd-A nuclei in the f 7/2 shell region. Results of exact shell model calculations in the model space (f 7/2 , p 3/2 , p 1/2 ) (its usefulness has been demonstrated previously) are shown for A=47, 48, 49, 50 and 51 nuclei.