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Nuclear mass measurements have recently been extended conspicuously to proton-rich region in the upper $fp$ shell. The new data are utilized to study isospin symmetry breaking phenomena}using Coulomb displacement energy (CDE) and triplet displacement energy (TDE) as probes. The new mass data, either measured for the first time or with greatly improved accuracy, removed several previously found ``anomalies" in the systematical behavior in the $fp$ shell. Remarkably, more regular odd-even staggering patterns can be established in both CDE and TDE, calling for a uniform explanation in terms of isospin-nonconserving (INC) forces across the $sd$, $f_{7/2}$, and upper $fp$ shells. By extending the large-scale shell-model calculation [Phys. Rev. Lett. \textbf{110}, 172505 (2013)] to the upper $fp$-shell region, we found that, in order to describe the new data, the same INC force is required as previously used for the $f_{7/2}$ shell. Especially, we propose the $T=1$ TDE for those triplet nuclei, that have $pp$, $nn$, and $pn$ pairs on top of a common even-even $N=Z$ core, to be a good indicator for the isotensor component of isospin violating interactions, which is estimated here to be 150 keV., Comment: 7 pages, 2 figures

The region of $N\approx Z\approx 40$ has long been associated with strongly deformed nuclear configurations. The presence of this strong deformation was recently confirmed through lifetime measurements in $N\approx Z$ Sr and Zr nuclei. Theoretically, however, these nuclei present a challenge due to the vast valence space required to incorporate all deformation driving interactions. Recent state-of-the-art predictions indicate a near axial prolate deformation for $N=Z$ and $N=Z+2$ nuclei between $N=Z=36$ and $N=Z=40$. In this work we investigate the shores of this island of deformation through a sub-barrier Coulomb excitation study of the $N=Z+4$ nucleus, \textsuperscript{80}Sr. Extracting a spectroscopic quadrupole moment of $Q_s(2^+_1) = 0.45^{+0.83}_{-0.88}$~eb, we find that \textsuperscript{80}Sr is inconsistent with significant axial prolate deformation. This indicates that the predicted region of strong prolate deformation around $N=Z=40$ is tightly constrained to the quartet of nuclei: \textsuperscript{76,78}Sr and \textsuperscript{78,80}Zr., Comment: Submitted to Physics Letters B

We report first precision mass measurements of the $1/2^-$ isomeric and $9/2^+$ ground states of $^{101}$In. The determined isomeric excitation energy continues a smooth trend of odd-$A$ indium isotopes up to the immediate vicinity of $N=50$ magic number. This trend can be confirmed by dedicated shell model calculations only if the neutron configuration mixing is considered. We find that the single particle energies are different for different states of the same isotope. The presented configuration-dependent shell evolution, type II shell evolution, in odd-$A$ nuclei is discussed for the first time. Our results will facilitate future studies of single-particle neutron states., Comment: 5 pages, 5 figures, submitted to physical review C, under review

The isoscalar neutron-proton pairing is thought to be important for nuclei with equal number of protons and neutrons but its manifestation in structure properties remains to be understood. We investigate the Gamow-Teller (GT) transitions for the f7/2-shell nuclei in large-scale shell-model calculations with the realistic Hamiltonian. We show that the isoscalar T=0, J=1+ neutron-proton pairing interaction plays a decisive role for the concentration of GT strengths at the first-excited 1+ state in 42Sc, and that the suppression of these strengths in 46V, 50Mn, and 54Co is mainly caused by the spin-orbit force supplemented by the quadrupole-quadrupole interaction. Based on the good reproduction of the charge-exchange reaction data, we further analyze the interplay between the isoscalar and isovector pairing correlations. We conclude that even for the most promising A=42 nuclei where the SU(4) isoscalar-isovector-pairing symmetry is less broken, the probability of forming an isoscalar neutron-proton pairing condensation is less than 60% as compared to the expectation at the SU(4)-symmetry limit., Comment: 5 pages, 4 figures, accepted in Phys. Rev. C

We investigate isospin-symmetry breaking effects in the sd-shell region with large-scale shell-model calculations, aiming to understand the recent anomalies observed in superallowed Fermi beta-decay. We begin with calculations of Coulomb displacement energies (CDE's) and triplet displacement energies (TDE's) by adding the T=1,J=0 isospin nonconserving (INC) interaction into the usual isospin-invariant Hamiltonian. It is found that CDE's and TDE's can be systematically described with high accuracy. A total number of 122 one- and two-proton separation energies are predicted accordingly, and locations of the proton drip-line and candidates for proton-emitters are thereby suggested. However, attempt to explain the anomalies in the superallowed Fermi beta-decay fails because these well-fitted T=1,J=0 INC interactions are found no effects on the nuclear matrix elements. It is demonstrated that the observed large isospin-breaking correction in the 32Cl beta-decay, the large isospin-mixing in the 31Cl beta-decay, and the small isospin-mixing in the 23Al beta-decay can be consistently understood by introducing additional T=1,J=2 INC interactions related to the s1/2 orbit., Comment: 7 pages, 3 figures, accepted in Phys. Lett. B

The recently-proposed effective shell-model interaction, the pairing-plus-multipole Hamiltonian with the monopole interaction obtained by empirical fits starting from the monopole-based universal force (PMMU), is systematically applied to nuclei of the pf5/2g9/2 shell region. It is demonstrated that the calculation describes reasonably well a wide range of experimental data, including not only the low-lying and high-excitation spectra, E2 transitions, quadrupole moments, and magnetic moments, but also the binding energies, for Ni, Cu, Zn, Ga, Ge, As, and Se isotopes with A=64-80. In particular, a structure of the neutron-rich Ge and Se isotopes is discussed in detail., Comment: 21 pages, 31 figures, accepted in Phys. Rev. C

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 66Se, 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 fp 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., Comment: 5 pages, 5 figures, accepted in Phys. Rev. C

We propose a unified realistic shell-model Hamiltonian employing the pairing plus multipole Hamiltonian combined with the monopole interaction constructed starting from the monopole-based universal force by Otsuka it et al. (Phys. Rev. Lett. 104, 012501 (2010)). It is demonstrated that the proposed PMMU model can consistently describe a large amount of spectroscopic data as well as binding energies in the pf and pf5/2g9/2 shell spaces, and could serve as a practical shell model for even heavier mass regions., Comment: 5 pages, 4 figures, accepted in Phys. Rev. C

For mirror nuclei with masses A=42-95, the effects of isospin nonconserving nuclear forces are studied with 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 f7/2 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., Comment: 5 pages, 5 figures, accepted for publication in Physical Review Letters

The anomaly in Coulomb energy differences (CED) between the isospin T=1 states in the odd-odd N=Z nucleus 70Br and the analogue states in its even-even partner 70Se 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 fp-shell to the g9/2 intruder orbit with the enhanced electromagnetic spin-orbit contribution at this special nucleon number., Comment: 4 pages, 4 figures, accepted for publication in Physical Review Letters

Recent experimental data have revealed large mirror energy differences (MED) between high-spin states in the mirror nuclei 67Se and 67As, the heaviest pair where MED have been determined so far. The MED are generally attributed to the isospin symmetry breaking caused by the Coulomb force and by the isospin nonconserving part of the nucleon-nucleon residual interaction. The different contributions of the various terms have been extensively studied in the fp shell. By employing large-scale shell model calculations, we show that the inclusion of the g9/2 orbit causes interference between the electromagnetic spin-orbit and the Coulomb monopole radial terms at high spin. The large MED are attributed to the aligned proton pair excitations from the p3/2 and f5/2 orbits to the g9/2 orbit. The relation of the MED to deformation is discussed., Comment: 5 pages, 4 figures, accepted in Phys. Rev. C

To discuss whether an enhanced isomer decay is a preferred process in a plasma environment it is required to know the structure of the isomer as well as the nearby states. The spin-21/2, 6.85-hour high-spin isomer in 93Mo is investigated within a shell model which well describes nuclei in this mass region. By using the obtained wave-functions which correctly reproduce the observed B(E2), B(E4), and B(M1) transitions, characteristics of the isomer are shown in comparison with the isomeric states in neighboring nuclei. Calculations suggest that these high-spin isomers are formed with almost pure single-particle-like configurations. The 93Mo 21/2^+ isomer has the predominant configuration $\pi (g_{9/2})^2_{8} \otimes \nu d_{5/2}$ lying below the 15/2^+, 17/2^+, and 19/2^+ states due to neutron-proton interaction, which is the physical origin of its long lifetime. The key E2 transition that connects the 21/2^+ isomer to the upper 17/2^+ level is predicted to be substantial (3.5 W.u), and therefore there is a real prospect for observing induced isomer deexcitation., Comment: 10 pages, 2 figures, accepted by Phys. Lett. B

The structure of neutron-rich Cr isotopes is systematically investigated by using the spherical shell model. The calculations reproduce well the known energy levels for the even-even $^{52-62}$Cr and odd-mass $^{53-59}$Cr nuclei, and predict a lowering of excitation energies around neutron number N=40. The calculated $B(E2;2_{1}^{+}\to 0_{1}^{+})$ systematics shows a pronounced collectivity around N=40; a similar characteristic behavior has been suggested for Zn and Ge isotopes. Causes for the sudden drop of the $9/2_{1}^{+}$ energy in $^{59}$Cr and the appearance of very low $0_{2}^{+}$ states around N=40 are discussed. We also predict a new band with strong collectivity built on the $0_{2}^{+}$ state in the N=40 isotope $^{64}$Cr., Comment: 11 pages, 14 figures, accepted in Phys. Rev. C

Using a shell model which is capable of describing the spectra of upper $g_{9/2}$-shell nuclei close to the $N=Z$ line, we study the structure of two isomeric states $7^{+}$ and $21^{+}$ in the odd-odd $N=Z$ nucleus $^{94}$Ag. It is found that both isomeric states exhibit a large collectivity. The $7^{+}$ state is oblately deformed, and is suggested to be a shape isomer in nature. The $21^{+}$ state becomes isomeric because of level inversion of the $19^{+}$ and $21^{+}$ states due to core excitations across the $N=Z=50$ shell gap. Calculation of spectroscopic quadrupole moment indicates clearly an enhancement in these states due to the core excitations. However, the present shell model calculation that produces the $19^{+}$-$21^{+}$ level inversion cannot accept the large-deformation picture of Mukha {\it et al.} in Nature {\bf 439}, 298 (2006)., Comment: 10 pages, 14 figures, accepted for publication in Phys. Rev. C

By applying particle-number projection to the static-path approximation (SPA), the heat capacity and the breakdown of pairing correlations are investigated in the thermally excited, superfluid systems 172Yb, 94Mo, and 56Fe. For the heavy nucleus 172Yb, the heat capacities in both the SPA and the number-projected SPA (NPSPA) exhibit an S shape; the difference between the SPA and NPSPA heat-capacity curves is not very large and the particle-number projection thereby enhances the S shape already seen in the SPA. The temperature at which the S-shape of heat capacity curve occurs parallels the temperature of the breakdown of pairing correlations as indicated by the effective pairing gap. However, for the comparatively lighter nuclei 94Mo and 56Fe, the SPA does not produce an S-shaped heat capacity on its own; only after particle-number projection the S shape appears in the heat-capacity curve. For 94Mo, we compare the NPSPA result with thermal odd-even mass differences, which are regarded as a direct measure of the pairing gap., Comment: 7 pages, 5 figures, accepted for publication in Phys. Rev. C

We present a thermal and quantum-mechanical treatment of nuclear rotation using the formalism of static path approximation (SPA) plus random-phase approximation (RPA). Naive perturbation theory fails because of the presence of zero-frequency modes due to dynamical symmetry breaking. Such modes lead to infrared divergences. We show that composite zero-frequency excitations are properly treated within the collective coordinate method. The resulting perturbation theory is free from infrared divergences. Without the assumption of individual random spin vectors, we derive microscopically the spin distribution of the level density. The moment of inertia is thereby related to the spin-cutoff parameter in the usual way. Explicit calculations are performed for 56^Fe; various thermal properties are discussed. In particular, we demonstrate that the increase of the moment of inertia with increasing temperature is correlated with the suppression of pairing correlations., Comment: 12 pages, 8 figures, accepted for publication in Physical Review C

The long-standing problem of dramatic structure change near N=40 in Ge isotopes is investigated by means of large-scale shell model calculation. The analysis of simulated calculations suggests a possible understanding of the problem in terms of rapid increase in the $g_{9/2}$ proton and neutron occupation. The observed variation in excitation of the second $0^+$ state in $^{70,72,74}$Ge appears to correlate closely with the $g_{9/2}$ occupations induced by strong proton-neutron interactions. The enhancement of the $g_{9/2}$ occupancies is probably due to correlations in the $1g2d3s$ shell., Comment: 11 pages, 5 figures, accepted for publication in Nuclear Physics A

The abrupt structure change from the nuclei of $N=Z \le 35$ to those of $N=Z \ge 36$ is investigated by means of shell model calculations. The basic features of the even-even and odd-odd nuclei under consideration are nicely reproduced. A sudden jump of nucleons into the upper $g_{9/2}d_{5/2}$ shell at $N=Z=36$ is found to be the main reason that causes the qualitative structure difference. It is argued that the structure change can be viewed as a decisive change of the mean field, or a phase transition, along the $N=Z$ line., Comment: 4 pages, 5 figures, submitted to Phys. Rev. Lett

The S shape of the canonical heat capacity is known as a signature of the pairing transition and along an isotopic chain it is significantly more pronounced for nuclei with an even number of neutrons than with an odd number. Although the heat capacities extracted from experimental level densities in 93-98Mo exhibit a clear S shape, they do not show such an odd-even staggering. To understand the underlying physics, we analyze thermal quantities evaluated from the partition function calculated using the static-path plus random-phase approximation (SPA+RPA) in a monopole pairing model with number-parity projection. The calculated level densities reproduce very well the experimental data and they also agree with estimates using the back-shifted Fermi-gas model. We clarify the reason why the heat capacities for Mo isotopes do not show odd-even staggering of the S shape. We also discuss thermal odd-even mass differences in 94-97Mo using the three-, four-, and five-point formula. These thermal mass differences are regarded as indicators of pairing correlations at finite temperature., Comment: 6 pages, 6 figures, accepted for publication in Phys. Rev. C

Experimental energy spectrum and B(E2) values in 68Ni and 90Zr indicate a double-magic character in these neutron-rich nuclei with N or Z=40. The data nevertheless do not show any pronounced irregularity in two-nucleon separation energy. To understand the underlying physics, we carry out both shell-model and mean-field calculations. The shell-model calculation can well reproduce all the observations. It is understood from the mean-field results for 68Ni that the shell gap at N=40 disappears due to dynamical correlations of the isovector J=0 pairing interaction. In 90Zr, however, such a dynamic process with the J=0 pairing appears not important because of the strong contribution of the J>0 interaction. We study also level schemes in the Ni isotopes and N=50 isotones. We predict a new band built on the $0_{2}^{+}$ state in both 68Ni and 90Zr. The states of this band are dominated by two-particle-two-hole excitations from the fp-shell to the intruder g_{9/2} orbit., Comment: 12 pages, 18 figures, accepted for publication in Phys. Rev. C

The partition function by means of the static path approximation (SPA) plus the random-phase approximation (RPA) treatment can be written as a contour integral form without solving the RPA equations for a separable interaction. This method is an efficient way to evaluate numerically the partition function for realistic calculations. As an illustration, we adopt the pairing model at finite temperature., Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. C

We apply a large-scale shell model to the study of proton-rich odd-mass nuclei with $N \approx Z$. Calculations predict unexpected structure in the $^{69}$As nucleus for which a detailed experiment was recently performed. In this odd-proton nucleus, one neutron competes with one proton for occupying the high-$j$ intruder orbit $g_{9/2}$ in the $9/2_1^+$ state and almost solely occupies the $g_{9/2}$ orbit in other low-lying positive-parity states. The T=0, J=9 one-proton-one-neutron alignment takes place in the negative-parity states with medium-high spins. A unique coexistence of two lowest bands with positive and negative signs of spectroscopic quadrupole moments is predicted., Comment: 7 pages, 5 figures, accepted for publication in Pyhs. Rev. C

Thermal behavior of isoscalar and isovector proton-neutron (pn) pairing energies at finite temperature are investigated by the shell model calculations. These pn pairing energies can be estimated by double differences of "thermal" energies which are extended from the double differences of binding energies as the indicators of pn pairing energies at zero temperature. We found that the delicate balance between isoscalar and isovector pn pairing energies at zero temperature disappears at finite temperature. When temperature rises, while the isovector pn pairing energy decreases, the isoscalar pn pairing energy rather increases. We discuss also the symmetry energy at finite temperature., Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. C

We extract pairing gap in $^{184}$W at finite temperature for the first time from the experimental level densities of $^{183}$W, $^{184}$W, and $^{185}$W using "thermal" odd-even mass difference. We found the quenching of pairing gap near the critical temperature $T_c = 0.47$ MeV in the BCS calculations. It is shown that the monopole pairing model with a deformed Woods-Saxon potential explains the reduction of the pairing correlation using the partition function with the number parity projection in the static path approximation plus random-phase approximation., Comment: 5 pages, 4 figures, accepted for publication in PRC

Strong residual correlations between neutrons and protons in N ~ Z systems can lead to unusual structure. Using the spherical shell model, we show that a low-excitation shape isomer can occur in the odd-odd N=Z nucleus 66As. This extends the picture of shape coexistence beyond even-even nuclei. Furthermore, it is demonstrated that in 66As and in the N=Z+1 nucleus 67As, a new type of isomer, which we term j-isomer, can be formed. The underlying mechanism for the isomerism formation is structure change in the isomeric states, which involves either an alignment of a neutron-proton pair from the high-j intruder orbitals, or a simultaneous occupation of these neutron and proton high-j orbitals., Comment: 11 pages, 2 figures

A typical form of mass formula is re-explained in terms of nuclear structure. For $ N \approx Z $ nuclei, we propose to start with the shell model picture and to consider the T=0 $2n-2p$ ($\alpha$-like) correlations as the fundamental concept, instead of the symmetry energy. Subsequently, the symmetry energy is described on the basis of the $\alpha$-like superfluidity caused by the T=0 $2n-2p$ correlations, in parallel with the pairing energy described on the basis of the pairing superfluidity. This re-explanation gives useful insight for understanding the nuclear mass formula. The origin of the Wigner energy is also explained in an interacting boson model for the Cooper pairs in the $\alpha$-like superfluid vacuum. Adding a correction term due to the T=0 $2n-2p$ correlations, which determines the T=0 base level for nuclear masses, can improve the mass formulas in practice., Comment: to be published in Prog. Theor. Phys. Vol. 113, No. 6

A study of the energies of the first excited $0^+$ states in all even-even $Z$ $\geq$ 8 nuclei reveals an anomalous behavior in some nuclei with $N$ = $Z$, $Z$ $\pm$ 2. We analyze these irregularities in the framework of the shell model. It is shown that proton-neutron correlations play an important role in this phenomenon., Comment: 4 pages, 5 figures

The competition between the isovector (T=1) and isoscalar (T=0) proton-neutron ($p-n$) correlations in $N=Z$ nuclei is investigated by calculating their correlation energies with a realistic effective interaction which reproduces observed nuclear properties very well, in a strict shell model treatment. It is shown in the realistic shell model that the double-differences of binding energies $(B(A+pn:T) + B(A) - B(A+p) - B(A+n))$ ($B(A)$ being the binding energy) are good indicators of the T=1 and T=0 $p-n$ correlations. Each of them, however, originates in plural kinds of correlations with T=1 or T=0., Comment: 9pages, 3figures, accepted for publication in Nuclear Pyhsics A

Nuclear shape transition and oblate-prolate coexistence in $N=Z$ nuclei are investigated within the configuration space ($2p_{3/2}$, $1f_{5/2}$, $2p_{1/2}$, and $1g_{9/2}$). We perform shell model calculations for $^{60}$Zn, $^{64}$Ge, and $^{68}$Se and constrained Hartree-Fock (CHF) calculations for $^{60}$Zn, $^{64}$Ge, $^{68}$Se, and $^{72}$Kr, employing an effective pairing plus quadrupole residual interaction with monopole interactions. The shell model calculations reproduce well the experimental energy levels of these nuclei. From the analysis of potential energy surface in the CHF calculations, we found shape transition from prolate to oblate deformation in these $N=Z$ nuclei and oblate-prolate coexistence at $^{68}$Se. The ground state of $^{68}$Se has oblate shape, while the shape of $^{60}$Zn and $^{64}$Ge are prolate. It is shown that the isovector matrix elements between $f_{5/2}$ and $p_{1/2}$ orbits cause the oblate deformation for $^{68}$Se, and four-particle four-hole ($4p-4h$) excitations are important for the oblate configuration., Comment: 6 pages, 5 figures, accepted for publication in Phys. Rev. C

The $^{66}$Ge and $^{68}$Ge nuclei are studied by means of the shell model with the extended $P+QQ$ Hamiltonian, which succeeds in reproducing experimentally observed energy levels, moments of inertia and other properties. The investigation using the reliable wave-functions predicts T=0, J=9 one-proton-one-neutron ($1p1n$) alignment in the $g_{9/2}$ orbit, at high spins ($14_1^+$, $16_1^+$ and $18_1^+$) in these $N \approx Z$ even-even nuclei. It is shown that a series of the even-$J$ positive-parity yrast states (observed up to $26_1^+$ for $^{68}$Ge) consists of the ground-state band and successive three bands with different types of particle alignments (two-neutron, $1p1n$, two-proton-two-neutron) in the $g_{9/2}$ orbit., Comment: 4 pages, 5 figures, to be published in Pyhs. Rev. C

The structure of the $N \approx Z$ nuclei $^{66}$Ge and $^{68}$Ge is studied by the shell model on a spherical basis. The calculations with an extended $P+QQ$ Hamiltonian in the configuration space ($2p_{3/2}$, $1f_{5/2}$, $2p_{1/2}$, $1g_{9/2}$) succeed in reproducing experimental energy levels, moments of inertia and $Q$ moments in Ge isotopes. Using the reliable wave functions, this paper investigates particle alignments and nuclear shapes in $^{66}$Ge and $^{68}$Ge. It is shown that structural changes in the four sequences of the positive- and negative-parity yrast states with even $J$ and odd $J$ are caused by various types of particle alignments in the $g_{9/2}$ orbit. The nuclear shape is investigated by calculating spectroscopic $Q$ moments of the first and second $2^+$ states, and moreover the triaxiality is examined by the constrained Hatree-Fock method. The changes of the first band crossing and the nuclear deformation depending on the neutron number are discussed., Comment: 18 pages, 21 figures; submitted to Phys. Rev. C

Pairing transition at finite temperature was investigated by the shell model and BCS calculations. The definitive signature of pairing transition is identified by a "transition temperature" $T_t$ estimated from a "thermal" odd-even mass difference, while there is no sharp phase transition because of the finiteness of nucleus. It is found that $T_t$ is in good agreement with predictions of critical temperature $T_c$ in the BCS approximation, and the pairing correlations almost vanish at two points of the transition temperature $T\approx 2T_{t}$. The BCS calculations show that the critical temperature $T_c$ increases with increasing deformation., Comment: 12 pages, 6 figures, accepted for publication in Nuclear Physics A

Experimentally observed heaviest $N \approx Z$ 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 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 $\Delta J=2$ bands with different particle alignments including the T=0 $p-n$ pair alignment., Comment: 11 pages including 10 figures, to be published in Phys. Rev. C

The extended pairing plus $QQ$ interaction with the $J$-independent isoscalar proton-neutron force as an average monopole field, which has succeeded in describing collective yrast states of $N \approx Z$ 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 $N \approx 28$ 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.

To study collective motion, the extended pairing plus $QQ$ force model proposed recently is applied to $A$=46, 48 and 50 nuclei in the $fp$ shell region. Exact shell model calculations in the truncated model space $(f_{7/2},p_{3/2},p_{1/2})$ prove the usefulness of the interaction. The simple model with the pairing plus quadrupole pairing plus $QQ$ force and $J$-independent isoscalar proton-neutron force reproduces unexpectedly well observed binding energies, energy levels of collective (yrast) states and reduced $E2$ transition probabilities in $^{46}$Ti, $^{46}$V, $^{48}$V, $^{48}$Cr, $^{50}$Cr and $^{50}$Mn. The correspondence between theory and experiment is almost comparable to that attained by the full $fp$ shell model calculations with realistic effective interactions. Some predictions are made for energy levels and variations of $B(E2)$ in the yrast bands, in these nuclei. Characteristics of the interaction are investigated by comparing with the realistic effective interactions., Comment: 34 pages including 14 figures

We study global features of proton-neutron (p-n) interactions and symmetry energy over a wide range of nuclei, using a schematic model interaction with four forces proposed recently. Calculations are performed by the BCS approximation in N,Z=20-50 and N,Z=50-82 regions. The experimental double differences of binding energies and symmetry energy are reproduced quite well. It is shown that the isoscalar p-n interactions with all J are indispensable for explaining the binding energies of not only $N\approx Z$ but also N>Z nuclei in the A=40-160 region., Comment: 15 pages, 4 figures, submitted to Phys. Lett. B

An extended pairing plus QQ force model, which has been shown to successfully explain the nuclear binding energy and related quantities such as the symmetry energy, is applied to study the alpha-like four-nucleon correlations in 1f_{7/2} shell nuclei. The double difference of binding energies, which displays a characteristic behavior at $N \approx Z$, is interpreted in terms of the alpha-like correlations. Important roles of proton-neutron interactions forming the alpha-like correlated structure are discussed., Comment: 10 pages, 2 figures, RevTex, submitted to Phys. Rev. C

Proton-neutron (p-n) interactions and its various aspects in $N\approx Z$ nuclei of $g_{9/2}$- and $f_{7/2}$ subshell are studied using a schematic model interaction with four force parameters proposed recently. It is shown that the model interaction well reproduces observed physical quantities: the double differences of binding energies, symmetry energy, Wigner energy, odd-even mass difference and separation energy, which testifies the reliability of the model interaction and its p-n interactions. First of all, the double differences of binding energies are used for probing the p-n interactions. The analysis reveals different contributions of the isoscalar and isovector p-n pairing interactions to two types of double difference of binding energies, and also indicates the importance of a unique form of isoscalar p-n pairing force with all $J$ components. Next, it is shown that this p-n force is closely related to the symmetry energy and the Wigner energy. Other calculations demonstrate significant roles of p-n interactions in the odd-even mass difference and in the separation energy at $N=Z$., Comment: 36 pages, 11 figures, to be published Phys. Rev. C