Excited states in low-energy spectra in $^{70-76}$Ni are considered. To this end, pairing forces in form of surface delta interaction are employed to account for formation of the ground state multiplet with seniority $ν= 2$ states. The multiplet splitting is described with mass relations of masses of neighbouring nuclei. Subsequently, seniority model is used to reproduce or predict the states $ν= 3$ in odd-even isotopes and $ν= 4$ in even-even isotopes. Correct account of $2_1^+$ state should allow for description of reversed order of states $J = 4$ with $ν= 2$ and $ν= 4$ observed in experiment. The results obtained are compared with the structure of similar multiplets in $N=50$ isotones.
We show for the first time that the generalized seniority scheme explains reasonably well the $B(E3)$ systematics for the $(0^+ \rightarrow 3_1^-)$ transitions in the Sn-isotopes, which are odd-tensor $E3$ transitions connecting different seniority states ($Δv = 2$). Additionally, we also present Large Scale Shell Model (LSSM) calculations to support our interpretation. The generalized seniority scheme points to the octupole character of these $3^-$ states in Sn isotopes.
In our recent paper [Phys. Lett. B 753, (2016) 122], we have shown that both the odd and even tensor electric transition probabilities exhibit similar behavior within the generalized seniority scheme in a multi-j environment. This microscopic approach was used to show for the first time the occurrence of seniority isomers in the $ {13}^-$ isomers of Sn-isotopes, which decay by odd tensor $E1$ transition to the same seniority ($Δv = 0$) state. In this letter, we extend our studies to odd tensor $E3$ transitions connecting different seniority states ($Δv = 2$), and show for the first time that t…
The yrast generalized seniority states are compared with the corresponding shell model states for the case of the Sn isotopes $^{104-112}$Sn. For most of the cases the energies agree within 100 keV and the overlaps of the wave functions are greater than 0.7.
In the present work available experimental data up to high-spin states of $^{119-126}$Sn isotopes with different seniority ($v$), including $v$ = 4, 5, 6, and 7 have been interpreted with shell model, by performing full-fledged shell model calculations in the 50-82 valence shell composed of $1g_{7/2}$, $2d_{5/2}$, $1h_{11/2}$, $3s_{1/2}$, and $2d_{3/2}$ orbitals. The results have been compared with the available experimental data. These states are described in terms of broken neutron pairs occupying the $h_{11/2}$ orbital. Possible configurations of seniority isomers in these nuclei are discus…
In this paper, we investigate the generalized seniority scheme and the validity of Generalized Seniority Schmidt Model in and around the $Z=82$ semi-magic region. A consistently same multi-j configuration is used to explain all the nuclear spectroscopic properties such as $g-$factors, $Q-$moments and $B(E2)$ trends for the ${13/2}^+$, ${12}^+$ and ${33/2}^+$ isomers in all the three Hg, Pb and Po isotopic chains. The inverted parabolic $B(E2)$ trends for the first $2^+$ states in Hg, Pb and Po isotopes are also explained using the generalized seniority scheme. A comparison with the experimenta…
We present a study of the spectroscopic factors for the (d,p) stripping reactions to the ${11/2}^-$ states in the chain of odd-mass Sn (A = 115 - 131) isotopes by using a multi-j generalized seniority approach. The results are in line with realistic shell model calculations and explain the experimental trend quite well. The multi-j configuration used in these calculations is consistent with earlier calculations for moments etc., and therefore, lends credence to the generalized seniority interpretation. To the best of our knowledge, this work presents the first calculation of spectroscopic fact…
Even tin isotopes of mass number $A = 108 \sim 124$ are calculated with realistic interactions in the generalized-seniority approximation of the nuclear shell model. For each nucleus, we compute the lowest ten thousand states ($5000$ of each parity) up to around $8$ MeV in excitation energy, by allowing as many as four broken pairs. The lowest fifty eigen energies of each parity are compared with the exact results of the large-scale shell-model calculation. The wavefunctions of the mid-shell nuclei show a clear pattern of the stepwise breakup of condensed coherent pairs with increasing excitat…
We study the quadrupole moments and the B(E2; $2^+ \rightarrow 0^+$) values for the ${11/2}^-$ states and the first $2^+$ states, respectively, by using a multi-j generalized seniority approach in the Cd (Z = 48), Sn (Z = 50) and Te (Z = 52) isotopic chains. The g-factor trends have also been discussed. Although, Cd and Te isotopes represent two-proton hole and two-proton particle systems, thus involving both kind of particles (protons and neutrons) in contrast to Sn (Z = 50) where only neutrons play a role, we find that a similar model based on neutron valence space alone is able to explain n…
Generalized seniority provides a truncation scheme for the nuclear shell model, based on pairing correlations, which offers the possibility of dramatically reducing the dimensionality of the nuclear shell-model problem. Systematic comparisons against results obtained in the full shell-model space are required to assess the viability of this scheme. Here, we extend recent generalized seniority calculations for semimagic nuclei, the Ca isotopes, to open-shell nuclei, with both valence protons and valence neutrons. The even-mass Ti and Cr isotopes are treated in a full major shell and with realis…
Symmetries are known to play an important role in the low lying level structure of Sn isotopes, mostly in terms of the seniority and generalized seniority schemes. In this paper, we revisit the multi-j generalized seniority approach for the first excited $2^+$ and $3^-$ states in the Cd ($Z=48$), Sn ($Z=50$) and Te ($Z=52$) isotopes, where the Cd and Te isotopes represent two-proton hole and two-proton particle nuclei, thus involving both kind of particles (protons and neutrons) in contrast to Sn isotopes. Interestingly, the approach based on neutron valence space alone is able to explain the …
The similar behavior of the B(E1) values of the recently observed 13- odd tensor E1 isomers and the B(E2) values of the 10+ and 15- even tensor E2 isomers in the Sn-isotopes has been understood in terms of the generalized seniority for multi-j orbits by using the quasi-spin scheme. This simple approach proves to be quite successful in explaining the measured transition probabilities and the corresponding half-lives in the high-spin isomers of the semi-magic Sn-isotopes. Hence, we show for the first time the occurrence of seniority isomers in the 13- Sn-isomers, which decay by odd-tensor E1 tra…
The neutron-rich $^{122-131}$Sb isotopes were produced as fission fragments in the reaction $^{9}$Be($^{238}$U,~f) with 6.2 MeV/u beam energy. An unique setup, consisting of AGATA, VAMOS++ and EXOGAM detectors, was used which enabled the prompt-delayed gamma-ray ($γ$) spectroscopy of fission fragments in the time range of 100 ns - 200 $μ$s. New isomers, prompt and delayed transitions were established in the even-A $^{122-130}$Sb isotopes. In the odd-A $^{123-131}$Sb isotopes, new prompt and delayed $γ$-ray transitions were identified, in addition to the confirmation of the previously known iso…
We apply a spin-projection method to calculate microscopically the level densities of a family of nickel isotopes $^{59-64}$Ni using the shell model Monte Carlo approach in the complete $pfg_{9/2}$ shell. Accurate ground-state energies of the odd-mass nickel isotopes, required for the determination of excitation energies, are determined using the Green's function method recently introduced to circumvent the odd particle-number sign problem. Our results are in excellent agreement with recent measurements based on proton evaporation spectra and with level counting data at low excitation energies…
We present freshly evaluated B$(E2\uparrow;0^+\rightarrow2^+)$ values across the even-even Sn-isotopes which confirm the presence of an asymmetric behavior as well as a dip in the middle of the full valence space. We explain these features by using the concept of generalized seniority. The dip in the B$(E2)$ values near $^{116}$Sn is understood in terms of a change in the dominant orbits before and after the mid shell, which also explains the presence of asymmetric peaks in the B$(E2)$ values. This approach helps in deciding the most active valence spaces for a given set of isotopes, and singl…
Isomeric studies in neutron-rich nuclei present a powerful tool to explore the structure at the nuclear extremes. We recently used the shell model calculations with Renormalized Charge Depen- dent Bonn (RCDB) effective interaction to calculate the properties of the $6^+$ seniority isomers in $^{134-138}$Sn in an attempt to resolve the anomalous B(E2) behavior of the $6^+$ isomer in $^{136}$Sn [Phys. Rev. C 91, 024321 (2015)]. We further explore these isomers by using the generalized seniority scheme for multi-j orbitals recently presented by us [Phys. Lett. B 753, 122 (2016)]; the B(E2) values…
We use the newly developed Multi-Reference In-Medium Similarity Renormalization Group to study all even isotopes of the calcium and nickel isotopic chains, based on two- plus three-nucleon interactions derived from chiral effective field theory. We present results for ground-state and two-neutron separation energies and quantify their theoretical uncertainties. At shell closures, we find excellent agreement with Coupled Cluster results obtained with the same Hamiltonians. Our results highlight the importance of the chiral 3N interaction to obtain a correct reproduction of experimental energy t…
Low-energy strength is predicted for the isoscalar monopole response of neutron-rich Ni isotopes, in calculations performed using the microscopic Skyrme HF+RPA and relativistic RHB+RQRPA models. Both models, although based on different energy density functionals, predict the occurrence of pronounced monopole states in the energy region between 10 MeV and 15 MeV, well separated from the isoscalar GMR. The analysis of transition densities and corresponding particle-hole configurations shows that these states represent almost pure neutron single hole-particle excitations. Even though their locati…
Collinear laser spectroscopy is performed on the nickel isotopes $^{58-68,70}$Ni, using a time-resolved photon counting system. From the measured isotope shifts, nuclear charge radii $R_c$ are extracted and compared to theoretical results. Three ab initio approaches all employ, among others, the chiral interaction NNLO$_{\rm sat}$, which allows an assessment of their accuracy. We find agreement with experiment in differential radii $δ\left\langle r_\mathrm{c}^2 \right\rangle$ for all employed ab initio methods and interactions, while the absolute radii are consistent with data only for NNLO$_{…
Shell model calculations with the neutron effective charge as single free parameter describe well the \bet and \bef rates for $N\le 64$ in the Cd and Sn isotopes. The former exhibit weak permanent deformation corroborating the prediction of a pseudo SU3 symmetry, which remains of heuristic value in the latter, though the pairing force erodes the quadrupole dominance. Calculations in $10^7$ and $10^{10}$-dimensional spaces exhibit almost identical patterns: A vindication of the shell model. For $N\ge 64$ quadrupole dominance is accentuated in the Cd isotopes and gives way to seniority dominance…
Isotopes of nickel play a key role during the silicon burning phase up to the presupernova phase of massive stars. Electron capture rates on these nickel isotopes are also important during the phase of core contraction. I present here the microscopic calculation of ground and excited states Gamow-Teller (GT) strength distributions for key nickel isotopes. The calculation is performed within the frame-work of pn-QRPA model. A judicious choice of model parameters, specially of the Gamow-Teller strength parameters and the deformation parameter, resulted in a much improved calculation of GT streng…
In this new era of radioactive beam facilities, the discovery of novel modes of excitation in nuclei far away from stability represents an area of intense research activity. In addition, these modes of excitation appear to be sensitive to the uncertain density dependence of the symmetry energy. We study the emergence, evolution, and nature of both the soft and giant isoscalar monopole modes as a function of neutron excess in three unstable Nickel isotopes: 56Ni, 68Ni, and 78Ni. The distribution of isoscalar monopole strength is computed in a relativistic random-phase approximation using severa…
The low-lying structures of the midshell $νg_{9/2}$ Ni isotopes $^{72}$Ni and $^{74}$Ni have been investigated at the RIBF facility in RIKEN within the EURICA collaboration. Previously unobserved low-lying states were accessed for the first time following $β$ decay of the mother nuclei $^{72}$Co and $^{74}$Co. As a result, we provide a complete picture in terms of the seniority scheme up to the first $(8^+)$ levels for both nuclei. The experimental results are compared to shell-model calculations in order to define to what extent the seniority quantum number is preserved in the first neutron $…
First-forbidden (FF) transitions can play an important role in decreasing the calculated half-lives specially in environments where allowed Gamow-Teller (GT) transitions are unfavored. Of special mention is the case of neutron-rich nuclei where, due to phase-space amplification, FF transitions are much favored. We calculate the allowed GT transitions in various pn-QRPA models for even-even neutron-rich isotopes of nickel. Here we also study the effect of deformation on the calculated GT strengths. The FF transitions for even-even neutron-rich isotopes of nickel are calculated assuming the nucl…
Recent observation of the 6$^+$ seniority isomers and measurements of the B${(E2)}$ values in the $^{134-138}$Sn isotopes lying close to the neutron drip line have raised some questions about the validity of the currently used effective interactions in the neutron-rich region. Simpson $\it{et}$ $\it{al.}$ [Phys. Rev. Lett. $\textbf{113}$, 132502 (2014)] had to modify the diagonal and non-diagonal $νf_{7/2}^2$ two body matrix elements of the "${Vlk}$" interaction by ${\sim150}$ keV in their shell model calculations in order to explain the data of $^{136}$Sn. In contrast, we are able to explain …
Large-scale shell-model calculations are carried out in the model space including neutron-hole orbitals $2p_{1/2}$, $1f_{5/2}$, $2p_{3/2}$, $0i_{13/2}$, $1f_{7/2}$ and $0h_{9/2}$ to study the structure and electromagnetic properties of neutron deficient Pb isotopes. An optimized effective interaction is used. Good agreement between full shell-model calculations and experimental data is obtained for the spherical states in isotopes $^{194-206}$Pb. The lighter isotopes are calculated with an importance-truncation approach constructed based on the monopole Hamiltonian. The full shell-model result…
We present a comparative study of the high-spin ${11/2}^-$, ${10}^+$ and ${27/2}^-$ nuclear isomers, observed commonly in the full semi-magic $Z=50$ isotopic and $N=82$ isotonic chains, which are found to display nearly identical systematics in excitation energy and half-lives. A constant and particle number independent energy gap of $\sim$ 4 MeV between the $0^+$ ground states and ${10}^+$ isomers and, the ${11/2}^-$ and ${27/2}^-$ isomers exists before the mid-shell, which declines near the mid-shell, and then becomes constant at $\sim$ 3 MeV after the mid-shell. Large scale shell model calc…
We present results from large-scale shell-model calculations of even and odd tin isotopes from 134Sn to 142}Sn with a shell-model space defined by the 1f7/2,2p3/2,0h9/2,2p1/2,1f5/2,0i13/2 single-particle orbits. An effective two-body interaction based on modern nucleon-nucleon interactions is employed. The shell-model results are in turn analyzed for their pairing content using a generalized seniority approach. Our results indicate that a pairing-model picture captures a great deal of the structure and the correlations of the lowest lying states for even and odd isotopes.
Neutron rich Ca and Ni nuclei have been studied in spherical Relativistic Mean Field formalism in co-ordinate space. A delta interaction has been has been adopted to treat the pairing correlations for the neutrons. Odd nuclei have been treated in the blocking approximation. The effect of the positive energy continuum and the role of pairing in the stability of nuclei have been investigated using the resonant-BCS (rBCS) approach. In Ca isotopes, N=50 is no longer a magic number while in Ni nuclei, a new magic number emerges at N=70. There is a remarkable difference in the relative positions of …
In astrophysical environments, allowed Gamow-Teller (GT) transitions are important, particularly for $β$-decay rates in presupernova evolution of massive stars, since they contribute to the fine-tuning of the lepton-to-baryon content of the stellar matter prior to and during the collapse of a heavy star. In environments where GT transitions are unfavored, first-forbidden transitions become important especially in medium heavy and heavy nuclei. Particularly in case of neutron-rich nuclei, first-forbidden transitions are favored primarily due to the phase-space amplification for these transition…
177 neutron spectroscopic factors for nickel isotopes have been extracted by performing a systematic analysis of the angular distributions measured from (d,p) transfer reactions. A subset of the extracted spectroscopic factors are compared to predictions of large-basis shell models in the full pf model space using the GXPF1A effective interaction, and the (f5/2, p3/2, p1/2, g9/2) model space using the JJ4PNA interaction. For ground states, the predicted spectroscopic factors using the GXPF1A effective interaction in the full pf model space agree very well with the experimental values, while pr…
We carry out a systematic study of electric dipole mode (E1) for neutron-rich isotopes from nickel (Z=28) to tin (Z=50) using a time-dependent mean-field theory. Our time-dependent scheme is the canonical-basis time-dependent Hartree-Fock-Bogoliubov theory which can self-consistently describe nuclear dynamics with pairing correlation. We focus our discussion on the pygmy dipole resonance (PDR) and E1 polarizability. The correlation between neutron-skin thickness and PDR strongly depends on the neutron number, but the correlation between the skin thickness and E1 polarizability is much more sta…
Mass measurements continue to provide invaluable information for elucidating nuclear structure and scenarios of astrophysical interest. The transition region between the $Z = 20$ and $28$ proton shell closures is particularly interesting due to the onset and evolution of nuclear deformation as nuclei become more neutron rich. This provides a critical testing ground for emerging ab-initio nuclear structure models. Here, we present high-precision mass measurements of neutron-rich chromium isotopes using the sensitive electrostatic Multiple-Reflection Time-Of-Flight Mass Spectrometer (MR-TOF-MS) …
In the single j-shell, the configuration of an even-even Ti isotope consists of 2 protons and n neutrons. The I=0 wave function can be written in terms of D(J,Jv)'s, which are the probability amplitudes for the 2 protons to couple to J and the n neutrons to couple to Jv (where J stands for the angular momentum and v for the seniority quantum number). There are several states with isospin Tmin=|(N-Z)/2|, but only one with Tmax=Tmin+2. By demanding that the Tmax wave function be orthogonal to the Tmin ones, we obtain the following simple expressions for the number of J=0 np pairs in these Ti iso…
Impact of ab initio E1 strength on neutron capture rates along the nickel isotopic chain
Facility for Rare Isotope Beams, Michigan State University（稀有同位素束设施，密歇根州立大学）；Physics Division, Oak Ridge National Laboratory（橡树岭国家实验室物理部）；Department of Physics, Chalmers University of Technology（查尔姆斯理工大学物理系）
We have computed dipole strength distributions for nickel and tin isotopes within the Relativistic Quasiparticle Time Blocking approximation (RQTBA). These calculations provide a good description of data, including the neutron-rich tin isotopes $^{130,132}$Sn. The resulting dipole strengths have been implemented in Hauser-Feshbach calculations of astrophysical neutron capture rates relevant for r-process nucleosynthesis studies. The RQTBA calculations show the presence of enhanced dipole strength at energies around the neutron threshold for neutron rich nuclei. The computed neutron capture rat…
We perform Hartree-Fock-Bogoliubov (HFB) calculations for semi-magic Calcium, Nickel, Tin and Lead isotopes and $N$=20, 28, 50 and 82 isotones using density-dependent pairing interactions recently derived from a microscopic nucleon-nucleon interaction. These interactions have an isovector component so that the pairing gaps in symmetric and neutron matter are reproduced. Our calculations well account for the experimental data for the neutron number dependence of binding energy, two neutrons separation energy, and odd-even mass staggering of these isotopes. This result suggests that by introduci…
We calculate the B(E2) strength in 68Ni and other nickel isotopes using several theoretical approaches. We find that in 68Ni the gamma transition to the first 2+ state exhausts only a fraction of the total B(E2) strength, which is mainly collected in excited states around 5 MeV. This effect is sensitive to the energy splitting between the fp shell and the g_{9/2}orbital. We argue that the small experimental B(E2) value is not strong evidence for the double-magic character of 68Ni.
