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 realistic interactions, in the generalized seniority scheme with one broken proton pair and one broken neutron pair. Results for level energies, orbital occupations, and electromagnetic observables are compared with those obtained in the full shell-model space. We demonstrate that, even for the Ti isotopes, significant benefit would be obtained in going beyond the approximation of one broken pair of each type, while the Cr isotopes require further broken pairs to provide even qualitative accuracy.
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 have recently applied the generalized seniority approach successfully to explain the B(E1)/B(E2)/B(E3) properties of the semi-magic nuclei. In the present paper, we extend this approach to the Schmidt model as Generalized Seniority Schmidt Model and calculate the g-factors of the various seniority states in the semi-magic nuclei. We find that the magnetic moments and the g-factors do show a particle number independent behavior in multi-j configurations, as expected in the seniority scheme. The calculated results explain the experimental trends quite well. We find that the g-factors of all t…
Analytic proof of partial conservation of seniority in $j=9/2$ shells
最近在一个数值应用中发现了$j=9/2$壳的量子数的部分守恒性。在本文中，作为Zamick和P. Van Isacker [Phys. Rev. C 78（2008）044327]工作的扩展，导出了这个问题的完整解析证明。我们利用分数双亲的单粒子系数和二粒子系数分析了非对角矩阵元素的性质。它被发现，所有的非对角（和相关的对角）矩阵元素可以用简单的方式重新表示，并与某些单粒子cfp的成比例。这种部分动力学对称性的显著发生是$j=9/2$壳层的特殊性质的结果，其中所有$v=3$和5个状态都是唯一定义的。
The generalized seniority approach proposed by us to understand the B(E1)/B(E2)/B(E3) properties of semi-magic nuclei has been widely successful in the explanation of the same and has led to an expansion in the scope of seniority isomers. In the present paper, we apply the generalized seniority scheme to understand the behavior of g-factors in semi-magic nuclei. We find that the magnetic moment and the gfactors do show a particle number independent behavior as expected and the understanding is consistent with the explanation of transition probabilities.
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…
The neutron-rich nuclei 130Cd and 206Hg, so important in the astrophysical processes, may also be useful in tracking the evolution of nuclear shell gaps as one traverses the neutron-rich region. The high spin 8+ isomer in 130Cd and the 10+ isomer in 206Hg turn out to be the lampposts, which may shed light on the shell gaps and validity of the seniority scheme in the neutron-rich systems. We explore the robustness of the N=82 and N=126 magic numbers in the neutron-rich 130Cd and 206Hg nuclides, respectively. A parallel between the two nuclides in terms of the high-spin isomers allows us to inve…
There exist two uniquely defined $v=4$ states in systems within a $j=9/2$ subshell, which automatically conserve seniority and do not mix with other states. Here I show that the partial conservation of seniority plays an essential role in our understanding of the electric quadrupole transitions of the semimagic nuclei involving $j=9/2$ subshells, including the long-lived $8^{+}$ isomer in $^{94}$Ru. The effects of configuration mixing from neighboring subshells on the structure of those unique states are analysed. It is shown that a sharp transition from pure seniority coupling to a significan…
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…
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 $…
We study mode-entanglement in the seniority model, derive analytic formulas for the one-body reduced density matrix of states with seniority $ν= 0,\;1,\;2$, and $ν=3$, and also determine the particle number dependence of the one-body reduced density matrix for arbitrary seniority. We carry out numerical calculations for the lightest calcium isotopes and for $^{94}{\rm Ru}$ nucleus, and investigate the structure of their ground and low energy yrast states. We investigate the fulfillment of several predictions of the seniority model regarding the behavior of one-mode entropies, which we compare …
With nucleons occupying several shell model $j$ orbits, the isovector pair creation operator $A^1_μ$ (creates a two particle state with angular momentum $J=0$ and isospin $T=1$) is no longer unique. Choosing it to be a sum of single-$j$ isovector pair creation operators each with a phase, there will be multiple pair $SO(5)$ algebras with isospin; with $r$ number of $j$ orbits, there will be $2^{r-1}$ $SO(5)$ algebras each with a corresponding complementary $Sp(2Ω)$ algebra [$2Ω= \sum_j (2j+1)$] that gives seniority and reduced isospin quantum numbers. Three applications of multiple $SO(5)$ alg…
In this paper we model low-lying states of atomic nuclei in the nucleon-pair approximation of the shell model, using three approaches to select collective nucleon pairs: the generalized seniority scheme, the conjugate gradient method, and the Hartree-Fock approach. We find the collective pairs obtained from the generalized seniority scheme provides a good description for nearly spherical nuclei, and those from the conjugate gradient method or the Hartree-Fock approach work well for transitional and deformed nuclei. Our NPA calculations using collective pairs with angular momenta 0, 2, and 4 (d…
The puzzle of finding consistent nuclear configurations for explaining both the decay probabilities and moments of the ${9/2}^-$, ${8}^+$ and ${21/2}^-$ isomers in and around $N=126$ closed shell has been approached in the generalized seniority scheme. Though $h_{9/2}$ is the dominant orbital near Fermi energy, the role of configuration mixing from the surrounding $f_{7/2}$ and $i_{13/2}$ orbitals is found to be very important for the consistent explanation of all the isomeric properties such as the $B(E2)$ rates, $Q-$moments and $g-$factors. The structural behavior of the closed shell $N=126$…
Manifestation of three-body forces in f7/2-shell nuclei
传统的核壳模型方法被扩展到包括多体力。本文构造了0 f ~（7/2）壳层上全同核子在三体作用下的经验哈密顿量。研究了三体力在光谱、结合能、资历混合、粒子-空穴对称性、电磁和粒子跃迁率等方面的表现。结果表明，除了通常的扩展的价空间内的transmittance两体壳模型，在哈密顿量的三体组件可以是一个重要的组成部分，提高质量的理论方法。
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 …
Effective interactions and shell model studies of heavy tin isotopes
本文给出了在1f ~（7/2），2 p ~（3/2），0 h ~（9/2），2 p ~（1/2），1f ~（5/2），0 i ~（13/2）单粒子轨道定义的壳模型空间下，对134 ~ 142}Sn的偶、奇锡同位素的大尺度壳模型计算结果.采用基于现代核子-核子相互作用的有效两体相互作用。壳模型的结果反过来分析其配对的内容，使用广义的资历方法。我们的研究结果表明，一个配对模型的图片捕捉了大量的结构和最低躺态的偶，奇同位素的相关性。
