F. Q. Luo, M. A. Caprio
A recursive calculational scheme is developed for matrix elements in the generalized seniority scheme for the nuclear shell model. Recurrence relations are derived which permit straightforward and efficient computation of matrix elements of one-body and two-body operators and basis state overlaps.
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The generalized seniority scheme has long been proposed as a means of dramatically reducing the dimensionality of nuclear shell model calculations, when strong pairing correlations are present. However, systematic benchmark calculations, comparing results obtained in a model space truncated according to generalized seniority with those obtained in the full shell model space, are required to assess the viability of this scheme. Here, a detailed comparison is carried out, for semimagic nuclei taken in a full major shell and with realistic interactions. The even-mass and odd-mass Ca isotopes are …
Recent studies show that for systems with four identical fermions in the $j=9/2$ shell two special states, which have seniority $v=4$ and total spins I=4 and 6, are eigenstates of any two-body interaction. These states have good seniority for an arbitrary interaction. In this work an analytic proof is given to this peculiar occurrence of partial conservation of seniority which is the consequence of the special property of certain coefficients of fractional parentage. Further calculations did not reveal its existence in systems with other $n$ and/or $I$ for shells with $j\leq15/2$.
A discussion of the seniority quantum number in many-body systems is presented. The analysis is carried out for bosons and fermions simultaneously but is restricted to identical particles occupying a single shell. The emphasis of the paper is on the possibility of {\em partial} conservation of seniority which turns out to be a peculiar property of spin-9/2 fermions but prevalent in systems of interacting bosons of any spin. Partial conservation of seniority is at the basis of the existence of seniority isomers, frequently observed in semi-magic nuclei, and also gives rise to peculiar selection…
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…
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…
The g_{9/2} shell of identical particles is the first one for which one can have seniority-mixing effects. We consider three interactions: a delta interaction that conserves seniority, a quadrupole-quadrupole (QQ) interaction that does not, and a third one consisting of two-body matrix elements taken from experiment (98Cd) that also leads to some seniority mixing. We deal with proton holes relative to a Z=50,N=50 core. One surprising result is that, for a four-particle system with total angular momentum I=4, there is one state with seniority v=4 that is an eigenstate of any two-body interactio…
A partial conservation of the seniority quantum number in $j=9/2$ shells has been found recently in a numerical application. In this paper a complete analytic proof for this problem is derived as an extension of the work by Zamick and P. Van Isacker [Phys. Rev. C 78 (2008) 044327]. We analyze the properties of the non-diagonal matrix elements with the help of the one-particle and two-particle coefficients of fractional parentage (cfp's). It is found that all non-diagonal (and the relevant diagonal) matrix elements can be re-expressed in simple ways and are proportional to certain one-particle …
Monopole and Seniority Truncations in the Large-Scale Configuration Interaction Shell Model Approach
本文针对核物理中大规模组态相互作用壳模型计算量大的问题，提出了保持角动量守恒和转动对称性的单极相互作用截断与辛弱截断策略，有效降低了计算维度并在Sn、Xe和Pb同位素中验证了其能在极小维度比例下实现良好能量收敛。
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…
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…
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…
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.
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.
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…
The $10^+$ and $27/2^-$ isomers of the $Z>64$, $N=82$ nuclei are investigated in the shell model framework. We derive an extended seniority reduction formula for the relevant $E2$ transition strengths. Based on the extended formula, as well as on the approximate degeneracy among the $0h_{11/2}$, $2s_{1/2}$ and $1d_{3/2}$ orbits, we argue that the $B(E2)$ data require the $^{146}$Gd core excitation. The energy levels of both parities and the $B(E2)$ values are simultaneously reproduced by a multi-$j$ shell model calculation with the MSDI, if the excitations from $(0g_{7/2}1d_{5/2})$ to $(0h_{11…
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…
We investigate the generic pairing properties of shell-model many-body Hamiltonians drawn from ensembles of random two-body matrix elements. Many features of pairing that are commonly attributed to the interaction are in fact seen in a large part of the ensemble space. Not only do the spectra show evidence of pairing with favored J=0 ground states and an energy gap, but the relationship between ground state wave functions of neighboring nuclei show signatures of pairing as well. Matrix elements of pair creation/annihilation operators between ground states tend to be strongly enhanced. Furtherm…
The particle-hole symmetry (equivalence) of the full shell-model Hilbert space is straightforward and routinely used in practical calculations. In this work we show that this symmetry is preserved in the subspace truncated at a certain generalized seniority, and give the explicit transformation between the states in the two types (particle and hole) of representations. Based on the results, we study the particle-hole symmetry in popular theories that could be regarded as further truncations on top of the generalized seniority, including the microscopic interacting boson (fermion) model, the nu…
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…
Ab initio calculations of anomalous seniority breaking in the $πg_{9/2}$ shell for the $N=50$ isotones
该研究利用从头算价空间介质内相似重整化群方法，基于手征核子相互作用研究N=50同中子素的反常seniority破缺，重现了低激发谱与E2跃迁，揭示芯激发是破缺的成因，为核相互作用与模型提供了严格检验。
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 …
New shell model Hamiltonians are derived for the T=1 part of the residual interaction in the f5/2 p3/2 p1/2 g9/2 model space based on the analysis and fit of the available experimental data for 57Ni-78Ni isotopes and 77Cu-100Sn isotones. The fit procedure, properties of the determined effective interaction as well as new results for valence-mirror symmetry and seniority isomers for nuclei near 78Ni and 100Sn are discussed.
Recently we proposed [62] a fast computing scheme for generalized seniority on spherical single-particle basis. This work redesigns the scheme to make it applicable to deformed single-particle basis. The algorithm is applied to the rare-earth nucleus $^{158}_{~64}$Gd$_{94}$ for intrinsic (body-fixed frame) neutron excitations under the low-momentum {\emph{NN}} interaction $V_{\rm{low}-k}$. By allowing as many as four broken pairs, we compute the lowest $300$ intrinsic states of several multipolarity. These states converge well to the exact ones, showing generalized seniority is very effective …
The use of the seniority quantum number in many-body systems is reviewed. A brief summary is given of its introduction by Racah in the context of atomic spectroscopy. Several extensions of Racah's original idea are discussed: seniority for identical nucleons in a single-$j$ shell, its extension to the case of many, non-degenerate $j$ shells and to systems with neutrons and protons. To illustrate its usefulness to this day, a recent application of seniority is presented in Bose--Einstein condensates of atoms with spin.
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…
For a system with three identical nucleons in a single-$j$ shell, the states can be written as the angular momentum coupling of a nucleon pair and the odd nucleon. The overlaps between these non-orthonormal states form a matrix which coincides with the one derived by Rowe and Rosensteel [Phys. Rev. Lett. {\bf 87}, 172501 (2001)]. The propositions they state are related to the eigenvalue problems of the matrix and dimensions of the associated subspaces. In this work, the propositions will be proven from the symmetric properties of the $6j$ symbols. Algebraic expressions for the dimension of the…
Partial conservation of seniority in semi-magic nuclei
本文研究了半魔法核中偶极守恒的部分保持现象，探讨了j=9/2系统中特定态的可求解性及实验验证。
Seniority-two valence-shell building blocks of the octupole phonon
通过简化壳模型和谐振子波函数，研究双体激发多重态中$J^-$能级顺序，揭示$Δj=3, Δl=3$子壳层组合在粒子-粒子通道的能量增益偏好，并解释八极软核中3$^-_1$激发能较低的原因。
The seniority scheme has been shown to be extremely useful for the classification of nuclear states in semi-magic nuclei. The neutron-proton ($np$) correlation breaks the seniority symmetry in a major way. As a result, the corresponding wave function is a mixture of many components with different seniority quantum numbers. In this contribution we show that the $np$ interaction may favor a new kind of coupling in $N=Z$ nuclei, i.e., the so-called isoscalar spin-aligned $np$ pair mode. Shell model calculations reveal that the ground and low-lying yrast states of the $N = Z$ nuclei $^{92}$Pd and …
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 $N=126$…
Charge radii of neutron-rich scandium isotopes and the seniority symmetry in the $0f_{7/2}$ shell
通过共线激光光谱测量富中子⁴⁷⁻⁴⁹Sc同位素的核电荷半径，发现其在N=20至28间的特殊趋势及与钙同位素的呼应，现有理论模型无法解释，新数据揭示N=28同中子素与Z=20同位素的相似趋势，且与seniority模型预测一致。
We suggest that the extension of the Racah seniority description of strongly interacting fermions in the nuclear shell model is directly generalizable to describe pairing of atoms in cold Fermi systems. We illustrate this by the fermionic pairing in the much studied cold two-component gas of Li atoms. Our pairing interaction is two orders of magnitude stronger than that used in the usual BCS approach. We also explain why the Racah scheme is less applicable to nuclei, and discuss the similarities of the strongly-coupled matter in cold fermion systems and the new form of matter found in RHIC clo…
The traditional nuclear shell model approach is extended to include many-body forces. The empirical Hamiltonian with a three-body force is constructed for the identical nucleons on the 0f7/2 shell. Manifestations of the three-body force in spectra, binding energies, seniority mixing, particle-hole symmetry, electromagnetic and particle transition rates are investigated. It is shown that in addition to the usual expansion of the valence space within the tranditional two-body shell model, the three-body component in the Hamiltonian can be an important part improving the quality of the theoretica…
There has been a great deal of attention to the low lying energy spectum in a nucleus becuse of the abundance of experimetal data. Likewise ,perhaps to a lesser extent but still significant the high end for a given configuratiion has been examined. Here ,using single j shell calculations as a guide we examine the middle part of the spectum resulting form single j shell calculations.Seniority arguments are used to partially explain the midshell behaviours even though in general seniority is not a good quantum number for mixed systems of neutrons and protons.
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 …
In nuclei with valence nucleons are say identical nucleons and say these nucleons occupy several-$j$ orbits, then it is possible to consider pair creation operator $S_+$ to be a sum of the single-$j$ shell pair creation operators $S_+(j)$ with arbitrary phases, $S_+=\sum_j α_j S_+(j); α_j=\pm 1$. In this situation, it is possible to define multi-orbit or generalized seniority that corresponds to the quasi-spin $SU(2)$ algebra generated by $S_+$, $S_-=(S_+)^\dagger$ and $S_0=(\hat{n} -Ω)/2$ operators; $\hat{n}$ is number operator and $Ω=[\sum_j (2j+1)]/2$. There are now multiple pairing quasi-s…
Seniority and Hierarchy Configuration Interaction for Radicals and Excited States
本研究将层级组态相互作用（hCI）推广至任意参考行列式以计算自由基和激发态，发现其优于基于激发的CI，且结合EN2微扰校正能显著加速收敛并提升低阶模型的准确性。
Coulomb excitation of $^{124}$Te: Emerging collectivity and persisting seniority structure in the $6_1^+$ level
本研究测量了$^{124}$Te的库仑激发跃迁强度，发现其$6_1^+$能级在接近中壳区时仍保留seniority结构，与低激发态的集体性增强形成对比。
Spectroscopy of 211,213,215Pb isotopes and seniority properties
本研究针对价中子处于g9/2壳层的211Pb、213Pb、215Pb，对比相关能级分裂与态性质，讨论未发现的J=3/2+态及超出g9/2的组态计算，明确J=21/2+态为同质异能态。
We calculate the nuclear matrix elements (NMEs) for neutrinoless double-beta decays ($0νββ$) of $pf$-shell nuclei using the shell model (SM) and energy density functional (EDF) methods. The systematic study of non-physical decays (except for $^{48}$Ca) of Ca$\rightarrow$Ti, Ti$\rightarrow$Cr and Cr$\rightarrow$Fe allows for a detailed comparison between the two nuclear structure approaches. We observe that while the dominant Gamow-Teller part of the NME differs roughly by a factor of two between SM and EDF, when we restrict the calculations to spherical EDF states and seniority-zero SM configu…
Recent progress in configuration-interaction shell model
本文综述组态相互作用壳模型（CISM）近十年在奇特核、镜像核、中重核及有效哈密顿量构造方面的进展，并介绍 NPA、MCSM、PSM、GSM 等相关模型的发展。
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 …
Experimental mirror energy differences (MED) for nuclei lying in the middle and the second part of $1f_{7/2}$ shell are compared with shell model calculations in the $1f_{7/2}$ and in the full $pf$ configuration spaces, as well as with CSM calculations. MED plots are fully consistent with the description which emerges from the interpretation of SM calculations: i.e. the band crossing of the gs band with high-$K$ bands in $A$=51 and 50 mirror pairs, as well as the seniority-3 quasi band-termination at $I^π$=19/2$^-$ in $A$=49. Rotational alignment effects are excluded, contrarily to what even r…
We present a program for solving exactly the general pairing Hamiltonian based on diagonalization. The program generates the seniority-zero shell-model-like basis vectors via the `01' inversion algorithm. The Hamiltonian matrix is constructed in that seniority-zero space. The program evaluates all non-zero elements of the Hamiltonian matrix "on the fly" using the scattering operator and the search algorithm that act on the generated basis. The matrix is diagonalized by using the iterative Lanczos algorithm. The program thus developed, PairDiag, can calculate efficiently the ground-state eigenv…
Monte Carlo computation of pair correlations in excited nuclei
提出了一种基于Fock空间中路径积分的量子Monte Carlo方法，该方法可以计算正则系综中具有双原子对相互作用的多体核系统的有限温度性质.它使热力学变量的精确计算，如内能，熵，或比热，从测量时刻的跳数的路径中的核配置。单壳层$(h_{11/2})^6$模型的Monte Carlo计算与资深模型中多体谱的精确计算一致。
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 study in this letter the behavior of the neutrinoless double beta decay nuclear matrix elements (NME's) in the framework of the Interacting Shell Model. We analize them in terms of the total angular momentum of the decaying neutron pair and as a function of the seniority truncations in the nuclear wave functions. This point of view turns out to be very adequate to gauge the accuracy of the NME's predicted by different nuclear structure models. In addition, it gives back the due protagonism in this process to the pairing interaction, the interaction which is responsible for the very existenc…
For single-$j$ shells with $j={7/2}, {9/2}$ and 11/2, we relate the large probability of $I^+$ ground states to the largest (smallest) coefficients $α^J_{I(v β)} = <nv βI |$ $A^{J \dagger} \cdot A^J | n vβI>$, where $n$ is the particle number, $v$ is the seniority, $β$ is an additional quantum number, and $I$ is the angular momentum of the state. Interesting regularities of the probabilities of $I^+$ ground states are noticed and discussed for 4-particle systems. Several counter examples of the $0^+$ ground state (0GS) predominance are noticed for the first time.
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…
In this paper, we discuss the angular momentum distribution in the ground states of many-body systems interacting via a two-body random ensemble. Beginning with a few simple examples, a simple approach to predict P(I)'s, angular momenta I ground state (g.s.) probabilities, of a few solvable cases, such as fermions in a small single-j shell and d boson systems, is given. This method is generalized to predict P(I)'s of more complicated cases, such as even or odd number of fermions in a large single-j shell or a many-j shell, d-boson, sd-boson or sdg-boson systems, etc. By this method we are able…
In this article we analyze the nuclear matrix elements (NME) of the neutrinoless double beta decays of the nuclei 48-Ca, 76-Ge, 82-Se, 124-Sn, 130-Te and 136-Xe in the framework of the Interacting Shell Model (ISM). We study the relative value of the different contributions to them, such as higher order terms in the nuclear current, finite nuclear size effects and short range correlations, as well as their evolution with the maximum seniority permitted in the wave functions. We discuss also the build-up of the NME's as a function of the distance between the decaying neutrons. We calculate the …
Background: Microscopic calculations of heavy nuclei face considerable difficulties due to the sizes of the matrices that need to be solved. Various approximation schemes have been invoked, for example by truncating the spaces, imposing seniority limits, or appealing to various symmetry schemes such as pseudo-SU(3). This paper proposes a new symmetry scheme also based on SU(3). This proxy-SU(3) can be applied to well-deformed nuclei, is simple to use, and can yield analytic predictions. Purpose: To present the new scheme and its microscopic motivation, and to test it using a Nilsson model calc…
[Background] The BE2 rates of the Sn isotopes for $N\le 64$ exhibit enhancements hitherto unexplained. The same is true for the Cd isotopes. [Purpose] Describe the electromagnetic properties of the Sn and Cd isotopes [Method] Shell model calculations with a minimally renormalized realistic interaction, supplemented by Quasi and Pseudo-SU3 symmetries and Nilsson-SU3 selfconsistent calculations. [Results for $N\le 64$] Shell model calculations with the neutron effective charge as single free parameter describe well the BE2(2>0) and BE2(4>2) rates for $N\le 64$ in the Cd and Sn isotopes. The form…
We apply high-order many-body perturbation theory for the calculation of ground-state energies of closed-shell nuclei using realistic nuclear interactions. Using a simple recursive formulation, we compute the perturbative energy contributions up to 30th order and compare to exact no-core shell model calculations for the same model space and Hamiltonian. Generally, finite partial sums of this perturbation series do not show convergence with increasing order, but tend to diverge exponentially. Nevertheless, through a simple resummation via Pade approximants it is possible to extract rapidly conv…
The Similarity Renormalization Group (SRG) is investigated as a powerful yet practical method to modify nuclear potentials so as to reduce computational requirements for calculations of observables. The key feature of SRG transformations that leads to computational benefits is the decoupling of low-energy nuclear physics from high-energy details of the inter-nucleon interaction. We examine decoupling quantitatively for two-body observables and few-body binding energies. The universal nature of this decoupling is illustrated and errors from suppressing high-momentum modes above the decoupling s…
Background: Ab initio many-body methods have been developed over the past ten years to address mid-mass nuclei... As progress in the design of inter-nucleon interactions is made, further efforts must be made to tailor many-body methods. Methods: We formulate a truncated configuration interaction method that consists of diagonalizing the Hamiltonian in a highly truncated subspace of the total N-body Hilbert space. The reduced Hilbert space is generated via the particle-number projected BCS state along with projected seniority-zero two and four quasi-particle excitations. Furthermore, the extent…
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