Effective Shell-model Interaction Research Articles

Systematic shell-model study of 98−130Cd isotopes and 8+ isomeric states

We present systematic shell-model studies of even-even 98−130Cd isotopes using a realistic effective shell-model interaction derived from the G-matrix approach with an inert core 88Sr. Our calculated low-lying excited energy spectra and electromagnetic properties are compared with the experimental data. On the basis of recently available experimental data, we predict spins and parities corresponding to unconfirmed states. We also discuss the properties of 8+ isomeric states in 98−104,130Cd isotopes.

Robustness of pair structures for nuclear yrast states* *Supported by the National Natural Science Foundation of China (11875134, 11875188, 12175071, 11975151, 11961141003), and the Shanghai Key Laboratory of Particle Physics and Cosmology (21DZ2271500-2)

In this study, we investigate the robustness of pair structures for nuclear yrast states, that is, whether the structures of relevant collective pairs as building blocks of different yrast states are the same. We focus on deformed and transitional nuclei and study the yrast states of Si, Cr, and Xe, whose experimental values are 2.60, 2.40, and 2.16, respectively, using the nucleon-pair approximation (NPA) and shell-model effective interactions. For each yrast state, we consider optimized pair structures to be those providing the energy minimum for this state. To find the minimum, many full NPA calculations are performed with varying pair structures, and the numerical optimization procedure of the conjugate gradient method is implemented. Our results suggest that optimized pair structures remain the same for all states within a rotational band of a deformed nucleus. Our results also suggest that after backbending, that is, changing of the intrinsic state, the structure of the S pair, which is essential to build the monopole pairing correlation, remains approximately unchanged, whereas the structures of the non-S pairs, which are essential to build the quadrupole correlation, change significantly.

Effective shell-model interaction for nuclei “southeast” of Sn100

We construct an effective shell-model interaction for the valence space spanned by single-particle neutron and single-hole proton states in $^{100}$Sn. Starting from chiral nucleon-nucleon and three-nucleon forces and single-reference coupled-cluster theory for $^{100}$Sn we apply a second similarity transformation that decouples the valence space. The particle-particle components of the resulting effective interaction can be used in shell model calculations for neutron deficient tin isotopes. The hole-hole interaction can be used to calculate the $N = 50$ isotones south of $^{100}$Sn, and the full particle-hole interaction describes nuclei in the region southeast of $^{100}$Sn. We compute low-lying excited states in selected nuclei southeast of $^{100}$Sn, and find reasonable agreement with data. The presented techniques can also be applied to construct effective shell-model interactions for other regions of the nuclear chart.

Quadrupole phonon excitations and transition probabilities for low-lying states of neutron-rich Cd isotopes

In this paper we study the low-lying states of neutron-rich $^{122,124,126,128}\mathrm{Cd}$ and $^{130,132,134,136,138}\mathrm{Cd}$ within the nucleon-pair approximation of the shell model. We adopt the phenomenological Hamiltonian for $^{122,124,126,128}\mathrm{Cd}$, and the shell-model effective interaction $jj46$ for $^{130,132,134,136,138}\mathrm{Cd}$. The available experimental excitation energies and quadrupole transition probabilities are well reproduced by our calculation, and we also make predictions for very neutron-rich Cd nuclei. Based on our calculation, the $B(E2;{0}_{\mathrm{g}.\mathrm{s}.}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})$ values exhibit an asymmetric feature with respect to the $N=82$ shell closure, which mainly comes from the contributions of the proton transition matrix elements. We also investigate for the eight open-shell Cd nuclei, whether two low-lying yrast states with spins differing by 2 can be connected by a quadrupole-phonon excitation, and here we take the proton and neutron quadrupole operators multiplied by $1/{r}_{0}^{2}$ as our quadrupole phonon operators. We calculate explicit overlaps between the low-lying yrast states and the constructed quadrupole-phonon states based on the low-lying yrast states with lower spins, and the results indicate that, for all eight open-shell Cd nuclei, $|{2}_{1}^{+}\ensuremath{\rangle}$ and $|{4}_{1}^{+}\ensuremath{\rangle}$ can be well described to be the states constructed by coupling the proton or neutron phonon to $|{0}_{\mathrm{g}.\mathrm{s}.}^{+}\ensuremath{\rangle}$ and $|{2}_{1}^{+}\ensuremath{\rangle}$, respectively. Very interestingly, for $^{126,124,122}\mathrm{Cd}$ and $^{136,138}\mathrm{Cd}$, the ${2}_{1}^{+}$ state can be well described to be both the proton phonon state and the neutron phonon state, which indicates a nonorthogonal feature of these two phonon states. We further present an analytic relation for the overlap between these two phonon states, which implies that the proton and neutron phonon states constructed using the quadrupole operators and the ${0}_{\mathrm{g}.\mathrm{s}.}^{+}$ state in an open-shell nucleus are almost impossibly orthogonal.

Lifetime measurements of excited states in neutron-rich Ti53 : Benchmarking effective shell-model interactions

Level lifetimes of the yrast (5/2(-)) to 13/2(-) states in the neutron-rich nucleus Ti-53, produced in a multinucleon-transfer reaction, have been measured for the first time. The recoil distance Doppler-shift method was employed and lifetimes of the excited states were extracted by a lineshape analysis aided by GEANT4-based Monte-Carlo simulations. The experiment was performed at the Grand Accelerateur National d'Ions Lourds facility in Caen, France, by using the Advanced Gamma Tracking Array for the gamma-ray detection coupled to the large-acceptance variable mode spectrometer for an event-by-event particle identification and the Cologne plunger for deep-inelastic reactions. Reduced transition probabilities, deduced from the lifetimes, give new information on the nuclear structure of Ti-53, and are used to benchmark different shell-model calculations using established interactions in the f p shell.

Effective interactions in the sd shell

We perform a quantitative study of the microscopic effective shell-model interactions in the valence sd shell, obtained from modern nucleon-nucleon potentials, chiral N3LO, JISP16 and Daejeon16, using No-Core Shell-Model wave functions and the Okubo-Lee-Suzuki transformation. We investigate the monopole properties of those interactions in comparison with the phenomenological universal sd-shell interaction, USDB. Theoretical binding energies and low-energy spectra of O isotopes and of selected sd-shell nuclei, are presented. We conclude that there is a noticeable improvement in the quality of the effective interaction when it is derived from the Daejeon16 potential. We show that its proton-neutron centroids are consistent with those from USDB. We then propose monopole modifications of the Daejeon16 centroids in order to provide an adjusted interaction yielding significantly improved agreement with the experiment. A spin-tensor decomposition of two-body effective interactions is applied in order to extract more information on the structure of the centroids and to understand the reason for deficiencies arising from our current theoretical approximations. The issue of the possible role of the three-nucleon forces is addressed.

Is the Structure of ^{42}Si Understood?

A more detailed test of the implementation of nuclear forces that drive shell evolution in the pivotal nucleus ^{42}Si-going beyond earlier comparisons of excited-state energies-is important. The two leading shell-model effective interactions, SDPF-MU and SDPF-U-Si, both of which reproduce the low-lying ^{42}Si(2_{1}^{+}) energy, but whose predictions for other observables differ significantly, are interrogated by the population of states in neutron-rich ^{42}Si with a one-proton removal reaction from ^{43}P projectiles at 81 MeV/nucleon. The measured cross sections to the individual ^{42}Si final states are compared to calculations that combine eikonal reaction dynamics with these shell-model nuclear structure overlaps. The differences in the two shell-model descriptions are examined and linked to predicted low-lying excited 0^{+} states and shape coexistence. Based on the present data, which are in better agreement with the SDPF-MU calculations, the state observed at 2150(13)keV in ^{42}Si is proposed to be the (0_{2}^{+}) level.

Shell-model coupled-cluster method for open-shell nuclei

We present an approach to derive effective shell-model interactions from microscopic nuclear forces. The similarity-transformed coupled-cluster Hamiltonian decouples the single-reference state of a closed-shell nucleus and provides us with a core for the shell model. We use a second similarity transformation to decouple a shell-model space from the excluded space. We show that the three-body terms induced by both similarity transformations are crucial for an accurate computation of ground and excited states. As a proof of principle we use a nucleon-nucleon interaction from chiral effective field theory, employ a $^4$He core, and compute low-lying states of $^{6-8}$He and $^{6-8}$Li in $p$-shell model spaces. Our results agree with benchmarks from full configuration interaction.

Many-body correlations in shell model effective interactions derived by ab initio methods and the Vlow-k approach**Supported by National Natural Science Foundation of China (11505056, U1732138, 11605054, 11790325, 11305108, 11575290, 11675148, 11747312, 11775316) and the Outstanding Young Talent Research Fund of Zhengzhou University (1521317002)

We investigate many-body correlations caused by two- and three-body (2-, 3bd) forces. Shell-model effective interactions derived from ab initio methods (coupled-cluster method, no-core shell model) are adopted. Vlow-k potentials, based on many-body perturbation theory, are also tested, especially for their cut-off dependence. We compare the central, tensor and spin-orbit interactions from microscopic theory to the fitted interactions. After the inclusion of the three-body force, the matrix elements become fairly close to those fitted directly to experimental data. Calculations of neutron-rich oxygen isotopes are performed, to clarify the effects of 3bd forces, tensor, and spin-orbit interactions on the nuclear binding and excitation energies. We find that the 3bd force can influence the binding energies greatly, which also determines the drip line position, while its effect on excitation energies is not very pronounced. The spin-orbit force, which is part of the 2bd force, can affect the shell structure explicitly, at least for neutron-rich systems.

Experimental study of the effective nucleon-nucleon interaction using the F21(d,p)F22 reaction

The single-neutron configurations of several low-lying states in $^{22}\mathrm{F}$ have been determined from neutron-adding cross sections of a ($d,p$) reaction using a $^{21}\mathrm{F}$ radioactive beam in inverse kinematics. Final states in $^{22}\mathrm{F}$ consisting of a proton in the $\ensuremath{\pi}0{d}_{5/2}$ orbital coupled to a neutron in either the $\ensuremath{\nu}0{d}_{5/2}$, $\ensuremath{\nu}1{s}_{1/2}$, or $\ensuremath{\nu}0{d}_{3/2}$ orbitals were observed up to an excitation energy of $\ensuremath{\sim}5$ MeV. Spectroscopic factors and strengths were determined from the angular distribution of the cross sections using a distorted wave Born approximation method. The distribution of the $\ensuremath{\nu}0{d}_{5/2}$ and $\ensuremath{\nu}1{s}_{1/2}$ strength was well described by all USD effective shell model interactions, while only the more recent USDA/USDB interactions showed a marked improvement in describing the observed $\ensuremath{\nu}0{d}_{3/2}$ strength. Diagonal two-body matrix elements of the ${(0{d}_{5/2})}_{J=0--5}^{2}$ effective nucleon-nucleon interaction were extracted from the data and compared with previous determinations of the same matrix elements from particle-particle and hole-hole spectra, as well as the calculated results of the USDA interactions. No significant discrepancies were observed. Inspection of the monopole energies showed that an improved agreement between the different empirical matrix elements is found if a mass dependence is included.

Neutron knockout from 68,70Ni ground and isomeric states.

Neutron-rich isotopes are an important source of new information on nuclear physics. Specifically, the spin-isospin components in the nucleon-nucleon (NN) interaction, e.g., the proton-neutron tensor force, are expected to modify shell structure in exotic nuclei. These potential changes in the intrinsic shell structure are of fundamental interest. The study of the excitation energy of states corresponding to specific configurations in even-even isotopes, together with the single-particle character of the first excited states of odd-A, neutron-rich Ni isotopes, probes the evolution of the neutron orbitals around the Fermi surface as a function of the neutron number a step forward in the understanding of the region and the nature of the NN interaction at large N/Z ratios.In an experiment carried out at the National Superconducting Cyclotron Laboratory [1], new spectroscopic information was obtained for 68Ni and the distribution of single-particle strengths in 67,69Ni was characterized by means of single-neutron knockout from 68,70Ni secondary beams. The spectroscopic strengths, deduced from the measured partial cross sections to the individual states tagged by their de-exciting gamma rays, is used to identify and quantify configurations that involve neutron excitations across the N = 40 harmonic oscillator shell closure. The de-excitation γ rays were measured with the GRETINA tracking array [2].The results challenge the validity of the most current shell-model Hamiltonians and effective interactions, highlighting shortcomings that cannot yet be explained. These results suggest that our understanding of the low-energy states in such nuclei is not complete and requires further investigation.

An investigation of ab initio shell-model interactions derived by no-core shell model

The microscopic shell-model effective interactions are mainly based on the many-body perturbation theory (MBPT), the first work of which can be traced to Brown and Kuo’s first attempt in 1966, derived from the Hamada-Johnston nucleon-nucleon potential. However, the convergence of the MBPT is still unclear. On the other hand, ab initio theories, such as Green’s function Monte Carlo (GFMC), no-core shell model (NCSM), and coupled-cluster theory with single and double excitations (CCSD), have made many progress in recent years. However, due to the increasing demanding of computing resources, these ab initio applications are usually limited to nuclei with mass up to A = 16. Recently, people have realized the ab initio construction of valence-space effective interactions, which is obtained through a second-time renormalization, or to be more exactly, projecting the full-manybody Hamiltonian into core, one-body, and two-body cluster parts. In this paper, we present the investigation of such ab initio shell-model interactions, by the recent derived sd-shell effective interactions based on effective J-matrix Inverse Scattering Potential (JISP) and chiral effective-field theory (EFT) through NCSM. In this work, we have seen the similarity between the ab initio shellmodel interactions and the interactions obtained by MBPT or by empirical fitting. Without the inclusion of three-body (3-bd) force, the ab initio shell-model interactions still share similar defects with the microscopic interactions by MBPT, i.e., T = 1 channel is more attractive while T = 0 channel is more repulsive than empirical interactions. The progress to include more many-body correlations and 3-bd force is still badly needed, to see whether such efforts of ab initio shell-model interactions can reach similar precision as the interactions fitted to experimental data.

In-beamγ-ray spectroscopy ofMn63

Background: Neutron-rich, even-mass chromium and iron isotopes approaching neutron number $N=40$ have been important benchmarks in the development of shell-model effective interactions incorporating the effects of shell evolution in the exotic regime. Odd-mass manganese nuclei have received less attention, but provide important and complementary sensitivity to these interactions.Purpose: We report the observation of two new $\ensuremath{\gamma}$-ray transitions in $^{63}\mathrm{Mn}$, which establish the $(9/{2}^{\ensuremath{-}})$ and $(11/{2}^{\ensuremath{-}})$ levels on top of the previously known $(7/{2}^{\ensuremath{-}})$ first-excited state. The lifetime for the $(7/{2}^{\ensuremath{-}})$ and $(9/{2}^{\ensuremath{-}})$ excited states were determined for the first time, while an upper limit could be established for the $(11/{2}^{\ensuremath{-}})$ level.Method: Excited states in $^{63}\mathrm{Mn}$ have been populated in inelastic scattering from a $^{9}\mathrm{Be}$ target and in the fragmentation of $^{65}\mathrm{Fe}$. $\ensuremath{\gamma}\ensuremath{\gamma}$ coincidence relationships were used to establish the decay level scheme. A Doppler line-shape analysis for the Doppler-broadened $(7/{2}^{\ensuremath{-}})\ensuremath{\rightarrow}5/{2}^{\ensuremath{-}}$, $(9/{2}^{\ensuremath{-}})\ensuremath{\rightarrow}(7/{2}^{\ensuremath{-}}),$ and $(11/{2}^{\ensuremath{-}})\ensuremath{\rightarrow}(9/{2}^{\ensuremath{-}})$ transitions was used to determine (limits for) the corresponding excited-state lifetimes.Results: The low-lying level scheme and the excited-state lifetimes were compared with large-scale shell-model calculations using different model spaces and effective interactions in order to isolate important aspects of shell evolution in this region of structural change.Conclusions: While the theoretical $(7/{2}^{\ensuremath{-}})$ and $(9/{2}^{\ensuremath{-}})$ excitation energies show little dependence on the model space, the calculated lifetime of the $(7/{2}^{\ensuremath{-}})$ level and calculated energy of the $(11/{2}^{\ensuremath{-}})$ level reveal the importance of including the neutron ${g}_{9/2}$ and ${d}_{5/2}$ orbitals in the model space. The LNPS effective shell-model interaction provides the best overall agreement with the new data.

Testing the importance of collective correlations in neutrinolessββdecay

We investigate the extent to which theories of collective motion can capture the physics that determines the nuclear matrix elements governing neutrinoless double-beta decay. To that end we calculate the matrix elements for a series of isotopes in the full $pf$ shell, omitting no spin-orbit partners. With the inclusion of isoscalar pairing, a separable collective Hamiltonian that is derived from the shell model effective interaction reproduces the full shell-model matrix elements with good accuracy. A version of the generator coordinate method that includes the isoscalar pairing amplitude as a coordinate also reproduces the shell model results well, an encouraging result for theories of collective motion, which can include more single-particle orbitals than the shell model. We briefly examine heavier nuclei relevant for experimental double-beta decay searches, in which shell-model calculations with all spin-orbit partners are not feasible; our estimates suggest that isoscalar pairing also plays a significant role in these nuclei, though one we are less able to quantify precisely.

Pairing properties of realistic effective interactions

We investigate the pairing properties of an effective shell-model interaction defined within a model space outside 132 Sn and derived by means of perturbation theory from the CD-Bonn free nucleon-nucleon potential. It turns out that the neutron pairing component of the effective interaction is significantly weaker than the proton one, which accounts for the large pairing gap difference observed in the two-valence identical particle nuclei 134 Sn and 134 Te. The role of the contribution arising from one particle-one hole excitations in determining the pairing force is discussed and its microscopic structure is also analyzed in terms of the multipole decomposition.

Revisiting the monopole components of effective interactions for the shell model

In this paper, we revisit the monopole components of effective interactions for the shell model. Without going through specific nuclei or shell gaps, universal roles of central, tensor, and spin–orbit forces can be proved, reflecting the intrinsic features of shell model effective interactions. For monopole matrix elements, even and odd channels of central force often have a canceling effect. However, for the contributions to the shell evolution, its even and odd channels could have both positive or negative contributions, enhancing the role of central force on the shell structure. Tensor force is generally weaker than central force. However, for the effect on shell evolutions, tensor force can dominate or play a competitive role. A different systematics has been discovered between T = 1 and 0 channels. For example, tensor force, well established in the T = 0 channel, becomes uncertain in the T = 1 channel. We calculate the properties of neutron-rich oxygen and calcium isotopes in order to study T = 1 channel interactions further. It is learned that the main improvements of empirical interactions are traced to the central force. For non-central forces, antisymmetric spin–orbit (ALS) force, originated from many-body perturbations or three-body force, could also play an explicit role. T = 1 tensor forces are less constrained so their effect can differ in different empirical interactions. The influence of tensor force may sometimes be canceled by many-body effects. For T = 0 channels of effective interactions, which is the main source of neutron–proton correlations, central and tensor forces are the leading components. For T = 1 channels, which can act between like-particles, the request for many-body correlations could be more demanding, so that the monopole anomaly of the T = 1 channel might be more serious.

Large-scale shell-model study of the Sn isotopes

We summarize the results of an extensive study of the structure of the Sn isotopes using a large shell-model space and effective interactions evaluated from realistic two-nucleon potentials. For a fuller account, see ref. [1].

Large-scale shell-model study of the Sn isotopes

We summarize the results of an extensive study of the structure of the Sn isotopes using a large shell-model space and effective interactions evaluated from realistic two-nucleon potentials. For a fuller account, see ref. [1].

Non-degenerate shell-model effective interactions from the Okamoto–Suzuki and Krenciglowa–Kuo iteration methods

Abstract We present calculations of shell-model effective interactions for both degenerate and non-degenerate model spaces using the Krenciglowa–Kuo (KK) and the extended Krenciglowa–Kuo iteration method recently developed by Okamoto, Suzuki et al. (EKKO). The starting point is the low-momentum nucleon–nucleon interaction V low − k obtained from the N3LO chiral two-nucleon interaction. The model spaces spanned by the sd and sdpf shells are both considered. With a solvable model, we show that both the KK and EKKO methods are convenient for deriving the effective interactions for non-degenerate model spaces. The EKKO method is especially desirable in this situation since the vertex function Z ˆ -box employed therein is well behaved while the corresponding vertex function Q ˆ -box employed in the Lee–Suzuki (LS) and KK methods may have singularities. The converged shell-model effective interactions given by the EKKO and KK methods are equivalent, although the former method is considerably more efficient. The degenerate sd-shell effective interactions given by the LS method are practically identical to those from the EKKO and KK methods. Results of the sd one-shell and sdpf two-shell calculations for 18O, 18F, 19O and 19F using the EKKO effective interactions are compared, and the importance of an inter-space consistency between the sd and sdpf calculations is discussed.

Shell and shape evolution atN=28: TheMg40ground state

A measurement of the direct two-proton removal from Si42 has provided the first structural information on the N=28 isotone Mg40. The value for the inclusive cross section for two-proton removal from Si42 of 40+27−17 μb is significantly lower than that predicted by structure calculations using the recent SDPF-MU shell-model effective interaction combined with eikonal reaction theory. This observed discrepancy is consistent with the interpretation that only one of the predicted low-lying 0+ states in Mg40 is bound. A two-state mixing analysis describing two-proton knockout cross sections along N=28 provides support for the interpretation of a prolate-deformed Mg40 ground state.