We study the two-neutrino double electron capture on $^{124}$Xe based on an effective theory (ET) and large-scale shell model calculations, two modern nuclear structure approaches that have been tested against Gamow-Teller and double-beta decay data. In the ET, the low-energy constants are fit to electron capture and $β^{-}$ transitions around xenon. For the nuclear shell model, we use an interaction in a large configuration space that reproduces the spectroscopy of nuclei in this mass region. For the dominant transition to the $^{124}$Te ground state, we find half-lives $T^{2ν{\rm ECEC}}_{1/2}=(1.3-18)\times 10^{22}$ y for the ET and $T^{2ν{\rm ECEC}}_{1/2} = (0.43-2.9)\times 10^{22}$ y for the shell model. The ET uncertainty leads to a half-life almost entirely consistent with present experimental limits and largely within the reach of ongoing experiments. The shell model half-life range overlaps with the ET, but extends less beyond current limits. Our findings thus suggest that the two-neutrino double electron capture on $^{124}$Xe has a good chance to be discovered by ongoing or future experiments. In addition, we present results for the two-neutrino double electron capture to excited states of $^{124}$Te.
Large-scale shell model calculations including two major shells are carried out, and the ingredients of nuclear matrix element for two-neutrino double beta decay are investigated. Based on the comparison between the shell model calculations accounting only for one major shell ($pf$-shell) and those for two major shells ($sdpf$-shell), the effect due to the excitation across the two major shells is quantitatively evaluated.
Constraining excitation energy at which nuclear shell effect washes out has important implications on the production of super heavy elements and many other fields of nuclear physics research. We report the fission fragment mass distribution in alpha induced reaction on an actinide target for wide excitation range in close energy interval and show direct evidence that nuclear shell effect washes out at excitation energy ~40 MeV. Calculation shows that second peak of the fission barrier also vanishes around similar excitation energy.
We present developments and applications for the diagonalization of shell-model hamiltonians in a discrete non-orthogonal basis (DNO-SM). The method, and its actual numerical implementation CARINA, based on mean-field and beyond-mean field techniques has already been applied in previous studies and is focused on basis states selection optimization. The method is benchmarked against a full set of $sd$ shell exact diagonalizations, and is applied for the first time to the heavy deformed $^{254}$No nucleus.
Non-local orbital-free density functional theory incorporating nuclear shell effects
Fuzhou University（福州大学）；Università degli Studi di Milano（米兰大学）；INFN, Sezione di Milano（意大利国家核物理研究所米兰分部）；Kyoto University（京都大学）；RIKEN Nishina Center for Accelerator-based Science, RIKEN（理化学研究所西村加速器科学中心）；Peking University（北京大学）
Inelastic neutron scattering was used to study the low-lying nuclear structure of $^{132}$Xe. A comprehensive level scheme is presented, as well as new level lifetimes, multipole mixing ratios, branching ratios, and transition probabilities. Comparisons of these data as well as previously measured $E2$ strengths and $g$ factors are made with new shell-model calculations for $^{132,134,136}$Xe to explore the emergence of collectivity in the Xe isotopes with $N$ < 82 near the closed shell.
We evaluate the allowed $β^-$-decay properties of nuclei with $Z = 8 - 15$ systematically under the framework of the nuclear shell model with the use of the valence space Hamiltonians derived from modern $ab~intio$ methods, such as in-medium similarity renormalization group and coupled-cluster theory. For comparison we also show results obtained with fitted interaction derived from the chiral effective field theory and phenomenological USDB interaction. We have performed calculations for O $\rightarrow$ F, F $\rightarrow$ Ne, Ne $\rightarrow$ Na, Na $\rightarrow$ Mg, Mg $\rightarrow$ Al, Al $\…
Some emerging concepts of nuclear structure are overviewed. (1) Background: the many-body quantum structure of atomic nucleus, a complex system comprising protons and neutrons (called nucleons collectively), has been studied largely based on the idea of the quantum liquid (a la Landau), where nucleons are quasiparticles moving in a (mean) potential well, with weak "residual" interactions between nucleons. The potential is rigid in general, although it can be anisotropic. While this view was a good starting point, it is time to look into kaleidoscopic aspects of the nuclear structure brought in…
One of the common methods used to investigate the nuclear structures of atomic nuclei is the nuclear shell model. Similar to the placement of atomic electrons into orbits, in the nuclear shell model, protons and neutrons are thought to fill the orbits within the nucleus, following the principle of Pauli's exclusion. These orbits are grouped together to form shells, which are said to be closed if all possible places in a shell are full. Atomic nuclei with closed shells are very stable and valence nucleons that are more than these nuclei are included in the nuclear shell model calculations. In t…
We have performed a systematic study of the log$ft$ values, shape factors and electron spectra for the second-forbidden nonunique $β^-$ decays of $^{24}$Na$(4^+) \rightarrow ^{24}$Mg$(2^+)$ and $^{36}$Cl$(2^+) \rightarrow ^{36}$Ar$(0^+)$ transitions under the framework of the nuclear shell model. We have performed the shell model calculations in the $sd$ model space, using more recent microscopic effective interactions such as Daejeon16, chiral N3LO, and JISP16. These interactions are derived from the no-core shell model wave functions using Okubo-Lee-Suzuki transformation.For comparison, we h…
Nuclei exhibit both single-particle and collective degrees of freedom, with the latter often subdivided into vibrational and rotational motions. Experimentally identifying the relative roles of these collective modes is extremely challenging, particularly in the face of possible shape coexistence. Model-independent, invariant quantities describing the deformation of a nucleus in the intrinsic frame have long been known but their determination potentially requires a large quantity of experimental data to achieve convergence. Through comparison with the nuclear shell model, the question of conve…
In the present work, we have done a systematic shell model study of $N=82$ and $N=126$ isotones. For the $N=82$ isotones, we have performed calculations using SN100PN interaction, while for $N=126$ isotones, we have used KHPE interaction. Similarities between these two isotonic chains have been reported, using the strong resemblance between the high-$j$ orbitals. Apart from the nuclear spectroscopic properties, we have also explained different isomeric states in these two regions. In the $N$ =82 region, we have mainly discussed the properties of the $6^+$ and $17/2^+$ isomers, while in the $N=…
The concept of single-nucleon shells constitutes a basic pillar of our understanding of nuclear structure. Effective single-particle energies (ESPEs) introduced by French and Baranger represent the most appropriate tool to relate many-body observables to a single-nucleon shell structure. As briefly discussed in [T. Duguet, G. Hagen, Phys. Rev. C {\bf 85}, 034330 (2012)], the dependence of ESPEs on one-nucleon transfer probability matrices makes them purely theoretical quantities that "run" with the non-observable resolution scale $λ$ employed in the calculation. Given that ESPEs provide a way …
Bayesian neural network (BNN) approach is employed to improve the nuclear mass predictions of various models. It is found that the noise error in the likelihood function plays an important role in the predictive performance of the BNN approach. By including a distribution for the noise error, an appropriate value can be found automatically in the sampling process, which optimizes the nuclear mass predictions. Furthermore, two quantities related to nuclear pairing and shell effects are added to the input layer in addition to the proton and mass numbers. As a result, the theoretical accuracies a…
Neutrinoless double beta decay searches are currently among the major foci of experimental physics. The observation of such a decay will have important implications in our understanding of the intrinsic nature of neutrinos and shed light on the limitations of the Standard Model. The rate of this process depends on both the unknown neutrino effective mass and the nuclear matrix element associated with the given neutrinoless double-beta decay transition. The latter can only be provided by theoretical calculations, hence the need of accurate theoretical predictions of the nuclear matrix element f…
We introduce a novel method to obtain level densities in large-scale shell-model calculations. Our method is a stochastic estimation of eigenvalue count based on a shifted Krylov-subspace method, which enables us to obtain level densities of huge Hamiltonian matrices. This framework leads to a successful description of both low-lying spectroscopy and the experimentally observed equilibration of $J^π=2^+$ and $2^-$ states in $^{58}$Ni in a unified manner.
Semiclassical periodic-orbit theory (POT) is applied to the physics of nuclear structures, with the use of a realistic nuclear mean-field model given by the radial power-law potential. Evolution of deformed shell structures, which are responsible for various nuclear deformations, are clearly understood from the contribution of short classical periodic orbits (POs). Bifurcations of short POs, which imply underlying local dynamical symmetry, play significant role there. The effect of the spin degree of freedom is also investigated in relevance to the pseudospin symmetry in spherical nuclei and t…
There have been many empirical evindences which show that the single-particle picture holds to a good approximation in atomic nuclei. In this picture, protons and neutrons move independently inside a mean-field potential generated by an interaction among the nucleons. This leads to the concept of nuclear shells, similar to the electronic shells in atoms. In particular, the magic numbers due to closures of the nucleonic shells, corresponding to noble gases in elements, have been known to play an important role in nuclear physics. Here we propose a periodic table for atomic nuclei, in which the …
We introduce a mean field model based on realistic 2-body baryon interactions and calculate spectra of a set of p-shell and sd-shell Λ hypernuclei - 13ΛC, 17ΛO, 21ΛNe, 29ΛSi and 41ΛCa. The hypernuclear spectra are compared with the results of a relativistic mean field (RMF) model and available experimental data. The sensitivity of Λ single-particle energies to the nuclear core structure is explored. Special attention is paid to the effect of spin-orbit ΛN interaction on the energy splitting of the Λ single particle levels 0p3/2 and 0p1/2. In particular, we analyze the contribution of the symme…
Accurate knowledge of the nuclear level density is important both from a theoretical viewpoint as a powerful instrument for studying nuclear structure and for numerous applications. For example, astrophysical reactions responsible for the nucleosynthesis in the universe can be understood only if we know the nuclear level density. We use the configuration-interaction nuclear shell model to predict nuclear level density for all nuclei in the $sd$-shell, both total and for individual spins (only with positive parity). To avoid the diagonalization in large model spaces we use the moments method ba…
The shell model Monte Carlo (SMMC) approach allows for the microscopic calculation of statistical and collective properties of heavy nuclei using the framework of the configuration-interaction shell model in very large model spaces. We present recent applications of the SMMC method to the calculation of state densities and their collective enhancement factors in rare-earth nuclei.
We devise a framework based on the generalized contact formalism that combines the nuclear shell model and quantum Monte Carlo methods and compute the neutrinoless double-beta decay of experimentally relevant nuclei, including $^{76}$Ge, $^{130}$Te, and $^{136}$Xe. In light nuclei, we validate our nuclear matrix element calculations by comparing against accurate variational Monte Carlo results. Due to additional correlations captured by quantum Monte Carlo and introduced within the generalized contact formalism, in heavier systems, we obtain long-range nuclear matrix elements that are about 30…
Applications of configuration mixing methods for nuclei near the proton and neutron drip lines are discussed. A short review of magic numbers is presented. Prospects for advances in the regions of four new "outposts" are highlighted: $^{28}$O, $^{42}$Si, $^{60}$Ca and $^{78}$Ni. Topics include: shell gaps, single-particle properties, islands-of-inversion, collectivity, neutron decay, neutron halos, two-proton decay, effective charge, and quenching in knockout reactions.
