Semi-magic Nuclei Research Articles

Comparative study on charge radii and their kinks at magic numbers

Isotope dependences of charge radii, i.e., isotope shifts, calculated by the Skyrme Hartree-Fock, the relativistic mean-field, and the relativistic Hartree-Fock calculations are compared against the experimental data of magic and semimagic nuclei. It is found that the tensor interaction plays a role in reproducing the ``kink'' behavior, irregularity of isotope shifts at the neutron magic number, in the relativistic Hartree-Fock approach. With several Skyrme models, it is found that the kink behavior can be reproduced with the spin-orbit interaction having nonzero isovector channel. The single-particle orbitals near the Fermi energy are crucial to determine the kink size. The effects of the symmetry energy and the pairing interaction are also discussed in relation to the kink behavior.

Effects of two-particle–two-hole configurations and tensor force on β decay of magic nuclei

The $\ensuremath{\beta}$-decay half-lives of four semimagic and magic nuclei, $^{34}\mathrm{Si}, ^{68,78}\mathrm{Ni}$, and $^{132}\mathrm{Sn}$, have been investigated using the self-consistent Hartree-Fock (HF) plus subtracted second random-phase approximation (SSRPA) model with Skyrme energy density functions (EDFs). The inclusion of the two-particle--two-hole (2p-2h) configurations in SSRPA model shifts low-lying Gamow-Teller (GT) states downward. It leads to an increase of the $\ensuremath{\beta}$-decay phase space, which ensures the half-lives of the four nuclei are finite and reduces the $\ensuremath{\beta}$-decay half-lives dramatically. The effect of tensor interaction on the $\ensuremath{\beta}$-decay half-life in the SSRPA model is to change the half-lives greatly by about one to two orders of magnitude with respect to the ones obtained without tensor force.

Bayes goes fast: Uncertainty quantification for a covariant energy density functional emulated by the reduced basis method

A covariant energy density functional is calibrated using a principled Bayesian statistical framework informed by experimental binding energies and charge radii of several magic and semi-magic nuclei. The Bayesian sampling required for the calibration is enabled by the emulation of the high-fidelity model through the implementation of a reduced basis method (RBM)—a set of dimensionality reduction techniques that can speed up demanding calculations involving partial differential equations by several orders of magnitude. The RBM emulator we build—using only 100 evaluations of the high-fidelity model—is able to accurately reproduce the model calculations in tens of milliseconds on a personal computer, an increase in speed of nearly a factor of 3,300 when compared to the original solver. Besides the analysis of the posterior distribution of parameters, we present model calculations for masses and radii with properly estimated uncertainties. We also analyze the model correlation between the slope of the symmetry energy L and the neutron skin of 48Ca and 208Pb. The straightforward implementation and outstanding performance of the RBM makes it an ideal tool for assisting the nuclear theory community in providing reliable estimates with properly quantified uncertainties of physical observables. Such uncertainty quantification tools will become essential given the expected abundance of data from the recently inaugurated and future experimental and observational facilities.

Manipulation of nuclear isomers with lasers: mechanisms and prospects

Over one hundred years have passed since the nuclear isomer was first introduced, in analogy with chemical isomers to describe long-lived excited nuclear states. In 1921, Otto Hahn discovered the first nuclear isomer $^{234m}$Pa. After that, step by step, it was realized that different types of nuclear isomers exist, including spin isomer, K isomer, seniority isomers, and ``shape and fission'' isomer. The spin isomer occurs when the spin change $\Delta I$ of a transition is very large. The larger $\Delta I$, the lower the electromagnetic transition rates, the longer the half-lives. The K-isomer exists due to the significant change in K, where K is the projection of the total angular momentum on the symmetry axis. The seniority isomers arise due to a very small transition probability in seniority conserving transitions around semi-magic nuclei, where the seniority, which corresponds to the number of unpaired nucleons, is a reasonably pure quantum number. For a so-called shape isomer, the inhibition of the decay transition comes from the associated shape changes. It is caused by that a nucleus is trapped in a deformed shape which is its secondary minimum and is hard to decay back to its ground state.

Commissioning the FAst TIMing array (FATIMA) at FAIR Phase-0: Half-lives of excited states in the N=50 isotones 96Pd and 94Ru

This paper reports results of the first experiment of the DESPEC Phase-0 campaign at GSI, which focused on the study of neutron-deficient nuclei approaching 100Sn. These data provide the first extended commissioning experiment for the DESPEC collaboration within NuSTAR. We present results on electromagnetic transition rates associated with the decays from excited states populated following the formation of Iπ = 8+ proton ‘seniority-isomer’ states in the N = 50 isotones 94Ru and 96Pd. Direct half-life measurements via γ−γ coincidences using the FATIMA detector array consisting of 36 LaBr3(Ce) scintillators have determined the reduced matrix elements associated with decays between low-lying states in these semi-magic nuclei. The extracted half-lives for yrast Iπ = 6+ and 4+ states in 96Pd and the 6+ state in 94Ru are consistent with the published, highest-precision values for these nuclei.

Enhanced quadrupole collectivity in doubly-magic 56Ni: Lifetime measurements of the [formula omitted] and [formula omitted] states

Lifetime measurements of excited states in doubly-magic 56Ni have been performed exploiting the Doppler-shift attenuation method in order to determine reduced transition probabilities. For the 41+ and 61+ states, the deduced B(E2) values are compared with results from shell-model calculations employing the GXPF1A and the modern PFSDG-U interactions. In addition, valence ab-initio calculations were performed using a novel realistic Hamiltonian derived from chiral perturbation theory including three-body potential contributions and are confronted with the experimental findings. The new results show maximum E2 strength in comparison with known values along the N=28 chain of isotones. The results corroborate the high collectivity for the double shell closure at N=Z=28 which was anticipated from the large B(E2;21+→0g.s.+) value despite the considerable increase of its excitation energy as compared to neighboring semi-magic nuclei. Based on similarities in the shell structures of the self-conjugate doubly-magic nuclei 56Ni and 100Sn, the new values could be an indication for an expected comparable collective behavior of the 61+ state in 100Sn.

Nuclear charge densities in spherical and deformed nuclei: Toward precise calculations of charge radii

Background: Precise measurements of atomic transitions affected by electron-nucleus hyperfine interactions offer sensitivity to explore basic properties of the atomic nucleus and study fundamental symmetries, including the search for new physics beyond the standard model of particle physics. In particular, such measurements, augmented by atomic and nuclear calculations, will enable extraction of the higher-order radial moments of the charge-density distribution in spherical and deformed nuclei. The new data impose higher precision requirements on a theoretical description.Purpose: The nuclear charge density is composed of the proton point distribution folded with the nucleonic charge distributions. The latter induce subtle relativistic corrections due to the coupling of nucleon magnetic moments with the nuclear spin-orbit density. Additional corrections come from the effect of center-of-mass projection. We assess the precision of nuclear charge density calculations by studying the behavior of relativistic and center-of-mass motion corrections to the second and fourth charge radial moments. Special attention has been paid to the magnetic spin-orbit density associated with the local variations of the spin-orbit current.Methods: The calculations for semimagic and open-shell nuclei are performed in the framework of self-consistent mean-field theory using quantified energy density functionals and density-dependent pairing forces. We used the general expression for the spin-orbit form factor that is valid for spherical and deformed nuclei.Results: We studied the impact of various correction terms on the charge radii, fourth radial moments, diffraction radii, and surface thickness of spherical and deformed nuclei. The spin-orbit corrections to charge radial moments and surface thickness show strong shell fluctuations which can make an appreciable effect when aiming at high-precision predictions of isotopic shifts. The inclusion of relativistic and center-of-mass corrections impacts the quality of energy density functionals optimized to charge radii data.Conclusions: To establish reliable constraints on the existence of new forces from isotope shift measurements, precise calculations of nuclear charge densities of deformed nuclei are needed. The proper inclusion of the spin-orbit charge density and other correction terms is essential when aiming at extraction of subtle effects which become particularly visible in isotopic trends. It is also important when developing high-quality nuclear energy density functionals optimized using heterogeneous datasets involving absolute charge radii, differential charge radii, and charge form factor properties deduced from electron-scattering data.

Manifestation of the Berry phase in the atomic nucleus 213Pb

The neutron-rich 213Pb isotope was produced in the fragmentation of a primary 1 GeV A238U beam, separated in FRS in mass and atomic number, and then implanted for isomer decay γ-ray spectroscopy with the RISING setup at GSI. A newly observed isomer and its measured decay properties indicate that states in 213Pb are characterized by the seniority quantum number that counts the nucleons not in pairs coupled to angular momentum J=0. The conservation of seniority is a consequence of a geometric phase associated with particle-hole conjugation, which becomes observable in semi-magic nuclei where nucleons half-fill the valence shell. The γ-ray spectroscopic observables in 213Pb are thus found to be driven by two mechanisms, particle-hole conjugation and seniority conservation, which are intertwined through a Berry phase.

Fully self-consistent calculation of β-decay half-lives within Skyrme energy density functional * *Supported by the National Natural Science Foundation of China (11975096, 11805280, 11775014, 11635003, 11161130520), National Basic Research Program of China (2010CB832903), European Commission's 7th Framework Programme (Fp7-PEOPLE-2010-IRSES) under Grant Agreement Project (269131), and Continuous Basic Scientific Research Project (WDJC-2019-13)

-decay half-lives of some magic and semi-magic nuclei have been studied in a fully self-consistent Skyrme Hartree-Fock (HF) plus charge-exchange random phase approximation (RPA). The self-consistency is addressed, in that the same Skyrme energy density functional is adopted in the calculation of ground states and Gamow-Teller excited states. First, the impact of terms on the -decay half-lives is investigated by using the SGII interaction, revealing a large influence. Subsequently, numerical calculations are performed for the selected nuclei with Skyrme energy density functionals SGII, LNS, SKX, and SAMi. Finally, comparisons to available experimental data and predictions of different theoretical models are discussed.

Polarizability effects in atomic nuclei

This work sheds light upon how the atomic nucleus polarizes throughout the nuclear chart. Deviations from the well-known behavior of the nuclear dipole polarizability — which smoothly increases with increasing atomic mass number — are investigated. Relative enhancements are found for light nuclei as the nuclear symmetry energy decreases and, within a nucleus, as its excitation energy increases. These two properties are related by a diminishing binding energy of the nuclear system. Contrarily, hindrances of nuclear polarizability are observed in the photo-neutron cross-section data and photon-strength functions of semi-magic nuclei with [Formula: see text], 50 and 82, which support the presence of shell effects at low-lying excitations and — assuming validity of the Brink-Axel hypothesis — at high-excitation energies up to the quasi-continuum region. These features assign the nuclear dipole polarizability as a sensitive measure of the long-range correlations of the nuclear force, and provide a new spectroscopic probe to investigate collective phenomena, shell closures, and the elusive nuclear symmetry energy. Particular cases of quadrupole collectivity are also discussed in terms of the available, and yet so scarce, information on nuclear polarizability (e.g. Sn and Ni isotopes).

Anharmonic Effects in the Theory of Finite Fermi Systems

Some results obtained by E.E. Saperstein and his coauthors in the theory of the ground state and low-lying excited states of magic and semimagic nuclei are discussed briefly. Corrections to the creation amplitude $$g$$ for one low-lying phonon are considered for the first time. These corrections, treated on the basis of the existence of a small parameter, include the tadpole-induced coupling of the amplitudes for the creation of one and two phonons.

Detailed spectroscopy of Ca46 : A study of the β− decay of K46

We report on high-statistics data from the $\beta^-$ decay of the $^{46}$K $J^{\pi}$ = 2$^-$ ground state taken with the GRIFFIN spectrometer located at the TRIUMF-ISAC facility. In total, 199 $\gamma$ rays and 42 excited states were placed in the level scheme, and from the observed $\beta$ feeding and angular correlations of pairs of cascading $\gamma$ rays, it was possible to assign spins and parities to excited states and determine mixing ratios for selected $\gamma$ rays. The level structure of $^{46}$Ca is compared to theoretical predictions from a microscopic valence-space Hamiltonian derived from two- (NN) and three-nucleon (3N) forces. These calculations are in reasonable agreement with the experimental data and indicate that the protons in this region are not as inert as would be expected for semi-magic nuclei.

Nucleon-pair picture of low-lying states in semi-magic and open-shell nuclei

Nucleon-pair picture of low-lying states in semi-magic and open-shell nuclei

Ignatyuk damping factor: A semiclassical formula

Data on nuclear-level densities extracted from transmission data or gamma energy spectrum store the basic statistical information about nuclei at various temperatures. Generally, this extracted data goes through model fitting using computer codes like CASCADE. However, recently established semiclassical methods involving no adjustable parameters to determine the level density parameter for magic and semi-magic nuclei give a good agreement with the experimental values. One of the popular ways to paramaterize the level density parameter which includes the shell effects and its damping was given by Ignatyuk. This damping factor is usually fitted from the experimental data on nuclear-level density and it comes around 0.05 [Formula: see text]. In this work, we calculate the Ignatyuk damping factor for various nuclei using semiclassical methods.

Results of Microscopic Self-Consistent Theory of Quasiparticle—Phonon Interaction in Nuclei

A self-consistent approach in the problem of taking into account quasiparticle-phonon interaction provides a high predictive power and is free from adjustable parameters (this is of crucial importance for astrophysics). Moreover, it is consistent and makes it possible to take into account new effects. A brief survey of the results obtained within this approach on the basis of Skyrme or Fayans functionals by employing the smallness parameter g2, where g is the phonon-production amplitudes, with allowance for tadpole effects is presented. The contribution of quasiparticle-phonon interaction to ground-state electromagnetic moments of odd nuclei; second-order anharmonic effects in g2, including quadrupole moments of the first 2+ and 3− states and EL transitions between one-phonon states; third-order anharmonic effects; pygmy dipole and giant resonances; and the contribution of quasiparticle-phonon interaction to radiative properties of nuclear reactions are considered. For magic and semimagic nuclei, additional effects and structures arising in nuclear features because of quasiparticle-phonon interaction are discussed along with new—that is, three- and four-quasiparticle ground-state—correlations. Earlier unknown values of the above features, including the features of the pygmy dipole resonance in neutron-rich nickel isotopes, are predicted. It is shown that, in all of the aforementioned problems, the contributions of quasiparticle-phonon interaction is sizable, is of fundamental importance, and is necessary for explaining experimental data.

Generalized seniority Schmidt model and the g-factors in semi-magic nuclei

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 the seniority states arising from a given multi-j configuration for identical nucleons is equal to the g-factor of the seniority v=1 state from that configuration. Also, the g-factors are found to be a sensitive probe for fixing the multi-j configuration, which are fully consistent with the configurations assigned to explain the B(EL) properties in our previous works. We are also able to make definite predictions for many cases.

Continuing influence of shell effects at high-excitation energies

Empirical drops in ground-state nuclear polarizabilities indicate deviations from the effect of giant dipole resonances and may reveal the presence of shell effects in semi-magic nuclei with neutron magic numbers N=50, 82 and 126. Similar drops of polarizability in the quasi-continuum of nuclei with, or close to, magic numbers N=28, 50 and 82, could reflect the continuing influence of shell closures up to the nucleon separation energy. These findings open a new avenue to investigating magic numbers at high-excitation energies and strongly support recent large-scale shell-model calculations in the quasi-continuum region, which describe the origin of the low-energy enhancement of the photon strength function as induced paramagnetism. The nuclear-structure dependence of the photon-strength function asserts the generalized Brink-Axel hypothesis as more universal than originally expected.

How do we infer shell effects at high-excitation energies? A new spectroscopic probe to search for magic numbers

The nuclear dipole polarizability is mainly governed by the dynamics of the giant dipole resonance and, assuming validity of the brink-Axel hypothesis, has been investigated along with the effects of the low-energy enhancement of the photon strength function for nuclides in medium- and heavy-mass nuclei. Cubic-polynomial fitsto both data sets extrapolated down to a gamma-ray energy of 0.1 MeV show a significantreduction of the nuclear dipole polarizability for semi-magic nuclei, with magic numbers N =28, 50 and 82, which supports shell effects at high-excitation energies in the the quasi-continuum region. This work assigns σ-2 values as sensitive measures of long-range correlations of the nuclear force and provides a new spectroscopic probe to search for “old” and “new” magic numbers at high-excitation energies.

Quasi shell gap at 23F

The experimental states of nuclei, close to semi-magic nuclei, having one extra proton on top of closed proton core, in general, connote the arrangement of proton orbitals within a shell. Herein, we have studied the arrangement of proton orbitals (π0d5/2, π1s1/2 and π0d3/2) in sd-shell for Fluorine isotopes within the nuclear shell model framework. The contribution of different components of effective nucleon-nucleon interaction in the evolution of the energies of proton orbitals, and the orbital energy gaps π0d5/2−π1s1/2 and π0d5/2−π0d3/2 at 23,25F has been examined. Results show the evolution of quasi-shell gap at 23F due to key contribution of central force, in particular, of its even-channel, and destructive interference in the contribution of spin–orbit and tensor force. The excitation energies of 121+ and 321+ states of 23F, and 121+ state of 25F are in good agreement with their respective orbital energy gaps. The origin of 321+ state of 25F and its excitation energy has been delineated as an effect of the breakdown of semi-magic core 24O.

Inclusion of particle-vibration coupling in the Fayans functional: Odd-even mass differences of semimagic nuclei

A method to evaluate the particle-phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei, based on the direct solution of the Dyson equation with PC corrected mass operator, is presented. It is used for finding the odd-even mass difference between even Pb and Sn isotopes and their odd-proton neighbors. The Fayans energy density functional (EDF) DF3-a is used which gives rather highly accurate predictions for these mass differences already at the mean-field level. In the case of the lead chain, account for the PC corrections induced by the low-laying phonons $2^+_1$ and $3^-_1$ makes agreement of the theory with the experimental data significantly better. For the tin chain, the situation is not so definite. In this case, the PC corrections make agreement better in the case of the addition mode but they spoil the agreement for the removal mode. We discuss the reason of such a discrepancy.