M1 Excitations Research Articles

On the low-energy electromagnetic dipole modes in 151,153,155Sm Nuclei

The recently observed low-energy magnetic dipole (M1) and electric dipole (E1) excitations in deformed 151,153,155Sm are theoretically analysed. Rotational Invariant (RI-) and Translational-Galilean Invariant (TGI-) Quasiparticle Nuclear Model (QPNM) are used in the calculation of M1 and E1 properties, respectively. Both theories consider monopole pairing between nucleons, and the deformed Woods-Saxon potential is used as the mean-field potential. Pyatov's symmetry restoration procedure is applied in these models to eliminate the spurious modes from the intrinsic nuclear excitations. Model calculations show that although E1 transitions dominate the low-energy dipole spectra of 151,153,155Sm, many low-lying M1 transitions exist in these nuclei. It is shown that the most significant contribution to E1 and M1 excitation comes from ΔK=±1 transitions. The theory satisfactorily reproduces the gross features of low-lying dipole modes determined from the Oslo Method analysis of the experimental spectra.

Charge Radii of ^{55,56}Ni Reveal a Surprisingly Similar Behavior at N=28 in Ca and Ni Isotopes.

Nuclear charge radii of ^{55,56}Ni were measured by collinear laser spectroscopy. The obtained information completes the behavior of the charge radii at the shell closure of the doubly magic nucleus ^{56}Ni. The trend of charge radii across the shell closures in calcium and nickel is surprisingly similar despite the fact that the ^{56}Ni core is supposed to be much softer than the ^{48}Ca core. The very low magnetic moment μ(^{55}Ni)=-1.108(20) μ_{N} indicates the impact of M1 excitations between spin-orbit partners across the N,Z=28 shell gaps. Our charge-radii results are compared to abinitio and nuclear density functional theory calculations, showing good agreement within theoretical uncertainties.

Scissors mode and effects of the low-lying E1 excitations on the dipole distributions in 175Lu

The low-lying magnetic (M1) and electric (E1) dipole modes in well-deformed odd-proton 175Lu have been investigated in the framework of the Rotational, Translational, and Galilean Invariant-Quasiparticle Phonon Nuclear Model (RTGI-QPNM) for the first time. In this model, the single-particle basis obtained from an axially symmetric Woods-Saxon potential, E1 and M1 excitations are assumed to be generated by isovector dipole-dipole and spin-spin interactions between nucleons, respectively. It also includes the restoration forces for breaking the Rotational, Translational and Galilean symmetries of the nuclear Hamiltonian. The transition probabilities, radiation widths and the structure for both M1 and E1 transitions in 175Lu have been calculated. The theory has satisfactorily reproduced the observed fragmentation in dipole spectra. However, the individual dipole strength of the states is higher than the experimental ones, which may be attributed to the lack of multiphonon configurations in the model used. Besides, the predicted total dipole radiation width and its reduced value are almost twice the experimental data. This difference is a well-known phenomenon for odd-mass deformed nuclei, called ‘missing strength’, arising in the Nuclear Resonance Flouracanse experiment due to the high-level densities.

Discerning nuclear pairing properties from magnetic dipole excitation

Pairing correlation of Cooper pair is a fundamental property of multi-fermion interacting systems. For nucleons, two modes of the Cooper-pair coupling may exist, namely of $$S_{12}=0$$ with $$L_{12}=0$$ (spin-singlet s-wave) and $$S_{12}=1$$ with $$L_{12}=1$$ (spin-triplet p-wave). In nuclear physics, it has been an open question whether the spin-singlet or spin-triplet coupling is dominant, as well as how to measure their role. We investigate a relation between the magnetic-dipole (M1) excitation of nuclei and the pairing modes within the framework of relativistic nuclear energy-density functional (RNEDF). The pairing correlations are taken into account by the relativistic Hartree-Bogoliubov (RHB) model in the ground state, and the relativistic quasi-particle random-phase approximation (RQRPA) is employed to describe M1 transitions. We have shown that M1 excitation properties display a sensitivity on the pairing model involved in the calculations. The systematic evaluation of M1 transitions together with the accurate experimental data enables us to discern the pairing properties in finite nuclei.

Relativistic nuclear energy density functional approach to magnetic-dipole excitation

Magnetic-dipole (M1) excitations of 18O and 42Ca nuclei are investigated within a relativistic nuclear energy density functional framework. In our last work [1], these nuclei are found to have unique M1 excitation and its sum rule, because of their characteristic structure: the system consists of the shell-closure core plus two neutrons. For a more systematic investigation of the M1 mode, we have implemented a framework based on the relativistic nuclear energy density functional (RNEDF). For benchmark, we have performed the RNEDF calculations combined with the random-phase approximation (RPA). We evaluate the M1 excitation of 18O and 42Ca, whose sum-rule value (SRV) of the M1 transitions can be useful to test the computational implementation [1]. We also apply this RNEDF method to 208Pb, whose M1 property has been precisely measured [2, 3, 4, 5]. Up to the level of the M1 sum rule, our result is in agreement with the experiments, except the discrepancy related with the quenching factors for g coefficients.

Magnetic dipole excitations based on the relativistic nuclear energy density functional

Magnetic dipole (M1) excitations build not only a fundamental mode of nucleonic transitions, but they are also relevant for nuclear astrophysics applications. We have established a theory framework for description of M1 transitions based on the relativistic nuclear energy density functional. For this purpose the relativistic quasiparticle random phase approximation (RQRPA) is established using density dependent point coupling interaction DD-PC1, supplemented with the isovector-pseudovector interaction channel in order to study unnatural parity transitions. The introduced framework has been validated using the M1 sum rule for core-plus-two-nucleon systems, and employed in studies of the spin, orbital, isoscalar and isovector M1 transition strengths, that relate to the electromagnetic probe, in magic nuclei $^{48}$Ca and $^{208}$Pb, and open shell nuclei $^{42}$Ca and $^{50}$Ti. In these systems, the isovector spin-flip M1 transition is dominant, mainly between one or two spin-orbit partner states. It is shown that pairing correlations have a significant impact on the centroid energy and major peak position of the M1 mode. The M1 excitations could provide an additional constraint to improve nuclear energy density functionals in the future studies.

Investigation of the electric dipole (E1) excitations in $$^{\mathrm {181}}$$Ta nucleus

E1 transition properties such as the reduced transition probabilities, excitation energies and photon–absorption cross-sections have been theoretically investigated for $$^{\mathrm {181}}$$ Ta nucleus within the framework of Translational and Galileo Invariant-Quasiparticle Phonon Nuclear Model (TGI-QPNM). The model Hamiltonian includes the single-particle and the isovector dipole–dipole interaction terms along with the restoration forces. The strength of the isovector dipole–dipole interaction has been chosen to be $$\chi = 500/\hbox {A}^{\mathrm {5/3}} MeV \cdot fm^{-2}$$ . Theoretical calculations show that in addition to the M1 excitations, there is considerable amount of E1 transitions especially between 2.6–3 MeV, which gives remarkable contribution to the fragmentation in the low-energy region of the dipole spectrum. Thus, the agreement between theory and experiment in terms of the fragmentation increases. Furthermore, the photon–absorption cross-sections in the Pigmy Dipole Resonance (PDR) region below the neutron separation energy ( $$S_{n}$$ ) is compatible with experimental data.

Role of residual interaction in the relativistic description of M1 excitation

Magnetic dipole (M1) excitation is the leading mode of multi-nucleon excitations induced by the magnetic field, and is a phenomenon of the spin–orbit splitting and residual interactions involved. In this work, we investigate the effects of the residual interactions on the M1 excitation from a novel perspective, the framework of relativistic nuclear energy-density functional. The relativistic Hartree–Bogoliubov model is utilized to determine the nuclear ground state properties, while the relativistic quasi-particle random-phase approximation is employed for the description of M1-excitation properties. From the analysis of M1 mode in the Ca isotope chain, role of the isovector–pseudovector residual interaction is discussed. For open-shell nuclei, the pairing correlation also plays a noticeable role in the M1 mode. The experimental data on M1 mode is expected to provide a suitable reference to improve and optimize the theoretical models to describe the residual interactions.

Electric and magnetic dipole strength inSn112,114,116,118,120,124

Background: There is renewed interest in electric dipole strength distributions for a variety of reasons including the extraction of the dipole polarizability related to properties of the symmetry energy and a measure for the neutron skin thickness, understanding the structure of low-energy E1 strength in nuclei with neutron excess, and establishing the systematics of the isovector giant dipole resonance (IVGDR). Inelastic proton scattering at energies of a few hundred MeV and very forward angles including 0∘ has been established as a tool for the study of electric and magnetic dipole strength distributions in nuclei. Purpose: The present work aims at a systematic investigation of the electric and magnetic dipole strength distributions in the chain of stable even-mass tin isotopes. Methods: Inelastic proton scattering experiments were performed at the Research Center for Nuclear Physics, Osaka, with a 295-MeV beam covering laboratory angles 0∘–6∘ and excitation energies 6–22 MeV. Cross sections due to E1 and M1 excitations were extracted with a multipole decomposition analysis (MDA) and then converted to reduced transition probabilities with the “virtual photon method” for E1 and the “unit cross section method” for M1 excitations, respectively. Including a theory-aided correction for the high-excitation-energy region not covered experimentally, the electric dipole polarizability was determined from the E1 strength distributions. Results: Total photoabsorption cross sections derived from the E1 and M1 strength distributions show significant differences compared to those from previous (γ,xn) experiments in the energy region of the IVGDR. The widths of the IVGDR deduced from the present data with a Lorentz parametrization show an approximately constant value of about 4.5 MeV in contrast to the large variations between isotopes observed in previous work. The IVGDR centroid energies are in good correspondence to expectations from empirical systematics of their mass dependence. Furthermore, a study of the dependence of the IVGDR energies on bulk matter properties is presented. The E1 strengths below neutron threshold show fair agreement with results from (γ,γ′) experiments on Sn112,116,120,124 in the energy region between 6 and 7 MeV, where also isoscalar E1 strength was found for Sn124. At higher excitation energies, large differences are observed, pointing to a different nature of the excited states with small ground-state branching ratios. The isovector spin-M1 strengths exhibit a broad distribution between 6 and 12 MeV in all studied nuclei. Conclusions: The present results contribute to the solution of a variety of nuclear structure problems including the systematics of the energy and width of the IVGDR, the structure of low-energy E1 strength in nuclei, new constraints to energy density functionals (EDFs) aiming at a systematic description of the dipole polarizability across the nuclear chart, from which properties of the symmetry energy can be derived, and the systematics of the isovector spin-M1 strength in heavy nuclei.16 MoreReceived 12 July 2020Accepted 2 September 2020DOI:https://doi.org/10.1103/PhysRevC.102.034327©2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsElectromagnetic transitionsH & He induced nuclear reactionsNuclear density functional theoryNuclear structure & decaysPhotonuclear reactionsNuclear Physics

Study of dipole excitations in even-even 156-166Dy with QRPA using the Gogny force

The success encountered in the systematic studies of the electric and magnetic strength functions for almost all even-even nuclei proves the quality of our HFB+QRPA calculations which use the Gogny interaction within the whole nuclear chart. In this paper, we study the dipole electromagnetic strength distribution in 158-166Dy. The scalar or the vector nature, in the isospin as well as in the spin space, is analysed according to transition density for some of the M1 excitations in 162Dy.

Magnetic dipole excitation and its sum rule in nuclei with two valence nucleons

Background: Magnetic dipole (M1) excitation is the leading mode of nuclear excitation by the magnetic field, which couples unnatural-parity states. Since the M1 excitation occurs mainly for open-shell nuclei, the nuclear pairing effect is expected to play a role. As expected from the form of operator, this mode may provide the information on the spin-related properties, including the spin component of dineutron and diproton correlations. In general, the sum rule for M1 transition strength has not been derived yet. Purpose: To investigate the M1 excitation of the systems with two valence nucleons above the closed-shell core, with pairing correlation included, and to establish the M1 sum rule that could be used to validate theoretical and experimental approaches. Possibility to utilize the M1 excitation as a tool to investigate the pairing correlation in medium is also discussed. Method: Three-body model, which consists of a rigid spherical core and two valence nucleons, is employed. Interactions for its two-body subsystems are phenomenologically determined in order to reproduce the two-body and three-body energies. We also derive the M1 sum rule within this three-body picture. Conclusion: The introduced M1 sum rule can be utilized as a benchmark for model calculations of M1 transitions in the systems with two valence nucleons. The total sum of the M1 transition strength is related with the coupled spin of valence nucleons in the open shell, where the pairing correlation is unnegligible. The three-body-model calculations for 18 O, 18 Ne, and 42 Ca nuclei demonstrate a significant effect of the pairing correlations on the low-lying M1 transitions. Therefore, further experimental studies of M1 transitions in those systems are on demand, in order to validate proposed sum rule, provide a suitable probe for the nuclear pairing in medium, as well as to optimize the pairing models.

Low-energy M1 excitations in Pb208 and the spin channel of the Skyrme energy-density functional

We investigate the spin dependent part of the Skyrme energy-density functional, in particular its impact on the residual particle-hole interaction in self-consistent calculations of excitations. Test cases are the low-energy M1 excitations in $^{208}$Pb treated within the self-consistent random-phase approximation based on the Skyrme energy-density functional. We investigate different parametrizations of the functionals to find out which parameters of the functional have strongest correlations with M1 properties. We explore a simple method of the modification of the spin-related parameters which delivers a better description of M1 excitations while basically maintaining the good description of ground state properties.

The Nuclear Spin Scissors Mode --- Theory and Experiment

A new type of nuclear collective motion—the spin scissors mode—was predicted seven years ago. Promising signs of its existence in 232Th were found. We perform a systematic analysis of experimental data on M1 excitations in rare earth nuclei to find traces of the spin scissors mode in this area. Obvious signs of its existence will be demonstrated. We propose new criteria to attribute the observed 1+ states to the scissors mode, entailing that the agreement of the experimental data with the results of our calculations and with the sum rules is improved substantially.

The Nuclear Spin Scissors Mode—Theory and Experiment

A new type of nuclear collective motion—the spin scissors mode—was predicted seven years ago. Promising signs of its existence in 232Th were found. We perform a systematic analysis of experimental data on M1 excitations in rare earth nuclei to find traces of the spin scissors mode in this area. Obvious signs of its existence will be demonstrated. We propose new criteria to attribute the observed 1+ states to the scissors mode, entailing that the agreement of the experimental data with the results of our calculations and with the sum rules is improved substantially.

Magnetic dipole response of the 169Tm nucleus

The magnetic dipole (M1) response of the 169Tm nucleus is investigated from a theoretical point of view. The theoretical tool used in this study is the Rotational Invariant Quasiparticle Phonon Nuclear Model (RI-QPNM) which gives a possibility to eliminate spurious contributions in the M1 spectrum. In the framework of this model, both the low-lying and high-lying parts of the M1 excitation spectrum of 169Tm are calculated. The result shows that the low-lying excitations have almost pure orbital character and can be interpreted as scissors mode, whereas the high-lying transitions can be read as spin-flip mode because of its spin nature. The reduced transition probability summed up in the energy range 2–4 MeV is found to be B(M1↑)=3.040μN2 which agrees with the available experimental data. The fragmentation of the low-energy M1 strength is also well reproduced. This is also the first study in which both the low-lying and high-lying M1 spectrum of the 169Tm nucleus is theoretically investigated.

Nuclear spin scissors mode – experimental status

A new type of nuclear collective motion - the spin scissors mode - was predicted seven years ago. Promising signs of its existence in 232Th were found. We perform a systematic analysis of experimental data on M1 excitations in rare-earth nuclei to find traces of the spin scissors mode in this area. Obvious signs of its existence are demonstrated.

Explanation of the puzzle of 164Dy scissors

The solution of TDHFB equations by Wigner Function Moments method with the isovectorisoscalar coupling taken into account leads to the prediction of the new type of nuclear spin scissors mode. It turns out that the lower group of M1 excitations in 164Dy, which is usually not included in the systematics of the scissors mode, can be quite naturally attributed to this new type of scissors.

Microscopic investigation of the low-lying magnetic dipole transitions in the odd-mass 155–169Ho isotopes

The low-lying magnetic dipole (M1) strength in deformed odd-mass 155–169Ho nuclei is investigated using rotational invariant (RI-) Quasiparticle Phonon Nuclear Model (QPNM). The gross features and fragmentation of the scissors mode in 165Ho is well reproduced by RI-QPNM calculations. The systematics of the low-energy M1 excitation in Ho isotopic chain is discussed with respect to summed strength. Besides, the results for M1 excitations in odd-mass Ho isotopes are compared with the systematics of the scissors mode in the neighbouring even–even nuclei. The obtained results generally match the systematic and trends typical for the scissors motion. In addition to the low-lying M1 excitations, a M1 giant resonance in the 7–15 MeV energy region is predicted for 155–169Ho nuclei in the present study.

Electromagnetic Selection Rules for $$\varvec{^{12}}$$ 12 C in a 3 $$\varvec{\alpha }$$ α Cluster Model

The recent successful application of the Algebraic Cluster Model to the energy spectrum of \(^{12}\)C has brought a new impetus on spectroscopy of this and other \(\alpha -\)conjugate nuclei. In fact, known spectral properties have been reexamined on the basis of vibrations and rotations of three \(\alpha \) particles at the vertexes of an equilateral triangle and new excited states have been measured that fit into this scheme. The analysis of this system entails the application of molecular models for rotational–vibrational spectra to the nuclear context and requires deep knowledge of the underlying group-theoretical properties, based on the \(\mathcal {D}_{3h}\) symmetry, similarly to what is done in quantum chemistry. We have recently analyzed the symmetries of the model and the quantum numbers in great depth, reproducing the all-important results of Wheeler and we have derived electromagnetic selection rules for the system of three \(\alpha \) particles, finding, for instance, that electric dipole E1 and magnetic dipole M1 excitations are excluded from the model. The lowest active modes are therefore E2, E3,\(\cdots \) and M2, M3, \(\cdots \) although there are further restrictions between certain types of bands. The selection rules summarized in the text provide a criterion for assigning of observed lines to the alpha cluster model or not and they might help to further unravel the electromagnetic properties of \(^{12}\)C. With the perspective of new facilities (such as ELI) where photo-excitation and photo-dissociation experiments will play a major role, a complete understanding of e.m. selection rules as a tool to confirm or disprove nuclear structure models, is mandatory.

Microscopic description of ground state magnetic moment and low-lying magnetic dipole excitations in heavy odd-mass 181Ta nucleus

The ground state magnetic moments and the low-lying magnetic dipole (Ml) transitions from the ground to excited states in heavy deformed odd-mass [Formula: see text]Ta have been microscopically investigated on the basis of the quasiparticle-phonon nuclear model (QPNM). The problem of the spurious state mixing in M1 excitations is overcome by a restoration method allowing a self-consistent determination of the separable effective restoration forces. Due to the self-consistency of the method, these effective forces contain no arbitrary parameters. The results of calculations are compared with the available experimental data, the agreement being reasonably satisfactory.