Low-energy Dipole Strength Research Articles

Low-Energy Dipole Strength in 8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^8$$\\end{document}He

In this work, we present new ab initio coupled-cluster calculations of dipole-excited state properties of 8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^8$$\\end{document}He based on the chiral effective field theory interaction 1.8/2.0 (EM). We focus on the dipole polarizability, and compare the results to our previous study [Phys. Rev. C 105, 034313 (2022)] and subsequent theoretical work. With the aim of connecting the presence of low-lying dipole strength to structure properties of 8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^8$$\\end{document}He, we compute the point-neutron radius, finding excellent agreement with available experimental data, and investigate its correlation with the dipole polarizability.

Nuclear excitations within microscopic EDF approaches: Pairing and temperature effects on the dipole response

In the present work, the isovector dipole responses, both in the resonance region and in the low-energy sector, are investigated using the microscopic nuclear Energy Density Functionals (EDFs). The self-consistent QRPA model based on Skyrme Hartree Fock BCS approach is applied to study the evolution of the isovector dipole strength by increasing neutron number and temperature. First, the isovector dipole strength and excitation energies are investigated for the Ni isotopic chain at zero temperature. The evolution of the low-energy dipole strength is studied as a function of the neutron number. In the second part, the temperature dependence of the isovector dipole excitations is studied using the self-consistent finite temperature QRPA, below and above the critical temperatures. It is shown that new excited states become possible due to the thermally occupied states above the Fermi level, and opening of the new excitations channels. In addition, temperature leads to fragmentation of the low-energy strength around the neutron separation energies, and between 9 and 12 MeV. We find that the cumulative sum of the strength below E$\leq12$ MeV decreases in open-shell nuclei due to the vanishing of the pairing correlations as temperature increases up to T=1 MeV. The analysis of the transition densities in the low-energy region shows that the proton and neutron transition densities display a mixed pattern: both isoscalar and isovector motion of protons and neutrons are obtained inside nuclei, while the neutron transition density is dominant at the surface region.

Exploring enhanced low-energy magnetic dipole strength in photon scattering

Strengths of $M1$ transitions depopulating high-lying ${1}^{+}$ states and of subsequent transitions in cascades populating the first excited state were determined on the basis of large-scale shell-model calculations for the nuclide $^{54}\mathrm{Fe}$. The results reveal that the spectra of primary $M1$ transitions from ${1}^{+}$ states as well as the subsequent cascades of $M1$ transitions show an enhancement of strength toward low energy, which is similar to that found for a huge number of transitions between states of a wide spin range as observed in light-ion induced reactions. This allows, in principle, the study of low-energy $M1$ strength using photon scattering. Based on these results, intensities of $M1$ transitions under experimental conditions are estimated.

Low-energy dipole strength in even–even 152–164Dy isotopes within the quasiparticle random phase approximation (QRPA) including symmetry restoring interactions

A systematic study of the low-lying magnetic (M1) and electric dipole (E1) transitions from ground- to excited-states in the doubly-even 152–164Dy isotopes has been performed within the framework of the rotational (RI-), translational and Galilean invariant (TGI-) Quasiparticle Random Phase Approximation (QRPA). According to the results of the calculations dipole strength is fragmented over several states in 2–4 MeV interval and as a rule, one-phonon Iπ=1+ states are rather fragmented than the one-phonon states with Iπ=1−. It is found that even though almost all the M1 strengths are dominated by the orbital motion, the weaker contributions from spin motion plays a relatively major role in shaping the M1 spectra due to its constructive interference with orbital motion in these energies. For 160,162,164Dy the calculated total M1 transition strengths, centroid energies of M1 resonance and gamma widths at the energies between 2 and 4 MeV are in fair agreement with relevant experiment data. It has been shown that in addition to the ΔK=0E1 transitions there are also E1 transitions with ΔK=1 in the low-energy E1 spectrum of all the even–even Dy isotopes under investigation.

Finite-Temperature Relativistic Nuclear Field Theory: An Application to the Dipole Response

Nuclear response theory beyond the one-loop approximation is formulated for the case of finite temperature. For this purpose, the time blocking approximation to the time-dependent part of the in-medium nucleon-nucleon interaction amplitude is adopted for the thermal (imaginary-time) Green's function formalism. We found that introducing a soft blocking, instead of a sharp blocking at zero temperature, brings the Bethe-Salpeter equation to a single-frequency variable equation also at finite temperatures. The method is implemented self-consistently in the framework of quantum hadrodynamics and designed to connect the high-energy scale of heavy mesons and the low-energy domain of nuclear medium polarization effects in a parameter-free way. In this framework, we investigate the temperature dependence of dipole spectra in the even-even nuclei ^{48}Ca and ^{100,120,132}Sn with a special focus on the giant dipole resonance's width problem and on the low-energy dipole strength distribution.

Systematics of the electric dipole response in stable tin isotopes

The electric dipole is an important property of heavy nuclei. Precise information on the electric dipole response provides information on the electric dipole polarisability which in turn allows to extract important constraints on neutron-skin thickness in heavy nuclei and parameters of the symmetry energy. The tin isotope chain is particularly suited for a systematic study of the dependence of the electric dipole response on neutron excess as it provides a wide mass range of accessible isotopes with little change of the underlying structure. Recently an inelastic proton scattering experiment under forward angles including 0º on 112,116,124Sn was performed at the Research Centre for Nuclear Physics (RCNP), Japan with a focus on the low-energy dipole strength and the polarisability. First results are presented here. Using data from an earlier proton scattering experiment on 120Sn the gamma strength function and level density are determined for this nucleus.

Astrophysical relevance of the low-energy dipole strength of 206Pb

The dipole strength of 206Pb was studied below the neutron separation energy using photon scattering experiments at the HIGS facility. Utilizing the technique of nuclear resonance fluorescence with 100% linearly-polarized photon beams, the spins, parities, branching ratios and decay widths of excited states in 206Pb from 4.9 - 8.1 MeV have been measured. The new experimental information is used to reliably predict the neutron capture cross section of 205Pb, an important branch point nucleus along the s-process path of nucleosynthesis.

Low energy dipole strength from large scale shell model calculations

Low energy enhancement of radiative strength functions has been deduced from experiments in several mass regions of nuclei. Such an enhancement is believed to impact the calculated neutron capture rates which are crucial input for reaction rates of astrophysical interest. Recently, shell model calculations have been performed to explain the upbend of the γ-strength as due to the M 1 transitions between close-lying states in the quasi-continuum in Fe and Mo nuclei. Beyond mean-↓eld calculations in Mo suggested, however, a non-negligible role of electric dipole in the low energy enhancement. So far, no calculations of both dipole components within the same theoretical framework have been presented in this context. In this work we present newly developed large scale shell model appraoch that allows to treat on the same footing natural and non-natural parity states. The calculations are performed in a large sd − pf − gds model space, allowing for 1p{1h excitations on the top of the full pf -shell con↓guration mixing. We restrict the discussion to the magnetic part of the dipole strength, however, we calculate for the ↓rst time the magnetic dipole strength between states built of excitations going beyond the classical shell model spaces. Our results corroborate previous ↓ndings for the M 1 enhancement for the natural parity states while we observe no enhancement for the 1p{1h contributions. We also discuss in more detail the e↑ects of con↓guration mixing limitations on the enhancement coming out from shell model calculations.

Toroidal resonance: Relation to pygmy mode, vortical properties, and anomalous deformation splitting

We review a recent progress in investigation of the isoscalar toroidal dipole resonance (TDR). A possible relation of the TDR and low-energy dipole strength (also called a pygmy resonance) is analyzed. It is shown that the dipole strength in the pygmy region can by understood as a local manifestation of the collective vortical toroidal motion at the nuclear surface. Application of the TDR as a measure of the nuclear dipole vorticity is discussed. Finally, an anomalous splitting of the TDR in deformed nuclei is scrutinized.

Low-energy electric dipole response of Sn isotopes

We study the low-energy dipole (LED) strength distribution along the Sn isotopic chain in both the isoscalar (IS) and the isovector (IV, or E1) electric channels, to provide testable predictions and guidance for new experiments with stable targets and radioactive beams. We use the self-consistent Quasi-particle Random-Phase Approximation (QRPA) with finite-range interactions and mainly the Gogny D1S force. We analyze also the performance of a realistic two-body interaction supplemented by a phenomenological three-body contact term. We find that from N=50 and up to the N=82 shell closure (132Sn) the lowest-energy part of the IS-LED spectrum is dominated by a collective transition whose properties vary smoothly with neutron number and which cannot be interpreted as a neutron-skin oscillation. For the neutron-rich species this state contributes to the E1 strength below particle threshold, but much more E1 strength is carried by other, weak but numerous transitions around or above threshold. We find that strong structural changes in the spectrum take effect beyond N=82, namely increased LED strength and lower excitation energies. Our results with the Gogny interaction are compatible with existing data. On this basis we predict that a) the summed IS strength below particle threshold shall be of the same order of magnitude for N=50-82, b) the summed E1 strength up to approximately 12 MeV shall be similar for N=50-82 MeV, while c) the summed E1 strength below threshold shall be of the same order of magnitude for N ~ 64 - 82 and much weaker for the lighter, more-symmetric isotopes. We point out a general agreement of our results with other non-relativistic studies, the absence of a collective IS mode in some of those studies, and a possibly radical disagreement with relativistic models.

Probing the neutron skin thickness in collective modes of excitation

Nuclear collective motion provides valuable constraint on the size of neutron-skin thickness and the properties of nuclear matter symmetry energy. By employing relativistic nuclear energy density functional (RNEDF) and covariance analysis related to $\chi^2$ fitting of the model parameters, relevant observables are identified for dipole excitations, which strongly correlate with the neutron-skin thickness $(r_{np})$, symmetry energy at saturation density $(J)$ and slope of the symmetry energy $(L)$. Using the RNEDF framework and experimental data on pygmy dipole strength ($^{68}$Ni, $^{132}$Sn, $^{208}$Pb) and dipole polarizability ($^{208}$Pb), it is shown how the values of $J$, and $L$, and $r_{np}$ are constrained. The isotopic dependence of moments associated to dipole excitations in $^{116-136}$Sn shows that the low-energy dipole strength and polarizability in neutron-rich nuclei display strong sensitivity to the symmetry energy parameter $J$, more pronounced than in isotopes with moderate neutron-to-proton number ratios.

Information content of the low-energy electric dipole strength: Correlation analysis

We study the information content carried by the electric dipole strength with respect to isovector and isoscalar indicators characterizing bulk nuclear matter and finite nuclei. To separate isoscalar and isovector modes, and low-energy strength and giant resonances, we analyze the E1 strength as a function of excitation energy $E$ and momentum transfer $q$. We use the self-consistent nuclear density functional theory with Skyrme energy density functionals, augmented by the random phase, to compute the E1 strength, and covariance analysis to assess correlations between observables. Calculations are performed for spherical, doubly-magic nuclei $^{208}$Pb and $^{132}$Sn. We demonstrate that E1 transition densities in the low-energy region below the giant dipole resonance exhibit appreciable state dependence and multi-nodal structures, which are fingerprints of weak collectivity. The correlation between the accumulated low-energy strength and symmetry energy is weak, and dramatically depends on the energy cutoff assumed. On the other hand, a strong correlation is predicted between isovector indicators and the accumulated isovector strength at $E$ around 20 MeV and momentum transfer $q\sim 0.65$ fm$^{-1}$. Momentum- and coordinate-space pattern of the low-energy dipole modes indicate a strong fragmentation into individual particle-hole excitations. The global measure of low-energy dipole strength poorly correlates with the nuclear symmetry energy and other isovector characteristics. Consequently, our results do not support the suggestion that there exists a collective "pygmy dipole resonance," which is a strong indicator of nuclear isovector properties.

Fragmentation of electric dipole strength inN=82isotones

Fragmentation of the dipole strength in the N=82 isotones 140Ce, 142Nd and 144Sm is calculated using the second random-phase approximation (SRPA). In comparison with the result of the random-phase approximation (RPA), the SRPA provides the additional damping of the giant dipole resonance and the redistribution of the low-energy dipole strength. Properties of the low-energy dipole states are significantly changed by the coupling to two-particle-two-hole (2p2h) states, which are also sensitive to the correlation among the 2p2h states. Comparison with available experimental data shows a reasonable agreement for the low-energy E1 strength distribution.

Low-energy dipole strength and the critical case of 48Ca

Recent theoretical work has not led to a consensus regarding the nature of the low-energy E1 strength in the 40,44,48Ca isotopes, for which high-resolution (γ,γ′) data exist. Here we revisit this problem using the first-order quasiparticle random-phase approximation (QRPA) and different interactions. First we examine all even Ca isotopes with N=14–40. All isotopes are predicted to undergo dipole transitions at low energy, of large and comparable isoscalar strength but of varying E1 strength. Provided a moderate and uniform energetic shift is introduced to the results, QRPA with the Gogny D1S interaction is able to account for the (γ,γ′) data, because, up to N=28, it yields a rather pure isoscalar oscillation. A neutron-skin oscillation is anticipated for N⩾30. This contradicts existing predictions that 44,48Ca develop a neutron-skin mode. Which theoretical result is correct cannot be resolved conclusively using the available data. We propose that alpha-scattering, possibly followed by an electroexcitation experiment, could resolve the situation and thereby help to improve the different models aspiring to describe reliably the low-energy dipole strength of nuclei.

SPECTROSCOPIC FEATURES OF LOW-ENERGY EXCITATIONS IN SKIN NUCLEI

Systematic studies of dipole and other multipole excitations in stable and exotic nuclei are discussed theoretically. Exploring the relation of the strengths of low-energy dipole and quadrupole pygmy resonances to the thickness of the neutron (proton) skin a close connection between static and dynamic properties of the nucleus is observed. The fine structure of low-energy dipole strength in 138 Ba nucleus is revealed from E1 and spin-flip M1 strengths distributions.

Photon scattering experiments on the quasistable, odd-odd mass nucleusLu176

The quasistable odd-odd-mass nucleus $^{176}\mathrm{Lu}$ is of special interest in nuclear structure physics and, above all, in nuclear astrophysics. Systematic photon scattering experiments have been performed at the bremsstrahlung facility of the 4.3-MV Stuttgart Dynamitron accelerator with bremsstrahlung end-point energies of 2.3 and 3.1 MeV to determine the low-energy dipole strength distribution in the s-only isotope $^{176}\mathrm{Lu}$. The main goal was to pin down possible intermediate states (IS) for the photoactivation of the short-lived 123-keV isomer, which is the key process determining the effective lifetime of $^{176}\mathrm{Lu}$ in a stellar photon bath and hence for the use of this isotope as a stellar chronometer. Using an enriched sample, 29 transitions ascribed to $^{176}\mathrm{Lu}$ were detected below 2.9-MeV excitation energy. The corresponding excitation strengths were determined. For the previously proposed lowest IS at 839 keV, an upper limit for the excitation strength corresponding to a lifetime of $\ensuremath{\tau}\ensuremath{\geqslant}$ 1.5 ps can be given. Astrophysical consequences, also in view of new Stuttgart photoactivation experiments, are discussed. The fragmentation of the dipole strength is compared to those in neighboring even-even and odd-even nuclei.

Low energy dipole strength in light drip line nuclei

We have studied electric dipole $(E1)$ strength distribution in neutron and proton drip line nuclei ${}_{ 4}^{12}{\mathrm{Be}}_{8},$ ${}_{ 4}^{14}{\mathrm{Be}}_{10},$ and ${}_{ 8}^{13}{\mathrm{O}}_{5}$ by large scale shell model calculations with the effect of loosely-bound single particle wave functions. Large $E1$ strength is found in the low excitation energy region below ${E}_{x}=3 \mathrm{MeV}$ in both ${}_{ 4}^{12}{\mathrm{Be}}_{8}$ and ${}_{ 8}^{13}{\mathrm{O}}_{5},$ while strong $E1$ strength is found only in high excitation energy region above ${E}_{x}=7 \mathrm{MeV}$ in ${}_{ 4}^{14}{\mathrm{Be}}_{10}.$ The effect of extended wave functions and the coherence in the transition amplitudes enhance significantly the $E1$ strength in the low energy region. A manifestation of melting of the shell magicity at $N=8$ and $Z=8$ is pointed out in the systematics of $E1$ transitions in Be and O isotopes.

Complete scissors mode strength in heavy deformed odd-mass nuclei: a case study of 165Ho and 169Tm

The low-energy dipole strength distributions in 165Ho and 169Tm have been studied in nuclear resonance fluorescence experiments at the S-DALINAC utilizing a Euroball Cluster detector. In the energy interval between 2.5 and 4.0 MeV, where the scissors mode is expected, 35 ground state transitions could be observed in 165Ho and 53 in 169Tm. Assuming M1 character for all these transitions corresponds to ΣB(M1) ↑= 1.54(23), μ N 2 and ΣB(M1) ↑= 2.15(63), μ N 2 for 165Ho and 169Tm, respectively. A statistical analysis is applied to the measured spectra which is capable of reconstructing the complete strength, including contributions of transitions below the observation limit, with the ratio between M1 and E1 excitations and their total strengths taken as an average over the even-mass neighbours. This results in summed M1 transition strengths of ΣB(M1) ↑= 3.54 −0.95 +0.75, μ N 2 ( 165Ho) and ΣB(M1) ↑= 3.36 −0.57 +1.00 μ N 2 ( 169Tm). The large variations of the summed dipole strength and the fragmentation in other deformed odd-mass nuclei can be reproduced by the same statistical ansatz. The total low-lying M1 strength in heavy deformed odd-mass nuclei is in agreement with the findings in the neighbouring even-mass nuclides as well as with sum-rule predictions.

Distribution of dipole and spin-dipole strength in nuclei

The schematic model of Goswami and Pal is applied to heavy nuclei and the dipole strength is shown to reside in just four non-degenerate levels. The collection of all the strength into a single level is discussed. The distribution of strength due to non-constancy of radial integrals and non-degeneracy of unperturbed particle-hole orbits is demonstrated in “realistic” calculations for 208Pb, 132Sn, 90Zr and 56Ni. The collection of low energy dipole strength into “mini-resonances” is shown to be sensitive to the mean energy difference between neutron and proton particle-hole states.