Dipole Strength Distribution Research Articles

Pygmy resonances and neutron skins

In a study motivated by a recent experiment, the distribution of electric dipole strength in the neutron-rich $^{68}\mathrm{Ni}$ isotope was computed using a relativistic random-phase approximation with a set of effective interactions that---although well calibrated---predict significantly different values for the neutron-skin thickness in $^{208}\mathrm{Pb}$. The emergence of low-energy ``pygmy'' strength that exhausts about $5%$--$8%$ of the energy-weighted sum rule (EWSR) is clearly identified. In addition to the EWSR, special emphasis is placed on the dipole polarizability. In particular, our results suggest a strong correlation between the dipole polarizability of $^{68}\mathrm{Ni}$ and the neutron-skin thickness of $^{208}\mathrm{Pb}$. Yet we find a correlation just as strong, and an even larger sensitivity, between the neutron-skin thickness of $^{208}\mathrm{Pb}$ and the fraction of the dipole polarizability exhausted by the pygmy resonance. These findings suggest that dipole polarizability may be used as a proxy for the neutron skin.

Investigation of low-lying electric dipole strength in the semimagic nucleusCa44

The dipole-strength distribution in the semimagic nucleus $^{44}\mathrm{Ca}$ has been measured up to 10 MeV excitation energy in photon-scattering experiments using bremsstrahlung and monoenergetic 100% linearly polarized photon beams. The combination of both measurements allows a clear determination of spin and parity quantum numbers of the excited states as well as absolute cross sections and transition probabilities. The results show that the majority of the dipole strength in $^{44}\mathrm{Ca}$ below 10 MeV is due to $E1$ transitions while $M1$ strength plays only a minor role. The experimental results are compared to the strength in the neighboring doubly magic nuclei $^{40,48}\mathrm{Ca}$ and to microscopic calculations within the extended theory of finite Fermi systems in order to investigate the evolution of the low-lying $E1$ strength in this isotopic chain. Both, experiment and calculations, show a nontrivial dependence of the total $E1$ strength as a function of the neutron number.

Pygmy dipole resonance in stable nuclei

Two examples of recent work on the structure of low-energy electric dipole modes are presented. The first part discusses the systematics of the pygmy dipole resonance (PDR) in stable tin isotopes deduced from high-resolution (γ, γ′) experiments. These help to distinguish between microscopic QRPA calculations based on either a relativistic or a non-relativistic mean-field description, predicting significantly different properties of the PDR. The second part presents a novel approach to measure the complete electric dipole strength distribution from excitation energies starting at about 5 MeV across the giant dipole resonance (GDR) with high-resolution inelastic proton scattering under 0° at energies of a few 100 MeV/nucleon. The case of 208Pb is discussed in detail and first result from a recent experiment on 120Sn is presented.

Electric dipole strength distribution below the E1 giant resonance in N = 82 nuclei

AbstractIn this study quasiparticle random-phase approximation with the translational invariant Hamiltonian using deformed mean field potential has been conducted to describe electric dipole excitations in 136Xe, 138Ba, 140Ce, 142Nd, 144Sm and 146Gd isotones. The distribution of the calculated E1 strength shows a resonance like structure at energies between 6–8 MeV exhausting up to 1% of the isovector electric dipole Energy Weighted Sum Rule and in some aspects nicely confirms the experimental data. It has been shown that the main part of E1 strength, observed below the threshold in these nuclei may be interpreted as main fragments of the Pygmy Dipole resonance. The agreement between calculated mean excitation energies as well as summed B(E1) value of the 1− excitations and the available experimental data is quite good. The calculations indicate the presence of a few prominent positive parity 1+ States in heavy N = 82 isotones in the energy interval 6–8 MeV which shows not all dipole excitations were of electric character in this energy range.

Low-lying dipole response in the relativistic quasiparticle time blocking approximation and its influence on neutron capture cross sections

We have computed dipole strength distributions for nickel and tin isotopes within the Relativistic Quasiparticle Time Blocking Approximation (RQTBA). These calculations provide a good description of data, including the neutron-rich tin isotopes 130,132Sn. The resulting dipole strengths have been implemented in Hauser–Feshbach calculations of astrophysical neutron capture rates relevant for r-process nucleosynthesis studies. The RQTBA calculations show the presence of enhanced dipole strength at energies around the neutron threshold for neutron rich nuclei. The computed neutron capture rates are sensitive to the fine structure of the low lying dipole strength, which emphasizes the importance of a reliable knowledge of this excitation mode.

Low-lying magnetic and electric dipole strength distribution in the 176Hf nucleus

In this study the QRPA approach with the rotational and translational invariant Hamiltonians has been carried out to describe magnetic and electric dipole excitations in 176Hf . Calculations show that the 176Hf nucleus demonstrates a very rich B(M1) strength structure and in some aspects nicely confirm the experimental data. It has been shown that the main part of spin-1 states, observed at 2-4MeV in 176Hf , may be attributed to have a M1 character and may be interpreted as the main fragments of the scissors mode. The agreement between the calculated mean excitation energies as well as the summed B(M1) values of the scissors mode excitations and the available experimental data is quite good. The constructive interference between the orbit and the spin part of M1 strength has been found to be below 3.5MeV. The calculations indicate the presence of a few prominent negative-parity \(\ensuremath K^{\pi} = 1^{-}\) states in the 2-4MeV energy interval. This suggests that the supposition of the experiment “all stronger \( \Delta\)K = 1 low-lying dipole excitations were of magnetic character” cannot be generalized.

Pygmy dipole strength inZr90

The dipole response of the $N=50$ nucleus $^{90}\mathrm{Zr}$ was studied in photon-scattering experiments at the electron linear accelerator ELBE with bremsstrahlung produced at kinetic electron energies of 7.9, 9.0, and 13.2 MeV. We identified 189 levels up to an excitation energy of 12.9 MeV. Statistical methods were applied to estimate intensities of inelastic transitions and to correct the intensities of the ground-state transitions for their branching ratios. In this way we derived the photoabsorption cross section up to the neutron-separation energy. This cross section matches well the photoabsorption cross section obtained from ($\ensuremath{\gamma}$, $n$) data and thus provides information about the extension of the dipole-strength distribution toward energies below the neutron-separation energy. An enhancement of $E1$ strength has been found in the range of 6 to 11 MeV. Calculations within the framework of the quasiparticle-phonon model ascribe this strength to a vibration of the excessive neutrons against the $N=Z$ neutron-proton core, giving rise to a pygmy dipole resonance.

Low-energy tail of the giant dipole resonance inMo98andMo100deduced from photon-scattering experiments

Dipole-strength distributions in the nuclides $^{98}\mathrm{Mo}$ and $^{100}\mathrm{Mo}$ up to the neutron-separation energies have been studied in photon-scattering experiments at the bremsstrahlung facility of the Forschungszentrum Dresden-Rossendorf. To determine the dipole-strength distributions up to the neutron-emission thresholds, statistical methods were developed for the analysis of the measured spectra. The measured spectra of scattered photons were corrected for detector response and atomic background by simulations using the code GEANT3. Simulations of $\ensuremath{\gamma}$-ray cascades were performed to correct the intensities of the transitions to the ground state for feeding from higher-lying levels and to determine their branching ratios. The photoabsorption cross sections obtained for $^{98}\mathrm{Mo}$ and $^{100}\mathrm{Mo}$ from the present $(\ensuremath{\gamma},{\ensuremath{\gamma}}^{'})$ experiments are combined with $(\ensuremath{\gamma},n)$ data from literature, resulting in a photoabsorption cross section covering the range from 4 to about 15 MeV of interest for network calculations in nuclear astrophysics. Novel information about the low-energy tail of the giant dipole resonance and its energy dependence is derived. The photoabsorption cross sections deduced from the present photon-scattering experiments are compared with existing data from neutron capture and $^{3}\mathrm{He}$-induced reactions.

Photon strength distributions in stable even–even molybdenum isotopes

Electromagnetic dipole-strength distributions up to the particle separation energies are studied for the stable even–even nuclides 92,94,96,98,100Mo in photon-scattering experiments at the superconducting electron accelerator ELBE of the Forschungszentrum Dresden-Rossendorf. The influence of inelastic transitions to low-lying excited states has been corrected by a simulation of γ cascades using a statistical model. After corrections for branching ratios of ground-state transitions, the photon-scattering cross sections smoothly connect to data obtained from (γ, n) reactions. With the newly determined electromagnetic dipole response of nuclei well below the particle separation energies, the parametrization of the isovector giant dipole resonance is done with improved precision.

Nuclear symmetry energy and neutron skins derived from pygmy dipole resonances

By exploiting Coulomb dissociation of high-energy radioactive beams of the neutron-rich nuclei $^{129\ensuremath{-}132}\mathrm{Sn}$ and $^{133,134}\mathrm{Sb}$, their dipole-strength distributions have been measured. A sizable fraction of ``pygmy'' dipole strength, energetically located below the giant dipole resonance, is observed in all of these nuclei. A comparison with available pygmy resonance data in stable nuclei ($^{208}\mathrm{Pb}$ and $N=82$ isotones) indicates a trend of strength increasing with the proton-to-neutron asymmetry. On theoretical grounds, employing the RQRPA approach, a one-to-one correlation is found between the pygmy strength and parameters describing the density dependence of the nuclear symmetry energy, and in turn with the thicknesses of the neutron skins. On this basis, by using the experimental pygmy strength, parameters of the nuclear symmetry energy (${a}_{4}=32.0\ifmmode\pm\else\textpm\fi{}1.8$ MeV and ${p}_{o}=2.3\ifmmode\pm\else\textpm\fi{}0.8$ MeV/fm${}^{3}$) are deduced as well as neutron-skin thicknesses ${R}_{n}\ensuremath{-}{R}_{p}$ of $0.24\ifmmode\pm\else\textpm\fi{}0.04$ fm for $^{132}\mathrm{Sn}$ and of $0.18\ifmmode\pm\else\textpm\fi{}0.035$ fm for $^{208}\mathrm{Pb}$, both doubly magic nuclei. Astrophysical implications with regard to neutron stars are briefly addressed.

Dipole response ofSr88up to the neutron-separation energy

The dipole response of the magic $N=50$ nucleus $^{88}\mathrm{Sr}$ was studied in photon-scattering experiments at the electron linear accelerator ELBE with bremsstrahlung produced at kinetic electron energies of 9.0, 13.2, and 16.0 MeV. We identified 160 levels up to an excitation energy of 12 MeV. By using polarized photons linear polarizations of about 50 \ensuremath{\gamma} transitions were measured that enabled parity assignments to the corresponding states. In the energy range of 6--12 MeV we identified only one $M1$ transition; all other transitions have $E1$ character. Thus, $E1$ character was proven for 63% of the total dipole strength of the observed levels in the given energy range. Statistical methods were applied to estimate intensities of inelastic transitions and to correct the intensities of the ground-state transitions for their branching ratios. In this way we derived the photoabsorption cross section up to the neutron-separation energy. This cross section matches well the photoabsorption cross section obtained from $(\ensuremath{\gamma},n)$ data and thus provides information about the extension of the dipole-strength distribution toward energies below the neutron-separation energy. An enhancement of $E1$ strength at 6--11 MeV may be considered as an indication for a pygmy dipole resonance.

Low-Lying electric dipole transitions in tin isotopic chain within the RPA model

A nuclear structuremodel based on a finite rank approximation of Skyrme interaction is applied to calculate the distribution of dipole strength in tin isotopes. The model is based on the quasiparticle random phase approximation. The results obtained with the three types of parametrizations of the Skyrme forces (SLy4, SkM*, and SIII) are compared. The low-lying part of dipole strength distribution reveals the existence of a group of slightly collective states, and the corresponding E1 transition strength increases with the enlargement of neutron excess. The group is associated with the pygmy resonance.

Dipole strength distributions of the stable odd-massN=82isotonesLa139andPr141

The low-lying dipole strength distributions of the odd-mass isotopes {sup 139}La and {sup 141}Pr were studied in nuclear resonance fluorescence experiments using bremsstrahlung beams. Excited states were observed at excitation energies up to 4 MeV. Spectroscopic information was obtained on excitation energies, decay widths, decay branching ratios, and transition probabilities. The states belonging to the [[2{sup +}(multiply-in-circle sign)3{sup -}](multiply-in-circle sign)particle/hole] coupling were a special focus, and the results are compared with other stable odd-mass nuclei at or near the N=82 shell closure.

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.

GIANT DIPOLE RESONANCE IN DEFORMED NUCLEI: DEPENDENCE ON SKYRME FORCES

The giant dipole resonance (GDR) in deformed nuclei is analyzed using the self-consistent separable random-phase-approximation (SRPA) with Skyrme forces SkT6, SkM*, SLy6 and SkI3. The deformed nuclei 150 Nd and 238 U are used as representative rare-earth and actinide samples. Dependences of the dipole strength distributions on some basic characteristics of the Skyrme functional and nuclear matter properties (isoscalar and isovector effective masses, time-odd contributions) are discussed. Particular attention is paid to the fragmentation structure of the GDR strength which is shown to depend sensitively to spin-orbit intruder states with large angular momentum.

Dipole-strength distributions up to the particle-separation energies and photodissociation of Mo isotopes

Dipole-strength distributions in the nuclides 92 Mo, 98 Mo and 100 Mo have been investigated in photon-scattering experiments with bremsstrahlung at the superconducting electron accelerator ELBE of the Forschungszentrum Rossendorf. A simulation of γ cascades was performed in order to estimate the distribution of inelastic transitions to low-lying states and thus to deduce the primary dipole-strength distribution up to the neutron-separation energies. The absorption cross sections obtained connect smoothly to ( γ , n ) cross sections and give novel information about the low-energy tail of the Giant Dipole Resonance below the neutron-separation energies. The experimental cross sections are compared with predictions of a Quasiparticle-Random-Phase Approximation (QRPA) in a deformed basis. Photoactivation experiments were performed at various electron energies to study the 92 Mo( γ , n ), 92 Mo( γ , p ), 92 Mo( γ , α ) and 100 Mo( γ , n ) reactions. The deduced activation yields are compared with theoretical predictions.

Relativistic quasiparticle random-phase approximation description of isoscalar compression modes in open-shell nuclei in theA≈60mass region

Very recent inelastic $\alpha$-scattering data on the isoscalar monopole and dipole strength distributions in $^{56}$Fe, $^{58}$Ni, and $^{60}$Ni are analyzed in the relativistic quasiparticle random-phase approximation (RQRPA) with the DD-ME2 effective nuclear interaction (nuclear matter compression modulus K$_{nm}= 251$ MeV). In all three nuclei the calculation nicely reproduces the observed asymmetric shapes of the monopole strength, and the bimodal structure of the dipole strength distributions. The calculated centroid and mean energies are in very good qualitative agreement with the experimental values both for the monopole, and for the low- and high-energy components of the dipole transition strengths. It is noted, however, that while DD-ME2 reproduces in detail the excitation energies of the giant monopole resonances (GMR) in nuclei with $A \ge 90$, the theoretical centroids are systematically above the experimental values in lighter nuclei with $A \leq 60$. The latter can be reproduced with an effective interaction with a lower value of K$_{nm} \approx $ 230 MeV but, because of the asymmetric shapes and pronounced fragmentation of the monopole strength distributions, isoscalar GMR data in light nuclei cannot provide accurate estimates of the nuclear matter compression modulus.

Magnetic Dipole Strength and the T = 0 Proton–Neutron Residual Interaction

The impact of the isoscalar proton–neutron ( p n ) residual interaction on magnetic dipole strength distributions is investigated for the examples 46,48 Ti. Shell-model calculations with different interactions are performed, where either the full set of T = 0 two-body matrix elements (TBME) from the FPD6 effective interaction, a set of constant TBME, or no TBME at all are considered. The comparison with experimental data from high-resolution electron scattering reveals clear experimental signatures of the T = 0 p n interaction part.

Pygmy dipole strength close to particle-separation energies --The case of the Mo isotopes

The distribution of electromagnetic dipole strength in 92, 98, 100 Mo has been investigated by photon scattering using bremsstrahlung from the new ELBE facility. The experimental data for well separated nuclear resonances indicate a transition from a regular to a chaotic behaviour above 4 MeV of excitation energy. As the strength distributions follow a Porter-Thomas distribution much of the dipole strength is found in weak and in unresolved resonances appearing as fluctuating cross section. An analysis of this quasi-continuum - here applied to nuclear resonance fluorescence in a novel way - delivers dipole strength functions, which are combining smoothly to those obtained from (g,n)-data. Enhancements at 6.5 MeV and at ~9 MeV are linked to the pygmy dipole resonances postulated to occur in heavy nuclei.

Low-lying magnetic dipole strength distribution in the γ-soft even-even 130-136Ba

In this study the scissors mode 1+ states are systematically investigated within the rotational invariant Quasiparticle Random Phase Approximation (QRPA) for 130-136Ba isotopes. We consider the 1+ vibrations generated by the isovector spin-spin interactions and the isoscalar and isovector quadrupole-type separable forces restoring the broken symmetry by a deformed mean field according to A.A. Kuliev et al. (Int. J. Mod. Phys. E 9, 249 (2000)). It has been shown that the restoration of the broken rotational symmetry of the Hamiltonian essentially decreases the B(M1) value of the low-lying 1+ states and increases the collectivization of the scissors mode excitations in the spectroscopic energy region. The agreement between the calculated mean excitation energies as well as the summed B(M1) value of the scissors mode excitations and the available experimental data of 134Ba and 136Ba is rather good. A destructive interference between the orbit and spin part of the M1 strength has been found for barium isotopes near the shell closer. For all the nuclei under investigation, the low-lying M1 transitions have ΔK = 1 character as it is the case for the well-deformed nuclei.