Dipole Strength Function Research Articles

Low-energy limit of the radiative dipole strength in nuclei

We explain the low-energy anomaly reported in several experimental studies of the radiative dipole strength functions in medium-mass nuclei. These strength functions at very low $\ensuremath{\gamma}$ energies correspond to the $\ensuremath{\gamma}$ transitions between very close nuclear excited states in the quasicontinuum and attract an increasing interest because of their substantial astrophysical impact. We show that the low-energy enhancement of the strength functions in highly excited compound nuclei is explained by nucleonic transitions from the thermally unblocked single-quasiparticle states to the single-(quasi)particle continuum. The case of radiative dipole strength functions at the nuclear excitation energies typical for the thermal neutron capture is illustrated for ${}^{94,96,98}$Mo and ${}^{116,122}$Sn in comparison to available data.

Continuum dipole response near the threshold and the direct neutron capture cross section at astrophysical energies

We apply the continuum quasiparticle random phase approximation to calculate the direct neutron capture cross section relevant to the r-process nucleo-synthesis. The electric dipole strength function in an even-even n-rich nucleus is decomposed with respect to the channels of direct neutron decays. Using the detailed balance relation, the partial dipole strengths are converted to obtain the direct neutron-capture cross sections. Numerical examples are given for 142Sn.

Toroidal, compression and vortical dipole strengths in 124Sn

The toroidal, compression and vortical dipole strength functions in semi-magic 124Sn (and partly in doubly magic 100,132Sn) are analyzed within the random-phase-approximation method with the SkT6, SkI3, SLy6, SV-bas and SkM* Skyrme forces. The isoscalar (T = 0), isovector (T = 1) and electromagnetic (‘elm’) channels are considered. Both convection jc and magnetization jm nuclear currents are taken into account. The calculations basically confirm the previous results obtained for 208Pb with the force SLy6. In particular, it is shown that the vortical and toroidal strengths are dominated by jc in the T = 0 channel and by jm in the T = 1 and ‘elm’ channels. The compression strength is always determined by jc. It is also shown that the ‘elm’ strength (relevant for the (e,e′) reaction) is very similar to the T = 1 one. The toroidal mode resides in the region of the pygmy resonance. So, perhaps, this region embraces both irrotational (pygmy) and vortical (toroidal) flows.

Bound states of dipolar bosons in one-dimensional systems

We consider one-dimensional tubes containing bosonic polar molecules. The long-range dipole–dipole interactions act both within a single tube and between different tubes. We consider arbitrary values of the externally aligned dipole moments with respect to the symmetry axis of the tubes. The few-body structures in this geometry are determined as a function of polarization angles and dipole strength by using both essentially exact stochastic variational methods and the harmonic approximation. The main focus is on the three-, four- and five-body problems in two or more tubes. Our results indicate that in the weakly coupled limit the intertube interaction is similar to a zero-range term with a suitable rescaled strength. This allows us to address the corresponding many-body physics of the system by constructing a model where bound chains with one molecule in each tube are the effective degrees of freedom. This model can be mapped onto one-dimensional Hamiltonians for which exact solutions are known.

Ab Initio Study of Electroweak Responses of 4He

In this contribution, we discuss the electroweak responses of 4He based on a full four-body calculation. The wave function of the ground state is obtained accurately using an explicitly correlated basis. Four-body final states are expressed in a superposition of many basis functions including configurations which have 3+1 and 2+1+1 cluster partitions of four-nucleon system explicitly. The continuum is properly treated by taking the two approaches: one is the complex scaling method and the other is the microscopic R-matrix method. The calculated photoabsorption cross sections agree up to the rest energy of a pion. The spin–dipole strength function is also presented and its relationship between the spectrum of 4He is discussed.

Linear responses in time-dependent Hartree-Fock-Bogoliubov method with Gogny interaction

A numerical method to integrate the time-dependent Hartree-Fock Bogoliubov (TDHFB) equations with Gogny interaction is proposed. The feasibility of the TDHFB code is illustrated by the conservation of the energy, particle numbers, and center-of-mass in the small amplitude vibrations of oxygen 20. The TDHFB code is applied to the isoscalar quadrupole and/or isovector dipole vibrations in the linear (small amplitude) region in oxygen isotopes (masses A = 18,20,22 and 24), titanium isotopes (A = 44,50,52 and 54), neon isotope (A = 26), and magnesium isotopes (A = 24 and 34). The isoscalar quadrupole and isovector dipole strength functions are calculated from the expectation values of the isoscalar quadrupole and isovector dipole moments.

Investigation of dipole strength at the ELBE accelerator in Dresden-Rossendorf

Using the methods of cold neutron capture and photon scattering the electric dipole strength function and the level density of the nuclei 78Se and 196Pt are investigated. Considering that the deexcitation process could be described by the same strength functions one could describe both experiments in a statistical model code. The report shows the data analysis as well as a new very fast statistical code, which was used to get the complete strength information up to the neutron separation energy.

Renewed Database of GDR Parameters for Atomic Nuclei

Updated values of giant dipole resonance parameters with uncertainties are presented which were obtained by a chi-square fit of the theoretical photoabsorption cross sections to the experimental data. Renewed systematics for giant dipole resonance parameters are given. Different Lorentzian-type models of dipole strength functions are tested by comparison of the calculations with experimental data. It is demonstrated that closed-form approaches with asymmetric shape of the gamma strength provide the most reliable simple method for estimation of the γ-decay.

Strength Function in Continuum with a Square Integrable Basis

We present a new approach to describe the three-body continuum with a square integrable basis and show some examples to assess its efficiency. The formulation is done elegantly in the hyperspherical formalism and the tail behavior is appropriately corrected with use of the Green’s function. The efficiency of this approach is shown in a simple solvable problem by calculating the electric dipole strength function of a three-body system and comparing it to that obtained with the complex scaling method, which is widely used for calculating the strength function.

Experimental study of the electric dipole strength in the even Mo nuclei and its deformation dependence

Two methods based on bremsstrahlung were applied to the stable even Mo isotopes for the experimental determination of the photon strength function covering the high excitation energy range above 4 MeV with its increasing level density. Photon scattering was used up to the neutron separation energies ${S}_{n}$ and data up to the maximum of the isovector giant resonance (GDR) were obtained by photoactivation. After a proper correction for multistep processes the observed quasicontinuous spectra of scattered photons show a remarkably good match to the photon strengths derived from nuclear photoeffect data obtained previously by neutron detection and corrected in absolute scale by using the new activation results. The combined data form an excellent basis to derive a shape dependence of the $E1$ strength in the even Mo isotopes with increasing deviation from the $N=50$ neutron shell (i.e., with the impact of quadrupole deformation and triaxiality). The wide energy coverage of the data allows for a stringent assessment of the dipole sum rule and a test of a novel parametrization developed previously which is based on it. This parametrization for the electric dipole strength function in nuclei with $A>80$ deviates significantly from prescriptions generally used previously. In astrophysical network calculations it may help to quantify the role the p-process plays in cosmic nucleosynthesis. It also has impact on the accurate analysis of neutron capture data of importance for future nuclear energy systems and waste transmutation.

Photon strength function deduced from photon scattering and neutron capture

The dipole strength function of 78 Se and 196 Pt are investigated by two different experimental methods, capture of cold neutrons in 77 Se and 195 Pt and photon scattering experiments on 78 Se and 196 Pt. Considering the different ways of excitation, the strength function deduced from the results are expected to agree.The report shows the status of the data analysis and presents first preliminary results.

Time-dependent description for nuclear reaction dynamics in the continuum

We have recently developed time-dependent few-body approaches to describe reactions involving halo nuclei. In this report, we demonstrate usefulness of the time-dependent description taking two applications as examples: the fusion reaction of halo nuclei, and the dipole strength function of two-neutron halo nuclei.

Systematic Study of 9,10,11Li with the Tensor and Pairing Correlations

We make a systematic study of Li isotopes (A=9,10,11) in the tensor optimized shell model for 9Li and treat the additional valence neutrons in the cluster model approach by taking into account the Pauli-blocking effect caused by the tensor and pairing correlations. We describe the tensor correlations in 9Li fully in the tensor-optimized shell model, where the variation of the size parameters of the single particle orbits is essential for getting strong tensor correlations. We have shown in our previous study that in $^{10,11}$Li the tensor and pairing correlations in 9Li are Pauli-blocked by additional valence neutrons, which make the p-shell configurations pushed up in energy. As a result, the $s^2$ valence neutron component increases to reveal the halo structure of 11Li and the inversion phenomenon of the single particle spectrum in 10Li arises. Following the previous study, we demonstrate the reliability of our framework by performing a detailed systematic analysis of the structures of $^{9,10,11}$Li, such as the charge radius, the spatial correlation of halo neutrons of 11Li and the electromagnetic properties of Li isotopes. The detailed effects of the Pauli-blocking on the spectroscopic properties of $^{10,11}$Li are also discussed. It is found that the blocking acts strongly for the 11Li ground state rather than for 10Li and for the dipole excited states of 11Li, which is mainly caused by the interplay between the tensor correlation in 9Li and the halo neutrons. The results obtained in these analyses clearly show that the inert core assumption of 9Li is not realistic to explain the anomalous structures observed in $^{10,11}$Li. For the dipole excitation spectrum of 11Li, the effect of the final state interactions is discussed in terms of the dipole strength function.

Equilibrium polymerization and gas-liquid critical behavior in the Stockmayer fluid

We develop a simple theory explaining the dependence of the gas-liquid critical point in the Stockmayer fluid on dipole strength. The theory is based on the Flory-Huggins lattice description for polymer systems in conjunction with a transfer matrix model for isolated chains of reversibly assembled dipolar particles. We find that the shift of the critical point as a function of dipole strength, which originally was found in computer simulation, strongly resembles the critical point shift as a function of chain length in ordinary linear polymer systems. In particular, the decrease of the critical density with increasing dipole strength is a consequence of the existence of reversible chains near criticality. In addition we report simulation results for gas-liquid critical points well above the limiting dipole strength found previously.

Dielectric properties and the ferroelectric transition of the Stockmayer-fluid via computer simulation

We report extensive molecular dynamics simulations of the Stockmayer fluid near the transition to fluid ferroelectric ordering monitored via the divergence of the static dielectric constant. The dependence of the transition on dipole strength, μ2, temperature, T, and system size is investigated. The results are compared to a large number of previous simulations in the literature. We find that the effective transition temperature T/(ρ μ2) ≈ 0.19 for ρ = 0.8 is a good estimate in the range of the other parameter values considered here. In addition, we study the local field in relation to the structure and dynamics of the liquid phase as a function of temperature, dipole strength and polarizability.

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.

Self-consistent description of multipole strength in exotic nuclei: Method

We use the canonical Hartree-Fock-Bogoliubov basis to implement a completely self-consistent quasiparticle-random-phase approximation with arbitrary Skyrme energy density functionals and density-dependent pairing functionals. The point of the approach is to accurately describe multipole strength functions in spherical even-even nuclei, including weakly-bound drip-line systems. We describe the method and carefully test its accuracy, particularly in handling spurious modes. To illustrate our approach, we calculate isoscalar and isovector monopole, dipole, and quadrupole strength functions in several Sn isotopes, both in the stable region and at the drip lines.

Pygmy dipole resonances as a manifestation of the structure of the neutron-rich nuclei

Dipole excitations in neutron-rich nuclei below the neutron threshold are investigated. The method is based on Hartree-Fock-Bogoliubov (HFB) and Quasiparticle-Phonon Model (QPM) theory. Of our special interest are the properties of the low-lying 1−Pygmy Resonance and the two-phonon quadrupole-octupole 1− states in Sn-isotopes including exploratory investigations for the experimentally unknown mass regions. In particular we investigate the evolution of the dipole strength function with the neutron excess. The use of HFB mean-field potentials and s.p. energies is found to provide a reliable extrapolation into the region off stability.

Pygmy dipole resonances as a manifestation of the structure of the neutron-rich nuclei

Dipole excitations in neutron-rich nuclei below the neutron threshold are investigated. The method is based on Hartree-Fock-Bogoliubov (HFB) and Quasiparticle-Phonon Model (QPM) theory. Of our special interest are the properties of the low-lying 1 − Pygmy Resonance and the two-phonon quadrupole-octupole 1 − states in Sn-isotopes including exploratory investigations for the experimentally unknown mass regions. In particular we investigate the evolution of the dipole strength function with the neutron excess. The use of HFB mean-field potentials and s.p. energies is found to provide a reliable extrapolation into the region off stability.

Cross section measurements of the181Ta(γ,n)180Tareaction near neutron threshold and thep-process nucleosynthesis

New measurements of the photoneutron reaction on ${}^{181}\mathrm{Ta}$ have been conducted with the AIST-LCS (laser Compton scattering) beam in the $7.8\ensuremath{\lesssim}E[\mathrm{MeV}]\ensuremath{\lesssim}12$ energy range. The major advantage of the present $\ensuremath{\gamma}$-ray experiment is its intense peaking in the energy window of astrophysical interest, i.e., close to the neutron threshold. Details on photon beams from the laser Compton scattering, neutron counting, and experimental determination of the ${}^{181}\mathrm{Ta}$ photoneutron cross section are given. The present experimental data are in good agreement with the IAEA evaluation. Reaction rate calculations in the Hauser-Feshbach statistical model are performed and confronted with the experimental data. The data provide constraints on the low-energy tail of the dipole strength function. It is found that among the three different models for the $E1$-strength considered, only the microscopic quasiparticle random phase approximation model can reproduce the extra strength observed in the ${}^{181}\mathrm{Ta}(\ensuremath{\gamma}{,n)}^{180}\mathrm{Ta}$ reaction at energies of about 8.5 MeV. Such an experiment helps to improve the determination of the corresponding stellar photodisintegration rate of ${}^{181}\mathrm{Ta}$ which directly influences the p-process production of ${}^{180}\mathrm{Ta}.$