Giant Dipole Resonance Width Research Articles

Impact of magnetic field on the giant dipole resonance ofCa40using an extended quantum molecular dynamics model

By taking into account the magnetic field in the extended quantum molecular dynamics model, we analyzed its effects on giant dipole resonance (GDR) by studying the responses and strengths of the dipole moments. The selected system is the $^{40}\mathrm{Ca}$ nucleus which is excited through the Coulomb interaction by $^{16}\mathrm{O}$. The particle acceleration term in the Li\'enard-Wiechert potential is discussed which, however, has small impact on the magnetic field. The peak energy, strength, and width of GDR, temperature, and angular momentum of $^{40}\mathrm{Ca}$ as a function of beam energy are investigated. It is found that the magnetic field enhances the peak energy, strength, and width of GDR which is not only due to the temperature effects, but also due to the enhancement of the angular momentum of nucleus. At beam energy $E >$ 200 MeV/nucleon, the magnetic field maintains a constant value for the strength of GDR. The paper sheds light on examining important roles of the magnetic field on the nuclear structure in low-intermediate energy heavy-ion collisions.

Systematical studies of theE1photon strength functions combining the Skyrme-Hartree-Fock-Bogoliubov plus quasiparticle random-phase approximation model and experimental giant dipole resonance properties

Valuable theoretical predictions of nuclear dipole excitations in the whole nuclear chart are of great interest for different applications, including in particular nuclear astrophysics. We present here the systematic study of the electric-dipole $(E1)$ photon strength functions combining the microscopic Hartree-Fock-Bogoliubov plus quasiparticle random-phase approximation (HFB $+$ QRPA) model and the parametrizations constrained by the available experimental giant dipole resonance (GDR) data. For about 10 000 nuclei with $8\ensuremath{\le}\mathrm{Z}\ensuremath{\le}124$ lying between the proton and the neutron drip-lines on nuclear chart, the particle-hole (ph) strength distributions are computed using the HFB + QRPA model under the assumption of spherical symmetry and making use of the BSk27 Skyrme effective interaction derived from the most accurate HFB mass model (HFB-27) so far achieved. Large-scale calculations of the BSk27 + QRPA $E1$ photon strength functions are performed in the framework of a specific folding procedure describing the damping of nuclear collective motion empirically. In particular, three phenomenological improvements are considered in this folding procedure. First, two interference factors are introduced and adjusted to reproduce at best the available experimental GDR data. Second, an empirical expression accounting for the deformation effect is applied to describe the peak splitting of the strength function. Third, the width of the strength function is corrected by a temperature-dependent term, which effectively increases the deexcitation photon strength function at low energy. The theoretical $E1$ photon strength functions as well as the extracted GDR peaks and widths are comprehensively compared with available experimental data. A relatively good agreement with data indicates the reliability of the present calculations. Eventually, the astrophysical rates of $(n,\ensuremath{\gamma})$ reactions for all the 10 000 nuclei with $8\ensuremath{\le}Z\ensuremath{\le}124$ lying between the proton and the neutron drip lines are estimated using the present $E1$ photon strength functions. The resulting reaction rates are compared with the previous BSk7 + QRPA results as well as the Gogny-HFB + QRPA predictions based on the D1M interaction.

No signature of the saturation of giant dipole resonance width in medium-mass nuclei

An experimental study on the temperature ($T$) dependence of giant dipole resonance (GDR) width was performed for the medium mass nucleus $^{74}\mathrm{Kr}$ in the range of $T\ensuremath{\approx}2--2.5$ MeV at an average angular momentum of $26\ensuremath{\hbar}$ using the $^{16}\mathrm{O}+^{58}\mathrm{Ni}$ fusion reaction. The emitted high-energy $\ensuremath{\gamma}$ rays and evaporated neutrons were measured in coincidence with low-energy discrete $\ensuremath{\gamma}$-ray multiplicities. The GDR parameters, nuclear level density parameter, and nuclear temperature were determined by the statistical model analysis of the high-energy $\ensuremath{\gamma}$-ray spectra as well as evaporated neutron spectra. The measured GDR width is found to increase monotonically with temperature, in contradiction with the recent observation of the width saturation in $^{88}\mathrm{Mo}$. Comparisons of the measured data with predictions of the adiabatic thermal shape fluctuation model and its refined version, the critical temperature included fluctuation model, are presented and discussed.

The description of giant dipole resonance key parameters with multitask neural networks

Giant dipole resonance (GDR) is one of the fundamental collective excitation modes in nucleus. Continuous efforts have been made to the evaluation of GDR key parameters in different nuclear data libraries. We introduced multitask learning (MTL) approach to learn and reproduce the evaluated experimental data of GDR key parameters, including both GDR energies and widths. Compared to the theoretical GDR parameters in RIPL-3 library, the accuracies of MTL approach are almost doubled for 129 nuclei with experimental data. The significant improvement is largely due to the right classification of unimodal nuclei and bimodal nuclei by the classification neural network. Based on the good performance of the neural network approach, an extrapolation to 79 nuclei around the β-stability line without experimental data is made, which provides an important reference to future experiments and data evaluations. The successful application of MTL approach in this work further proofs the feasibility of studying multi-output physical problems with multitask neural network in nuclear physics domain.

Effect of high angular momentum on η/s of nuclear matter

The shear viscosity ($\ensuremath{\eta}$) of nuclear matter is investigated in different nuclei (nuclear mass $A\ensuremath{\approx}59--194$) using experimental giant dipole resonance (GDR) width ($\mathrm{\ensuremath{\Gamma}}$) at high angular momenta ($J=12--54$ $\ensuremath{\hbar}$) and temperatures ($T=1.2--2.1$ MeV) collected from the existing literature. $\ensuremath{\eta}$, calculated from $\mathrm{\ensuremath{\Gamma}}$, is found to increase with $T$ and $J$. We show that critical temperature included fluctuation model (CTFM) successfully describes $J$-induced $\ensuremath{\eta}$ even beyond critical angular momentum ${J}_{c}$ at different values of $T$. However, the Fermi liquid drop model (FLDM) could not explain the data at higher angular momenta. We propose the addition of a $J$-dependent term with the FLDM $\ensuremath{\eta}$ to improve the prediction at such high-$J$ region. The $\ensuremath{\eta}/s$ ratio, highly important for measuring fluidity, is calculated using $\ensuremath{\eta}$ and the entropy density $s$. The latter is estimated using the Fermi gas formula. Interestingly, the experimental value of the ratio is independent of $J$ and $A$ and comes within 2.6--6.0 $\ensuremath{\hbar}/4\ensuremath{\pi}{k}_{\mathrm{B}}$, which is very close to those of a partonic system like quark gluon plasma at high temperature.

Nuclear Collective Dynamics in Transport Model With the Lattice Hamiltonian Method

We review the recent progress on studying the nuclear collective dynamics by solving the Boltzmann-Uehling-Uhlenbeck (BUU) equation with the lattice Hamiltonian method treating the collision term by the full-ensemble stochastic collision approach. This lattice BUU (LBUU) method has recently been developed and implemented in a GPU parallel computing technique, and achieves a rather stable nuclear ground-state evolution and high accuracy in evaluating the nucleon-nucleon (NN) collision term. This new LBUU method has been applied to investigate the nuclear isoscalar giant monopole resonances and isovector giant dipole resonances. While the calculations with the LBUU method without the NN collision term (i.e., the lattice Hamiltonian Vlasov method) describe reasonably the excitation energies of nuclear giant resonances, the full LBUU calculations can well reproduce the width of the giant dipole resonance of $^{208}$Pb by including a collisional damping from NN scattering. The observed strong correlation between the width of nuclear giant dipole resonance and the NN elastic cross section suggests that the NN elastic scattering plays an important role in nuclear collective dynamics, and the width of nuclear giant dipole resonance provides a good probe of the in-medium NN elastic cross section.

Constraining the in-medium nucleon-nucleon cross section from the width of nuclear giant dipole resonance

We develop a new lattice Hamiltonian method for solving the Boltzmann-Uehling-Uhlenbeck (BUU) equation. Adopting the stochastic approach to treat the collision term and using the GPU parallel computing to carry out the calculations allows for a rather high accuracy in evaluating the collision term, especially its Pauli blocking, leading thus to a new level of precision in solving the BUU equation. Applying this lattice BUU method to study the width of giant dipole resonance (GDR) in nuclei, where the accurate treatment of the collision term is crucial, we find that the obtained GDR width of 208Pb shows a strong dependence on the in-medium nucleon-nucleon cross section σNN⁎. A very large medium reduction of σNN⁎ is needed to reproduce the measured value of the GDR width of 208Pb at the Research Center for Nuclear Physics in Osaka, Japan.

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.

Study of giant dipole resonance in hot rotating light mass nucleus 31P

An exclusive systematic study of the giant dipole resonance (GDR) parameters has been performed in very light mass nucleus P31 in the temperature range of ∼0.8–2.1MeV and average angular momentum of ∼11–16ħ. The high-energy γ rays from the decay of the GDR, evaporated neutrons and γ-ray multiplicities have been measured. The angular distribution of high-energy γ rays has also been measured at Ebeam=42MeV. The GDR parameters, nuclear level density parameter and nuclear temperature were precisely determined by simultaneous statistical model analysis of high-energy γ ray and evaporated neutron spectra. It is observed that the measured width remains roughly constant up to a temperature of ∼1.6MeV. Moreover, the thermal pairing plays no role in describing the GDR width in this open-shell light nucleus at the above-mentioned temperatures and angular momenta. The present measurements provide an excellent platform to extend the applicability of the existing theoretical models down to the very light mass nuclei.

Giant dipole resonance and shape transitions in hot and rotating Mo88

The giant dipole resonance (GDR) observables are calculated within the thermal shape fluctuation model by considering the probability distributions of different angular momentum ($I$) and temperature ($T$) values estimated recently in the deexcitation process of the compound nucleus $^{88}\mathrm{Mo}$. These results are found to be very similar to the results obtained with the average $T$ (${T}_{\mathrm{ave}}$) and average $I$ (${I}_{\mathrm{ave}}$) corresponding to those distributions. The shape transitions in $^{88}\mathrm{Mo}$ at different $T$ and $I$ are also studied through the free energy surfaces calculated within the microscopic-macroscopic approach. The deformation of $^{88}\mathrm{Mo}$ is found to increase considerably with $T$ and $I$, leading to the Jacobi shape transition at $I\ensuremath{\sim}50\phantom{\rule{0.28em}{0ex}}\ensuremath{\hbar}$. The combined effect of increasing deformation, larger fluctuations at higher $T$, and larger Coriolis splitting of GDR components at higher $I$, leads to a rapid increase in the GDR width.

Giant dipole resonance studies in Ba isotopes at E/A≈5 MeV

Exclusive measurements of high energy $\gamma$-rays are performed in $\rm ^{124}Ba$ and $\rm ^{136}Ba$ at the same excitation energy ($\sim$ 49 MeV), to study properties of the giant dipole resonance (GDR) over a wider $N/Z$ range. The high energy $\gamma$-rays are measured in coincidence with the multiplicity of low energy $\gamma$-rays to disentangle the effect of temperature ($T$) and angular momentum ($J$). The GDR parameters are extracted employing a simulated Monte Carlo statistical model analysis. The observed $\gamma$-ray spectra of $\rm ^{124}Ba$ can be explained with prolate deformation, whereas a single component Lorentzian function which corresponds to a spherical shape could explain the $\gamma$-ray spectra from $\rm ^{136}Ba$. The observed GDR width in $\rm ^{136}Ba$ is narrower compared to that of $\rm ^{124}Ba$. The statistical model best fit GDR cross sections are found to be in good agreement with the thermal shape fluctuation model (TSFM) calculations. Further, it is shown that the variation of GDR width with $T$ is well reproduced by the TSFM calculations over the temperature range of 1.1--1.7MeV.

Comment on “Thermal shape fluctuation model study of the giant dipole resonance in Gd152 ”

A recent paper [A. K. Rhine Kumar and P. Arumugam, Phys. Rev. C 92, 044314 (2015)] presented calculations of the giant dipole resonance width and $\ensuremath{\gamma}$-ray absorption cross sections for $^{152}\mathrm{Gd}$ at various temperatures and angular momenta and compared these with the experimental data. In the comparison of the cross sections, the authors used the linearized representations of the experimental spectra which actually represent the absorption cross sections divided by the $\ensuremath{\gamma}$-ray energy. In this Comment we make the comparison with the appropriate absorption cross sections derived from the data. The comparison shows a reasonable agreement if the higher value of the dipole-dipole interaction parameter, mentioned in the paper, is used in the calculation.

Temperature dependence of the giant dipole resonance width inGd152

To investigate the dependence of giant dipole resonance (GDR) width on temperature $(T)$ and angular momentum $(J)$, high energy $\ensuremath{\gamma}$-ray spectra were measured in the reaction $^{28}\mathrm{Si}+^{124}\mathrm{Sn}$ at ${E}_{^{28}\mathrm{Si}}=135$ MeV. The $J$ information was deduced from multiplicity of low-energy $\ensuremath{\gamma}$ rays. The GDR parameters, namely, the centroid energy and width are extracted using statistical model analysis. The observed variation of the GDR width for $T\ensuremath{\sim}1.2$\char21{}1.37 MeV and $J\ensuremath{\sim}20\ensuremath{\hbar}$\char21{}$40\ensuremath{\hbar}$ is consistent with the universal scaling given by Kusnezov et al., which is applicable in the liquid-drop regime. The GDR input cross sections extracted from the statistical model best fits are compared with thermal shape fluctuation model (TSFM) calculations and are found to be in good agreement. The TSFM calculations predominantly favor the noncollective oblate shape, while the statistical model fit with both prolate and oblate shapes describes the data. The present data together with earlier measurements indicate a very slow variation of the GDR width for $T\ensuremath{\sim}1.2$ to 1.5 MeV. The observed trend is well explained by the TSFM calculations, although the calculated values are $\ensuremath{\sim}4$%\char21{}13% higher than the data.

Giant dipole resonance in hot rotating nuclei

Over the last several decades, extensive experimental and theoretical work has been done on the giant dipole resonance (GDR) in excited nuclei covering a wide range of temperature (T), angular momentum (J) and nuclear mass. A reasonable stability of the GDR centroid energy and an increase of the GDR width with T (in the range $ \sim 1 - 3$ MeV) and J are the two well-established results. Some experiments have indicated the saturation of the GDR width at high T . The gradual disappearance of the GDR vibration at much higher T has been observed. Experiments on the Jacobi transition and the GDR built on superdeformed shapes at high rotational frequencies have been reported in a few cases. Theoretical calculations on the damping of the collective dipole vibration, characterised by the GDR width, have been carried out within various models such as the thermal shape fluctuation model and the phonon damping model. These models offer different interpretations of the variation of the GDR width with T and J and have met with varying degrees of success in explaining the experimental data. In this review, the present experimental and theoretical status in this field will be discussed along with the future outlook. The interesting phenomenon of the pre-equilibrium GDR excitation in nuclear reactions will be briefly addressed.

Finite amplitude method applied to the giant dipole resonance in heavy rare-earth nuclei

Background: The quasiparticle random phase approximation (QRPA), within the framework of nuclear density functional theory (DFT), has been a standard tool to access the collective excitations of atomic nuclei. Recently, the finite amplitude method (FAM) was developed in order to perform the QRPA calculations efficiently without any truncation on the two-quasiparticle model space.Purpose: We discuss the nuclear giant dipole resonance (GDR) in heavy rare-earth isotopes, for which the conventional matrix diagonalization of the QRPA is numerically demanding. A role of the Thomas-Reiche-Kuhn (TRK) sum rule enhancement factor, connected to the isovector effective mass, is also investigated.Methods: The electric dipole photoabsorption cross section was calculated within a parallelized FAM-QRPA scheme. We employed the Skyrme energy density functional self-consistently in the DFT calculation for the ground states and FAM-QRPA calculation for the excitations.Results: The mean GDR frequency and width are mostly reproduced with the FAM-QRPA, when compared to experimental data, although some deficiency is observed with isotopes heavier than erbium. A role of the TRK enhancement factor in actual GDR strength is clearly shown: its increment leads to a shift of the GDR strength to higher-energy region, without a significant change in the transition amplitudes.Conclusions: The newly developed FAM-QRPA scheme shows remarkable efficiency, which enables one to perform systematic analysis of GDR for heavy rare-earth nuclei. The theoretical deficiency of the photoabsorption cross section could not be improved by only adjusting the TRK enhancement factor, suggesting the necessity of an approach beyond self-consistent QRPA and/or a more systematic optimization of the energy density functional (EDF) parameters.

Thermal shape fluctuation model study of the giant dipole resonance inGd152

We have studied the giant dipole resonance (GDR) in the hot and rotating nucleus $^{152}\mathrm{Gd}$ within the framework of the thermal shape fluctuation model (TSFM) built on the microscopic-macroscopic calculations of the free energies with a macroscopic approach for the GDR. Our results for GDR cross sections are in good agreement with the experimental values except for a component peaking around 17 MeV, where the data has large uncertainties. Such a component is beyond our description which properly takes care of the splitting of GDR components due to the deformation and Coriolis effects. Around 17 MeV lies the half maximum in experimental cross sections, and hence the extracted GDR widths and deformations (estimated from these widths) turn out to be overestimated and less reliable. Reproducing these widths with empirical formulas could conceal the information contained in the cross sections. Fully microscopic GDR calculations and a more careful look at the data could be useful to understand the GDR component around 17 MeV. We also discuss the occurrence of $\ensuremath{\gamma}$ softness in the free energy surfaces of $^{152}\mathrm{Gd}$ and its role on GDR.

Giant dipole resonance built on hot rotating nuclei produced during evaporation of light particles from theMo88compound nucleus

High-energy giant dipole resonance (GDR) γ rays were measured following the decay of the hot, rotating compound nucleus of Mo88, produced at excitation energies of 124 and 261 MeV. The reaction Ti48 + Ca40 at 300 and 600 MeV bombarding energies has been used. The data were analyzed using the statistical model Monte Carlo code gemini++. It allowed extracting the giant dipole resonance parameters by fitting the high-energy γ-ray spectra. The extracted GDR widths were compared with the available data at lower excitation energy and with theoretical predictions based on (i) The Lublin-Strasbourg drop macroscopic model, supplemented with thermal shape fluctuations analysis, and (ii) The phonon damping model. The theoretical predictions were convoluted with the population matrices of evaporated nuclei from the statistical model gemini++. Also a comparison with the results of a phenomenological expression based on the existing systematics, mainly for lower temperature data, is presented and discussed. A possible onset of a saturation of the GDR width was observed around T=3 MeV.2 MoreReceived 27 February 2015Revised 16 April 2015DOI:https://doi.org/10.1103/PhysRevC.91.054313©2015 American Physical Society

Thermal pairing and giant dipole resonance in highly excited nuclei

Recent results are reported showing the effects of thermal pairing in highly excited nuclei. It is demonstrated that thermal pairing included in the phonon damping model (PDM) is responsible for the nearly constant width of the giant dipole resonance (GDR) at low temperature T < 1 MeV. It is also shown that the enhancement observed in the recent experimentally extracted nuclear level densities in 104Pd at low excitation energy and various angular momenta is the first experimental evidence of the pairing reentrance in finite (hot rotating) nuclei. In the study of GDR in highly excited nuclei, the PDM has been extended to include finite angular momentum. The results of calculations within the PDM are found in excellent agreement with the latest experimental data of GDR in the compound nucleus 88Mo. Finally, an exact expression is derived to calculate the shear viscosity η as a function of T in finite nuclei directly from the GDR width and energy at zero and finite T. Based on this result, the values η/s of specific shear viscosity in several medium and heavy nuclei were calculated and found to decrease with increasing T to reach (1.3 – 4) × ℏ/(4πkB) at T = 5 MeV, that is almost the same value obtained for quark-gluon-plasma at T > 170 MeV.

Spin gated GDR widths at moderate temperatures

We present the evolution of giant dipole resonance (GDR) width as a function of angular momentum in the compound nucleus 144 Sm in the temperature range of 1.5-2.0 MeV. The high energy γ rays emitted from the decay of excited 144 Sm were measured using large NaI detector in coincidence with 4π sum spin spectrometer. GDR widths were found to comply with thermal shape fluctuation model in this temperature range over a wide range of spin. Experimental widths tend to increase rapidly at high angular momentum values.

Pairing effect in the thermal shape-fluctuation model on the width of the giant dipole resonance

We present an approach that includes temperature-dependent shell effects and fluctuations of the pairing field in the thermal shape fluctuation model (TSFM). We apply this approach to study the width of giant dipole resonance (GDR) in $^{97}$Tc, $^{120}$Sn and $^{208}$Pb. Our results demonstrate that the TSFM that includes pairing fluctuations can explain the recently observed quenching in the GDR width. We also show that to validate pairing prescriptions and the parameters involved, we require more and precise data.