Giant Dipole Resonance Width in near-Sn Nuclei at Low Temperature and High Angular Momentum
Srijit Bhattacharya, S. Mukhopadhyay, Deepak Pandit, Surajit Pal, A. De, S. Bhattacharya, C. Bhattacharya, K. Banerjee, S. Kundu, T. K. Rana, A. Dey, G. Mukherj… 展开作者
Srijit Bhattacharya, S. Mukhopadhyay, Deepak Pandit, Surajit Pal, A. De, S. Bhattacharya, C. Bhattacharya, K. Banerjee, S. Kundu, T. K. Rana, A. Dey, G. Mukherjee, T. Ghosh, D. Gupta, S. R. Banerjee
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19 pages, 10 figures, Submitted to Physics Review C
High energy gamma-rays in coincidence with low energy yrast gamma-rays have been measured from 113Sb, at excitation energies of 109 and 122 MeV, formed by bombarding 20Ne on 93Nb at projectile energies of 145 and 160 MeV respectively to study the role of angular momentum (J) and temperature (T) over Giant Dipole Resonance (GDR) width. The maximum populated angular momenta for fusion were 67hbar and 73hbar respectively for the above-mentioned beam energies. The high energy photons were detected using a Large Area Modular BaF2 Detector Array (LAMBDA) along with a 24-element multiplicity filter. After pre-equilibrium corrections, the excitation energy E* was averaged over the decay steps of the compound nucleus (CN). The average values of temperature, angular momentum, CN mass etc. have been calculated by the statistical model code CASCADE. Using those average values, results show the systematic increase of GDR width with T which is consistent with Kusnezov parametrization and the Thermal Shape Fluctuation Model. The rise of GDR width with temperature also supports the assumptions of adiabatic coupling in the Thermal Shape Fluctuation Model. But the GDR widths and corresponding reduced plots with J are not consistent with the theoretical model at high spins.
The semi-magic nuclei Ba-138, Ce-140, and Sm-144 have been investigated in photon scattering experiments up to an excitation energy of about 10 MeV. The distribution of the electric dipole strength shows a resonance like structure at energies between 5.5 and 8 MeV exhausting up to 1% of the isovector E1 Energy Weighted Sum Rule.
The strength distribution of the isoscalar giant dipole resonance (ISGDR) in $^{58}$Ni has been obtained over the energy range 10.5--49.5 MeV via extreme forward angle scattering (including 0$^{\circ}$) of 386 MeV $α$ particles. We observe a ``bi-modal'' ${E1}$ strength distribution for the first time in an A $<$ 90 nucleus. The observed ISGDR strength distribution is in good agreement with the predictions of a recent QRPA calculation.
On the basis of new photon scattering measurements and a reevaluation of average neutron resonance capture data we investigate how well Lorentzians adjusted to photo-neutron data in the giant dipole resonances give a good description of the photon strength also below the neutron threshold. If deformation effects are properly taken into account this is verified down to about 5 MeV for various nuclei with A>80 such that the previously employed differentiation between deformed and non-deformed nuclei is no longer necessary.
The isoscalar giant dipole resonance (ISGDR) has been investigated in 208Pb using inelastic scattering of 400 MeV alpha particles at forward angles, including 0deg. Using the superior capabilities of the Grand Raiden spectrometer, it has been possible to obtain spectra devoid of any "instrumental" background. The ISGDR strength distribution has been extracted from a multipole-composition of the observed spectra. The implication of these results on the experimental value of nuclear incompressibility are discussed.
Giant Electric Dipole Resonance (GDR) parameters for gamma decay to excited states with finite spin and temperature are compiled. Over 100 original works have been reviewed and from some 70 of which more than 300 parameter sets of hot GDR parameters for different isotopes, excitation energies, and spin regions have been extracted. All parameter sets have been brought onto a common footing by calculating the equivalent Lorentzian parameters. The current compilation is complementary to an earlier compilation by Samuel S. Dietrich and Barry L. Berman (At. Data Nucl. Data Tables 38(1988)199-338) o…
The expression for polarized electric dipole moment of well-deformed reflection asymmetric nuclei is obtained in the framework of liquid-drop model in the case of geometrically similar proton and neutron surfaces. The expression for polarized electric dipole moment consists of the first and second orders terms. It is shown that the second-order correction terms of the polarized electric dipole moment are important for well-deformed nuclei.
High resolution experimental data has been obtained for the 40,42,44,48Ca(3He,t)Sc charge exchange reaction at 420 MeV beam energy, which favors the spin-isospin excitations. The measured angular distributions were analyzed for each state separately, and the relative spin dipole strength has been extracted for the first time. The low-lying spin-dipole strength distribution in 40Sc shows some interesting periodic gross feature. It resembles to a soft, dumped multi-phonon vibrational band with $\hbarω$= 1.8 MeV, which might be associated to pairing vibrations around $^{40}$Ca.
The remaining uncertainties of isovector nuclear interactions call for reliable experimental measurements of isovector probes in finite nuclei. Based on the Bayesian analysis, although the neutron-skin thickness data or the isovector giant dipole resonance data in $^{208}$Pb can constrain only one isovector interaction parameter, correlations between other parameters are built. Using combined data of both the neutron-skin thickness and the isovector giant dipole resonance helps to constrain significantly all isovector interaction parameters, thus serves as a useful way in the future analysis.
In conformity to new findings about the widespread occurrence of triaxiality arguments are given in favor of a description of the giant dipole resonance in heavy nuclei by the sum of three Lorentzians. This TLO parameterization allows a strict use of resonance widths Γ in accordance to the theoretically founded power law relation to the resonance energy. No additional variation of Γ with the photon energy and no violation of the sum rule are necessary to obtain a good agreement to nuclear photo-effect, photon scattering and radiative capture data. Photon strength other than E1 has a small effe…
The excitation and subsequent proton decay of the isoscalar giant dipole resonance (ISGDR) in $^{208}$Pb have been investigated via the $^{208}$Pb($α, α^{\prime}p)^{207}$Tl reaction at 400 MeV. Excitation of the ISGDR has been identified by the difference-of-spectra method. The enhancement of the ISGDR strength at high excitation energies observed in the multipole-decomposition-analysis of the singles $^{208}$Pb($α,α^{\prime}$) spectra is not present in the excitation energy spectrum obtained in coincidence measurement. The partial branching ratios for direct proton decay of ISGDR to low-lying…
The systematics of the giant dipole resonance (GDR) widths in hot and rotating nuclei are studied in terms of temperature T, angular momentum J and mass A. The different experimental data in the temperature range of 1 - 2 MeV have been compared with the thermal shape fluctuation model (TSFM) in the liquid drop formalism using a modified approach to estimate the average values of T, J and A in the decay of the compound nucleus. The values of the ground state GDR widths have been extracted from the TSFM parametrization in the liquid drop limit for the corrected T, J and A for a given system and …
The systematic evolution of the giant dipole resonance (GDR) width in the temperature region of 0.9 ~ 1.4 MeV has been measured experimentally for 119Sb using alpha induced fusion reaction and employing the LAMBDA high energy photon spectrometer. The temperatures have been precisely determined by simultaneously extracting the vital level density parameter from the neutron evaporation spectrum and the angular momentum from gamma multiplicity filter using a realistic approach. The systematic trend of the data seems to disagree with the thermal shape fluctuation model (TSFM). The model predicts t…
The development of nuclear shapes under the extreme conditions of high spin and/or temperature is examined. Scaling properties are used to demonstrate universal properties of both thermal expectation values of nuclear shapes as well as the minima of the free energy, which can be used to understand the Jacobi transition. A universal correlation between the width of the giant dipole resonance and quadrupole deformation is found, providing a novel probe to measure the nuclear deformation in hot nuclei.
The thermal pairing gap obtained by embedding the exact solutions of the pairing problem into the canonical ensemble is employed to calculate the width and strength function of the giant dipole resonance (GDR) within the phonon damping model. The results of calculations describe reasonably well the data for the GDR width as well as the GDR linearized strength function, recently obtained for $^{201}$Tl in the temperature region between 0.8 and 1.2 MeV, which other approaches that neglect the effect of non-vanishing thermal pairing fail to describe.
We present an ab-initio calculation of the giant dipole resonance in 16O based on a nucleon-nucleon (NN) interaction from chiral effective field theory that reproduces NN scattering data with high accuracy. By merging the Lorentz integral transform and the coupled-cluster methods, we extend the previous theoretical limits for break-up observables in light nuclei with mass numbers (A<=7), and address the collective giant dipole resonance of 16O. We successfully benchmark the new approach against virtually exact results from the hyper-spherical harmonics method in 4He. Our results for 16O reprod…
Updated values and corresponding uncertainties of Isovector Giant Dipole Resonance (GDR) parameters which are obtained by the least-squares fitting of theoretical photoabsorption cross sections to experimental data are presented. The theoretical photoabsorption cross sections are taken as a sum of the components corresponding to the excitation of the GDR and quasideuteron photodisintegration. The current compilation is an extension and improvement of the earlier compilations of Lorentzian parameters for ground-state photoneutron and photoabsorption cross sections and covers experimental data m…
Insights into the equation of state of neutron rich matter obtained from the neutron skin thickness of 208Pb are in sharp conflict with earlier measurements of the electric dipole polarizability. We use a set of accurately calibrated energy density functionals to highlight the tension and to articulate how plans for a highly-intense Gamma Factory may alleviate the tension.
In this proceeding, we present the results of the theoretical evaluations of the electric dipole moment (EDM) of light nuclei, including the preliminary value for the 11B nucleus. From the data, we can infer an approximate counting rule, and predict the EDM of other light nuclei.
Proton capture reaction is an important process concerning the astrophysical origin of the elements. In present work, we focus on giant dipole resonance (GDR) in proton capture reactions, such as $^{11}$B$(p, γ)^{12}$C, $^{27}$Al$(p, γ)^{28}$Si, $^{39}$K$(p, γ)^{40}$Ca, and $^{67}$Co$(p, γ)^{68}$Ni in a framework of an extended quantum molecular dynamics model. The systematic properties of GDR parameters including the peak energy, the strength and full width at half maximum (FWHM) have been studied. The dependence of FWHM on temperature has also been discussed. Some comparisons with experiment…
The isotopic dependence of the isovector Pygmy dipole response in tin is studied within the framework of the relativistic random phase approximation. Regarded as an oscillation of the neutron skin against the isospin-symmetric core, the pygmy dipole resonance may place important constraints on the neutron skin of heavy nuclei and, as a result, on the equation of state of neutron-rich matter. The present study centers around two questions. First, is there a strong correlation between the development of a neutron skin and the emergence of low-energy isovector dipole strength? Second, could one u…
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 gamma-energies correspond to the gamma-transitions between very close nuclear excited states in the quasicontinuum. In terms of the thermal mean-field, 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. This result is obtained within the finite-tempe…
In this review, we summarize the theoretical development on the electric dipole moment of light nuclei. We first describe the nucleon level CP violation and its parametrization. We then present the results of calculations of the EDM of light nuclei in the ab initio approach and in the cluster model. The analysis of the effect of several models beyond standard model is presented, together with the prospects for its discovery. The advantage of the electric dipole moment of light nuclei is focused in the point of view of the many-body physics. The evaluations of the nuclear electric dipole moment…
Spin dipole (SD) strengths for double beta-decay (DBD) nuclei were studied experimentally for the first time by using measured cross sections of (3He,t) charge exchange reactions (CERs). Then SD nuclear matrix elements (NMEs) for low-lying 2- states were derived from the experimental SD strengths by referring to the experimental GT (Gamow-Teller) and F (Fermi) strengths. They are consistent with the empirical SD NMEs based on the quasi-particle model with the empirical effective SD coupling constant. The CERs are used to evaluate the SD NME, which is associated with one of the major components…
We combine the coupled-cluster method and the Lorentz integral transform for the computation of inelastic reactions into the continuum. We show that the bound-state-like equation characterizing the Lorentz integral transform method can be reformulated based on extensions of the coupled-cluster equation-of-motion method, and we discuss strategies for viable numerical solutions. Starting from a chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order, we compute the giant dipole resonances of 4He, 16,22O and 40Ca, truncating the coupled-cluster equation-of-motion method at the…
The isoscalar giant monopole, dipole, and quadrupole strength distributions have been deduced in $^{90, 92}$Zr, and $^{92}$Mo from "background-free" spectra of inelastic $α$-particle scattering at a beam energy of 385 MeV at extremely forward angles, including 0$^{\circ}$. These strength distributions were extracted by a multipole-decomposition analysis based on the expected angular distributions of the respective multipoles. All these strength distributions for the three nuclei practically coincide with each other, affirming that giant resonances, being collective phenomena, are not influence…
A set of high resolution zero-degree inelastic proton scattering data on 24Mg, 28Si, 32S, and 40Ca provides new insight into the long-standing puzzle of the origin of fragmentation of the Giant Dipole Resonance (GDR) in sd-shell nuclei. Understanding is provided by state-of-the-art theoretical Random Phase Approximation (RPA) calculatios for deformed nuclei using for the first time a realistic nucleon-nucleon interaction derived from the Argonne V18 potential with the unitary correlation operator method and supplemented by a phenomenological three-nucleon contact interaction. A wavelet analysi…
The giant dipole resonance's (GDR) width and shape at finite temperature and angular momentum are described within the phonon damping model (PDM), which predicts an overall increase in the GDR's total width at low and moderate temperature T, and its saturation at high T. At T< 1 MeV the GDR width remains nearly constant because of thermal pairing. The PDM description is compared with the experimental systematics obtained from heavy-ion fusion, inelastic scattering of light particles on heavy targets, and alpha induced fusion reactions, as well as with predictions by other theoretical approache…
The phonon damping model (PDM) is extended to include the effect of angular momentum at finite temperature. The model is applied to the study of damping of giant dipole resonance (GDR) in hot and noncollectively rotating spherical nuclei. The numerical results obtained for Mo88 and Sn106 show that the GDR width increases with both temperature T and angular momentum M. At T > 4 MeV and M<= 60 hbar the increase in the GDR width slows down for Sn106, whereas at M<= 80 hbar the GDR widths in both nuclei nearly saturate. By adopting the nuclear shear viscosity extracted from fission data at T= 0, i…
The evolution of the giant dipole resonance's (GDR) width and shape at finite temperature $T$ and angular momentum $J$ is described within the framework of the phonon damping model (PDM). The PDM description is compared with the established experimental systematics obtained from heavy-ion fusion and inelastic scattering of light particles on heavy target nuclei, as well as with predictions by other theoretical approaches. Extended to include the effect of angular momentum $J$, its strength functions have been averaged over the probability distributions of $T$ and $J$ for the heavy-ion fusion-e…
By taking into account the magnetic field in the extended quantum molecular dynamics model (EQMD), we analyzed its effects on giant dipole resonance (GDR) by studying the responses and strengths of the dipole moments. The selected system is the $^{40}$Ca nucleus which is excited through the Coulomb interaction by $^{16}$O. Particle acceleration term in Liénard-Wiechert potential is discussed which, however, has small impact on magnetic field. The peak energy, strength and width of GDR, temperature, and angular momentum of $^{40}$Ca as a function of beam energy are investigated. It is found tha…
The systematic study of the correlation between the experimental giant dipole resonance (GDR) width and the average deformation <β> of the nucleus at finite excitation is presented for the mass region A ~ 59 to 208. We show that the width of the GDR (Γ) and the quadrupole deformation of the nucleus do not follow a linear relation, as predicted earlier, due to the GDR induced quadrupole moment and the correlation also depends on the mass of the nuclei. The different empirical values of <β> extracted from the experimental GDR width match exceptionally well with the thermal shape fluctuation mode…
Pygmy and Giant Dipole Resonance (PDR and GDR) in Ni isotopes have been investigated by Coulomb excitation in the framework of the Isospin-dependent Quantum Molecular Dynamics model (IQMD). The spectra of $γ$ rays are calculated and the peak energy, the strength and Full Width at Half Maximum (FWHM) of GDR and PDR have been extracted. Their sensitivities to nuclear equation of state, especially to its symmetry energy term are also explored. By a comparison with the other mean-field calculations, we obtain the reasonable values for symmetry energy and its slope parameter at saturation, which gi…
The electric dipole moments of the nucleon and light ions are discussed and strategies for disentangling the underlying sources of CP violation beyond the Kobayashi-Maskawa quark-mixing mechanism of the Standard Model are indicated. Contribution to "45 years of nuclear theory at Stony Brook: a tribute to Gerald E. Brown".
The Green-Kubo relation and fluctuation-dissipation theorem are employed to calculate the shear viscosity $η$ of a finite hot nucleus directly from the width and energy of the giant dipole resonance (GDR) of this nucleus. The ratio $η/s$ of shear viscosity $η$ to entropy density $s$ is extracted from the experimental systematics of the GDR in copper, tin and lead isotopes at finite temperature $T$. These empirical results are then compared with the predictions by several independent models, as well as with almost model-independent estimations. Based on these results, it is concluded that the r…
A recent theoretical prediction of a breaking of axial symmetry in quasi all heavy nuclei is confronted to a new critical analysis of photon strength functions of nuclei in the valley of stability. For the photon strength in the isovector giant dipole resonance (IVGDR) regime a parameterization of GDR shapes by the sum of three Lorentzians (TLO) is extrapolated to energies below and above the IVGDR. The impact of non-GDR modes adding to the low energy slope of photon strength is discussed including recent data on photon scattering and other radiative processes. These are shown to be concentrat…
The measurement of the electric dipole moment (EDM) is an excellent test of the standard model of particle physics, and the detection of a finite value is signal of a new source of CP violation beyond it. Among systems for which the EDM can be measured, light nuclei are particularly interesting due to their high sensitivity to new physics. In this proceedings contribution, we examine the sensitivity of the EDM of several light nuclei to the CP-odd one pion-exchange nucleon-nucleon interaction within the cluster model. We suggest an approximate sum rule for the nuclear EDM.
It is studied how the $α$ cluster degrees of freedom, such as $α$ clustering configurations close to the $α$ decay threshold in $^{12}$C and $^{16}$O, including the linear chain, triangle, square, kite, and tetrahedron, affect nuclear collective vibrations with a microscopic dynamical approach, which can describe properties of nuclear ground states well across the nuclide chart and reproduce the standard giant dipole resonance (GDR) of $^{16}$O quite nicely. It is found that the GDR spectrum is highly fragmented into several apparent peaks due to the $α$ structure. The different $α$ cluster co…
The line shapes of giant dipole resonance (GDR) in the decay of the compound nucleus $^{88}$Mo, which is formed after the fusion-evaporation reaction $^{48}$Ti + $^{40}$Ca at various excitation energies $E^{*}$ from 58 to 308 MeV, are generated by averaging the GDR strength functions predicted within the phonon damping model (PDM) using the empirical probabilities for temperature and angular momentum. The average strength functions are compared with the PDM strength functions calculated at the mean temperature and mean angular momentum, which are obtained by averaging the values of temperature…
The systematic study of isoscalar (IS) and isovector (IV) giant quadrupole responses (GQR) in normal and superfluid nuclei presented in [G. Scamps and D. Lacroix, Phys. Rev. 88, 044310 (2013)] is extended to the case of axially deformed and triaxial nuclei. The static and dynamical energy density functional based on Skyrme effective interaction are used to study static properties and dynamical response functions over the whole nuclear chart. Among the 749 nuclei that are considered, 301 and 65 are respectively found to be prolate and oblate while 54 do not present any symmetry axis. For these …
The universality of the Critical Temperature included Fluctuation Model (CTFM) in explaining the evolution of the giant dipole resonance (GDR) width as a function of angular momentum is examined in the light of recent experimental data on $^{144}$Sm and $^{152}$Gd. We compare both the data sets with the phenomenological formula based on the CTFM and the thermal shape fluctuation model (pTSFM). The CTFM describes both the data sets reasonably well using the actual ground state GDR width ($Γ_0$) values, whereas, the pTSFM describes the $^{144}$Sm data well but is unable to explain the $^{152}$Gd…
We show that the proposed measurements of the electric dipole moments of light nuclei in storage rings would put strong constraints on models of flavor-diagonal CP violation. Our analysis is exemplified by a comparison of the Standard Model including the QCD theta term, the minimal left-right symmetric model, a specific version of the so-called aligned two-Higgs doublet model, and briefly the minimal supersymmetric extension of the Standard Model. By using effective field theory techniques we demonstrate to what extend measurements of the electric dipole moments of the nucleons, the deuteron, …
Microscopic study of low-lying states in odd-mass nuclei for atomic electric dipole moment searches
School of Physics and Astronomy, Sun Yat-sen University（中山大学物理学院）；Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, Sun Yat-Sen University（中山大学广东省量子计量与传感重点实验室）
Cross sections for the 90,92,94Zr(p,n) reactions were measured at energies of 79.2 and 119.4 MeV. A phenomenological model was developed to describe the variation with bombarding energy of the position of the L=1 peak observed in these and other (p,n) reactions. The model yields the splitting between the giant dipole and giant spin dipole resonances. Values of these splittings are obtained for isotopes of Zr and Sn and for 208Pb.
