Pairing Nambu-Goldstone Modes within Nuclear Density Functional Theory

Hinohara, Nobuo; Nazarewicz, W.

doi:10.1103/physrevlett.116.152502

Cited by 29 publications

(31 citation statements)

References 66 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The discrepancy between calculated and experimental values of ∆ ee E was discussed in Ref. [38]: the static pairing in 42,46 Ca is close to the unphysical pairing phase transition. For 212 Pb, the spread of predicted values of ∆ ee E is significant, with Fy(std) and Sk+PFy functionals overestimating pairing correlations significantly.…”

Section: B Optimized Functionalsmentioning

confidence: 99%

“…It is seen that for 44 Ca, 124 Sn, and 204 Pb, there is a great consistency between different functionals employed. Indeed, most information on pairing correlations is contained in the mass surface of even-even nuclei [38], and all our functionals shown in Fig. 3 utilize masses from the basic dataset of SV-min.…”

Section: B Optimized Functionalsmentioning

confidence: 99%

“…For open-shell systems, ∆ ee E is proportional to the inverse of the pairing rotational moment of inertia, i.e., it is an excellent indicator of nucleonic pairing [38]. For the calibration of the spin-orbit functional, we also look at differences of single-particle energies, ε ls .…”

Section: E Observables Studiedmentioning

confidence: 99%

See 2 more Smart Citations

Toward a global description of nuclear charge radii: Exploring the Fayans energy density functional

Reinhard¹,

Nazarewicz²

2017

Phys. Rev. C

118

102

View full text Add to dashboard Cite

Background: Binding energies and charge radii are fundamental properties of atomic nuclei. When inspecting their particle-number dependence, both quantities exhibit pronounced odd-even staggering. While the odd-even effect in binding energy can be attributed to nucleonic pairing, the origin of staggering in charge radii is less straightforward to ascertain.Purpose: In this work, we study the odd-even effect in binding energies and charge radii, and systematic behavior of differential radii, to identify the underlying components of the effective nuclear interaction.Method: We apply nuclear density functional theory using a family of Fayans and Skyrme energy density functionals fitted to similar datasets but using different optimization protocols. We inspect various correlations between differential charge radii, odd-even staggering in energies and radii, and nuclear matter properties. Detailed analysis is carried out for medium-mass and heavy semi-magic nuclei with a particular focus on the Ca chain.Results: By making the surface and pairing terms dependent on density gradients, the Fayans functional offers the superb simultaneous description of odd-even staggering effects in energies and charge radii. Conversely, when the data on differential radii are added to the pool of fit-observables, the coupling constants determining the strengths of the gradient terms of Fayans functional are increased by orders of magnitude. The Skyrme functional optimized in this work with the generalized Fayans pairing term offers results of similar quality. We quantify these findings by performing correlation analysis based on the statistical linear regression technique. The nuclear matter parameters characterizing Fayans and Skyrme functionals optimized to similar datasets are fairly close. Conclusion:Fayans paring functional, with its generalized density dependence, significantly improves description of charge radii in odd and even nuclei. Adding differential charge radii to the set of fit-observables in the optimization protocol is helpful for both description of radii and for improving pairing functional. In particular, Fayans functional constrained in this way is capable of explaining charge radii in the even-even Ca isotopes. However, in order to obtain good description of differential radii data in both medium-mass and heavy nuclei, an A-dependent scaling of Fayans pairing functional is still needed. Various extensions of the current model are envisioned that carry out a promise for the global description.

show abstract

Section: B Optimized Functionalsmentioning

confidence: 99%

Section: B Optimized Functionalsmentioning

confidence: 99%

See 1 more Smart Citation

Toward a global description of nuclear charge radii: Exploring the Fayans energy density functional

Reinhard¹,

Nazarewicz²

2017

Phys. Rev. C

118

102

View full text Add to dashboard Cite

show abstract

“…[25,26,[35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51] for applications of the FAM). We start from the HFB code using the two-basis method of the 3D Cartesian coordinate representation.…”

mentioning

confidence: 99%

Multipole modes of excitation in triaxially deformed superfluid nuclei

Washiyama

Nakatsukasa

2017

Phys. Rev. C

View full text Add to dashboard Cite

Background:The five-dimensional quadrupole collective model based on energy density functionals (EDFs) has often been employed to treat long-range correlations associated with shape fluctuations in nuclei. Our goal is to derive the collective inertial functions in the collective Hamiltonian by the local quasiparticle random-phase approximation (QRPA) that correctly takes into account time-odd mean-field effects. Currently, a practical framework to perform the QRPA calculation with the modern EDFs on the (β,γ ) deformation space is not available. Purpose: Toward this goal, we develop an efficient numerical method to perform the QRPA calculation on the (β,γ ) deformation space based on the Skyrme EDF. Methods: We use the finite amplitude method (FAM) for the efficient calculation of QRPA strength functions for multipole external fields. We construct a computational code of FAM-QRPA in the three-dimensional Cartesian coordinate space to handle triaxially deformed superfluid nuclei. Introduction. The shape of atomic nuclei is influenced strongly by the quantum nature of nuclear systems. Excitation spectra and their transition probabilities clearly indicate the existence of shape fluctuations and shape coexistence [1], particularly in transitional regions from spherical to deformed shapes in the ground state. The long-lived fission products (LLFP) from uranium fueled reactors, such as Pd and Zr isotopes, are located in transitional regions on the nuclear chart and demonstrate the shape mixing and coexistence. It is important to understand the basic properties of the LLFPs to develop a possible nuclear transmutation method, which is the main target of an ImPACT program "Reduction and Resource Recycling of High-level Radioactive Wastes through Nuclear Transmutation" [2].One of the standard methods of investigating nuclear manybody problems is the nuclear energy density functional (EDF) theory [3]. The nuclear EDF well describes the ground-state properties of atomic nuclei. However, on the mean-field level, it cannot describe shape fluctuations and shape coexistence. We need to go beyond the mean field for a description of such phenomena, including quantum fluctuations associated with the large-amplitude collective motion. If the EDF were constructed as an expectation value of a well-defined Hamiltonian, a possible extension would be the generator coordinate method (GCM) [4][5][6]. However, most of the EDFs are known to have a singular behavior [7,8], which prevents us from the straightforward application of the GCM.

show abstract

“…In other words, the distribution of the magnitudes of eigenvalues associated with a variety of models (from radioactive decay to systems biology) and reflecting the relevance of different parameters, fell, according to Transtrum et al, roughly log-linearly, a few parameters (or combinations thereof) tend to be of much greater importance than all others [31]. The above arguments, are to be supplemented with the phenomena of emergent properties, like generalized rigidity in e.g., gauge space [10,8] and pairing rotational bands in nuclei [28,[32][33][34] associated with the phenomenon of spontaneous symmetry breaking restoration. These phenomena are also at the basis of the simplicity of the behavior of complex many-body systems in general, and of the validity of the concepts of collective variables (CV) in nuclei, among which the single-particle motion enters on a par with quadrupole and pairing vibrations and rotations.…”

mentioning

confidence: 99%

Challenges in the description of the atomic nucleus: Unification and interdisciplinarity

Bortignon

Broglia

2016

Eur. Phys. J. A

View full text Add to dashboard Cite

Abstract. Nuclear physics, in general, and theoretical nuclear physics, in particular, have provided the physics community at large, among other things, with the paradigm of spontaneous symmetry breaking phenomena in finite many-body systems. The study of the associated mechanisms of symmetry restoration has shed light on the microscopic structure of the corresponding condensates, in particular on the superfluid phase, allowing to study Cooper pair tunnelling into superfluid nuclei (related to the Josephson effect), in terms of individual quantum states and reaching, in doing so, a new milestone: that of unifying structure and reactions, these last processes being found at the basis of the formulation of quantum mechanics (probability interpretation, Born). In the process, nuclear physicists have extended the validity of BCS theory of superconductivity to the single Cooper pair situation, let alone discovering unexpected mechanism to break gauge invariance. The insight obtained from pair transfer research is likely to have important consequences in the study of double charge exchange processes, and thus in the determination of the nuclear matrix element associated with neutrinoless double beta decay, eventually providing an important test of the Standard Model. Time, thus, seems ripe for nuclear theorists to take centre stage, backed by a wealth of experimental information and by their interdisciplinary capacity to connect basic physical concepts across the borders. With the help of these elements they can aim at fully revealing the many facets of their femtometer many-body system, from vacuum zero point fluctuations to new exotic modes of nuclear excitations and of their interweaving, resulting in powerful effective field theories. Unless. Unless they are not able to free themselves from words like ab initio or fundamental, and to adapt a relax attitude concerning Skyrme, tensor, etc., forces, as well as regarding the quest for "the" Hamiltonian.The modern theory of nuclear structure results from the merging of the liquid drop and of the shell model, which contributed to the concepts of collective excitations and of independent-particle motion, respectively. These apparently contradictory views became eventually unified in the paradigm of broken symmetry restoration to determine the elementary modes of nuclear excitation, their interweaving being a consequence of the particle-vibration coupling mechanism [1]. The resulting clothed bosonic and fermionic degrees of freedom constitute the physical, elementary modes of nuclear excitation which diagonalize the many-body nuclear Hamiltonian restoring symmetries spontaneously broken. The associated spectroscopic amplitudes provide, together with the theory of reactions [2][3][4][5], the elements to calculate the absolute value of the differential cross sections and transition rates. In partica e-mail: Pierfrancesco.Bortignon@mi.infn.it ular, those associated with: a) inelastic scattering and Coulomb excitation, b) one-particle and, c) two-particle transfer processes. ...

show abstract

Pairing Nambu-Goldstone Modes within Nuclear Density Functional Theory

Cited by 29 publications

References 66 publications

Toward a global description of nuclear charge radii: Exploring the Fayans energy density functional

Toward a global description of nuclear charge radii: Exploring the Fayans energy density functional

Multipole modes of excitation in triaxially deformed superfluid nuclei

Challenges in the description of the atomic nucleus: Unification and interdisciplinarity

Contact Info

Product

Resources

About