Particle-vibration Coupling Research Articles

Magnetic moments of thallium isotopes in the vicinity of magic N = 126

The magnetic dipole moments (μ) of 209Tlg (N=128) and 207Tlm (N=126) have been measured for the first time using the in-source laser resonance-ionization spectroscopy technique with the Laser Ion Source and Trap (LIST) at ISOLDE (CERN). The application of the LIST suppresses the usually overwhelming background of the isobaric francium isotopes and allows access to heavy thallium isotopes with A⩾207. The self-consistent theory of finite Fermi systems based on the energy density functional by Fayans et al. well describes the N dependence of μ for 1/2+ thallium ground states, as well as μ for the 11/2− isomeric states in europium, gold and thallium isotopes. The inclusion of particle-vibration coupling leads to a better agreement between the theory and experiment for μ(Tlg, Iπ=1/2+). It is shown that beyond mean-field contributions to μ cannot be neglected at least for thallium isotopes with Iπ=1/2+.

Manipulation of Giant Multipole Resonances via Vortex γ Photons.

Traditional photonuclear reactions primarily excite giant dipole resonances, making the measurement of isovector giant resonances with higher multipolarities a great challenge. In this Letter, the manipulation of collective excitations of different multipole transitions in even-even nuclei via vortex γ photons is investigated. We develop the calculation method for photonuclear cross sections induced by the vortex γ photon beam using the fully self-consistent random-phase approximation plus particle-vibration coupling (RPA+PVC) model based on Skyrme density functional. We find that the electromagnetic transitions with multipolarity J<|m_{γ}| are forbidden for vortex γ photons due to the angular momentum conservation, with m_{γ} being the projection of total angular momentum of γ photon on its propagation direction. For instance, this allows for probing the isovector giant quadrupole resonance without interference from dipole transitions using vortex γ photons with m_{γ}=2. Furthermore, the electromagnetic transition with J=|m_{γ}|+1 vanishes at a specific polar angle. Therefore, the giant resonances with specific multipolarity can be extracted via vortex γ photons. Moreover, the vortex properties of γ photons can be meticulously diagnosed by measuring the nuclear photon-absorption cross section. Our method opens new avenues for photonuclear excitations, generation of coherent γ photon laser and precise detection of vortex particles, and consequently, has significant impact on nuclear physics, nuclear astrophysics and strong laser physics.

Core of F25 studied by the F25(−p ) proton-removal reaction

The $^{9}\mathrm{Be}(^{25}\phantom{{}^{B}e}\mathrm{F}(5/{2}^{+}),^{24}\phantom{{}^{B}e}\mathrm{O}$)X proton-removal reaction was studied at the NSCL using the S800 spectrometer. The experimental spectroscopic factor for the ground-state to ground-state transition indicates a substantial depletion of the proton ${d}_{5/2}$ strength compared to shell-model expectations, similar to the findings of an inverse-kinematics $(p,2p)$ measurement performed at RIBF. The $^{25}\phantom{{}^{B}e}\mathrm{F}$ to $^{24}\phantom{{}^{B}e}\mathrm{O}$ ground-states overlap is considerably less than anticipated if the core nucleons behaved as rigid, doubly-magic $^{24}\phantom{{}^{B}e}\mathrm{O}$ within $^{25}\phantom{{}^{B}e}\mathrm{F}$. We interpret the new results within the framework of the Particle-Vibration Coupling (PVC) model, of a ${d}_{5/2}$ proton coupled to a quadrupole phonon of an effective core. This approach provides a good description of the experimental data, requiring an effective $^{24}\phantom{{}^{B}e}\mathrm{O}^{*}$ core with a phonon energy of $\ensuremath{\hbar}{\ensuremath{\omega}}_{2}$= 3.2 MeV and a $B(E2)\ensuremath{\approx}2.7$ W.u. -- softer and more collective than a bare $^{24}\phantom{{}^{B}e}\mathrm{O}$. Both the Nilsson deformed mean field and the PVC models appear to capture the properties of the effective core of $^{25}\phantom{{}^{B}e}\mathrm{F}$, suggesting that the additional proton polarizes $^{24}\phantom{{}^{B}e}\mathrm{O}$ in such a way that it becomes either slightly deformed or a quadrupole vibrator.

Nuclear shell structure in a finite-temperature relativistic framework

The shell evolution of neutron-rich nuclei with temperature is studied in a beyond-mean-field framework rooted in the meson-nucleon Lagrangian. The temperature-dependent Dyson equation with the dynamical kernel taking into account the particle-vibration coupling (PVC) is solved for the fermionic propagators in the basis of the thermal relativistic mean-field Dirac spinors. The calculations are performed for $^{68-78}$Ni in a broad range of temperatures $0 \leq T \leq 4$ MeV. The special focus is put on the fragmentation pattern of the single-particle states, which is further investigated within toy models in strongly truncated model spaces. Such models allow for quantifying the sensitivity of the fragmentation to the phonon frequencies, the PVC strength and to the mean-field level density. The model studies provide insights into the temperature evolution of the PVC mechanism in real nuclear systems under the conditions which may occur in astrophysical environments.

Damping of the isovector giant dipole resonance in 40,48Ca

The fine structure of the IsoVector Giant Dipole Resonance (IVGDR) in the doubly-magic nuclei 40,48Ca observed in inelastic proton scattering experiments under 0∘ is used to investigate the role of different mechanisms contributing to the IVGDR decay width. Characteristic energy scales are extracted from the fine structure by means of wavelet analysis. The experimental scales are compared to different theoretical approaches allowing for the inclusion of complex configurations beyond the mean-field level. Calculations are performed in the framework of RPA and beyond-RPA in a relativistic approach based on an effective meson-exchange interaction, with the UCOM effective interaction and, for the first time, with realistic two- plus three-nucleon interactions from chiral effective field theory employing the in-medium similarity renormalization group. All models highlight the role of Landau fragmentation for the damping of the IVGDR, while the differences in the coupling strength between one particle-one hole (1p-1h) and two particle-two hole (2p-2h) correlated (relativistic) and non-correlated (non-relativistic) configurations lead to very different pictures of the importance of the spreading width resulting in wavelet scales being a sensitive measure of their interplay. The relativistic approach with particle-vibration coupling, in particular, shows impressive agreement with the number and absolute values of the scales extracted from the experimental data.

Isovector density and isospin impurity in 40Ca

We study isoscalar (IS) and isovector (IV) densities in Ca40 in comparison with theoretical densities calculated by Skyrme Hatree-Fock (HF) models. The charge symmetry breaking and the charge independence breaking forces are introduced to study the effect on the IV density. The effect of isospin mixing in the ground-state density is examined by using the particle-vibration coupling model taking into account the collective IV giant monopole excitation. We show a clear correlations in the IV density and isospin impurity of Ca40 within the HF and the particle-vibration coupling model. We extract for the first time the experimental information of isospin impurity from the magnitude of IV density.

Charge radii in covariant density functional theory: A global view

The authors provide a systematic global study of differential charge radii of nuclei within covariant density functional theory. They present results for chains of isotopes as they cross major closed neutron shell numbers, where there is usually a change of slope (kink) in the charge radii. The odd-even staggering of charge radii is also investigated, and particle-vibration coupling in odd-mass nuclei is suggested to play a significant role in addition to pairing. This detailed study lays a solid foundation to assess how various forms of interactions within the nuclear many-body system affect fundamental nuclear properties such as nuclear radii and how they evolve with nucleon number.

Global study of separable pairing interaction in covariant density functional theory

A systematic global investigation of pairing properties based on all available experimental data on pairing indicators has been performed for the first time in the framework of covariant density functional theory. It is based on separable pairing interaction of Ref. [1]. The optimization of the scaling factors of this interaction to experimental data clearly reveals its isospin dependence in neutron subsystem. However, the situation is less certain in proton subsystem since similar accuracy of the description of pairing indicators can be achieved both with isospin-dependent and mass-dependent scaling factors. The differences in the functional dependencies of scaling factors lead to the uncertainties in the prediction of proton and neutron pairing properties which are especially pronounced at high isospin and could have a significant impact on some physical observables. For a given part of nuclear chart the scaling factors for spherical nuclei are smaller than those for deformed ones; this feature exists also in non-relativistic density functional theories. Its origin is traced back to particle-vibration coupling in odd-$A$ nuclei which is missing in all existing global studies of pairing. Although the present investigation is based on the NL5(E) covariant energy density functional (CEDF), its general conclusions are expected to be valid also for other CEDFs built at the Hartree level.

Low-lying electric and magnetic dipole strengths in Pb207

Low-lying dipole transitions in $^{207}\mathrm{Pb}$ were measured via nuclear photon scattering using a quasimonochromatic, linearly polarized photon beam. The spins and/or parities of the states observed in $^{207}\mathrm{Pb}$ were determined from the intensity asymmetry of resonantly scattered $\ensuremath{\gamma}$ rays with respect to the polarization plane of the incident photon beam. The electric ($E1$) and magnetic ($M1$) dipole strengths were obtained for excitation energies from 5.49 to 6.75 MeV. The present experimental results, combined with $(\ensuremath{\gamma},n)$ data from the literature, were used to investigate the $E1$ and $M1$ photoabsorption cross sections near the neutron separation energy by comparison with predictions from the particle-vibration coupling with the quasiparticle random-phase approximation model.

Laser Spectroscopy of Neutron-Rich ^{207,208}Hg Isotopes: Illuminating the Kink and Odd-Even Staggering in Charge Radii across the N=126 Shell Closure.

The mean-square charge radii of ^{207,208}Hg (Z=80, N=127, 128) have been studied for the first time and those of ^{202,203,206}Hg (N=122, 123, 126) remeasured by the application of in-source resonance-ionization laser spectroscopy at ISOLDE (CERN). The characteristic kink in the charge radii at the N=126 neutron shell closure has been revealed, providing the first information on its behavior below the Z=82 proton shell closure. A theoretical analysis has been performed within relativistic Hartree-Bogoliubov and nonrelativistic Hartree-Fock-Bogoliubov approaches, considering both the new mercury results and existing lead data. Contrary to previous interpretations, it is demonstrated that both the kink at N=126 and the odd-even staggering (OES) in its vicinity can be described predominately at the mean-field level and that pairing does not need to play a crucial role in their origin. A new OES mechanism is suggested, related to the staggering in the occupation of the different neutron orbitals in odd- and even-A nuclei, facilitated by particle-vibration coupling for odd-A nuclei.

Temperature evolution of the nuclear shell structure and the dynamical nucleon effective mass

We study the fermionic Matsubara Green functions in medium-mass nuclei at finite temperature. The single-fermion Dyson equation with the dynamical kernel of the particle-vibration-coupling (PVC) origin is formulated and solved in the basis of Dirac spinors, which minimize the grand canonical potential with the meson-nucleon covariant energy density functional. The PVC correlations beyond mean field are taken into account in the leading approximation for the energy-dependent self-energy, and the full solution of the finite-temperature Dyson equation is obtained for the fermionic propagators. Within this approach, we investigate the fragmentation of the single-particle states and its evolution with temperature for the nuclear systems $^{56,68}$Ni and $^{56}$Fe relevant for the core-collapse supernova. The energy-dependent, or dynamical, nucleon effective mass is extracted from the PVC self-energy at various temperatures.

Effects of velocity-dependent and spin-orbit terms of the Skyrme interaction on neutron elastic scattering observables

Elastic scattering of a series of doubly closed-shell nuclei at low energy has been described in the framework of optical potential model generated from the particle-vibration coupling approach on top of the collective excited states obtained from the random-phase approximation. We focus on the effects of the spin-orbit and velocity-dependent interaction on the angular distributions and analyzing powers by comparing these observables with experimental data. It has been found that the contribution of the two-body velocity-dependent and two-body spin-orbit terms are important to improve results for $^{16}\mathrm{O},\phantom{\rule{0.16em}{0ex}}^{40}\mathrm{Ca},\phantom{\rule{0.16em}{0ex}}^{48}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$. The velocity-dependent interactions strongly reduce the absorption on the surface while the spin-orbit interactions sightly increase the absorption in the interior.

Pairing effects on neutron elastic scattering at low-energies

For the first time, a realistic microscopic calculation for low-energy neutron-nucleus elastic scattering off open-shell nuclei is carried out within the framework of particle-vibration coupling (PVC). In this study, the pairing correlations of the ground state are taken into account. The dependence of the angular distributions on the pairing gaps is discussed.

Pairing effects on neutron elastic scattering at low-energies

For the first time, a realistic microscopic calculation for low-energy neutron-nucleus elastic scattering off open-shell nuclei is carried out within the framework of particle-vibration coupling (PVC). In this study, the pairing correlations of the ground state are taken into account. The dependence of the angular distributions on the pairing gaps have been discussed.

Particle-vibration coupling for giant resonances beyond the diagonal approximation

A self-consistent particle-vibration coupling (PVC) model without diagonal approximation is presented. The diagonal approximation, that neglects completely the interaction between the doorway states, has been removed by taking into account the interaction between the two particle-holes inside the doorway states. As applications, isoscalar giant monopole, dipole, and quadrupole resonances in 16O are investigated based on the use of Skyrme functionals. The diagonal approximation is found to clearly impact the strength distribution of the giant quadrupole resonance, and the description of the experimental data is improved without this approximation. The impact of the diagonal approximation is analyzed in detail, especially its effect on the eigenenergies and the induced coupling between neutron and proton particle-hole configurations. The latter is a direct and physically sound effect of the improvement on our formalism. The importance of using self-consistently the full effective interaction in the PVC vertex, and the effect of its renormalization via the subtraction method, are also discussed. For completeness, we also analyze the dependence of our results on the Skyrme parametrization.

Fragmentation of Single-Particle Strength around the Doubly Magic Nucleus ^{132}Sn and the Position of the 0f_{5/2} Proton-Hole State in ^{131}In.

Spectroscopic factors of neutron-hole and proton-hole states in ^{131}Sn and ^{131}In, respectively, were measured using one-nucleon removal reactions from doubly magic ^{132}Sn at relativistic energies. For ^{131}In, a 2910(50)-keV γ ray was observed for the first time and tentatively assigned to a decay from a 5/2^{-} state at 3275(50)keV to the known 1/2^{-} level at 365keV. The spectroscopic factors determined for this new excited state and three other single-hole states provide first evidence for a strong fragmentation of single-hole strength in ^{131}Sn and ^{131}In. The experimental results are compared to theoretical calculations based on the relativistic particle-vibration coupling model and to experimental information for single-hole states in the stable doubly magic nucleus ^{208}Pb.

Mean-field theory for fermion pairs and the ab initio particle-vibration coupling approach

A Dyson Bethe-Salpeter equation (Dyson-BSE) for fermion pairs is presented whose kernel has a static and a one frequency dependent contribution, analogous to the self energy of the single particle Dyson equation with the (static) mean field term and the energy dependent correlation term. The static part of the Dyson-BSE is the self-consistent mean field for the vibrations. At the same time, for the correlated single particle self-energy a full particle-vibration coupling (PVC) scattering equation is established where the vibration is the same as obtained from the Dyson-BSE. Both equations, single particle Dyson equation and Dyson-BSE, are coupled through self-consistency. Numerical results for Lipkin and 1D Hubbard chain are very promising.

The effective single particle potential and the tadpole

The Energy Density Functional (EDF) theory is extremely successful within the effective force approach, noticeably the Skyrme or Gogny forces, in reproducing the nuclear binding energies and other nuclear properties along the whole mass table. The EDF is in this case represented formally as the Hartree-Fock (HF) mean field of an effective force, and the associated single particle states can be considered the eigenstates of the corresponding effective mean field. In general, the phenomenological single particle spectrum is not accurately reproduced. To overcome this difficulty one can improve the functional in order to incorporate in the mean field additional correlations in an effective way. In an alternative viable scheme one can introduce explicitly many-body correlations which affect the single particle motion at both dynamic and static levels. In particular, the particle-vibration coupling scheme modifies the positions of the individual single particle energies. In this case one also introduce the fragmentation of the single particle states, a feature that cannot be described at the mean field level. At the same time the so-introduced correlations modify the static single particle potential, and the single particle states that diagonalize the corresponding density matrix are not the orbitals of a mean field with occupation numbers 1 (occupied orbitals) and 0 (unoccupied orbitals) anymore. In this paper we show that both static and dynamic effects on the single particle motion can be introduced within a previously developed scheme, based on the conserving approximations, and that the static part can be identified with the so-called tadpole term introduced by Khodel in the self-consistent theory of finite Fermi systems. The treatment remains at the formal level, but we hope that several aspects of the particle-vibration coupling scheme will be clarified.

Time-Reversed Particle-Vibration Loops and Nuclear Gamow-Teller Response.

The nuclear response theory for charge-exchange modes in the relativistic particle-vibration coupling approach is extended to include for the first time particle-vibration coupling effects in the ground state of the parent nucleus. In a framework based on the effective meson-nucleon Lagrangian, we investigate the role of such complex ground-state correlations in the description of Gamow-Teller transitions in ^{90}Zr in both (p, n) and (n, p) channels. The particle-vibration coupling effects are calculated without introducing new parameters. We find that this new correlation mechanism is fully responsible for the appearance of the strength in the (n, p) branch. Comparison of our results to the available experimental data shows a very good agreement up to excitation energies beyond the giant resonance region when taking into account a phenomenological admixture of the isovector spin monopole transitions. The parent-daughter binding-energy differences are also greatly improved by the inclusion of the new correlations.

Skyrme Functional with Tensor Terms from ab initio Calculations: Results for the Spin--Orbit Splittings

A new Skyrme functional including tensor terms is presented. The tensor terms have been determined by fitting the results of relativistic Brueckner-Hartree-Fock (RBHF) studies on neutron-proton drops. Unlike all previous studies, where the tensor terms were usually determined by fitting to experimental data of single-particle levels, the pseudodata calculated by RBHF does not contain beyond mean-field effect such as the particle-vibration coupling and, therefore, can provide information on the tensor term without ambiguities. The obtained new functional, named SAMi-T, can describe well ground-state properties such as binding energies, radii, spin-orbit splittings and, at the same time, the excited state properties such as those of the Giant Monopole Resonance (GMR), Giant Dipole Resonance (GDR), Gamow-Teller Resonance (GTR), and Spin-Dipole Resonance (SDR).