Particle-vibration Coupling Model Research Articles

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.

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.

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.

Some aspects of self-consistent higher-order interactions

After a brief review of the formalism of the self-consistent higher-order interactions, applications of a ([Q3Q3](2) · Q2) type of three-body interaction to the quadrupole moment of the 3− state in 208Pb and the energy splitting of the septuplet of states (h9/23−)I with I = 3/2, 5/2, …, 15/2 in 209Bi are discussed. It is shown that if the contribution of the three-body interaction is included, the theoretical value of the Qel(3−) moment becomes rather small compared to the experiment, but the observed small energy splitting of the septuplet can essentially be understood within the particle-vibration coupling model. Roles of non-linear field couplings provided by the self-consistent higher-order interactions are also discussed.

Pion–nucleon correlations in finite nuclei in a relativistic framework: Effects on the shell structure

The relativistic particle-vibration coupling (RPVC) model is extended by the inclusion of spin- and isospin-flip excitation modes into the phonon space, introducing a new mechanism of dynamical interaction between nucleons with different isospin in the nuclear medium. Protons and neutrons exchange by collective modes which are formed by isovector $\pi$ and $\rho$-mesons, in turn, softened considerably because of coupling to nucleons of the medium. These modes are investigated within the proton-neutron relativistic random phase approximation (pn-RRPA) and relativistic proton-neutron time blocking approximation (pn-RTBA). The appearance of isospin-flip states with sizable transition probabilities at low energies points out that they are likely to couple to the single-particle degrees of freedom and, in addition to isoscalar low-lying phonons, to modify their spectroscopic characteristics. Such a coupling is quantified for the shell structure of $^{100,132}$Sn and found significant for the location of the dominant single-particle states.

The Gamow–Teller excitation and its spreading mechanism

Gamow–Teller excitations attract the constant interest of physicists not only within nuclear structure but also in astrophysics. In this paper, the random phase approximation (RPA) plus particle-vibration coupling model is applied to the investigation of Gamow–Teller excitations in the doubly magic nuclei 208Pb and 132Sn. It is found that the Gamow–Teller resonance develops a large spreading width and that the excitation energies are shifted downward by phonon coupling. Good agreement with experiment is obtained for the line shape of the Gamow–Teller distribution for 208Pb using the Skyrme interactions SkM* and SGII. It is also found that the collective isovector giant dipole phonons play an important role in the width of both nuclei, and the related microscopic mechanism is analyzed in detail.

Changes in rotational characters of one- and two-phonon gamma-vibrational bands in 105Mo

The $\gamma$ vibration is the most typical low-lying collective motion prevailing the nuclear chart. But only few one-phonon rotational bands in odd-$A$ nuclei have been known. Furthermore, two-phonon states, even the band head, have been observed in a very limited number of nuclides not only of odd-$A$ but even-even. Among them, that in $^{105}$Mo is unique in that Coriolis effects are expected to be stronger than in $^{103}$Nb and $^{105}$Nb on which theoretical studies were reported. Then the purpose of the present work is to study $^{105}$Mo paying attention to rotational character change of the one-phonon and two-phonon bands. The particle-vibration coupling model based on the cranking model and the random-phase approximation is used to calculate the vibrational states in rotating odd-$A$ nuclei. The present model reproduces the observed yrast zero-phonon and one-phonon bands well. Emerging general features of the rotational character change from low spin to high spin are elucidated. In particular, the reason why the one-phonon band does not exhibit signature splitting is clarified. The calculated collectivity of the two-phonon states, however, is located higher than observed.

Single-phonon and multi-phonon excitations of theγvibration in rotating odd-Anuclei

Multi-phonon excitations in atomic nuclei were observed very rarely although collective motions in quantum many-body systems are described as bosonic excitations. In particular, the first two-phonon $\gamma$ vibrational ($2\gamma$) excitation in odd-$A$ nuclei was reported in 2006 and only a few have been known. Quite recently, conspicuously enhanced $B(E2)$s feeding $2\gamma$ states were observed in $^{105}$Nb and conjectured that their parent states are candidates of $3\gamma$ states. In the present work, the model space is enlarged from the present author's previous calculation for $^{103}$Nb. The purpose is twofold: One is to see how the description of $2\gamma$ states is improved, and the other is to examine the existence of collective $3\gamma$ states, and when they exist, study their collectivity through calculating interband $B(E2)$s. The particle-vibration coupling model based on the cranking model and the random-phase approximation is used to calculate the vibrational states in rotating odd-$A$ nuclei. Interband $B(E2)$s are calculated by adopting the method of the generalized intensity relation. The present calculation reproduces the observed spectra of $0\gamma$ - $2\gamma$ states well and gives collective $3\gamma$ states with enhanced $B(E2)$s to $2\gamma$ states in $^{103}$Nb and $^{105}$Nb. The most collective $3\gamma$ state with the highest $K$ at zero rotation is thought to be the main component of the observed band.

Probing particle-phonon-coupled states in the neutron-rich nucleusCu65by lifetime measurements with fast-timing techniques

The Cu65 nucleus was populated by the Ni64(Li7,α2n)Cu65 reaction and the lifetime of the 9/2+ state at 2.5 MeV was measured by electronic fast-timing technique, providing the value τ= 37(3) ps. The reduced transition probability B(E3)=8.82(165) W.u. is deduced and compared to theoretical predictions in the framework of a particle-vibration (weak) coupling model. The results indicate that the 9/2+ state is a member of the 3−⊗πp3/2 multiplet, built by coupling the octupole 3− phonon of Ni64 to an unpaired proton in the p3/2 level, confirming the robustness of core excitations in the medium mass nucleus Ni64.3 MoreReceived 4 March 2014DOI:https://doi.org/10.1103/PhysRevC.89.054302©2014 American Physical Society

Continuum particle-vibration coupling method in coordinate-space representation for finite nuclei

In this paper we present a new formalism to implement the nuclear particle-vibration coupling (PVC) model. The key issue is the proper treatment of the continuum, that is allowed by the coordinate space representation. Our formalism, based on the use of zero-range interactions like the Skyrme forces, is microscopic and fully self-consistent. We apply it to the case of neutron single-particle states in $^{40}$Ca, $^{208}$Pb and $^{24}$O. The first two cases are meant to illustrate the comparison with the usual (i.e., discrete) PVC model. However, we stress that the present approach allows to calculate properly the effect of PVC on resonant states. We compare our results with those from experiments in which the particle transfer in the continuum region has been attempted. The latter case, namely $^{24}$O, is chosen as an example of a weakly-bound system. Such a nucleus, being double-magic and not displaying collective low-lying vibrational excitations, is characterized by quite pure neutron single-particle states around the Fermi surface.

Erosion of [formula omitted] shell in [formula omitted] investigated through the ground-state electric quadrupole moment

Electric quadrupole moment Q of the Al33 ground state has been measured by means of β-NMR spectroscopy using a spin-polarized Al33 beam produced in a projectile fragmentation reaction. The obtained Q moment, |Qexp(33Al)|=132(16) emb, shows a significant excess from the prediction of shell model calculations within the sd shell. The result indicates sizable admixing of pf intruder configurations in the ground state, demonstrating that the N=20 shell closure certainly erodes in Al33, a nucleus located on the border of the island of inversion. Comparison was made with predictions of the Monte Carlo shell model, and also a particle-vibration coupling model treating the neutron pairing correlations in the ground state of Al33. Again, a significant admixture of pf intruder configurations to the Al33 ground state was needed in both theoretical approaches to explain the observed large Q.

Microscopic Effective Charges and the B(E2) Values of Terminating States in Mirror Nuclei 51Mn and 51Fe

The microscopic effective charges in mirror nuclei 51Mn and 51Fe are investigated with the particle-vibration coupling model based on the self-consistent Skyrme-Hartree-Fock and continuum random-phase-approximation approaches. The isovector parts are predicted to be around 0.15, and the proton effective charges are around 1.25 e, which is less than the empirical value of eeffp = 1.5 e. The microscopic effective charges in neutron rich 51Mn are about 10% less than its proton rich mirror. These effective charges are combined with the shell model to calculate the reduced electric quadrupole transition probability B(E2) values in 51Mn and 51Fe. It turns out that the microscopic effective charges have well reproduced the B(E2) values and its ratio in the terminating states.

Dynamics of nuclear single-particle structure in covariant theory of particle-vibration coupling: From light to superheavy nuclei

The impact of particle-vibration coupling and polarization effects due to deformation and time-odd mean fields on single-particle spectra is studied systematically in doubly magic nuclei from low-mass $^{56}\mathrm{Ni}$ up to superheavy ones. Particle-vibration coupling is treated fully self-consistently within the framework of the relativistic particle-vibration coupling model. Polarization effects due to deformation and time-odd mean field induced by odd particle are computed within covariant density functional theory. It has been found that among these contributions the coupling to vibrations makes a major impact on the single-particle structure. The impact of particle-vibration coupling and polarization effects on calculated single-particle spectra, the size of the shell gaps, the spin-orbit splittings and the energy splittings in pseudospin doublets is discussed in detail; these physical observables are compared with experiment. Particle-vibration coupling has to be taken into account when model calculations are compared with experiment since this coupling is responsible for observed fragmentation of experimental levels; experimental spectroscopic factors are reasonably well described in model calculations.

Two-phononγ-vibrational states in rotating triaxial odd-Anuclei

The distribution of the two-phonon $\ensuremath{\gamma}$-vibrational collectivity in the rotating triaxial odd-$A$ nucleus $^{103}\mathrm{Nb}$, which is one of the three nuclides for which experimental data were reported recently, is calculated in the framework of the particle vibration coupling model based on the cranked shell model plus random phase approximation. This framework was previously utilized for analyses of the zero- and one-phonon bands in another mass region and is applied to the two-phonon band for the first time. In the present calculation, three sequences of two-phonon bands share collectivity almost equally at finite rotation whereas the $K=\ensuremath{\Omega}+4$ state is the purest at zero rotation.

Core polarization for the electric quadrupole moment of neutron-rich aluminum isotopes

The core polarization effects for the electric quadrupole moments of the neutron-rich $^{31}\mathrm{Al}$, $^{33}\mathrm{Al}$, and $^{35}\mathrm{Al}$ isotopes in the vicinity of the island of inversion are investigated by means of the microscopic particle-vibration coupling model in which the Skyrme Hartee-Fock-Bogoliubov and quasiparticle random-phase approximations are used to calculate the single-quasiparticle wave functions and the excitation modes. It is found that the polarization charge for the proton $1{d}_{5/2}$ hole state in $^{33}\mathrm{Al}$ is quite sensitive to coupling to the neutrons in the $\mathit{pf}$-shell associated with the pairing correlations and that the polarization charge in $^{35}\mathrm{Al}$ becomes larger due to the stronger collectivity of the low-lying quadrupole vibrational mode in the neighboring $^{36}\mathrm{Si}$ nucleus.

Quadrupole moment and a proton halo structure in 17F (Iπ = 5/2+)

The quadrupole moment of light nuclei 17F in the ground state (Iπ = 5/2+) is measured by the β–NMR method. The effective charge of the last proton in a d5/2 orbit for 17F is extracted from the measured quadrupole moment Q(17F) divided by the quadrupole moment Qsp calculated with a single particle model. A proton effective charge of eeffp = 1.12 ± 0.07e is obtained, which is in agreement with that given by a particle–vibration coupling model calculation within the experimental error. The present value of the proton effective charge is strong evidence for the existence of a proton skin in 17F (Iπ = 5/2+).

Polarization charge of O isotopes

Isospin dependence of polarization charges in O isotopes is studied based on a microscopic particle-vibration coupling model in which the Hartree–Fock single-particle wavefunctions and RPA quadrupole strengths are used. Both isoscalar and isovector parts are included in the vertex of particle-vibration coupling. The effects of the different possible dynamical structures at a given excitation energy on polarization charges are also discussed. A large quenching of the polarization charges is found with a large value of (N − Z)/A for most single particle orbits. It is also found that the polarization charges are sensitive to the binding energy of the single particle orbit.

Covariant response theory beyond RPA and its application

The covariant particle-vibration coupling model within the time-blocking approximation is employed to supplement the relativistic random phase approximation (RRPA) with coupling to collective vibrations. The Bethe—Salpeter equation in the particle—hole channel with an energy-dependent residual particle—hole (ph) interaction is formulated and solved in the shell-model Dirac basis as well as in the momentum space. The same set of coupling constants generates the Dirac—Hartree single-particle spectrum, the static part of the residual ph interaction, and the particle-phonon coupling amplitudes. This approach is applied to a quantitative description of damping phenomenon in even—even spherical nuclei with closed shells 208Pb and 132Sn. Since phonon coupling enriches the RRPA spectrum with a multitude of ph ⊗ phonon states, a noticeable fragmentation of giant monopole and dipole resonances is obtained in the examined nuclei. The results are compared with experimental data and results of the nonrelativistic approach.