Vibrational Nuclei Research Articles

E2strengths and transition radii difference of one-phonon2+states of92Zr from electron scattering at low momentum transfer

Background: Mixed-symmetry ${2}^{+}$ states in vibrational nuclei are characterized by a sign change between dominant proton and neutron valence-shell components with respect to the fully symmetric ${2}^{+}$ state. The sign can be measured by a decomposition of proton and neutron transition radii with a combination of inelastic electron and hadron scattering [C. Walz et al., Phys. Rev. Lett. 106, 062501 (2011)]. For the case of ${}^{92}$Zr, a difference could be experimentally established for the neutron components, while about equal proton transition radii were indicated by the data.Purpose: Determination of the ground-state (g.s.) transition strength of the mixed-symmetry ${2}_{2}^{+}$ state and verification of the expected vanishing of the proton transition radii difference between the one-phonon ${2}^{+}$ states in ${}^{92}$Zr.Method: Differential cross sections for the excitation of one-phonon ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states in ${}^{92}$Zr have been measured with the ($e,{e}^{\ensuremath{'}}$) reaction at the S-DALINAC in a momentum transfer range $q\ensuremath{\simeq}0.3--0.6$ fm${}^{\ensuremath{-}1}$.Results: Transition strengths $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})=6.18(23)$, $B(E2;{2}_{2}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})=3.31(10)$, and $B(E3;{3}_{1}^{\ensuremath{-}}\ensuremath{\rightarrow}{0}_{1}^{+})=18.4(1.1)$ Weisskopf units are determined from a comparison of the experimental cross sections to quasiparticle-phonon model (QPM) calculations. It is shown that a model-independent plane wave Born approximation (PWBA) analysis can fix the ratio of $B(E2)$ transition strengths to the ${2}_{1,2}^{+}$ states with a precision of about 1$%$. The method furthermore allows to extract their proton transition radii difference. With the present data $\ensuremath{\Delta}R=\ensuremath{-}0.12(51)$ fm is obtained.Conclusions: Electron scattering at low momentum transfers can provide information on transition radii differences of one-phonon ${2}^{+}$ states even in heavy nuclei. Proton transition radii for the ${2}_{1,2}^{+}$ states in ${}^{92}$Zr are found to be identical within uncertainties. The g.s. transition probability for the mixed-symmetry state can be determined with high precision limited only by the available experimental information on the $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+}$) value.

Descriptive New features of high angular momentum rotational states in some rear-earth nuclei

The results from the variable moment of inertia (VMI) and cubic polynomial (CP) models with the available experimental information on transition energies for the yrast band levels in all studied nuclei. These models has been generalized so as to be applicable to transitional and vibrational nuclei by requiring that the extended models reduce at low angular momentum, to the polynomial dependence which gives excellent fits to the experimental spectra in the spherical, transitional and deformed regions. The level structure indicate a transition from collective to few-particle characteristics at high spin, possibly suggesting a change shape from prolate through triaxial to oblate. The loss of collectivity occurs at much lower angular momentum than predicted by calculations. The calculated Qt-value of the yrast band of the nucleus with N = 90.

On quadrupole vibrations in nearly spherical nuclei

A new understanding of low-lying quadrupole vibrations in nuclei is emerging through lifetime measurements performed with fast neutrons at the accelerator laboratory of the University of Kentucky in combination with high-sensitivity measurements with other probes. In the stable cadmium nuclei, which have long been considered to be the best examples of vibrational behavior, we find that many E2 transition probabilities are well below harmonic vibrator expectations, and the B(E2)s cannot be explained with calculations incorporating configuration mixing between vibrational phonon states and intruder excitations. These data place severe limits on the collective models, and it is suggested that the low-lying levels of the Cd isotopes may not be of vibrational origin. An additional example of an apparent quadrupole vibrational nucleus, 62Ni, is considered.

Direct Evidence for Proton-Neutron Out-of-Phase Coupling in Mixed-Symmetry States from Scattering Experiments on 92Zr

The coupling of the giant quadrupole resonance to valence space configurations is shown to dominantly contribute to the formation of low-lying quadrupole collective structures in vibrational nuclei with symmetric and mixed-symmetric character with respect to the proton-neutron degree of freedom. Experimental evidence is obtained from electron- and proton scattering experiments on the nucleus 92Zr that are directly sensitive to the relative phase of valence space amplitudes by quantum interference.

Origin of Low-Energy Quadrupole Collectivity in Vibrational Nuclei

The coupling of the giant quadrupole resonance to valence-space configurations is shown to be the origin of the formation of low-lying quadrupole-collective structures in vibrational nuclei with symmetric and mixed-symmetric character with respect to the proton-neutron degree of freedom. For the first time experimental evidence for this picture is obtained from electron- and proton scattering experiments on the nucleus ^{92}Zr that are sensitive to the relative phase of valence-space amplitudes by quantum interference.

Experimental studies of proton-neutron mixed symmetry states in the mass A ≈ 130 region

Considerable progress has been achieved recently in the experimental investigation of quadrupole-collective isovector excitations in the valence shell, the so called mixed-symmetry states (MSSs), in the mass A ≈ 130 region. This is due to a new experimental technique for study MSSs which is based on the observation of low-multiplicity γ-ray events from inverse kinematics Coulomb excitation with the large 4π spectrometer, such as Gammasphere. The obtained experimental information for the MSSs of stable N = 80 isotones indicates that for low-collective vibrational nuclei the underlying single-particle structure can be the most important factor for preserving or fragmenting the MSSs through the mechanism of shell stabilization. The evolution of the MSSs from 134Xe to 138Ce is also used to determine the local strength of the proton-neutron interaction derived for first time from states with symmetric and antisymmetric nature.

γ-ray spectroscopy approaching the limits of existence of atomic nuclei: A study of the excited states ofPt168andPt169

Excited states in the $N=90$ and $N=91$ Pt nuclei have been investigated using the JUROGAM and GREAT spectrometers in conjunction with the RITU gas-filled separator. These nuclei were populated via the reactions $^{92}\mathrm{Mo}(^{78}\mathrm{Kr},2n)$ and $^{94}\mathrm{Mo}(^{78}\mathrm{Kr},3n)$ at 335 and 348 MeV, respectively. The recoil-decay tagging technique has been used to correlate prompt $\ensuremath{\gamma}$ radiation with the characteristic $\ensuremath{\alpha}$ decays of $^{168}\mathrm{Pt}$ and $^{169}\mathrm{Pt}$. A $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ analysis has allowed a level scheme for $^{168}\mathrm{Pt}$ to be reported for the first time and the level scheme for $^{169}\mathrm{Pt}$ to be extended. The excitation energies of the proposed positive-parity yrast states of $^{168}\mathrm{Pt}$ are compared with calculations based on the interacting boson model and found to be in excellent agreement. These data show a continuation of the trend toward vibrational nuclei as the $N=82$ shell gap is approached. In addition, new excited states constituting two decay paths have been discovered in $^{169}\mathrm{Pt}$.

Sandwich complexes of the Sb 42− aromatic ring with some transition metals

The equilibrium geometries, energies, harmonic vibrational frequencies, molecular orbital (MO), stability, and nucleus independent chemical shifts (NICS) of the new type sandwich structures [Sb 4MSb 4] n − (M = Fe, Ru, Os, Co, Rh, and Ir; n = 1, or 2) are researched at the B3LYP level of theory. The calculations reveal that the [Sb 4MSb 4] n − complexes adopt the staggered D 4 d conformers as their stable structures, and the Sb 4 2− ring of them exhibit σ and π aromaticity. Some of MOs for [Sb 4MSb 4] n − originated from the interactions between the orbitals of the ligands and the atomic orbitals of the metal, and the other directly inherited from the ligands, and once the sandwich complexes are formed, the Sb 4 2− square properties remain unchanged. The addition of sodium to [Sb 4MSb 4] 2− (M = Fe, Ru, and Os) can yield stabilization toward electron detachment, and the sandwich structures are all stable thermodynamically because the dissociations of [Sb 4MSb 4] n − and [Sb 4MSb 4Na] − into separated fragments are both endothermic reaction.

Isovector Quadrupole Excitations in the Valence Shell studied in Projectile Coulomb Excitation

One-phonon states of heavy vibrational nuclei with mixed proton-neutron symmetry have recently been made accessible by the technique of projectile Coulomb excitation. Gamma-rays following Coulomb excitation of the nuclides 136,138 Ce and 134 Xe have been measured with the Gammasphere-array run in singles-mode. M 1, E 2, and E 3 transition matrix elements from low-spin states were measured relative to the known B ( E 2 ; 0 1 + → 2 1 + ) values. The 2 + → 2 1 + M 1 strength distributions up to about 2.7 MeV serve for identifying the main fragment of the 2 1 , ms + one-quadrupole phonon mixed-symmetry state. The data are presented and their significance is discussed.

THE NUMBER SELF-CONSISTENT RENORMALIZED RANDOM PHASE APPROXIMATION

RPA and its quasiparticle generalization (QRPA) have been widely used to study electromagnetic transitions and beta decays in medium and heavy nuclei, being the pn-QRPA charge exchange mode extensively employed in the description of single and double beta decays in vibrational nuclei. However develops a collapse, i.e. it presents imaginary eigen-values for strengths beyond a critical value of the force. Extensions called renormalized QRPA (RQRPA) do not develop any collapse going beyond the simplest quasiboson approximation, however they present several drawbacks which will be analyzed.

Exactly solvable models of proton and neutron interacting bosons

We describe a class of exactly-solvable models of interacting bosons based on the algebra SO(3,2). Each copy of the algebra represents a system of neutron and proton bosons in a given bosonic level interacting via a pairing interaction. The model that includes s and d bosons is a specific realization of the IBM2, restricted to the transition regime between vibrational and gamma-soft nuclei. By including additional copies of the algebra, we can generate proton-neutron boson models involving other boson degrees of freedom, while still maintaining exact solvability. In each of these models, we can study not only the states of maximal symmetry, but also those of mixed symmetry, albeit still in the vibrational to gamma-soft transition regime. Furthermore, in each of these models we can study some features of F-spin symmetry breaking. We report systematic calculations as a function of the pairing strength for models based on s, d, and g bosons and on s, d, and f bosons. The formalism of exactly-solvable models based on the SO(3,2) algebra is not limited to systems of proton and neutron bosons, however, but can also be applied to other scenarios that involve two species of interacting bosons.

Low-lying dipole excitations in vibrational nuclei: The Cd isotopic chain studied in photon scattering experiments

High-resolution nuclear resonance fluorescence experiments (NRF) were performed on $^{110,111,112,114,116}\mathrm{Cd}$ at the bremsstrahlung facility of the 4.3-MV Dynamitron accelerator in Stuttgart to study the low-lying dipole strength distributions in these vibrational nuclei. Numerous excited states, most of them previously unknown, were observed in the excitation energy range up to 4 MeV. Detailed spectroscopic information has been obtained on excitation energies, spins, decay widths, decay branchings, and transition probabilities. For states in the even-even isotopes $^{110,112,114,116}\mathrm{Cd}$, parities could be assigned from linear polarization measurements. Together with our previous results for $^{108,112,113,114}\mathrm{Cd}$ from NRF studies without polarization measurements, systematics was established for the dipole strength distributions of the stable nuclei within the Cd isotopic chain. The results are discussed with respect to the systematics of $E1$ two-phonon excitations and mixed-symmetry states in even-even nuclei near the $Z=50$ shell closure and the fragmentation of these excitation modes in the odd-mass Cd isotopes.

Probing multiphonon excitations in nearly spherical nuclei with fast neutrons

Multiphonon excitations in a number of nearly spherical nuclei have been investigated with the (n,n′γ) reaction. Quadrupole three-phonon quintets and candidates for members of the four-phonon octets have been identified in the Cd region. In addition, complete quadrupole–octupole quintets have been characterized in this region, and mixed-symmetry states in vibrational nuclei are now well known. Our best examples of two-phonon octupole states have also emerged in spherical nuclei, such as 208Pb.

Investigation of dipole excitations inCe142using resonant photon scattering

A photon scattering experiment with bremsstrahlung has been performed on the vibrational nucleus $^{142}\mathrm{Ce}$ up to a photon endpoint energy of $4.1\phantom{\rule{0.3em}{0ex}}\text{MeV}$. Fourteen dipole excitations have been observed between 2.1 and $3.9\phantom{\rule{0.3em}{0ex}}\text{MeV}$, five of them for the first time. A candidate for the ${1}^{\ensuremath{-}}$ dipole member of the recently proposed quintuplet of negative parity ${({2}_{1,\text{ms}}^{+}\ensuremath{\bigotimes}{3}_{1}^{\ensuremath{-}})}^{({J}^{\ensuremath{-}})}$, involving the ${2}_{1,\text{ms}}^{+}$ isovector quadrupole excitation in the valence shell, has been identified. This exotic ${1}_{\text{ms}}^{\ensuremath{-}}$ state has been predicted within the $sdf$-IBM-2 and is expected to be accessible to photon scattering measurements. Solely one of nine $J=1$ states in the energy region of interest shows a decay pattern compatible with the model predictions for the ${1}_{\text{ms}}^{\ensuremath{-}}$ state.

High-spin states in the vibrational nucleus 114 Cd

High-spin states of the neutron-rich vibrational nucleus 114 Cd have been studied using the incomplete fusion reaction 110 Pd(7Li, p2n) and the GASP spectrometer in conjunction with the ISIS Si ball. About 50 new states with excitation energies up to 7 MeV and angular momentum $I \le (18^ + )$ were observed and for many of them, spin and parity could be firmly assigned. The band-like stuctures in 114 Cd are compared to the corresponding ones in the even-even neighbour 112 Cd.

Interpretation of the2+anomaly in vibrational nuclei

The $``{2}_{1}^{+}$ anomaly'' in vibrational nuclei is studied in the context of alternate vibrational potentials. It is shown that a better reproduction of phonon and multiphonon multiplet energy centroids in vibrational nuclei is obtained with potentials having a strong quartic $(V\ensuremath{\sim}{\ensuremath{\beta}}^{4})$ component.

Singular character of critical points in nuclei

The concept of critical points in nuclear phase transitional regions is discussed from the standpoints of Q-invariants, simple observables and wave function entropy. It is shown that these critical points very closely coincide with the turning points of the discussed quantities, establishing the singular character of these points in nuclear phase transition regions between vibrational and rotational nuclei, with a finite number of particles.

Low-lying dipole excitations in the stable Cd isotopes: A systematics

Low-lying dipole excitations in the medium-weight vibrational nuclei of the Cd isotopic chain were investigated by means of nuclear resonance fluorescence experiments performed at the bremsstrahlung beam of the Stuttgart Dynamitron accelerator (endpoint energy 4.1 MeV). Detailed information has been obtained on excitation energies, spins, decay widths, and transition probabilities of numerous excited states in 110–114,116Cd. Additionally, the use of two Compton polarimeters enabled model-independent parity assignments for excitations in the even-even isotopes. Strongly excited Jπ = 1− states are found in all even-even Cd nuclei at excitation energies near the sumof the energies of the first 2+ and 3− states. These excitations are interpreted as the 1− member of the quadrupole-octupole coupled quintuplet (2+⊗3−). The fragmented strength observed in the odd isotopes 111,113Cd is compared with the strength distributions in the neighboring even-even Cd isotopes.

Discrete structures in fusion-barrier distributions for vibrational nuclei

We obtain a closed-form expression for the distribution of fusion barriers for vibrational nuclei using a generalization of Dasso, Landowne, and Winther's model, which represents the nuclear surface vibrations as a number of harmonic oscillators, and allows the excitation of an arbitrary number of phonons in the target and/or projectile. We find that this expression is in reasonable agreement with the average trends of the empirical distributions for the fusion of 16O with 92Zr, 144Sm and 208Pb, but fails to reproduce the double peaking of the distribution for the 144Sm target. Only when we restrict the number of excited phonons to a limited number, we are able to reproduce such discrete structures. We show that limiting the number of coupled channels, particularly in the case of strong coupling, increases the spacings between the channel eigenvalues that determine the positions of the peaks of the barrier distribution and modifies their heights.

One- and two-proton transfer reactions with vibrational nuclei

We extend a semiclassical model of transfer reactions to the case in which one of the collision partners is a vibrational nucleus. The model is applied to one- and two-proton stripping reactions in the 37Cl + 98Mo system, for which a rapid transition from normal to anomalous slope in the two proton transfer reaction at energies around the Coulomb barrier is experimentally observed. This behavior is satisfactorily reproduced by the present extension of the model.