Isovector Quadrupole Research Articles

Odd-even staggering of binding energy for nuclei in thesdshell

In this paper we study odd-even staggering phenomena of binding energy in the framework of the nuclear shell model for nuclei in the $sd$ shell. We decompose the USDB effective interaction into the monopole interaction and multipole (residual) interactions. We extract the empirical proton-neutron interaction, the Wigner energy, and the one-neutron separation energy using calculated binding energies. The monopole interaction, which represents the spherical mean field, provides contributions to the empirical proton-neutron interaction, the symmetry energy, and the Wigner energy. It does not induce odd-even staggering of the empirical proton-neutron interaction or the one-neutron separation energy. Isovector monopole and quadrupole pairing interactions and isoscalar spin-1 pairing interactions play a key role in reproducing an additional binding energy in both even-even and odd-odd nuclei. The Wigner energy coefficients are sensitive to residual two-body interactions. The nuclear shell structure has a strong influence on the evolution of the one-neutron separation energy, but not on empirical proton-neutron interactions. The so-called three-point formula is a good probe of the shell structure.

Symmetry energy from the nuclear collective motion: constraints from dipole, quadrupole, monopole and spin-dipole resonances

The experimental and theoretical studies of Giant Resonances, or more generally of the nuclear collective vibrations, are a well established domain in which sophisticated techniques have been introduced and firm conclusions reached after an effort of several decades. From it, information on the nuclear equation of state can be extracted, albeit not far from usual nuclear densities. In this contribution, which complements other contributions appearing in the current volume, we survey some of the constraints that have been extracted recently concerning the parameters of the nuclear symmetry energy. Isovector modes, in which neutrons and protons are in opposite phase, are a natural source of information and we illustrate the values of symmetry energy around saturation deduced from isovector dipole and isovector quadrupole states. The isotopic dependence of the isoscalar monopole energy has also been suggested to provide a connection to the symmetry energy: relevant theoretical arguments and experimental results are thoroughly discussed. Finally, we consider the case of the charge-exchange spin-dipole excitations in which the sum rule associated with the total strength gives in principle access to the neutron skin and thus, indirectly, to the symmetry energy.

Systematics of isovector and isoscalar giant quadrupole resonances in normal and superfluid spherical nuclei

The isoscalar (IS) and isovector (IV) quadrupole responses of nuclei are systematically investigated using the time-dependent Skyrme Energy Density Functional including pairing in the BCS approximation. Using two different Skyrme functionals, Sly4 and SkM*, respectively 263 and 304 nuclei have been found to be spherical along the nuclear charts. The time-dependent evolution of these nuclei has been systematically performed giving access to their quadrupole responses. It is shown that the mean-energy of the collective high energy state globally reproduces the experimental IS and IV collective energy but fails to reproduce their lifetimes. It is found that the mean collective energy depends rather significantly on the functional used in the mean-field channel. Pairing by competing with parity effects can slightly affect the collective response around magic numbers and induces a reduction of the collective energy compared to the average trend. Low-lying states, that can only be considered if pairing is included, are investigated. While the approach provides a fair estimate of the low lying state energy, it strongly underestimates the transition rate $B(E2)$. Finally, the possibility to access to the density dependence of the symmetry energy through parallel measurements of both the IS- and IV-GQR is discussed.

Magnetic dipole excitations in nuclei: Elementary modes of nucleonic motion

The nucleus is one of the most multi-faceted many-body systems in the universe. It exhibits a multitude of responses depending on the way one 'probes' it. With increasing technical advancements of beams at the various accelerators and of detection systems the nucleus has, over and over again, surprised us by expressing always new ways of 'organized' structures and layers of complexity. Nuclear magnetism is one of those fascinating faces of the atomic nucleus we discuss in the present review. We shall not just limit ourselves to presenting the by now very large data set that has been obtained in the last two decades using various probes, electromagnetic and hadronic alike and that presents ample evidence for a low-lying orbital scissors mode around 3 MeV, albeit fragmented over an energy interval of the order of 1.5 MeV, and higher-lying spin-flip strength in the energy region 5 - 9 MeV in deformed nuclei, nor to the presently discovered evidence for low-lying proton-neutron isovector quadrupole excitations in spherical nuclei. To the contrary, we put the experimental evidence in the perspectives of understanding the atomic nucleus and its various structures of well-organized modes of motion and thus enlarge our discussion to more general fermion and bosonic many-body systems.

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.

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.

Isovector quadrupole resonance observed in the 60Ni(13C,13N)60Co reaction at E/A=100 MeV.

The charge-exchange reaction 60Ni(13C,13N)60Co at E/A=100 MeV has been studied to locate isovector (deltaT=1) non-spin-flip (deltaS=0) giant resonances. Besides the giant dipole resonance at E(x)=8.7 MeV, another resonance has been observed at E(x)=20 MeV with a width of 9 MeV. Distorted-wave Born approximation analysis on the angular distribution clearly indicated the L=2 multipolarity, attributing the E(x)=20 MeV state to the giant isovector quadrupole resonance.

Isovector dipole and quadrupole excitations in66Zn

The nucleus ${}^{66}\mathrm{Zn}$ is investigated using $\ensuremath{\gamma}\ensuremath{\gamma}$-coincidence studies following the $\ensuremath{\beta}$ decay of the ${0}^{+}$ ground state of ${}^{66}\mathrm{Ga}.$ The data survey short-lived ${J}^{\ensuremath{\pi}}{=1}^{+}{,2}^{+}$ states, $E2/M1$ mixing ratios, and, together with the previously known lifetimes, also absolute transition strengths $B(\ensuremath{\sigma}L).$ The proton-neutron mixed-symmetry states ${2}_{\mathrm{ms}}^{+}$ (isovector quadrupole excitation) and ${1}_{\mathrm{ms}}^{+}$ (``scissors mode'') were identified from their decay patterns and absolute transition strengths. A $\ensuremath{\gamma}$ transition between these mixed-symmetry states was observed and its rate is discussed. We additionally present a candidate for the two-phonon ${2}_{2,ms}^{+}$ state, whose structure is closely related to the ${1}_{\mathrm{ms}}^{+}$ excitation. Fifteen $M1$ and $E2$ strengths involving mixed-symmetry states show a reasonable agreement with the prediction of the pure O(6) limit of the proton-neutron extension of the interacting boson model (IBM-2) using the effective quadrupole boson charges ${e}_{\ensuremath{\pi}}{+e}_{\ensuremath{\nu}}$ and the g-factor difference ${g}_{\ensuremath{\pi}}\ensuremath{-}{g}_{\ensuremath{\nu}}$ as the only free parameters.

Coulomb excitation of the2ms+state of96Ruin inverse kinematics

We identify the ${J}^{\ensuremath{\pi}}{=2}_{3}^{+}$ state of ${}^{96}\mathrm{Ru}$ as the proton-neutron mixed-symmetry ${2}_{\mathrm{ms}}^{+}$ state of this nucleus. This identification is based on the measurement of the transition strengths ${B(M1,2}_{3}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})=0.78(23) {\ensuremath{\mu}}_{N}^{2}$ and ${B(E2;2}_{3}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})=1.6(3)$ W.u. These transition strengths were obtained from the Coulomb excitation yield for the population of the ${2}_{3}^{+}$ state relative to the yield of the ${2}_{1}^{+}$ state with known $E2$ excitation strength. The Coulomb excitation was done in inverse kinematics using the reaction ${}^{\mathrm{nat}}\mathrm{C}{(}^{96}\mathrm{Ru}{,}^{96}{\mathrm{Ru}}^{\ensuremath{\star}})$ at 280 MeV. This work demonstrates the accessibility of the isovector quadrupole excitation in the valence shell using experiments with an accelerated beam of the nuclei of interest.

Isovector quadrupole excitations in the valence shell of the vibrator nucleus136Ba:Evidence from photon scattering experiments

Photon scattering experiments have been performed on the nucleus ${}^{136}$Ba with photon energies of ${E}_{\ensuremath{\gamma}}<~4.1$ MeV and ${E}_{\ensuremath{\gamma}}<~2.8$ MeV. At 2.1 MeV clear evidence for the ${2}_{\mathrm{ms}}^{+}$ state has been found. From the measured lifetime we extract signatures for the isovector quadrupole excitation in the valence shell: a weakly collective $E2$ decay to the ground state and a strong $M1$ decay to the ${2}_{1}^{+}$ state. As the resonant photon scattering with bremsstrahlung is a complete reaction, we can conclude that the ${2}^{+}$ state at 2129 keV is a rather pure ${2}_{\mathrm{ms}}^{+}$ state with little fragmentation. This is in contrast to the ${1}^{+}$ scissors state. A comparison with an IBM-2 calculation is given.

Excitation and neutron decay of xenon by forward-angle scattering of 250 A MeV 17O ions

A technique to study giant resonances by forward-angle scattering of heavy ions in the energy range 100–470 A MeV, using one quadrant of the CELSIUS storage ring as a magnetic spectrometer, is presented. The reaction nat Xe( 17O, 17O′n) has been studied at E( 17O) =250A MeV . A structure in the excitation energy spectrum, compatible with the isovector dipole resonance and the isoscalar quadrupole resonance, was observed, together with a possible candidate for the isovector quadrupole resonance. In addition to neutrons from statistical decay, a large number of non-statistical neutrons in the range E n =5–30 MeV was observed, with a forward-peaked angular distribution.

Effects of neutron skin on the excitation of isovector modes of neutron-rich nuclei

The existence of a neutron skin in neutron-rich nuclei is discussed in connection with the excitation of isovector dipole and quadrupole giant modes via isoscalar nuclear probes. In the case of large neutron excess, important contributions are obtained from the nuclear excitation, which may even become predominant according to proper kinematical conditions. At variance with the usual situation encountered in inelastic processes, constructive interference can be found between nuclear and Coulomb contributions.

Need for an isovector quadrupole term in the sum rule relating scissors mode excitations toB(E2)values

For a $Q\ensuremath{\cdot}Q$ interaction the energy-weighted sum rule for isovector orbital magnetic dipole transitions is proportional to the difference $\ensuremath{\sum}B(E2,\mathrm{isoscalar})\ensuremath{-}\ensuremath{\sum}B(E2,\mathrm{isovector})$, not just to $\ensuremath{\sum}B(E2,\mathrm{physical})$. This fact is important in ensuring that one gets the correct limit as one goes to nuclei, some of which are far from stability, for which one shell (neutron or proton) is closed.

(γ,n)study of the isovector quadrupole resonance in40Ca

The forward-to-backward asymmetry of neutrons emitted in the 40Ca(γ,n0) reaction was measured at photon energies in the range of 27–50 MeV. An energy-dependent asymmetry was observed that is interpreted as evidence of interference between the isovector quadrupole resonance and the giant dipole resonance. Data analysis in terms of semiclassical and direct-semidirect models estimate the isovector quadrupole resonance to be at an excitation energy of 31.0±1.5 MeV, with a width of 16.0±1.5 MeV, and exhausting most of the energy-weighted sum rule for the isovector quadrupole resonance.

Spectral line shape of exotic nuclei.

The quadrupole strength function of $^{28}\mathrm{O}$ is calculated making use of the SIII interaction, within the framework of continuum-RPA and taking into account collisions among the nucleons (doorway coupling). The centroid of the giant resonance is predicted at \ensuremath{\approx} 14 MeV, which is much below the energy expected for both isoscalar and isovector quadrupole resonances in nuclei along the stability valley. About half of its width arises from the coupling of the resonance to the continuum and about half is due to doorway coupling. This result is similar to that obtained in the study of giant resonances in light, $\ensuremath{\beta}$-stable nuclei, and shows the lack of basis for the expectation, entertained until now in the literature, that continuum decay was the main damping mechanism of giant resonances in halo nuclei.

Evidence for a weaker isovector potential.

Estimates for a weaker isovector potential than previously adopted are put forward. It is also strongly mass and energy dependent. The resulting isovector particle-hole interaction is weaker in lighter nuclei and the isovector quadrupole resonance should be located at lower energy than previously expected. The uncertainties arising from the separation of the potential asymmetry energy in nuclear matter calculations are discussed. {copyright} {ital 1996 The American Physical Society.}

Computer program for the time-evolution of a nuclear system in relativistic mean-field theory

A C-program is presented which calculates the time-evolution of a nuclear system in the framework of relativistic mean field theory (RMFT). Subject to some initial conditions, a coupled system of Dirac and Klein-Gordon partial differential equations describes the evolution of nucleon and meson fields in time. The present version of the program describes isovector dipole, isoscalar and isovector monopole, isoscalar and isovector quadrupole axially symmetric collective motion in a nucleus.

Relativistic mean-field description of small- and large-amplitude collective motion in nuclei

The dynamics of collective motion in nuclei is described in the framework of time-dependent relativistic mean-field theory. For a given set of initial conditions (stationary solution for the ground state, initial velocities of the proton and neutron densities, initial deformations), the model describes the time evolution of the nuclear system. In the limit of small-amplitude motion we investigate isovector dipole, isoscalar quadrupole, and isovector quadrupole oscillations. Model calculations are performed for the nuclei 16O, 40Ca, 48Ca and compared with experimental data on energies and widths of giant resonances. For 48Ca we also investigate the dynamics of large-amplitude isovector dipole motion. With increasing excitation energy the motion becomes strongly anharmonic and clusters of particles evaporate from the surface of the nucleus. At the highest energies we find a rapid dissociation of the nucleus in proton and neutron clusters.

Quadrupole contribution to two-neutron removal in heavy ion collisions.

In this Brief Report, electric quadrupole corrections to the two-neutron removal cross section measured in heavy ion collisions are estimated for {sup 197}Au and {sup 59}Co targets. The quadrupole process is assumed to proceed primarily through excitation of the giant isovector quadrupole resonance, which then decays by neutron emission. For {sup 59}Co, the contribution from {ital E}2 radiation is found to be small, while for {sup 197}Au we find the quadrupole contribution resolves the discrepancy between experiment and the simple predictions of the Weissacker-Williams virtual photon method.

Some suggestions about the research of theE2(T=1) resonance excitation by (n, γ) reaction on cerium

Determining at microscopic level the interaction responsible for the excitation of collective states of140Ce makes it possible to use in a coherent way the direct-semidirect model in the study of the140Ce(\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {n} \), γ) reaction. Computations of differential cross-sections give useful pieces of information about the effects caused by the excitation of the isovector quadrupole giant resonance on the γ-ray emission geometry, closely connected with the polarization state of the incident neutron. Thus, the results supply helpful suggestions on a possible experimental research of theE2(T=1) excitation by means of the radiative capture reaction.