Isoscalar Transition Research Articles

RPA calculations with Gaussian expansion method

The Gaussian expansion method (GEM) is applied to calculations of the nuclear excitations in the random-phase approximation (RPA). We adopt the mass-independent basis-set that is successful in the mean-field calculations. The RPA results obtained by the GEM are compared with those obtained by several other available methods in Ca isotopes, by using a density-dependent contact interaction along with the Woods–Saxon single-particle states. It is confirmed that energies, transition strengths and widths of their distribution are described by the GEM with good precision, for the 1 − , 2 + and 3 − collective states. The GEM is then applied to the self-consistent RPA calculations with the finite-range Gogny D1S interaction. The spurious center-of-mass motion is well separated from the physical states in the E1 response, and the energy-weighted sum rules for the isoscalar transitions are fulfilled reasonably well. Properties of low-energy transitions in 60Ca are investigated in some detail.

Isovector response and energy-weighted sums in hot nuclei

We investigate the collective response function and the energy-weighted sums (EWS) m k for isovector mode in hot nuclei. The approach is based on the collisional kinetic theory and takes into consideration the temperature and the relaxation effects. We have evaluated the temperature dependence of the adiabatic, E 1 = m 1 / m −1 , and scaling, E 3 = m 3 / m 1 , energy centroids of the isovector giant dipole resonances (IVGDR). The centroid energy E 3 is significantly influenced by the Fermi surface distortion effects and, in contrast to the isoscalar mode, shows much weaker variation with temperature. Taking into account a connection between the isovector sound mode and the corresponding surface vibrations we have established the A-dependence of the IVGDR centroid energy which is in a good agreement with experimental data. We have shown that the enhancement factor for the “model independent” sum m 1 is only slightly sensitive to the temperature change.

ALPHA-CLUSTER STRUCTURE IN 13C

We study the structure of low-lying states of 13 C with a microscopic cluster model. In addition to the 3α-n model space, the breaking effect of one of the α-clusters due to the spin-orbit interaction is also taken into account. The iso-scalar E0 transition probabilities from the ground 1/2- state to the excited 1/2- states have been shown to be large associated with the cluster structure of these states. However the values are small due to the effect of one additional valence neutron compared to the case of the second 0+ state in 12 C .

PROBING THE ISOSCALAR EXCITATIONS OF 12C WITH INELASTIC ALPHA SCATTERING

The robust (spin and isospin zero) α-particle remains one of the best projectiles to probe the nuclear isoscalar excitations. In the present work, a microscopic folding model analysis of the α+12 C inelastic scattering to the 2+ (4.44 MeV), 0+ (7.65 MeV), 3- (9.64 MeV), 0+ (10.3 MeV) and 1- (10.84 MeV) states in 12 C has been performed using the 3-α resonating group method wave functions. The isoscalar transition strengths of these states were carefully studied based on the coupled-channel analysis using the microscopic folded form factors. A correlation between the weak binding and/or short lifetime of the excited state and absorption in the exit channel of inelastic scattering has been established.

Subnanosecond lifetime measurement for theT=0,31+state of odd-odd N = ZCu58

We have measured the lifetime of the T=0,J{sup {pi}}=3{sub 1}{sup +} state of {sup 58}Cu at 444 keV. The excited states in {sup 58}Cu were populated with the {sup 58}Ni(p,n{gamma}) reaction at the SUNY at Stony Brook TANDEM-LINAC facility. A lifetime {tau} = 0.468 {+-} 0.085 ns was found with the delayed {gamma}-radiofrequency coincidence method with respect to the pulsed LINAC beam. It corresponds to an isoscalar E2 transition strength of 7.6 {+-} 1.4 W.u. to the T=0,J{sup {pi}}=1{sub 1}{sup +} ground state. The result agrees with the interpretation of the 3{sub 1}{sup +} state as a collective quadrupole excitation of the 1{sub 1}{sup +} ground state of {sup 58}Cu.

Isovector giant monopole resonances in spherical nuclei

We study isovector giant monopole resonances in spherical nuclei using the time-dependent Hartree–Fock method with different Skyrme forces. The aim of the investigation is to study how, for example, mass number and neutron excess influence the isovector giant monopole resonances and their mixing with isoscalar modes. We also study how nuclear matter properties, such as the asymmetry energy, of different Skyrme forces affect the behaviour of giant resonances. We find isovector and isoscalar modes to be strongly mixed and that there is little correlation between asymmetry energy and isovector resonance energy.

Formation of mesic nuclei by [formula omitted] reactions

We present a theoretical study on formation rates of η and ω meson–nucleus systems induced by ( γ , p ) reactions on nuclear targets at ideal recoilless condition. We find that the smaller distortion effect in the ( γ , p ) reaction enables us to investigate properties of the mesons created deeply inside nucleus more clearly. We also consider excitation of scalar–isoscalar ( σ ) mode in nucleus in order to investigate spectral enhancement around two-pion threshold caused by partial restoration of chiral symmetry. We conclude that valuable information of meson–nucleus interactions can be extracted from global structure of the missing mass spectra in the ( γ , p ) reaction.

Coulomb nuclear interference with deuterons in even palladium isotopes

Angular distributions for the inelastic scattering of 13.0 MeV deuterons on 104;106;108;110Pd were measured with the Sao Paulo Pelletron-Enge-Spectrograph facility in the range of 120 < qlab < 640. A Coulomb-Nuclear Interference analysis, employing the Distorted Wave Born Approximation with the Deformed Optical Model as transition potential, under well established global optical parameters, was applied to the first quadrupolar excitations. The values of C = / , the ratio of charge to isoscalar deformation lengths, and of ()2 were extracted through the comparison of experimental and predicted cross section angular distributions. The ratios of reduced charge to isoscalar transition probabilities, B(EL) to B(ISL) respectively, are related to the square of the parameter C and were thus obtained with the advantage of scale uncertainties cancellation. For 104Pd, and preliminary for 108Pd, the respective values of C = 1.18(3) and C = 1.13(4) reveal an enhanced contribution of the protons relative to the neutrons to the excitation, while a smaller effect is found for 106Pd, C = 1.06(3) and for 110Pd, C = 1.07(3), in comparison with the value C = 1.00 expected for homogenous collective excitations.

Probing the isovector transition strength of the low-lying nuclear excitations induced by inverse kinematics proton scattering

A compact approach based on the folding model is suggested for the determination of the isoscalar and isovector transition strengths of the low-lying ($\Delta S=\Delta T=0$) excitations induced by inelastic proton scattering measured with exotic beams. Our analysis of the recently measured inelastic $^{18,20}$O+p scattering data at $E_{\rm lab}=30$ and 43 MeV/nucleon has given for the first time an accurate estimate of the isoscalar $\beta_0$ and isovector $\beta_1$ deformation parameters (which cannot be determined from the (p,p') data alone by standard methods) for 2$^+_1$ and $3^-_1$ excited states in $^{18,20}$O. Quite strong isovector mixing was found in the 2$^+_1$ inelastic $^{20}$O+p scattering channel, where the strength of the isovector form factor $F_1$ (prototype of the Lane potential) corresponds to a $\beta_1$ value almost 3 times larger than $\beta_0$ and a ratio of nuclear transition matrix elements $M_n/M_p\simeq 4.2$.

Stability and instability of a hot and dilute nuclear droplet

Results on dissipative isoscalar modes of a hot and dilute nuclear droplet are presented. As compared to the adiabatic limit (part I), realistic dissipation yields a substantial reduction of the growth rates for all unstable modes, while the area of spinodal instability in the (ϱ,T)-plane remains unchanged. The qualitative features of multifragmentation through spinodal decomposition as obtained in the adiabatic limit are not significantly affected by dissipation.

Sound modes in hot nuclear matter

The propagation of the isoscalar and isovector sound modes in a hot nuclear matter is considered. The approach is based on the collisional kinetic theory and takes into account the temperature and memory effects. It is shown that the sound velocity and the attenuation coefficient are significantly influenced by the Fermi surface distortion (FSD). The corresponding influence is much stronger for the isoscalar mode than for the isovector one. The memory effects cause a nonmonotonous behavior of the attenuation coefficient as a function of the relaxation time leading to a zero-to-first sound transition with increasing temperature. The mixing of both the isoscalar and the isovector sound modes in an asymmetric nuclear matter is evaluated. The condition for the bulk instability and the instability growth rate in the presence of the memory effects is studied. It is shown that both the FSD and the relaxation processes lead to a shift of the maximum of the instability growth rate to the longer-wavelength region.

Coulomb-nuclear interference with deuterons: Isospin character of the21+and31−excitations in94,98Mo

Angular distributions of inelastic-scattering cross sections were measured for deuterons of 13.2 and 16.0 MeV, exciting the ${2}_{1}^{+}$ and ${3}_{1}^{\ensuremath{-}}$ states of ${}^{94}\mathrm{Mo}$ and ${}^{98}\mathrm{Mo}.$ The analysis of the Coulomb-nuclear interference patterns displayed by these angular distributions was favored by the quality of the data obtained with the S. Paulo Pelletron-Enge-Spectrograph facility. The distorted-wave Born approximation--deformed-optical-model analysis with global parameters yielded values for the ratio ${C}_{L}={\ensuremath{\delta}}_{L}^{C}/{\ensuremath{\delta}}_{L}^{N}$ and for ${\ensuremath{\delta}}_{L}^{N}$ (where ${\ensuremath{\delta}}_{L}^{C}$ and ${\ensuremath{\delta}}_{L}^{N}$ are, respectively, the charge and isoscalar deformation lengths), which inform the reader about the isospin character of the excitations. A reduced isoscalar transition probability, $B(\mathrm{ISL}),$ was defined, in analogy to $B(\mathrm{EL}),$ the ratio $B(\mathrm{EL})/B(\mathrm{ISL})$ being proportional to the square of ${C}_{L}.$ The latter quantity is, however, experimentally better determined. The results obtained for ${C}_{2},$ ${C}_{3},$ ${\ensuremath{\delta}}_{2}^{N},$ and ${\ensuremath{\delta}}_{3}^{N}$ at the two incident energies, 13.2 and 16.0 MeV, are consistent for each ${}^{94}\mathrm{Mo}$ and ${}^{98}\mathrm{Mo}.$ The values of ${C}_{L}$ reveal a slight predominance of the protons in the quadrupolar transitions, in both ${}^{94}\mathrm{Mo}$ and ${}^{98}\mathrm{Mo}.$ The ${2}_{1}^{+}$ and the ${3}_{1}^{\ensuremath{-}}$ states are more collective in ${}^{98}\mathrm{Mo}$ than in ${}^{94}\mathrm{Mo},$ both with respect to the protons (charge) and with respect to protons and neutrons (mass).

GIANT RESONANCE PROPERTIES IN β STABLEAND UNSTABLE NUCLEI

We study the giant resonances of stable and unstable nuclei in the framework of the consistent relativistic random phase approximation built on the nonlinear relativistic mean field (RMF) ground states. The isoscalar and isovector modes of giant resonances for stable nuclei, such as 208Pb,144Sm,116Sn,90Zr,40Ca,16O and Ca isotope chains are investigated. The contribution to the giant resonances from the Dirac sea states and the currents of vector mesons are examined. The results show that the effects of the Dirac sea states on the isoscalar giant modes are pronounced, but become weaker for light nuclei, while the contributions of the isovector modes are negligible. The few sets of parameterizations of nonlinear RMF model, which are commonly used to give a good description of ground-state properties of finite nuclei, could also well describe the nuclear dynamic properties-giant resonances. For nuclei with the extreme value of N/Z, low-lying collective excitations are found in isovector dipole modes, which are mainly due to the ph excitation of the weakly bound states near Fermi surface and the isospin mixture effect.

Stability and instability of a hot and dilute nuclear droplet

The diabatic approach to collective nuclear motion is reformulated in the local-density approximation in order to treat the normal modes of a spherical nuclear droplet analytically. In a first application the adiabatic isoscalar modes are studied and results for the eigenvalues of compressional (bulk) and pure surface modes are presented as function of density and temperature inside the droplet, as well as for different mass numbers and for soft and stiff equations of state. We find that the region of bulk instabilities (spinodal regime) is substantially smaller for nuclear droplets than for infinite nuclear matter. For small densities below 30% of normal nuclear matter density and for temperatures below 5 MeV all relevant bulk modes become unstable with the same growth rates. The surface modes have a larger spinodal region, reaching out to densities and temperatures way beyond the spinodal line for bulk instabilities. Essential experimental features of multifragmentation, like fragmentation temperatures and fragment-mass distributions (in particular the power-law behavior) are consistent with the instability properties of an expanding nuclear droplet, and hence with a dynamical fragmentation process within the spinodal regime of bulk and surface modes (spinodal decomposition).

Nonlinear dynamics of giant resonances in atomic nuclei.

The dynamics of monopole giant resonances in nuclei is analyzed in the time-dependent relativistic mean-field model. The phase spaces of isoscalar and isovector collective oscillations are reconstructed from the time series of dynamical variables that characterize the proton and neutron density distributions. The analysis of the resulting recurrence plots and correlation dimensions indicates regular motion for the isoscalar mode, and chaotic dynamics for the isovector oscillations. Information-theoretic functionals identify and quantify the nonlinear dynamics of giant resonances in quantum systems that have spatial as well as temporal structure.

Proton scattering on the radioactive nucleus [formula omitted]O and the 0 gs+→2 1+ transition in the neutron-rich oxygen isotopes

Elastic and inelastic proton scattering to the 2 1 + state of the single closed shell radioactive nucleus 20 O have been measured in inverse kinematics with a beam energy of 30 MeV/u. The matrix element determined for the 0 gs +→2 1 + transition in this work is compared with the corresponding electromagnetic matrix element to determine the ratio of the neutron and proton multipole matrix elements for this transition, M n / M p =2.9(4), which is quite different from the value M n / M p = N/ Z=1.5 that would be expected for a purely isoscalar transition. A comparison of this result to a corresponding result for 18 O suggests that the strength of the core polarizing interactions between the valence neutrons and the core protons and neutrons is changing significantly with mass.

Damping of giant resonances in asymmetric nuclear matter

The giant collective modes in asymmetric nuclear matter are investigated within a dynamic relaxation time approximation. We derive a coupled dispersion relation and show that two sources of coupling appear: (i) a coupling of isoscalar and isovector modes due to different mean-fields acting and (ii) an explicit new coupling in asymmetric matter due to collisional interaction. We show that the latter one is responsible for a new mode arising besides isovector and isoscalar modes.

Effect of large neutron excess in the region of the giant dipole and quadrupole resonance

We study the dipole and quadrupole modes of neutron rich nuclei within the selfconsistent HF + RPA. The presence of neutron skin enhances the mixing of isoscalar and isovector modes. Then it is possible to excite modes of isovector character by an isoscalar probe. In particular we analize the excitation of dipole modes by alpha scattering. The excitation of compressional isoscalar mode is also studied.

New collective mode due to collisional coupling

Starting from a non-Markovian conserving relaxation time approximation for collisions we derive coupled dispersion relations for asymmetric nuclear matter. The isovector and isoscalar modes are coupled due to asymmetric nuclear meanfield acting on neutrons and protons differently. A further coupling is observed by collisional correlations. The latter one leads to the appearance of a new soft mode besides isoscalar and isovector modes in the system. We suggest that this mode might be observable in asymmetric systems. This soft mode approaches the isovector mode for high temperatures. At the same time the isovector mode remains finite and approaches a constant value at higher temperatures showing a transition from zero sound like damping to first sound. The damping of the new soft mode is first sound like at all temperatures.

Effect of large neutron excess on the dipole response in the region of the giant dipole resonance

The evolution of the dipole response in nuclei with strong neutron excess is studied in the Hartree-Fock plus random phase approximation with Skyrme forces. We find that the neutron excess increases the fragmentation of the isovector giant dipole resonance, while pushing the centroid of the distribution to lower energies beyond the mass dependence predicted by the collective models. The radial separation of proton and neutron densities associated with a large neutron excess leads to non-vanishing isoscalar transition densities to the GDR states, which are therefore predicted to be excited also by isoscalar nuclear probes. The evolution of the isoscalar compression dipole mode as a function of the neutron excess is finally studied. We find that the large neutron excess leads to a strong concentration of the strength associated with the isoscalar dipole operator ∑ i r i 3 Y 10, that mainly originates from uncorrelated excitations of the neutrons of the skin.