Excitation of the giant dipole resonance in the scattering of isoscalar projectiles

The excitation of the giant dipole resonance in nuclei with N > Z by isoscalar projectiles α and d is discussed within a simple collective model for isoscalar dipole excitations. Calculations have been performed for ²⁰⁸Pb; they are compared to recent data on the excitation of the new giant resonance at E_x = 13.8 MeV. For α scattering the effect of dipole excitation is quite weak but significant contributions are obtained for d scattering.     

Direct neutron decay of the isoscalar giant dipole resonance

The direct and statistical neutron decay of the isoscalar giant dipole resonance has been studied in ⁹⁰Zr, ¹¹⁶Sn, and ²⁰⁸Pb using the (α, α’ n) reaction at a bombarding energy of 200 MeV. The spectra of fast decay neutrons populating valence hole states of the Z, N − 1 nuclei were analyzed, and estimates for the branching ratios were determined. The observation of the nucleon-direct-decay channels helped to select giant-resonance strengths and suppress the underlying background and continuum, which led to an indication of the existence of a new mode with L = 2 character, presumably the overtone of the isoscalar giant quadrupole resonance. The text was submitted by the authors in English.     

Do we understand the electric quadrupole strength distributions in magic nuclei?

A comparison between the electric quadrupole (E2) strength distributions in ^{40, 48}Ca with new results from ⁵²Cr is presented. The deduced E2 strength distributions and the exhaustion of the isoscalar energy-weighted E2 sum rule are very different. Microscopic approaches fail to reproduce these differences. A survey of the available data shows that the exhaustion of the energy-weighted isoscalar E2 sum rule in doubly magic nuclei below the isoscalar giant quadrupole resonance is typically more than two times larger than in semi-magic nuclei. On the other hand, the E2 strength in this energy region exhausts about 50% of the total E2 strength, independent from shell closures.     

Compression modes and the nuclear matter incompressibility coefficient

We review the current status of the nuclear matter (N=Z and no Coulomb interaction) incompressibility coefficient, K _nm , and describe the theoretical and the experimental methods used to determine K _nm from properties of compression modes in nuclei. In particular we consider the long standing problem of the conflicting results obtained for K _nm , deduced from experimental data on excitation cross sections for the isoscalar giant monopole resonance (ISGMR) and data for the isoscalar giant dipole resonance (ISGDR).     

Collective excitations of the element <Emphasis Type="Italic">Z</Emphasis> = 120

The low-lying vibrational excitations of superheavy even-even nuclei around Z=120 and N=172, predicted to be spherical by the relativistic mean-field (RMF) model, are studied within a phenomenological collective approach. In the framework of the macroscopic model for giant resonances, we compute the transition densities of the isoscalar monopole, quadrupole, and octupole and isovector dipole modes for the superheavy nucleus ²⁹²120, whose ground-state density is determined from the RMF model. The results are also compared to those for²⁰⁸Pb.     

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 ∑_ir_i³Y₁₀, that mainly originates from uncorrelated excitations of the neutrons of the skin.     

Competition of isoscalar and isovector proton-neutron pairing in nuclei

We use shell model techniques in the complete pf shell to study pair correlations in nuclei. Particular attention is paid to the competition of isoscalar and isovector proton-neutron pairing modes which is investigated in the odd-odd N = Z nucleus ⁴⁶V and in the chain of even Fe-isotopes. We confirm the dominance of isovector pairing in the ground states. An inspection of the level density and pair correlation strength in ⁴⁶V, however, shows the increasing relative importance of isoscalar correlations with increasing excitation energy. In the Fe-isotopes we find the expected strong dependence of the proton-neutron isovector pairing strength on the neutron excess, while the dominant J = 1 isoscalar pair correlations scale much more gently with neutron number. We demonstrate that the isoscalar pair correlations depend strongly on the spin-orbit splitting.     

Breaking of the SU(4) limit for the Gamow-Teller strength in N ∼ Z nuclei

We have performed large-scale shell model calculations of the Gamow-Teller strength distributions in N ∼ Z pf -shell nuclei. These calculations were motivated by the experimental attempts to measure the low-lying GT strength for the even-even N = Z + 2 or N = Z - 2 nuclei ⁴⁶Ti , ⁵⁰Cr , ⁵⁴Fe and ⁶²Ge , where a sizable low-energy GT strength could be interpreted as reminiscence of SU(4) symmetry; in the limit of exact SU(4) symmetry the GT_- strength would be concentrated in a single transition to the lowest T = 0, J = 1⁺ state in the daughter. We confirm that the SU(4) symmetry is strongly broken by the spin-orbit interaction and by increasing neutron excess.     

Isoscalar monopole and dipole transition matrix elements from inelastic alpha scattering

Using an implicit folding procedure, isoscalar monopole and dipole transition matrix elements are expressed in terms of deformation parameters and moments of the optical potential forα-scattering. Application to monopole states in light nuclei gives good agreement with data determined electromagnetically. For isoscalar dipole states, the method gives information on 〈r ³〉 matrix elements which cannot be obtained otherwise.     

Electric dipole strength distribution below the <Emphasis Type="Italic">E</Emphasis>1 giant resonance in <Emphasis Type="Italic">N</Emphasis> = 82 nuclei

In this study quasiparticle random-phase approximation with the translational invariant Hamiltonian using deformed mean field potential has been conducted to describe electric dipole excitations in ¹³⁶Xe, ¹³⁸Ba, ¹⁴⁰Ce, ¹⁴²Nd, ¹⁴⁴Sm and ¹⁴⁶Gd isotones. The distribution of the calculated E1 strength shows a resonance like structure at energies between 6–8 MeV exhausting up to 1% of the isovector electric dipole Energy Weighted Sum Rule and in some aspects nicely confirms the experimental data. It has been shown that the main part of E1 strength, observed below the threshold in these nuclei may be interpreted as main fragments of the Pygmy Dipole resonance. The agreement between calculated mean excitation energies as well as summed B(E1) value of the 1⁻ excitations and the available experimental data is quite good. The calculations indicate the presence of a few prominent positive parity 1⁺ States in heavy N = 82 isotones in the energy interval 6–8 MeV which shows not all dipole excitations were of electric character in this energy range.     

Forward on the <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis> line with GASP

The experimental study of the proton-rich nuclei close to the N = Z line is a constant challenge for nuclear spectroscopy, mainly due to the difficulty to produce them with the currently available beam/target combinations. Significant advances on this direction were obtained from experiments performed with the GASP array during the last two years: the yrast line of ⁸⁴Mo was extended up to 10 ⁺ , ⁸⁸Ru observed for the first time, and the N = Z + 1 line was mapped from ⁸¹Zr to ⁹⁵Ag. These new results allow us to have a more complete image of the transition from the well-deformed shell closure at N,Z = 40 to the spherical-shell closure at N,Z = 50, and highlights some particular effects that can be observed only in the vicinity of the N = Z line.Received: 10 January 2003, Published online: 23 March 2004PACS: 21.10.-k Properties of nuclei; nuclear energy levels - 21.10.Pc Single-particle levels and strength functions - 21.10.Re Collective levels - 23.20.-g Electromagnetic transitions     

Shell model Monte Carlo studies of N = Zpf-shell nuclei with pairing-plus-quadrupole Hamiltonian

We perform shell model Monte Carlo calculations of selected N = Z pf-shell nuclei with a schematic Hamiltonian containing isovector pairing and quadrupole-quadrupole interactions. Compared to realistic interactions, this Hamiltonian does not give rise to the SMMC “sign problem”, while at the same time resembles essential features of the realistic interactions. We study pairing correlations in the ground states of N = Z nuclei and investigate the thermal dependence of selected observables for the odd-odd nucleus ⁵⁴Co and the even-even nuclei ⁶⁰Zn and ⁶⁰Ni. Comparison of the present results to those with the realistic KB3 interaction indicates a transition with increasing temperature from a phase of isovector pairing dominance to one where isoscalar pairing correlations dominate. In addition, our results confirm the qualitative reliability of the procedure used to cure the sign problem in the SMMC calculations with realistic forces.     

The low-energy dipole structure of <Superscript>232</Superscript>Th , <Superscript>236</Superscript>U and <Superscript>238</Superscript>U actinide nuclei

In this study, I^p = 1⁺\ensuremath I^{\pi} = 1^{+} and I^p = 1^-\ensuremath I^{\pi} = 1^{-} dipole mode excitations are systematically investigated within the rotational and translational + Galilean invariant quasiparticle random-phase approximation for ²³²Th , ²³⁶U , and ²³⁸U actinide nuclei. It is shown that the investigated nuclei reach a B(M1) strength structure, which corresponds to the scissors mode. The calculated mean excitation energies as well as the summed B(M1) value of the scissors mode excitations are consistent with the available experimental data. The results of calculations indicate large differences to the rare-earth nuclei as is the case for the experiment: a doubling of the observed dipole strengths and a shift of the energy centroid to the lower energies by about 800keV. The calculations indicate the presence of a few prominent negative-parity K^p = 1^-\ensuremath K^{\pi} = 1^{-} states in the 2.0-4.0MeV energy interval. The occurrence of the negative-parity dipole states with the rather high B(E1) value less than 4MeV shows the necessity of explicit parity measurements for the correct determination of the scissors mode strength in ²³²Th , ²³⁶U , and ²³⁸U isotopes.     

Can strong electric dipole transitions in deformed rare earth nuclei be explained by the macroscopic behavior of the octupole phonon?

StrongE1 transitions of greater than 10^–3 Weisskopf units occur in many octupole states in the deformed rare earth region. It is shown using the droplet model that the electric dipole moment resulting from the macroscopic behaviour of the octupole phonon cannot by itself account for the observedE1 strengths, and it is observed that this result is consistent with the proposal of Donner and Greiner and of Zilges von Brentano and Richter that admixtures of the giant dipole resonance into the low energy octupole states are responsible for the fastE1 transitions. It is also suggested that calculations similar to those performed by Egido and Robledo forN 92 nuclei may be able to reproduceE1 transitions inN=94–104 nuclei.Supported by the National Science Foundation and the State of Florida     

Nuclear equation of state and compression modes

The nuclear matter (N = Z and no Coulomb interaction) incompressibility coefficient, K _nm , which is directly related to the curvature of the nuclear matter equation of state, is a very important physical quantity in the study of properties of nuclei, supernova collapse, neutron stars and heavy-ion collisions. We review the current status of K _nm and the experimental and theoretical methods used to determine the value of K _nm from the excitation crosssections σ(E) and the transition strength distributions S(E) of compression modes in nuclei. In particular, we will consider the isoscalar giant monopole resonance (ISGMR) and the isoscalar giant dipole resonance (ISGDR) and provide a simple explanation to the long standing problem of the conflicting results obtained for K _nm , deduced from experimental data on excitation cross sections for the ISGMR and data for the ISGDR.     

Electric dipole transitions in neutron-rich nuclei

The structure of neutron-rich nuclei in several isotopes is investigated by shell model calculations. We study the electric dipole (E1) transitions in C isotopes focusing on the interplay between the low-energy Pigmy strength and the giant dipole resonance (GDR). Reasonable agreement is obtained with available experimental data for the photoreaction cross sections in ¹²C, ¹³C, and ¹⁴C with the inclusion of the quenching effects. A low-energy peak in the dipole strength in ¹⁵C is associated with a single-particle motion of the 1s_1/2 valence neutron relative to the ¹⁴C core. The calculated transition strength below the GDR in C isotopes heavier than ¹⁵C is found to exhaust about 50–80% of the cluster sum rule value and 12–16% of the classical Thomas-Reiche-Kuhn sum rule value. Next, we point out that the quadrupole and magnetic moments in the odd C isotopes strongly depend on configuration, which will be useful to determine the spin parities and the deformations of the ground states of these nuclei. The electric quadrupole (E2) transitions in even C isotopes are also studied. The isotopic dependence of the E2 transition strength is found to be reasonably well explained, although the calculated strength largely overestimates the unexpectedly small strength observed in ¹⁶C. The E1 strength in ¹⁸N and ¹⁹N as well as in Ne isotopes is also investigated.     

Microscopic description of the E0, E2 and E1 giant resonances in 40Ca, 48Ca and 56Ni

The isovector E1 as well as the isoscalar, isovector and full electromagnetic E2 and E0 strength distributions for ⁴⁰Ca, ⁴⁸Ca and ⁵⁶Ni have been calculated in a large energy range up to 50 MeV of excitation. The microscopic model used includes the continuum RPA, 1p1h⊗phonon configurations and ground state correlations induced by these configurations. It is shown that the latter effect gives an increase of the energy weighted sum rules of 4–7%. In all these nuclei the isoscalar E0 and E2 resonances are spread out over the broad energy region. We obtained a reasonable good agreement with the available experimental data including the recent ones for the isoscalar E0 resonance in ⁴⁰Ca. The theoretical transition densities show a rather strong dependence on the excitation energy.