Isotopic dependence of giant multipole resonances

A procedure is presented which allows the application of linear response theory and the random phase approximation to an open shell. The procedure is applied to Ca isotopes. The general features of giant multipole resonances are found to vary smoothly with the mass. The resonances exhibit more structure in the open 1f_{$\text{7}\text{2}$} shell nuclei. While the energy-weighted dipole sum is practically constant in all isotopes, the isoscalar quadrupole and octupole energy weighted sums increase continuously by ~ 30 % from ⁴⁰Ca to ⁴⁸Ca.     

Semiclassical description of isoscalar giant multipole resonances

The scaling approximation in a semiclassical theory of nuclear collective motions based on the Vlasov equation is applied to the study of isoscalar giant resonances. Analytic forms are obtained for the frequencies of any multipolarity, expressed just in terms of local density distributions, using realistic nuclear effective forces. The importance of non local interactions and diffuse surfaces is clearly shown. The limits of the scaling picture in describing high multipolarity resonances are finally discussed.     

Fragmentation of giant multipole resonances in deformed nuclei

The fragmentation of the giant monopole resonance in deformed nuclei is first studied by coupling the monopole oscillation with the quadrupole oscillation by means of the variational procedure for resonance frequencies. It is shown that, for non-axial symmetry, the monopole oscillation couples with both m = 0 and 2 modes of the quadrupole oscillation and the giant monopole resonance is split into three components, whereas for axial symmetry, the fragmentation is given by E₀(1 + 0.86δ² ± 1.25δ³) and E₀(0.74 ± 0.22δ ? 0.21δ² ± 0.57δ³), where E₀ is the g monopole resonance energy for spherical nuclei, δ is the deformation parameter, and the upper and lower signs stand for prolate and oblate deformations, respectively. The initial fragmentation of the giant quadrupole resonance is seen to be little modified by the coupling, except for the m = 0 mode which is split into two components. The variational method is extended to general multipoles for an ellipsoid and the fragmentation of giant multipole resonances in deformed nuclei is investigated for both axial and non-axial symmetries. A brief discussion is also made about the meaning of the energy eigenvalue involved in the model wave equation in terms of multipole sum rules. The giant dipole resonance for the static octupole deformation is shortly considered. The giant E0 and E3 resonances for largely deformed nuclei are finally examined by solving the spheroidal eigenvalue equation and they are compared with the results of the giant dipole and quadrupole resonances.     

Positive parity giant multipole resonances in16O

Distributions of the (J =0⁺, 1⁺, 2⁺, 3⁺, 4⁺) isoscalar and isovector strength in¹⁶O have been calculated in then particle —n hole (n=0, 1, 2) shell model. The isoscalar quadrupole giant resonance comes out fragmentated over eight peaks which exhaust 33% of the EWSR betweenE ^*=17 and 25 MeV. This result agrees nicely with the recent³He and alpha inelastic scattering experiments. Giant monopole isoscalar (isovector) resonance appears to exhaust more than 50% of the EWSR nearE ^*=30 MeV (E ^*=40 MeV). Several collective states of other multipolarities are predicted either near to 30 MeV or between 50 and 60 MeV. The ground state correlations of the 2p2h type give rise to a considerable strength redistributions as compared with the case of the closed shell ground state.On leave fromInstitute of Nuclear Physics, Czechosl. Acad. Sci., 250 68 e, Czechoslovakia.     

The decay width of higher multipole giant resonances

The decay width of higher multipole giant resonances is described within the framework of the newly developed Fourier-Bessel random-phase approximation. We calculate the distribution of the isoscalar and isovector multipole strength for electric resonances up to $\text{J}{}^{\mathrm{\pi }}\text{= 7}{}^{\mathrm{?}}$. In our model we find no concentrated multipole strength beyond the hexadecapole.     

Regge poles in multiparticle scattering amplitudes

A study is made of the high-energy limits of multi-particle scattering amplitudes in a φ³ theory. A limited set of chekerboard diagrams dominate the asymptotic behavior .The diagrams sum to produce Regge poles. If N is the number of particles bound together, the trajectory functions of the leading Regge poles are given by α(N)=? (2N ? 3) +g²8π²m². Comparison is made with the generalized multiperipheral model of Auerbach, Aviv, Sugar and Blankenbecler in which the corresponding trajectories have the form α(N)=a?bN+cN².     

Splitting of the isoscalarE0 andE2 giant multipole resonances in16O

The recently observed distribution of the transition strength of the isoscalar Giant Quadrupole Resonances can be explained by the admixture of (2p 2h)-excitations to the conventional (1p 1h)-configurations. The calculations agree nicely with (α, α′) and (e, e′) experiments. Due to the same mechanisme the Giant Monopole Strength is expected to be spread between 20 MeV and 40 MeV which makes it probably very difficult to detect such resonances experimentally.     

Landau zeroth-sound and nuclear giant resonances

Analytical solution for the zeroth-sound in the infinite matter is used as a basis for constructing the distribution functions in finite-size nuclei. Simple characteristic equation is obtained which determines frequencies of isoscalar nuclear giant resonances due to the zeroth-sound modes coupled to the surface distortions.     

Effect of low-lying collective states on the structure of giant resonances

The influence of coupling of the usual particle-hole states to particle-hole states built on a collective state has been estimated. Numerical calculations are performed for Ni⁶⁰Zr⁹⁰ and²⁰⁸Pb.     

Structure of nuclear multipole resonances as a function of momentum transfer

The momentum-transfer dependence of transverse and longitudinal isovector form factors is studied for the electroexcitation of sd-shell self-conjugate nuclei. The effect of the interference between the orbital and spin components of the intranuclear current on the behavior of transverse form factors is traced. The results of the particle-core version of the shell model are compared with experimental data on E1 and M6 multipole resonances.     

On the coupling of the giant multipole resonances to the surface quadrupole oscillations of nuclei

Within the framework of the hydrodynamic model the exact coupling constants of the coupling of the giant multipole resonances to the surface quadrupole oscillations of nuclei are derived. The differences to former variational calculations are discussed. It is found that the coupling constants for the terms linear in the surface variables are almost the same whereas the coupling constants for the quadratic terms differ appreciably. The influence on the photon absorption and scattering cross sections of spherical nuclei is discussed.     

The\overrightarrow p - Si elastic scattering in the region of giant multipole resonances

Analyzing powers and cross sections for the scattering of polarized protons from Si have been measured at eight energies between 17 and 29MeV. The analysing powers show an “anomalous” behaviour and an optical model analysis yields a non-monotonic effect in the spin-orbit potential.     

Direct production of lightest Regge resonances

We discuss direct production of Regge excitations in the collisions of massless four-dimensional superstring states, focusing on the first excited level of open strings ending on D-branes extending into higher dimensions. We construct covariant vertex operators and identify “universal” Regge states with the internal parts either trivial or determined by the world-sheet SCFT describing superstrings propagating on an arbitrary Calabi–Yau manifold. We evaluate the amplitudes involving one such massive state and up to three massless ones and express them in the helicity basis. The most important phenomenological applications of our results are in the context of low-mass string (and large extra dimensions) scenarios in which excited string states are expected to be produced at the LHC as soon as the string mass threshold is reached in the center-of-mass energies of the colliding partons. In order to facilitate the use of partonic cross sections, we evaluate them and tabulate for all production processes: gluon fusion, quark absorbing a gluon, quark–antiquark annihilation and quark–quark scattering.     

Low energy spectrum and giant multipole resonances of12C (I)

In a consistent shell model approach excitation energies and electromagnetic transitions are calculated for the low energy part of the¹²C spectrum up to the giant resonance region within a (1p1h+2p2h) configuration space. Comparison with available experimental data shows that almost the complete spectrum up to 40MeV can be described consistently. Thereby it is found that whereas the low lying collective states remain nearly unchanged by the inclusion of (2p2h) configurations, the spreading widths of all (2?ω) giant resonances are influenced drastically. For serious discrepancies in a few levels (4p4h) configurations or mesonic and baryonic degrees of freedom might be responsible.