Excitation Of Giant Resonances Research Articles

Microscopic description of excitation of nuclear isoscalar giant resonances by inelastic scattering of 240 MeVαparticles

A microscopic description of the excitation of isoscalar giant monopole resonance (ISGMR) and quadrupole resonance (ISGQR) in ${}^{28}\mathrm{Si},$ ${}^{40}\mathrm{Ca},$ ${}^{58}\mathrm{Ni},$ and ${}^{116}\mathrm{Sn}$ by 240 MeV bombarding energy $\ensuremath{\alpha}$ particles is provided based on self-consistent Hartree-Fock-- (HF-) random-phase-approximation (RPA) approach and the distorted-wave Born approximation (DWBA). The folding model is used to obtain optical potentials from the HF ground-state density and a density dependent Gaussian nucleon-$\ensuremath{\alpha}$ interaction ${(V}_{\ensuremath{\alpha}n}).$ The parameters of ${V}_{\ensuremath{\alpha}n}$ are determined by fitting experimentally measured angular distributions for the case of elastic scattering. Angular distributions of inelastically scattered $\ensuremath{\alpha}$ particles for ISGMR and ISGQR excitations of the target nucleus are obtained using the folding model DWBA and both microscopic (RPA) and hydrodynamical (collective model) transition densities (found from HF ground state densities). A possible overestimation of the energy weighted sum rules and shifts of centroid energies due to the collective-model-based DWBA reaction description is reported.

Excitation of multiple giant dipole resonances: from spherical to deformed nuclei

The effect of deformation on the excitation of multiple giant dipole resonances is studied. Analytical expressions are derived in the framework of the interacting boson model for the energies and E1 properties of giant dipole resonances in spherical and deformed nuclei, and a numerical treatment of transitional nuclei is proposed. Coulomb-excitation cross sections are calculated in 238 U and in the samarium isotopes.

Electromagnetic Dissociation of Au Targets by Relativistic Pb Projectiles

Electromagnetic Dissociation (ED) occurs in collisions of relativistic heavy ions involving impact parameters larger than the nuclear interaction radius. In such collisions strong electromagnetic fields acting at the nucleus can produce, for high charges and ultrarelativistic energies, cross sections much larger than the total nuclear interaction cross section. In ED collisions absorption of a virtual photon generally leads to excitation of a nuclear giant resonance. The NA53 experiment studied ED by bombarding Au targets with 158 GeV/nucleon Pb projectiles from the SPS accelerator. Preliminary values of σED for the one- and two-neutron removal processes were determined to be 26.4 ± 4.0 and 4.6 ± 0.7 barns, respectively. Theoretical predictions for σED were calculated including the effects of both the E1 and E2 giant resonances. The calculations are extended to energies planned for heavy ion collisions at the RHIC and LHC colliders.

Electromagnetic dissociation of Au targets by relativistic Pb projectiles

Electromagnetic Dissociation (ED) occurs in collisions of relativistic heavy ions involving impact parameters larger than the nuclear interaction radius. In such collisions strong electromagnetic fields acting at the nucleus can produce, for high charges and ultrarelativistic energies, cross sections much larger than the total nuclear interaction cross section. In ED collisions absorption of a virtual photon generally leads to excitation of a nuclear giant resonance. The NA53 experiment studied ED by bombarding Au targets with 158 GeV/nucleon Pb projectiles from the SPS accelerator. Preliminary values of σ ED for the one- and two-neutron removal processes were determined to be 26.4 ± 4.0 and 4.6 ± 0.7 barns, respectively. Theoretical predictions for σ ED were calculated including the effects of both the E1 and E2 giant resonances. The calculations are extended to energies planned for heavy ion collisions at the RHIC and LHC colliders.

Impact-parameter dependence of giant resonance excitations in relativistic heavy-ion collisions

Angular distributions of Xe fragments produced in peripheral collisions of a 136 Xe beam ~700 MeV/nucleon! with 208 Pb and nat Sn targets were measured. Equivalent sharp-cutoff minimum impact parameters were derived on the basis of a semiclassical description for the electromagnetic excitation of one- and two-phonon giant resonances. The results are compared with current standard parametrizations of minimum impact parameters and with the soft-spheres model using realistic mass density distributions for projectile and targets. @S0556-2813~99!50611-0#

Theory of multiple giant dipole resonance excitation

Theory of multiple giant dipole resonance excitation

Spin-isospin flip giant resonances and shell dependence in7Liand9Bebyπ+photoproduction

The giant resonances of spin-isospin flip mode are studied by measuring the energy and angular distributions of ${\ensuremath{\pi}}^{+}$ electroproduced from ${}^{7}\mathrm{Li}$ and ${}^{9}\mathrm{Be}$ nuclei. Several strong ${\ensuremath{\pi}}^{+}$ groups are found and angular distributions of these groups are analyzed by distorted-wave impulse approximation calculations using the single particle shell model. The experimental cross section of the groups corresponds to an order of the charge exchange single particle transition strength, establishing them as spin-isospin flip giant resonances. The shell model nature of $(\ensuremath{\gamma},{\ensuremath{\pi}}^{+})$ results for ${1p}_{3/2}$ shell nuclei are summarized and presented together with previously published data. The obtained results are compared to previously published data for $({\ensuremath{\pi}}^{\ensuremath{-}},\ensuremath{\gamma}),$ (n,p), ${(e,e}^{\ensuremath{'}}p),$ and $(p,2p)$ reactions. Strong transitions consistent with the giant resonance excitations from the ${1s}_{1/2}$ shell in the core and from the ${1p}_{3/2}$ valence shell are observed.

Isospin structure of one- and two-phonon giant dipole resonance excitations

Isospin is included in the description of the Coulomb excitation of multiple giant isovector dipole resonances. In the excitation of even-even nuclei, a relevant portion of the excitation strength is shown to be associated with ${1}^{+}$ two-phonon states, which tends to be hindered or completely suppressed in calculations in which the isospin degree of freedom is not considered. We find that the excitation cross section is strongly dependent on the ground state isospin.

Time scales of multiple giant dipole resonance excitation and decay

A semiclassical description of multiple giant resonance excitation and decay that incorporates incoherent fluctuation contributions of the Brink-Axel type is developed. Numerical calculations show that the incoherent contributions are important at low to intermediate bombarding energies.

Excitation and decay of two-phonon giant dipole resonances

In heavy ion collisions at near relativistic energies, electromagnetic excitation of the double giant dipole resonance occurs with large cross sections. We summarize the presently available experimental data and discuss related theoretical efforts. Emphasis is paid to the question of anharmonicities and to the damping of the two-phonon states.

Electric giant resonances in 40Ca and 48Ca probed with electron and proton scattering coincidence experiments

Excitation and particle decay of electric giant resonances in 40Ca and 48Ca are studied with electron and proton beams. Recent results of a 48Ca(e,e′n) measurement performed at the S-DALINAC in Darmstadt with kinematics that selectively populate electric monopole, dipole and quadrupole excitations are presented. The extracted B(E1) strength distribution is in good agreement with photo nuclear data and the predictions of microscopic calculations. The summed B(E2+E0) strength distribution, however disagrees with the result of these calculations. The neutron emission of the giant dipole resonance in 48Ca shows a large fraction of direct decay to 47Ca hole states. In addition, isoscalar giant monopole resonance strength in 40Ca was extracted from (e,e′α 0) and (e,e′α 1) angular correlations. A study of the quadrupole strength in the α 0 decay channel of 40Ca with a (p,p′α) coincidence measurement reiterates the unsolved discrepancy between results from electromagnetic and hadronic probes.

Boson expansion methods applied to a two-level model in the study of multiple giant resonances

We apply boson expansion methods to an extended exactly solvable Lipkin-Meshkov-Glick model including anharmonicities in analogy with previous microscopic calculations. We study the effects of different approximations present in these calculations, among which the truncation of the Hamiltonian and of the space, in connection with the study of the properties of two-phonon states. By comparing the approximate results on the spectrum with the exact ones we conclude that the approximations made in the microscopic calculations on two-phonon states are well justified. We find also that a good agreement with the exact results for the three-phonon state is obtained by using a bosonic Hamiltonian truncated at the fourth order. This result makes us confident that such approximation can be used in future realistic calculations, thus allowing a theoretical study of triple excitations of giant resonances.

Nonlinear enhancement of the multiphonon Coulomb excitation in relativistic heavy ion collisions

We propose a soluble model to incorporate the nonlinear effects in the transition probabilities of the multiphonon Giant Dipole Resonances based on the SU(1,1) algebra. Analytical expressions for the multi-phonon transition probabilities are derived. Enhancement of the Double Giant Resonance excitation probabilities in relativistic ion collisions scales as $(2 k +1)(2k)^{-1}$ for the degree of nonlinearity $(2k)^{-1}$ and is able to reach values $1.5-2$ compatible with experimental data. The enhancement factor is found to decrease with increasing bombarding energy. [KEYWORDS: Relativistic Heavy Ion Collisions,Double Giant Resonance]

Excitation of the GDR and the compressional isoscalar dipole state by scattering

The excitation of the isovector giant dipole resonance (GDR) by alpha scattering is investigated as a method of probing the neutron excess in exotic nuclei. DWBA calculations are presented for and and the interplay of Coulomb and nuclear excitation is discussed. Since the magnitude of the Coulomb excitation amplitude is strongly influenced by the Q-value, the neutron excess plays an important role, as it tends to lower the energy of the GDR. The excitation of the compressional isoscalar dipole state in by alpha scattering is also investigated. It is shown that the population of this latter state may be an even more sensitive probe of the neutron skin than the isovector GDR.

Transitions between complex configurations in the excitation of the double giant resonance

The transitions between complex configurations, to which the giant dipole resonance (GDR) and the double giant dipole resonance (DGDR) doorway states are coupled, are taken into account in second order perturbation theory for the reaction amplitude. It is proved that only transitions between GDR and DGDR doorway states play an essential role in the Coulomb excitation of the DGDR.

Improved limit on the branching ratio of μ−→ e+ conversion on titanium

The SINDRUM II spectrometer at PSI is used in searches for μ→ e conversion in muonic atoms. Here we report on a search for the charge-changing μ −→ e + conversion on titanium. The measurements yielded the new upper limits Γ( μ −Ti → e +Ca GS )/ Γ( μ −Ti capture)<1.7×10 −12 (90% CL) for the ground state transition and Γ( μ −Ti → e +Ca GDR )/ Γ( μ −Ti capture)<3.6×10 −11 (90% CL) for a giant dipole resonance excitation with both a mean energy and a width of 20 MeV. These results improve on our previous best limits by a factor of 2.5.

Proton emission in inelastic scattering of40Ca on40Ca at 50 MeV/nucleon

Inelastic scattering of {sup 40}Ca on {sup 40}Ca at 50 MeV/nucleon has been measured in coincidence with light charged particles detected over a large angular domain. The giant resonance region of the inelastic spectrum is shown to be dominated by the isoscalar giant quadrupole resonance. The characteristics of the emitted protons allow us to separate four reaction mechanisms contributing to the high excitation energy region of the inelastic spectrum (E{sup {asterisk}}{gt} 30 MeV): pickup breakup, knockout, inelastic scattering to high-lying target states, and a new mechanism responsible for the emission of fast-moving protons. A sizable direct decay branch towards hole states of {sup 39}K is measured for the giant quadrupole resonance in {sup 40}Ca. Evidence is given for the excitation of the two-phonon giant quadrupole resonance, characterized by its direct decay scheme. The energy and width of this two-phonon state are in agreement with a harmonic picture for collective nuclear excitations. {copyright} {ital 1997} {ital The American Physical Society}

Probing the quantum-mechanical equivalent-photon spectrum for electromagnetic dissociation of relativistic uranium projectiles

Electromagnetic fission cross sections for the reactions U + (Be, C, Al, Cu, In, Au, U) at $E/A$ = 0.6 and 1.0 GeV are compared to theoretical calculations using recently proposed quantum-mechanical equivalent-photon spectra. In contrast to semiclassical calculations, systematically lower cross sections are obtained that cannot reproduce the experimental results. Since electromagnetic fission cross sections are virtually independent of the excitation of the double giant dipole resonance (DGDR), this conclusion is not influenced by the strength of the DGDR.

Magnetic dipole properties in deformed nuclei

The magnetic dipole response in deformed nuclei is investigated. Spurious states due to the rotation of the whole nucleus are removed by restricting the residual interaction in such a way that it commutes with the total angular momentum as a ground state expectation value in the quasi-particle random phase approximation. By this one guarantees that the spurious state due to rotations lies at energy zero and that it is a solution of the quasi-particle random phase equation (QRPA) and can easily be removed. The Hamiltonian is chosen to be a deformed Saxon Woods potential with a pairing force and an isoscalar and isovector generalized quadrupole-quadrupole and spin-spin interaction. The generalized isoscalar quadrupole operator is defined as the commutator of the independent quasi-particle Hamiltonian with the total angular momentum. The restoration of rotational symmetry mentioned above determines the isoscalar coupling constant. The generalized isovector quadrupole-quadrupole force does not commute with the total angular momentum. But one can find a linear “isovector” combination of the proton and the neutron total angular momentum which produces by a commutator with the independent quasiparticle Hamiltonian an “isovector” quadrupole operator which yields an isovector quadrupole-quadrupole force which always commutes with the total angular momentum. Thus one gets no restriction of the isovector quadrupole-quadrupole force constant. We fit it to the isovector giant quadrupole resonance ( E(E2) = 130 A 1 3 MeV ). The Hamiltonian contains in addition a spin-spin force, which always commutes with the total angular momentum and therefore does not spoil the restoration of rotational symmetry. The proton-proton, neutron-neutron and proton-neutron spin force constant is determined by solving the nuclear matter problem with the Reid soft core interaction within the Brückner theory and translating the result with the help of the Migdal force into finite nuclei. This yields an almost pure repulsive isovector spin-spin force. This Hamiltonian predicts a high lying ΔN = 2 scissors mode which lies between 17 and 26 MeV. It is spread over very many 1 + states with an average spacing of 15 keV. This highlying scissors mode consists of several hundred states and the overlap with an artificially constructed scissors mode is of the order of 38%, while the low lying scissors mode which shows up as 1 + states around 3 MeV has an overlap with the scissors mode of more than 50 %. In the same energy range as the high lying scissors mode lies also the isovector giant quadrupole resonance. Even at 180°, that means at completely backward angles, the E2 is comparable with the M1 excitation. This is due to the transversal quadrupole transition probability which is not disappearing in electron scattering at 180°. The same Hamiltonian is nicely describing the low lying scissors mode around 3 MeV in the rare earth and the transuranic nuclei. It gives the energies and the reduced magnetic dipole transition probabilities. It also can reproduce the formfactors measured by inelastic electron scattering. The Hamiltonian also reproduces the spin-flip states between 5 and 9 MeV excitation energy, which can be measured by inelastic proton scattering. One obtains in this region two maxima. The lowest one around 6 MeV is mainly of isoscalar nature and is weaker than the spin flip maximum at 7 to 8 MeV, which is mainly of isovector nature. The detailed form of this two-spin flip maxima depend very sensitively on the ratio of the isoscalar and isovector strength of the spin-spin force. In conclusion one can say: There exist a high lying scissors mode, but it is strongly fragmented over several hundred 1 + states between 17 and 26 MeV and even in electron scattering at backward angles the cross section for the excitation of the isovector giant quadrupole resonance is of comparable size. Thus it will be difficult to establish experimentally the existence of this high lying scissors mode.

Quenching of 1 + excitations in the double giant resonance

The electromagnetic excitation of the two-phonon isovector giant dipole resonance in relativistic projectiles incident on heavy targets can proceed via several intermediate 1 − one-phonon giant resonance states. In two-step electric dipole transitions the population of 0 +, 1 +, and 2 + two-phonon states are possible. We calculate the amplitude distribution of 1 − excitations with an RPA formalism, and use it to calculate the electromagnetic excitation of two-phonon states in second order perturbation theory and coupled-channels. We show that a conspiracy between angular momentum coupling and the strength of the electromagnetic fields suppresses contributions of 1 + states to the total cross sections.