Coulomb Excitation Cross Sections Research Articles

Coulomb excitation of radioactive nuclear beams in inverse kinematics

Two techniques for determining B( E2:0 1 + → 2 1 +) values using low-energy Coulomb excitation of Radioactive Nuclear Beams in inverse kinematics are presented. One method, applicable if the lifetime of the excited state is ∼1 ns, uses a linear array of NaI(Tl) detectors to measure the decay curve, and thus the 2 1 + state lifetime, for Coulomb excited radioactive beam nuclei as they decay in flight downstream from a carbon excitation target. In the second method, useful when lifetimes are short, <1 ns, or for low intensity beams, a through-well NaI(Tl) detector is used to measure the Coulomb excitation cross section from which the B( E2:0 1 + → 2 1 +) value is calculated. The results of test experiments with beams of stable Os isotopes are presented.

The electric polarizability of 23Na

Abstract Backward angle differential cross sections for Coulomb excitation of the first excited state ( 5 2 + , 0.439 MeV) of 23 Na on a 12 C target have been measured at 6.84 and 7.87 MeV CM energy. The effective strengths B eff of the quadrupole transition were determined from a comparison of data with coupled-channel calculations. An analysis of B eff from the present experiment together with those published previously allowed us to extract the experimental value of the electric polarizability τ 12 for the transition between the ground and first excited state of 23 Na.

Measured magnetic moments of 21+ states in 190–198Pt and interacting boson model description of M1 systematics in the platinum isotopes

Abstract The g-factor of the 21+ state in 190Pt has been measured for the first time using the thin-foil transient-field technique with a target enriched (to 4.19%) in 190Pt. Precessions for the 21+ states of 190,192,194,196,198Pt were measured simultaneously. The Coulomb excitation cross section to the 21+ state in 190Pt was also measured relative to the 01+ → 21+ excitations in 194Pt and 196Pt. The near constancy of g(21+) for the even 190–198Pt isotopes is in marked contrast with the behaviour observed in neighbouring even 182–186W and 186–192Os nuclei and the predictions of the proton-neutron interacting boson model in the limit of F-spin symmetry. It is shown that the observed g-factor and M1 transition systematics in the Pt isotopes can be described by appropriate F-spin symmetry breaking, while maintaining satisfactory descriptions of the energy levels and E2 properties.

Excitation of multiphonon states in relativistic heavy-ion collisions.

One- and two-step Coulomb excitation cross sections of the double-phonon giant dipole resonance are calculated in a semiclassical formalism. The contribution of nuclear interaction is shown to be small. The multipole sum rules are used to evaluate corresponding nuclear matrix elements; the widths of final and intermediate states are taken into account. The recent experimental data re discussed and compared to our calculations.

Soft giant dipole mode of 11Li.

The low-lying electric dipole distribution for {sup 11}Li is examined in detail in a large basis nonspurious shell model which includes up to 3{h bar}{omega} of excitation. A very strong enhancement of the {ital E}1 strength between 1 and 4 MeV of excitation is predicted when Woods-Saxon single-particle wave functions are used. The relativistic Coulomb excitation cross section is underestimated. However, an analysis of the contributions to the {ital E}1 matrix elements indicates that small changes in the structure of the low-lying states can lead to a significant increase in the predicted {ital E}1 strengths, so that excitations normally omitted from shell-model calculations are not necessarily needed to explain the anomalous Coulomb cross section.

Covariant formulation of Coulomb excitation in heavy- ion collisions at ultra-relativistic energies

Derivation of Coulomb excitation cross sections at relativistic energies is presented for the case where both projectile and target are considered as extended objects. Cross sections for projectile and/or target excitations are calculated as a function of bombarding energy in the context of a covariant theory. Several systems are analyzed and compared with available data.

Change of the hydrogen excitation cross sections due to the wake potential of a fast charged particle

The wake potential of a fast charged particle is derived for an atomic system using first-order quantum-mechanical perturbation theory. The Coulomb excitation cross sections of the target atoms by this wake potential are then derived and found to be considerable. Numerical results on a model system of condensed atomic hydrogen show that the wake potential is very important and must be included in calculating the integrated Coulomb excitation cross sections in condensed matter.

The K-shell ionisation of atoms with Z⩾60 by protons

The K-shell ionisation cross sections, sigma K, have been measured for 60Nd, 62Sm, 65Tb, 67Ho and 73Ta targets in the incident proton energy range from 2.7 to 10.0 MeV. The absolute sigma K values have been determined by normalisation to the known Coulomb excitation cross section of nuclear collective states. The experimental results are discussed with reference to the theoretical models and to the other proton-induced ionisation data.

The K-shell ionisation of73Ta induced by low-energy protons and deuterons

K-shell ionisation cross sections sigma K have been measured for a Ta target for incident proton energies of 1.1-3.8 MeV and for incident deuteron energies of 1.2-3.2 MeV. The absolute sigma K values have been determined by normalisation to the known Coulomb excitation cross section sigma C of the target nucleus. The experimental results are compared with the predictions of different theoretical models. The sigma p/ sigma d and sigma alpha /4 sigma d ratios of the cross sections are also compared with theoretical model predictions by using the results for alpha particles taken from the literature.

The cross sections for K-shell ionization of heavy elements with low energy protons and deuterons

The K-shell ionization cross sections. σ kl , have been measured for the natural 60Nd, 62Sm, 65Tb, 69Tm and 73Ta targets for incident proton energies of 0.8–3.8 MeV and for 64Gd and 73Ta targets for incident deuteron energies of 0.9–3.2 MeV. The absolute σ kl values have been determined by normalization to the known Coulomb excitation cross sections σ c of the nuclear collective states of the target nuclei. The experimental results are compared with the predictions of the SCA and PWBA models including the electron binding, Coulomb repulsion and relativistic corrections. The σ He 4σ D and σ H σ D ratios of the ionization cross sections have been also compared with the SCA model predictions by using our earlier and literature results for protons and alpha particles for Gd and Ta targets.

The cross sections for K-shell ionisation of60Nd,62Sm and69Tm by low-energy protons

Cross sections for K-shell ionisation for natural 60Nd, 62Sm and 69Tm targets bombarded with 0.8-2.6 MeV protons have been determined relative to the known cross sections for Coulomb excitation of the nuclear collective states. The results are discussed with reference to those from other proton-induced ionisation experiments on Nd and Sm targets, and to the theoretical models for the ionisation process.

The K-shell ionisation of64Gd induced by low-energy deuterons

The K-shell ionisation cross sections sigma KI have been measured for a Gd target at incident deuteron energies of 0.9-2.8 MeV. The absolute sigma KI values have been determined by normalisation to the known Coulomb excitation cross section sigma C of the target nucleus. The experimental results are compared with the theoretical predictions of the semiclassical approximation (SCA) and the plane-wave Born approximation (PWBA) models including electron binding, Coulomb repulsion and relativistic corrections. The sigma He/4 sigma D and sigma H/ sigma D ratios of the cross sections have also been compared with the SCA model predictions by using the earlier results for protons and alpha particles.

Relativistic coulomb collisions and the virtual radiation spectrum

We evaluate the Coulomb-excitation cross sections in relativistic heavy-ion collisions by means of the plane-wave Born approximation. The final total cross section is shown to be equal to that obtained by a semiclassical method. As a byproduct the virtual photon spectrum for similar electromagnetic processes is derived. Comparison with other methods is performed.

Relativistic coulomb collisions and the virtual radiation spectrum

We evaluate the Coulomb-excitation cross sections in relativistic heavy-ion collisions by means of the plane-wave Born approximation. The final total cross section is shown to be equal to that obtained by a semiclassical method. As a byproduct the virtual photon spectrum for similar electromagnetic processes is derived. Comparison with other methods is performed.

The K-shell ionisation of64Gd,74W and90Th induced by heavy, charged particles

The total K-shell ionisation cross sections were measured relative to nuclear Coulomb excitation cross sections for 64Gd, 74W and 90Th targets bombarded by 4He and 16O projectiles. In the case of 74W, projectiles of 12C and 19F were also applied. The experimental results are compared with the predictions of the SCA-LAL model, and the overall agreement is very good. The data are presented as reduced cross sections and compared with a 'universal' cross section function.

Differential cross sections for electric quadrupole coulomb excitation I

Title of program: DXS1 Catalogue number: ABQE Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland (see application form in this issue) Computer for which the program is designed and others upon which it is operable Computer: IBM 360/75. Installation: Triangle University Computation Center, Research Triangle Park, North Carolina Operating system or monitor under which the program is executed: OS-360-MVT Programming languages used: FORTRAN-IV (G) High speed store required: 35000 words. No. of bits in a word: 32 Is the program overlaid? No No. of magnetic tapes required: None Whatother peripherals are used? Card Reader; Line Printer No. of cards in combined program and test deck: 1172 Card punching code: EBCDIC

Coulomb Excitation of 7Li

Coulomb excitation of the 0�478 MeV, J1t = t-, first excited state of 7Li has been studied using beams of 7Li ions and targets of 138Ba and 208Pb. Spectra of the scattered particles were measured at 171� using an annular Si surface-barrier detector (l 38Ba and 208Pb targets) and at 90� using an Enge split-pole magnetic spectrometer (208Pb targets). For each experimental configuration, the bombarding energy at which nuclear interference became significant was determined experimentally. An analysis based upon the reorientation effect yielded the following results: the static electric quadrupole moment of the J1t = t- ground state (Q3/2-) is -4�0� 1�1 efm", the contribution of the giant dipole resonance (GDR) to the Coulomb-excitation cross section is 2�7 �0�2 times as great as would be calculated from the hydrodynamic model, and B(E2;t-~t-) is 7�42�0�14e2fm4 ? The value obtained for Q3/2- is in excellent agreement with results reported from atomic- and molecular-beam spectroscopy and from Coulomb scattering of aligned 7Li. Thus it provides a strong verification of the validity of the reorientation-effect technique for the determination of nuclear quadrupole moments, provided that the GDR effect is treated adequately.

The K-shell ionisation of64Gd and74W by low-energy protons

The cross sections have been measured for K-shell ionisation of 64Gd and 74W by 0.8-2.8 MeV and 1.1-7.7 MeV protons, respectively. The absolute values have been determined by normalisation to the accurately known Coulomb excitation cross sections of these target nuclides. The experimental results are compared with the predictions of the SCA and PWBA models, including the electron binding, Coulomb deflection, and relativistic electron velocity corrections. Good agreement with the theories is observed for both tungsten and gadolinium. The discussion also covers earlier K-shell ionisation data for high-Z elements.

Coulomb excitation of the giant dipole resonance in light-ion inelastic scattering fromPb208

A coupled-channel calculation including Coulomb excitation has been done for excitation of the isovector giant dipole resonance in light-ion inelastic scattering from $^{208}\mathrm{Pb}$ at forward angles. It is found that the predicted cross sections for excitation of the giant dipole resonance with alpha inelastic scattering, calculated including Coulomb excitation, are much smaller than the experimental isoscalar giant monopole resonance cross section at incident energies around 100 MeV. The predicted cross section for Coulomb excitation of the giant dipole resonance increases rapidly with increasing incident energy, and the giant dipole and monopole resonance cross sections become comparable above ${E}_{\ensuremath{\alpha}}=300$ MeV. For inelastic scattering of $^{3}\mathrm{He}$, deuterons, and protons at forward angles, Coulomb excitation of the giant dipole resonance is found to be comparable to the giant monopole resonance cross section at $100l{E}^{\mathrm{lab}}l200$ MeV. Coulomb excitation of the giant dipole resonance is strongly inhibited by momentum mismatch between incident and outgoing waves due to the large negative $Q$ values. This mismatch is reduced for lighter projectile masses and higher incident energies. As the giant monopole and dipole resonances are almost coincident, giant dipole resonance excitation must be properly accounted for in studies of the giant monopole resonance.NUCLEAR REACTIONS Coupled-channel calculation of $\ensuremath{\sigma}(\ensuremath{\theta})$; for Coulomb excitation of isovector dipole resonance in $^{208}\mathrm{Pb}$; from ($\ensuremath{\alpha}$,${\ensuremath{\alpha}}^{\ensuremath{'}}$), ($^{3}\mathrm{He}$, $^{3}\mathrm{He}$'), ($d$,${d}^{\ensuremath{'}}$), and ($p$,${p}^{\ensuremath{'}}$) scattering.

The K-shell ionisation of90Th by protons and alpha particles

The cross sections have been measured for K-shell ionisation of 90Th by 1.2-6.0 MeV protons and 2.5-16 MeV alpha particles. The results are derived from comparisons with well known Coulomb excitation cross sections for nuclear rotational transitions. The measured cross sections for protons are in good agreement with the predictions of both the SCA and PWBA models provided both models are supplemented by the same Coulomb deflection, binding and relativistic corrections. The cross sections measured for alpha particles are on the average 30% higher than predicted by the two models mentioned above.