Two Coulomb waves theory for direct excitation

A theoretical model of Dewangan, in which the total scattering wave function is approximated by a distorted wave containing two Coulomb wave functions, is discussed and its relation with the Brauner-Briggs-Klar model for ionization is examined. An important feature of the theory is that it includes a second Born amplitude naturally and in addition, contains, albeit approximately, both real and imaginary parts of all higher order Born terms. The theory is applied to study the 1s→2s excitation of hydrogen by electrons in the energy range 54.4 to 400eV. The differential and integral cross sections predicted by the theory are compared with the results of other theories and experimental data at 54.4eV and a good agreement is found.     

Coulomb excitation of 107Sn

The radioactive isotope ¹⁰⁷Sn was studied using Coulomb excitation at the REX-ISOLDE facility at CERN. This is the lightest odd-Sn nucleus examined using this technique. The reduced transition probability of the lowest-lying $\ensuremath 3/2^{+}$ state was measured and is compared to shell-model predictions based on several sets of single-neutron energies relative to ¹⁰⁰Sn . Similar to the transition probabilities for the $\ensuremath 2^{+}$ states in the neutron-deficient even-even Sn nuclei, the measured value is underestimated by shell-model calculations. Part of the strength may be recovered by considering the ordering of the $\ensuremath d_{5/2}$ and $\ensuremath g_{7/2}$ single-neutron states.     

Coulomb excitation of154Sm

The deformed nucleus¹⁵⁴Sm was studied by Coulomb excitation with NORDBALL by using a⁵⁸Ni beam. The ground-state band, the beta band, the gamma band and the octupole band (K=0-) were excited up to the 16+ state, the 6+ state, the 6+ state and the 13-state, respectively. A new band was established from 6+ to 14+ on the basis of the gamma-gamma coincidence spectra. The excitation probability of the new band is larger than that of the beta band.We would like to thank Dr. G. Sletten, Mr. J. Westergaard and the members of TAL, Niels Bohr Institute for their kind support. A part of this research is supported by Monbusho International Scientific Research Program (Joint Research No.01044037).     

The S-matrix for abstract scattering systems

Let S() be the S-matrix at energy for an abstract scattering system. We derive a bound, in terms of the interaction, on integrals of the form h () S()- _HS ² d, where denotes the Hilbert-Schmidt norm.Supported by the Swiss National Science Foundation.     

Coulomb excitation of 74Ge beam

⁷⁴Ge beam was Coulomb-excited on a ^natPb target. Ten E2 matrix elements including diagonal matrix elements for 5 low-lying states have been determined using the least-squares search code GOSIA. The expectation values of the rotational invariants 〈Q ²〉 and 〈cos3δ〉 show the small and triaxial deformation of the two lowest members of the ground-state band , while the 0₂ ⁺ and 2₂ ⁺ states are found to be almost spherical. Received: 31 August 2000 / Accepted: 4 December 2000     

Prospects for coherently driven nuclear radiation by Coulomb excitation

Possible experiments are discussed in which Coulomb excitation of nuclear isomers would be followed by sequential energy release. The possibility of coherent Coulomb excitation of nuclei ensconced in a crystal by channeled relativistic heavy projectiles is considered. The phase shift between neighbor-nuclei excitations may be identical to the photon phase shift for emission in the forward direction. Thus, the elementary string of atoms may radiate coherently with emission of characteristics nuclear γ rays, and the intensity of the radiation would be increased due to the summation of amplitudes. Mössbauer conditions should be important for this new type of collective radiation, which could be promising in the context of the γ-lasing problem.     

Multiple Coulomb excitation experiment of 66 Zn

A Coulomb excitation experiment was carried out with a ⁶⁶Zn beam bombarding a Pb target. Four E2 matrix elements and the quadrupole moment of the 2₁ ⁺ state were derived with the least-squares search code GOSIA. According to the B(E2) values, the ground band can be interpreted as a quasirotational band. It was found that the 2₁ ⁺ level has a positive quadrupole moment, which may be interpreted as a soft triaxial deformation.Received: 28 January 2003, Revised: 18 March 2003, Published online: 9 October 2003PACS: 25.70.De Coulomb excitation - 21.10.Ky Electromagnetic moments - 23.20.-g Electromagnetic transitions - 27.50.+e      

Coulomb excitation of 72 30Zn42

The reduced transition probability B(E2: 0₁ ⁺→ 2⁺) of ⁷²Zn has been measured for the first time by Coulomb excitation at intermediate energy. The result B(E2: 0₁ ⁺→ 2⁺) = 1740±210 e²fm⁴, corresponds to the deformation parameter β₂ of 0.23, in close agreement with expectations derived from the neighboring nucleus ⁷³Zn. A discussion of the evolution of the N = 40 sub-shell closure as a function of Z is presented. Received: 19 December 2001 / Accepted: 14 March 2002     

Coulomb excitation of the even-mass selenium nuclei

The properties of the low-lying states of the doubly even selenium nuclei have been investigated via multiple Coulomb excitation effected with 39.2 MeV oxygen projectiles. The excitation probabilities of the first 2⁺ states of ⁷⁶Se, ⁷⁸Se and ⁸⁰Se have been determined directly by resolving inelastically and elastically scattered ⁴He projectiles on thin targets. These measurements yielded values of B(E2; 0⁺ → 2⁺) equal to $\text{0.421 ± 0.009 (}{}^{76}\text{Se}\text{), 0.321 ± 0.009 (}{}^{78}\text{Se}\text{)}\text{and}\text{0.248 ± 0.005 (}{}^{80}\text{Se}\text{) e}{}^2\text{· b}{}^2$. The multiple Coulomb excitation experiments enabled us to detect 2⁺ and 4⁺ levels in all isotopes studied up to 2.1 MeV. Moreover the double Coulomb excitation of 0⁺' states at 854.1 keV (⁷⁴Se), 1498.5 keV (⁷⁸Se), and 1478.3 keV (⁸⁰Se) was also observed. The enhancement of the E2 transition between these 0⁺' levels and the first 2⁺ states decreases rapidly with the increase of the neutron number, i.e., $\text{B(}\text{E}\text{2; 0}{}^{\mathrm{+}}\text{′ → 2}{}^{\mathrm{+}}\text{)/B(}\text{E}\text{2; 2}{}^{\mathrm{+}}\text{→ 0}{}^{\mathrm{+}}\text{) = 2.04 ± 0.08 (}{}^{74}\text{Se}\text{), 0.91 ± 0.08 (}{}^{78}\text{Se),}\text{and}\text{0.28 ± 0.04 (}{}^{80}\text{Se}\text{)}$. States interpreted as the result of direct E3 Coulomb excitation have been observed at 2350.2, 2429.2, 2507.6, and 2717.6 keV in ⁷⁴Se, ⁷⁶Se, ⁷⁸Se and ⁸⁰Se, respectively. Their B(E3; 0⁺ → 3^?) values are $\text{2.1 ± 0.5 (}{}^{74}\text{Se}\text{), 4.0 ± 0.5 (}{}^{76}\text{Se}\text{), 2.7±0.3 (}{}^{78}\text{Se}\text{)}\text{and}\text{0.9 ± 0.2 ( × 10}{}^{\mathrm{?2}}\text{e}{}^2\text{·}\text{b}{}^3$ which represent enhancements of 9.2 ± 2.2, 16.6 ± 2.1, 10.8 ± 1.2 and 3.2 ± 0.7 respectively. Furthermore, angular distribution measurements of γ-rays following Coulomb excitation with 42 MeV ¹⁶O ions in ⁷⁸Se and ⁸⁰Se have been performed. The E2 content of the 2⁺' → 2⁺ transition in these two nuclei is 87.9 % (⁷⁸Se), and 96.2 % or 33.5 % (⁸⁰Se).     

Coulomb excitation of double giant dipole resonances

We implement the Brink–Axel hypothesis for the excitation of the double giant dipole resonance (DGDR): the background states which couple to the one-phonon giant dipole resonance are themselves capable of dipole absorption. These states (and the ones which couple to the two-phonon resonance) are described in terms of the gaussian orthogonal ensemble of random matrices. We use second-order time-dependent perturbation theory and calculate analytically the ensemble-averaged cross section for excitation of the DGDR. Numerical calculations illuminate the mechanism and the dependence of the cross section on the various parameters of the theory, and are specifically performed for the reaction ²⁰⁸Pb + ²⁰⁸Pb at a projectile energy of 640 MeV/nucleon. We show that the contribution of the background states to the excitation of the DGDR is significant. We find that the width of the DGDR, the energy-integrated cross section and the ratio of this quantity over the energy-integrated cross section for the single giant dipole resonance, all agree with experiment within experimental errors. We compare our approach with that of Carlson et al. who have used a similar physical picture.     

Projectile Coulomb excitation with fast radioactive beams

We report a search for γ rays emanating from Coulomb excitation of fast (30–46 MeV/u) radioactive projectiles⁸He,^11,12,14Be interacting with a lead target. These are clearly identified by their Doppler shift. The 320 keV 1/2^? → 1/2⁺ γ transition from¹¹Be was observed with a cross-section of 191±26 mb which is noticeably less than expected from the known lifetime and in the perturbation limit of pure Coulomb excitation. In the other nuclei rather stringent upper limits of 0.01 to 0.2 Weisskopf units, are placed on the hypothetical transition to 1^? states.     

Coulomb excitation in 180Hf

Coulomb excitation studies have been performed to measure transition probabilities of collective quadrupole vibrational states in ¹⁸⁰Hf. The I = 2 level of the K^π = 2⁺ collective γ-band is established at 1200.5 keV with B(E2)_exc = (11.0 ± 1.1) × 10^?50e² · cm⁴ (3.6 ± 0.4 s.p.u.). The angular distribution of the de-exciting γ-rays from this level yields δ = 9.6⁺²²_?5.8 or, less likely, 0.7 ± 0.2 for the 1107.2 keV 2_γ⁺ → 2_g⁺ transition. The B(E2)_exc for any K^πI = 0⁺2 stateorother 2⁺ states up to 1500 keV is less than 5 × 10^?51e² · cm⁴ (< 0.2. s.p.u.).     

Coulomb excitation of neutron-rich 138,140,142Xe at REX-ISOLDE

We report on “safe” Coulomb excitation of neutron-rich ^138,140,142Xe nuclei. The radioactive nuclei have been produced by ISOLDE at CERN and post-accelerated by the REX-ISOLDE facility. The γ-rays emitted by the decay of excited states have been detected by the MINIBALL array. Recent results are presented.     

Coulomb excitation of the 242m Am isomer

The ^242m Am isomer, a well-known candidate for photodepopulation research, has been studied in this first ever Coulomb excitation of a nearly pure (≈98%) isomer target. Thirty new states, including a new rotational band built on a K ^π = 6^? state, have been identified. Strong K-mixing results in nearly equal populations of the K ^π=5^? and 6^? states. Newly identified states have been assigned to the K ^π=3^? rotational band, the lowest states of which are known to decay into the ground-state band. Implications regarding K-mixing and Coulomb excitation paths to the ground state are discussed.     

Calculated polarization after Coulomb excitation in beam-foil interaction

The excitation of a hydrogen beam by the shielded Coulomb potentials of the ionic cores of an Aufoil is calculated in first Born approximation for a beam velocityv=1.4 a.u. Different formation depths of the final 2p term are considered and weighted with the survival probability. Stokes parameters for the emitted light are compared with He (n=3→ 2) transitions. It is demonstrated that the coherence of the excitation by neighbouring target cores tends to reduce the excitation amplitudes for the 2pm states withm≠0. Adsorbates are estimated to have a considerable effect on the polarization.