Coulomb Excitation Cross Sections Research Articles

0 + states and E0 and E2 transition rates in even Sn nuclei

0 + states and their depopulating E0 and E2 transitions have been studied in 112–124Sn. Several methods of γ-ray and electron spectrometry have been employed, including special coincidence techniques for lifetime, conversion electron and double Coulomb excitation measurements. For 114–118Sn the E2 transition probabilities from the first excited 0 +states (0 2 +) are about 20 W.u., which is compatible with a vibrational two-phonon character. Also the E0 transition probabilities from these states are within a factor of two from the vibrational values. For the second excited 0 + states (0 3 +) the corresponding E2 and E0 transition probabilities are considerably smaller. A total of 12 E0 transitions have been observed. The 0 3 + → 0 2 + transition is observed in 114–120Sn and has in 116Sn a reduced transition probability 1–2 orders of magnitude larger than those of the groundstate E0 transitions, which indicates that the 0 3 + and 0 2 + states are strong mixtures of components with different 〈 r 2〉. The 0 + states in 116Sn are discussed as possible rotational band heads associated with a deformation β 2 ≈ 0.2. The Coulomb excitation cross section of the 0 2 + state is found to be sensitive to an interference term including matrix elements with the 2 2 + state. The relative sign of this term has been determined.

Effects of Coulomb excitation and electrodisintegration of relativistic channeled nuclei

A simple calculation of the electrodisintegration and Coulomb excitation cross sections of nuclei by channeling nuclei at high energies in crystals is presented. The cross section of deuteron electrodisintegration is calculated. The experimental conditions for observation of these processes are discussed.

Co59(O16,O16)Co59elastic scattering

Differential cross sections for the $^{59}\mathrm{Co}$($^{16}\mathrm{O}$, $^{16}\mathrm{O}$)$^{59}\mathrm{Co}$ elastic scattering have been measured at laboratory energies 36, 40, 45.5, 49, 52, and 56 MeV. The angular range was 15\ifmmode^\circ\else\textdegree\fi{}-170\ifmmode^\circ\else\textdegree\fi{} (lab) in 5\ifmmode^\circ\else\textdegree\fi{} steps at lower energies. At higher energies detailed angular distributions were carried out in 1\ifmmode^\circ\else\textdegree\fi{} steps until the ratio to Rutherford was ${10}^{\ensuremath{-}3}$ with sample measurements at larger angles to assure that the differential cross sections were less than ${10}^{\ensuremath{-}4}$ ratio to Rutherford. The data have been analyzed with a four parameter optical model and the continuous ambiguities in this model are discussed. Strong absorption radii and the values of the nuclear potentials at these points are determined. Good fits to the data have been obtained using a $G$-matrix double-folding model with double-folded or Woods-Saxon forms for the imaginary potential. The required normalization of the real double-folded potential is near unity for all energies. Total reaction cross sections have been obtained by the optical model, quarter-point, "half partial-wave," and the sum of differences methods. The sum of differences method gives slightly larger total reaction cross sections than do the other methods by an amount consistent with estimates of the Coulomb excitation cross section. Estimates of the errors in the sum of differences values are computed by applying the optical theorem and are shown to be negligibly small.NUCLEAR REACTIONS: $^{59}\mathrm{Co}$($^{16}\mathrm{O}$, $^{16}\mathrm{O}$) $^{59}\mathrm{Co}$; measured $\ensuremath{\sigma}(\ensuremath{\theta}, E)$, ${E}_{\mathrm{lab}}=36, 40, 45.5, 49, 52, \mathrm{and} 56$ MeV; measured total reaction cross sections.

High-spin states of 174, 176Yb studied in Coulomb excitation with Kr AND Xe beams

Rotational states up to spin 20+ (18+) in 174Yb (176Yb) have been Coulomb excited using beams of 136Xe. Lifetimes up to and including the 14+ state have been measured using Doppler-broadened lineshape techniques with 136Xe and 86Kr beams. An annular gas-scintillation counter has been developed in order to perform particle-γ coincidence studies. Moments of inertia in 174, 176Yb behave very regularly, showing no signs of backbending effects. The measured lifetimes are in agreement with the rotational model predictions, and the measured cross sections for Coulomb excitation of the high-spin states are in agreement with the semiclassical Winther-de Boer calculation.

K-vacancy production in symmetric heavy-ion collisions

Recent calculations of Thorson and co-workers for ${\mathrm{H}}^{+}$ + H ionization mechanisms and the Briggs-Macek scaling law for $K$-vacancy production in symmetric heavy-ion collisions are used to show the following: (1) If Fano-Lichten-type electron promotion is inhibited because of the absence of a $2p$ vacancy, i.e., if $Z>10$, $K$ vacancies in symmetric collisions are produced mainly by $2p\ensuremath{\sigma}$ electron excitation to vacant bound and unbound molecular-orbital states. (2) The direct $1s\ensuremath{\sigma}$ excitation cross section to vacant bound and unbound states can be obtained experimentally. The relationship between atomic and molecular-orbital Coulomb excitation cross sections is discussed.

Static moments of the first excited states of 32, 34S and 204, 206Pb

The reorientation effect in Coulomb excitation has been used to measure the following static quadrupole moments: Q 2 + ( 32 S) = −0.066 ± 0.017 b, Q 2 + ( 34 S) = 0.026 ± 0.023 b, Q 2 + ( 204 Pb) = 0.19 ± 0.14 b . Interference effects from higher excited states have been included in the analysis, with the signs of the E2 matrix elements taken from an anharmonic model. The value obtained for Q 2 + ( 32 S) is in disagreement with two previous measurements. We attribute the discrepancy to the smaller internucleon separation distances involved in the previous experiments, which can cause deviations from Coulomb excitation cross sections. The other quadrupole moments have not been measured previously. The B (E2: 0 + → 2 +) measured were: 0.0305 ± 0.0016 e 2 · b 2( 32 S), 0.025 ± 0.004 e 2 · b 2( 34 S), and 0.166 ± 0.009 e 2 · b 2( 204 Pb) . From the angular distribution of the de-excitation γ-rays of the Pb nuclei following recoil into vacuum, we have determined the following g- factors: ¦g 2 + ( 204 Pb)¦ < 0.08 (two standard deviations), ¦g 2 + ( 206 Pb)¦ = 0.07 + 0.07 − 0.03 . Our value of g 2 + ( 206 Pb) is in agreement with a previous measurement.

K-Shell Ionization of Beryllium by Proton and Heavy Ions

Experimental cross sections are presented for the ionization of K-shells of beryllium in collision with heavy ions and proton; C + , N + , O + , Ne + and Ar + for bombarding energy ranging from 0.3 to 30 keV per amu, while that for protons is 10 to 200 keV per amu. Proton data show good agreement with the prediction for Coulomb excitation of K-shell electrons. The date for heavy ions are several orders of magnitude larger than that for proton. These results are understood in terms of pseudomolecule formation and crossings of molecular orbitals during the collisions. Heavy ion cross sections show the trend to converge to the theoretical Coulomb excitation cross sections in high energies above about 10 keV per amu.

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

The E2 strength of the 191 keV transition in 197Au

The (L 1 + L 2)/L 3 internal conversion ratio of the 191 keV gamma ray in 197Au was remeasured using a 197Hg source, and found to be 66 ± 5 corresponding to (1.9±0.3)% E2. Similarly, the 268 keV transition was found to be > 92 % E2. From these data and the known Coulomb excitation cross section of the 268 keV state a B(E2) value of 21 s.p.u. is deduced for the 191 keV transition.

E3 Coulomb excitation of 19F

The E3 matrix element connecting the ground state with the 5/2−, 1346-keV level in 19F has been measured by projectile excitation of a 19F beam and observation of the 1236-keV de-excitation gamma ray in Ge(Li) detectors. The thick-target yield of the 1236-keV gamma ray was 1.6, 6.0, 9.8, and 23 gammas per 1010 projectiles at bombarding energies of 22, 25, 26, and 28 MeV, respectively. The average value of the strength of the E3 transition deduced from these measurements is [Formula: see text] In addition, the E2 Coulomb-excitation cross section of the 1554-keV level was measured and the reduced transition strength of the E2 transition from the 1554-keV level to the ground state was found to be 6.8 ± 0.7 W.u. Comparisons are made with model predictions.

Determination of the Static Quadrupole Moments of the First2+States ofPt194,Pt196, andPt198

Static and dynamic electric quadrupole moments of the first ${2}^{+}$ states in $^{194}\mathrm{Pt}$, $^{196}\mathrm{Pt}$, and $^{198}\mathrm{Pt}$ have been determined from Coulomb-excitation cross sections for the scattering of 42-MeV $^{16}\mathrm{O}$ ions measured as a function of scattering angle. The results are compared with recent calculations performed by Kumar and Baranger.

Mössbauer Effect Following Coulomb Excitation in the Even-Even Isotopes of Ytterbium

M\"ossbauer levels in ${\mathrm{Yb}}^{172}$, ${\mathrm{Yb}}^{174}$, and ${\mathrm{Yb}}^{176}$ have been observed following the population of the first excited states by Coulomb excitation. Using oxide and metallic targets and absorbers, the quadrupole energy splittings and relative quadrupole moments were determined for each isotope. Coulomb-excitation cross-section data were used to determine the electric-field gradient at the nucleus for ${\mathrm{Yb}}^{3+}$ in ${\mathrm{Yb}}_{2}$${\mathrm{O}}_{3}$.

Multiple Coulomb excitation of nuclei

The excitation probabilities and the differential and total excitation cross sections for multiple Coulomb excitation of rotational states are evaluated without use of the approximation of instantaneous excitation.

Theory of Coulomb excitation in the collision of identical nuclei

A theory of Coulomb excitation in collisions of identical nuclei is developed. It is shown that under the usual quasi-classical conditions the differential cross sections for Coulomb excitation of nuclei (just as the Mott cross section for elastic Coulomb scattering of identical particles) display considerable oscillations with respect to the scattering angle. If the level excitation energy is sufficiently small as compared with the energy of colliding particles these oscillations are described by a simple modification of the exchange term in the Mott formula for elastic scattering. The character of oscillations in the neighbourhood of 90° (c.m.s.) proves essentially dependent on the multiple moment of the transition which points to a possible use of this relation for the unambiguous determination of multipole moments of the transitions.

Double Coulomb Excitation with Oxygen Ions

Total cross sections for Coulomb excitation of the first and second excited states of the ground-state rotational bands of eight even-even rare earth nuclei have been measured. Oxygen ions accelerated to energies in the range 14 to 50 MeV in the Wisconsin tandem accelerator produced the nuclear excitations. The transitions from the second excited state (${4}^{+}$) to the first (${2}^{+}$), and from the first to the ground state (${0}^{+}$), were detected by analyzing the emitted internal conversion electrons in a wedge-shaped magnetic beta-ray spectrometer. Cross sections for excitation of the ${2}^{+}$ levels yield $B(E2)$ values in satisfactory agreement with those obtained from lifetime measurements and from inelastic scattering of protons, deuterons, and alpha particles. Cross sections for double $E2$ excitation of the ${4}^{+}$ levels are in qualitative agreement with the multiple Coulomb excitation theory of Alder and Winther. The energies of the ${4}^{+}$ levels are ${\mathrm{Sm}}^{152}$, 366.2 keV; ${\mathrm{Sm}}^{154}$, 267.1 keV; ${\mathrm{Gd}}^{160}$, 248.6 keV; ${\mathrm{Dy}}^{162}$, 266.0 keV; ${\mathrm{Er}}^{170}$, 261.5 keV; ${\mathrm{Yb}}^{176}$, 271.9 keV; ${\mathrm{Hf}}^{180}$, 309.4 keV; and ${\mathrm{W}}^{184}$, 363.4 keV. In all cases the uncertainty is \ifmmode\pm\else\textpm\fi{}2 keV.

Large second order effects in in the Coulomb excitation of F 19

The possibility that large contributions to the observed F/sup 19/ transition rates might arise from second order Coulomb excitation stimulated this investigation. Employing computer calculations of the second order Coulomb excitation cross section formulas previously derived, it was shown that in heavy ion collisions such as were involved in F/sup 19/ studies, second order effects may be comparable in magnitude to first order effects and through their interference with first order ones, may permit measurement of transition probabilities sometimes unattainable by other means. (C.E.S.)

Numerical calculations of multiple Coulomb excitation cross sections

Alder and Winther's theoretical predictions for excitation amplitudes, probabilities and cross sections for multiple E2 Coulomb excitation of rotational states have been numerically evaluated on a high speed computer. The range of parameters chosen is particularly used in the analysis of excitations produced by heavy ions in the energy range obtainable with Tandem Van de Graaff accelerators. The results form a basis for further extension of the calculations.

Nuclear resonance effects in Coulomb excitation

The changes in the Coulomb excitation process due to nuclear interactions in the incident and exit channels are calculated. It is shown that resonances in the elastic scattering channel interfere coherently with the Coulomb excitation process and thus lead to anomalies in the cross section for Coulomb excitation. The predictions of the present work are compared with the results of Temmer and Heydenburg for the reaction Na 23(p, p′γ).

Lifetimes of Excited States of Nuclei with Odd Mass

The lifetimes of Coulomb-excited states in ${\mathrm{Ti}}^{47}$, ${\mathrm{Mn}}^{55}$, ${\mathrm{Fe}}^{57}$, ${\mathrm{Zn}}^{67}$, ${\mathrm{Ge}}^{73}$, ${\mathrm{Se}}^{77}$, and ${\mathrm{Mo}}^{95}$ have been measured by a pulsed-beam technique. The observed mean lifetimes were between 0.1 and 12.7 m\ensuremath{\mu}sec. By combining these data with the measured Coulomb-excitation cross sections, we obtained the partial mean life for magnetic-dipole radiation and the ratio ($\frac{E2}{M1}$) for these transitions. The partial $M1$ lifetimes are 20 to 200 times as long as the single-particle estimates.

Inelastic Scattering ofN14byC12

Inelastic scattering of ${\mathrm{N}}^{14}$ by carbon was studied at 27.3 Mev using two surface-barrier counters to detect both the scattered and the recoil particle in coincidence. The cross section for excitation of ${\mathrm{C}}^{12}$ to the first excited state (4.43 Mev) varies only slightly with angle and averages about 0.5 mb/sr. This is about 15 times greater than the theoretical cross section for Coulomb excitation. The cross sections for scattering to the second, third, and fourth excited states in ${\mathrm{N}}^{14}$ were found to be only 15 to 25% of that for the 4.43-Mev excitation in ${\mathrm{C}}^{12}$. Scattering to the first excited state of ${\mathrm{N}}^{14}$ was not observed, which is consistent with conservation of isotopic spin.