Coulomb Excitation Cross Sections Research Articles

Inelastic scattering from even rare earth isotopes

The Coulomb excitation cross sections for the first excited state of 15 even-mass nuclei in the region of the rare earths have been determined from measurements on inelastically scattered protons and deuterons. From the cross sections, reduced E2-transition probabilities are obtained, in general in good agreement with those derived from the directly measured lifetimes of the nuclear states. The intrinsic quadrupole moments determined from the transition probabilities show, for each element, a regular variation with the mass number, but discontinuities occur when passing from one element to another. This behaviour appears to be correlated with the variation in the moment of inertia for the same nuclei. The individual intrinsic quadrupole moments of odd-mass nuclei in the same region often deviate from the moments of the neighbouring even isotopes, but on the average the quadrupole moments of odd-mass nuclei are almost the same as those for even nuclei.

The decay of the 136 keV level in Fe 57

Coulomb excitation of the 136 keV state in Fe 57 has been made using 2 MeV helium ions and a number of its properties have been studied. The angular distributions of the γ-rays from this state have been measured. Considerable perturbation of the state is required to explain these results. For the intensity of the 122 keV gamma ray relative to that of the 136 keV gamma ray a value of 8.6±0.2 has been obtained. The half life of the state has been measured and found to be (8.6±0.8) × 10 −9 s. A measurement of the Coulomb excitation cross section leads to a value for the upward B(E2) of (0.043±0.005) × 10 −48 e 2cm 4. This is consistent within the errors of measurement with the lifetime result if we assume that the spin of the 136 keV level is 5 2 .

E2 transitions from the second 2+ level of even-even nuclei

A survey has been made of available data for the γ-ray branching of the second 2+ level of over 50 even nuclei with A > 30, together with data for the E2-M1 mixing of the (2′ → 2) cascade transition. In addition, presently available data for the Coulomb excitation cross sections for the second 2+ level of some 24 even nuclei have been collected. From these data, three ratios of reduced E2 transition probabilities have been calculated, and compared with the predictions of various theories. The comparisons indicate that by far the most successful theory to date for predicting such ratios is the recent asymmetric rotor model of Davydov and Filippov, Perhaps the most striking success of this theory is the prediction for the ratio B(E2; 2′ → 0)/ B(E2; 2 → 0) as a function of the energy ratio E 2(2+)/ E 1(2+). However, there are some experimental results which remain unexplained, particularly for the ratio B(E2; 2′ → 2)/ B(E2; 2′ → 0).

Coulomb excitation cross sections of gadolinium isotopes from inelastic scattering measurements

The cross sections for Coulomb excitation and the energies of the accessible low-lying rotational states in the six most abundant isotopes of gadolinium have been determined from measurements on the corresponding groups of inelastically scattered protons and deuterons. The projectiles were accelerated in an electrostatic generator to energies around 4 MeV. Particles scattered from isotopically pure targets prepared in an isotope separator were observed at an angle of 145° with respect to the beam by means of a magnetic spectrometer of high resolution. The lifetimes for the first excited states in Gd 154 and Gd 156 derived from the measured cross sections are in good agreement with the reported directly measured lifetimes of these states.

Shell-Model Theory ofPb206

A detailed nuclear shell model calculation of the energy levels and gamma-ray transition rates in ${\mathrm{Pb}}^{206}$ is carried through. For pure singlet two-body forces with the same effective range and strength as for the low-energy two-body system, energy level agreement is good---for 13 known levels, the mean discrepancy between theory and experiment is 0.057 Mev. For singlet forces 75% as strong as for the low-energy two-body system, plus weak coupling to collective vibration, the energy level agreement is somewhat better---the mean discrepancy between theory and experiment is 0.035 Mev per level. In the latter theory, the strength of collective motion is determined from the known Coulomb excitation cross section in ${\mathrm{Pb}}^{206}$. In either theory, the calculated transition rates are in qualitative accord with experiment, but quantitative agreement is lacking.Electric quadrupole transition rates are shown to be describable in terms of a neutron effective charge. The effective charge is about $1.15e$ and the same in ${\mathrm{Pb}}^{206}$ as in ${\mathrm{Pb}}^{207}$. Other calculated quantities in good agreement with experiment are the relative cross sections to final $p$ states in the ${\mathrm{Pb}}^{206}(d, p){\mathrm{Pb}}^{207}$ reaction and the difference in binding energies of the last neutron in ${\mathrm{Pb}}^{206}$ and ${\mathrm{Pb}}^{207}$. The results are shown to be insensitive to substantial amounts of triplet-odd force, either attractive or repulsive.

Investigation of Coulomb excitation of nuclei by nitrogen ions

The ratio of the cross sections for Coulomb nuclear excitation by heavy particles and protons has been computed. It is shown that in many cases it is more profitable to use heavy ions than protons for Coulomb excitation of nuclei. Preliminary results of a study of Coulomb excitation of a number of nucleides with 15.6 MeV nitrogen ions are presented.

Gamma-Ray Yields from Coulomb Excitation

The yields of $\ensuremath{\gamma}$ rays resulting from Coulomb excitation have been measured for the elements Ta, Au, Pt, Tl, Pb, Th, W, Hf, Ag, Pd, Rh, and Mo. The yields of the 137-, 166-, and 303-kev $\ensuremath{\gamma}$ rays in Ta and the (277+273)- and 550-kev $\ensuremath{\gamma}$ rays in Au were studied as a function of proton energy. No significant deviation from the predictions of the semiclassical theory of Alder and Winther was observed. Reduced transition probabilities for $E2$ and $M1$ transitions have been obtained from the $\ensuremath{\gamma}$-ray yields. In four cases these values may be compared to values obtained from direct half-life measurements. The good agreement indicates that the absolute cross section for Coulomb excitation is correctly given by the theory. Nuclear distortions based on the observed $E2$ transition probabilities are compared to those obtained from the observed excitation energies.