Quantal Corrections Research Articles

Nuclear moments of inertia in the absence of pairing

The nuclear moments of inertia in the absence of pairing are not equal to the rigid-body values because of quantal corrections due to the finite size of the system.

Coulomb excitation of ground bands inDy160,162,164withNe20andCl35ions

Multiple Coulomb excitation of states up to ${J}^{\ensuremath{\pi}}={12}^{+}$ in the ground band was measured to test the rigid-rotor prediction for intraband $B(E2)$ ratios. The deexcitation $\ensuremath{\gamma}$ rays were observed in singles and in the particle- $\ensuremath{\gamma}$ coincident mode following excitation by $^{20}\mathrm{Ne}$ or $^{35}\mathrm{Cl}$ ions from the Oak Ridge isochronous cyclotron. $B(E2)$ values were extracted by comparing experimental excitation probabilities with theoretical values calculated with the Winther- de Boer computer code. An unexpected result is that the $B(E2;4\ensuremath{\rightarrow}6)$ values for $^{162,164}\mathrm{Dy}$ are 15\ifmmode\pm\else\textpm\fi{}5% smaller than the rotational values. However, the most striking variation of $B(E2)$ with spin occurs for $^{160}\mathrm{Dy}$. We find $\frac{{B(E2)}_{\mathrm{exp}}}{{B(E2)}_{\mathrm{rotational}}}=0.77\ifmmode\pm\else\textpm\fi{}0.05$, 0.94\ifmmode\pm\else\textpm\fi{}0.06, and 1.29\ifmmode\pm\else\textpm\fi{}0.14 for the 4\ensuremath{\rightarrow}6, 6\ensuremath{\rightarrow}8, and 8\ensuremath{\rightarrow}10 transitions, respectively. The 10\ensuremath{\rightarrow}8 transition in $^{160}\mathrm{Dy}$ is significantly faster than rotational even when our approximate quantal correction of 6% is not included in the analysis.[NUCLEAR REACTIONS $^{160,\phantom{\rule{0ex}{0ex}}162,\phantom{\rule{0ex}{0ex}}164}\mathrm{Dy}$($^{35}\mathrm{Cl}$, $^{35}\mathrm{Cl}$\ensuremath{'}), $E=125$ MeV; ($^{20}\mathrm{Ne}$, $^{20}\mathrm{Ne}$\ensuremath{'}), $E=72$ MeV; measured Coulomb excitation yields. $^{160,\phantom{\rule{0ex}{0ex}}162,\phantom{\rule{0ex}{0ex}}164}\mathrm{Dy}$ levels, deduced ${E}_{\ensuremath{\gamma}}$, $B(E2)$.]

Third order perturbation treatment of Coulomb excitation withE2 andE4 interactions included

For one even-A rotational nucleus (152Sm) a semi-classical third order perturbation treatment of Coulomb excitation with a hexadecapolo interaction included has been carried out considering bombarding conditions which have formerly been found to be suitable for an experimental determination of certainE4 transition moments. Numerical values of the most important contributions to the perturbation hierarchy are given and the present state of quantal corrections is discussed.

Quantum mechanical corrections for double coulomb excitation in 152Sm and the determination of the E4 transition probability

Quantal corrections have been computed for the double Coulomb excitation. These corrections are significant for the determination of the E4 matrix element in 152Sm.

Quantal corrections and the WKB approximation of multiple Coulomb excitation

For an exact quantal calculation of multiple Coulomb excitation a set of coupled radial differential equations must be solved. The WKB method can be used to facilitate such computations. For large values of the angular momenta the set of coupled radial equations can be approximated by the simpler semiclassical equations. Also for large distances of the projectile from the target nucleus the WKB method simplifies the computation. The earlier suggested symmetrization of the relevant parameters of Coulomb excitation has been proved. For the case of the reorientation effect quantal corrections have been computed numerically for the excitation probability and the angular distribution of the de-excitation γ-rays. The slow convergence of the sum over the orbital momenta in the reaction amplitude can be improved by a method similar to the one used in electron scattering calculations. The numerical computations allow an estimate of the quantal correction for the reorientation effect for all experimental conditions up to a few percent.

Semiclassical Phase Shifts for Low-Energy ``Orbiting'' Collisions

A semiclassical expression for the phase shift in the literature which is applicable even when a maximum exists in the effective potential is re-expressed in terms of the simple JWKB phase integrals. This expression is employed to calculate phase shifts from tables of reduced functions for a Lennard-Jones (12–6) potential. These semiclassical calculations are compared with published exact values; excellent qualitative and good quantitative agreement is obtained. Finally, the qualitative nature of the quantal corrections to the classical total and differential cross sections and the collision lifetime is discussed.