Determination of the multipole deformation parameters of238U by 22MeV proton inelastic scattering

Abstract

Inelastic scattering 22 MeV proton from 238U has been studied. Angular distributions of the states of the rotational band have been measured. Coupled-channel analysis allows determination of the deformation parameters/32,/34 and/36. These values are somewhat in disagreement with other experimental results.Recent Hartree-Fock calculations of nuclear shapes have focussed renewed interest on the determination of nuclear shapes. In particular calculations have been systematically made in the actinide region by Quentin [1]. At the same time new experiments have been found to be extremely useful in the determination of multipole deformations of nuclei in this region. These experiments included inelastic scattering of protons [2], a-particles [3,4], neutrons [5] and electrons I-6] as well as Coulomb excitation 1-7, 8]. The X-ray emission of muonic atoms in the same nuclear region has also been studied [9]. The rotational spectrum of uranium allows the use of the simple rotor model with a radius given in terms of the usual deformation parameters /3L by R = R 0 (1 + fi2 ]120 + fi4 Y4o + fi6 Y60), where the YLO are the spherical harmonics. Table 1 presents the most recent values of these deformation parameters deduced in this model. Analysing these results, there appear to be important disagreements, in particular between the proton scattering result [2] and the others. In view of this disagreement, we have measured angular distributions for the z3SU(p,p') reaction at 22MeV incident proton energy. * On leave from Alberta University, Edmonton, CanadaThe experiment was performed using the Orsay MP Tandem. The target was 100~tg.cm -z of natural uranium obtained by evaporation on a 20 gg. cm-2 carbon backing. The scattered protons were detected using a position sensitive silicon counter of 2,000 ~tm thickness at the focal plane of a split-pole spectrograph. The small energy spread of the incident beam and the high resolution of the detection system yielded an overall resolution of 10 keV at forward angles. The measurements are limited to angles greater than 25 ~ for the other excited states. This limit is due to the contamination of the target by oxygen, nitrogen and carbon. The angular distribution for all states were measured up to 100 ~ . The angular distributions have been measured for the 0 +, 2 +, 4 + and 6 + members of the ground state rotational band. A coupled-channel analysis was performed using the ECIS code [10] of Raynal. The interaction potential arises from the deformation of the real and imaginary central potential, the spinorbit potential as derived by Sherif and Blair (full Thomas form) and the Coulomb potential. Initial optical-model parameters for the coupled-channel calculations were obtained by fitting only the elastic scattering cross-sections using the search code Magali of Raynal [10]. These parameters were then adjusted to preserve the fits to the elastic crosssection as coupling was added in the coupled-channel

Analysis of differences in the ENDL99 and ENDL2009 nuclear data libraries pertaining to 238U

“…We now use deformation lengths δ k = β k R, for R the radius of the real volume part, to describe the results of all these experiments. The averaged deformations from experiments [11,[15][16][17][18][19] are δ 2 = 1.721 ± 0.159 fm and δ 4 = 0.333 ± 123 fm. There is only weak evidence for a non-zero δ 6 , so this is set to zero in our calculations.…”

The determination of hexadecapole deformation parameters in actinide nuclei and their variation near the nuclear surface

“…Consid-erable differences were obtained for the/72,/?4 parameters: the proposed values vary from 0.198 to 0.279 for/?2 and from 0.001 to 0.100 for/?4. A tentative explanation for such discrepancies has been recently proposed [18]. Since the penetration of the projectile into the nucleus depends strongly on its nature and energy, differences in the shape of the equidensity surfaces could a priori account for systematical differences between parameters deduced from various experimental processes.…”

“…As a consequence, for scattering processes where the projectile is such that it touches only the outer nuclear surface, one obtains/32 and/~4 parameters larger than for those where it penetrates deeper inside the nucleus. If one estimates as in [18], according to the prescription of [34], the experimental cut-off radius for 22 MeV protons and 50 MeV alpha particles to be 4 fm and 8 fm respectively one may compare the calculated and experimental trend of/32 and /34 parameters as functions of R c. One sees on Fig. 2 that the small relative decrease of/32 is not reproduced by our calculations, whereas the large relative increase of /34 (30 %) is well accounted for.…”

“…From the density matrix represented in the harmonic oscillator basis, we have computed the total (neutron + proton) density function on a mesh of 64 equidistant points . Experimental data come from [11] for Rc=4fm and from [18] for R~=Sfm on the symmetry axis and 24 equidistant points in the perpendicular direction. This mesh is to be compared with the one used for solving the HartreeFock equations: 20 Gauss-Hermite and 10 GaussLaguerre points, on the symmetry axis and in the perpendicular plane respectively.…”