Comparision of quadrupole moment with experiment

Last modification: 1996/3/21
A figure ( GIF file of 3.8KB or PS file of 13KB ) presents a comparison between the experimental and the calculated intrinsic quadrupole moments in unit of barn. For each nucleus whose B(E2;0+ -> 2+) is given in Ref. [RMM87] (289 even-even nuclei ranging over 4 < = Z < = 98), an x symbol is put at a point whose abscissa is equal to the experimental value and its ordinate to the value calculated with the HF+BCS with SIII. The diagonal line is drawn so that one can see easily the quality of the agreement.

The intrinsic moment is defined for the HF+BCS solutions as

Q0 = sumprotons < 2 z2 - x2 - y2 >,
where z-axis is the symmetry axis (All of our solutions have practically axial shapes). The deduction of |Q0| from the B(E2) is based on the rigid rotor model [RMM87,BM75].

For nuclei with |Q0| > 3.5 b, the agreement with experiment is excellent. The even-even nuclei having the largest intrinsic quadrupole moment is 252Cf (indicated by letter A in the figure) in the experimental table [RMM87], while it is 244Rf among the 1029 HF+BCS solutions (Q0=16.6 b). The largest discrepancy is found in 222Th (indicated by letter D), whose experimental Q0 is 5.5 b while the HF solution is spherical. Two nuclei located at isolated points are 176Pt (indicated by letter B) and 222Ra (indicated by letter C).

For nuclei with smaller |Q0|, however, many nuclei falls not in the diagonal line but in a horizontal line, which means that the HF solution has a spherical shape when the experimental B(E2) is not necessarily very small. This may be explained by attributing the enhanced B(E2) not only to static deformations but also to the collective shape oscillation around the spherical equilibrium. It may also be related to the complicated landscapes of the potential energy curves of nuclei with A=50-100.