Analytic description of critical-point actinides in a transition from octupole deformation to octupole vibrations

Abstract

An analytic collective model in which the relative presence of the quadrupole and octupole deformations is determined by a parameter (φ 0 ), while axial symmetry is obeyed, is developed. The model [to be called the analytic quadrupole octupole axially symmetric model (AQOA)] involves an infinite well potential, provides predictions for energy and B(EL) ratios, which depend only on φ 0 , draws the border between the regions of octupole deformation and octupole vibrations in an essentially parameter-independent way, and describes well 226 Th and 226 Ra, for which experimental energy data are shown to suggest that they lie close to this border. The similarity of the AQOA results with φ 0 = 45 • for ground-state band spectra and B(E2) transition rates to the predictions of the X(5) model is pointed out. Analytic solutions are also obtained for Davidson potentials of the form β 2 + β 4 0 /β 2 , leading to the AQOA spectrum through a variational procedure.

Parameter-free solution of the Bohr Hamiltonian for actinides critical in the octupole mode

“…The parameter-free predictions of the model for the lowest bands are given in Table 1, together with the experimental spectra of 226 Ra [13] and 226 Th [14], which are known to lie near the border between the regions of octupole deformation and octupole vibrations [15,16], as also seen in Figs. 2(a) and 2(b), where the experimental spectra of 218−228 Ra and 220−234 Th are included.…”

“…where M is the angular momentum projection onto the laboratory-fixedẑ-axis, K = 0 is the projection onto the body-fixedẑ ′ -axis, and the functions |LM0, + and |LM0, − transform according to the irreducible representations (irreps) A and B 1 of the group D 2 respectively [17,18], their explicit form being given in [16,19]. Introducing [17,18] …”

Nuclear collective motion with a coherent coupling interaction between quadrupole and octupole modes

“…On the other hand, the square well potential of case III appears to be applicable to examining the possible critical behavior of the quadrupole-octupole collectivity in different nuclear regions. Studies in this direction have been implemented recently in the light actinide nuclei [33]. We suggest that further analysis of experimental data for quadrupole-octupole spectra would be of use for testing the prediction of the staggering pattern illustrated in Fig.…”

“…Now, in terms of the polar variables, the potential will depend on both η and φ, so that the variables in the Schrödinger equation cannot be directly separated. This could be done in a way similar to the adiabatic separation of the β and γ degrees of freedom in the X(5) model framework [12], as well as in the framework of the AQOA model [33]. Alternatively, the problem could be solved numerically in a way similar to the approach of Ref.…”

Electric dipole moments inU230,232and implications for tetrahedral shapes

“…Below N ∼ 140, the presence of alternating parity bands with sizable electric dipole moments D 0 , has been taken as evidence of rotation-induced octupole deformation; whereas above N = 140, the D 0 values are reduced and the positive-and negative-parity branches develop a sizable energy splitting. In this regime, the negative-parity bands have been interpreted in terms of octupole vibrations [1][2][3]. In recent years, a unified understanding of the above phenomena in terms of octupole phonons and their condensates has been suggested [4,5].…”