A study of fragmentation of the low energy octupole state is performed in order to study the dependence of this fragmentation on quadrupole deformation, determine the limitations of surveys of 3& states, and search for exceptional cases of fragmentation. A regular dependence of fragmentation on the deformation parameter P, is found, and it is demonstrated that the large degree of fragmentation observed in ' ' ' 'Pt is indeed unique. In many nuclei, which are generally spherical or weakly deformed, a large concentration of E3 strength occurs' in a single 3 state (the low energy octupole state) which exists at an energy below 4 MeV. However, in many deformed nuclei this strength fragments among several 3 states. These states often correspond to different alignments of the octupole phonon (E =0, l, 2, and 3) with respect to the symmetry axis of the deformed nucleus. Substantial fragmentation has also been observed in several nuclei which are not well deformed.This fragmentation of octupole strength can pose a significant problem in studies of the systematic behavior of the energies of 3& states, a number of which have been reported recently.In most regions of the Periodic Table, 3, state energies vary smoothly with both N and Z. Authors of the systematic studies generally aim to search for interesting nuclear structure phenomena by identifying octupole behavior which deviates from the usual smooth trends. For example, information on single-particle energies in the A =130 region has been obtained, and anomalous behavior in the heavy Cd isotopes has been demonstrated.However, the fragmentation which is well known to occur in many rare-earth and actinide nuclei has prevented extensive analysis of octupole behavior in these regions (limited analyses are performed in Refs. 4 -6).In addition, fragmentation was found to be responsible for an apparent anomaly in octupole behavior which occurs in the Pt (Z =78) and Hg (Z =80) isotopes near N =120, which are not well deformed. The energies of the 3, states in these Pt isotopes are approximately 1 MeV below those in the Hg isotopes; ' such a discontinuity does not occur anywhere else in the Periodic Table. Shortly after this anomaly was identified, strong and previously unknown 3 states were found 1 MeV above the 3, states in the N = 116 -120 isotopes Pt. When the centroids of octupole strength of nuclei in the vicinity of Pt were examined (instead of the 3, states), the usual smooth systematic behavior was found to occur. Octupole centroids have also been used for systematic analysis in the region near A =150. That study demonstrated the effects of the collapse of the Z =64 shell gap on octupole behavior in that neighborhood of nuclei.In the present article, we survey available data on fragmentation of the low energy octupole states in A )60 nuclei. This work was initiated with three objectives. First, it is interesting to determine the dependence of octupole fragmentation on quadrupole deformation. Second, it is important to determine in which nuclei the centroid of the low ...
We present a parameter that provides a unified interpretation of the 3, states of a large number of spherical and weakly deformed Z )28 nuclei. This parameter suggests criteria for identifying nuclei having anomalous octupole behavior.In an atomic nucleus, a collective octupole vibrational state can be understood as the coherent sum of a number of one-particle-one-hole (lp-lh) or two-quasiparticle (2qp) excitations which can couple to an angular momentum of 3A'. As pointed out by Bohr and Mottelson, ' excitations between orbits differing in orbital angular momentum I by 31)1 and having the same intrinsic spins (i.e., the change in total angular momentum b j=b,l) dominate the systematic behavior of low-energy octupole states because of geometric properties of angular momentum coupling. In heavy nuclei (Z and N )28), the proton and neutron valence shells each contain such a pair of orbits, which we shall call a b 1 =3 pair. The filling of the orbits in the b, 1 =3 pairs (both proton and neutron) determines the variation of the energy of the low-lying octupole states with changing N and Z in spherical and weakly deformed nuclei. ' This behavior lends itself to a highly schematic but useful description. As particles are added to the lower-energy orbit of a 61=3 pair and additional 1p-1h excitations contribute, the excitation energy of the lowenergy octupole state, which we denote by E(31 ), is driven downward.Likewise, as the higher-energy orbit of the pair is filled and 1p-1h excitations are blocked,Recently, a simple parametrization for E(3, ) based on this qualitative description has been developed and used to interpret the systematic behavior of low-energy octupole states in each of four regions of the periodic table where spherical and weakly deformed nuclei are found. In the present paper, we formulate a new parameter which provides a unified description of the nuclei of these four regions which are "well-behaved" with respect to the above description. In particular, when the energies of the first 3 states from all four mass regions are plotted on a single graph using this new parametrization, they fall nearly on a single line. When all the known 3& states of nuclei not falling in the two large regions of well-deformed nuclei -that %=88 -106 rare-earth isotopes and the heavy actinide isotopes -are added to the plot, it is possible to immediately determine those nuclei which cannot be described by the simple picture of octupole behavior presented here. The parameter B"+ B of Ref. 2 used for individual regions is calculated by using the energies of spherical single-particle orbits e"a rough estimate for the groundstate pairing gap (b, = 12/A ' j, where A is set to an average value for the region of interest), the number of valence particles S, and the Bardeen-Cooper-Schrieffer (BCS) equations 2g V"=N, V"=(1/2)[1 -(e"A,)/E"]-, [(~g )2+ g2]1/2The occupation probabilities V" the Fermi energy A. , and the quasiparticle energies E, are calculated iteratively.We then use these probabilities to calculate "occupation num...
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