γ-vibrational states in superheavy nuclei

Abstract

Recent experimental advances have made it possible to study excited structure in superheavy nuclei. The observed states have often been interpreted as quasiparticle excitations. We show that in superheavy nuclei collective vibrations systematically appear as low-energy excitation modes. By using the microscopic Triaxial Projected Shell Model, we make a detailed prediction on γ -vibrational states and their E2 transition probabilities to the ground state band in fermium and nobelium isotopes where active structure research is going on, and in 270 Ds, the heaviest isotope where decay data have been obtained for the ground-state and for an isomeric state.One of the important predictions in nuclear physics is the emergence of a region of long-lived superheavy elements beyond the actinides, the so-called 'island of stability'. The question concerns the precise location of the next closed nucleon shells beyond Z = 82 and N = 126. To reach the island, much of the experimental effort has been focused on the direct creation of superheavy elements. In recent years, progress has also been made in structure studies for nuclei beyond fermium, thanks to the development of detector systems for decay and in-beam studies using recoil separators and heavy ion fusion reactions [1,2]. It has been suggested that by studying the transfermium nuclei, in particular their excited structure, one can gain useful information on relevant single-particle states [3], which is key to locating the island.The nuclei of our interest, the Fm (Z = 100) and No (Z = 102) isotopes, belong to the heaviest mass region where structure can currently be studied experimentally. The yrast property of these nuclei shows that they are generally good rotors. Rotational behavior of some of these yrast bands has been successfully reproduced by several models (see, for example, ). The discussion on excited configurations so far has been focused on quasiparticle excitations [8][9][10][11]. On the other hand, a deformed rotor can, according to the collective model, undergo dynamical oscillations around the equilibrium shape, resulting in various low-lying collective vibrational states. Ellipsoidal oscillation of the shape is well known as γ vibration [12]. It is thus natural to consider γ vibrational states in superheavy nuclei, and in fact, this excitation mode has begun to draw one's attention [13,14]. Knowledge on vibrational states in superheavy nuclei is particularly useful for this less known mass region because of the interpretation of the observed low-lying spectroscopy.Early calculation of γ -vibrational states in heavy nuclei was performed by Marshalek and Rasmussen [15] using the qausiboson approximation, and by Bès et al. [16] using the quadrupole-plus-pairing model based on deformed Nilsson states [17]. Modern treatment of γ vibration includes the Tamm-Dancoff method, the random phase approximation [18], and others [19,20]. In Ref. [21], a shell-model-type method for describing γ -vibrational states was introduced, which is based on the Triaxial Projecte...

Nature ofγdeformation in Ge and Se nuclei and the triaxial projected shell model description

“…However, the TPSM is a fully microscopic theory, and fixed deformations are only used for construction of basis states. It is important to note that unlike the phenomenological asymmetric rotor model [6], our results depend not only on the deformation parameters but also on the detailed microscopic isotopedependent shell filling, and more importantly, on the configuration mixing of the various quasiparticle states [18,30]. We would also like to remind here that in the spherical shell model approach, although, starting from a bare spherical basis, it can equally describe the deformed nuclei as well.…”

“…Nevertheless, this model is clearly an over-simplified approach. It has been pointed out [18,30] that the underlying physical picture of generating γ-vibration in deformed nuclei, suggested in the framework of TPSM, is analogous to the classical picture of Davydov and Filippov [6], yet TPSM is a fully microscopic method. It is interesting to see that both shell models (SSM and TPSM), though starting from quite different bases (spherically symmetric vs. triaxially deformed) give nearly identical results for the low-lying states of 76 Ge, as seen in Figs.…”

Understanding the different rotational behaviors of252No and254No

“…Theoretically, various models have been applied to study the rotational properties of transfermium nuclei. The calculations include (i) cranking approximations of mean-field models such as the macroscopicmicroscopic approach [15][16][17], the Nilsson potential with the particle-number-conserving method [18][19][20], the HartreeFork-Bogoliubov (HFB) approach with the Skyrme force [21,22], the HFB approach with the Gogny force [23,24], and the relativistic Hartree-Bogoliubov approach [25]; (ii) the projected shell model [26][27][28] that incorporates beyond-meanfield effects such as symmetry restoration and configuration mixing. In general, the theories can reproduce the observations.…”

Extracting single-particle information for the superheavy mass region by studying excited structure in transfermium nuclei

“…For the model parameters in this mass region, we refer to Ref. [6]. In a so-called band diagram [5], each angular-momentum-projected state of the PSM basis produces a rotational band κ given by E κ (I) = Φ κ |ĤP I KK |Φ κ / Φ κ |P I KK |Φ κ .…”