New yrast energy formula for soft rotors

Our understanding of nuclear structure is framed within the context of a number of idealized benchmarks. These include the axial rotor [1], the harmonic vibrator [2], g-soft deformed nuclei [3,4] and, very recently, the new critical point symmetries [5–8] for phase transitional regions. These models generally predict sequences of energies and either a subset or all of the BsE2d values within the model space. For example, for the pure rotor, the yrast energies go as IsI+1d. No nucleus need obey these paradigms exactly and, historically, their proposal has been rather quickly followed by schemes that embody perturbations to the idealized structures they envision. Examples are the energy expansions in powers of IsI+1d, or the Harris formula [9], the variable moment of inertia (VMI) [10], the Ejiri formula [11], and the Holmberg-Lipas formula [12] for rotor-like nuclei, or the anharmonic vibrator (AHV) formula which actually describes a range of nuclei from spherical to deformed [13,14]. In the framework of the interacting boson model, to describe the increase of the moment of inertia at high spin states in deformed nuclei, a spin-dependent term 1/ s1+ fL ·Ld was included in the Hamiltonian [15]. These perturbation schemes embody expected physical effects, such as centrifugal stretching and rotation-vibration coupling for the rotor or phonon-phonon interactions for the vibrator. Of course, the further a nucleus is in structure from one of the paradigms, the larger the perturbations to the predictions of that paradigm will have to be, and, generally, the worse or less applicable, it will be. This is preeminently the case for transitional nuclei between spherical and deformed limits where neither the vibrator or rotor limits is very apt [16]. The value of any of the paradigms is that they provide an expected pattern that, once identified in an actual nucleus, helps establish its structure, and that deviations from them reveal additional degrees of freedom that would be difficult or impossible to spot without the prior existence of ideal guidelines. Therefore, the development of optimized benchmarks is a valuable effort. With the high spin data often available for transitional and well-deformed nuclei, perturbations to the rotor expansion for yrast (or other rotational band) energies, become quite important. Effects such as centrifugal stretching, pairing collapse, and bandmixing are at work and numerous perturbations to idealized models have attempted to take these into account. It is the purpose of this work to offer a new formula, simple in practical usage, which works as well as or nearly as well as existing expressions for well-deformed nuclei and better than any in the transitional region. The basis of this expression is utterly simple: it is the ideal rotor expression