Electromagnetic transition rates of C12 and O16 in rotational-vibrational models

Abstract

We develop a formalism to calculate electromagnetic (EM) transition rates for rotational-vibrational models of nuclei. The formalism is applied to recently proposed models of Carbon-12 and Oxygen-16 which are inspired by nuclear dynamics in the Skyrme model. We compare the results to experimental data, as well as other nuclear models. The results for Carbon-12 are in good agreement with the data across all models, making it difficult to differentiate the models. More experimental data is needed to do this, and we suggest which transitions would be most interesting to measure. The models of Oxygen-16 are less successful in describing the data, and we suggest some possible improvements to our approximations which may help. Carbon-12 has an approximate higher energy rotational band with spins 0 + , 2 + , 4 + , ... . Different authors model this band as a chain of α-particles [4], a "breathing" excitation of the triangle [5], or an admixture of several shapes [6]. All these models can reproduce the energy spectrum rather well.Rotational bands are not the only indicator of collective, geometric behaviour. Electromagnetic (EM) transition rates measure γ-decay between two nuclear states.

Magnetic dipole moments as a strong signature for $α$-clustering in even-even self-conjugate nuclei

“…Concerning 13 C, the states with excitation energy lying between 9.90 and 16.95 MeV are well reproduced by a molecular α-cluster model [81], in which the odd neutron lies between the 4 He nuclei arranged in a linear chain. Besides, for the (1/2) − 2 and (1/2) + 1 states of the same nucleus, the triangular α-cluster configuration with one neutron located in the same plane of the 4 He nuclei (π-orbit) and along the axis perpendicular to the 3α-plane (σ-orbit), respectively, has been proposed [81].…”

“…Z/A Concerning 17 O, attempts to reproduce the spectrum of the nucleus above the 13 C+α decay threshold in terms of the 4α + n configuration have been made [84,85] in the framework of the generator coordinate method (GCM) [86]. Nevertheless, for the lowest-energy states, SMbased approaches as the cluster-orbital shell model (COSM) [87] seem to provide a rather faithful description [88,89].…”

“…[10] and refs. [11,12,13]). In particular, the adoption of the equilateral triangle (D 3h ) [14,15,16], the tetrahedron (T d ) and the triangular bipyramid (D 3h ) as basis-configuration for the inspection of the structure properties of the 12 C [17] and 16 O [18,19] within the Algebraic Cluster Model (ACM) [12,20] and of the 20 Ne [21] within a geometric macroscopic α-cluster model, respectively, has revived the interest for the subject in recent times (cf.…”

Equivalence of generator coordinate Brink cluster model and nonlocalized cluster model and supersolidity of $α$ cluster structure in nuclei

“…For 16 O, from the geometrical cluster viewpoint, the ground state with the four α clusters at the vertices of the tetrahedron [68], which has been recently revisited in Refs. [69,70,71,72], makes a structure change to the α+ 12 C (0 + 1 ) cluster structure near the α threshold as revealed in Refs. [73,74] and to the loosely coupled well-developed four α cluster states with the dilute gas-like α+ 12 C(0 + 2 ) cluster structure near the four α threshold [75].…”

A False Vacuum Skyrme Model for Nuclear Matter

“…Another attempt deals with modifications of the so-called BPS Skyrme model [21,22] that has obtained reasonable values of binding energies for very heavy nuclei and on some aspects of neutron stars [23,24]. The Skyrme model has been applied to other aspects of nuclear matter [25,26], and recently, interesting results were obtained on the spectra of light nuclei [27][28][29][30] and on the spin-orbit interaction [31].…”