Bose-Einstein condensation of α clusters and new soft mode in C12 – Fe52

Abstract

Bose-Einstein condensation of α clusters in light and medium-heavy nuclei is studied in the frame of the field theoretical superfluid cluster model. The order parameter of the phase transition from the Wigner phase to the Nambu-Goldstone phase is a superfluid amplitude, square of the moduli of which is the superfluid density distribution. The zero mode operators due to the spontaneous symmetry breaking of the global phase in the finite number of α clusters are rigorously treated. The theory is systematically applied to N α nuclei from 12 C-52 Fe at various condensation rates. In 12 C it is found that the energy levels of the gas-like well-developed α cluster states above the Hoyle state are reproduced well in agreement with experiment for realistic condensation rates of α clusters. The electric E2 and E0 transitions are calculated and found to be sensitive to the condensation rates. The profound raison d'être of the α cluster gas-like states above the Hoyle state, whose structure has been interpreted geometrically in the nuclear models without the order parameter such as the cluster models or ab initio calculations, is revealed. It is found that in addition to the Bogoliubov-de Gennes vibrational mode states collective states of the zero mode operators appear systematically at low excitation energies from the N α threshold energy. These collective states, new-type soft modes in nuclei due to the Bose-Einstein condensation of the α clusters, emerge systematically in light and medium-heavy mass regions and are also located at high excitation energies from the ground state in contrast to the traditional concept of soft mode in the low excitation energy region.

Nonlinear Schrodinger Equation Solitons on Quantum Droplets

“…In this model, spontaneous symmetry breaks the global Wigner phase in a finite number n of α clusters, a Bose-Einstein condensation process. We compare our Bethe spectra for N = 4 with spectra resulting from condensation to n = 6 ( 24 Mg) and n = 8 ( 32 S) α−clusters, for two different available condensation rates of 70% and 100% calculated in [61]. In these cases, the comparison results in a good match between the two models above the Hoyle state (here 0 MeV).…”

“…Numerous studies show that alpha clustering occurs from light and medium-mass elements to heavy and superheavy elements. Various phenomenological and microscopic models have been proposed in literature to describe various aspects of alpha clustering, [57][58][59][60][61][62][63]. Among them, the large amplitude nonlinear collective model, [17, 24, 26, 27, 36-38, 48, 50], are of special interest to the present work.…”

“…The collective motion related to cluster condensation, or superfluidity in nuclei, has been paid attention in the frame of the many-body theory in the last decades. In [61] it was shown that collective states of the zero mode operators are new-type soft modes due to Bose-Einstein condensate of alpha clusters.…”

“…From the Bose-Einstein phenomenological Hamiltonian of a number of alpha particles trapped by an external potential it results a Gross-Pitaevskii equation (G-P) for the nuclear condensate component of the field operator. The solution of the G-P equation is the order parameter of the phase transition from the Wigner phase to the Nambu-Goldstone phase is a superfluid amplitude, square of the modulus of which is the superfluid density distribution [61], which ultimately describes the nuclear shape. The G-P equation is in the same hierarchy as the NLS equation just having in addition the potential trap linear term.…”

“…We notice that, even for the best fit, our model generates the first three energy levels below the Hoyle state. In the next four columns we fit our theoretical spectra with a field theoretical super-fluid cluster model [61]. In this model, spontaneous symmetry breaks the global Wigner phase in a finite number n of α clusters, a Bose-Einstein condensation process.…”