Deformation of Odd Nuclei 27Al, 31P and 35Cl in Single-Particle States

Using the evolutionary approach recently developed by us, the shapes of odd s-d-shell 27Al, 31P and 35Cl nuc­lei in the ground and single-particle excited states have been extracted from the experimental data on the energies, spins, and parities of these states, as well as the measured probabilities of electromagnetic transitions between them. The key ingredient of our procedure is the evolutionary algorithm that evolves the population of the bad-quality data-fitting nuclear shapes to the high-quality data-fitting nuclear shapes. We have found that the studied nuclei in the ground states are abnormally weakly deformed, which is not expected for the nuclei in the shell middle. Even in their low-laying single-particle excited states, the nuclei 27Al and 31P are found to be weakly deformed, too. With the increase of the single-particle excitation energy, the change of the state of the only one nucleon – the valence proton the spin and parity of which determine the spin and parity of the 35Cl nucleus – causes the shape phase transition from the high-symmetry phase – spherical ground state – to the low-symmetry phase – deformed excited states. The angular part of the 27Al and 31P nuclei shape is de­scribed by two harmonics – quadrupole and hexadecapole. The angular part of the 35Cl nucleus shape is de­scribed by three harmonics – quadrupole, hexadecapole, and hexacontatetrapole, but the contribution of hexadecapole deformation is not independent. At present, there are no fundamental nuclear models that account for or predict the dominant hexacontatetrapole deformation, especially for light and medium nuclei. We have found that the spin and parity of the 27Al, 31P and 35Cl nuc­lei are determined by the spin and parity of the last odd (valence) proton. At the same time, some of the nucleons of the nucleus core change their characteristics, too. Thus, the electromagnetic transitions between the single-particle states of the 27Al, 31P and 35Cl nuc­lei are the multi-particle processes.