Piet Van Isacker's research while affiliated with Grand Accélérateur National d'Ions Lourds and other places

David Rowe was a highly respected theoretical physicist who made seminal contributions that improved our understanding of the atomic nucleus, in particular of the collective behaviour of its constituent nucleons - results he often obtained with the use of sophisticated group-theoretical methods. He will also be remembered as the (co-)author of monographs on nuclear physics, written with the scientific rigour that was characteristic of his research.

We report on recent experimental results on β decay into self-conjugate (N=Z) nuclei with mass number 58≤A≤70. Super-allowed β decays from the Jπ=0+ ground state of a Z=N+2 parent nucleus are to the isobaric analogue state through so-called Fermi transitions and to Jπ=1+ states by way of Gamow–Teller (GT) transitions. The operator of the latter decay is a generator of Wigner’s SU(4) algebra and as a consequence GT transitions obey selection rules associated with this symmetry. Since SU(4) is progressively broken with increasing A, mainly as a consequence of the spin–orbit interaction, this symmetry is not relevant for the nuclei considered here. We argue, however, that the pseudo-spin–orbit splitting can be small in nuclei with 58≤A≤70, in which case nuclear states exhibit an approximate pseudo-SU(4) symmetry. To test this conjecture, GT decay strength is calculated with use of a schematic Hamiltonian with pseudo-SU(4) symmetry. Some generic features of the GT β decay due to pseudo-SU(4) symmetry are pointed out. The experimentally observed GT strength indicates a restoration of pseudo-SU(4) symmetry for A=70.

James Philip Elliott made important contributions to improve our understanding of the structure of atomic nuclei in the second half of the twentieth century. In 1958 he proposed the SU(3) model, explaining rotational behaviour of nuclei in the context of the shell model. His idea, based on elegant and seminal group-theoretical concepts, reconciled the independent-particle with the liquid-drop model, which until then existed as disconnected views of the nucleus. In the 1960s and 1970s he developed methods to extract properties of the nuclear interaction from the phase shifts of nucleon–nucleon scattering. From 1980 until his death he contributed to the development of the interacting boson model of Arima and Iachello, and its microscopic understanding in terms of symmetries of the shell model. For his outstanding achievements in theoretical physics, in 2002 he and Francesco Iachello were awarded the Lise Meitner prize of the European Physical Society for ‘their innovative applications of group-theoretical methods to the understanding of atomic nuclei’. His achievements were also recognized by the award of the Rutherford Medal and Prize of the Institute of Physics in 1994.

In the context of the sf-IBM, the interacting boson model with s and f bosons, the conditions are derived for a rotationally invariant and parity-conserving Hamiltonian with up to two-body interactions to have a minimum with tetrahedral shape in its classical limit. A degenerate minimum that includes a shape with tetrahedral symmetry can be obtained in the classical limit of a Hamiltonian that is transitional between the two limits of the model, Uf(7) and SOsf(8). The conditions for the existence of such a minimum are derived. The system can be driven towards an isolated minimum with tetrahedral shape through a modification of two-body interactions between the f bosons. General comments are made on the observational consequences of the occurrence of shapes with a higher-rank discrete symmetry in the context of algebraic models.

In the context of the sf-IBM, the interacting boson model with s and f bosons, the conditions are derived for a rotationally invariant and parity-conserving Hamiltonian with up to two-body interactions to have a minimum with tetrahedral shape in its classical limit. A degenerate minimum that includes a shape with tetrahedral symmetry can be obtained in the classical limit of a Hamiltonian that is transitional between the two limits of the model, U_f(7) and SO_{sf}(8). The conditions for the existence of such a minimum are derived. The system can be driven towards an isolated minimum with tetrahedral shape through a modification of two-body interactions between the f bosons. General comments are made on the observational consequences of the occurrence of shapes with a higher-rank discrete symmetry in the context of algebraic models.

The level structure of the N=82 nucleus Xe136 was studied with the inelastic neutron scattering reaction followed by γ-ray detection. A number of the spins and parities were reassigned, and many level lifetimes were determined for the first time using the Doppler-shift attenuation method. New shell-model calculations were also performed using both the full Z=50–82 model space, and a reduced model space including only the 1d5/2 and 0g7/2 orbitals. This new information characterizing Xe136 was used to identify the seniority structure of the low-lying levels and to assign (π0g7/2)υ=04, (π0g7/2)υ=24, (π0g7/2)υ=44, (π1d5/2)(π0g7/2)υ=13, and (π1d5/2)2(π0g7/2)υ=02 configurations to describe all observed states below 2.8 MeV.