We study the deformation property of Λ hypernuclei using the relativistic mean field (RMF) method. We find that 29 Λ Si and 13 Λ C hypernuclei have spherical shape as a consequence of the additional Λ particle, whereas the corresponding core nuclei, 28 Si and 12 C, are oblately deformed. Most of other hypernuclei have a similar deformation parameter to the core nucleus, in accordance with the previous study with the non-relativistic Skyrme-Hartree-Fock method. We discuss the sensitivity of our results to the choice of pairing interaction and to the parameter set of the RMF Lagrangian.

We study the change in nuclear deformation induced by the presence of one or two lambda hyperons in light and medium-heavy nuclei, comparing Skyrme-Hartree-Fock and relativistic mean field model predictions. The physical origin of the deformation changes is discussed in terms of the lambda and nucleon mean field potentials. We identify 30 Si and 30 S as candidates with possible large deformation differences between the core nucleus and hypernucleus.

We study the shape of Λ hypernuclei in the full (β, γ) deformation plane, including both axially symmetric and triaxial quadrupole deformations. To this end, we use the constrained Skyrme Hartree-Fock+BCS method on the three-dimensional Cartesian mesh. The potential energy surface is analyzed for carbon hypernuclei as well as for sd-shell hypernuclei such as 27,29 Λ Si and 25,27 Λ Mg. We show that the potential energy surface in the (β, γ) plane is similar to each other between the hypernuclei and the corresponding core nuclei, although the addition of Λ hyperon makes the energy surface somewhat softer along the γ direction.

Taking the ground state rotational band in 24 Mg as an example, we investigate the impurity effect of Λ hyperon on collective excitations of atomic nuclei in the framework of non-relativistic energy density functional theory. To this end, we take into account correlations related to the restoration of broken symmetries and fluctuations of collective variables by solving the eigenvalue problem of a five-dimensional collective Hamiltonian for quadrupole vibrational and rotational degrees of freedom. The parameters of the collective Hamiltonian are determined with constrained mean-field calculations for triaxial shapes using the SGII Skyrme force. We compare the low-spin spectrum for 24 Mg with the spectrum for the same nucleus inside 25 Λ Mg. It is found that the Λ hyperon stretches the ground state band and reduces the B(E2 : 2 + 1 → 0 + 1 ) value by ∼ 9%, mainly by softening the potential energy surface towards the spherical shape, even though the shrinkage effect on the average proton radius is only ∼ 0.5%.

We discuss low-lying collective excitations of Λ hypernuclei using the self-consistent mean-field approaches. We first discuss the deformation properties of Λ hypernuclei in the sd-shell region. Based on the relativistic mean-field (RMF) approach, we show that the oblate deformation for 28 Si may disappear when a Λ particle is added to this nucleus. We then discuss the rotational excitations of 25 Λ Mg using the three-dimensional potential energy surface in the deformation plane obtained with the Skyrme-Hartree-Fock method. The deformation of 25 Λ Mg is predicted to be slightly reduced due to an addition of a Λ particle. We demonstrate that this leads to a reduction of electromagnetic transition probability, B(E2), in the ground state rotational band. We also present an application of random phase approximation (RPA) to hypernuclei, and show that a new dipole mode, which we call a soft dipole Λ mode, appears in hypernuclei, which can be interpreted as an oscillation of the Λ particle against the core nucleus.