Splitting of theporbit in triaxially deformedΛ25Mg

Abstract

The excited states of 25 Mg with the hyperon in p orbit are studied within the framework of the antisymmetrized molecular dynamics for hypernuclei. We obtained five rotational bands in 25 Mg in which the hyperon in p orbit is coupled to the ground and K π = 2 + bands of 24 Mg. We predict that the corresponding bands of 25 Mg energetically split due to the triaxial deformation of the core nucleus 24 Mg and the spatial anisotropy of the p orbits of . Since a hyperon is unaffected by the Pauli principle governing the nucleons, it can be regarded as an impurity in nuclei and modifies nuclear properties such as clustering and deformation. For example, a hyperon in s orbit reduces the intercluster distance between α and d in 7 Li, which was confirmed from the reduction of B(E2) [1][2][3][4]. Furthermore, many authors have predicted the deformation change in p-sd shell hypernuclei by adding the hyperon in s orbit [1,2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].In the case of the hyperon in p orbit, on which we focus in this study, it can be regarded as a probe of nuclear deformation due to its spatial anisotropy. For example, in 9 Be, the splitting of the p states was predicted due to the axial symmetric deformation (2α clustering) of 8 Be [5,20]. Namely, the hyperon in p orbit generates two rotational bands in which moves along the parallel and perpendicular directions of the 2α clustering [20]. In other words, the anisotropy of the p orbit and axially symmetric deformation of 8 Be lead to the splitting of the p states. From this fact, we may deduce that the p states will split into three in the case of triaxial deformation, and we can probe triaxial deformation of the core nucleus by the observation of three different p states in hypernuclei. 24 Mg is one of the candidates of triaxially deformed nuclei with the presence of the low-lying 2 + 2 state [21][22][23][24][25][26]. Therefore, we expect that the p states of 25 Mg will split into three with different spatial density distribution of the hyperon. To investigate the splitting of p states of 25 Mg and its relation to triaxial deformation, we have employed the antisymmetrized molecular dynamics for hypernuclei (HyperAMD) [27]. The HyperAMD with generator coordinate method (GCM) has been successfully applied to investigate the excitation spectra and B(E2) values of 25 Mg with the hyperon in s orbit [28]. The Hamiltonian used in this study is given aŝHere,T N ,T , andT g are the kinetic energies of nucleons, a hyperon, and the center-of-mass motion, respectively. We have used the Gogny D1S The intrinsic wave function of a single hypernucleus composed of A nucleons and a hyperon is described by the parity-projected wave function, π =P π int , whereP π is the parity projector and int is the intrinsic wave function given as where φ i is ith nucleon single-particle wave packet consisting of spatial, spin χ i , and isospin η i parts. The single-particle wave function of (ϕ) is represented by a superposition of

Generator coordinate method for hypernuclear spectroscopy with a covariant density functional

“…In recent years, several other methods have also been developed for hypernuclear spectroscopy, including an abinitio method [14], the antisymmetrized molecular dynamics (AMD) [15][16][17], and the microscopic particlerotor model based on the covariant density functional theory [18,19]. The angular momentum projection (but with the scheme of variation-before-projection) for the total hypernuclear wave function has also been carried out with the Skyrme density functional [20], even though the important effect of configuration mixing was not taken into account.…”

Photoproduction of Typical Hypernuclei

“…The underlying folding potential for the p-state Λ is stronger in the case of l = 2 core angular momentum than in the case of l = 0, as shown in Fig. 7 Second, it is interesting to see the AMD prediction of five rotational bands in 25 Λ Mg that come from the splittings in the coupling of p-state Λ with triaxial deformation of the core nucleus 24 Mg [33]. In general this kind of splitting of the p or d orbits tends to occur due to the correlation between the Λ orbit spatial distribution and the nuclear potential deformation.…”

Shape and Energy Spectra of Λ Hypernuclei in the Framework of Skyrme–Hartree–Fock Model

“…In the calculation, for 12 C, 13 Λ C, 20 Ne, and 21 Λ Ne, the strength of the pairing force is V 0 = −410 MeV for both neutrons and protons and the strength of the spin-orbit term in the SGII force is reduced by a factor of 0.6 for 12 C and 13 Λ C to reproduce their oblate shapes as in Ref. [17].…”

“…Although the N-body cluster model is very successful to study p-shell hypernuclei [6,8,9] and even double-Λ hypernuclei [10], the dimensionality of Jacobi coordinates makes it difficult to describe Λ hypernuclei beyond the p shell. For sd-shell nuclei, the AMD method gives comprehensive energy spectra with both positive and negative parities, especially for 21 Λ Ne [11] and 25 Λ Mg [12,13]. Nonrelativistic and relativistic mean-field (RMF) models [14] can also describe a Λ hypernuclear system very well, in particular for heavy nuclear systems.…”

“…In laboratory, several kinds of phenomena have been observed when a Λ is added: The Λ can introduce spin splitting in the atomic nucleus, which was observed in 13 Λ C [1], and a shrinkage effect of Λ hyperon was observed in 7 Λ Li [2]. Theoretically, the study of Λ hypernuclei has made important progress and various models have been developed to describe the properties of such systems.…”