In this paper, we presented the ground state energies calculated for some single and double cascade hyperon($Ξ^{-}$) hypernuclei. For hypernuclei of the type $_Ξ^{A_c+1}$X we applied $Ξ+^A_c$X two-body model and for hypernuclei of the type $_{ΞΞ}^{A_c+2}$X we adopted $Ξ+Ξ+^A_c$X three-body model. A two-term Gaussian (Isle type) potential with adjustable parameters is chosen as the $Ξ$-nucleus interaction, while a two-term Yukawa-type potential has been chosen for the $ΞΞ$ pair. In the three-body model calculation, we adopted the hyperspherical harmonics expansion (HHE) formalism. The resulting two- and three-body Schr{ö}dinger equations subject to appropriate boundary condition's have been solved numerically to get the ground-state energies and wavefunctions. Computed values are in excellent agreement with the observed ones as found in the literature. Analysis of the calculated observables indicates that the hyperons stay close to the core-nucleus. Hypernuclei formed as a result of absorption of one or more $Ξ$-hyperon(s) by a normal nucleus (bound or unbound) are found to have more stability than those formed as a result of absorption of one or more $Λ$ hyperon(s) by the same nucleus. This fact flashes towards the possibility of the existence of a valley of strange hypernuclei near the drip lines.
Neutron and proton driplines of single-$Λ$ and double-$Λ$ hypernuclei, $Ξ^{-}$ hypernuclei as well as normal nuclei are studied within a relativistic mean field approach using an extended form of the FSU Gold Lagrangian density. Hyperons are found to produce bound nuclei beyond the normal nuclear driplines. Radii are found to decrease in hypernuclei near the driplines, in line with observations in light $Λ$ hypernuclei near the stability valley, The inclusion of a $Ξ^{-}$ introduces a much larger change in radii than one or more $Λ$'s.
Neutron dripline calculations for both magnesium nuclei and magnesium + $Λ$ hypernuclei have been carried out in a microscopic framework using a chiral effective model. The results are compared with two other relativistic mean field models, SPL-40 and NL3. All three models describe the $Λ$ separation energy of known hypernuclei adequately. The extrapolation to the driplines for moderately heavy hypernuclei are found to be strongly model-dependent.
We analyze hypernuclei coming from fragmentation and multifragmentation of spectator residues obtained in relativistic ion collisions. These hypernuclei have a broad distribution in masses and isospin. They reach beyond the neutron and proton drip lines, and they are expected to be stable with respect to neutron and proton emission. This gives us the opportunity to investigate the properties of exotic hypernuclei, as well as the properties of normal nuclei beyond the drip lines, which can be produced after weak decay of such hypernuclei.
Using as a tool the s-wave approximation (sWA), this work demonstrates that the nonmesonic weak decay transition rates $Γ_{n}$ and $Γ_{p}$ can be expressed in all hypernuclei up to $^{29}_Λ$Si (and very likely in heavier ones too) in the same way as in the s-shell hypernuclei, i.e. as a linear combination of only three elementary transition rates. This finding leads to the analytic prediction that, independently of the transition mechanism, all hypernuclei that are on the stability line (N = Z), i.e. $^5_Λ$He, $^7_Λ$Li, $^9_Λ$Be, $^{11}_Λ$B, $^{13}_Λ$C, $^{17}_Λ$O, $^{29}_Λ$Si, etc should roug…
Bound state properties of few single and double-$Λ$ hypernuclei is critically examined in the framework of core-$Λ$ and core+$Λ+Λ$ few-body model applying hyperspherical harmonics expansion method (HHEM). The $ΛΛ$ potential is chosen phenomenologically while the core-$Λ$ potential is obtained by folding a phenomenological $ΛN$ interaction into the density distribution of the core. The depth of the effective $ΛN$ potential is adjusted to reproduce the experimental data for the core-$Λ$ subsystem. The three-body Schrödinger equation is solved by hyperspherical adiabatic approximation (HAA) to ge…
The Non-Symmetrized Hyperspherical Harmonics method (NSHH) is introduced in the hypernuclear sector and benchmarked with three different ab-initio methods, namely the Auxiliary Field Diffusion Monte Carlo method, the Faddeev-Yakubovsky approach and the Gaussian Expansion Method. Binding energies and hyperon separation energies of three- to five-body hypernuclei are calculated by employing the two-body $Λ$N component of the phenomenological Bodmer-Usmani potential, and a hyperon-nucleon interaction simulating the scattering phase shifts given by NSC97f. The range of applicability of the NSHH me…
Simultaneous description of ordinary and hypernuclei masses by a single mass formula has been a great challenge in nuclear physics. Hyperon-separation energies of about forty Lambda($Λ$), three Lambda-Lambda($ΛΛ$), one Sigma($Σ$) and seven Cascade($Ξ$) hypernuclei have been experimentally found. Many of these nuclei are of light masses. We prescribe a new mass formula, called BWMH, which describes the normal and hypernuclei on the same footing. It is based on the modified-Bethe-Weizsäcker mass formula (BWM). BWM is basically an extension of the Bethe-Weizsäcker mass formula (BW) for light nucl…
In this paper, a nice theoretical scheme is presented to investigate resonant and bound states in weakly bound nuclear systems by the use of isospectral potentials together with hyperspherical harmonics expansion. In this scheme, a new potential is constructed which is strictly isospectral with the original shallow potential and has properties that are desirable to calculate resonances more accurately and elegantly. The effectiveness of the method has been checked in terms of its application to the $0^+$ resonances in the neutron-rich isotopes $^{18,20}$C in the two-neutron plus core three-bod…
We use the hyperspherical adiabatic expansion method to discuss the the two mechanisms of sequential and direct three-body decay. Both short-range and Coulomb interactions are included. Resonances are assumed initially populated by a process independent of the subsequent decay. The lowest adiabatic potentials describe the resonances rather accurately at distances smaller than the outer turning point of the confining barrier. We illustrate with realistic examples of nuclei from neutron ($^{6}$He) and proton ($^{17}$Ne) driplines as well as excited states of beta-stable nuclei ($^{12}$C).
The role of the isoscalar hyperon Lambda in probing the density dependence of the nuclear symmetry energy is studied in multi-Lambda hypernuclei, hyperon-rich matter and neutron stars in relativistic models. Relationships between the properties of three types of objects and the neutron thickness in 208Pb are established with respect to the isoscalar-isovector coupling that modifies the density dependence of the symmetry energy. The exotic isotopes far from the neutron drip line can be stabilized by filling in considerable Lambda hyperons. The difference of the binding energy of multi-Lambda hy…
Lying at the lower edge of the `island of inversion', neutron-rich Fluorine isotopes ($^{29-31}$F) provide a curious case to study the configuration mixing in this part of the nuclear landscape. Recent studies have suggested that a prospective two-neutron halo in the dripline nucleus $^{31}$F could be linked to the occupancy of the $pf$ intruder configurations. Focusing on configuration mixing, matter radii and neutron-neutron ($nn$) correlations in the ground-state of $^{31}$F, we explore various scenarios to analyze its possible halo nature as well as the low-lying electric dipole ($E$1) res…
We investigate the dripline mirror nuclei, $^{11}$Li and $^{11}$O, located on the neutron and proton dripline, respectively. We calculate the lowest four states, $3/2^-$, $1/2^+$, $3/2^+$ and $5/2^+$, built on double occupancy in the nuclear $s_{1/2}$ and $p_{1/2}$ valence single-particle states. We use the hyperspherical adiabatic expansion method to solve the three-body problem for a frozen nuclear core surrounded by two identical nucleons. The four analogue states in $^{11}$O are obtained with precisely the same interactions as used for the four states in $^{11}$Li, except for addition of t…
Dilated coordinate method for solving nuclear lattice effective field theory
State Key Laboratory of Nuclear Physics and Technology, Institute of Quantum Matter, South China Normal University（华南师范大学量子物质研究所核物理与技术国家重点实验室）；Key Laboratory of Atomic and Subatomic Structure and Quantum Control (MOE), Guangdong-Hong Kong Joint Laboratory of Quantum Matter（原子与亚原子结构及量子控制教育部重点实验室粤港澳量子物质联合实验室）；Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, Guangdong Provincial Key Laboratory of Nuclear Science（广东省物质结构与基本相互作用卓越研究中心广东省核科学重点实验室）；School of Physics, Peking University（北京大学物理学院）
The population and decay of two-nucleon resonances offer exciting new opportunities to explore dripline phenomena. The understanding of these systems requires a solid description of the three-body (core+N+N) continuum. The identification of a state with resonant character from the background of non-resonant continuum states in the same energy range poses a theoretical challenge. It is the purpose of this work to establish a robust theoretical framework to identify and characterize three-body resonances in a discrete basis. A resonance operator is proposed, which describes the sensitivity to ch…
A simultaneous description of non-strange nuclei, hypernuclei and multiply-strange nuclear systems is provided by a single mass formula which is shown to be useful for estimating binding energies of nuclear systems over a wide mass range, including the light mass nuclei. It not only provides a good fit to the existing experimental data on hyperon-separation energies but also reproduces results of the relativistic mean field (RMF) calculations. In addition, it can provide the Lambda($Λ$), Cascade-0($Ξ^0$) and Cascade-minus ($Ξ^-$) drip lines. The existence of a range of bound pure-hyperonic sys…
Instituto de Estructura de la Materia, CSIC（物质结构研究所，西班牙科学理事会）；Istituto Nazionale di Fisica Nucleare（意大利国家核物理研究所）；Université Côte d’Azur, CNRS, Institut de Physique de Nice（蔚蓝海岸大学，法国国家科学研究中心，尼斯物理研究所）；University of Pisa（比萨大学）；Technische Universität München（慕尼黑工业大学）
