image: Contour plots of the distribution of the nucleons and hyperon in ${}_{\Lambda }^{21}$Ne as a function of octupole deformation. The upper and lower panels correspond to the hyperon at the lowest- and secondly lowest- energy state, respectively. view more
Credit: ©Science China Press
A hypernucleus is a bound system of nucleons with one or more strange baryons, called hyperons. Neutron stars can be regarded as the biggest hypernuclei. The presence of hyperons will soften the equation of state of nuclear matter and thus affect the maximal mass of neutron stars. In this sense, the studies of hypernuclear structure are helpful to understand fundamental interaction in nature, new state of nuclear matter, and neutron stars. The structure of atomic nuclei is widely studied by mean-field models, the basic idea of which is that the nucleons, i.e., protons and neutrons, are approximated as non-interacting particles trapped in a potential well. The depth and width of this well are determined by the states of the particles themselves. The properties of the atomic nuclei are influenced when the potential well is changed by the addition of a hyperon. This effect is the so-called hyperon impurity effect. Since the hyperon is not subject to the Pauli exclusion principle for nucleons, i.e., it can occupy the state with the same quantum numbers of the state that has already been occupied by nucleons, the hyperon has more "freedoms" than the nucleons inside nuclei. When the hyperon occupies the lowest-energy state, its spatial distribution has a spherical symmetry. The previous studies have demonstrated that this hyperon shrinks nuclear size and decreases nuclear quadrupole deformation. These effects are exhibited in the quenched electric quadrupole transition strengths in hypernuclear low-lying states which can be measured with the techniques of hypernuclear gamma-ray spectroscopy.
In order to directly compare the theoretical predictions with the observations from hypernuclear experiments and to quantitatively study the impurity effects of hyperons in atomic nuclei, there are remarkable progresses in the development of beyond mean-field models with the implementation of quantum-number projection techniques and generator coordinate method into modern energy density functional theories. These beyond mean-field models open a window to determine the effective hyperon-nucleon interaction with hypernuclear spectroscopic data and eventually the equation of state for neutron stars in a more precise way.
The low-energy structure of pear-shaped hypernuclei is interesting as it usually accompanies with nucleon clustering structure. In the intrinsic coordinate frame, the pear-like shape is characterized with quadrupole and octupole deformations and a rotation symmetry along z-axis. This shape violates spatial inversion symmetry and rotational symmetry. As a result, the two most important quantum numbers parity and angular momentum are lost. In order to recover them, researchers introduced parity and angular momentum projections into a relativistic covariant density functional theory for hypernuclei. The method has been illustrated by taking ${}_{\Lambda }^{21}$Ne as an example, where the Λ is put on one of the two lowest-energy states, labeled by Λs and Λp respectively. They have found that the hyperon quenches the formation of molecular-like 16O+α clustering structure in 20Ne. They also studied in detail the configurations 20Ne (Kπ=0-)?Λs and 20Ne (Kπ=0+)?Λp which are close in energy but have very different structures. These two configurations only exist in hypernuclei and thus the hypernuclear states built on them are referred to as "genuine" hypernuclear states. The researchers found a very interesting behavior of the Λs (Λp) as a function of the octupole deformation. The hyperon in the lowest- and the secondly lowest-energy state becomes more and more concentrated around the bottom (top) of the "pear". It looks like the two dance actions, squatting and jumping. In addition, compared with the existing nuclear models for the pear-shaped hypernuclei, their newly developed theoretical model is more flexible for the hypernuclei in different mass region. This research is published in the Science China Vol. 62 No.4 (2019).
###
The study was completed by HaoJie Xia from Handan College, XianYe Wu from Jiangxi Normal University, Hua Mei from University of North Carolina and Tohoku University, and JiangMing Yao from Michigan state university. This research was funded by the National Natural Science Foundation, China (Grant No. 11575148).
See the article:
HaoJie Xia, XianYe Wu, Hua Mei, JiangMing Yao, Beyond mean-field approach for pear-shaped hypernuclei, SCIENCE CHINA Physics, Mechanics & Astronomy, 2019, Vol. 62, No. 4: 042011
http://engine.scichina.com/doi/10.1007/s11433-018-9308-0
https://link.springer.com/article/10.1007/s11433-018-9308-0