Isoscalar giant resonances of <inline-formula><tex-math id="M1">\begin{document}$^{{\bf{18}}}_{{\boldsymbol{\Lambda\Lambda}}}{\bf{O}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M1.png"/></alternatives></inline-formula> in relativistic approach

Abstract

The interactions between hyperon-nucleon and hyperon-hyperon have been an important topic in strangeness nuclear physics, which play important role in understanding the properties of hypernuclei and equation of state of strangeness nuclear matter. It is very difficult to perform a direct scattering experiment of the nucleon and hyperon because the short lifetime of the hyperon. Therefore, the hyperon-nucleon and hyperon-hyperon interactions have been mainly investigated experimentally by γ spectroscopy of single-Λ or double-Λ hypernuclei. There are also many theoretical methods developed to describe the properties of hypernuclei. These models are focused mostly on the ground state properties of hypernuclei, and have obtained exciting results in producing the banding energies, the energies of single-particle levels, deformation, and other properties of hypernuclei. Only a few work adopting Skyrme energy density functionals is devoted to study the collective excitation properties of hypernuclei. In present work, we have extended the relativistic mean field and relativistic random phase approximation theories to study the collective excitation properties of hypernuclei, and apply the methods to study the isoscalar collective excited state properties of double Λ hypernuclei. First, the effect of Λ hyperons on the single-particle energies of &lt;sup&gt;16&lt;/sup&gt;O and &lt;sup&gt;18&lt;/sup&gt;&lt;sub&gt;ΛΛ&lt;/sub&gt;O is discussed in the relativistic mean field theory, the calculations are performed within TM1 parameter set and related hyperon-nucleon and hyperon-hyperon interactions. We find that it gives a larger attractive effect on the 1&lt;i&gt;s&lt;/i&gt;&lt;sub&gt;1/2&lt;/sub&gt; states of protons and neutrons, while gives a weaker attractive effect on the states around Fermi surface. The self-consistent relativistic random phase approximation is applied to study the collective excited state properties of hypernucleus &lt;sup&gt;18&lt;/sup&gt;&lt;sub&gt;ΛΛ&lt;/sub&gt;O. The isoscalar giant monopole and quadrupole resonances are calculated and analysed in detail, we pay more attention to the effect of the inclusion of Λ hyperons on the properties of giant resonances. Compared to the strength distributions of &lt;sup&gt;16&lt;/sup&gt;O, changes on the response functions of &lt;sup&gt;18&lt;/sup&gt;&lt;sub&gt;ΛΛ&lt;/sub&gt;O are evidently found both on the isoscalar giant monopole and quadrupole resonances. It is shown that the difference comes mainly from the changes of Hartree energies of particle-hole configurations and the contributions of the excitations of Λ hyperons. We find that the hyperon-hyperon residual interactions have small effect on the monopole and quadrupole response functions in the low-energy region, and have almost no effect on the response functions in the high-energy region.