LXX INTERNATIONAL CONFERENCE "NUCLEUS – 2020. AND ELEMENTARY PARTICLE PHYSICS. NUCLEAR PHYSICS TECHNOLOGIES"

Structure of Light Λ-hypernuclei near Nucleon Drip Lines and Baryonic Interaction

1,3S.V. SIDOROV, 1D.E. LANSKOY, 2,3T.YU. TRETYAKOVA

1 Faculty of Physics, Moscow State University, Moscow, Russia 2 Skobel’tsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia 3 Joint Institute for Nuclear Research, Dubna, Russia

ST PETERSBURG, 2020 Hypernuclei S

Visible baryonic matter as we know it is primarily made of and , made in turn from u- and d- quarks. To study baryonic interaction properties for heavier quarks (such - as s-quarks), one may consider synthesizing hypernuclei, a.k.a. nuclei with protons, neutrons and . - Notation:

퐴 Λ푍 is a hypernucleus made of N neutrons, Z protons and 1 Λ- 4 ; mass number 퐴 = 푁 + 푍 + 1 1푝 퐻 퐴푍 is a hypernucleus made of N neutrons, Z protons and 2 ΛΛ 4 Λ-hyperons; mass number 퐴 = 푁 + 푍 + 2 1푠 Λ퐻

Structure Of Light Λ-hypernuclei Near Nucleon S.V. Sidorov et al 2/12 Drip Lines And Baryonic Interaction Chart of nuclei and hypernuclei

Structure Of Light Λ-hypernuclei Near Nucleon S.V. Sidorov et al 3/12 Drip Lines And Baryonic Interaction Motivation

➢ Study of the properties of baryonic interactions beyond nucleon-nucleon interactions ➢ Predictions for bound hypernuclei with an unbound nucleon core ➢ Research in star structure

Structure Of Light Λ-hypernuclei Near Nucleon S.V. Sidorov et al 4/12 Drip Lines And Baryonic Interaction Hartree-Fock approach for hypernuclei

• Energy density functional: 1 퐸 = 푔. 푠. 푇 + 푉 푔. 푠 = ∫ 퐻 𝜌, 휏, 퐽 푑푟, ȁ푔. 푠. ۧ = det 휙 풓 12 퐴! 푖 풋 • Hartree-Fock single particle states: 훿 2 퐸 − σ푖 푒푖∫ 휙푖 풓 푑푟 = 0 훿휙푖 • Hartree-Fock equations:

2 2 ′ ℏ ′′ 푙훼 푙훼 + 1 ℏ ′ ∗ −푅훼 푟 + 2 푅훼(푟) − ∗ 푅훼 푟 + 푈푞,Λ 푟 푅훼 푟 = 푒훼푅훼(푟) 2푚푞,Λ(푟) 푟 2푚푞,Λ 푟

Structure Of Light Λ-hypernuclei Near Nucleon S.V. Sidorov et al 5/12 Drip Lines And Baryonic Interaction Skyrme interaction for hypernuclei

• Nucleon-nucleon Skyrme potential: 1 2 ′2 푉푁푁 풓ퟏ, 풓ퟐ = 푡0 1 + 푥0푃휎 훿 풓ퟏퟐ + 푡1 1 + 푥1푃휎 풌 훿 풓ퟏퟐ + 훿 풓ퟏퟐ 풌 1 2 +푡 1 + 푥 푃 풌′훿 풓 풌 + 푡 𝜌훼 푹 1 + 푥 푃 훿 풓 + 푖푊 𝜎 + 𝜎 [풌′ × 훿 풓 풌] 2 2 휎 ퟏퟐ 6 3 3 휎 ퟏퟐ 1 2 • Hyperon-nucleon Skyrme potential: 1 푉 풓 , 풓 = 푡Λ 1 + 푥Λ푃 훿 풓 + 푡Λ 풌2훿 풓 + 훿 풓 풌′2 Λ푁 횲 풒 0 0 휎 횲퐪 2 1 횲퐪 횲퐪 1 +푡Λ풌′훿 풓 풌 + 푡Λ𝜌훼 푹 훿 풓 2 횲퐪 6 3 횲퐪 • NN: SLy4 • ΛN: SLL4’, YBZ1, YBZ5, LY1, YMR, SkSH1 Structure Of Light Λ-hypernuclei Near Nucleon S.V. Sidorov et al 6/12 Drip Lines And Baryonic Interaction 퐴+1 Hyperon binding energies and radii of nuclear cores in Λ푍

Structure Of Light Λ-hypernuclei Near Nucleon S.V. Sidorov et al 7/12 Drip Lines And Baryonic Interaction 퐴+1 Hyperon binding energies and radii of nuclear cores in Λ푍

Structure Of Light Λ-hypernuclei Near Nucleon S.V. Sidorov et al 8/12 Drip Lines And Baryonic Interaction 퐴+1 Hyperon binding energies and radii of nuclear cores in Λ푍

Structure Of Light Λ-hypernuclei Near Nucleon S.V. Sidorov et al 9/12 Drip Lines And Baryonic Interaction Nuclear core distortion (polarization) by hyperon

Structure Of Light Λ-hypernuclei Near Nucleon S.V. Sidorov et al 10/12 Drip Lines And Baryonic Interaction Nuclear core distortion (polarization) by hyperon

Structure Of Light Λ-hypernuclei Near Nucleon S.V. Sidorov et al 11/12 Drip Lines And Baryonic Interaction Conclusions

Hypernuclear Hartree-Fock approach was utilized to study the properties of light neutron-rich Λ-hypernuclei.

➢ Hyperon binding energy depends on excess of neutrons or protons in the nucleus ()

➢ Various choices of ΛN-interaction can lead to significantly different predictions of BΛ

➢ Hyperon binding energy vs isospin dependence is more pronounced for the cases with more dramatic density changes, and the corresponding nuclei should be chosen as primary sources of information on ΛN-interaction

It is planned to improve the predictive power of the approach by taking charge symmetry breaking into consideration.

Structure Of Light Λ-hypernuclei Near Nucleon S.V. Sidorov et al 12/12 Drip Lines And Baryonic Interaction Thank you for your attention Back-up slides Hyperon binding energy

퐴 퐴 퐴−1 퐵Λ Λ푍 = 퐵푡표푡 Λ푍 − 퐵푡표푡 푍

➢ The difference in neighboring isobar chains is around 1 MeV for lighter hypernuclei, smaller as A increases

➢ Symmetric character of 퐵Λ with respect to isospin 푁 − 푍

➢ 퐵Λ is almost constant for nuclei in the same isobar chain

Structure Of Light Λ-hypernuclei Near Nucleon S.V. Sidorov et al 7/n Drip Lines And Baryonic Interaction Hypernuclear radii

Structure Of Light Λ-hypernuclei Near Nucleon S.V. Sidorov et al 8/n Drip Lines And Baryonic Interaction