A formulation of the equations of motion phonon method (EMPM) suited for hypernuclei is outlined and illustrated through an application to B ∧ 12 . A self-consistent calculation using realistic modern potentials is performed using a multiphonon basis which enables us to couple the Λ-particle-proton-hole (pΛ - h) Tamm-Dancoff (TDΛ) states to the excitations of the nuclear core. The impact of such a coupling on the energy levels and on the electroproduction cross section of B ∧ 12 suggests that complex configurations accounting for the excitation of the nuclear core are needed for approaching the experimental data.

The electroproduction of selected $p$- and $sd$-shell hypernuclei was studied within a many-body approach using realistic interactions between the constituent baryons. The cross sections were computed in distorted-wave impulse approximation using two elementary amplitudes for the electroproduction of the $\Lambda$ hyperon. The structure of the hypernuclei was investigated within the framework of the self-consistent $\Lambda$-nucleon Tamm-Dancoff approach and its extension known as the $\Lambda$-nucleon equation of motion phonon method. Use was made of the NNLOsat chiral potential plus the effective Nijmegen-F YN interaction. The method was first implemented on light nuclei for studying the available experimental data and establishing a relation to other approaches. After this proof test, it was adopted for predicting the electroproduction cross section of the hypernuclei $^{40}_{~\Lambda}$K and $^{48}_{~\Lambda}$K in view of the E12-15-008 experiment in preparation at JLab. On the ground of these predictions, appreciable effects on the spectra are expected to be induced by the YN interaction.

We present two methods, the Nucleon-Lambda Tamm Dancoff Approximation (NΛ TDA) and the Equation of Motion Phonon Method (EMPM) suitable for calculating hypernuclear energy spectra and structure. These methods are applicable for hypernuclei of wide range of masses with one Λ particle replacing one nucleon in an even-even nuclear cores. Using an effective Lambda-nucleon (ΛN) potential both methods were applied to calculate the energy spectrum of 12ΛB and also one body density matrix elements (OBDME). The OBDME were applied to calculate the electroproduction cross section of 12ΛB. We obtained better agreement with the experimental data by using EMPM than NΛ TDA. We plan to provide theoretical prediction (by applying the same methods and ΛN potentials) of the cross section in electroproduction of 40ΛK and 48ΛK.

In a previous analysis of electroproduction of hypernuclei the cross sections were calculated in distorted-wave impulse approximation where the momentum of the initial proton in the nucleus was set to zero (the frozen-proton approximation). In this paper we go beyond this approximation assuming a non zero effective proton momentum due to proton Fermi motion inside of the target nucleus discussing also other kinematical effects. To this end we have derived a more general form of the two-component elementary electroproduction amplitude (Chew-Goldberger-Low-Nambu like) which allows its use in a general reference frame moving with respect to the nucleus-rest frame. The effects of Fermi motion were found to depend on kinematics and elementary amplitudes. The largest effects were observed in the contributions from the longitudinal and interference parts of the cross sections. The extension of the calculations beyond the frozen-proton approximation improved the agreement of predicted theoretical cross sections with experimental data and once we assumed the optimum on-shell approximation, we were able to remove an inconsistency which was previously present in the calculations.