Matter and charge distributions of6Heand5,6,7,9Liwithin the dynamic-correlation model

Abstract

The matter and the charge distributions of the 6 He and 5,6,7,9 Li isotopes are investigated within the dynamiccorrelation model ~DCM! which describes the ground states of light nuclei in terms of microscopic correlated clusters: the valence particles and the intrinsic vacuum states. The amplitudes of these mixed-mode wave functions are calculated in the framework of nonperturbative solutions of the equation of motion method ~EOMM!. The matter and charge mean square radii are in good agreement with experimental results. The calculated matter distribution of the 6 He nucleus is characterized by a halo structure less pronounced than that calculated by the three cluster models. The charge distribution of 6 Li reproduces well the electron scattering data. Good agreement with experimental data has been also achieved for the proton scattering cross sections of p- 6 He at an energy of 0.7 GeV/nucleon. PACS number~s!: 21.10.Gv, 21.10.Ft, 21.60.2n, 27.20.1n The shape of the matter and of the charge distributions, as well as the matter and the charge radii of light nuclei can be extracted unambiguously from the analysis of proton scattering @1#, electron scattering @2#, and from isotope shift @3# measurements. The distributions of 6 He and 6 Li reveal a new type of nuclear structure, where the core is surrounded by nuclear matter which contribute to the formation of an extended, far reaching one or two neutron halo @4#. Theoretical calculations of the 2n-halo structures have been, up to now, performed in the Borromean three rings approximation @4# firstly introduced to investigate the halo structure of 11 Li. Within this assumption the valence neutrons interact via the neutron-neutron interaction, without exciting the closed-shell reference nucleus which remains in its ground state. The interaction between the valence- and the core-particle has been neglected under the assumption that the valence neutrons are weakly bound. In the three-cluster model of Ref. @4# the a-particle core is simply represented by a $0s% 4 harmonic oscillator state. Only recently the excitations of the a particle @5# have been introduced in the calculations of the halo structure within a macroscopic core breakup mechanism @6#. This paper provides a new microscopic description of the matter and charge distributions of 6 He and 5,6,7,9 Li isotopes based on the DCM which was first introduced in Refs. @7,8# to investigate the electromagnetic structure of heavy nuclei. The model describes the ground and excited states of nuclei in terms of valence particles interacting with the excited structure of the core. These additional terms, not considered by the up to now published theories, are important in the analysis of the halo structure of exotic nuclei because the deformation of the nuclear core is reshaping, at high momenta, the tail of the nuclear distributions. The theoretical formalism discussed in this paper is used to describe simultaneously either nuclei characterized by an odd or by an even number of valence particles. For odd nuclei we perform calculations according to Refs. @7,8#, while to describe nuclei with an even number of valence particles we modify the dynamic model via introducing the boson dynamic correlation model ~BDCM!. Within the DCM and the BDCM, the charge and the matter distributions of 6 He and 5,6,7,9 Li ground states are calculated defining mixed-mode states as non-perturbative solutions of the EOMM. The following mixed-mode states have been discussed: the $p%1$2p 21h% for 5 Li, the $h%1$2h21p% for 7 Li, the $2p%1$3p 21h% for 6 He and 6 Li, and the $2p21h%1$3p22h% for 9 Li. The higher order components of the ground state wave functions have an unperturbed energy much larger than the corresponding $n% body matrix elements and contribute poorly to the active subspaces and are not included explicitly in the model space. These components however, properly linearized, define the mean field potential of the mixed-mode states. The mixed-mode states obtained within this approximation form the base-vectors in which the ground state energies, the matter and charge radii, and the matter and charge distributions are calculated. The charge radii of the radioactive lithium isotopes preliminarily calculated in Ref. @9#, have not yet been measured. They will be provided by isotope shift measurements on the 2 2 S-3 2 S transitions which is theoretically supported by the analysis performed in Ref. @10#. These experiments are going on presently at GSI @11#. With the calculated distributions it is possible then to analyze ~matter distributions! the elastic proton scattering in the inverse scattering geometry done at GSI and ~charge distributions! the electron scattering experiments. In recent experi