Shell model and Hartree-Fock calculations of longitudinal and transverse electroexcitation of positive and negative parity states in ${}^{17}\mathrm{O}$

The nuclear structure of the ${}^{17}\mathrm{O}$ nucleus has been investigated using shell model and self-consistent Hartree-Fock calculations. In particular, elastic and inelastic electron scattering form factors, energy levels, and transition probabilities are calculated for positive and negative low-lying states. Two different shell model spaces have been used for this purpose. The first one is the psdpn model space for positive parity states and the second one is $p_{1/2}sd$ model space for negative parity states. For all selected excited states, Skyrme interactions are adopted to generate from them a one-body potential in Hartrre-Fock theory to calculate the single-particle matrix elements. The deduced results are discussed for the longitudinal and transverse form factors and compared with the available experimental data. It has been confirmed that combining the shell model plus Hartree-Fock mean field method with the Skyrme interaction can accommodate very well the nuclear excitation properties, and work better for low lying states than for higher excitations. Furthermore, the combination can be used to reproduce the positive and negative parity states after choosing the suitable model space, effective two-body interaction, and parameterization to reach highly descriptive and predictive results.

Figure 1

Theoretical elastic longitudinal (a) and transverse (b) form factors for $5/2^{+}$, and their multipole contributions using SkXcsb parametrization, compared with the experimental data taken from Ref. [32].

Figure 2

Theoretical elastic transverse form factors for $5/2^{+}$, using SLy4, SkXcsb parametrizations, HO, and WS compared with the experimental data taken from Ref. [32].

Figure 3

Theoretical longitudinal (a) and transverse (b) form factors for the $1/2^{+}$, 0.870 MeV state using SLy4, SkXcsb parametrizations, HO, and WS compared with the experimental data taken from Ref. [10]. The $E2$ and $M3$ multipole contributions are shown for the HO potential (c).

Figure 4

Theoretical longitudinal $C2$ form factors using SLy4 parameterization for the (a) $1/2_2^{+}$, 6.356 MeV state and (b) $1/2_3^{+}$, 7.956 MeV state compared with the experimental data taken from Ref. [10].

Figure 5

Theoretical longitudinal (a) and transverse (b) form factors and their multipole contributions for $3/2^{+}$, 5.084 MeV using SLy4, SkXcsb parametrizations, HO, and WS compared with the experimental data taken from Ref. [10]. The multipole contributions are shown for the HO potential.

Figure 6

Theoretical longitudinal $C2$ form factors using the HO potential for the $3/2_2^{+}$, 5.869 MeV state compared with the experimental data taken from Ref. [10].

Figure 7

Theoretical longitudinal form factors for the $5/2^{+}$, 6.862 MeV state using SLy4, SkXcsb parametrizations, HO, and WS compared with the experimental data taken from Ref. [10]. Multipole contributions are shown for the SLy4 parametrization.

Figure 8

Theoretical longitudinal C2 form factors using the SLy4 parametrization for the $5/2_3^{+}$, 8.402 MeV state compared with the experimental data taken from Ref. [10].

Figure 9

Theoretical longitudinal form factors for the $7/2^{+}$, 7.576 MeV state using SLy4, SkXcsb parametrizations, HO, and WS compared with the experimental data taken from Ref. [10]. Multipole contributions are shown for the SLy4 parametrization.

Figure 10

Theoretical longitudinal form factors and their multipoles contributions for the $9/2^{+}$, 8.470 MeV state using SLy4, SkXcsb parametrizations, HO, and WS compared with the experimental data taken from Ref. [10].

Figure 11

Theoretical longitudinal (a) and transverse (b) form factors for the $1/2^{-}$, 3.055 MeV state using SLy4, SkXcsb parametrizations, HO, and WS compared with the experimental data taken from Ref. [10]. $M2$ and $E3$ multipole contributions for the Sly4 parametrization are shown in (c).

Figure 12

Theoretical longitudinal (a) form factors for the $1/2_2^{-}$, 5.939 MeV state using SLy4, SkXcsb parametrizations, HO, and WS compared with the experimental data taken from Ref. [10]. Transverse form factors and their $M2$ and $E3$ multipole contributions calculated with the Sly4 parametrization are shown in (c) in comparison with the experimental data of Ref. [10].

Figure 13

Theoretical longitudinal form factors for the $3/2^{-}$, 4.553 MeV state using SLy4, SkXcsb parametrizations, HO, and WS compared with the experimental data taken from Ref. [10]. Multipole contributions are shown for the SLy4 parametrization.

Figure 14

Theoretical longitudinal form factors and their multipole contributions for $3/2_2^{-}$, 5.379 MeV using the SLy4 parametrization compared with the experimental data taken from Ref. [10].

Figure 15

Theoretical longitudinal form factors for $5/2^{-}$, 3.84 MeV using SLy4, SkXcsb parametrizations, HO, and WS compared with the experimental data taken from Ref. [10]. Multipole contributions are shown for the SLy4 parametrization.

Figure 16

Theoretical longitudinal C3 form factors for the $5/2_2^{-}$, 5.732 MeV state using the SLy4 parametrization compared with the experimental data taken from Ref. [10].

Figure 17

Theoretical longitudinal form factors for the $7/2^{-}$, 5.697 MeV state using SLy4, SkXcsb parametrizations, HO, and WS compared with the experimental data taken from Ref. [10]. Multipole contributions are shown for the SLy4 parametrization.

Figure 18

Theoretical longitudinal form factors for the $9/2^{-}$, 5.215 MeV state using SLy4, SkXcsb parametrizations, HO, and WS compared with the experimental data taken from Ref. [10].

Figure 19

Theoretical longitudinal form factors for the $11/2^{-}$ 7.757 MeV state using SLy4, SkXcsb parametrizations, HO, and WS compared with the experimental data taken from Ref. [10].

Figure 20

Energy levels for the positive and negative parity states in ${}^{17}\mathrm{O}$ in the psdpn and zbme SM spaces. The experimental energy levels are plotted on the left-hand side. The blue and red lines are for positive and negative parity states, respectively.