Elastic magnetic electron scattering from deformed nuclei

Magnetic form factors corresponding to elastic electron scattering from odd-$A$ nuclei are presented. The calculations are carried out in plane-wave Born approximation. The one-body properties are obtained in a deformed self-consistent mean-field calculation based on a Skyrme HF+BCS method. Collective effects are also included in the cranking approximation. Results on several stable nuclei are compared with the available experimental information. It is shown that a deformed formalism improves the agreement with experiment in deformed nuclei, while reproducing equally well spherical nuclei by taking properly the spherical limit of the deformed model and the effect of nucleon-nucleon correlations. Thus, the capability of the model to describe magnetic form factors is demonstrated. This opens the door to explore also unstable nuclei of particular interest that could be measured in future experiments on electron-radioactive beam colliders.

Figure 1

Magnetic form factors of ${}^{17}\mathrm{O}$ ($I^{\pi }=5/2^{+}$) decomposed into M1, M3, and M5 multipole components in the deformed model (top) and in its spherical limit (middle). We also show (bottom) the results from standard spherical calculations alone and together with CDFM (see text). Data are taken from [7, 66].

Figure 2

Same as in Fig. 1, but for ${}^{39}\mathrm{K}$ ($I^{\pi }=3/2^{+}$) decomposed into M1 and M3 multipole components. Data are taken from [7] and references therein.

Figure 3

Same as in Fig. 1, but for ${}^{41}\mathrm{Ca}$ ($I^{\pi }=7/2^{-}$) decomposed into M1, M3, M5, and M7 multipole components. Data are taken from Ref. [67].

Figure 4

Same as in Fig. 1, but for ${}^{51}\mathrm{V}$ ($I^{\pi }=7/2^{-}$) decomposed into M1, M3, M5, and M7 multipole components. Data are taken from Refs. [7] (circles), [68] (triangles), and [69] (squares).

Figure 5

Same as in Fig. 1, but for ${}^{93}\mathrm{Nb}$ ($I^{\pi }=9/2^{+}$) decomposed into M1, M3, M5, M7, and M9 multipole components. Data are taken from [7] (circles), [70] (squares), and [71] (triangles).

Figure 6

Magnetic form factors of ${}^{25}\mathrm{Mg}$ ($I^{\pi }=5/2^{+}$) in the deformed formalism and in its spherical limit, as well as in the spherical CDFM (top). The multipole decomposition is shown in the deformed model for single-particle contributions (middle), and including collective contributions from the rotating core in the cranking approximation (bottom). Data used in Ref. [7] are taken from [70] (circles) and [72] at different kinematical conditions (squares and triangles).

Figure 7

Magnetic form factors of ${}^{29}\mathrm{Si}$ ($I^{\pi }=1/2^{+}$) in the deformed and spherical models. Only the M1 multipole contributes. Data are taken from Ref. [7] and references therein.

Figure 8

Magnetic form factors of ${}^{59}\mathrm{Co}$ ($I^{\pi }=7/2^{-}$) in the deformed and spherical models (top). The multipole decomposition is shown in the deformed model for single-particle contributions (middle) and including collective contributions from the rotating core in the cranking approximation (bottom). Data used in Ref. [7] are taken from [73] (circles) and [71] (triangles).

Figure 9

Same as in Fig. 8, but for ${}^{115}\mathrm{In}$ ($I^{\pi }=9/2^{+}$) Data are taken from Ref. [7] and references therein.