Nuclear shape transitions and elastic magnetic electron scattering

Backward elastic electron scattering from odd-$A$ nuclear targets is characterized by magnetic form factors containing precise information on the nuclear structure. We study the sensitivity of the magnetic form factors to structural effects related to the evolution and shape transitions in both isotopic and isotonic chains. Calculations of magnetic form factors are performed in the plane-wave Born approximation. The nuclear structure is obtained from a deformed self-consistent mean-field calculation based on a Skyrme $\mathrm{HF}+\mathrm{BCS}$ formalism. Collective effects are included in the cranking approximation, whereas nucleon-nucleon correlations are taken into account in the coherent density fluctuation model. The evolution of the magnetic form factors is found to exhibit signatures of shape transitions that show up in selected isotopic and isotonic chains involving both stable and unstable nuclei. Several cases are identified as suitable candidates for showing such fingerprints of shape transitions. A new generation of electron scattering experiments involving electron-radioactive beam colliders will be available in the near future, leading to a renewed interest in this field.

Figure 1

Total magnetic form factors for the $Z=23$ isotopes ${}^{49,51,53}\mathrm{V}$ (a) and their decomposition into the contributing multipoles for ${}^{49}\mathrm{V}$ (b), ${}^{51}\mathrm{V}$ (c), and ${}^{53}\mathrm{V}$ (d). CDFM calculations are shown for the spherical cases. Data are taken from Refs. [15, 59, 60].

Figure 2

Same as described in the caption of Fig. 1, but for the $Z=13$ isotopes ${}^{25,27,29}\mathrm{Al}$. Data are taken from Refs. [15, 61, 62].

Figure 3

Same as described in the caption of Fig. 1, but for the $Z=9$ isotopes ${}^{17,19,21}\mathrm{F}$. Data are taken from Refs. [63, 64].

Figure 4

Same as described in the caption of Fig. 1, but for the $Z=25$ isotopes ${}^{51,53,55}\mathrm{Mn}$.

Figure 5

Same as described in the caption of Fig. 1, but for the $Z=53$ isotopesr ${}^{125,127,129}\mathrm{I}$.

Figure 6

Same as described in the caption of Fig. 1, but for the $Z=55$ isotopes ${}^{131,133,135}\mathrm{Cs}$.

Figure 7

Same as described in the caption of Fig. 1, but for the $N=9$ isotones ${}^{15}\mathrm{C}$, ${}^{17}\mathrm{O}$, and ${}^{19}\mathrm{Ne}$. Data are taken from Refs. [15, 65].

Figure 8

Same as described in the caption of Fig. 1, but for the $N=11$ isotones ${}^{19}\mathrm{O}$, ${}^{21}\mathrm{Ne}$, and ${}^{23}\mathrm{Mg}$.

Figure 9

Same as described in the caption of Fig. 1, but for the $N=25$ isotones ${}^{45}\mathrm{Ca}$, ${}^{47}\mathrm{Ti}$, and ${}^{49}\mathrm{Cr}$.

Figure 10

Same as described in the caption of Fig. 1, but for the $N=57$ isotones ${}^{99}\mathrm{Mo}$, ${}^{101}\mathrm{Ru}$, and ${}^{103}\mathrm{Pd}$.