Transverse response of bound single-nucleon Dirac-4 spinors of spin-orbit partners to elastic electron scattering

Transverse responses of the upper components, lower components, and crossed term of the bound single-nucleon Dirac-4 spinors of spin-orbit partners to elastic magnetic electron scattering are investigated. For the nuclear spin-orbit partners with $l\le 3$ or in the $s$-d $f$shell or lower, results show that in the elastic magnetic electron scattering process the lower component of the $j=(l-\frac{1}{2})$ partner may play a relatively more important role than that of the $j=(l+\frac{1}{2})$ partner, while the upper component of the $j=(l+\frac{1}{2})$ partner may play a relatively more important role than that of $j=(l-\frac{1}{2})$ partner. The results also show that for the response of the crossed term the $j=(l+\frac{1}{2})$ partner may play a relatively more important role than the $j=(l-\frac{1}{2})$ partner. In addition, it is also found that the dominant $M1$ multipole of the magnetic form factors in the small momentum transfer region may mainly originate from the convection current transition density.

Figure 1

The response functions $R_L^u\left(q\right)$ and $R_L^l\left(q\right)$ for the $1p_{1/2}\text{−}1p_{3/2}$ spin-orbit partners of ${}^{16}\text{O}$, where $L$ denotes the multipoles.

Figure 2

The same as Fig. 1 but for ${}^{40}\text{Ca}$.

Figure 3

The same as Figs. 1 and 2 but for ${}^{132}\text{Sn}$.

Figure 4

The response functions $R_L^u\left(q\right)$ and $R_L^l\left(q\right)$ for the $1d_{3/2}\text{−}1d_{5/2}$ partners of ${}^{40}\text{Ca}$.

Figure 5

The same as Fig. 4 but for ${}^{132}\text{Sn}$.

Figure 6

The response functions $R_L^u\left(q\right)$ and $R_L^l\left(q\right)$ for the $1f_{5/2}\text{−}1f_{7/2}$ partners of ${}^{132}\text{Sn}$.

Figure 7

The same as Fig. 6 but for the neutron $1g_{7/2}\text{−}1g_{9/2}$ partners of ${}^{132}\text{Sn}$.

Figure 8

The response functions $R_L^u\left(q\right)$ and $R_L^l\left(q\right)$ for the $2p_{1/2}\text{−}2p_{3/2}$ partners of ${}^{132}\text{Sn}$.

Figure 9

The same as Fig. 8 but for the neutron $2d_{3/2}\text{−}2d_{5/2}$ partners of ${}^{132}\text{Sn}$.

Figure 10

The response functions $R_L^c\left(q\right)$ for the proton $1p_{1/2}\text{−}1p_{3/2}$, $1d_{3/2}\text{−}1d_{5/2}$, and $1f_{5/2}\text{−}1f_{7/2}$ partners of ${}^{16}\text{O}$, ${}^{40}\text{Ca}$, and ${}^{132}\text{Sn}$.

Figure 11

The response functions $R_L^c\left(q\right)$ for the proton $2p_{1/2}\text{−}2p_{3/2}$ partners of ${}^{132}\text{Sn}$.