Parity violating elastic electron scattering from ${}^{27}\mathrm{Al}$ and the Qweak measurement

I calculate the parity violating asymmetry $A_{pv}$ for elastic electron scattering from ${}^{27}\mathrm{Al}$ in order to compare with the Qweak experiment “background” ${}^{27}\mathrm{Al}$ measurement. I find that Coulomb distortions, and the quadrupole form factor, reduce $A_{pv}$ near the diffraction minimum. The Qweak data can be used to confirm the neutron radius of ${}^{27}\mathrm{Al}$, if nuclear structure uncertainties are indeed small, as I suggest, and one can estimate inelastic and impurity contributions. This could provide an important check of the measurement, analysis, and theory.

Figure 1

Square of the proton form factors $C_0^2$ (solid), $C_2^2$ (dashed), and $C_4^2$ (dotted), Eqs. (7, 8, 9), vs momentum transfer $q$.

Figure 2

Cross section for elastic scattering of 250-MeV electrons from ${}^{27}\mathrm{Al}$ vs laboratory scattering angle $\Theta$. The red circles are experimental results from Ref. [21] while the solid line is Eq. (11) with ${\xi }^2=1$. The upper (and lower) dotted lines correspond to ${\xi }^2=0.5$ (1.5) and indicate a very generous estimate for nuclear structure uncertainties. The average momentum transfer of the Qweak experiment corresponds to the arrow near 37${}^{\circ }$.

Figure 3

Parity violating asymmetry $A_{pv}$ for elastic scattering of 1160-MeV electrons from ${}^{27}\mathrm{Al}$ vs scattering angle $\Theta$. The blue dot dashed curve shows plane wave Born approximation results for the same shaped neutron and proton densities, $A_{pv}^0$ in Eq. (13). The red dashed curve shows full distorted wave results for spherically symmetric neutron and proton densities, $A_{DW}\left(C_0\right)$. Distorted wave results for $C_0$ plus plane wave $C_2$ and $C_2^W$ contributions, Eq. (18), are shown by the black upper dotted line, solid line, and lower dotted line for ${\xi }^2=0.5$,1, and 1.5. The average momentum transfer of the Qweak experiment is shown by the red arrow, while the angular acceptance is very roughly indicated by the the blue arrows.