Speaker
Description
In [1], in the framework of a general approach to the covariant description of
the structure of half-integer spin nuclei, analytical expressions were found for
the multipole expansion of the structure functions, entering into the
differential cross section for elastic scattering of longitudinally polarized
leptons
$
\frac{{d\sigma }}{{d\Omega }} = {\sigma _{Mott}}\left\{ {{W_1} +
2t{g^2}\frac{\theta }{2}{W_2} - \zeta \tau \left[ {\frac{M}{E} + \left( {1 +
\frac{M}{E}} \right)t{g^2}\frac{\theta }{2}} \right]{W_4}} \right\}.
$
In the effective current approximation, valid for high energies $E > > {m_l}$
of the scattered lepton, structure functions ${W_k}$ depend upon $\tau = -
{{{q^2}} \mathord{\left/
{\vphantom {{{q^2}} {4{M^2}}}} \right.
} {4{M^2}}}$, lepton helicity $\zeta $, and
electromagnetic and weak nucleus form factors, and lepton electroweak constants.
In this work using Rarita-Schwinger formalism to describe [2] nuclei with
half-integer spin $J \le 7/2$, we construct explicit expressions for covariant
electromagnetic and weak vertex functions $\Gamma _{em,\;weak}^{\mu {{\left(
\alpha \right)}_j}{{\left( \beta \right)}_j}}\;\left( {j = J - 1/2} \right)$,
as well as for the density matrix ${\Lambda _{{{\left( \alpha
\right)}_j}{{\left( \beta \right)}_j}}}$ of an unpolarized nucleus state. Then,
using multipole expansion technique in the Breit zero energy transfer system, we
consider traditional multipole form factors -- vector ${F_{Cl}}(\tau )\;\left( {l
= 0,2,\;...\;2J - 1} \right)$ and ${F_{Ml}}(\tau )\;\left( {l = 1,\;3,\;...\;2J}
\right)$, as well as axial ${F_{5El}}(\tau )$ and ${F_{5Ll}}(\tau )\;\left( {l =
1,\;3,\;...\;2J} \right)$ -- and get expressions for them through the covariant
form factors of the vertex functions $F_E^{(n)}(\tau ),\;F_M^{(n)}(\tau
),\;G_1^{(n)}(\tau )$ and $g_E^{(n)}(\tau ),\;g_M^{(n)}(\tau ),\;g_A^{(n)}(\tau )$.
Then we obtain and discuss expressions for the right-left asymmetry ${A_{RL}}$,
as well as the spin correlations of transversely polarized incident and scattered
leptons. We show, that elastic scattering is helicity conserving due to smallness
of the lepton mass, and right-left asymmetry contains contribution from anapole
moment of the target, whereas transverse correlations arise only with
simultaneous polarization of incident and scattered leptons.
- M.Ya.Safin. Izv. Russ. Akad. Nauk, Ser. Fiz., 2020, vol. 84, no. 4, p. 527.
- Yu.P.Bogdanov, B.K.Kerimov, M.Ya.Safin. Izv. Acad. Sci. SSSR. Ser.Fiz. 1980.
vol. 44. no. 11. p. 2337; Izv. Acad. Sci. SSSR. Ser. Fiz. 1983. vol. 47. no. 1.
p. 103.
