  We present a comprehensive table of recurrence and differential relations
obeyed by spin one-half spherical spinors (spinor spherical harmonics)
$\Omega_{\kappa\mu}(\mathbf{n})$ used in relativistic atomic, molecular, and
solid state physics, as well as in relativistic quantum chemistry. First, we
list finite expansions in the spherical spinor basis of the expressions
$\mathbf{A}\cdot\mathbf{B}\,\Omega_{\kappa\mu}(\mathbf{n})$ and
{$\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})\,
\Omega_{\kappa\mu}(\mathbf{n})$}, where $\mathbf{A}$, $\mathbf{B}$, and
$\mathbf{C}$ are either of the following vectors or vector operators:
$\mathbf{n}=\mathbf{r}/r$ (the radial unit vector), $\mathbf{e}_{0}$,
$\mathbf{e}_{\pm1}$ (the spherical, or cyclic, versors), $\boldsymbol{\sigma}$
(the $2\times2$ Pauli matrix vector),
$\hat{\mathbf{L}}=-i\mathbf{r}\times\boldsymbol{\nabla}I$ (the dimensionless
orbital angular momentum operator; $I$ is the $2\times2$ unit matrix),
$\hat{\mathbf{J}}=\hat{\mathbf{L}}+1/2\boldsymbol{\sigma}$ (the dimensionless
total angular momentum operator). Then, we list finite expansions in the
spherical spinor basis of the expressions
$\mathbf{A}\cdot\mathbf{B}\,F(r)\Omega_{\kappa\mu}(\mathbf{n})$ and
$\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})\,
F(r)\Omega_{\kappa\mu}(\mathbf{n})$, where at least one of the objects
$\mathbf{A}$, $\mathbf{B}$, $\mathbf{C}$ is the nabla operator
$\boldsymbol{\nabla}$, while the remaining ones are chosen from the set
$\mathbf{n}$, $\mathbf{e}_{0}$, $\mathbf{e}_{\pm1}$, $\boldsymbol{\sigma}$,
$\hat{\mathbf{L}}$, $\hat{\mathbf{J}}$.
