text:
\section{Introduction}

The experimental work with cold and ultracold molecules is predicted to lead to many
fundamental applications in quantum computation \cite{Rabl},
condensed-matter physics \cite{Demler}, precision spectroscopy \cite{Precision}, and physical chemistry \cite{RomanReview}. Recent theoretical work has  shown that ultracold ensembles of molecules trapped in optical lattices can be used to develop novel schemes for quantum information processing \cite{DeMille}, design experiments for quantum simulations of condensed matter physics \cite{Demler,Bloch}, engineer novel phases with topological order \cite{Zoller}, and explore many-body dynamics of strongly interacting systems \cite{Efimov}. Polar molecules in external field traps may form chains, which can be used to study rheological phenomena with non-classical behavior \cite{Demler}.  The creation of a Bose-Einstein condensate of molecules may enable the study of Bose-enhanced chemistry \cite{ami} and the effects of symmetry breaking on chemical interactions at ultracold temperatures \cite{ourPRL}.  The realization of these proposals as well as the creation of dense ensembles of ultracold molecules depends critically on
the possibility of controlling binary molecule - molecule interactions in molecular gases by external electromagnetic fields.
The discovery of magnetic Feshbach resonances in atomic collisions \cite{Verhaar,Ketterle}
opened the door to many groundbreaking experiments with ultracold gases such as
the realization of the BEC-BCS crossover \cite{Jin}, the observation of quantum phase transitions \cite{Bloch} and the creation of ultracold molecules using time-varying magnetic fields \cite{JulienneFeshbach}. Extension of this work to molecular collisions may similarly lead to the development of new research directions such as cold controlled chemistry
\cite{RomanReview}, quantum coherent control of bimolecular reactions \cite{Moshe}, and quantum condensed-matter physics with molecular condensates
\cite{DDI}.

Fueled by the promise of new discoveries, the experimental research of cold and ultracold molecular collisions is expanding rapidly.
Some recent landmark experiments include the observation of threshold collision
laws in Xe-OH scattering using slow molecular beams \cite{Meijer}, measurements of cross sections for
D$_2$-OH collisions in a magnetic trap \cite{Ye}, and the detection of magnetic Feshbach resonances in collisions
of Cs$_2$ molecules \cite{Chin}. Further progress in the experimental study of  complex molecule-molecule collisions and chemical reactions at cold and ultracold temperatures requires rigorous theoretical calculations elucidating the mechanisms of energy transfer in ultracold molecular collisions.
Theoretical studies of molecule-molecule collisions at low temperatures are also necessary to understand the prospects for evaporative cooling of molecules in a magnetic trap. The evaporative cooling
relies on elastic molecule - molecule collisions as the trap depth is gradually reduced
\cite{Ketterle}. In order to sustain efficient evaporative
cooling down to quantum degeneracy, the ratio of the probabilities for elastic scattering and spin relaxation ($\gamma$) in molecule - molecule collisions must exceed $10^4$ \cite{Ketterle}.
The magnitudes of the rate constants for elastic and inelastic collisions and the dependence of the scattering observables in molecule - molecule encounters on the magnetic field are, however, completely unknown.

Previous theoretical work by Krems and Dalgarno \cite{Roman2004} and Volpi and Bohn \cite{VolpiBohn} identified the main mechanisms of spin relaxation in atom-molecule collisions. It was found that spin relaxation in collisions of $^3\Sigma$ molecules with He atoms
occurs through coupling to rotationally excited states mediated by the spin-spin interaction \cite{Roman2004}.
While the mechanisms of spin relaxation in molecule-molecule collisions should be similar, an accurate computational study
of molecule-molecule scattering in a magnetic field is urgently needed to elucidate the rates of energy relaxation in dense ensembles of trapped
molecules and understand the prospects for evaporative cooling of molecules.
The quantum dynamics of ultracold molecule-molecule collisions in the absence of external fields has been studied by several authors
(see, {\it e.g.}, Refs. \cite{Takayanagi,Alexander,HF}). Avdeenkov and Bohn calculated the rates of spin relaxation in collisions of O$_2(^3\Sigma_g^-)$
molecules at zero magnetic field and observed Feshbach resonances due to molecular rotation \cite{AvdeenkovBohn,RotFR}.
Krems and Dalgarno \cite{Roman2004} presented a formalism for quantum scattering calculations of cross sections for
molecule-molecule collisions in a magnetic field. However,
they did not consider the symmetrization procedure required to properly describe collisions between identical molecules.
Here, we extend the approach of Krems and Dalgarno to study collisions of identical $^3\Sigma$ molecules.
The use of exchange symmetry reduces the number of scattering channels by a factor of two, which allowed us to obtain
converged cross sections for elastic scattering and spin relaxation of O$_2(^3\Sigma^-_g)$ molecules in an external magnetic field.

We consider ultracold collisions of O$_2$ molecules in their ground electronic state of $^3\Sigma_g^-$ symmetry.
O$_2$--O$_2$ collisions play an important role in atmospheric chemistry \cite{rovib1,rovib2}. The O$_2$--O$_2$ dimer
is an interesting molecular complex \cite{VanDerAvoird1,VanDerAvoird2,JACS,prlO2,rovib1,rovib2,Lamoneda,review,Bartolomei}
(for a recent review, see Ref. \cite{review}). The binding in the complex is affected
by the Heisenberg exchange interaction and the formation of incipient chemical bond \cite{JACS,prlO2}.
Molecular beam scattering experiments \cite{JACS,prlO2} and high-level {\it ab initio} calculations \cite{Lamoneda}
have previously been used to elucidate the nature of the chemical bond in the O$_2$--O$_2$ dimer.
Here, we calculate the magnetic field dependence of the probabilities for spin relaxation in O$_2$--O$_2$ collisions at both
ultracold (down to $10^{-6}$ K) and cold (0.5 K) temperatures relevant for magnetic trapping experiments.
Our calculations elucidate the possibility of evaporative cooling
of paramagnetic $^3\Sigma$ molecules in a magnetic trap and indicate that spin depolarization in molecular collisions
can be controlled by an external magnetic field. The results of our work will be useful for the interpretation of collision
experiments involving slow beams of O$_2$ molecules produced by Zeeman deceleration \cite{Ed} and cryogenic cooling
\cite{DavePatterson}.

\section{Theory}

\subsection{Hamiltonian and symmetrized basis functions}

The Hamiltonian for two $^3\Sigma$ molecules in an external magnetic field can be written as \cite{Roman2004,AvdeenkovBohn}
\begin{equation}\label{H}
\hat{H} = -\frac{1}{2\mu R}\frac{\partial^2}{\partial R^2}R + \frac{\hat{\ell}^2}{2\mu R^2}
+ \hat{V}_\text{el}({\bm R}, {\bm r}_\text{A} ,{\bm r}_\text{B})
+ \hat{H}_\text{as},
\end{equation}
where the vectors ${\bm r}_\text{A}$ and ${\bm r}_\text{B}$ describe the orientation of the molecules A and B in the space-fixed
frame, ${\bm R}$ is the vector joining the molecules, $\hat{\ell}$ is the orbital angular momentum of the collision complex, $\mu$
is the reduced mass, and $\hat{V}_\text{el}$ is the electrostatic interaction potential (see Sec. IIB).
The asymptotic Hamiltonian $\hat{H}_\text{as}$
describes the individual molecules A and B in the presence of a magnetic field \cite{Roman2004}.
\begin{equation}\label{Has}
\hat{H}_\text{as} = \hat{H}_\text{A} + \hat{H}_\text{B},
\end{equation}
The Hamiltonians of an individual $^3\Sigma^-$ molecule can be written as \cite{Mizushima}
\begin{equation}\label{Has2}
 \hat{H}_\nu = B_{e}\hat{N}_\nu^2 +2\mu_\text{B}\bm{B}\cdot \hat{S}_\nu
+ \gamma \hat{N}_\nu \cdot \hat{S}_\nu
  + \frac{2}{3}\lambda_\text{SS}\left( \frac{24\pi}{5}\right)^{1/2}\sum_{q} Y_{2q}^\star (\hat{r}_\nu) [\hat{S}_\nu\otimes \hat{S}_\nu]^{(2)}_q,
\end{equation}
where the index $\nu=\text{A},\text{B}$ labels the molecule, $\hat{N}_\nu^2$ is the rotational angular momentum, $B_e$ is the rotational constant,
$\mu_\text{B}$ is the Bohr magneton, ${\bm B}$ is the magnetic field vector and
 $\hat{S}_\nu$ is the electron spin. The spin-rotation and spin-spin interactions in Eq. (\ref{Has2}) are parametrized by
the phenomenological constants $\gamma$ and $\lambda_\text{SS}$, which do not depend on $\nu$ since we
consider collisions of identical molecules. The spin-spin interaction given by the last term in Eq. (\ref{Has2})
can be represented as a sum of tensor products of two identical spin operators and
spherical harmonics, which depend on the orientation $\hat{r}_\nu$ of the diatomic molecule in the space-fixed (SF) coordinate frame \cite{Mizushima}.
We use the rigid rotor approximation $({\bm r}_\nu =  \hat{r}_\nu)$ and neglect the weak magnetic dipole-dipole interaction and
the hyperfine interaction of~$^{17}$O \cite{AvdeenkovBohn}.

We solve the scattering problem for two identical bosonic molecules by expanding the total wave function in a space-fixed uncoupled basis
introduced in Ref. \cite{Roman2004}. The uncoupled basis functions are products of the eigenfunctions of the operators $\hat{N}_\nu^2$ and $\hat{S}_\nu^2$,
their projections along the space-fixed $z$-axis $\hat{N}_{\nu_z}$ and $\hat{S}_{\nu_z}$, and the spherical harmonics $|\ell m_\ell\rangle$
\begin{equation}\label{UnsymmetrizedBasis}
| \tau_\text{A} \tau_\text{B}  \ell m_\ell \rangle = | \tau_\text{A} \rangle |\tau_\text{B} \rangle | \ell m_\ell \rangle
\end{equation}
where $|\tau_\nu\rangle = |N_\nu M_{N_\nu}\rangle |S_\nu M_{S_\nu}\rangle$. The matrix elements of the Hamiltonians (\ref{H}), (\ref{Has}) in the basis (\ref{UnsymmetrizedBasis}) were derived by Krems and Dalgarno \cite{Roman2004}
for the case of distinguishable molecules. The basis functions for identical molecules must be the eigenfunctions of the permutation operator
$\hat{P}: {\bm r}_\text{A} \to {\bm r}_\text{B}; {\bm r}_\text{B} \to {\bm r}_\text{A}; {\bm R} \to -{\bm R}$, which commutes with the total Hamiltonian (\ref{H}).
The symmetrized basis functions can be constructed by applying the operator $1+\hat{P}$ to Eq.~(\ref{UnsymmetrizedBasis}) and normalizing
the result \cite{Roman2004,Green,Kouri, Alexander}
\begin{equation}\label{SymmetrizedBasis}
\phi_{\tau_\text{A} \tau_\text{B} \ell m_\ell}^{\eta\epsilon}
= \frac{1}{[2(1+\delta_{\tau_\text{A} \tau_\text{B}})]^{1/2}}
\bigl{[} |\tau_\text{A} \tau_\text{B}\rangle + \eta \epsilon |\tau_\text{B} \tau_\text{A}\rangle \bigr{]} |\ell m_\ell \rangle
\end{equation}
where $\epsilon = (-)^\ell$ and the symmetry of the basis functions with respect to the interchange of identical molecules is given
by index $\eta$ which is equal to 1 for composite bosons and $-1$ for composite fermions~\cite{SoldanHutsonIRPC}.
In what follows we assume that the first basis function in each product on the right-rand side of Eq. (\ref{SymmetrizedBasis}) depends
on the coordinates of molecule A,
and the second basis function depends on the coordinates of molecule B \cite{footnote1}.
Equaton~(\ref{SymmetrizedBasis}) defines the well-ordered (combined) molecular states with
$\tau_\text{A}\ge \tau_\text{B}$.
The normalization factor $[2(1+\delta_{\tau_\text{A}\tau_\text{B}})]^{1/2}$ takes into account
the fact that the basis function (\ref{SymmetrizedBasis}) with $\tau_\text{A}=\tau_\text{B}$ need not be symmetrized when
$\eta\epsilon=+1$ (i.e. when the colliding molecules are in the same state). The symmetrized
function (\ref{SymmetrizedBasis}) with $\tau_\text{A}=\tau_\text{B}$ vanishes identically when $\eta\epsilon = -1$.

The basis functions given by Eqs. (\ref{UnsymmetrizedBasis}) and (\ref{SymmetrizedBasis}) are also the
eigenfunctions of the inversion operator, with eigenvalues given by $(-)^{N_\text{A}+N_\text{B}+\ell}$ \cite{Kouri}.
Since for homonuclear molecules both $N_\text{A}$ and $N_\text{B}$ are either even or odd,
the quantity $\epsilon=(-)^\ell$ is conserved as well. Thus, it is convenient to rewrite Eq. (\ref{SymmetrizedBasis}) in
a factorized form
\begin{equation}\label{I1}
\phi_{\tau_\text{A} \tau_\text{B} \ell m_\ell}^{\eta\epsilon} =  \mathcal{I}_{\tau_\text{A}\tau_\text{B}}^{\eta\epsilon}(\hat{r}_\text{A},\hat{r}_\text{B})
|\ell m_\ell\rangle
\end{equation}
where
\begin{equation}\label{I2}
\mathcal{I}_{\tau_\text{A}\tau_\text{B}}^{\eta\epsilon}(\hat{r}_\text{A},\hat{r}_\text{B}) = \frac{1}{[2(1+\delta_{\tau_\text{A} \tau_\text{B}})]^{1/2}}
\bigl{[} |\tau_\text{A} \tau_\text{B}\rangle + \eta\epsilon |\tau_\text{B} \tau_\text{A}\rangle \bigr{]}.
\end{equation}
We note that no such symmetry exists for heteronuclear molecules, where the basis functions with $\Delta \ell = \pm 1$
are coupled by the interaction potential, and $\epsilon$ is not conserved.

The uncoupled symmetrized basis functions given by Eq. (\ref{SymmetrizedBasis}) are not the eigenfunctions
of the asymptotic Hamiltonian (\ref{Has}) because the spin-rotation and spin-spin interactions couple the states
with different $N$, $M_N$, and $M_S$. Since the scattering $S$-matrix must be defined in terms of the eigenfunctions
of $\hat{H}_\text{as}$, it is necessary to transform the wave function to a new basis \cite{Roman2004}
\begin{equation}\label{Transformation1}
\mathcal{I}_{\gamma_\text{A} \gamma_\text{B}}^{\eta\epsilon}(\hat{r}_\text{A},\hat{r}_\text{B}) =
\sum_{\tau_\text{A}\ge\tau_\text{B}} C_{\tau_\text{A}\tau_\text{B}, \gamma_\text{A}\gamma_\text{B}}^{\eta\epsilon} \mathcal{I}_{\tau_\text{A} \tau_\text{B}}^{\eta\epsilon}(\hat{r}_\text{A},\hat{r}_\text{B}),
\end{equation}
where the coefficients $C_{\tau_\text{A}\tau_\text{B}, \gamma_\text{A}\gamma_\text{B}}^{\epsilon\eta}$ form the matrix, which diagonalizes the asymptotic Hamiltonian
in the symmetrized basis~(\ref{SymmetrizedBasis}). More explicitly, $\mathsf{C}^\text{T}\mathsf{H}_\text{as}\mathsf{C} = \mathsf{E}$,
where $\mathsf{E}$ is the diagonal matrix of asymptotic energies and $\epsilon_{\gamma_\text{A}\gamma_\text{B}} = \epsilon_{\gamma_\text{A}}+\epsilon_{\gamma_\text{B}}$.
The energies of individual molecules $\epsilon_\nu$ can be obtained by diagonalization
of individual molecule Hamiltonians $\hat{H}_\nu$ (\ref{Has}) in the subspace of functions $|\tau_\nu\rangle$.
Exploiting the properties of the interchange operator $\hat{P}^\dagger = \hat{P}$ and $\hat{P}^2=1$ and using
Eq.~(\ref{SymmetrizedBasis}), we obtain the following expression for the matrix elements of $\hat{H}_\text{as}$
\begin{multline}
\langle \phi_{\tau_\text{A}\tau_\text{B}\ell m_\ell}^{\eta\epsilon}|\hat{H}_\text{as}| \phi_{\tau_\text{A}'\tau_\text{B}'\ell' m_\ell'}^{\eta\epsilon}\rangle
= \frac{\delta_{\ell\ell'}\delta_{m_\ell m_\ell'}}{ [{(1+\delta_{\tau_\text{A}\tau_\text{B}})(1+\delta_{\tau_\text{A}'\tau_\text{B}'})}]^{1/2} }
\bigr{[}\delta_{\tau_\text{B},\tau_\text{B}'}\langle \tau_\text{A}| \hat{H}_\text{A}|\tau_\text{A}'\rangle
+\eta \epsilon \delta_{\tau_\text{B},\tau_\text{A}'}\langle \tau_\text{A}| \hat{H}_\text{A}|\tau_\text{B}'\rangle
\bigr{]}.
\end{multline}
This expression provides a convenient method of constructing the matrix elements of the asymptotic Hamiltonian (\ref{Has})
in the symmetrized basis. Alternatively, one can obtain the transformation
coefficients (\ref{Transformation1}) directly from the eigenvectors of $\hat{H}_\text{A}$ defined as
\begin{equation}\label{gA}
|\gamma_\text{A} \rangle=\sum_{\tau_\text{A}}C_{\tau_\text{A} \gamma_\text{A}}|\tau_\text{A}\rangle.
\end{equation}
The transformation can be derived by multiplying Eq. (\ref{gA}) by a similar expression for $|\gamma_\text{B} \rangle$ and rearranging the terms.
The result is
\begin{equation}\label{Connection}
C_{\tau_\text{A}\tau_\text{B}, \gamma_\text{A}\gamma_\text{B}}^{\eta\epsilon} =
\frac{1}{[(1+\delta_{\tau_\text{A},\tau_\text{B}})(1+\delta_{\gamma_\text{A},\gamma_\text{B}})]^{1/2}}
[C_{\tau_\text{A} \gamma_\text{A}}C_{\tau_\text{B} \gamma_\text{B}}
+ \eta \epsilon C_{\tau_\text{A} \gamma_\text{B}}C_{\tau_\text{B} \gamma_\text{A}}]
\end{equation}
We have verified by numerical tests that Eqs. (\ref{Transformation1}) and (\ref{Connection}) give identical
results up to an unimportant overall phase. In practice, however, it is more convenient to use Eq. (\ref{Connection}) because it
requires the evaluation and the diagonalization of smaller matrices.

\subsection{Interaction Potential}

The spin-dependent interaction potential between two $^3\Sigma$ molecules can be represented in the form
\begin{equation}\label{VS}
\hat{V}_\text{el}({\bm R},\hat{r}_\text{A},\hat{r}_\text{B}) = \sum_{S=-1}^1\sum_{M_S=-S}^S V_S({\bm R},\hat{r}_\text{A},\hat{r}_\text{B}) |SM_S\rangle \langle SM_S|,
\end{equation}
where $\hat{S} = \hat{S}_\text{A}+\hat{S}_\text{B}$ is the total spin and $M_S=M_{S_\text{A}} + M_{S_\text{B}}$.
The representation (\ref{VS}) is often used to describe the interactions of ultracold alkali metal atoms \cite{Verhaar}.
Here, we choose an alternative approach proposed by van der Avoird and coworkers \cite{VanDerAvoird1,VanDerAvoird2},
in which the full interaction potential is separated into the spin-independent and spin-dependent parts
\begin{equation}\label{Vseparation}
\hat{V}_\text{el}({\bm R},\hat{r}_\text{A},\hat{r}_\text{B}) = \hat{V}_\text{si}({\bm R},\hat{r}_\text{A},\hat{r}_\text{B}) + \hat{V}_\text{sd}({\bm R},\hat{r}_\text{A},\hat{r}_\text{B}).
\end{equation}
The spin-dependent part, also known as the Heisenberg exchange interaction \cite{VanDerAvoird1,VanDerAvoird2}, can be parametrized
for two $^3\Sigma$ molecules as
\begin{equation}\label{Heisenberg}
\hat{V}_\text{sd}({\bm R},\hat{r}_\text{A},\hat{r}_\text{B}) = -2J({\bm R},\hat{r}_\text{A},\hat{r}_\text{B})\hat{S}_\text{A}\cdot\hat{S}_\text{B},
\end{equation}
where $J({\bm R},\hat{r}_\text{A},\hat{r}_\text{B})$ is a scalar function similar to the
interaction potential but decreasing exponentially with $R$ \cite{VanDerAvoird2}. We expand
the interaction potential in the angular basis \cite{Roman2004,VanDerAvoird1,footnote2}
\begin{equation}\label{V}
V_\text{si}({\bm R},\hat{r}_\text{A},\hat{r}_\text{B})
= (4\pi)^{3/2}\sum_{\lambda_\text{A},\lambda_\text{B},\lambda}V_{\lambda_\text{A}\lambda_\text{B}\lambda}(R) A_{\lambda_\text{A}\lambda_\text{B}\lambda}(\hat{R},\hat{r}_\text{A},\hat{r}_\text{B}),
\end{equation}
with the space-fixed angular basis functions defined as
\begin{equation}\label{A}
A_{\lambda_\text{A}\lambda_\text{B}\lambda}(\hat{R},\hat{r}_\text{A},\hat{r}_\text{B})=
\sum_{m_{\lambda_\text{A}},m_{\lambda_\text{B}},m_\lambda}\threejm{\lambda_\text{A}}{m_{\lambda_\text{A}}}{\lambda_\text{B}}{m_{\lambda_\text{B}}}{\lambda}{m_{\lambda}}Y_{\lambda_\text{A} m_{\lambda_\text{A}}}(\hat{r}_\text{A})
Y_{\lambda_\text{B} m_{\lambda_\text{B}}}(\hat{r}_\text{B})Y_{\lambda m_\lambda}(\hat{R}),
\end{equation}
where (:::) denotes a 3-$j$ symbol. An efficient procedure for the evaluation of the radial expansion coefficients in
Eq. (\ref{V}) is described in Appendix A.

The matrix elements of the spin-indepenent interaction potential between the symmetrized
basis functions (\ref{SymmetrizedBasis}) have the form
\begin{align}\label{MatrixElementV1}
\langle \phi_{\tau_\text{A}\tau_\text{B}\ell m_\ell}^{\eta\epsilon} |V_\text{si}| \phi_{\tau_\text{A}'\tau_\text{B}'\ell'm_\ell'}^{\eta\epsilon}\rangle
&= \frac{1}{[(1+\delta_{\tau_\text{A}\tau_\text{B}})(1+\delta_{\tau_\text{A}'\tau_\text{B}'})]^{1/2}} \\ &\times \notag
\bigl{[}   \langle {\tau_\text{A}} {\tau_\text{B}} \ell m_\ell|  V_\text{si}  | {\tau_\text{A}'} {\tau_\text{B}'}\ell'  m_\ell' \rangle
+ \eta\epsilon\langle \tau_\text{A} \tau_\text{B} \ell m_\ell | V_\text{si} | \tau_\text{B}' \tau_\text{A}' \ell' m_\ell'\rangle \bigl{]}
\end{align}
The first (direct) term on the right-hand side is a matrix element in the unsymmetrized basis.
Krems and Dalgarno \cite{Roman2004} evaluated this matrix element using the
expansion of $V_\text{si}$ in terms of the angular basis functions (\ref{V}). Using the conservation of the total angular momentum
projection $M=M_{N_\text{A}}+M_{S_\text{A}}+M_{N_\text{B}}+M_{S_\text{B}}+m_\ell$ for collisions in a magnetic
field, we obtain
\begin{multline}\label{DirectMatrixElement}
\langle {\tau_\text{A}} {\tau_\text{B}} \ell m_\ell | V_\text{si} | {\tau_\text{A}'} {\tau_\text{B}'} \ell' m_\ell'\rangle
=\delta_{M_{S_\text{A}},M_{S_\text{A}'}} \delta_{M_{S_\text{B}},M_{S_\text{B}'}}\sum_{\lambda_\text{A},\lambda_\text{B},\lambda}
V_{\lambda_\text{A}\lambda_\text{B}\Lambda}(R) [(2N_\text{A}+1)(2N_\text{A}'+1) \\ \times
(2N_\text{B}+1)(2N_\text{B}'+1)(2\ell+1)(2\ell'+1)
(2\lambda_\text{A} + 1)(2\lambda_\text{B}+1)(2\lambda+1)]^{1/2}(-)^{ M_{N_\text{A}} + M_{N_\text{B}} + m_\ell } \\ \times
\threejm{\lambda_\text{A}}{ M_{N_\text{A}} - M_{N_\text{A}}' }{\lambda_\text{B}} { M_{N_\text{B}} - M_{N_\text{B}}' }{\lambda}{ m_\ell - m_\ell' }
\threejm{N_\text{A}} {-M_{N_\text{A}}} {\lambda_\text{A}}{M_{N_\text{A}}-M_{N_\text{A}}'} {N_\text{A}'} {M_{N_\text{A}}'}
\threejm{N_\text{A}} {0} {\lambda_\text{A}}{0} {N_\text{A}'} {0}  \\ \times
\threejm{N_\text{B}} {-M_{N_\text{B}}} {\lambda_\text{B}}{M_{N_\text{B}}-M_{N_\text{B}}'} {N_\text{B}'} {M_{N_\text{B}}'}
\threejm{N_\text{B}} {0} {\lambda_\text{B}}{0} {N_\text{B}'} {0}
\threejm{\ell} {-m_\ell} {\lambda}{m_\ell - m_\ell'} {\ell'} {m_\ell'}
\threejm{\ell} {0} {\lambda}{0} {\ell'} {0}
\end{multline}
The second (exchange) matrix element appears as a result of the symmetrization procedure
(\ref{SymmetrizedBasis}). It can be obtained from Eq. (\ref{DirectMatrixElement}) by interchanging
the indexes $N_\text{A}'\leftrightarrow N_\text{B}'$, $M_{N_\text{A}}' \leftrightarrow M_{N_\text{B}}'$, and $M_{S_\text{A}}' \leftrightarrow M_{S_\text{B}}'$.

The matrix elements of the Heisenberg exchange interaction are obtained
using the same procedure:
\begin{align}\label{MatrixElementJ}
\langle \phi_{\tau_\text{A}\tau_\text{B}\ell m_\ell}^{\eta\epsilon} |\hat{V}_\text{ex}&| \phi_{\tau_\text{A}'\tau_\text{B}'\ell' m_\ell'}^{\eta\epsilon}\rangle
= \frac{1}{[(1+\delta_{\tau_\text{A}\tau_\text{B}})(1+\delta_{\tau_\text{A}'\tau_\text{B}'})]^{1/2}} \\ &\times \notag
\bigl{[} \langle S_\text{A} M_{S_\text{A}} | \langle S_\text{B} M_{S_\text{B}} | \hat{S}_\text{A}\cdot \hat{S}_\text{B}
|S_\text{A} M_{S_\text{A}}'\rangle |S_\text{B} M_{S_\text{B}}'\rangle
\langle {\tau_\text{A}} {\tau_\text{B}} \ell m_\ell | -2J_\text{AB} | {\tau_\text{A}'} {\tau_\text{B}'} \ell' m_\ell'\rangle \\ &+ \notag
\eta \epsilon
\langle S_\text{A} M_{S_\text{A}} | \langle S_\text{B} M_{S_\text{B}} | \hat{S}_\text{A}\cdot\hat{S}_\text{B}
|S_\text{B} M_{S_\text{B}}'\rangle |S_\text{A} M_{S_\text{A}}'\rangle
\langle \tau_\text{A} \tau_\text{B} \ell m_\ell | -2J_\text{AB} | \tau_\text{B}' \tau_\text{A}' \ell' m_\ell'\rangle \bigl{]}.
\end{align}
The matrix elements of the prefactor $-2J(R,\theta_\text{A},\theta_\text{B},\varphi)$ are given by
Eq. (\ref{DirectMatrixElement}) with $V_{\lambda_\text{A}\lambda_\text{B}\lambda}(R)$ replaced by $-2J_{\lambda_\text{A}\lambda_\text{B}\lambda}(R)$.
Equation (\ref{MatrixElementJ}) shows that unlike the spin-independent matrix elements (\ref{MatrixElementV1}),
both the direct and exchange contributions to the Heisenberg exchange matrix element are not diagonal
in spin quantum numbers $M_{S_\text{A}}$ and $M_{S_\text{B}}$. For completeness, we give
here the expressions for the matrix elements of the operator
$\hat{S}_\text{A}\cdot\hat{S}_\text{B}$.
The direct matrix element has the form \cite{Roman2004}
\begin{multline}\label{SASB}
\langle S_\text{A} M_{S_\text{A}} | \langle S_\text{B} M_{S_\text{B}} | \hat{S}_\text{A}\cdot\hat{S}_\text{B}
|S_\text{A} M_{S_\text{A}}'\rangle |S_\text{B} M_{S_\text{B}}'\rangle = \delta_{M_{S_\text{A}} M_{S_\text{A}}'}
\delta_{M_{S_\text{B}} M_{S_\text{B}}'}M_{S_\text{A}} M_{S_\text{B}} \\ +
\textstyle \frac{1}{2} \delta_{M_{S_\text{A}}, M_{S_\text{A}}'\pm 1} \delta_{M_{S_\text{B}}, M_{S_\text{B}}'\mp 1}
\bigl{[}S_\text{A}(S_\text{A}+1) - M_{S_\text{A}}'(M_{S_\text{A}}' \pm 1)\bigr{]}^{1/2}
\bigl{[}S_\text{B}(S_\text{B}+1) - M_{S_\text{B}}'(M_{S_\text{B}}' \mp 1)\bigr{]}^{1/2},
\end{multline}
and the exhange matrix element can be obtained from Eq. (\ref{SASB})
by interchanging the indexes $M_{S_\text{A}}'$ and $M_{S_\text{B}}'$.

\subsection{Close-coupling equations, scattering amplitudes, and cross sections}

The symmetrized wave function of the collision complex can be expanded as
\begin{equation}\label{Expansion2}
\psi^\eta =\frac{1}{R} \sum_{\gamma_\text{A}\ge \gamma_\text{B}} \sum_{\ell,m_\ell}
F^\eta_{\gamma_\text{A}\gamma_\text{B}\ell m_\ell}(R) Y_{\ell m_\ell}(\hat{R}) \mathcal{I}^{\eta\epsilon}_{\gamma_\text{A}\gamma_\text{B}}(\hat{r}_\text{A},\hat{r}_\text{B}).
\end{equation}
Substituting this expansion into the Schr\"odinger equation,
$H\psi^\eta = E\psi^\eta$, where $E$ is the total energy,
we obtain the close-coupling equations for the radial expansion coefficients
\begin{equation}\label{CC}
\Bigl{[} \frac{d^2}{dR^2} - \frac{\ell(\ell+1)}{R^2}+2\mu E\Bigr{]} F^\eta_{\gamma_\text{A}\gamma_\text{B}\ell m_\ell}(R)
= \sum_{\gamma_\text{A}'\gamma_\text{B}'}\sum_{\ell'm_\ell'}
\bigl{[}\mathsf{C}^\text{T}\mathsf{V}\mathsf{C}\bigr{]}_{\gamma_\text{A}\gamma_\text{B}\ell m_\ell;\gamma_\text{A}'\gamma_\text{B}'\ell'm_\ell'}
 F^\eta_{\gamma_\text{A}'\gamma_\text{B}'\ell' m_\ell'}(R).
\end{equation}
The asymptotic form of the solutions $F^\eta_{\gamma_\text{A}\gamma_\text{B}\ell m_\ell;\gamma_\text{A}'\gamma_\text{B}'\ell'm_\ell'}(R)$
at $R\to\infty$ defines the symmetrized scattering matrix
\begin{align}\notag
F^\eta_{\gamma_\text{A}\gamma_\text{B}\ell m_\ell;\gamma_\text{A}'\gamma_\text{B}'\ell'm_\ell'}(R\to\infty) &\to \delta_{\gamma_\text{A}\gA'}\delta_{\gamma_\text{B}\gB'}
\delta_{\ell\ell'}\delta_{m_\ell m_\ell'} \exp[-\i (k_{\gamma_\text{A}\gamma_\text{B}}R-\pi \ell/2)] \\  \label{DefinitionS}
 &- \biggl{(}\frac{k_{\gamma_\text{A}\gamma_\text{B}}}{k_{\gamma_\text{A}'\gamma_\text{B}'}}\biggr{)}^{1/2}S^\eta_{\gamma_\text{A}\gamma_\text{B}\ell m_\ell;\gamma_\text{A}'\gamma_\text{B}'\ell'm_\ell'}
\exp[\i(k_{\gamma_\text{A}'\gamma_\text{B}'}R-\pi \ell'/2)]
\end{align}
The scattering amplitude for indistinguishable molecules can be written as \cite{HF,MottMassey}
\begin{equation}\label{qsymm}
\tilde{q}^\eta_{\gamma_\text{A}\gamma_\text{B}\to \gamma_\text{A}'\gamma_\text{B}'}(\hat{R}_\i,\hat{R}) =  q_{\gamma_\text{A}\gamma_\text{B} \to \gamma_\text{A}'\gamma_\text{B}'}(\hat{R}_\i,\hat{R}) + \eta q_{\gamma_\text{A}\gamma_\text{B} \to \gamma_\text{B}'\gamma_\text{A}'}(\hat{R}_\i,-\hat{R}).
\end{equation}
where the scattering amplitudes on the right-hand side can be written in terms of unsymmetrized $T$-matrix elements
\begin{equation}\label{qT}
q_{\gamma_\text{A}\gamma_\text{B} \to \gamma_\text{A}'\gamma_\text{B}'}(\hat{R}_\i,\hat{R}) = 2\pi\sum_{\ell,m_\ell}\sum_{\ell',m_\ell'} \i^{\ell-\ell'}
Y^*_{\ell m_\ell}(\hat{R}_\i)
Y_{\ell' m_\ell'}(\hat{R}) T_{\gamma_\text{A}\gamma_\text{B} \ell m_\ell ; \gamma_\text{A}'\gamma_\text{B}' \ell' m_\ell'}.
\end{equation}
Substituting this expression into Eq. (\ref{qsymm}) and rearranging the terms, we find
\begin{multline}\label{qT}
\tilde{q}^\eta_{\gamma_\text{A}\gamma_\text{B} \to \gamma_\text{A}'\gamma_\text{B}'}(\hat{R}_\i,\hat{R})=
2\pi[(1+\delta_{\gamma_\text{A}\gamma_\text{B}})(1+\delta_{\gamma_\text{A}'\gamma_\text{B}'})]^{1/2}
\sum_{\ell,m_\ell}\sum_{\ell',m_\ell'} \i^{\ell-\ell'}
Y^*_{\ell m_\ell}(\hat{R}_\i)
Y_{\ell' m_\ell'}(\hat{R})  \\ \times
T^\eta_{\gamma_\text{A}\gamma_\text{B} \ell m_\ell ; \gamma_\text{A}'\gamma_\text{B}' \ell' m_\ell'},
\end{multline}
where
\begin{equation}\label{T}
T^\eta_{\gamma_\text{A}\gamma_\text{B} \ell m_\ell ; \gamma_\text{A}'\gamma_\text{B}' \ell' m_\ell'}
=\frac{1}{[(1+\delta_{\gamma_\text{A}\gamma_\text{B}})(1+\delta_{\gamma_\text{A}'\gamma_\text{B}'})]^{1/2}}
\bigl{[}
T_{\gamma_\text{A}\gamma_\text{B} \ell m_\ell ; \gamma_\text{A}'\gamma_\text{B}' \ell' m_\ell'} + \eta\epsilon T_{\gamma_\text{A}\gamma_\text{B} \ell m_\ell ; \gamma_\text{B}'\gamma_\text{A}' \ell' m_\ell'}
\bigr{]}.
\end{equation}
These $T$-matrix elements are exactly the same as those obtained from the solution of the close-coupling equations
in the symmetrized basis set (as described above). They are related to the $S$-matrix elements
via \cite{Dalgarno}
\begin{equation}\label{S2T}
T^\eta_{\gamma_\text{A}\gamma_\text{B} \ell m_\ell ; \gamma_\text{A}'\gamma_\text{B}' \ell' m_\ell'}
= \delta_{\gamma_\text{A}\gA'}\delta_{\gamma_\text{B}\gB'}\delta_{\ell\ell'}\delta_{m_\ell m_\ell'}
-S^\eta_{\gamma_\text{A}\gamma_\text{B} \ell m_\ell ; \gamma_\text{A}'\gamma_\text{B}' \ell' m_\ell'}.
\end{equation}

The integral cross section for indistinguishable molecules in fully polarized nuclear spin states can be obtained
from the scattering amplitude as described in Appendix B. The final result is
\begin{equation}\label{ICSfinal}
\sigma_{\gamma_\text{A}\gamma_\text{B}\to\gamma_\text{A}'\gamma_\text{B}'} =
\frac{\pi (1+\delta_{\gamma_\text{A}\gamma_\text{B}})}
{k^2_{\gamma_\text{A}\gamma_\text{B}}} \sum_{\ell,m_\ell}\sum_{\ell' m_\ell'}|T^\eta_{\gamma_\text{A}\gamma_\text{B}\ell m_\ell ; \gamma_\text{A}'\gamma_\text{B}'\ell' m_\ell'}|^2,
\end{equation}
where $k^2_{\gamma_\text{A}\gamma_\text{B}} = 2\mu(E-\epsilon_{\gamma_\text{A}} - \epsilon_{\gamma_\text{B}})$ is the wave vector for the initial collision channel.
This equation shows that the elastic cross section
of indistinguishable bosons (or fermions) is twice as large as that of distinguishable particles.
Our Eq. (\ref{ICSfinal}) agrees with the results presented by Avdeenkov and Bohn \cite{AvdeenkovBohn} and
Burke \cite{Burke}.

\subsection{Computational details}

To parametrize the asymptotic Hamiltonian (\ref{Has}), we used the accurate spectroscopic constants of $^{17}$O$_2$ (in units of cm$^{-1}$):
$B_e = 1.353$, $\gamma = -0.00396$, $\lambda_\text{SS} = 1.985$ \cite{Gazzoli}.
In order to obtain converged cross sections at collision energies below 0.5 K,
we used a basis set comprising 3 rotational states ($N_\text{A},\, N_\text{B}=0-4$) and 4 partial waves ($\ell=0-6$). These parameters resulted
in 2526 coupled differential equations for $M=0$. At the lowest collision energy of $10^{-6}$ K, four partial
waves were sufficient to achieve convergence. The coupled equations (\ref{CC}) were solved on a grid of $R$ from 2~$a_0$ to 200 $a_0$
with a step size of $0.04$ $a_0$ yielding the cross sections converged to within 10\%.
The spin-independent and spin-dependent parts of the interaction potential for the oxygen dimer were constructed
to reproduce the integral cross sections measured in molecular beam scattering experiments \cite{JACS,prlO2}.
The lowest-order isotropic part $V_{000}(R)$ was determined with high accuracy from an analysis of the glory pattern
in high-velocity collisions of rotationally ``hot'' O$_2$ molecules. The anisotropic coefficients $V_{202}(R)$,
$V_{220}(R)$, and $V_{222}(R)$ were inferred from the scattering experiments with rotationally cold, supersonic beams of aligned
O$_2$ \cite{JACS,prlO2}. Recent {\it ab initio} studies \cite{Bartolomei,PCCP} have shown that the O$_2$--O$_2$ interaction
may be more anisotropic than suggested in Ref. \cite{JACS}. The inelastic transition probabilities in molecule-molecule collisions increase with
the anisotropy of the interaction potential \cite{Roman2004}, so the cross sections for spin relaxation presented in this work
should be viewed as lower bounds to the actual magnitudes.

\section{Results and discussion}

We consider collisions of two identical oxygen molecules in the ground electronic state $^3\Sigma_g^-$. We choose the $^{17}$O
isotope because the $^{17}$O$_2$ molecule is characterized by the $J_\text{A}=1$ ground state required for magnetic trapping
(where $\hat{J}_\text{A}=\hat{N}_\text{A}+\hat{S}_\text{A}$ is the total angular momentum of O$_2$ exclusive of nuclear spin).
The Zeeman levels of $^{17}$O$_2$ obtained by diagonalizing the asymptotic Hamiltonian are shown in Fig. 1($a$). Magnetic fields
split the $J_\text{A}=1$ ground state of $^{17}$O$_2$ into three Zeeman states corresponding to $M_{S_\text{A}}=0$, $-1$, and $+1$.
We first consider collisions of two oxygen molecules in the spin-aligned state $|M_{S_\text{A}}=1,M_{S_\text{B}}=1\rangle$,
relevant for magnetic trapping and cryogenic cooling experiments.
Molecules prepared in this state can scatter elastically or undergo spin-changing inelastic transitions.
The lower panel of Fig. 2 shows that spin-changing collisions are suppressed
at low magnetic fields ($<1$ mT) leading to a large value of the elastic to inelastic ratio $\gamma \sim 10^4$ which is favorable for evaporative cooling.
Since $M$ is conserved, the spin relaxation transitions must be accompanied by the transition
$\ell=0\to \ell'=2$, which leads to a centrifugal barrier in the outgoing reaction channel suppressing the $s$-wave inelastic scattering. Because
the $\ell=2$ barrier has a fixed height of 13 mK \cite{AvdeenkovBohn}, this suppression occurs only at low magnetic fields
where the energy difference between the initial and final Zeeman states does not exceed the barrier height \cite{AvdeenkovBohn,VolpiBohn}.
At larger magnetic fields, the spin-changing transitions are much more efficient, as shown in Fig. 2($b$).
This suggests that evaporative cooling of $^3\Sigma$ molecules in a deep magnetic trap will be challenging.
However, our results indicate that evaporative cooling may be possible in shallow magnetic traps ($<1$ mT deep).
The maximum temperature of the molecules that can be held in such a trap is determined by the parameter
\begin{equation}
\eta = \frac{|\mu B|}{k_\text{B}T},
\end{equation}
where $T$ is the temperature, $k_\text{B}$ is the Boltzmann's constant, and $\mu = 2\mu_0$ for $^3\Sigma$ molecules.
Efficient trapping requires $\eta>5$ \cite{Doyle}, which corresponds to a temperature of 0.25 mK for $^3\Sigma$ molecules at $B=1$ mT.
Such temperatures can be reached using optical Stark deceleration \cite{Barker} or Zeeman slowing~\cite{Ed}.

Spin relaxation in collisions of $\Sigma$-state molecules
in fully spin-stretched states can only occur through coupling to the rotationally excited states assisted by
the spin-spin interaction \cite{Roman2004}. This is a two-step mechanism illustrated schematically in Fig. 1($b$).
The spin-spin interaction (denoted by $V_\text{SS}$ in Fig. 1) mixes the ground rotational state $|N=0,M_N=0,M_S=1\rangle$
with the excited rotational states $|N=2,M_N,M_S=-1\rangle$. Spin relaxation is then induced by the anisotropy of the interaction potential leading to the
$|N=2,M_N,M_S=-1\rangle \to |N'=0,M_N',M_S'=-1\rangle$ transition. The anisotropy of molecule - molecule interaction potentials is usually very strong; our results yield the rate constant for spin relaxation
$6.1\times 10^{-11}$ cm$^3$/s at $T=0.1$ K and $B=0.1$ T.

Figure 3 shows the magnetic field dependence of O$_2$ - O$_2$ scattering at a collision
energy of 10$^{-6}$ K. The spin relaxation cross section increases from zero to a large value over a narrow region
of magnetic fields $B=0-1$ mT.
For magnetic fields larger than 10 mT, the spin relaxation cross section summed over all final Zeeman states is
a factor of 10 larger than the elastic scattering cross section.
The cross section displays several broad resonances. Figure 1($b$) illustrates that
at certain magnetic fields, the energy in the incoming collision channel becomes degenerate with that of
a quasibound state supported by the uppermost curve. This results in the formation of a long-lived complex in which
one of the molecules is in the $N=2$ rotationally excited state \cite{AvdeenkovBohn}.
The lifetime of the complex is determined by the strength of the couplings induced by the spin-rotation interaction and the intermolecular potential as well as
the presence of inelastic loss processes. In particular, the peaks shown in Fig. 3 are relatively
broad because inelastic spin relaxation leads to suppression of the $S$-matrix poles \cite{Jeremy}.

The magnetic field dependence of the scattering cross sections for collisions of  molecules in the absolute ground high-field-seeking state $|M_{S_\text{A}}=-1,M_{S_\text{B}}=-1\rangle$ is dramatically different (see Figure 4).  The $s$-wave elastic scattering cross section
displays a manifold of resonance peaks which we attribute to the combined action of the interaction potential and the spin-spin interaction (\ref{H}).
As a result of an interplay between these interactions, avoided crossings occur between the incoming scattering state
$|M_{S_\text{A}}=-1,M_{S_\text{B}}=-1\rangle$ and the quasibound states of the O$_2$--O$_2$ complex shown in Fig.~1($b$)
leading to the resonant variation of the elastic cross section.
This suggests that the resonances depicted in Fig. 4 are similar to the magnetic Feshbach resonances in collisions of the alkali metal atoms
\cite{Verhaar} and that the $s$-wave scattering length in an ultracold gas of $^3\Sigma$ molecules can be efficiently manipulated with magnetic fields.

In order to elucidate the possibility for evaporative cooling of $^3\Sigma$ molecules, it is useful to analyze the dependence of the
spin relaxation rates on the rotational constant \cite{Roman2004,OurWork}. In Fig. 5, we plot
the ratio of the cross sections for elastic scattering and spin relaxation as a function of the splitting between the
rotational levels. All other parameters of the Hamiltonian were unchanged in this calculation.
The probability for spin relaxation in atom-molecule and molecule-molecule collisions decreases with increasing $B_e$ because
the matrix element between the different spin states due to the spin-spin interaction scales as $\lambda_\text{SS}/B_e$ \cite{Roman2004,OurWork}.
Figure 5 shows that the elastic to inelastic ratio at a collision energy of 0.1 K improves dramatically with
increasing the rotational constant. The dependence on $B_e$ is, however, not monotonic because of the manifold of
Feshbach resonances (see Figs. 3-4), which are most pronounced at low collision energies.
The results shown in Fig. 5 indicate that evaporative cooling of molecules with larger rotational constants should generally be more efficient.

Previous theoretical and experimental work has established that the cross sections for spin-changing transitions in
$^3\Sigma$ molecules are sensitive to the splitting between the $N=0$ and the $N=2$ rotational levels.
The approximate $1/B_e^2$ scaling law \cite{OurWork} suggests that spin relaxation occurs at a slower rate in collisions
of atoms and molecules with larger rotational constants. This result is important because the splitting between
different rotational levels can be altered with electric, microwave, or off-resonant laser fields, thereby enabling control
over the spin degrees of freedom of cold molecules. We illustrate the idea using the example of a nonpolar $^3\Sigma$ molecule
such as O$_2$ in the presence of far off-resonant, continuous-wave laser field. The energy levels are determined by
the Hamiltonian (\ref{Has2}) with an additional term~\cite{Friedrich}
\begin{equation}\label{L}
\hat{V}_\text{L} = -\frac{\epsilon_0^2}{4}\left[ \Delta \alpha \cos^2\chi +\alpha_\perp \right],
\end{equation}
where $\Delta \alpha = \alpha_{||}-\alpha_\perp$ is the polarizability anisotropy, $\chi$ is the angle between the molecular axis and
the laser polarization vector (which we assume to be parallel to ${\bm B}$), and $\epsilon_0$ is the amplitude of the laser field.
Figure 6 shows the energy levels of $^{17}$O$_2$ as functions of the laser field strength (we transform away the $\chi$-independent terms
by properly choosing the zero of energy). The effective rotational constant defined as the splitting between the closest field-dressed
Zeeman levels in the $N=0$ and $N=2$ manifolds, increases by a factor of 1.6 as the laser field intensity is varied from zero to
$5\times 10^{11}$ W/cm$^2$. For polar molecules, similar effects can be induced by dc and microwave laser fields \cite{OurWork2}.

As shown in Fig. 6, any substantial modification of molecular energy levels requires laser field intensities of order 10$^{11}$ W/cm$^2$.
The maximum cw laser field intensity currently available in the laboratory is about $2.5 \times 10^5$ W/cm$^2$ for a 0.5 mm size sample.
However, if the trapped cloud is compressed to one-tenth its original size, the maximum attainable laser intensity increases
by a factor of 100, so the required field strengths of $10^{11}$ W/cm$^2$ are well within reach for microscopic clouds ($10^{-3}$ mm).
Samples of such size can be produced and stored in magnetic microtraps recently demonstrated for cold polar molecules \cite{MeijerChip}.
An alternative solution is to use pulsed lasers, whose intensity is typically much stronger than that of cw lasers.
However, the time-independent description used in this work can only be applied if the duration of the laser pulse is long compared to
the collision time. This condition is necessary to ensure the validity of the quasistatic approximation for the molecule-field interaction \cite{Friedrich}.

Figures 7 and 8 show the cross sections for spin relaxation and elastic scattering in O$_2$--O$_2$ collisions as functions of the rotational constant at
different collision energies. At the highest energy of 0.1 K, the cross section for spin relaxation decreases monotonically and that for
elastic scattering increases with increasing $B_e$. For a molecule with $B_e/B_{\text{O}_2}>10$, the spin relaxation would be suppressed
by two orders of magnitude.
As the collision energy decreases, the variation of the cross sections with $B_e$ becomes more complicated.
At the lowest collision energy of $10^{-6}$ K, both the elastic and spin-changing cross sections decrease with increasing $B_e$,
and the suppression of spin relaxation in very efficient for large rotational constants. In contrast, for the intermediate kinetic energy
of 1 mK, the probability for spin relaxation remains large even for $B_e/B_{\text{O}_2}>10$, and the cross sections
show oscillations due to Feshbach resonances (see Fig. 4). The results shown in Figs. 7 and 8 indicate that off-resonant laser fields
may be used to suppress spin-changing transitions and induce Feshbach resonances in ultracold collisions of $^3\Sigma$ molecules.
We note that it order to establish that the laser-induced magnetic Feshbach resonances do occur at practicable laser field intensities,
it will be necessary
to perform accurate quantum scattering calculations in superimposed magnetic and off-resonant laser fields. Such calculations can be
carried out using the formalism presented in this work.

\section{Summary}

We have presented a quantum mechanical theory and converged quantum mechanical calculations for collisions of identical $^3\Sigma$ molecules
in a magnetic field. The cross sections for spin relaxation at magnetic fields above 1 mT are comparable to the elastic cross
sections, and they are not very sensitive to the applied field. At low magnetic fields, the spin-flipping transitions are suppressed
by $d$-wave centrifugal barriers in the outgoing collision channel, suggesting that $^3\Sigma$ molecules can be evaporatively
cooled in shallow magnetic traps. Our calculations shown in Fig. 4 suggest that the cross sections for collisions of molecules in the absolute ground state display a dense spectrum of Feshbach resonances, which may be used to tune molecule - molecule scattering lengths in a very wide range of magnetic fields.
These resonances can be used to create tetra-atomic molecules via magnetoassociation \cite{Chin},
manipulate molecule-molecule interactions in optical lattices \cite{Bloch}, control chemical reactions of polyatomic molecules \cite{RomanReview},
or facilitate evaporative cooling of molecules in an optical dipole trap \cite{Cs}.
Our results show that the number of Feshbach resonances for molecule-molecule scattering in the absolute
ground state ($\sim100$ T$^{-1}$) is larger by a factor of 10 than the density of the resonances for the low-field-seeking states.

\begin{acknowledgments}
We acknowledge useful discussions with Kirk Madison, Nathan Brahms, and Simonetta Cavalli.
This work was supported by NSERC of Canada and an NSF grant to the Institute for Theoretical Atomic, Molecular, and Optical Physics
at Harvard University and the Smithsonian Astrophysical Observatory.
\end{acknowledgments}


Here I am again, reading and commenting on the sixth post from Rat in the Walls, the blog I wrote during the final year of my brother's battle with ALS. The post is titled "Empathic Alchemy," and you can read it below the video.
Blood is sometimes thicker than gold.


Digital Design: An Embedded Systems Approach Using VHDL provides a foundation in digital design for students in computer engineering, electrical engineering and computer science courses.
It takes an up-to-date and modern approach of presenting digital logic design as an activity in a larger systems design context. Rather than focus on aspects of digital design that have little relevance in a realistic design context, this book concentrates on modern and evolving knowledge and design skills.
Hardware description language (HDL)-based design and verification is emphasized--VHDL examples are used extensively throughout.
By treating digital logic as part of embedded systems design, this book provides an understanding of the hardware needed in the analysis and design of systems comprising both hardware and software components. Includes a Web site with links to vendor tools, labs and tutorials.


text:
EYE-OPENERS
- InfoZone News Museum, Robert Hoag Rawlings Public Library, 100 E. Abriendo Ave., is open from 9 a.m. to 9 p.m. Monday through Thursday, 9 a.m. to 6 p.m. Friday and Saturday and 1 to 5 p.m. Sunday. Admission is free.
- Hose Co. No. 3 — Fire Museum, 116 Broadway Ave., is open by appointment only. There are artifacts and photographs, including the 1882 hand-pulled Orman Hose Co. hose cart. Admission is by donation. Call Gary Micheli, 821-1273, or Mark Pickerel, 564-2794, to schedule a tour or for more information. - Pueblo Railway Museum, 132 B St., is open from 10 a.m. to 4 p.m. Saturdays and other times by appointment. The Colorado & Wyoming GP7 locomotive, The Patriot, is now on display. For information or appointments, call 251-5024.
- Steelworks Museum of Industry and Culture, 215 Canal St., is open from 10 a.m. to 4 p.m. Monday through Saturday. Admission is $5 for adults, $3 for ages 4-12 and free for children younger than 4 and museum members. Admission includes tours of the CF&I Mine Rescue Car No. 1. The museum's main exhibit is the Story of Steel: 1915-1936. There also are photographic displays of mills and mines owned by the Colorado Fuel and Iron Co.; a medical display in the former company dispensary and a company-store gift shop, carrying many CF&I-related items. For information, call 564-9086 or visit www.steelworks.us.
- Gornick Slovenian Library and Museum and St. Mary's Genealogy Center, 211 E. Mesa Ave., is open from 1 to 4 p.m. Wednesday or by appointment. Free library/museum tours are available by calling 564-6779. Genealogy research is available through sacramental records of all churches in the Pueblo Diocese from the 1800s through 1957, and naturalization, census, cemetery and Internet-immigration records. There is a minimal research fee. For information, call 564-1539.
- Lincoln Home, 2713 Grand Ave., is open from 10 a.m. to 3 p.m. Tuesday through Friday and by appointment Saturday and Sunday.
- The Gallery of the Spanish Peaks Arts Council (SPACe), 132 W. Ryus Ave., La Veta, is open from 10 a.m. to 2 p.m. Tuesday and Thursday and 10 a.m. to 3 p.m. Saturday, featuring original art by local artists. For information, call 719-742-3074 during regular hours.
- Pueblo Art Guild and Gallery, 1500 N. Santa Fe Ave., Mineral Palace Park., is open from noon to 4 p.m. Wednesday through Sunday, showing a variety of works by local artists. 543-2455 or www.puebloartguild.com.
- Trinidad History Museum, 312 E. Main St., Trinidad, is open from 10 a.m. to 4 p.m. Monday through Saturday, May 1 to Sept. 30. The complex consists of the Baca House, Bloom Mansion, Santa Fe Trail Museum, Heritage Gardens, book and gift shop, and a Tourist and State Byways Information Center located in El Corazon de Trinidad National Historic District. Admission is $8 for adults, $6 for seniors 65 and older, $3 for children 6-16, and free for children 5 and younger and History Colorado members. For information, call 719-846-7217 or visit www.historycolorado.org.
- El Pueblo History Museum, 301 N. Union Ave., is open from 10 a.m. to 4 p.m. Tuesday through Saturday. Admission is $5 for adults and $4 for children ages 6-12, military and seniors. History Colorado members and children 5 and younger are free. Saturdays are Family Days with free admission for children younger than 12. Docent-led tours are available for 10 or more people by calling a week in advance. For information or to book a tour, call 583-0453.
- Rosemount Museum, 419 W. 14th St., is open from 10 a.m. to 4 p.m. Tuesday through Saturday. 545-5290.
- Sangre de Cristo Arts and Conference Center's gallery hours are 11 a.m. to 4 p.m. Tuesday through Saturday. 295-7200. - Buell Children's Museum's hours are 11 a.m. to 4 p.m. Tuesday through Saturday. 295-7200.
- Pueblo County Historical Society and Edward Broadhead Library, located in the Southeastern Colorado Heritage Center, 201 W. B St., is open from 10 a.m. to 4 p.m. Tuesday through Friday. Research library includes many books on Pueblo history, local school yearbooks, city directories and extensive photo collection. 543-6772.
- Pueblo Zoo and White Discovery Room are open from 9 a.m. to 4 p.m. Monday through Saturday and noon to 4 p.m. Sunday. Call 561-1452 for hours or visit www.pueblozoo.org.
- Pueblo Weisbrod Aircraft Museum, Memorial Airport, is open from 10 a.m. to 4 p.m. weekdays and Saturday and from 1 to 4 p.m. Sunday. Tours: 948-9219.
- Nature and Raptor Center of Pueblo, 5200 Nature Center Road, featuring natural beauty, picnic areas, fishing, trails, bookstore, gift shop, Coyote Grille and Raptor Center exhibits. The Raptor Center's winter hours are 11 a.m. to 4 p.m. Tuesday through Sunday. For information, call 549-2414.
- Fowler Historical Society, Fowler, is open from 9 a.m. to 4 p.m. each Thursday and 11 a.m. to 4 p.m. Wednesday, Thursday and Friday. New exhibits are shown every six months. For information, call 719-263-4046.
- Southeastern Colorado Heritage Center and Museum, 201 W. B St., is open from 10 a.m. to 4 p.m. Tuesday through Saturday. Admission is $4 for adults, $3 for children 6-12 and free for children 5 and younger and center members. The museum features an extensive saddle collection, the Carlile piano, railroad exhibit, Depression Era parlor and kitchen pictographs from western Pueblo county, Hispanic genealogy and more. Tours are available by calling 295-1517.
- Koshare Indian Museum, 115 W. 18th St., La Junta, is open from 10 a.m. to 5 p.m. Monday through Saturday and 10 a.m. to 5 p.m. Sunday. 719-384-4411.
- Centennial High School Historical Museum, 2525 Mountview Ave., is open from 9 a.m. to noon Fridays, when school is in session. For information or to schedule a tour, call 545-2141 or 543-7211. The museum features clothing, annuals, photos and memorabilia originating with the first graduating class in 1884.
- Colorado State University-Pueblo Fine Art Gallery, 2200 Bonforte Blvd., Art/Music Building, is open from 10 a.m. to 4 p.m. Monday through Friday. For information, call 549-2835.
- Colorado State University-Pueblo Observatory, 4028 W. 11th St., is open to the public at 30 minutes past sunset the third Tuesday of each month for viewing the sky. For information, call 549-2683.
- Fremont Center for the Arts, 505 Macon Ave., Canon City, is open from 10 a.m. to 4 p.m. Saturday and noon to 4 p.m. Sunday.
- Trinidad Area Arts Council, First Street Gallery, 150 E. First St., is open from 10 a.m. to 3 p.m. Tuesday through Saturday. For information, call 719-846-1441.
- A.R. Mitchell Museum & Gallery, 150 E. Main St., Trinidad, is open from 10 a.m. to 4 p.m. Tuesday through Saturday and noon to 4 p.m. Sunday. The museum displays three main categories of art; Western art, devotional art and historic photographs. Admission is $3 for adults and free for seniors and children. For information, call 719-846-4224.
- Otero Museum, 218 Anderson St., La Junta, is open from 1 to 5 p.m. daily Monday through Saturday. Admission is free, but donations are accepted.
— Compiled by Shirley Whittmore

redpajama_set_name: RedPajamaCommonCrawl


text:
Robert Nielsen Diary
Western Michigan University Archives & Regional History Collections
This collection contains the diary of Robert Nielsen between the years of 1942 and 1946, recording his everyday life and routine during his time in high school. This routine included attending school during the week, and playing around and attending Sunday School on the weekends. This diary provided a record of the activities Robert did, giving insight on what growing up in the 1940s was like, rather than his thoughts or feelings about his life.
Majority of material found within 1942-1946
Nielsen, Robert Arthur, approximately 1928- (Author, Person)
Robert Arthur Nielsen was born in Muskegon, Michigan around 1928 by his father, Charles Edward Nielsen, and his mother, Selma Alvena Anderson. He later married Virginia Elouise Hudson on July 23, 1949. Virginia Hudson was also born in Muskegon, Michigan around 1930 by her father, Eugene Malcom Hudson, and her mother, Jennie M. Shannock. According to Roberts marriage records, he was 21 when he was married in 1949, putting him in high school over the years of 1942 to 1946, when the diary was dated. Robert and Virginia had five children together. Later on he married Tesaline Marie Cramblit on April 11, 1966. Robert also served in the U.S. Navy immediately after high school, between 1946-1948 where he was honorably discharged.
.10 Cubic Feet
This collection amounts to 0.10 cubic feet and contains enough pages to write an entry for everyday between 1941 to 1946. The cover is black leather with a lock on the front that contains no key. Inside the cover reads "This is My Personal Diary: Robert Nielsen 1969 Ruddiman St. Muskegon, Michigan. Five Years from 1941 to 1946." Each page provides enough room for five days' worth of diary entries, however there are several pages left blank.
There is minor tearing and staining on the pages, leaving the diary in good condition.
Muskegon (Mich.) -- Social life and customs -- 20th century
Robert Nielsen Diary Finding Aid
Nicole Aquino
2018- 06- 11
Part of the Western Michigan University Archives & Regional History Collections Repository
https://wmich.edu/library/collections/archives
Charles C. and Lynn L. Zhang Legacy Collections Center
1650 Oakland Drive
Kalamazoo MI 49008-5307 US
arch-collect@wmich.edu
Robert Nielsen Diary, RH-A-3954. Western Michigan University Archives & Regional History Collections.
Robert Nielsen Diary, RH-A-3954. Western Michigan University Archives & Regional History Collections. https://aspace.library.wmich.edu/repositories/3/resources/176 Accessed February 01, 2023.


Need a brain break? Find water!
People are watery beings - you may know that the average human body is 65% water! Our brain especially loves water. We think more clearly when we are hydrated and spending time near water calms us down.
Step into a shower or bath after a long, stressful day and it feels wonderful, yes? Simply the sound of water offers soothing 'white noise' to our brain. If you are able to spend time near natural bodies of water you combine the added benefits of fresh air, time in nature, and sunshine.
Enjoy a brain break right now, wherever you are! Sit back, breathe deeply, and gaze using the link below.


Regulation and collateral costs have made the cleared derivatives market much more attractive for the buy-side. Joe Parsons asks what else will it take for them to voluntarily take part?
The seismic shift in the derivatives market post-financial crisis has seen not only a change in the way the products are traded and cleared, but also in the nature of relationships throughout the process.
The clearing of interest rate swaps was not completely alien to the buy-side prior to the financial crisis, however asset managers and pension funds were never directly attached to the clearing process of derivatives. With less clearing activity pre-2008, a middle-man between the clearing house and the executor made sense.
So imagine their surprise when asset managers were told that not only would they be clearing inflation swaps, single-name credit default swaps and repo, but they could actually become direct clearing members of central counterparties (CCPs) such as LCH, Eurex and DTCC.
Throughout 2016 and 2017, a number of clearing houses have established direct clearing routes to enable more buy-side volumes to flow through. Last year LCH onboarded the UK's Insight Investment as the first sponsored clearing member of RepoClear, Eurex signed up signed Dutch pension fund PGGM as its first buy-side member for its securities lending clearing house, and in April Northern Trust helped facilitate the first directly cleared cash and repo trade on behalf of the Healthcare of Ontario Pension Plan (HOOPP) with Canada's main derivatives clearing house.
Hedge funds were also one of the early movers into voluntary clearing, largely due to the margin efficiencies offered to them as opposed to trading in the bilateral market. Regulation has become one the main incentives for the buy-side to take up voluntary clearing of their derivatives. Dodd Frank and EMIR have made clearing for the most widely traded swaps mandatory, while the uncleared margin rules have made it too costly for the buy-side to stay in the bilaterally traded world.
"Currently there exists a price spread between cleared and uncleared derivatives," says Rob Scott, head of custody and clearing, Commerzbank. "The commercial cost of operating in a non-cleared, bilateral environment is becoming increasingly apparent in terms of price and margin requirement. This is leading to increases and an incentive to voluntary clearing activities.
LCH has posted a number of record-breaking achievements in cleared volumes, largely due to massive uptick in voluntary clearing of certain products from the buy-side. SwapClear, LCH's interest rate derivatives clearing service processed over $873 trillion in notional volumes during 2017, with member and client flow increasing 31% year-on-year. It also saw over $3.1 trillion of inflation swaps cleared, meanwhile compression volumes rose 58% from 2016 to over $608 trillion.
"We've seen significant growth in volumes across multiple asset classes driven by new customers as well as additional flow from existing customers," said Daniel Maguire, chief executive of LCH Group in January. LCH's RepoClear service cleared $175 trillion over the course of the year, a 25% increase on 2016, while EquityClear processed over one billion trades and ForexClear processed more than $11 trillion in notional. The CDSClear service recorded $1.1 trillion in notional processed across its CDS index and single-names offering.
"The size of credit lines given for cleared trades rather than for bilateral is more favourable due to the credit profile of facing a clearing house, and they [hedge funds] are seeing better pricing in some cases," says Jamie Gavin, head of OTC clearing EMEA and APAC, Societe Generale Prime Services.
Now that mandatory clearing is entrenched in the OTC markets, more and more market participants are moving to a cleared market not because they are required to, but because that is where the liquidity is. Regulations such as EMIR and the uncleared margin rules have made it pricier to do business bilaterally, and instead have shifted focus to the benefits clearing offers.
This is most evident in the FX market, in which 40-50% of the FX non-deliverable forward (NDF) interdealer market has moved to clearing over the past year. Societe Generale's Gavin believes the next big asset class to move to clearing is FX options and repo. "We expect FX options will follow the same trend. The big one coming next is around repo, and the we are seeing demand from clients wanting to become sponsored clearing members," adds Gavin.
For pension funds that are currently exempt from EMIR, repo clearing is becoming increasingly attractive to them, as with the case with PGGM joining Eurex as a clearing member and Insight Investment with LCH's RepoClear. According to Nick Gant, head of sales trading and EMEA head of fixed income prime brokerage at Societe Generale, pension funds and money market funds, as opposed to hedge funds, have been the early adopters of this model.
However, the extent to which all of the buy-side are taking part in voluntary clearing has been limited, says Nick Rustad, global head of clearing at JP Morgan, in which the majority of activity in NDF and inflation clearing has been the inter- dealer community.
"The banking and inter-dealer community has been active in non-mandated voluntary cleared trades, however you have yet to see demand from the client clearing side reach that level. For OTC derivatives, demand is still in those mandated categories i.e. G4 interest rate swaps, some emerging markets currency swaps and index CDS. The most client interest for non-mandated products are in instruments where there is a cost and liquidity difference at the point of execution. If that changes or you get to a point where banks only want to quote on a cleared basis, you may see a shift to voluntary clearing," says Rustad.
Certainly, a lot of buy-siders have taken a wait-and-see approach, each one interested in moving to clearing but wary of being the first mover. Furthermore, smaller-sized asset managers and hedge funds may not have the infrastructure in place to clear their trades or even the tools to quantify the impacts of the collateral requirements on their portfolio and the cost differences in moving to clearing.
Commerzbank's Scott believes it is up to their sell-side partners to provide these tools and help facilitate this move. "It is therefore incumbent upon the service community, i.e. custodians that offer clearing services, to be able to help clients in both understanding and impact assessment," says Scott. "Once the commercial and counterparty risk benefits are better understood, there should be no reason why you wouldn't move most of your activities and operate in a cleared world.
It is also on banks and other clearing infrastructures to provide both the access and the capabilities for the buy-side to move into clearing. Direct clearing models are large step to help this, but take-up has been very slow. Furthermore, liquidity will continue to be one of the main determinations for where the buy-side clear and what banks they use.
"Given these new products are being established all the time, there are more clearinghouses expanding in to OTC. However, some clearers are struggling with scale, and this is where more client clearing volumes will concentrate with the top FCMs," adds JP Morgan's Rustad.
BNP Paribas' Smith says it has become easier for banks to clear bilateral derivatives, given most banks went through a learning phase with the first set of products. However, there remains challenges on the risk management side for client clearing, such as whether the default management processes are appropriate for certain products.
"FCMs and CCP's will have to adapt their products, but clients will want their banks to be able to clear a wide range of models and be involved in various access models to CCPs," Smith says.
To a large extent, the ability to venture into voluntary clearing is there amongst the buy-side. The tools are there for the larger players that have the scale to clear their bilateral trades, but for many that are in wait-and-see mode, they will have to rely on their banks and brokers to migrate from bilateral to a cleared world. Furthermore, even for those larger asset managers, voluntary clearing will mean a rejig of broker relationships.
"For large and active OTC players this means that clearing is sometimes spread across multiple clearing relationships. The move towards voluntary clearing will lead to organisations being more strategic towards their clearing brokers and who they partner with," says Scott.


text:
Citizens Business Bank Arena drops Ticketmaster
By Andrew Edwards | aedwards@scng.com | Inland Valley Daily Bulletin
May 8, 2012 at 12:00 a.m.
Photo Gallery: Brand new game on seating at Citizens Business Bank Arena
ONTARIO – Citizens Business Bank Arena will join other Anschutz Entertainment Group venues today by leaving Ticketmaster's fold and beginning to sell tickets through the company's own platform.
AEG calls its ticket-sales platform Axs, pronounced "access." The system goes into effect today at the arena.
"We're hoping that Axs becomes as much of a household word, as it would, as Ticketmaster has been," arena marketing director Sue Oxarart said.
AEG's foray into ticket sales stems from the antitrust settlement that followed the government's acceptance of a merger between Ticketmaster and concert promotion firm Live Nation.
Denver-based AEG began selling tickets through Axs last summer and plans to have the system in effect at all of its venues, including Staples Center in Los Angeles, by the end of March 2013, senior vice president Todd Sims said.
AEG already uses Axs to sell tickets at Home Depot Center in Carson, which is the home stadium for the Los Angeles Galaxy and Chivas USA soccer teams.
For many consumers, the process of buying tickets can be an especially frustrating exercise in mathematics as a series of fees raises the final price well above the advertised dollar amount.
AEG does not go as far as saying the new ticketing system will eliminate fees, but the company does say Axs will reveal the full price of admission at the start of a transaction, instead of at the end.
As unpopular as those fees are to consumers, they are operating revenue for event promoters, venues and ticketing companies, like Ticketmaster, said Dave Brooks, a senior writer for the trade magazine Venues Today.
For years, Ticketmaster "had no problem being the bad guy" and collected those fees for venues, said Brooks, who also credited current Ticketmaster CEO Nathan Hubbard with improving customer relations by adding clarity to fee charges.
"If the final cost to see Social Distortion is going to be $60, just say $60," Brooks said.
Whether consumers will come to view Axs in a positive light is an interesting question, Brooks said. People often don't like ticketing companies, so "from that place it would seem Axs could only go up."
AEG and another company, Outbox Enterprises, created Axs after the Justice Department approved the Ticketmaster-Live Nation merger in January 2010.
The combination resulted in the world's largest ticket seller joining the planet's biggest concert promoter in a single enterprise. The government approved the merger after the Justice Department's antitrust division and 17 state attorneys general reached a settlement that required, among other things, the merged company to divest some of its assets to AEG to preserve a measure of competition within the ticketing industry.
The government's decree then allowed AEG venues to free themselves from Ticketmaster contracts and switch to Axs, Sims said.
"We had a variety of contracts at a variety of lengths, and we were able to do a timeline of our own choosing," Sims said.
Axs sales' features include a "virtual waiting room" for high-demand events.
In practice, the feature works like a lottery, Brooks said. Customers can submit bids for tickets and later find out if they win instead of having to rush for tickets as soon as an event goes on sale.
AEG plans to link Axs to social networking sites like Facebook to simplify the work that goes into buying tickets for a large group of friends and family, Oxarart said.
The planned feature will let one person buy tickets and notify others, who would have a time window to buy tickets for adjacent seats. The idea is to eliminate the need for one person to assume the role of organizer and buy all tickets for a large group, Oxarart said.
Citizens Business Bank Arena managers also announced the first five shows for which customers can buy tickets at the venue via Axs.
Those events:
American Idol Live Tour, July 25
Kellogg's Tour of Gymnastics Champions, Sept. 8
Los Angeles Kings vs. Anaheim Ducks preseason game: Oct. 6
Los Angeles Lakers vs. Portland Trailblazers preseason game, Oct. 10
Cirque du Soleil: Dralion, Oct 24-28
Reach Andrew via email, call him at 909-483-8550, or find him on Twitter @InlandBizz.
Andrew Edwards | reporter
Andrew Edwards is part of the Southern California News Group's business team and focuses on housing stories for the Inland Empire. He's based at the Inland Valley Daily Bulletin and has also worked for publications including the Long Beach Press-Telegram and The San Bernardino Sun. He graduated from UCLA in 2003 after studying political science and history.
aedwards@scng.com
Follow Andrew Edwards @AndrewEdwardsIE


Air conditioning systems are a costly investment, and it is imperative that they are maintained in good order to ensure that they continue to be safe and efficient. Minor faults with air conditioning systems can result in incremental increases in operating costs, and whilst these may not be immediately obvious they can result in unnecessary expenditure.
Repair and replacement of failed parts or complete air conditioning systems can be extremely expensive, so skimping on maintenance represents false economy. Added to this, the safety and comfort of staff in industrial environments is paramount, so ensuring that air conditioning units are in good condition can boost staff productivity and ensure compliance with health and safety legislation.


text:
Congress Must Investigate U.S. Loans To Azerbaijan's Secretive Silk Way Airline
Silk Way Airlines
By Harut Sassounian
Last year, I wrote an article reporting that the Silk Way Airlines of Azerbaijan made 350 secret flights to transport hundreds of tons of weapons from Bulgaria to ISIS terrorists in Syria and other Middle Eastern countries between 2014 and 2017. We now have a new surprising revelation that Silk Way received $419.5 million of loans from the U.S. Export-Import Bank (EXIM) to buy three 747-8 cargo planes from Boeing to continue its sinister operations.
The disclosure was made by a reporter for the Organized Crime and Corruption Reporting Project (OCCRP) by filing a Freedom of Information Act (FOIA) request with the U.S. government in 2016. It is noteworthy that Silk Way, "owned by a company with past ties to Azerbaijan's Aliyev family, won some lucrative contracts from the U.S. military," according to FOIA documents. In fact, "Silk Way was given contracts worth more than $400 million with the U.S. Defense Department's Transportation Command for more than decade," according to Devansh Mehta of OCCRP. Silk Way transported "ammunition and other non-lethal materials" to Afghanistan as of 2005. "In addition to its relationship with the U.S. government, Silk Way Airlines has also worked as a subcontractor for the Canadian Department of National Defense, the German armed forces, and the French army," Mehta revealed.
In April 2017, Silk Way increased its purchases from Boeing, signing a $1 billion deal for 10 new 737 MAX passenger planes, according to reporter Mehta. However, it is not known how the new acquisition was financed. Last October, Silk Way announced plans to buy two more 747-8 cargo planes.
Mehta disclosed that "the airline is owned by Silk Way Group, which, at least at one point, was closely associated with Azerbaijan's ruling Aliyev family (which has used its planes for private trips) and has benefited from benevolent state deals. Information obtained through FOIA shows that Silk Way Airlines took steps to conceal its owners' identity, perhaps to improve its chances of winning the valuable U.S. loan guarantees and military contracts."
Mehta added that "Azerbaijan ranks 122nd out of 180 countries in Transparency International's corruption perception index, while President Ilham Aliyev's family owns luxury properties around the world worth over $140 million. The Panama Papers and other leaks have implicated the country's first family as being involved in nearly all sectors of the Azerbaijani economy, from luxury hotels to mining to banking."
According to the terms of the Export-Import Bank's $419.5 million loan to Silk Way, in case of default the loss would be repaid by the state-owned International Bank of Azerbaijan (IBA). The problem is that IBA has been "implicated in the Azerbaijani Laundromat, a massive scheme that pumped nearly $3 billion out of the country through various shell companies," Mehta wrote. Furthermore, IBA is not in a position to guarantee the Silk Way loan, as the IBA itself declared bankruptcy in 2015, unable to pay its $3.3 billion debt!
Nate Schenkkan, project director of the Nations in Transit report at Freedom House, a US-based nonprofit that monitors democracy and human rights around the world, questioned the wisdom of EXIM Bank's loan to Silk Way: "In Azerbaijan, where one family dominates economically and politically, and is then using state institutions to back its economic projects, there's an obvious conflict of interest."
Arzu Aliyeva, Pres. Aliyev's 21-year-old daughter in 2010, was one of the three owners of Silk Way Bank, the financial arm of Silk Way Holding. Since 2017, her name is no longer mentioned as an owner. "Silk Way Holding, also referred to as Silk Way Group (SW Group) on its website, is a conglomerate that has currently listed 11 companies in its portfolio, including the airline," according to Mehta. Silk Way Holding dominated Azerbaijan's aviation sector after the state carrier AZAL airlines was privatized in a highly secretive manner without any bids and tenders. Mehta wrote that "a similar privatization of the telecom sector ended up with the [Aliyev] family earning about $1 billion in bribes in cash and share value, according to an earlier OCCRP story. The investigation also found that the money was funneled to the first family through various secret offshore companies. These companies have enabled the Aliyevs to control stakes in gold mines, telecommunications and construction businesses in Azerbaijan."
According to a filing in 2006, Silk Way Airlines was owned by IHC (International Handling Company), an offshore entity based in the British Virgin Islands. In a 2017 filing, Silk Way Airlines stated that 40% of the company was owned by IHC, while 60% was owned by SW Holding, "effectively controlled" by Zaur Akhundov, an Azerbaijani citizen. Mehta stated that "IHC is linked to the Aliyev family through its director Jaouad Dbila who reportedly served as a proxy for the first family's business interests in the past."
In 2011, a Russian-born manager, Grigory Yurkov, was given power of attorney for both Silk Way Holding and IHC, according to Luxembourg's official gazette. This appointment was used as a means to conceal the true owners of IHC.
Meanwhile, Zaur Akhundov had mysteriously become the 100% owner of the entire Silk Way Group in 2014. By that time, the firm and its many holdings were already worth billions of dollars, Mehta declared, based on the company's loan guarantee application. Akhundov, 50, had held several official positions in Azerbaijan. "It is unclear how Akhundov became the owner of a billion-dollar conglomerate with more than 10 aircrafts, an insurance company, a construction company and an aircraft maintenance company, to name a few of the enterprises in the Silk Way Group," Mehta wondered.
According Schenkkan of Freedom House, "Azerbaijan can be described as a centralized, vertical pyramid where the benefits go to one family that collects rents throughout the economy. This includes all sorts of transactions, not only official state transactions that might involve taxes and public funds, but also things that involve what we normally consider the private sector: import-export, consumer goods, transport—any area of the economy, the family has a stake in it and receives a cut on what takes place."
The U.S. Congress should hold a hearing to investigate the appropriateness of EXIM Bank's $419.5 million loan guarantee to Silk Way Airlines, its arms shipments to terrorist groups in the Middle East, and its hidden ownership by the ruling Aliyev family. After all, why should Azerbaijan, a country with billions of petrodollars, be given a U.S. loan?
Posted in General Update, International, News, Politics
Tags: Afghanistan, Arzu Aliyeva, Azerbaijan, Boeing, Bulgaria, Canada, Congress, Devansh Mehta, EXIM, Export-Import Bank, France, Freedom House, Ilham Aliyev, ISIS, Nate Schenkkan, OCCRP, Silk Way Airlines, Syria, Transparency International, Turkish Lira
Armenian-American Film "HERE" Premiers This Thursday at Ft. Lauderdale International Film Festival
Ft. Lauderdale, FL – Florida Armenians cordially invites you to a special evening for the premier of the Armenian-American film "HERE," this Thursday, October 25th at Cinema Paradiso, the home of the Ft. Lauderdale International Film Festival (FLIFF). Director Braden King will be in attendance to meet guests and participants. FLArmenians will offer brief program immediately preceding the film's premier.
We hope you can join us for this very special occasion. A limited number of FREE tickets are available for the premier by contacting FLArmenians, and online ticket purchase is available here.
Film Times:
Premier Thursday night 8:00 PM, Program begins at 7:30 PM. Also showing Friday night 8:00 PM & Saturday night 8:00 PM
Cinema Paradiso is located at 503 SE 6th St., Ft. Lauderdale, FL 33301. Driving directions, map and parking information can be found here.
Language: English & Armenian w/English sub-titles
Director: Braden King
Producer: Lars Knudsen, Jay Van Hoy, Jeff Kalousdian, Julia
Cast: Ben Foster, Peter Coyote and Lubna Azabal
Will Shepard is an American satellite-mapping engineer contracted to create a new, more accurate survey of the country of Armenia. Within the industry, his solitary work – land-surveying satellite images to check for accuracy and resolve anomalies – is called "ground-truthing". He's been doing it on his own, for years, all over the world, but on this trip, his measurements are not adding up.
Will meets Gadarine Najarian at a rural hotel. Tough and intriguing, she's an expatriate Armenian art photographer on her first trip back in ages, passionately trying to figure out what kind of relationship – if any – she still has with her home country and culture. Fiercely independent, Gadarine is struggling to resolve the life she's led in Canada and Europe with the Armenian roots that run so deeply, if unconsciously, through her. There is an almost instant, unconscious bond between these two lone travelers; they impulsively decide to continue together. HERE tells the story of their unique journey and the dramatic personal transformations it leads each of them through.
Sponsored by Margaret Ahnert and featuring Special Guest, Director Braden King.
About FLIFF:
The Fort Lauderdale International Film Festival (FLIFF), founded in 1986, is dedicated to foreign and independent film. FLIFF annually showcases over 200 films from over 35 countries. A recipient of The Guiness World Record for the longest film festival in the world, FLIFF prides itself as being the friendly non-pretentious fest where access to filmmakers is basically unfiltered.
FLIFF takes programming throughout South Florida, including The Weston Foreign Film Series, The Bay Harbor Islands Family Festival, The Hollywood Arts Park screenings, among other satellite operations.
FLIFF also tours the State of Florida and Grand Bahama Island, partnering with The Daytona Beach Film Festival, The St Augustine Film Festival, The Amelia Island Film Festival, and FLIFF On-Location Grand Bahama Island. Filmmakers who submit to FLIFF will have their films considered for one or all of the above festivals, providing a bargain to budget stretched filmmakers.
Since 1998, over $1 million had been raised and invested in our year-round space, now known as Cinema Paradiso. Today, Cinema Paradiso operates year-round featuring foreign and independent film, student films, children's movies, and serves as a mecca for just about every kind of arts event you can imagine. Benefits for other non-profits, poetry, dance, music, as well as corporate events, book signings and celebrity appearances take place in this versatile space.
The Fort Lauderdale International Film Festival and Cinema Paradiso are just two of the programs presented by The Broward County Film Society.
Posted in Arts & Culture, Events, General Update, News, Press Release
Tags: Armenia, Ben Foster, Braden King, Broward, Canada, Cinema, Europe, Festival, Film, Ft. Lauderdale, Gadarine Najarian, Here, International, Jay Van Hoy, Jeff Kalousdian, Lars Knudsen, Lubna Azabal, Paradiso, Peter Coyote, Will Shepard


Killer Instinct's 2013 reboot started out as nostalgia-fueled fanservice for die-hard fans of Rare's classic fighter, but after two full "seasons" of content additions it has matured into a fantastic fighting game that can truly stand on its own. The cast is large and amazingly varied. The graphics keep getting better, the fighting is continually improved through balance adjustments and tweaks, and new modes have been added. It isn't an overstatement to say Killer Instinct was a totally different game after Season 2 compared to Season 1. And now it all evolves again with Killer Instinct Season 3.
Something important to note is that Killer Instinct is also now available on Windows 10 PCs, and online multiplayer is cross platform with Xbox One, so you don't have to own an Xbox One to play KI now. Also good news is that if you own Killer Instinct on either platform, you can play it on the other platform – with all of the characters and other stuff you've bought - for free.
Now on to Season 3. Killer Instinct is still technically a free to play game, which means you download the base game for free, which comes with Jago, and then each week a different character is available to try out for free. Whether you buy KI Season 3 or not, your copy of Killer Instinct will be automatically updated to add all of the new updates and enhancements and features and will also allow you to fight against the new characters online even if you don't own them. If you do want to buy KI Season 3 (and of course you do), you can either buy characters a-la-carte for $5 each, or you can buy bundles that include all of the characters plus other goodies.
You can buy the KI Season 3 Combo Breaker Edition for $20, that comes with all 8 Season 3 characters (4 available now, 4 to be released in the future). You can also buy the KI Season 3 Ultra Edition for $40, which comes with all 8 characters plus bonus costumes and colors and other stuff. It has to be noted that the Ultra Edition of Season 3 is a bit of a disappointment compared to the Ultra Editions for Season 1 and 2 considering they came with Killer Instinct 1 and 2 Classic respectively which actually justified their $40 asking price (even if KI 1 and 2 haven't aged particularly well …). KI Season 3's Ultra Edition, on the other hand, is pretty lame since you're paying $20 extra purely for cosmetic stuff. If you care about costumes and colors, by all means, buy the KI Season 3 Ultra Edition. If you don't, there is no reason whatsoever to buy the Ultra Edition so save $20 and just get the Combo Breaker pack.
If you have never purchased any Killer Instinct content yet, you could also consider picking up the brand new Killer Instinct Supreme Edition that includes all of the Killer Instinct Season 1, 2, and 3 characters, plus KI 1 and 2 Classic, and everything else all for $60. Considering all of that content cost twice that much if you bought the Ultra Editions for each season, $60 is a pretty darn amazing price. The game has more than enough content now to justify paying $60, as well, so if you waited this long before jumping into Killer Instinct, the Supreme Edition is definitely the way to go.
What's New In KI Season 3?
New characters in Season 3 are sort of like a Microsoft All-Stars-esque lineup. At launch, classic Killer Instinct 2 characters Kim Wu and Tusk are available, along with The Arbiter from the Halo franchise as well as Rash from Battletoads (play Battletoads in Rare Replay). Coming in the next few months are General Raam from Gears of War, Mira (a new female vampire), and Gargos (the final boss from Killer Instinct 2). The final Season 3 character has yet to be revealed. Also not available at launch but coming soon is a new single-player mode called Shadow Lords, as well as a new multiplayer mode that will tie into Shadow Lords.
In addition to new characters, modes, and stages, Season 3 also brings a ton of balance changes for the existing cast as well as a new visual look. The menus and character select have been overhauled and look better than ever, and I quite like the new purple and green color scheme. The graphics have been touched up as well, and new lighting in the stages really make them pop so you can see all of the detail that went into them. All of the existing cast have been re-balanced and tweaked as well and every old character has a new ability.
One Season 3 addition we're not so keen on is the Combo Assist option. With Combo Assist turned on, you only have to press a single button to use a special move or linker during a combo rather than having to also use the appropriate directional inputs for the move you want to do. You still have to use the right directional input for a special move to start the combo, but once the combo starts, single button presses continue it. The idea is that this eases players into Killer Instinct and lets them see the cool moves and stuff, but it doesn't actually teach them how to play. You still have to time the button presses properly or else you drop the combo, so there is still some technique required, but if you don't have to learn the complicated directional inputs you're not really learning anything.
Killer Instinct is already a very accessible, easy to learn game once you know the basics, and the game basically automatically does combos for you anyway. You still have to put in the appropriate moves at the right time, which you do have to learn, but you can kind of just mash buttons and pull off 15-hit combos without Combo Assist, so using it in hopes of seeing all the flashy moves and combos is pointless – you can do that already. I just think you're better off learning the right way from the start instead of relying on combo assist.
All in all, though, Killer Instinct is only getting better overall with the additions in Season 3. One last thing I want to touch on is how fantastic the cast is. Every character plays differently from the others and range from simple (Jago, Saberwulf, Orchid) on up to incredibly challenging and complicated characters like Aganos, Kan Ra, Hisako, Tusk, and others. Every character controls differently and has a unique style that makes picking up a new character a fresh fun challenge because you have to learn to play all over again. Right now, Killer Instinct has the most diverse cast of genuinely interesting and unique characters of any modern fighting game, which is why it is so fun to keep playing and keep learning. It is the fighting genre at its best, and it keeps getting better with each new mode and character that is added. If you like fighting games at all, you need to play Killer Instinct.


text:
Home Soccer Pep Guardiola and 1000 Barcelona Days – The Numbers
Pep Guardiola and 1000 Barcelona Days – The Numbers
Two and a half years at the helm as FC Barcelona's head coach, 1000 days. Josep Guardiola. A seemingly meteoric rise from Barca's youth team and B team yo being considered one of the top managers in La Liga and Europe. Surely, with the talent that he's had at his disposal anyone can look like a genius, right? I'm not sure. One things is – The numbers following Guardiola's 33 months with the club are incredible.
La Liga Titles – 2 (2009, 2010), the third one is well within grasp, having a four point lead with a game in hand, 11 games before the season ends. Perfect so far.
Champions League – 1 (2009). Barcelona were knocked out by Inter in last season's semi final. Barcelona have reached the quarter finals and are considered the favorites to win it this year.
Copa Del Rey – 1 (2009). Barcelona have reached the final this year as well and will face Real Madrid, the first time since 1990 that both of the Spanish giants will meet in the Spanish Cup Final.
UEFA Super Cup – 1 (2009).
FIFA Club World Cup – 1 (2009).
There's also the Spanish Supercopa (2) but you get the picture. Since his arrival, without changing the personnel radically, Barcelona are back on top of the European game, as they were during Rijkaard's 2005-2006 season. Remember, just about half a decade ago Barca were the fashionable club, with Ronaldinho getting the best-ever comparisons, just like Messi. Things deteriorated quickly with that star studded team, mostly due to a destructive social situation.
Guardiola joined the senior club after two years of finishing behind Real Madrid and that humiliating 4-1 loss at the Bernabeu after the Barcelona player had to give Real a champions welcome. Since Guardiola's coaching the senior side (he was Barcelona B head coach before), Barcelona have won all five matches with Real Madrid, including a 6-2 win at the Bernabeu and the most recent win, a 5-0 demolition with Jose Mourinho on the Real sidelines.
In terms of the match records, Barcelona have played a total of 166 matches in all competitions, winning 122, drawing 29 and losing 15, winning 73.5% of his matches. In the league, Guardiola has coached 103 matches, winning 82, drawing 14 and losing only 7(!!!) in nearly three seasons. They have won 84.1% of the possible points. Style and scoring? This Barcelona side, with the changes it has seen up front (Eto'o-Henry in 2008-2009, Zlatan Ibarhimoic in 2009-2010 and David Villa this year) have scored 419, conceding 121, averaging over 2.5 goals per game.
Barcelona were always a trendy club, known for it's style and commitment to attacking football. The last few years, under Guardiola, it's been taken to another level, which brought Barcelona a lot more neutral fans but also a lot of haters, around the world. Because they really are too good sometimes, almost to a point it isn't fair on some nights (like the way they dominated Arsenal last week). Because it seems they get preferential treatment from the refs and the FA (true. They don't win just because of it, but it certainly helps). Because perfection, which Barcelona do achieve on some nights and afternoons, brings adoration and flattery from those suppose to be objective, and it does get a bit much.
How long will Guardiola stay at the Nou Camp? He's insisting on renewing his one year contract each year, nothing longer. Other plans, countries, roles in mind? As long as his Barcelona machine keeps ticking like it has since his arrival, I don't think he's going anywhere. Bad news for La Liga and Europe.
great head coaches
Los Cules
mes que un club
Previous articleMirco Bergamasco – Hero For a Day
Next articleNBA Saturday Night – Heat, Bulls and Lakers Win


text:
Q: How to update view data on android when change in MySql server? I am develop my android application with Java and Restful API's. The API's server has used MySQL server.
I faced a problem that is, when I change on my server, The view can't updated as per as firebase realtime database. It's work when I go back and open the activity again, or I used onResume method and declare here the code for fetch data.
How can I do it automatically?
Thank you for Advanced.

A: I would personally make it so where the code that changes the data in the database, it also sends a message to the client (I'd have a websocket open for this) saying that there is an update, on receiving this they can re-fetch the api.
You could also make it so that the server sends the updated data but there is a chance what the user sees and the true data desync.
You could also just have the client re-fetch the api every x seconds depending on how often you expect changes to be made but this option really depends on your ccu and resources.

redpajama_set_name: RedPajamaStackExchange


Our experienced Bolingbrook estate planning attorneys will guide you through the creation of your affordable will or trust, your powers of attorney, and healthcare directives. We will give you peace of mind in every aspect of your estate plan and ensure it's tailored to you. We take pride in giving our clientsxactly what we need and guide them thorough their estate planning.
In this video, Bolingbrook estate planning attorney Kevin O'Flaherty describes why O'Flaherty Law is the best choice for your estate planning matter.
We Go Above-And-Beyond! Our Bolingbrook estate planning attorneys want to impress our clients and believe that when you feel like you've received the best representation, you will tell your friends and family about us. This is how we build our business and start the best relationships with our clients. Our support from them has helped us achieve Avvo's Client's Choice Award for Estate Planning in 2016.
We Know Our Stuff! Bolingbrook estate planning attorneys have the skill and experience to provide you with technical estate planning options. We help with advanced and complex estate plans such as estate tax avoidance, creditor avoidance,special needs planning, and medicaid planning.
Bolingbrook estate planning lawyer Kevin O'Flaherty explains estate planning for minor children.
Using trusts to create a long-term plan for the distribution of your children's inheritance.
Read the full article by our Bolingbrook estate planning attorneys explaining estate planning for minor children.
In this article, our Bolingbrook estate planning lawyers explain powers of attorney in estate planning. Generally, if you become mentally incompetent through old age, disease, or accident, your loved ones will have to institute a guardianship court case in order to gain the power to make financial and major life decisions on your behalf. Guardianship cases can be stressful and costly. Fortunately, if you execute power of attorney forms before you become mentally incompetent, a guardianship case will be unnecessary. A financial power of attorney allows you to name a loved one to manage your finances if you are no longer competent to do so. A healthcare power of attorney allows you to name a loved one to make non-financial decisions on your behalf.
Read the full article by our Bolingbrook estate planning lawyers explaining powers of attorney in estate plans.
Bolingbrook estate planning attorney Kevin O'Flaherty explains the use of powers of attorney in an estate plan.
Bolingbrook estate planning lawyer Kevin O'Flaherty explains how to plan for distribution of your assets through wills and trusts.
In this article, our Bolingbrook estate planning attorneys explain how we can use revocable living trusts and wills to plan for distribution of our assets when we pass. We discuss what happens if you die without a will or a trust in place, and the differences between a will and a trust with respect to asset distribution. Finally we explain some situations in which planning for asset distribution is often a particular concern, including clients who are divorced with minor children, who are estranged from a family member, who are interested in charitable giving, or who do not want their assets distributed in a single lump sum to minor or young adult children.
Read the full article by our Bolingbrook estate planning attorneys explaining how to plan for the distribution of asses with a will or a trust.