<s>
In	O
chemistry	O
and	O
physics	O
,	O
the	O
exchange	B-General_Concept
interaction	I-General_Concept
(	O
with	O
an	O
exchange	B-General_Concept
energy	I-General_Concept
and	O
exchange	O
term	O
)	O
is	O
a	O
quantum	O
mechanical	O
effect	O
that	O
only	O
occurs	O
between	O
identical	O
particles	O
.	O
</s>
<s>
Despite	O
sometimes	O
being	O
called	O
an	O
exchange	B-General_Concept
force	I-General_Concept
in	O
an	O
analogy	O
to	O
classical	O
force	O
,	O
it	O
is	O
not	O
a	O
true	O
force	O
as	O
it	O
lacks	O
a	O
force	O
carrier	O
.	O
</s>
<s>
Both	O
bosons	O
and	O
fermions	O
can	O
experience	O
the	O
exchange	B-General_Concept
interaction	I-General_Concept
.	O
</s>
<s>
For	O
fermions	O
,	O
this	O
interaction	O
is	O
sometimes	O
called	O
Pauli	B-General_Concept
repulsion	I-General_Concept
and	O
is	O
related	O
to	O
the	B-General_Concept
Pauli	I-General_Concept
exclusion	I-General_Concept
principle	I-General_Concept
.	O
</s>
<s>
For	O
bosons	O
,	O
the	O
exchange	B-General_Concept
interaction	I-General_Concept
takes	O
the	O
form	O
of	O
an	O
effective	O
attraction	O
that	O
causes	O
identical	O
particles	O
to	O
be	O
found	O
closer	O
together	O
,	O
as	O
in	O
Bose	O
–	O
Einstein	O
condensation	O
.	O
</s>
<s>
The	O
exchange	B-General_Concept
interaction	I-General_Concept
alters	O
the	O
expectation	O
value	O
of	O
the	O
distance	O
when	O
the	O
wave	O
functions	O
of	O
two	O
or	O
more	O
indistinguishable	O
particles	O
overlap	O
.	O
</s>
<s>
Among	O
other	O
consequences	O
,	O
the	O
exchange	B-General_Concept
interaction	I-General_Concept
is	O
responsible	O
for	O
ferromagnetism	O
and	O
the	O
volume	O
of	O
matter	O
.	O
</s>
<s>
Exchange	B-General_Concept
interaction	I-General_Concept
effects	O
were	O
discovered	O
independently	O
by	O
physicists	O
Werner	O
Heisenberg	O
and	O
Paul	O
Dirac	O
in	O
1926	O
.	O
</s>
<s>
The	O
exchange	B-General_Concept
interaction	I-General_Concept
is	O
sometimes	O
called	O
the	O
exchange	B-General_Concept
force	I-General_Concept
.	O
</s>
<s>
However	O
,	O
it	O
is	O
not	O
a	O
true	O
force	O
and	O
should	O
not	O
be	O
confused	O
with	O
the	O
exchange	B-General_Concept
forces	I-General_Concept
produced	O
by	O
the	O
exchange	O
of	O
force	O
carriers	O
,	O
such	O
as	O
the	O
electromagnetic	O
force	O
produced	O
between	O
two	O
electrons	O
by	O
the	O
exchange	O
of	O
a	O
photon	B-Application
,	O
or	O
the	O
strong	O
force	O
between	O
two	O
quarks	B-Operating_System
produced	O
by	O
the	O
exchange	O
of	O
a	O
gluon	O
.	O
</s>
<s>
Although	O
sometimes	O
erroneously	O
described	O
as	O
a	O
force	O
,	O
the	O
exchange	B-General_Concept
interaction	I-General_Concept
is	O
a	O
purely	O
quantum	O
mechanical	O
effect	O
unlike	O
other	O
forces	O
.	O
</s>
<s>
Multiple	O
bosons	O
may	O
occupy	O
the	O
same	O
quantum	O
state	O
;	O
however	O
,	O
by	O
the	B-General_Concept
Pauli	I-General_Concept
exclusion	I-General_Concept
principle	I-General_Concept
,	O
no	O
two	O
fermions	O
can	O
occupy	O
the	O
same	O
state	O
.	O
</s>
<s>
Treating	O
the	O
exchange	B-General_Concept
interaction	I-General_Concept
in	O
the	O
hydrogen	O
molecule	O
by	O
the	O
perturbation	O
method	O
,	O
the	O
overall	O
Hamiltonian	O
,	O
composed	O
of	O
the	O
Hamiltonian	O
of	O
the	O
unperturbed	O
separate	O
hydrogen	O
atoms	O
and	O
the	O
perturbation	O
is	O
:	O
</s>
<s>
Dirac	O
pointed	O
out	O
that	O
the	O
critical	O
features	O
of	O
the	O
exchange	B-General_Concept
interaction	I-General_Concept
could	O
be	O
obtained	O
in	O
an	O
elementary	O
way	O
by	O
neglecting	O
the	O
first	O
two	O
terms	O
on	O
the	O
right-hand	O
side	O
of	O
Eq	O
.	O
</s>
<s>
It	O
follows	O
that	O
the	O
exchange	B-General_Concept
interaction	I-General_Concept
Hamiltonian	O
between	O
two	O
electrons	O
in	O
orbitals	O
Φa	O
and	O
Φb	O
can	O
be	O
written	O
in	O
terms	O
of	O
their	O
spin	O
momenta	O
and	O
.	O
</s>
<s>
If	O
Jab	O
is	O
positive	O
the	O
exchange	B-General_Concept
energy	I-General_Concept
favors	O
electrons	O
with	O
parallel	O
spins	O
;	O
this	O
is	O
a	O
primary	O
cause	O
of	O
ferromagnetism	O
in	O
materials	O
in	O
which	O
the	O
electrons	O
are	O
considered	O
localized	O
in	O
the	O
Heitler	O
–	O
London	O
model	O
of	O
chemical	O
bonding	O
,	O
but	O
this	O
model	O
of	O
ferromagnetism	O
has	O
severe	O
limitations	O
in	O
solids	O
(	O
see	O
below	O
)	O
.	O
</s>
<s>
Although	O
these	O
consequences	O
of	O
the	O
exchange	B-General_Concept
interaction	I-General_Concept
are	O
magnetic	O
in	O
nature	O
,	O
the	O
cause	O
is	O
not	O
;	O
it	O
is	O
due	O
primarily	O
to	O
electric	O
repulsion	O
and	O
the	B-General_Concept
Pauli	I-General_Concept
exclusion	I-General_Concept
principle	I-General_Concept
.	O
</s>
<s>
Exchange	B-General_Concept
energy	I-General_Concept
splittings	O
are	O
very	O
elusive	O
to	O
calculate	O
for	O
molecular	O
systems	O
at	O
large	O
internuclear	O
distances	O
.	O
</s>
<s>
Normally	O
,	O
exchange	B-General_Concept
interactions	I-General_Concept
are	O
very	O
short-ranged	O
,	O
confined	O
to	O
electrons	O
in	O
orbitals	O
on	O
the	O
same	O
atom	O
(	O
intra-atomic	O
exchange	O
)	O
or	O
nearest	O
neighbor	O
atoms	O
(	O
direct	B-General_Concept
exchange	I-General_Concept
)	O
but	O
longer-ranged	O
interactions	O
can	O
occur	O
via	O
intermediary	O
atoms	O
and	O
this	O
is	O
termed	O
superexchange	B-General_Concept
.	O
</s>
<s>
as	O
estimated	O
from	O
the	O
Curie	O
temperatures	O
via	O
TC	O
≈	O
2⟨J⟩	O
/3kB	O
where	O
⟨J⟩	O
is	O
the	O
exchange	B-General_Concept
interaction	I-General_Concept
averaged	O
over	O
all	O
sites	O
)	O
.	O
</s>
<s>
rare-earth	O
systems	O
)	O
,	O
the	O
Ruderman	O
–	O
Kittel	O
–	O
Kasuya	O
–	O
Yosida	O
(	O
RKKY	B-General_Concept
)	O
model	O
is	O
the	O
currently	O
accepted	O
mechanism	O
.	O
</s>
