Environmental Engineering Reference
In-Depth Information
Figure 4.5 Measured cross section [50] for D-T
-
T reaction (solid curve) compared to resonant
tunneling model (
þ
) and measured values for D
-
D reaction (circles).
m
for fusion of the D particles
is about 1.5 ns, based on detecting the neutrons that are emitted by the fusion. It is
also known that during the 2200 ns lifetime of a single muon in a dense deuterium
gas several hundred cycles of molecule formation and fusion can occur!
The DD
It is experimentally known that the lifetime of the DD
ion can be understood by scaling the properties of the HHe (H
2
þ
) ion as
described in Equations 3.36
-
3.39. The scaling of the Bohr radius and Bohr energy
leads to an equilibriumspacing
R
m
648 f. The binding energy of the
scaled ion is 519.4 eV. (We will see later in this chapter that this binding energy is
reduced by about half by the positive con
¼
r
e
¼
2.4
a
o
/196
¼
nement energy of the vibrational motion.)
Following the discussion of Equation 3.38a, we equate the energy
E
with the
potential sketched in Figure 4.5. First estimate the vibrational frequency
v¼
(
E
00
/
m
red
)
1/2
, where the curvature
E
00
¼
d
2
E
/d
r
2
. We scale the curvature quantity
d
2
E
d
r
2
E
00
ð
a
2
ð
r
e
Þ=
¼
r
e
Þ¼
0
:
1257
E
o
=
ð
4
:
13
Þ
m
with Bohr energy and Bohr radius to get the DD
oscillation frequency
E
00
=
1
=
2
610
19
67 10
27
1
=
2
10
17
s
1
v ¼ð
m
red
Þ
¼ð
0
:
1257 13
:
6 196 1
:
=
1
:
Þ
=
270
¼
6
:
64
:
ð
4
:
14
Þ
