Numerical study of nuclear collisions induced by superintense ultrashort laser pulses incident
on aligned molecules
Miaochan Zhi
*
and Alexei V. Sokolov
Department of Physics and Institute for Quantum Studies, Texas A&M University, College Station, Texas 77843-4242, USA
Received 20 April 2009; published 20 August 2009
We propose a possible way to realize nuclear fusion, via an approach which involves aligned molecules. We
compare results from quantum and classical simulations of two nuclei originating from an HT molecule
moving under a superintense field intensities approaching 10
23
W / cm
2
and ultrashort few-femtosecond,
single-cycle laser pulse. Classical simulations show that when the field is strong enough, it may make the
nuclei collide with high kinetic energy needed to overcome the Coulomb barrier, therefore leading to fusion. A
quantum-mechanical calculation solving the Schrödinger equation displays analogous behavior and reveals
additional information about the wave packet evolution around the collision point.
DOI: 10.1103/PhysRevA.80.023415 PACS numbers: 34.80.Qb, 42.62.-b, 33.80.-b
I. INTRODUCTION
Nowadays, laser-induced nuclear reactions have been
demonstrated by taking advantage of the intense laser field,
as reviewed by Ledingham et al. 1. The fusion reaction
occurs when two nuclei approach within about 10
-15
m,
where the strong-force attraction between the nuclei over-
comes the electrical repulsion. Such close encounters only
occur when nuclei collide with sufficient kinetic energy.
Laser-driven fusion was proposed long time ago 2. Most of
the present-day techniques for laser-controlled fusion rely on
production of hot plasma. One scheme which is being exten-
sively studied in recent years uses interaction of intense laser
pulses with atomic clusters, and has been shown to produce
high flux of fusion neutrons 3. In those experiments, a
short-pulse laser field expels electrons from a cluster, which
then explodes due to strong Coulomb forces. The laser-
cluster interactions are quite efficient at converting laser en-
ergy to ion energy. Zweiback et al. have carried out detailed
studies of femtosecond laser-driven deuterium clusters ex-
plosions which can be energetic enough to drive nuclear fu-
sion 4.
We consider collisions within pairs of nuclei that originate
from aligned molecules. In this well-controlled configuration
the individual nuclei are driven into each other directly by
the laser field electrons are assumed to be removed early in
the rising pulse edge. The basic idea was proposed in our
earlier paper 5. We considered the possibility for energetic
nuclear collisions in a gas of molecules driven by a super
intense field intensities approaching 10
23
W / cm
2
and ul-
trashort few-femtosecond, single-cycle laser pulse which
might be available in the near future 6–8. This proposal
relied on the fact that nuclei of different masses would ac-
quire different velocities when driven by the same electric
field. When the field is strong enough, it would make the
nuclei collide with high kinetic energy needed to overcome
the Coulomb barrier. In that paper we presented results of a
classical simulation of nuclear collisions for molecules HT
and DT exposed to ultrashort intense laser fields. Our results
showed that the collisions occur on a subattosecond time
scale, during which the nuclei experience large acceleration
and emit zeptosecond bursts of light. A related idea was con-
sidered by Chelkowski et al. who performed a theoretical
calculation of nuclear fusion of muonic molecules controlled
by superintense laser fields 9,10.
The present paper extends our previous theoretical inves-
tigation to a fully quantum-mechanical calculation. We cal-
culate the wave function dynamics for two nuclei of unequal
mass in a strong laser field and use classical trajectories as a
reference. The quantum calculation enables us to see the
wave packet behavior at the collision point, and can also
easily allow incorporation of magnetic field effects if a
space-dependent vector potential is used.
Please note that collective effects are not taken into ac-
count in our calculations described below. Fast ejection of
electrons resulting in strong fields acting on nuclei, laser-
driven plasma dynamics, and other important and fascinating
collective phenomena 11 are all beyond the scope of our
present work.
II. QUANTUM-MECHANICAL CALCULATION
We consider a system of two nuclei driven by an electro-
magnetic field. Even though for two charged particles of
equal mass an analytical solution exists, when the two
masses are unequal a numerical solution is necessary. The
Hamiltonian for the relative motion of the two charges in a
laser field with vector potential A is
H =
1
2m
1
p
1
-
q
1
A
c
2
+
1
2m
2
p
2
-
q
2
A
c
2
+
q
1
q
2
R
. 1
Let R = r
1
- r
2
, R
cm
=
m
1
R
1
+m
2
R
2
m
1
+m
2
, p =
m
2
p
1
-m
1
p
2
m
1
+m
2
, p
cm
= p
1
+ p
2
,
M = m
1
+ m
2
, =
m
1
m
2
m
1
+m
2
, q =
q
1
m
1
-
q
2
m
2
, we get
H =
p
2
2
-
qp · A
c
+
q
1
q
2
R
+
A
2
2c
2
q
1
2
m
1
+
q
2
2
m
2
+
p
cm
2
2M
-
2p
cm
qA
cM
.
2
The last two terms are related to the center of mass energy.
Therefore in the center of mass frame the Hamiltonian can be
written as 12
*
mczhi@neo.tamu.edu
PHYSICAL REVIEW A 80, 023415 2009
1050-2947/2009/802/0234156 ©2009 The American Physical Society 023415-1