Proceedings of the 1st Annual Meeting of Particle Accelerator Society of Japanand the 29th Linear Accelerator Meeting in Japan (August 4 - 6, 2004, Funabashi Japan)

Simulation of neutron beam with two accelerators
Kouichi Jimbo
Institute of Advanced Energy, Kyoto University,
Gokasho, Uji, Kyoto 611-0011
Abstract
Physical differences of neutrons and charged particles
are exemplified so that understanding of dual ion beamirradiation technique, in which two accelerator systems
are used, is promoted. Then low energy losing mechanismof charged particles in materials, which is quite different
from that of neutrons, is discussed with a simple model.

1 INTRODUCTION
In nuclear fusion and fission materials research, dual
ion beam irradiation technique is a powerful tool tosimulate synergistic effects of displacement andtransmutation damages introduced by high-energy
neutrons.1 In ordinary situation, it is very difficult to test a
new material in a neutron environment. Two ion beams
that are accelerated charged particles are used tounderstand dynamic behavior of a structural material inplace of a neutron beam.

2 MATERIAL DAMAGE CAUSEDBY NEUTRONS
A neutron collides directly with the nucleus ofatom in the target material. The initial elastic collision of
a neutron with an atom can lead to displacement of atarget nucleus (which received a significant recoil energy
and be displaced from its lattice site). The ejected target
nucleus is called the primary knock-on atom (PKA). The
PKA itself can take the roll of bombarding particle anddisplace other lattice atoms. A branching tree-likestructure of successive collisions is produced and theinitial PKA energy is dissipated. This cascade process ofcollisions ultimately gives rise to a number of changes in
the physical state of the target material.2 The
displacement energy Ed is the minimum energy necessary
to displace an atom permanently from its lattice site.
Displacement per atom (dpa) is a calculated
representation of the fraction of target atoms that are
displaced from their lattice sites as a result of collisions
with incident particles. In the calculation, E d ≈ 25eV iswidely used for any materials as a good approximation.
Neutrons may be replaced with charged
particles kinetically unless charged particles induceadditional chemical reactions in the target material.
Especially useful are self-ions, which are chemically
identical with atoms there. The initial elastic collisions ofcharged particles with atoms can lead to atomic
displacements of target nuclei and PKAs will be created.
Physically PKAs are charged particles and created wheneither a neutron or a charged particle collides with anatom in the target material. However, the damage profilethat 1st PKAs are created is quite different between
neutron and charged particle collisions.

3 PASSAGES OF CHARGED PARTICLESTROUGH MATERIALS
We had to recognize physical difference between
neutrons and charged particles. The cross section for
scattering of a charged particle is known as theRutherford scattering. The motion of a charged particle
through a target material is treated in two energy regions.
They are the high-energy region where atomic electrons
are excited and ionized, and the lower energy region
where collisions with atoms are elastic. In the high energy
region a charged particle loses its energy in collisions
with atomic electrons, in each of which small energytransfer occurs without appreciable path deflection. A
charged particle rarely collides with nuclei directly. The
passage of charged particles (the range) in a target
material is rectilinear. However, in the low energy region,
charged particles displace target atoms and create PKAs if
the kinetic energy is larger than but close to thedisplacement energy Ed. High energy PKAs are rarely
created compared to the case of neutrons. Most of their
damages are done when their energy is close to Ed, whichis rarely discussed in nuclear physics. Charged particlesgave most damages against the target material in lowenergies. Its physical mechanism was not discussed
completely. We are going to discuss about it with asimple model.

4 COLLISIONS WITH A SIMPLE MODEL
4-1 Rutherford scattering formula
Rutherford scattering formula gives following differential
cross section for charged particles,C Z1 Z 2 e 2

dσ
1
=
θ dΩ Ecm 4 sin 2 cm 
2 

E-mail: Jimbo@iae.kyoto-u.ac.jp
1852.

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Proceedings of the 1st Annual Meeting of Particle Accelerator Society of Japanand the 29th Linear Accelerator Meeting in Japan (August 4 - 6, 2004, Funabashi Japan)

ItThe differential cross section of Eq. (1) is not isotropic.
hasespeciallyforwardpeakeddσC→ ∞ as θ cm → 0 ), which indicates that glancingdΩ
collisions are dominant. The integral of this formula over
the total solid angle diverges. As it is well known inplasma physics, the extreme long range character of thecoulomb interaction has serious consequences in practicalapplication.3 Even the coulomb cross section for
momentum transfer diverges, albeit only logarithmicallyif E d → 0 .
(And me is the electron mass and ve is the electronvelocity.

4-2 Massey scattering formula
Massey shows that if polarization effects are ignored
the potential energy of an incident particle of charge Z ata distance r from a ground-state hydrogen atom is give as
follows:4

1

V ( r ) = − Ze 
2+r

1  2r exp  −  .
aB  aB 

(2)

2−9aB =Where= 5.29 × 10 cm .

(3)
me e
When the Born approximation is accurate,5 this formula
gives the shielding field of electron force falling offexponentially with distance.
Massey scattering formula that is thedeferential cross section when a charged particle isscattered by a hydrogen atom is,62( K a + 8)
= 4a ZdΩ( K a + 4)

dσ2H

2222B

2

B

24.

5 DISCUSSIONS
Consider the case that a charged particle (ofcharge Z and atomic mass unit A ) and an electron collidewith a hydrogen atom. If their velocities are the same, theelectron is considered to be an atomic electron of theatom. From Eqs.(4) and (7),dσK = 2k sin

Wherek=pMv=2,2.

K e = 2 k e sinke =pe=42eWhere2B

2B(7)m e ve2.

,

Eng. Design 51-52 (2000) 789-795.
2) C.Ishino:“Shousha sonshou (Japanese)” (TokyoUniversity Publication, 1979) , p25.
3) M.Mitchner and C.H.Kruger,Jr., “Partially Ionizedgases”, (John Wiley & Sons, New York, 1973), p57.
4) H.S.W.Massey,“Negative ions”, (Cambridge universitypress, Cambridge, 1950) 2nd ed.,p5.
5) J.J.Sakurai, “Modern quantum mechanics ”, (AddisonWesley Publishing Company, Inc., New York, 1985),
p386.

Bθ cm2(5)(6)2eZ1) A. Kohyama, Y. Katoh, M. Ando and K. Jimbo, Fusion( K a + 8) .
= 4adΩ( K a + 4)
2

∼ 10 −13

REFERENCES

although it approaches Rutherford scattering formula
asymptotically in large angle scatterings.
On the same way, the deferential cross section
between an electron and a hydrogen atom isHH

(4)

And M is the mass, and v is the velocity of the chargedparticle.
Massey scattering formula does not diverge insmall angle scatterings. The cross section has a finite
value at θ cm → 0 as that of the rigid body scatteringdσ edσ e

1.
(10)
4dΩdΩ
A
We infer from this result that collision with an atomic
electron is dominant compared to collision with a nucleus
when the atom collides with a hydrogen atom. We
approximate atoms in the target material with Massey
scattering formula since it shields the positiveelectrostatic field of nuclei of atoms there. Massey
scattering formula represent more realistic situationcompared to Rutherford scattering formula. In highenergy, incoming charged particles lose most of their
atomic electrons in the target material. However, as theylose energy, they start to pick up electrons there. Finallycharged particles become neutral atoms. Then atomic
electrons of incoming atoms interact with atomic
electrons of the target material. As shown in Eq.(10), theelectron cross-section which represents incoming neutral
atoms is very large compared with the cross section ofincoming charged particles. Therefore, charged particles
turn to be neutral atoms, which gave most damages
against materials in low energies. This explanation isconsistent with observations.

Bθ cmH(8)6) B.H.Bransden and C.J.Joachain, “Physics of atomsand”, (Longman Scientific & Technical.), p509.

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