Indian Journal of Pure & Applied Physics
Vol. 51, October 2013, pp. 696-700
Measurement and evaluation of the excitation functions in (Į,xn) reactions on
Tantalum from 20 to 80 MeV
Damewan Suchiang, J Joseph Jeremiah & B M Jyrwa*
Department of Physics, North Eastern Hill University, Shillong 793 022, Meghalaya, India
*E-mail: [email protected]
Received 24 September 2012; revised 21 March 2013; accepted 21 June 2013
The excitation function for (Į,xn) reactions from 20 to 80 MeV on Tantalum have been calculated using TALYS-1.2
nuclear model code involving the fixed set of global parameters. Level density parameter is varied to get good agreement
between the calculated and measured data with minimum effort on parameter fitting. This is of importance required for the
validation of nuclear model approaches with increased predictive power. The alpha induced cross-sections provide clues to
the problem of nuclear structure and offer the testing ground for ideas about nuclear forces. Accurate knowledge of crosssection in alpha induced reaction at energy levels where resonance occurs is crucial while designing nuclear reactors.
Keywords: Tantalum target, Alpha reactions, Excitation function, Level density, Pre-equilibrium
1 Introduction
Using TALYS-1.2 Nuclear Reaction Code, the
excitation curves for the (Į,xn) reaction on natural Ta
have been calculated. The main purpose of the present
work is to check the predictive power of the nuclear
model calculations on the excitation functions and
understand the mechanisms of compound nucleus and
pre-equilibrium models over the alpha projectile
energy from 20 to 80 MeV.
Intermediate-energy fission data are of interest not
only for understanding fundamental physics, but also
for applied nuclear research. First of all, it is
connected with problems of Accelerator Driven
Systems (ADS) for power production and
transmutation of long-lived radioactive waste1. Such
elements like Ta, Pb and Bi are either already used as
neutron producing target materials or considered as
potential candidates. Since fission and spallation
reactions at intermediate energies are the main
reaction channels of neutron interactions with heavy
nuclei, they have the most practical significance, but
are poorly investigated. Fission reaction contributes to
the generation of the neutron field in the targetblanket assembly, as well as to the production of
radionuclide and chemically toxic products in the
target.
One of the key and the most strained elements of
ADS is the target, which is designed to generate the
maximum amount of neutrons and remove the heat
releasing in inter nuclear cascade. This heat power is
usually 60-70% of the proton beam power. The target
is usually located in a heavy-water blanket, where
high thermal neutron flux density is achieved. One of
the most stressed components of ADS is the spallation
target which is designed to generate the maximum
amount of neutrons while ensuring the removal of the
heat released in the spallation process. As the proton
beam power being deposited in such a target attains
several MW, even up to about 20 MW, very high
power densities of several hundreds of kW per litre,
occurring in the structure and in the spallation
material, need to be safely removed. In addition, the
mixed proton-neutron irradiation field in the target
imposes very specific conditions on the design and
operability of the target and influences strongly all the
thermo-mechanical options for such targets. Gas,
heavy water or liquid metals are under consideration
as coolants for these targets. At present, only solid
targets are used in operating spallation neutron
sources. They are usually assemblies of rods or disks
fabricated from Ta, W, or U and cooled with heavy
water.
2 Tantalum Target
A major use of Ta is in constructing structural
material in nuclear reactor cores, specifically requires
for the first wall of fusion reactors and component
parts of irradiation chambers2 and in medical
prosthetic devices for nuclear medical applications.
Irradiation of bulk fusion materials produces damage
and induced radioactivity. Ta is interesting, as
component material in irradiation chambers due to the
SUCHING et al.: EXCITATION FUNCTIONS IN (α,xn) REACTIONS ON TANTALUM
large stopping power and the low neutron yield at low
bombarding energies3. The physical property of Ta
enables it to be used as an alloy additive and is
frequently combined with Nb to increase Nb's
corrosion resistance properties. When mixed with
alloys such as Nb, it has excellent resistance to a wide
variety of corrosive environment. These environments
include mineral acids, most organic acids, most salts
and liquid metals. These characteristics are applied to
prevent damage to solid state detectors and reduce
neutron back ground in neutron detection. Control of
wear, corrosion and erosion by Thin Layer Activation
method (TLA) requires accurate knowledge of
excitation functions, also of longer-lived products4.
Accurate knowledge of cross-section data for alpha
induced reactions on Ta are also of great importance
for thermo-nuclear reaction rate determination, since
the models used in the study of stellar nucleosynthesis
are strongly dependent on these rates5. Another
important field of the application of these activation
cross-section data is the TLA which is widely used for
measuring material losses during wear, corrosion and
erosion. Ta is practically mono-isotopic, it is a
‘‘plastic’’ metal with a high melting point and high
thermal conductivity and is relatively cheap and has
good physical and chemical properties making it
nearly ideal for thin foil target preparation. Ta has
good resistance to molten metals, hence it is used as
crucibles and casting molds. It is one of the few
metals to resist attack by molten Pu and is widely
used as casting molds and nozzles used for casting
this material. Due to the above nature of Ta, extensive
investigations of alpha induced nuclear reactions have
been done for studying the contributions of the
equilibrium and pre-equilibrium to the reaction
mechanism6-8. The properties of Ta make it also an
ideal target material for production of different
radioisotopes used in nuclear medicine.
3 Nuclear Models
TALYS-1.2 is a nuclear reaction program, which
provides a complete and accurate simulation of
nuclear reactions in the range 1KeV-200MeV incident
energy, for target mass number between 12 and
heavier elements and treats n,Ȗ,p,d,t,h and Į as
projectiles and ejectiles. In the input file, all the
choices can be made and many models and
parameters can be adjusted such as the level density
parameter, optical model, compound nucleus reaction
and pre-equilibrium mechanisms. Much of the
information regarding the choices of input parameter,
nuclear models and level density parameters are
697
described and explained in detail in the TALYS user
manual9,10. Since nuclear model calculations and fits
to experiments generally require many adjustable
parameters, it is important that these parameters all
remain within physically acceptable limits. In
statistical models for predicting cross sections,
nuclear level densities are used at excitation energies
where discrete level information is not available or
incomplete. Level density plays an important role in
calculating the nuclear reaction model statistically,
such as in calculating the evaporation model of
nuclear reaction, spallations reaction measurements,
and in studies of intermediate-energy of heavy ion
collision11. Although there are some theoretical
approaches that have been developed to study the
level density12-14, one of the parameters that holds
very important role in the level density calculation is
the Level Density Parameter 15 (LDP). The commonly
use of level density parameter is the energy dependent
value16,17. The asymptotic value of the LDP is reached
at the infinite excitation energy18. With this approach,
the variation of its LDP value is small. This is caused
by the highly excitation states. This approach is
different from the shell correction approach, which
gives bigger value of the variation of the LDP. Shell
correction is a result of the difference between nuclear
mass experiment and semi-empirical nuclear mass19.
In level density study, semi-empirical nuclear mass is
influenced mainly by pair and shell correction. In
shell correction, fission barrier determines the
variation value of eigen energy to smooth curve parts.
We use several models for the level density in
TALYS, which range from phenomenological
analytical expressions, to tabulated level densities
derived from microscopic models. The level density
ρ ( E x , J , Π ) corresponds to the number of nuclear
levels per MeV around excitation energy Ex for
certain spin J and parity ɉ. The total level density
ρ tot ( E x ) corresponds to the total number of levels
per MeV around Ex, and is obtained by summing the
level density over spin and parity:
ρ tot ( E x ) = ¦¦ ρ ( E x , J , Π )
j
…(1)
π
The nuclear levels are degenerate in M, the
magnetic quantum number, which gives rise to the
total state density Ȧtot(Ex) which includes the 2J+1
states for each level, i.e.:
ω tot ( E x ) = ¦¦ ( 2 J + 1) ρ ( E x , J , Π )
j
π
…(2)
INDIAN J PURE & APPL PHYS, VOL 51, OCTOBER 2013
698
when level densities are given by analytical
expressions they are usually factorized as follows:
ρ ( E x , J , Π ) = P ( E x , J , Π ) R ( Ex , J ) ρ tot ( E x )
…(3)
where P(Ex,J,ɉ) is the parity distribution and R(Ex,J)
is the spin distribution.
For the level density calculations, Fermi Gas Model
has been used. The Fermi Gas Model20 is an
independent particle model with additional
approximation which consists in assuming that the
single particle states are equally distributed. In the
Fermi Gas Model, the density of single particle states
for a nucleus with fermions, if the Z protons and N
neutrons of the nucleus are distinguished,it reads:
ω Ftot ( E x ) =
π exp ª¬ 2 aU º¼
a1/ 4U 5/ 4
12
…(4)
with U defined by
…(5)
U = Ex − ∆
where ∆ is the energy shift, the underlying idea is that
∆ account for the fact that pairs of nucleons must be
separated before each component can be excited
individually. Eq. (5) also contains the level density
parameter a which is given by:
π2
…(6)
( gπ + g v )
6
where gπ and gv denote the spacing of proton and
neutron single particle states near the Fermi energy.
The value of level density is approximated by the
following formula21:
a=
ª § δW ·
−γ U º
a = ã «1 + ¨
¸ 1− e
»
¬ © U ¹
¼
(
)
…(7)
where ã is the asymptotic level density parameter of a
at high excitation energy U one would obtain in the
absence of any shell effects, i.e. ã = a(Exĺ∞) in
general, but also ã = a(Ex) for all Ex if δW=0. The
damping parameter Ȗ determines how rapidly a(Ex)
approaches ã. Finally, δW is the shell correction
energy. The absolute magnitude of δW determines
how different a(Ex) is from ã at low energies, while
the sign of δW determines whether a(Ex) decreases or
increases as a function of Ex.
The asymptotic value ã is given by the smooth
form:
ã = α A + β A2/3
…(8)
where A is the mass number, Į and ȕ are global
parameters that have been determined to give the best
average level density description over a whole range
of nuclides. The α and β parameters can be changed
within the input file.
The following systematical formula for the
damping parameter is used,
γ=
γ1
A1/3
+γ2
…(9)
The parameters of γ1,2 can be adjusted in the input
file. We define įW (expressed in MeV), as the
difference between the experimental mass of the
nucleus Mexp and its mass according to the spherical
liquid-drop model mass MLDM (both expressed in
MeV).
For the real mass, we take the value from the
experimental mass compilation22. Following Mengoni
and Nakajima23, for MLDM we take the formula by
Myers and Swiatecki24 mass formula considering a
liquid drop with the shell correlation without pairing
i.e the level density pairing is observed in the binding
energies.
4 Results and Discussion
Alpha particle induced activation cross-sections
have been measured for production of 181,182,183,184Re
on natural Ta target up to 80 MeV. From the
production of cross-section for many contributing
reaction isotopic cross-section can be deduced from
selected energy ranges. This calculation and
experimental data show good agreement. From the
investigated reactions, the 181Ta(Į,2n)183Re reaction
has practical important for applications in TLA due to
very convenient half-life and the production crosssection.
The excitation function for 181Ta is obtained by
varying the level density model and by fine tuning of
the shell damping factor in the input file which gives
a fit close enough to that of experimental data. The
excitation curve for 181Ta(Į,n)184Re is shown in Fig. 1
and is plotted along with EXFOR database.
Investigation carried out by Talys-1.2 indicate that the
emission of neutrons from nuclear systems at
excitation energies beyond a few MeV is caused by
the pre-equilibrium contribution of the system in a
time much shorter than the time for evaporation from
an equilibrated compound nucleus. This is indirectly
indicated by the high-energy tails of the excitation
function which signify a less rapid fall for the crosssection than predicted by the compound nucleus
SUCHING et al.: EXCITATION FUNCTIONS IN (α,xn) REACTIONS ON TANTALUM
699
Fig. 4 — Excitation function for 181Ta(Į,4n)181Re
Fig. 1 — Excitation function for 181Ta(Į,n)184Re
Table 1 — Parameters used in the calculations
Reactions
a
MeV−1
ã
MeV−1
Ȗ
MeV−1
P
MeV
Esh
MeV
181
25.71
25.803
20.413
22.027
21.724
21.724
17.167
18.525
0.243
0.256
0.260
0.260
1.338
1.338
1.338
1.338
1.427
1.427
1.427
1.427
Ta(Į,n)
Ta(Į,2n)
181
Ta(Į,3n)
181
Ta(Į,4n)
181
Fig. 2 — Excitation function for 181Ta(Į,2n)183Re
Fig. 3 — Excitation function for 181Ta(Į,3n)182Re
model. Thus, the emitted neutrons spectra and the
compound nucleus contribution are dominated by low
energy emitted neutrons and the pre-equilibrium
contribution mainly comes from the high energy
emitted neutrons. The excitation curve for
181
Ta(Į,2n)183Re is shown in Fig. 2. All the parameters
are calculated in a similar manner as done for the
previous reaction except the shell damping factor. The
overall agreement between the measured and
calculated cross-section is excellent. The excitation
curve for 181Ta(Į,3n)182Re is shown in Fig. 3. The
observed excitation functions show a high energy tail
following the usual compound nucleus bump at low
energy. The excitation curve for 181Ta(Į,4n)181Re is
shown in Fig 4. In the observed high energy tails of
the excitation function of (Į,xn) reaction, there are the
remarkable signatures of pre-equilibrium contribution
as they show, quite convincingly, a radical departure
from the traditional ‘bell shape’ of the excitation
functions due to compound nucleus mechanism. The
parameters governing the level density model are
presented in Table 1.
5 Conclusions
We have analyzed the excitation function of natural
Ta which is important in the construction material
components in nuclear reactors, required for the first
wall of fusion reactors and component parts of
irradiation chambers with TALYS-1.2 nuclear
reaction code. It is concluded that by choosing the
appropriate level density, and by adjusting the shell
700
INDIAN J PURE & APPL PHYS, VOL 51, OCTOBER 2013
damping factors one can predict (Į,xn) reaction crosssections for natural Ta from ~20 to ~80 MeV closer to
the available experimental data.
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