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ORIGINAL PAPER
Energy dependence of pre-equilibrium emission for the (p,xn)
reactions in niobium
I A Rizvi
1
, K Kumar
1
*, T Ahmad
1
, A Agarwal
2
and A K Chaubey
3
1
Department of Physics, Aligarh Muslim University, Aligarh 202002, Uttar Pradesh, India
2
Department of Physics, Bareilly College, Bareilly 243005, Uttar Pradesh, India
3
Department of Physics, Addis Ababa University, P.O. Box 1176, Addis Ababa, Ethiopia
Received: 22 January 2011 / Accepted: 21 February 2012 / Published online: 24 June 2012
Abstract: Proton induced reactions have been studied in the energy region from &7.0 to 12.5 MeV for niobium, using
the stacked foil activation technique followed by gamma ray spectroscopy. The excitation functions for the production of
93m
Mo,
93m
Nb and
89g
Zr have been determined. The experimental data have been compared with theoretical calculations
based on compound reactions in statistical equilibrium as well as on pre-equilibrium reactions.
Keywords: Excitation functions; Nuclear reactions; Niobium; Proton induced reactions; Stacked foil activation
technique; Pre-equilibrium emission; GDH model
PACS Nos.: 25.40.-h; 25.70.Gh
1. Introduction
Nuclear reaction cross-section data are generated by
nuclear physics experiments and also by nuclear theory
model codes [1]. To determine the optimum irradiation
condition for the production yield of various radioisotopes
more and more experimental nuclear reactions cross-sec-
tion data are needed. These reaction cross-sections are also
in demand in order to know the transmutation probabilities
for the proposed accelerator driven systems [2] popularly
known as energy amplifiers. Though several investigations
[3] are available in literature for the determination of
reaction cross-sections related to the production of radio-
nuclides, there are large discrepancies in the cross-sections
measured for the same reaction by different authors.
Besides, analysis of these excitation functions in the past
has been carried out on the basis of compound nucleus
(statistical equilibrium) model and in general this mecha-
nism of reaction could not account for the high energy tails
of the excitation functions.
The possibility of particles being emitted after the first
stage of nuclear interaction but long before the establish-
ment of statistical equilibrium (pre-equilibrium [PE]
emission) has been the point of interest for the last several
years [4–6]. Many attempts have been made to understand
such reactions. Starting from the pioneer work of Griffin
[7], which provides the first explanation spectral shapes of
the excitation function in the frame work of exciton model,
many other semi-classical models have been proposed [8–
12]. The hybrid and geometry dependent hybrid (GDH)
models proposed by Blann [10,11] have been found to be
relatively simple and closed form models for the successful
reproduction of the experimental data.
In this context, a careful and systematic study of exci-
tation function and a comparison with the predictions of
some of these models would help the understanding of the
intricate mechanism of PE emission. With this motivation,
the present work was undertaken to measure the excitation
functions for residues
93m
Mo,
93m
Nb and
89g
Zr in
93
Nb
proton interaction. Though present measurements were
done up to 12.5 MeV beam energy but comparison of
theory with literature values [13–20] has been made up to
30 MeV, to see the PE effect. As a matter of confidence the
relative intensities of the identified c-rays have also been
measured.
*Corresponding author, E-mail: kamalkumar1908@gmail.com
Indian J Phys (October 2012) 86(10):913–918
DOI 10.1007/s12648-012-0134-y
2012 IACS
2. Experimental details
2.1. Target preparation
A spectroscopically pure niobium target was made of thick-
ness &10.5 mg/cm
2
,withpurity&99.99 %. The niobium
foil was cut into pieces of size 1.5 cm 91.5 cm, and each of
them was glued to an aluminum frame, having a circular hole
of diameter 1.2 cm in its centre. Energy degrader aluminum
foils of thickness &13.5 mg/cm
2
were sandwiched between
the niobium foils whenever required, so as to get the wide
range of energy of desired proton beam incident on each foil.
2.2. Irradiation
The stack comprising of eight target and degrader foils was
irradiated for about 30 min with a &12.5 MeV diffused
proton beam of diameter &5 mm, at the Variable Energy
Cyclotron Centre, Kolkata, India. The beam energy was
determined from a curve that related to the cyclotron RF
with energy constructed from experimental data on elastic
scattering. The energy of the proton particle after travers-
ing half of the thickness of each target foil was computed
from the stopping power table of Northcliffe and Schilling
[21]. A typical experimental set up for the stack irradiation
is shown in Fig. 1.
2.3. Flux measurements
During the irradiation of the stack, the counting of the incoming
proton particles was done from an integrated beam charge. The
beam was totally stopped in the electrically insulated irradia-
tion heads serving as a kind of Faraday Cup [22]whereelec-
trons were prevented from escaping. Using this charge, flux
was calculated. Copper foil of thickness &10.68 mg/cm
2
was
used as a flux monitor [23] for checking the flux and good
agreement was found with \10 % discrepancy.
2.4. Efficiency and energy calibration
The efficiency and energy calibration of the HPGe detector
was employed using various standard sources, i.e.,
22
Na,
57
Co,
60
Co,
133
Ba and
152
Eu of known strengths. The
geometry dependent efficiency (e
G
) of the detector for
different source detector distances was computed using the
relation [24]
eG¼Cekt=Sohð1Þ
where Cis the number of counts per second under the
photo peak, his the absolute intensity of the relative
gamma ray, kand S
o
are the decay constant and strength of
the source at the time of its manufacture respectively, tis
the time lapse between the date of manufacture of the
source and the time of experiment. The values of hand k
were taken from the Table of Radioactive Isotopes, by
Browne and Firestone [25]. The values of e
G
thus obtained
were plotted as a function of energy using the program
origin 6.0. A polynomial of degree 4 having the following
form was found to give the best fit for these curves.
eG¼a0þa1xþa2x2þa3x3þa4x4ð2Þ
where a
0
,a
1
,a
2
,a
3
and a
4
are the coefficients having
different values for different source detector distances.
xBeing the energy of the characteristic c-ray. A typical
geometry dependent efficiency curve of the 100 cm
3
HPGe
detector obtained at a particular distance from the detector
surface is shown in Fig. 2.
Fig. 1 Typical experimental setup for stack irradiation with proton
beam
Fig. 2 Geometry dependent efficiency curve of the 100 cm
3
HPGe
detector at a particular source to detector surface distance
914 I A Rizvi et al.
2.5. Recording of gamma ray spectra and identification
of reaction residue
After the irradiation of the stack, the characteristic c-
activities induced in the individual foils were recorded with
a high resolution (&2 keV for 1,332 keV c-ray of
60
Co)
HPGe detector coupled to the ORTEC PC based multi-
channel analyzer. The counting geometry was chosen by
adjusting the target detector surface separation in such a
way that the dead time remains less than 10 %. Evapora-
tion residues were identified using their characteristic
gamma rays adopted from the Table of Radioactive Iso-
topes by Browne and Firestone [25].
2.6. Formulation
The activation cross-section was computed using the fol-
lowing expression [26].
rðEÞ¼ Akexpðkt2Þ
No/ðeGÞhK½1expðkt1Þ½1expðkt3Þ
ð3Þ
where K=[1 -exp (-ld)]/(ld) is the correction factor
for the self-absorption of gamma rays in the sample of
thickness d(g/cm
2
) and of absorption coefficient l(cm
2
/g).
Ais the counts under the photo peak of the characteristic
gamma ray, kis the decay constant of the residual radio-
isotope, N
o
is the number of nuclei in the sample, his the
absolute intensity of the characteristic c-ray, e
G
is the
geometry dependent efficiency of the HPGe detector, /is
the average flux of the incident proton beam, t
1
is the
irradiation time, t
2
is the time lapse between stopping the
beam and start of counting, and t
3
is counting time.
3. Experimental results
The spectroscopic data of identified gamma rays are given
in Table 1. Other details viz. residual nucleus, Qvalue, half
life, gamma ray energies, and corresponding intensities are
also given in Table 1.TheQvalues of different reactions
were taken from Atomic Data Nuclear Data Tables by
Wapstra and Bos [27] and other decay data from Table of
Radioactive Isotopes by Browne and Firestone [25]. To
check the identification of the gamma rays, the relative
intensities of detected gamma rays have been calculated. It
can be seen from Table 1that the measured relative
intensities are in good agreement with their respective lit-
erature values [25].
The activation cross-section for the same reaction has
been calculated from the intensities of the various identi-
fied c-rays emitted from the same residual nucleus. The
reported value has been taken as the weighted average [28]
of the various cross-section values so obtained. The overall
error in the present measurement is estimated to be £38 %
including the statistical errors. The measured cross-sections
for the population of residues
93m
Mo,
93m
Nb and
89g
Zr are
presented in Table 2.
4. Model calculations
The excitation functions have been evaluated theoretically
using the computer code ALICE-91 [29]. This code
employs the Weisskopf–Ewing model [30] for statistical
component and GDH model of Blann [11] for the PE
emission. Since several authors have already discussed the
code and the theories involved, we restrict ourselves here
by referring only to the review of Blann [12] on PE decay.
Table 1 Spectroscopic data and measured relative intensities of gamma rays
c-Rays
Energy (kev)
Absolute abundance (h)[15] Normalized relative intensity
Present measurement Literature value [15]
Reaction
93m
Nb(p,n)
93
Mo, t
1/2
of product nucleus 6.85 h, Qvalue -1.20 MeV
114 0.0067 7.1 ±0.5 6.8
263 0.5676 627.1 ±2.6 569.0
685 0.9968 1000.0 ±4.6 1000.0
a
1363 0.0078 7.9 ±1.0 7.9
1477 0.9900 999.6 ±5.6 994.0
Reaction
93
Nb(p,pn)
92m
Nb, t
1/2
of product nucleus 10.15 days, Qvalue -8.816 MeV
934 0.9900 …100.0
Reaction
93
Nb(p,an)
89g
Zr, t
1/2
of product nucleus 3.268 days, Qvalue -5.498 MeV
909 0.9901 …100.0
a
Normalization has been done with respect to this value from literature
Energy dependence of pre-equilibrium emission 915
In this code, the level density parameter constant Kmay be
varied to match the experimental data. In the present cal-
culations, a value of K=8 has been found to reproduce
experimental data satisfactorily. For the PE calculations the
initial exciton number (n
0
) was taken to be 3 (1p ?1n ?
1h) as it was derived from the investigation of nucleon
spectra [31].
5. Results and discussion
The measured excitation functions together with the litera-
ture values [13–20] and ALICE-91 [29] calculations are
shown in Figs. 3,4and 5. The excitation function of the
93
Nb(p,n)
93m
Mo reaction, measured in this work (Fig. 3),
was found to be in good agreement with the values reported
by Levkovskij [15], Avila-Rodriguez et al. [16] and Ditroi
et al. [17]. The data of Albert [13], Chodil et al. [14], Singh
et al. [18] and Kiselev and Faizrakhmanova [19] for this
nuclear reaction shows considerable discrepancies in the
magnitude of cross-section values. A better agreement in the
trend of the excitation functions of our measured data and
the literature values was found when executing theoretical
calculations using GDH model (solid line) [11]. The theo-
retical and the experimental data for the
93
Nb(p,pn)
92m
Nb
reaction is shown in Fig. 4. The good agreement between the
experimental data and the theoretical values was found when
executing GDH model (solid line) calculations using the
ALICE-91 code. However, discrepancies in the magnitude
of cross-section values are evident between the data reported
by Levkovskij [15] and Kiselev and Faizrakhmanova [19].
Figure 5shows the excitation function of
93
Nb(p,an)
89
Zr
reaction. As can be seen from Fig. 5, discrepancies in the
magnitude of cross-section values are evident between the
data reported by different groups [15–17,19] Again, the
trend of the excitation functions of literature values and
theoretical values in the high energy range agree with the
ALICE-91 [29] GDH Model calculations (solid line) except
with data of Kiselev and Faizrakhmanova [19].
The present analysis indicates clearly the presence of
significant PE contributions in proton induced reactions.
The PE fraction (f
PE
) is a measure of the relative weight of
Table 2 Experimental cross-sections for (p,n) (p,pn) and (p,an)
reactions
Cross-section (mb)
Projectile energy
(MeV)
(p,n)
93m
MO (p,pn)
92m
Nb (p,an)
89g
Zr
7.2 5.7 ±0.6
8.0 9.9 ±0.6
8.7 15.1 ±0.9
9.8 18.6 ±1.1
10.6 22.9 ±1.0
11.2 26.7 ±1.4
11.9 30.4 ±2.0 1.2 ±0.4 0.4 ±0.08
12.5 31.2 ±1.4 1.3 ±0.5 0.2 ±0.05
Fig. 3 Experimental and theoretical excitation function for the
93
Nb(p,n)
93m
Mo reaction
Fig. 4 Experimental and theoretical excitation function for the
93
Nb(p,pn)
92m
Nb reaction
Fig. 5 Experimental and theoretical excitation function for the
93
Nb(p,an)
89g
Zn reaction
916 I A Rizvi et al.
the PE contribution needed for the reproduction of exci-
tation functions and it reflects the relative importance of PE
and equilibrium processes. It is more meaningful to look
for the total PE fraction of all type of emitted particles [32].
In a given target nucleus the total PE fraction, for all types
of reactions like (p,xn) reactions, are calculated using the
ALICE-91 [29] code. Because of the considerable contri-
butions to the PE fraction from the PE emission of charged
particles, the calculated total PE fraction are not directly
comparable with the measured excitation functions for
(p,xn) type reactions. However, no definite trend for the
variation of the PE fraction with the excitation function
energy or compound mass number and changes in initial
exciton number are reported [32], yet it is reasonable to
assume that f
PE
depends on the excitation energy of the
compound system [12]. In the present calculations, the f
PE
is inherently energy dependent. This dependence is derived
from consideration of the internal transition rates and of the
continuum decay rates. The f
PE
has been taken to be pro-
portional to the cumulative sum of the probability of
finding the particle in the continuum for every possible
configuration during the process of equilibrium. The cal-
culation f
PE
for the system
93
Nb is shown in Fig. 6,asa
function of bombarding energy in the energy ran-
ge &7–30 MeV. It can be seen that the f
PE
increases with
incident proton beam energy.
6. Conclusions
In general, it is evident from Figs. 3,4and 5, that PE
emission of multi-particles is necessary before the system
is equilibrated and hence the experimentally observed high
energy tail of the excitation function can be explained only
when the combination of semi-classically treated PE
emission GDH model followed by particle evaporation
from the equilibrated system (Weisskopf–Ewing model) is
taken into account. The pure equilibrated reaction in its
decay is unable to explain the experimental data in the high
energy tail portion of the excitation function. It is clear
from Figs. 3,4and 5that calculated values shown by
broken lines (based on the pure equilibrium model) do not
reproduce the experimental data. These data are repro-
duced only when the PE emission is also taken into
account, as shown by solid lines.
Acknowledgments The authors are thankful to the Chairman,
Department of Physics, Aligarh Muslim University, Aligarh (India)
for providing necessary facilities to carry out this work. Thanks are
also due to the IUC UGC-CSR Kolkata for financial support through
IUC project.
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Energy dependence of pre-equilibrium emission 917
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