isobar is derived from two Greek words “isos” that
mean equal and the word “baros” that mean weight.
A British chemist by the name Alfred Walter Steward
suggested this category of nuclides in the year 1918
(Kauffman 1983; McArthur 1947;. Isobars just like
isotopes have several applications in several fields,
which include nuclear energy, nuclear medicine, and
industrial applications. It is well established that the
atomic number of elements in the periodic table determines the chemical properties of all the elements in
the nuclear landscape (Epiotis & Henze 2003). Therefore, the atomic structures of all isobaric nuclei differ
among themselves since their atomic numbers vary
for a fixed mass number of nuclei leading to different chemical properties, and different applications in
everyday life. For instance, among the isobars whose
mass number is 60, a special mention is given to
Cobalt, Nickel and Ferrous. Cobalt-60 is a synthetic
radioactive nuclei, which produces gamma rays that
are used in the treatment of malignant tissues in medical field as well as sterilization of medical equipment
(Masefield et al. 2008). Similarly, Nickel-60 is a stable
naturally occurring metal that can also be produced by
fission reaction. The applications of Nickel-60 include
stereotactic radiosurgery and radiotherapy (Akram et
al. 2018; Guo 2018;. Another special isobar in this
category is Ferrous-60. This is a rare isotope of iron
which can only be created through massive supernova
explosion and it is presumed to have been the primary
source of planetary heating and chronometer in the
early solar system (Kohman & Robison 1980; Wallner
et al. 2016).
In production of nuclear power, some isobars have
contributed immensely in the operations of the nuclear
reactors. These isobars, namely Tellurium-135, Iodine135 and Xenon-135 undergo beta minus decay and
their decay chains lead to the Xenon poisoning in the
nuclear reactors. Similarly, Neodymium-149 decays
to Promethium-149 which subsequently decays to
Samarium-149 that is responsible for Samarium poisoning (Stacey 2018). The presence of Samarium-149
and Xenon-135 in the nuclear reactors that are fueled
by Uranium-235 plays a critical role in controlling the
power levels generated. This is because Samarium149 and Xenon-135 have a very large neutron capture
cross-sections, thus, they are added to the control rods
of the nuclear reactors in order to control the neutron
flux hence regulating the fluctuations of the concentration of the radioactive nuclides (Cameron 2012;
Jevremovic 2005).
Other properties of isobars are described by the isobaric analogue states (IAS), which are nuclei that have
the same isospin and spin parity in a fixed mass number
(A) (Xu et al. 2016). Isobaric analogue states among
the medium-mass nuclei were discovered in 1961. This
came as a surprise to many nuclear physicists due to
the assumptions that the Coulomb interaction among
the light nuclei was insignificant, and the isobaric spin
could not carry any weight (Anderson 1962; Feshbach
& Kerman 1967). Research has shown that, the measurement of the properties of isobaric analogue states
such as Coulomb displacement energy and its width
can reveal the halo structures of the neutron-dripline
of nuclei (Takeuchi et al. 2001). Therefore, isospin is
an important entity in the study of nucleons in nuclear
spectroscopy as well as in recognizing the existence of
elementary particles such as quarks, which were proposed by Murray Gell-Mann and his student George
Zweig in 1964, and later discovered experimentally
by SLAC-MIT team of researchers between 1968 and
1972 (Friedman 1991; Gell-mann & Fritzsch 2010).
From the above discussion, it is evident that nuclei
especially isobars undergo nuclear decay in order to
gain stability. Consequently, these nuclei release some
energy in form of radiations that can be harnessed
and applied in nuclear medicine, nuclear reactors and
industrial applications. Nonetheless, the concept of
nuclear stability, which is determined by the interaction of nucleons in the nucleus of an atom, has not
been fully exploited since the nature of interactions
between the nucleons and the limits of Coulomb stability (Oganessian 2012) are not known especially in the
super heavy nuclei. Therefore, investigation of some
isobaric nuclei among the super heavy nuclei with
Z > 92 is carried out in this paper, in order to find out
the role of the modified Coulomb potential in determining the stability of isobars as they undergo nuclear
decay.
3 METHODS
The Coulomb potential according to the assumptions
on the liquid drop model (Bjornholm & Lynn 1980)
can be written as,
E C =
3
5
Z 1 Z 2 e
2
4πε 0 r
(1)
where, e is the electron charge, Z 1 and Z 2 are the proton
nuclear charges, r is the distance between the charges
and it is given by with being the nuclear radius parameter, A is the mass number and is the permittivity of
free space.
Coulomb interaction is a long-range force whereas
very small size protons are confined inside the nucleus
whose size is also very small. Thus, the Coulomb
potential inside the nucleus has to be modified in order
to confine the Coulomb energy within the boundary
of the nucleus and to make it more effective. The
modification of Coulomb energy was based on the
following assumptions: Firstly, the charge distribution inside the nucleus is assumed uniform. Secondly,
for a nucleus of an atom with N > Z, the nuclear
core is composed of equal number of protons and
neutrons (N = Z) and the excess neutrons reside in
the surface region. Finally, the nuclear core radius
is given by and this radius provides the maximum
nuclear charge radius resulting from the proton-proton
repulsion. From the above assumptions and our own
intuition, a multiplier exponential correction term (C t )
was proposed and Equation 1 was modified to obtain
196
mean equal and the word “baros” that mean weight.
A British chemist by the name Alfred Walter Steward
suggested this category of nuclides in the year 1918
(Kauffman 1983; McArthur 1947;. Isobars just like
isotopes have several applications in several fields,
which include nuclear energy, nuclear medicine, and
industrial applications. It is well established that the
atomic number of elements in the periodic table determines the chemical properties of all the elements in
the nuclear landscape (Epiotis & Henze 2003). Therefore, the atomic structures of all isobaric nuclei differ
among themselves since their atomic numbers vary
for a fixed mass number of nuclei leading to different chemical properties, and different applications in
everyday life. For instance, among the isobars whose
mass number is 60, a special mention is given to
Cobalt, Nickel and Ferrous. Cobalt-60 is a synthetic
radioactive nuclei, which produces gamma rays that
are used in the treatment of malignant tissues in medical field as well as sterilization of medical equipment
(Masefield et al. 2008). Similarly, Nickel-60 is a stable
naturally occurring metal that can also be produced by
fission reaction. The applications of Nickel-60 include
stereotactic radiosurgery and radiotherapy (Akram et
al. 2018; Guo 2018;. Another special isobar in this
category is Ferrous-60. This is a rare isotope of iron
which can only be created through massive supernova
explosion and it is presumed to have been the primary
source of planetary heating and chronometer in the
early solar system (Kohman & Robison 1980; Wallner
et al. 2016).
In production of nuclear power, some isobars have
contributed immensely in the operations of the nuclear
reactors. These isobars, namely Tellurium-135, Iodine135 and Xenon-135 undergo beta minus decay and
their decay chains lead to the Xenon poisoning in the
nuclear reactors. Similarly, Neodymium-149 decays
to Promethium-149 which subsequently decays to
Samarium-149 that is responsible for Samarium poisoning (Stacey 2018). The presence of Samarium-149
and Xenon-135 in the nuclear reactors that are fueled
by Uranium-235 plays a critical role in controlling the
power levels generated. This is because Samarium149 and Xenon-135 have a very large neutron capture
cross-sections, thus, they are added to the control rods
of the nuclear reactors in order to control the neutron
flux hence regulating the fluctuations of the concentration of the radioactive nuclides (Cameron 2012;
Jevremovic 2005).
Other properties of isobars are described by the isobaric analogue states (IAS), which are nuclei that have
the same isospin and spin parity in a fixed mass number
(A) (Xu et al. 2016). Isobaric analogue states among
the medium-mass nuclei were discovered in 1961. This
came as a surprise to many nuclear physicists due to
the assumptions that the Coulomb interaction among
the light nuclei was insignificant, and the isobaric spin
could not carry any weight (Anderson 1962; Feshbach
& Kerman 1967). Research has shown that, the measurement of the properties of isobaric analogue states
such as Coulomb displacement energy and its width
can reveal the halo structures of the neutron-dripline
of nuclei (Takeuchi et al. 2001). Therefore, isospin is
an important entity in the study of nucleons in nuclear
spectroscopy as well as in recognizing the existence of
elementary particles such as quarks, which were proposed by Murray Gell-Mann and his student George
Zweig in 1964, and later discovered experimentally
by SLAC-MIT team of researchers between 1968 and
1972 (Friedman 1991; Gell-mann & Fritzsch 2010).
From the above discussion, it is evident that nuclei
especially isobars undergo nuclear decay in order to
gain stability. Consequently, these nuclei release some
energy in form of radiations that can be harnessed
and applied in nuclear medicine, nuclear reactors and
industrial applications. Nonetheless, the concept of
nuclear stability, which is determined by the interaction of nucleons in the nucleus of an atom, has not
been fully exploited since the nature of interactions
between the nucleons and the limits of Coulomb stability (Oganessian 2012) are not known especially in the
super heavy nuclei. Therefore, investigation of some
isobaric nuclei among the super heavy nuclei with
Z > 92 is carried out in this paper, in order to find out
the role of the modified Coulomb potential in determining the stability of isobars as they undergo nuclear
decay.
3 METHODS
The Coulomb potential according to the assumptions
on the liquid drop model (Bjornholm & Lynn 1980)
can be written as,
E C =
3
5
Z 1 Z 2 e
2
4πε 0 r
(1)
where, e is the electron charge, Z 1 and Z 2 are the proton
nuclear charges, r is the distance between the charges
and it is given by with being the nuclear radius parameter, A is the mass number and is the permittivity of
free space.
Coulomb interaction is a long-range force whereas
very small size protons are confined inside the nucleus
whose size is also very small. Thus, the Coulomb
potential inside the nucleus has to be modified in order
to confine the Coulomb energy within the boundary
of the nucleus and to make it more effective. The
modification of Coulomb energy was based on the
following assumptions: Firstly, the charge distribution inside the nucleus is assumed uniform. Secondly,
for a nucleus of an atom with N > Z, the nuclear
core is composed of equal number of protons and
neutrons (N = Z) and the excess neutrons reside in
the surface region. Finally, the nuclear core radius
is given by and this radius provides the maximum
nuclear charge radius resulting from the proton-proton
repulsion. From the above assumptions and our own
intuition, a multiplier exponential correction term (C t )
was proposed and Equation 1 was modified to obtain
196