Advances in Phytochemistry, Textile and Renewable Energy Research for
Industrial Growth – Nzila et al. (Eds)
© 2022 Copyright the Author(s), ISBN: 978-1-032-11871-0
Open Access: www.taylorfrancis.com, CC BY-NC-ND 4.0 license
Role of modified Coulomb potential in determining stability of isobars
H.K. Cherop, K.M. Muguro & K.M. Khanna
Department of Physics, University of Eldoret, Eldoret, Kenya
ABSTRACT: The binding energy of an atomic nucleus is composed of a number of different forms of energy.
The most important ones are the nuclear interaction energy and the Coulomb energy due to the Coulomb repulsion
between the protons. The recently proposed modified Coulomb potential model has been used to calculate the
most stable nuclei for a fixed mass number, for a few nuclei (rather isobars) with Z > 92. Calculations from this
study show that the modified Coulomb potential model generates the most stable nuclei (Z STABLE ) for the isobars
when n > 21. As the values of n increase, some occurrence of nuclear transformations that include beta decay
and gamma decay, which the isobars undergo in order to gain stability are revealed. However, some unknown
kind of radiations that require further investigations are predicted to be emitted when the value of n increases
consecutively at the initial stages of nuclear decay.
1 INTRODUCTION
Theoretical and experimental research on the nucleus
of an atom in nuclear theory has given rise to new
information and data, which is vital in understanding
the structure of the nucleus and the nucleon-nucleon
interactions. In spite of the spectacular advances made
in nuclear theory and experimental nuclear physics,
it is still not known exactly as to how many protons
and neutrons can constitute a bound atomic nucleus,
especially in the region of periodic table when Z varies
from Z > 92 to say Z = 120 or more.
It is now sufficiently confirmed experimentally and
theoretically that the nucleus of an atom is composed
of neutrons (N), protons (Z), and that its mass number
(A), is given by A = N + Z. A proton being positively charged has slightly less mass compared to the
mass of the neutron that has no charge. The magnetic
moment of the proton is positive, but that of the neutron is negative. Inside the nucleus, the protons and
neutrons are referred to as nucleons since the nuclear
forces between the neutrons and protons are charge
independent. In addition, there exist different types
of nuclei. Some nuclei have proton number constant
(Z constant) but different mass number (A), and such
nuclei are called isotopes while the nuclei that have
constant mass number but different atomic number are
called isobars. Then there are nuclei with constant neutron number (N), but different A and Z. Such nuclei
are called isotones. There is another set of nuclei, in
which the proton number is equal to the neutron number (Z = N ) in two or more nuclei. Such nuclei are
called isomers or mirror nuclei, for instance, and in
which has two neutrons and has two protons.
Quite a number of nuclear models that include
liquid drop model, Bethe-Weizsäcker mass formula,
collective model, evaporation model, Fermi gas model,
shell model, individual particle model, nuclear pairing
model, superfluid model among others, have been proposed from time to time to explain the properties of
nuclei in different regions of mass number (Greiner &
Maruhn 1996; Rowe & Wood 2010). However, none of
these nuclear models can explain all the properties of
nuclei. The basic parameters that come into play in the
formulation of such nuclear models are the nuclear
masses and the binding energy of the nuclei. As the
nuclear size increases among the nuclei, the nuclear
binding energies in the ground state also increase due
to the effect of increased shells that are occupied
by paired nucleons. The nucleons in this interaction
experience several forces that are dominated by the
Coulomb repulsion in the proton pairs. The Coulomb
force being a long range type increases with increase
in nuclear size, thus, Coulomb interaction is predicted
to contribute greatly to the stabilization of the super
heavy nuclei (SHN) that are likely to exist in the “island
of stability” (Oganessian 2012). Therefore, investigation of some isobaric nuclei among the super heavy
nuclei with Z > 92 is carried out in order to find out
the role of the modified Coulomb potential in determining the stability of super heavy isobaric nuclei. The
calculations of this study are essential in identifying
the transuranic elements that are likely to reside in
the island of stability. Consequently, providing some
fundamental information in the synthesis of the super
heavy nuclei.
2 LITERATURE REVIEW
Nuclei with different atomic number (Z) and constant mass number (A) are called isobars. The word
DOI 10.1201/9781003221968-26
195
Industrial Growth – Nzila et al. (Eds)
© 2022 Copyright the Author(s), ISBN: 978-1-032-11871-0
Open Access: www.taylorfrancis.com, CC BY-NC-ND 4.0 license
Role of modified Coulomb potential in determining stability of isobars
H.K. Cherop, K.M. Muguro & K.M. Khanna
Department of Physics, University of Eldoret, Eldoret, Kenya
ABSTRACT: The binding energy of an atomic nucleus is composed of a number of different forms of energy.
The most important ones are the nuclear interaction energy and the Coulomb energy due to the Coulomb repulsion
between the protons. The recently proposed modified Coulomb potential model has been used to calculate the
most stable nuclei for a fixed mass number, for a few nuclei (rather isobars) with Z > 92. Calculations from this
study show that the modified Coulomb potential model generates the most stable nuclei (Z STABLE ) for the isobars
when n > 21. As the values of n increase, some occurrence of nuclear transformations that include beta decay
and gamma decay, which the isobars undergo in order to gain stability are revealed. However, some unknown
kind of radiations that require further investigations are predicted to be emitted when the value of n increases
consecutively at the initial stages of nuclear decay.
1 INTRODUCTION
Theoretical and experimental research on the nucleus
of an atom in nuclear theory has given rise to new
information and data, which is vital in understanding
the structure of the nucleus and the nucleon-nucleon
interactions. In spite of the spectacular advances made
in nuclear theory and experimental nuclear physics,
it is still not known exactly as to how many protons
and neutrons can constitute a bound atomic nucleus,
especially in the region of periodic table when Z varies
from Z > 92 to say Z = 120 or more.
It is now sufficiently confirmed experimentally and
theoretically that the nucleus of an atom is composed
of neutrons (N), protons (Z), and that its mass number
(A), is given by A = N + Z. A proton being positively charged has slightly less mass compared to the
mass of the neutron that has no charge. The magnetic
moment of the proton is positive, but that of the neutron is negative. Inside the nucleus, the protons and
neutrons are referred to as nucleons since the nuclear
forces between the neutrons and protons are charge
independent. In addition, there exist different types
of nuclei. Some nuclei have proton number constant
(Z constant) but different mass number (A), and such
nuclei are called isotopes while the nuclei that have
constant mass number but different atomic number are
called isobars. Then there are nuclei with constant neutron number (N), but different A and Z. Such nuclei
are called isotones. There is another set of nuclei, in
which the proton number is equal to the neutron number (Z = N ) in two or more nuclei. Such nuclei are
called isomers or mirror nuclei, for instance, and in
which has two neutrons and has two protons.
Quite a number of nuclear models that include
liquid drop model, Bethe-Weizsäcker mass formula,
collective model, evaporation model, Fermi gas model,
shell model, individual particle model, nuclear pairing
model, superfluid model among others, have been proposed from time to time to explain the properties of
nuclei in different regions of mass number (Greiner &
Maruhn 1996; Rowe & Wood 2010). However, none of
these nuclear models can explain all the properties of
nuclei. The basic parameters that come into play in the
formulation of such nuclear models are the nuclear
masses and the binding energy of the nuclei. As the
nuclear size increases among the nuclei, the nuclear
binding energies in the ground state also increase due
to the effect of increased shells that are occupied
by paired nucleons. The nucleons in this interaction
experience several forces that are dominated by the
Coulomb repulsion in the proton pairs. The Coulomb
force being a long range type increases with increase
in nuclear size, thus, Coulomb interaction is predicted
to contribute greatly to the stabilization of the super
heavy nuclei (SHN) that are likely to exist in the “island
of stability” (Oganessian 2012). Therefore, investigation of some isobaric nuclei among the super heavy
nuclei with Z > 92 is carried out in order to find out
the role of the modified Coulomb potential in determining the stability of super heavy isobaric nuclei. The
calculations of this study are essential in identifying
the transuranic elements that are likely to reside in
the island of stability. Consequently, providing some
fundamental information in the synthesis of the super
heavy nuclei.
2 LITERATURE REVIEW
Nuclei with different atomic number (Z) and constant mass number (A) are called isobars. The word
DOI 10.1201/9781003221968-26
195