Table 3. Calculated values of Z STABLE for A = 292, A = 340, A = 360, A = 364, A = 392, A = 416, A = 432 and A = 476.
Z STABLE
Z STABLE
Z STABLE
Z STABLE
Z STABLE
Z STABLE
Z STABLE
Z STABLE
for
for
for
for
for
for
for
for
n
A = 292
A = 340
A = 360
A = 364
A = 392
A = 416
A = 432
A = 476
1
80
90
94
94
100
102
108
111
2
97
111
116
116
124
128
134
141
3
103
117
122
123
131
136
142
151
4
105
120
125
126
135
140
146
155
5
107
122
127
128
137
142
148
158
6
108
123
128
129
138
143
149
159
7
108
123
129
130
139
144
150
160
8
109
124
130
131
139
145
151
161
9
109
124
130
131
140
145
151
162
10
109
124
130
131
140
146
151
162
11
110
125
131
132
140
146
152
163
12
110
125
131
132
140
146
152
163
13
110
125
131
132
140
147
152
163
14
110
125
131
132
140
147
152
163
15
110
125
131
132
141
147
152
164
16
110
125
131
132
141
147
152
164
17
110
125
131
132
141
147
152
164
18
110
125
131
132
141
147
152
164
19
110
125
131
132
141
147
152
164
20
110
125
131
132
141
147
152
164
21
110
125
131
133
141
147
152
164
n > 21
111
126
132
133
141
148
152
164
since the last known element currently in the periodic
table of elements is Oganesson with atomic number
Z = 118. However, atomic calculations suggest that
the existence of nuclei on earth or in interstellar bodies
may end at Z 172 (Fricke et al. 1971; Indelicato et al.
2011; Pyykkö 2011). This implies that, investigations
are on course to discover the existence of such nuclei
experimentally.
The results in Table 3 show that, the application of
Equation 8 predicts the existence of the most stable or
the longest-lived nuclei for the given mass numbers.
These nuclei include
292 111which might fall under the
category of Roentgenium isotopes. Other stable isobars predicted by the model include
340 126,
360 132,
364 133,
392 141,
416 148,
432 152 and
476 164. The elements
340 126 and
432 152 have magic proton number
and a semi-magic proton number respectively. Since
occurrence of magic numbers corresponds to nuclei
having extra stability, it is expected that these nuclei
will be more stable than their neighbouring isotopes.
The reduction in the correction term as n increases
from n = 1 to n > 21, leads to generation of new values of the most stable nuclei for which the nucleus of
a given A is stable.
Other methods of determining the stability of isobaric nuclei include the use of the mass parabolas.
The mass parabolas predict accurately the stable isobaric nuclei among the light and intermediate mass
nuclei. However, they are not accurate in determining the stability of super heavy isobaric nuclei. This is
because the shapes of the mass parabolas change into
exponential curves (Cherop 2020). Thus, the modified
Coulomb potential enriches the mass parabolas in the
sense that, it generates the stable values of all the super
heavy isobaric nuclei accurately. Consequently, predicting the most stable isobaric nuclei that might exist
in the island of stability.
5 CONCLUSIONS AND RECOMMENDATIONS
One of the properties of nuclei that determine the
existence of elements in the nuclear landscape is the
nuclear stability, which is determined by the neutron
to proton ratio. As the number of protons increase
in the nucleus of an atom, the number of neutrons
also increases in order to maintain the stability of the
nucleus. Any imbalance between the ratio of protons
and neutrons may lead to imbalance in the nuclear
forces causing nuclear instability. In this paper, the
category of nuclei investigated fall under the group of
super heavy nuclei, which are unstable. However, some
mathematical models have predicted for the existence
of stable super weights in the “island of stability”.
The type of nuclei that may exist in island of stability
may include isobars, isotones and isotopes. In order to
investigate the nature of isobaric nuclei that may exist
in the island of stability, a modified Coulomb potential model having a multiplier exponential correction
term has been used to calculate the values of Z STABLE
for which the nucleus for a given A is fixed. Our calculations reveal that, the modified Coulomb potential
model generates the most stable nuclei (Z STABLE ) for
a given isobar when n > 21. The model also reveals
199
Z STABLE
Z STABLE
Z STABLE
Z STABLE
Z STABLE
Z STABLE
Z STABLE
Z STABLE
for
for
for
for
for
for
for
for
n
A = 292
A = 340
A = 360
A = 364
A = 392
A = 416
A = 432
A = 476
1
80
90
94
94
100
102
108
111
2
97
111
116
116
124
128
134
141
3
103
117
122
123
131
136
142
151
4
105
120
125
126
135
140
146
155
5
107
122
127
128
137
142
148
158
6
108
123
128
129
138
143
149
159
7
108
123
129
130
139
144
150
160
8
109
124
130
131
139
145
151
161
9
109
124
130
131
140
145
151
162
10
109
124
130
131
140
146
151
162
11
110
125
131
132
140
146
152
163
12
110
125
131
132
140
146
152
163
13
110
125
131
132
140
147
152
163
14
110
125
131
132
140
147
152
163
15
110
125
131
132
141
147
152
164
16
110
125
131
132
141
147
152
164
17
110
125
131
132
141
147
152
164
18
110
125
131
132
141
147
152
164
19
110
125
131
132
141
147
152
164
20
110
125
131
132
141
147
152
164
21
110
125
131
133
141
147
152
164
n > 21
111
126
132
133
141
148
152
164
since the last known element currently in the periodic
table of elements is Oganesson with atomic number
Z = 118. However, atomic calculations suggest that
the existence of nuclei on earth or in interstellar bodies
may end at Z 172 (Fricke et al. 1971; Indelicato et al.
2011; Pyykkö 2011). This implies that, investigations
are on course to discover the existence of such nuclei
experimentally.
The results in Table 3 show that, the application of
Equation 8 predicts the existence of the most stable or
the longest-lived nuclei for the given mass numbers.
These nuclei include
292 111which might fall under the
category of Roentgenium isotopes. Other stable isobars predicted by the model include
340 126,
360 132,
364 133,
392 141,
416 148,
432 152 and
476 164. The elements
340 126 and
432 152 have magic proton number
and a semi-magic proton number respectively. Since
occurrence of magic numbers corresponds to nuclei
having extra stability, it is expected that these nuclei
will be more stable than their neighbouring isotopes.
The reduction in the correction term as n increases
from n = 1 to n > 21, leads to generation of new values of the most stable nuclei for which the nucleus of
a given A is stable.
Other methods of determining the stability of isobaric nuclei include the use of the mass parabolas.
The mass parabolas predict accurately the stable isobaric nuclei among the light and intermediate mass
nuclei. However, they are not accurate in determining the stability of super heavy isobaric nuclei. This is
because the shapes of the mass parabolas change into
exponential curves (Cherop 2020). Thus, the modified
Coulomb potential enriches the mass parabolas in the
sense that, it generates the stable values of all the super
heavy isobaric nuclei accurately. Consequently, predicting the most stable isobaric nuclei that might exist
in the island of stability.
5 CONCLUSIONS AND RECOMMENDATIONS
One of the properties of nuclei that determine the
existence of elements in the nuclear landscape is the
nuclear stability, which is determined by the neutron
to proton ratio. As the number of protons increase
in the nucleus of an atom, the number of neutrons
also increases in order to maintain the stability of the
nucleus. Any imbalance between the ratio of protons
and neutrons may lead to imbalance in the nuclear
forces causing nuclear instability. In this paper, the
category of nuclei investigated fall under the group of
super heavy nuclei, which are unstable. However, some
mathematical models have predicted for the existence
of stable super weights in the “island of stability”.
The type of nuclei that may exist in island of stability
may include isobars, isotones and isotopes. In order to
investigate the nature of isobaric nuclei that may exist
in the island of stability, a modified Coulomb potential model having a multiplier exponential correction
term has been used to calculate the values of Z STABLE
for which the nucleus for a given A is fixed. Our calculations reveal that, the modified Coulomb potential
model generates the most stable nuclei (Z STABLE ) for
a given isobar when n > 21. The model also reveals
199