15 Studies on Hypernuclei and Superheavy Elements
205
15.2 Theory
15.2.1 Methodology to Study the Properties of Hypernuclei
The lambda–nucleon (N) interaction inside a hypernucleus can be understood by
studying its binding and separation energies. Different formalisms are there for studying the properties of hypernuclei. One among them is the use of semi-empirical
methods for evaluating the binding and separation energies.
In a recent study [36], we have proposed a new semi-empirical formula, by extending the Bethe–Weizsäcker mass formula (BWMF), for calculating the binding energy
of singe hypernuclei, which is given by
B(N , Z , ,) = a v A c − a s A
2/3
c − a c
Z (Z − 1)
A
1/3
c
− a sym
(N − Z ) 2
A c
+ δ −
b 0
A 2/3
1 −
b 1
A 2/3
+ b 2 .
(15.1)
Here A is the mass number of the hypernucleus, given by, A = Z + N + , and A c
is the mass number of core nucleus, A c = Z + N , where Z and N are the number of
protons and number of neutrons. a v , a s , a c and a sym are the usual BWMF constants,
given by, a v = 15.79 MeV, a s = 18.34 MeV, a c = 0.71 MeV, a sym = 23.21 MeV. δ is
the pairing term, which is 12 A
−1/2
c
for even N even Z nuclei, −12 A
−1/2
c
for odd N
odd Z nuclei and 0 otherwise. b 0 , b 1 and b 2 are given as, b 0 = 119.445 MeV, b 1 =
1.119 MeV, b 2 = 33.047 MeV.
A new formula is also suggested [36] using the least square regression to the
updated experimental data of single hypernuclei, given as
S = a 0 +
a 1
A 2/3 +
a 2
A 4/3 .
(15.2)
Here a 0 = 28.442 MeV, a 1 = −119.445 MeV and a 2 = 133.651 MeV.
These two new formulae for the binding and separation energies of hypernuclei
are found to be more suitable for obtaining the experimental results as well as for
making theoretical predictions [36].
Another important part in the studies of hypernuclei is the decay of hypernuclei. Even though many studies have been put forward for studying the weak decay
of hypernuclei, only a few numbers of studies [18–21] have been performed on
the hypernuclear decay triggered by strong interaction, such as alpha and cluster
emission. We have modified the Coulomb and proximity potential model (CPPM)
proposed by Santhosh et al. [22] with the inclusion of a -nucleus potential, for
studying the alpha and cluster emissions from hypernuclei. In CPPM, the interacting
potential between two nuclei is taken as the sum of Coulomb potential, proximity
potential, and centrifugal potential. It is given by
V =
Z 1 Z 2 e
2
r
+ V p (z) +
2 l(l + 1)
2μr 2 , f or z > 0.
(15.3)
205
15.2 Theory
15.2.1 Methodology to Study the Properties of Hypernuclei
The lambda–nucleon (N) interaction inside a hypernucleus can be understood by
studying its binding and separation energies. Different formalisms are there for studying the properties of hypernuclei. One among them is the use of semi-empirical
methods for evaluating the binding and separation energies.
In a recent study [36], we have proposed a new semi-empirical formula, by extending the Bethe–Weizsäcker mass formula (BWMF), for calculating the binding energy
of singe hypernuclei, which is given by
B(N , Z , ,) = a v A c − a s A
2/3
c − a c
Z (Z − 1)
A
1/3
c
− a sym
(N − Z ) 2
A c
+ δ −
b 0
A 2/3
1 −
b 1
A 2/3
+ b 2 .
(15.1)
Here A is the mass number of the hypernucleus, given by, A = Z + N + , and A c
is the mass number of core nucleus, A c = Z + N , where Z and N are the number of
protons and number of neutrons. a v , a s , a c and a sym are the usual BWMF constants,
given by, a v = 15.79 MeV, a s = 18.34 MeV, a c = 0.71 MeV, a sym = 23.21 MeV. δ is
the pairing term, which is 12 A
−1/2
c
for even N even Z nuclei, −12 A
−1/2
c
for odd N
odd Z nuclei and 0 otherwise. b 0 , b 1 and b 2 are given as, b 0 = 119.445 MeV, b 1 =
1.119 MeV, b 2 = 33.047 MeV.
A new formula is also suggested [36] using the least square regression to the
updated experimental data of single hypernuclei, given as
S = a 0 +
a 1
A 2/3 +
a 2
A 4/3 .
(15.2)
Here a 0 = 28.442 MeV, a 1 = −119.445 MeV and a 2 = 133.651 MeV.
These two new formulae for the binding and separation energies of hypernuclei
are found to be more suitable for obtaining the experimental results as well as for
making theoretical predictions [36].
Another important part in the studies of hypernuclei is the decay of hypernuclei. Even though many studies have been put forward for studying the weak decay
of hypernuclei, only a few numbers of studies [18–21] have been performed on
the hypernuclear decay triggered by strong interaction, such as alpha and cluster
emission. We have modified the Coulomb and proximity potential model (CPPM)
proposed by Santhosh et al. [22] with the inclusion of a -nucleus potential, for
studying the alpha and cluster emissions from hypernuclei. In CPPM, the interacting
potential between two nuclei is taken as the sum of Coulomb potential, proximity
potential, and centrifugal potential. It is given by
V =
Z 1 Z 2 e
2
r
+ V p (z) +
2 l(l + 1)
2μr 2 , f or z > 0.
(15.3)