Role of Fluctuations on the Pairing
Properties of Nuclei in the Random
Spacing Model
M. A. A. Mamun, C. Constantinou, and M. Prakash
1 Pairing in Systems of Large and Small Numbers of
Particles
The Bardeen-Cooper- Schrieffer (BCS) theory of superconductivity [1, 2] predicts
a sharp discontinuity in the constant-volume specific heat C V at a certain critical
temperature T c for which the pairing gap Δ of fermions determined from the gap
and number equations [3, 4]
G ≡
k
1
E k
tanh
E k
2T
−
2
G
(1)
N =
k
1 −
k − λ
E k
tanh
E k
2T
+
Δ
T
∂Δ
∂α
G
(2)
vanishes. Above, G is the strength of the pairing interaction, T is the temperature,
λ is the chemical potential, α = λ/T , E k =
(( k − λ) 2 + Δ 2 is the quasiparticle
energy, and k are the single particle (sp) energies. The corresponding energy E and
entropy S are obtained from
M. A. A. Mamun () · M. Prakash
Department of Physics and Astronomy, Ohio University, Athens, OH, USA
e-mail: ma676013@ohio.edu; prakash@ohio.edu
C. Constantinou
Department of Physics, Kent State University, Kent, OH, USA
e-mail: cconsta5@kent.edu
© This is a U.S. government work and not under copyright protection
in the U.S.; foreign copyright protection may apply 2021
J. Escher et al. (eds.), Compound-Nuclear Reactions, Springer Proceedings in
Physics 254, https://doi.org/10.1007/978-3-030-58082-7_17
145
Properties of Nuclei in the Random
Spacing Model
M. A. A. Mamun, C. Constantinou, and M. Prakash
1 Pairing in Systems of Large and Small Numbers of
Particles
The Bardeen-Cooper- Schrieffer (BCS) theory of superconductivity [1, 2] predicts
a sharp discontinuity in the constant-volume specific heat C V at a certain critical
temperature T c for which the pairing gap Δ of fermions determined from the gap
and number equations [3, 4]
G ≡
k
1
E k
tanh
E k
2T
−
2
G
(1)
N =
k
1 −
k − λ
E k
tanh
E k
2T
+
Δ
T
∂Δ
∂α
G
(2)
vanishes. Above, G is the strength of the pairing interaction, T is the temperature,
λ is the chemical potential, α = λ/T , E k =
(( k − λ) 2 + Δ 2 is the quasiparticle
energy, and k are the single particle (sp) energies. The corresponding energy E and
entropy S are obtained from
M. A. A. Mamun () · M. Prakash
Department of Physics and Astronomy, Ohio University, Athens, OH, USA
e-mail: ma676013@ohio.edu; prakash@ohio.edu
C. Constantinou
Department of Physics, Kent State University, Kent, OH, USA
e-mail: cconsta5@kent.edu
© This is a U.S. government work and not under copyright protection
in the U.S.; foreign copyright protection may apply 2021
J. Escher et al. (eds.), Compound-Nuclear Reactions, Springer Proceedings in
Physics 254, https://doi.org/10.1007/978-3-030-58082-7_17
145