• Source: Sommerfeld parameter

The Sommerfeld parameter η, named after Arnold Sommerfeld, is a dimensionless quantity used in nuclear astrophysics in the calculation of reaction rates between two nuclei and also appears in the definition of the astrophysical S-factor. It is defined as




η
=




Z

1



Z

2



e

2




4
π

ϵ

0


ℏ
v



=
α

Z

1



Z

2






μ

c

2




2
E






{\displaystyle \eta ={\frac {Z_{1}Z_{2}e^{2}}{4\pi \epsilon _{0}\hbar v}}=\alpha Z_{1}Z_{2}{\sqrt {\frac {\mu c^{2}}{2E}}}}

,
where e is the elementary charge, Z1 and Z2 are the atomic numbers of two interacting nuclides, v is the magnitude of the relative incident velocity in the center-of-mass frame, α is the unitless fine-structure constant, c is the speed of light, and μ is the reduced mass of the two nuclides of interest.
One of its best-known applications is in the exponent of the Gamow factor P (also known as the penetrability factor),




P
=
exp
⁡
(
−
2
π
η
)


{\displaystyle P=\exp(-2\pi \eta )}

,
which is the probability of an s-wave nuclide to penetrate the Coulomb barrier, according to the WKB approximation. This factor is particularly helpful in characterizing the nuclear contribution to low-energy nucleon-scattering cross-sections - namely, through the astrophysical S-factor.
One of the first articles in which the Sommerfeld parameter appeared was published in 1967.




References

Kata Kunci Pencarian:

• Teori kuantum lama
• Pajak
• Prinsip ketidakpastian Heisenberg
• Konstanta struktur halus
• Ryan Lewis
• Konfigurasi elektron
• Hukum Ohm
• Teori atom
• Mekanika kuantum
• Perdebatan Bohr–Einstein
• Sommerfeld parameter
• List of things named after Arnold Sommerfeld
• Fine-structure constant
• Sommerfeld number
• S-factor
• Geometrical optics
• Orr–Sommerfeld equation
• Euler–Rodrigues formula
• Heavy fermion material
• Gamow factor