Monday, 27 August 2018

nuclear physics - What is the "penetrability factor"?


I have read/heard this term a few times in nuclear physics papers. I'm guessing it has something to do with the Coloumb barrier of a nucleus. Could you maybe explain what this "penetrability factor" is?


[See page 63 of this paper]



Answer



The penetrability factor is a carefully defined factor that separates the coulomb-force and the interesting nuclear-forces in the relationship between the partial decay width and the reduced width (for R-Matrix analysis) of a particular resonance.


$$\Gamma = 2\gamma^2P(l,\rho,\eta)$$


Here $\Gamma$ is the partial decay width, $\gamma$ is the reduced width, $l$ is the orbital angular momentum of the state, $\rho$ is defined as $k$ (wavenumber) multiplied by $r$ the target particle radius, $\eta$ is the sommerfeld [nuclear] parameter, and $P(l,\eta,\rho)$ is the penetrability factor. The penetrability factor is defined as,



$$P(l,\rho,\eta)=\frac{\rho}{\left(F_l (\eta,\rho)\right)^2+\left(G_l (\eta,\rho)\right)^2}$$


where $F$ and $G$ are the regular and irregular coulomb wave functions, respectively.


Source: http://www.scholarpedia.org/article/The_R-matrix_theory_in_nuclear_and_atomic_physics (equation 10 and 13)


No comments:

Post a Comment

Understanding Stagnation point in pitot fluid

What is stagnation point in fluid mechanics. At the open end of the pitot tube the velocity of the fluid becomes zero.But that should result...