I What Is the Physical Significance of ##\beta_{tot}## in Molecular Polarization?

[Konte]

Hi everybody,

The tensor of first hyperpolarizability $\beta_{ijk}$ is define as giving the second order or molecular polarization:
$$\mu_i^{(2)}=\sum_{jk} \, \beta_{ijk} E^j E^k$$

Now, I saw somewhere that an entity $\beta_{tot}$ can be define as:
$$\beta_{tot}=\left( (\beta_{xxx}+\beta_{xyy}+\beta_{xzz})^2+(\beta_{yyy}+\beta_{yzz}+\beta_{yxx})^2+(\beta_{zzz}+\beta_{zxx}+\beta_{zyy})^2\right)^{1/2}$$
What is the physical signification of this magnitude $\beta_{tot}$ ?

Thank you everybody.

Konte

 

[PeterDonis]

I saw somewhere

Where? Please give a specific reference.