It depends on the electron density of the inner electron shells for the PE. Shell radius of the radial function is proportional to 1/Z. Volume is therefor proportional to Z**3. Electron density follows to 1/Z**3. Exact theory shows Z**5, see Heitler: The Quantumtheory of Radiation, Oxford (1954).

CS happens with outer electrons (valence el.). Outer shells are shielded from nuclear charge by the inner shells with Z-1 electrons. So one charge remains. So CS is proportional to Z/A. 

Thats fine sir @Hanno Krieger. But Why photoelectric interaction (for gamma photon) does not occur for low Z elements?

It occurs but with lower probability (see Z**5-law). Numerical data eg in http://physics.nist.gov/cgi-bin/Xcom/xcom3_2

That's exactly the point sir @Hanno Krieger. Suppose in organic scintillator (assume Z=6) and semiconductor Germanium (Z=32), Cross section for PE is prop to 6^5 = 7x10^3 and 32^5 = 3x10^7 respectively. But CS cross section is prop to 6 and 32 only.

If CS is observed for Z=6 where Cross section is Z^1, then why not PE where cross sect is Z^5?

No photo peak is seen in organic scintillator but CS is observed. Probability is more for PE than CS (7x10^3 vs 6, for Z=6).

You mix up interaction probabilities and detector efficiency. Try a short experiment. Imagine a PE in a material with Z. You can only measure the absorbed energy. The secondary radiations like photoelectron, characteristic X-rays, Auger-electrons after the first PE process have to be absorbed in the detector material. If not you get only the so called comton continuum. If you absorb all secondary radiations, possible if your detector is big enough, has high Z and density, all the energies sum up to the total energy. You get the photoline, but this is no hint for a PE. It can also be the sum of a series of subsequent comptoneffects. And please dont forget, cross sections for PE and CS also depend on energy functions. So the whole procedure also depends on energy of the primary photon.

I add a chapter from one of my radiation books. Its written in German, but I think you will be able to translate (use the google translator).

Mostly explained by Hanno. I would like to add that  by photoelectric interaction do occur for lighter elements but less (probability) compared to High Z. Only those gamma photons will interact which will have their energy closer to K, L etc shells or more crudely. If gamma photon is of 6 keV, (Fe55) it will interact with lighter elements.

But why high energy photons do not interact with low Z elements via photo electric effect. The reason is binding energy of the electron with which incoming photon will interact should be less than or comparable to energy of incident photon for better momentum conservation. THIS IS REQUIRED FOR THE EASE WITH WITH MOMENTUM IS CONSERVED IN THE INTERACTION. So with lighter element, 662 keV photon may not interact via Photo effect. The answer is preservation of momentum conservation.

The interaction (photo) is possible with tight bound electrons for the ease with which momentum is conserved. In fact visible light show photo effect with outer electrons of Na or Cs as they appear to be bound for visible photon and during photo interaction momentum is conserved.

Please note that absolutely free electron can not absorb photon.

Thanks Munish for your answer. Can you pl add some reference in support of ur answer?

Difficult to tell in which book its written or not but many know it, better you say it as private communication if u wish. Manytimes many things are not written in books.

For "this Please note that absolutely free electron can not absorb photon:

Please refer Book by A Beiser.

@Hanno Krieger

"So the whole procedure also depends on energy of the primary photon."

I though that is one reason why PE is not seen for low Z: For PE prop to Z^5/E^3 but for CS its prop to Z/E. So for a given Z and E, PE cross-section gets reduced E^2 times more compared to CS.

For Z=6, Eg= 662 keV

Cross section

PE prop to (6^5)/(662^3) = 2.7x10^(-5)

CS prop to (6)/(662) = 9.1x10^(-3)

This explains, PE also shall be there but shall have 300-400 times lower cross-sction wrt CS.

Is this ok?

Yes, your estimation shows the correct behaviour. But you have some additional factors for each effect, the numerical cross sections not only follow the dependencies on Z and energy, they have absolute scaling factors.

And please think about detector signals, the dont follow the PE or CS formulars because of the influences of geometry, detector Z, energy etc. You can get photopeaks without any PE as first interaction.

@Saha

See link

https://physics.stackexchange.com/questions/225522/free-electron-cant-absorb-a-photon

If the energy of photon is in the region of high energy spectrum (gamma), it will depend on the Z number of the target to decide the type of interaction.

In the photoelectric effect, the photon transfers all the energy to the atomic electron. The atomic electron must be tightly bound so that the photon can transfer all the energy to the atomic electron (Head-to-head collision); otherwise Compton scattering occurs.  Hence the photoelectric effect occurs with tightly bound electrons especially K-shell. The Binding energy of the K-shell electrons, which are most tightly bound, decreases for low Z elements. So the photoelectric effect is reduced for low Z media.

Cf. Krieger above. 

The cross section is proportional ~ Z^5.

@ saha see attached

due to lower no. of electrons, the probability of interactions is very low

The photoelectric process is the predominant mode of photon interaction at

relatively low photon energies & high atomic number Z. The probability of photoelectric absorption, symbolized τ (tau), is roughly proportional to 3)(ντhZn∝

where the exponent n varies between 3 and 4 over the gamma-ray energy region of interest. This severe dependence of the photoelectric absorption probability on the atomic number of the absorber is a primary reason for the preponderance of high-Z materials (such as lead) in gamma-ray shields. The photoelectric interaction is most likely to occur if the energy of the incident photon is just greater than the binding energy of the electron with which it interacts.