single and double escape peaks can give You information about efficiency of your system and can be use for calibration. But why you don`t use just 1368 and 2754 keV?

Some about that, You can find in my article:

Efficiency study of a big volume well type NaI(Tl) detector by point and voluminous sources and Monte-Carlo simulation

and also in many more articles and books.

Best regards.

For high energy gammas from nuclear reactions, the full energy peak could happen to be very small compared to SE and DE peaks. I recall we used the escape peaks in that case.

For example, please refer to Fig. 8 in  http://www.sciencedirect.com/science/article/pii/S0168900213016215

in addition to other examples.

Yes, you can use single (SEP) and double escape peaks (DEP) for energy as well as for efficiency calibration.

Using SEP and DEP in energy calibration is easy, you basically get two more peaks per transition with known positions. Also useful to quickly check your energy calibration at higher energies (>4 MeV), as you will see a "triplet" of peaks that should have a distance of 511keV.

However, at an γ-ray energy of ~2.7 MeV the SEP and DEP efficiency is very small. If you want to determine this efficiency, i would recommend using a source with higher (and more) energies, e.g. 56Co, as the shape is very different (see attachment). This results in three "independent" detector efficiencies at high energies.

Yes, you can use any of the escape peaks so long as you have their good size. In case of AmBe source Howitzer type tank of paraffin we had observed 3 escape peaks of n-p capture gamma.

You may be interested in giving a look to the following paper:

A.Fubini, F.Terrasi, I.Vata. A method to improve the energy calibration of a Ge(Li) Spectrometer. Nuclear Instruments and Methods 92(1971)309-311.

This is in fact a routine method used for calibration purposes in both NaI detectors and Ge detectors. The intensity of the SEP and DEP depends usually on the size of the Ge detector. In the case of 24Na those lines together with the photopeak of the 2754 and 1368 keV lines makes a good collection of 4 lines with which to calibrate your gamma spectrum. An interesting point should be noted in the case of 24Na is that the two gamma rays are emitted in cascade and hence there is a good chance that the energy sum of the two gammas namely 4122 keV line + SEP +DEP will be observed by the same detector thus extending the energy range of this gamma source up to ~ 4121 keV.

Yes, you can use SEP and DEP for energy calibration. It help you making errors of data will be smaller. Using SEP and DEP for energy calibration in (n,gamma) reaction makes effect too.

You must not use the escape peaks to calibrate a detector efficiency. Maybe this information can only be useful for calibrating energy.

Actually, SEP and DEP peaks can be used for energy calibration; as far as efficiency calibration, you cannot add these peaks for the calibration of full-energy-peak efficiency, but you can build up two separate additional efficiency curves for single escape and double escape events. In this case, when using the efficiency curves for calculating activities in an "unknown" spectrum, you should use the proper calibration curve depending on the peak you are considering (i.e. fep, sep or dep).