While the Primakoff cross section depends on the mass M of the produced meson as 1/M (at a given radiative width ), the diffractive one falls just as 1/M . But the essential quantity allowing to distinguish the two processes is the differential cross section where t is the four-momentum transferred squared. The Primakoff cross section reaches a maximum at t=2t =2 M /p (where p is the incoming meson momentum) and then falls rapidly as e (b=400 GeV for lead). The peak height scales as . The strong diffractive production falls off much smoother, as e . Thus, at low values of t the Coulomb excitation should lead to an excess in the cross section which can be extracted by partial wave analysis (PWA) and the different dependence of the two processes on the nuclear mass number.
A good example to illustrate the problem are the Primakoff production
measurements at p=200 GeV/c on lead and copper nuclei (e.g.
A rough estimate (valid within factor of 2-3)
shows that = 6.4 10 mb/GeV
for =640 keV  and M=1.25 GeV (on lead)
while the diffractive cross section is about 4 10
Thus the two processes are of the same order of magnitude and may still be
separated by their different t-dependence.
For the higher masses the situation is more problematic. In the region of M=1.8 GeV at 300 GeV on lead the Primakoff peak height is only about 200 mb/GeV assuming a typical radiative width of 100 keV. For the diffractive 3 pion cross-section we can expect a value of about 10 mb/GeV , 3-4 times lower than at M=1.3 GeV (extrapolated from VES data to a lead target and higher energies). Thus it is impossible to extract the Primakoff production of such a heavy object in this particular decay mode using the t-distribution alone. However, due to the difference in the population of the different helicity states at small values of t by the two processes PWA has to be employed as in the case of the at M 1.2 GeV/c . This allows a rather clean extraction of the Coulomb excitation amplitudes . Using again the 3 mode the same method also gives consistent results for the .
In order to ease the task at higher masses we will use a high beam energy of
300 GeV/c which gives a more than twofold
rise of the Primakoff peak cross section as compared to ref. using a
200 GeV/c beam.
We expect that the (radiative) study of the (1670) could be thus become
accessible, taking into account also its higher spin giving a factor of 2J+1
in the cross-section.
This measurement is also interesting for the owing to a discrepancy with different theoretical predictions. For instance recent calculations based on Chiral Theory give for its radiative width 250 keV  as compared to 640 keV from the measurement.
But there are still other classes of states which can be studied with Primakoff production at high masses. One of them is a class of states which can not be produced diffractively at all - for example . Even in this case there can be coherent production on nuclei (i.e. by means of -exchange) having a sharp t-distribution, but its cross-section drops with energy according to the corresponding Regge trajectory intersection. Another class is the diffractive production of states with non-zero spin projection onto the Gottfried-Jackson axis - as in the case of (and others 2 , 4 ,...). The energy dependence is similar to that of , but the t-distribution has a dip at small t.
In the following we estimate the apparatus resolution necessary to meet the required precision in the kinematic variable t. The scattering angle of each of the three outgoing 100 GeV/c pions has to be measured with an accuracy of 3 10 to achieve a t resolution of 0.3 10 GeV , which is half the t-value of the Primakoff cross sections peak at M=1.3 GeV/c at p=300 GeV/c. This corresponds to a required spatial resolution of 300 m/ at a lever arm of 10 m which seems reachable, if it is not degraded by multiple scattering in the detector itself. A target of 1/20 X is thin enough, but probably it gives too little yield per incoming beam particle. A four times thicker target would contribute about 4.2 10 to the multiple scattering angle. Thus the forward peak in the t-distribution could not be resolved cleanly. This, however, seems to be still permissible.