Theory of the coulomb photoproduction of π0 at high energy and the determination of the π0 lifetime

Abstract

The angular dependence of the cross-section for the coherent photoproduction of π0 on complex nuclei (Primakoff effect) is studied in detail in connection with the problem of determining the π0 lifetime. The effects of reabsorption of the photoproduced π0 on the angular distribution are calculated with the use of an optical model of the nucleus. It is shown that consideration of these effects is essential for establishing the angular dependence of the coherent nuclear matrix element and is also important for the Coulomb matrix element; it is also shown that in both cases these absorption effects can be written as a modification of the nuclear form factor. The modified form factors are calculated for lead at a photon energy of 1 GeV, assuming, for simplicity, an uniform spherical distribution of the nucleus. Three results of this calculation can be noted:a) both the modified nuclear and Coulomb form factors become complex quantities, although in the situation considered in this note, their imaginary part is generally an order of magnitude smaller than their real part,b) the absolute value of the modified nuclear form factor is depressed with respect to the value of the form factor calculated without taking the absorption into account by a factor which varies between 2 and 3 in the angular region of interest,c) at angles larger than ∼2° the modified Coulomb form factor also differs considerably from the no absorption form factor. Assuming that the nuclear shape and radius are known and relying on the above mentioned calculation of the form factors, the differential photoproduction matrix element can be written in terms of three (angle independent) parameters; one is the lifetimeτ to be determined and the other two are the real and imaginary part of a certain combinationη of the forward non-spin-flip complex amplitudes for π0 photoproduction on a nucleon. It is pointed out that while the present data on π0 photoproduction on a proton can, at best, only determine an upper limit to |η|, the coherent photoproduction data in the region 0°<θ<6° should allow an easy determination of the value of |η|, that is of the relative magnitude of the Coulomb and nuclear coherent matrix element. Only after this important parameter will be known, it will be possible to decide if the lifetime of the π0 can be determined using only the data at small angles 0<θ<1.5°, as suggested in a previous paper (1), or if it will be necessary to perform a complete three-parameter best fit using the results of the present note.