Photodisintegration of the Deuteron at High Energies

Abstract

The exchange current effects in the photodisintegration of the deuteron at high energies are discussed. Special consideration is given to (i) correlation of the exchange effects with the large direct E1 transition, whose behavior has been the object of the recent several investigations, (ii) consequences of gauge invariance for the electric transitions due to exchange effects, (iii) evaluation of the magnetic transition caused by the (33)-resonance in terms of the results of the Chew-Low theory. It is shown that exchange effects affect the electric dipole transition operator in a way consistent with the Siegert theorem. The resulting change in the electric dipole cross section is evaluated in the adiabatic approximation as well as in neglect of higher order retardation effect. It is appreciable only at photon energies above the pion threshold. Some characteristics of the (33) -resonance effect are revealed, although nucleonrecoil effects and uncertainty of nuclear force make it difficult to give any quantitative estimation. Finally the results obtained here are compared with experiment. § 1. IntroductionRecently the progress of knowledge about nuclear force has motivated several detailed reviews 1 )-5) on the photodisintegration of the deuteron at about 80 Mev photon energy. As the result it has become clear that the experimental data can be well explained in terms of E1 and E2 transitions alone, provided that we use a somewhat large value to the D-state probability of the deuteron as well as the phase shifts fit for the p-p scattering data to the final continuum states. It should be noted that any necessity to invoke specific exchange current effects is not felt.Subsequently, the analysis is extended on the same line to the higher energy region. 6 ),7)This shows that the transitions from the deuteron D-state make the actual E1 cross section considerably larger than the Schiff and Marshall-Guth estimation. S ) Since the contribution of the direct (i.e. not involving exchange current interaction) E1 transition is recognized to be remarkable even in the high energy region, it is desirable to investigate the effects of pion-exchange-current, taking into account their correlation with the direct transition.In this paper we shall discuss the exchange c:urrent effects in the region of photon energy 100 Mev to 350 Mev, and see where theprevious discussions on the exchange current interaction must be supplemented or amended by the existence of the large direct E1 transition. For simplicity our discussion is confined to the contribution of one-pion-exchange processes.

Cluster expansion approach to the effective potential in Φ 4 2+1 -theory

“…(4) 1 In the symmetry broken phase the two minima of the e ective potential are unitary equivalent in 4 1+1 -theory (which can be seen by the non-vanishing vacuum tunneling amplitude), while this is not the case in (2+1) dimensions (see e.g. 6,16]). tadpole (m 2 ) is linearly divergent and has the peculiarity of being independent of the external momentum, while the logarithmically divergent part of sunset (k 2 ; m 2 ) is given by the rst term of the corresponding Taylor expansion in the external momentum k 2 around k 2 = 0: sunset (k 2 ; m 2 ) = 1 X n=0 @ n @ n k 2 sunset (k 2 ; m 2 ) j k 2 =0 !…”

Cluster expansion approach to the effective potential in Φ 2+1 4 -theory

“…6,16]). (6) The subtraction of divergencies de ned in this way is completely equivalent to the familiar BPH or BPHZ 2 renormalization scheme 17,18].…”

“…Due to the separation of the eld into a classical and a quantum part according to (10) (16) In the cluster expansions (16) the integer numbers between the brackets stand for eld operators (i) or conjugate momenta (i) while P ij is the two-body permutation operator. We note that any application of the P ij operators has to ensure the original order of the eld operators within the connected Green functions occurring on the r.h.s.…”

“…h12345i c and h123456i c in (16). Inserting the truncated cluster expansions into the hierarchy of equations of motion (15) up to the 4-point functions on the l.h.s and hence up to the 6-point functions on the r.h.s.…”

“…This can be seen by a detailed analysis taking into account the cluster expansions (16). After inserting the normal ordered 2-point functions (18) Since we are interested not only in the e ective potential generated by the full set of equations but additionally in the in uence of the 2-, 3-and 4-point functions we introduce 4 limiting cases of the …”