A relativistic spin-3/2 particle in a spherical cavity and the problem of Δ resonance in the MIT bag model

Electromagnetic N transitions in the bag model including centre-of-mass corrections

“…The constants A , B and energy eigenvalue E for a given delta mass m and the well radius Tiell are determined by the boundary condition found in [12] aQ-= 3(2E -…”

“…Of course we are left with the problem of determining A' inside the well and computing its norm, but it may be easily done using the boundary condition found in [12] (appendix B).…”

“…(B4) dr m(r) This expression may be integrated to r = rtell -E using (Al) and from reel1 -E to rtell taking into account that for r$ell -E < r < rtell [12]: In fact for the well radii used in this paper the boundary part of the total norm is about 1% and may be neglected.…”

“…From (8) follows that from the four coefficients a , 6 , c, d only two are independent. Following the notation of [12] we obtain It is convenient to express Ar = A ( r / r ) and A' directly by A and B. Introducing two component vectors R and Q such that where @ = ypA, (= 0 for r < r$e,i -E ) , we have…”

Rarita–Schwinger particles under the influence of strong magnetic fields

“…which is in agreement with the minimal coupling prescription given in equation (10). This last result clearly shows that the minimal coupling prescription is mathematically consistent, in contrast to the introduction of a Lorentz scalar potential, which gets to a contradiction if we do the same in the RS equation written in the form (8), as addressed in [25,26,39,40]. To achieve the solutions of the RS equation embedded in an electromagnetic field, we follow the approach used in obtaining the solutions of the Dirac equation in [32].…”