Critical mass in a relativistic two-body problem
Tóm tắt
We use the relativistic 2-body Dirac Hamiltonian with a square-well vector interaction, to investigate how the finite mass of the source of the external field changes the behavior of the bound-state spectrum from that of one Dirac particle in an attractive square well. Limiting ourselves for simplicity to states of total spin zero, we find that, as long as the massm
2 of the heavier particle is smaller than some critical massm
c, the total energyE of the system does not reach the particle-antiparticle continuum, so that no difficulty of interpretation arises. If, however,m
2 is greater thanm
c, there exists, as in the one-body Dirac equation, one value of the coupling strengthV
c for whichE reaches the antiparticle continuum. Then, when the coupling strength exceedsV
c, the bound-state level disappears. Furthermore, for some coupling strengthV>V
c, there is a 2-particle bound-state level emerging from the particle-antiparticle continuum, whose total energyE increases until it reaches the particle-particle continuum. This latter result shows that, form
2>m
c, a 2-body analysis actually further complicates the interpretation of deep bound states in relativistic quantum mechanics.
Tài liệu tham khảo
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