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Papers by Jerome Malenfant
Physical Review D, 1988
The Breit equation for two equal-mass spin-, particles interacting through an attractive Coulomb ... more The Breit equation for two equal-mass spin-, particles interacting through an attractive Coulomb potential is separated into its angular and radial parts, obtaining coupled sets of first-order differentia equations for the radia1 wave functions. The radial equations for the 'JJ, JJ, and 'Po states are further reduced to a single, one-dimensional Schrodinger equation with a relatively simple effective potential. No approximations, other than the initial one of an instantaneous Coulomb interaction, are made in deriving this equation; it accounts for all relativistic effects, as well as for mixing between different components of the wave function. Approximate solutions are derived for this Schrodinger equation, which gives the correct O(c) term for the 1 'So energy and for the n 'JJ energies, for J &0. The radial equations for the '(J+1)J states are reduced to two second-order coupled equations. At small r, the Breit Coulomb wave functions behave as r' ', where v is either v J(J+1)+1at/4 or +J(J+1)a'/4. The 'So and 'Po wave functions therefore diverge at the origin as r ' '. This divergence of the J=0 states, however, does not occur when the spin-spin interaction,-(a/r)a cz, is added to the Coulomb potential.
Physical Review D, 1987
The wave function at the origin is an important factor in the leptonic decay rate of (QQ) states,... more The wave function at the origin is an important factor in the leptonic decay rate of (QQ) states, since the rate is proportional to the square of its value. However, relativistic wave functions for the color-Coulomb potential diverge at the origin. In this paper, we consider the QED version of this problem: the O(a) corrections to the decay (p+p) 3~e +e. After renormalization, the diver-1 gence of the wave function at the origin is shown to cancel via the one-photon annihilation graph. With all two-loop diagrams included, the decay rate of the nS state is 1/n ' that of the 1S state. This simple result is modified at the three-loop level by electron vacuum-polarization (VP) eft'ects, which are numerically large. With these VP eAects included, the decay rate of the 1 'Sl state is predicted to be 5. 571 & 10" sec 1091 (1965). Y. Tomozawa, Ann. Phys. (N.Y.) 128, 463 (1980).
Physical Review D, 1988
The Breit equation for two equal-mass spin-, particles interacting through an attractive Coulomb ... more The Breit equation for two equal-mass spin-, particles interacting through an attractive Coulomb potential is separated into its angular and radial parts, obtaining coupled sets of first-order differentia equations for the radia1 wave functions. The radial equations for the 'JJ, JJ, and 'Po states are further reduced to a single, one-dimensional Schrodinger equation with a relatively simple effective potential. No approximations, other than the initial one of an instantaneous Coulomb interaction, are made in deriving this equation; it accounts for all relativistic effects, as well as for mixing between different components of the wave function. Approximate solutions are derived for this Schrodinger equation, which gives the correct O(c) term for the 1 'So energy and for the n 'JJ energies, for J &0. The radial equations for the '(J+1)J states are reduced to two second-order coupled equations. At small r, the Breit Coulomb wave functions behave as r' ', where v is either v J(J+1)+1at/4 or +J(J+1)a'/4. The 'So and 'Po wave functions therefore diverge at the origin as r ' '. This divergence of the J=0 states, however, does not occur when the spin-spin interaction,-(a/r)a cz, is added to the Coulomb potential.
Physical Review D, 1987
The wave function at the origin is an important factor in the leptonic decay rate of (QQ) states,... more The wave function at the origin is an important factor in the leptonic decay rate of (QQ) states, since the rate is proportional to the square of its value. However, relativistic wave functions for the color-Coulomb potential diverge at the origin. In this paper, we consider the QED version of this problem: the O(a) corrections to the decay (p+p) 3~e +e. After renormalization, the diver-1 gence of the wave function at the origin is shown to cancel via the one-photon annihilation graph. With all two-loop diagrams included, the decay rate of the nS state is 1/n ' that of the 1S state. This simple result is modified at the three-loop level by electron vacuum-polarization (VP) eft'ects, which are numerically large. With these VP eAects included, the decay rate of the 1 'Sl state is predicted to be 5. 571 & 10" sec 1091 (1965). Y. Tomozawa, Ann. Phys. (N.Y.) 128, 463 (1980).