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The pion-pion interaction in τ decay
ANNALS
OF PHYSIC’S:
Abstracts
13,
308-316
(1961)
of Papers
to Appear
in Future
Issues
With this issue the 9nnals begins the policy of publishing, at. the earliest possible date after acceptance, abstracts of papers which will appear in future issues. Inlel~uclion in 7 Decay. E. LOMON, S. MORRIS, 6. J. IRWIN, JR. and T. TRWNG The momentum dependence of t,he 7 decay rate deviates considerably from that. predicted by the relativistic phase space factor and coulomb corrections. The difference is attributed here t,o the final state pion pion interaction. Three different, phenomenological analyses are made to determine the 7 = 0 and I” = 2, s state pion-pion force required for consistency with r and 7’ data: a scattering length approximation, an independent pair approximation for an exponential potential, and a Born approximation for a Yukawa potential. The results of all three approsimatjions agree where they are applicable and indicate a weak or repulsive 7’ = 0 force and an attractive or Teak 7’ = 2 force. !Z’he Pion-Pion
b’ecrtrino Emission Processes and Stellar Evollltiorl-Super,looQe-I. H. Y. CHILJ A general qualitative discussion of evolution of stars of masses <1.1 M. is presented. The role of gravitational contraction has been emphasized with respect to element synt,hesis. It is found that most. of the stars with masses above a few tenths solar mass will proceed through all phases of element synthesis and conseqiient.ly xi11 become a supernova. The URCA process suggested by Gamow and Schbnberg in 1941 will change this picture. I)uring the a-process of element synt,hesis the rate of gravitational energy release is of the same order as that lost due to URCA neutrinos, and the critical mass for supernovae is not certain, although the upper limit of it is less than the Chandrasekhar mass limit for degenerate gas spheres. The URCA process energy dissipation rates of a number of elements have been calculated for 2’ = G X 1O8, 1.2 X log, 2.-l X log, and cj X log “K respectively. Elertron Scattering in. a C’rystal Lattice. THORZAS H. I~PREE For some types of crystals it is permissible to assume that within a spherical region surrounding each ion the potential is spherically symmetric and t,hat in the innerspace bet,ween these spherical regions the potential is constant. Schriidinger’s equation is solved for such a potential distribution in which the spherical potent,ial wells are not all alike. Both propagating and non-propagating solutions a,re considered. An asymptotic evaluation of the of residual resist.wave scattered by an impurity ion is carried out. From this, a calculation ante in alkali metal alloys is obtained. Accelerators with a General Magwtic Field. Ci. PARZEN The linear motion of a particle moving in an accelerator having a general magnetic field is investigated. -4 solution is found which is valid for a wide class of accelerators, which includes the AG synchrotron, FFAG accelerators and the fixed-frequency cyclotron. Results are given for the equilibrium orbit, the betatron oscillation frequencies, t,he hetatron oacillations and other linear orbit properties. 308
OF PHYSIC’S:
Abstracts
13,
308-316
(1961)
of Papers
to Appear
in Future
Issues
With this issue the 9nnals begins the policy of publishing, at. the earliest possible date after acceptance, abstracts of papers which will appear in future issues. Inlel~uclion in 7 Decay. E. LOMON, S. MORRIS, 6. J. IRWIN, JR. and T. TRWNG The momentum dependence of t,he 7 decay rate deviates considerably from that. predicted by the relativistic phase space factor and coulomb corrections. The difference is attributed here t,o the final state pion pion interaction. Three different, phenomenological analyses are made to determine the 7 = 0 and I” = 2, s state pion-pion force required for consistency with r and 7’ data: a scattering length approximation, an independent pair approximation for an exponential potential, and a Born approximation for a Yukawa potential. The results of all three approsimatjions agree where they are applicable and indicate a weak or repulsive 7’ = 0 force and an attractive or Teak 7’ = 2 force. !Z’he Pion-Pion
b’ecrtrino Emission Processes and Stellar Evollltiorl-Super,looQe-I. H. Y. CHILJ A general qualitative discussion of evolution of stars of masses <1.1 M. is presented. The role of gravitational contraction has been emphasized with respect to element synt,hesis. It is found that most. of the stars with masses above a few tenths solar mass will proceed through all phases of element synthesis and conseqiient.ly xi11 become a supernova. The URCA process suggested by Gamow and Schbnberg in 1941 will change this picture. I)uring the a-process of element synt,hesis the rate of gravitational energy release is of the same order as that lost due to URCA neutrinos, and the critical mass for supernovae is not certain, although the upper limit of it is less than the Chandrasekhar mass limit for degenerate gas spheres. The URCA process energy dissipation rates of a number of elements have been calculated for 2’ = G X 1O8, 1.2 X log, 2.-l X log, and cj X log “K respectively. Elertron Scattering in. a C’rystal Lattice. THORZAS H. I~PREE For some types of crystals it is permissible to assume that within a spherical region surrounding each ion the potential is spherically symmetric and t,hat in the innerspace bet,ween these spherical regions the potential is constant. Schriidinger’s equation is solved for such a potential distribution in which the spherical potent,ial wells are not all alike. Both propagating and non-propagating solutions a,re considered. An asymptotic evaluation of the of residual resist.wave scattered by an impurity ion is carried out. From this, a calculation ante in alkali metal alloys is obtained. Accelerators with a General Magwtic Field. Ci. PARZEN The linear motion of a particle moving in an accelerator having a general magnetic field is investigated. -4 solution is found which is valid for a wide class of accelerators, which includes the AG synchrotron, FFAG accelerators and the fixed-frequency cyclotron. Results are given for the equilibrium orbit, the betatron oscillation frequencies, t,he hetatron oacillations and other linear orbit properties. 308