Neutron by emission of positron and a neutral particle of negligible mass
In the above reaction, proton is converted into neutron by emission of positron and a neutral particle of negligible mass called as neutrino, v. It cân be shown that if Z is the atomic number of daughter nucleus, the 1 difference in coulomb energies of mirror nuclei is equal to (6ze2 4TE0 5R where R is the radius of the daughter nucleus.
This energy is spent by providing rest mass energy m.c? to produce a positron of mass me, imparting a kinetic energy Eg+ to B* particle and providing rest mass (m, - mp)c required for converting a neutron of larger mass, mi, to a proton of smaller mass, mp 6Ze2 5R + mc? + (m, - mp) c The experimental value of kinetic energy, E, imparted to B"-particles in the case of mirror nuclei can be used tó estimate R. The average value of R found by this method is (1.23 + 0.03) xA3 x 10 m. (ii) Mešonic X-rays The nuclear radius can also be estimated from the energies of X-rays emitted by mu-mesons which are called mesonic X-rays.
. The methods c field due mu? 4TEGR 2e x Ze Ze R = or Substituting the typiçal values for Z = 20, m = 6.64 x 1027 kg, e = 1.6 x 10-1 Coulomb and velocity v 10' m/s, R will be approximately equal to 1.5 x 10-14 elastic scattering of a-particles from nuclei with Z varying from 29 to 90 as equal to 1.35 XA X10- m. R was also estimated equal to (1.2±0.1) m.
The average value of R has been estimated from the x 10- m from the life-time of radioactive alpha emitters obtained from Gamow's theory of a-decay by barrier penetration. The following typlcal methods have been generally 'used for an estimation of nuçlear radius, X A3 (i) Mirror Nuclei Method The mirror nuclei are pairs of nuclei which are obtained from each other by exchange of neutron with proton, e.g. H' He', 3Li' Be', C3, 19K 20Ca etc. A mirror nucleus like N is unstable and gets converted Into C3 by emitting B* (e*) and v as follows.
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