Mod-01 Lec-28 Beta decay Contd..

Fermi theory of beta decay, we had done and essentially it has got nuclear matrix element M i f. You have this M i f square and this is psi daughter and essentially, it is psi electron and psi neutron also neutrino and then you have this, whatever interaction Newtonian and here it is the parent, so this is the metrics element square. This is 1 factor,

but in Fermi theory what we had discussed this only depends on the nuclear wave functions, because these two things we had taken as constants 1 over root V, 1 over root V neglecting all those higher-order term in p dot r by h cross and to the energy dependence comes from that d n d E f. And we worked out that the number of electrons

in momentum range p to p plus d p. If this we work out this turns out to be some constant times p e square p nu square, then d p e right, so that is the N p d p. And then we bring this factor with depends on Z number of the daughter and the kinetic energy or momentum.

So, this is that affect it takes care of the coulomb interaction between the outgoing electron, positron and the daughter. So, this is how that this is all electrons, this is the momentum distribution, if you plot momentum as a function of the number of electrons as a function of it is momentum p, the value of more magnitude of the momentum,

then you will have this kind of relation. In terms of kinetic energy we can also do it in terms of kinetic energy. So, N K d K corresponding N K d K and when you put all these values in Fermi theory, it turns out to be some constant times. Then you had a

factor K k plus 2 m c square half of it, then you had a factor K plus m e c square and then you had a factor Q minus K square of this d K. So, this N K versus K we try to calculate and of course, this F-factor and match with the experimental shape. So, qualitatively we showed that it works, but if you wants