1.

A Sigma^(+) hyperon with kinetic energy T_(Sigma)= 320MeV distingrated during its flight into a neutrral particle and a positive pion outgoing with kinetic energy T_(pi)= 42MeV at right angles to the hyperon's motion direction. Find the rest mass of the neutral particle (in MeV units).

Answer»

Solution :
By ENERGY CONSERVATION
`sqrt(m_(SIGMA)^(2)c^(4)+c^(2)+P_(Sigma)^(2))=sqrt(m_(pi)^(2)c^(4)+c^(2)P_(pi)^(2))+sqrt(m_(N)^(2)c^(4)+c^(2)p_(pi)^(2)+c^(2)P_(Sigma)^(2))`
or `(sqrt(m_(Sigma)c^(4)+c^(2)P_(Sigma)^(2))-sqrt(m_(pi)^(2)c^(4)+c^(2)p_(pi)^(2)))^(2)=m_(n)^(2)c^(4)+c^(2)p_(pi)^(2)+c^(2)P_(Sigma)^(2)`
or `m_(Sigma)^(2)c^(4)+c^(2)P_(Sigma)^(2)+m_(pi)^(2)c^(4)+c^(2)p_(pi)^(2)-2sqrt(m_(pi)^(2)c^(4)+c^(2)P_(Sigma)^(2))sqrt(m_(pi)^(2)c^(2)+c^(2)p_(pi)^(2))`
`=m_(n)^(2)c^(2)+c^(2)p_(pi)^(2)+c^(2)P_(Sigma)^(2)`
or using the K.E o f `Sigma & pi`
`m_(n)^(2)=m_(Sigma)^(2)+m_(p)^(2)-2(m_(Sigma)+(T_(Sigma))/(c^(2)))(m_(pi)+(T_(pi))/(c^(2)))`
and `m_(n)sqrt(m_(Sigma)^(2)+m_(pi)^(2)-2(m_(pi)+(T_(Sigma))/(c^(2)))(m_(pi)+(T_(pi))/(c^(2))))= 0.949(GeV)/(c^(2))`


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