Inelastic Collisions with Changes of Mass and the Problem of Nuclear Disintegration with Capture or Non-Capture of a Neutron or Another Nuclear Projectile

Relativity equations are developed for the relations involved in the disintegration of an atomic nucleus by bombardment with a nuclear projectile which is not captured in the process. Similar equations for velocities not too close to that of light are also developed; these are based on the rest-masses and the only relativity term is that involved in the change of mass produced by the collision ($E_m=c^2\Delta m$). The relativity equation for the velocity of the projectile is: $V_A=\frac{{(k_C{m}_C{v}_C+k_D{m}_D{v}_D)}^2-c^2{(k_C{m}_C+k_D{m}_D-m_B)}^2+2\mathrm{}{c}^2{k}_A{m}_A(k_C{m}_C+k_D{m}_D-m_B)}{2k_A{m}_A(k_C{m}_C{v}_C+k_D{m}_D{v}_D)cos\alpha }$ while the similar equation for not too high velocities is: $V_A=\frac{\{M^2+2\mathrm{}{m}_A[E_C+E_D+c^2(m_C+m_D-m_B)\left]\right\}}{2m_{A}Mcos\alpha }$ in which $M$ represents momentum, $E$ is kinetic energy, $m$ mass, $v$ velocity, $c$ the velocity of light, and $A$, $B$, $C$ and $D$ are the nuclei involved. If a $\gamma$-ray is emitted the expression between brackets in Eq. (16) contains in addition a term $E\gamma$. A careful analysis is made of the evidence which has formerly seemed to indicate that in the majority of disintegrations produced by neutrons the neutron is captured. The conclusion is reached that this evidence is valid. A similar analysis of the evidence for non-capture of the neutron indicates that this evidence is not valid. Thus the velocities given for the neutron as calculated by either Eq. (5′) or Eq. (16) are in general higher, when the nitrogen nucleus is disintegrated, than that of any known neutron. It is found that the curve which gives the relation between the number of disintegrations and the velocities of the neutrons which produce them, is practically the same for scattered as for non-scattered neutrons, provided both are assumed to disintegrate by capture. There seems to be no evidence which indicates that any nucleus has been disintegrated by bombardment of another nucleus without capture. Obviously this does not prove that non-capture disintegrations are non-existent.