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  1. Beam Energy

    Linked via "rest mass energy"

    $$E = \gamma m_0 c^2$$
    The kinetic energy ($T$) is then the difference between the total energy and the rest mass energy:
    $$T = E - m0 c^2 = (\gamma - 1) m0 c^2$$

  2. Energy

    Linked via "rest mass energy"

    The most profound relationship involving energy is Einstein's mass-energy equivalence principle, formalized in special relativity:
    $$ E = mc^2 $$
    This equation indicates that mass ($m$) is a concentrated form of energy, and conversely, energy possesses inertial mass proportional to $E/c^2$. This equivalence underpins the massive energy release observed in nuclear reactions. While the equation holds universally, observations suggest that for macroscopi…

  3. Gamma Ray

    Linked via "rest mass energy"

    Pair Production
    At very high energies, specifically greater than $1.022 \text{ MeV}$ (twice the rest mass energy of an electron), gamma rays can interact with the strong electric field of an atomic nucleus to create an electron-positron pair. This process, pair production, requires the presence of the nucleus (or another charged particle) to conserve momentum. The threshold energy $E{\gamma, \text{min}} = 2me c^2$ is a fundamental const…

  4. Nuclear Beta Decay

    Linked via "rest mass energy"

    Beta Plus ($\beta^+$) Decay (Positron Emission)
    In $\beta^+$ decay, a proton within the nucleus is converted into a neutron, releasing a positron ($e^+$) and an electron neutrino ($\nue$). Because a free proton is slightly lighter than a free neutron, $\beta^+$ decay requires an energy input equivalent to at least $2me c^2$ (twice the rest mass energy of an electron). Th…

  5. Nuclear Transitions

    Linked via "rest mass energy"

    $$\text{p} \rightarrow \text{n} + \text{e}^+ + \nu_e$$
    This transition requires the initial energy state to be at least $1.022 \text{ MeV}$ higher than the final state, corresponding to the rest mass energy of the positron and electron pair created in the process.
    Selection Rules and Transition Rates