Particle lifetimes from the uncertainty principle

The Breit-Wigner distribution is similar to a gaussian near the peak, but the tails of the curve are flatter. 布里特-沃格ер分布在峰附近类似于高斯分布，但曲线的尾部更平坦。

The uncertainty principle provides a tool for characterizing the very short-lived products produced in high energy collisions in accelerators. The uncertainty principle in the form suggests that for particles with extremely short lifetimes, there will be a significant uncertainty in the measured energy. The measurment of the mass energy of an unstable particle a large number of times gives a distribution of energies called a Lorentzian or a Breit-Wigner distribution. 这表明对于寿命极短的粒子，测量其能量将会有显著的不确定性。对不稳定粒子的质能进行多次测量会得到一个称为洛伦兹分布或布里特-魏格纳分布的能量分布。 不确定性原理为表征加速器中高能碰撞产生的寿命极短的产物提供了一种工具。不确定性原理以

If the width of this distribution at half-maximum is labeled Γ , then the uncertainty in energy ΔE could be reasonably expressed as

where the particle lifetime τ is taken as the uncertainty in time τ = Δt.

In high energy scattering experiments, the energy uncertainty ΔE can be determined and the lifetime implied from it. In other cases, the lifetime is most conveniently measured and the "particle width" in energy implied from that lifetime measurement.

For linewidth 线宽

=x10^ eV = MeV = GeV, = 10^eV = MeV = GeV, 中文译文中的待填/计算数值依次对应：1：gb 2：gp 3：gmev 4：ggev。实际数值以上方原输入框为准。

and the energy uncertainty can be taken to be half of that value.

The associated lifetime is 相应的寿命是

= x10^seconds. = 10^ seconds. 中文译文中的待填/计算数值依次对应：1：tb 2：tp。实际数值以上方原输入框为准。

Γ is often referred to as the "natural line width". It is of great importance in high energy accelerator physics where it provides the means for determining the ultrashort lifetimes of particles produced. For optical spectroscopy it is a minor factor because the natural linewidth is typically 10^-7 eV, about a tenth as much as the Doppler broadening. Another source of linewidth is the recoil of the source, but that is negligible in the optical range.

For nuclear transitions involving gamma emission in the 0.1-1 MeV range, the recoil width is typically much greater than the natural line width. The recoil of the emitting nucleus implies that the emitted gamma photon cannot be absorbed by an identical nucleus because its energy is reduced by an amount greater than the natural line width of potential absorbing levels. Mossbauer discovered that the absorption could be accomplished by putting the source on a rotating arm to give it enough speed to compensate for the recoil effect. The Mossbauer effect became a useful experimental tool when it was discovered that the recoil could be suppressed by putting the emitting nucleus in a crystal lattice. The emitted gammas then exhibited something close to the natural linewidth and could be absorbed by other identical nuclei.