in progress of adapting things to siunitx, done chap4
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@@ -66,17 +66,17 @@ emission of particles with emphasis on proton.
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Theoretically, the capturing process can be described in the following
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stages~\cite{FermiTeller.1947, WuWilets.1969}:
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\begin{enumerate}
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\item High to low (a few \kilo\electronvolt) energy: the muon velocity are
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\item High to low (a few \si{\kilo\electronvolt}) energy: the muon velocity are
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greater than the velocity of the valence electrons of the atom. Slowing
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down process is similar to that of fast heavy charged particles. It takes
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about \sn{}{-9} to \sn{}{-10} \second~to slow down from a relativistic
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\sn{}{8} \electronvolt~energy to 2000 \electronvolt~in condensed matter,
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about \sn{}{-9} to \sn{}{-10} \si{\second}~to slow down from a relativistic
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\sn{}{8}~\si{\electronvolt}~energy to 2000~\si{\electronvolt}~in condensed matter,
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and about 1000 times as long in air.
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\item Low energy to rest: in this phase, the muon velocity is less than that
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of the valence electrons, the muon is considered to be moving inside
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a degenerate electron gas. The muon rapidly comes to a stop either in
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condensed matters ($\sim$\sn{}{-13} \second) or in gases ($\sim$\sn{}{-9}
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\second).
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condensed matters ($\sim$\sn{}{-13}~\si{\second}) or in gases ($\sim$\sn{}{-9}
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\si{\second}).
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\item Atomic capture: the muon has no kinetic energy, it is captured by the
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host atom into one of high orbital states, forming a muonic atom. The
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distribution of initial states is not well known. The details depend on
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@@ -86,9 +86,9 @@ stages~\cite{FermiTeller.1947, WuWilets.1969}:
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by the emission of Auger electrons or characteristic X-rays, or excitation
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of the nucleus. The time taken for the muon to enter the lowest possible
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state, 1S, from the instant of its atomic capture is
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$\sim$\sn{}{-14}\second.
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$\sim$\sn{}{-14}\si{\second}.
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\item Muon disappearance: after reaching the 1S state, the muons either
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decays with a half-life of \sn{2.2}{-6} \second~or gets captured by the
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decays with a half-life of \sn{2.2}{-6}~\si{\second}~or gets captured by the
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nucleus. In hydrogen, the capture to decay probability ratio is about
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\sn{4}{-4}. Around $Z=11$, the capture probability is roughly equal to the
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decay probability. In heavy nuclei ($Z\sim50$), the ratio of capture to
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@@ -98,7 +98,7 @@ stages~\cite{FermiTeller.1947, WuWilets.1969}:
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than a K-shell electron. The close proximity of the K-shell muon in the
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Coulomb field of a nuclear, together with its weak interaction with the
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nucleus, allows the muon to spend a significant fraction of time (\sn{}{-7}
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-- \sn{}{-6} \second) within the nucleus, serving as an ideal probe for the
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-- \sn{}{-6} \si{\second}) within the nucleus, serving as an ideal probe for the
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distribution of nuclear charge and nuclear moments.
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\end{enumerate}
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@@ -307,7 +307,7 @@ and of course not perfect, description of the existing data~\cite{Measday.2001}:
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- X_2\left(\frac{A-Z}{2A}\right)\right]
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\label{eq:primakoff_capture_rate}
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\end{equation}
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where $X_1 = 170$ \reciprocal\second~is the muon capture rate for hydrogen, but
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where $X_1 =$ \SI{170}{\second^{-1}}~is the muon capture rate for hydrogen, but
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reduced because a smaller phase-space in the nuclear muon capture compares to
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that of a nucleon; and $X_2 = 3.125$ takes into account the fact that it is
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harder for protons to transforms into neutrons due to the Pauli exclusion
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@@ -347,20 +347,20 @@ $n_{avg} = (0.3 \pm 0.02)A^{1/3}$~\cite{Singer.1974}.
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The neutron emission can be explained by several mechanisms:
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\begin{enumerate}
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\item Direct emission follows reaction~\eqref{eq:mucap_proton}: these neutrons
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have fairly high energy, from a few \mega\electronvolt~to as high as 40--50
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\mega\electronvolt.
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have fairly high energy, from a few \si{\mega\electronvolt}~to as high as 40--50
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\si{\mega\electronvolt}.
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\item Indirect emission through an intermediate compound nucleus: the energy
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transferred to the neutron in the process~\eqref{eq:mucap_proton} is 5.2
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\mega\electronvolt~if the initial proton is at rest, in nuclear
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\si{\mega\electronvolt} if the initial proton is at rest, in nuclear
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environment, protons have a finite momentum distribution, therefore the
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mean excitation energy of the daughter nucleus is around 15 to 20
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\mega\electronvolt~\cite{Mukhopadhyay.1977}. This is above the nucleon
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\si{\mega\electronvolt}~\cite{Mukhopadhyay.1977}. This is above the nucleon
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emission threshold in all complex nuclei, thus the daughter nucleus can
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de-excite by emitting one or more neutrons. In some actinide nuclei, that
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excitation energy might trigger fission reactions. The energy of indirect
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neutrons are mainly in the lower range $E_n \le 10$ \mega\electronvolt~with
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characteristically exponential shape of evaporation process. On top of that
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are prominent lines might appear where giant resonances occur.
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neutrons are mainly in the lower range $E_n \le 10$ \si{\mega\electronvolt}
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with characteristically exponential shape of evaporation process. On top of
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that are prominent lines might appear where giant resonances occur.
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\end{enumerate}
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Experimental measurement of neutron energy spectrum is technically hard, and it
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is difficult to interpret the results. Due to these difficulties, only a few
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