in progress of adapting things to siunitx, done chap4

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nam
2014-09-07 12:18:11 +09:00
parent 3530983370
commit 4166acb9f3
3 changed files with 92 additions and 83 deletions

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