Ratios of reduced transition probabilities
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Ratios of reduced transition probabilities
By measuring transition energies and intensities, together with the multipole mixing ratio (angular distributions/correlations), it is possible to extract ratios of reduced transition probabilities. Note that these ratios are easily obtained without the complicated measurement of the lifetimes of nuclear states!
The multipole mixing ratio for inband
=1
transitions may be expressed in terms of a ratio of reduced matrix
elements:
where 
is in MeV,
such that the phase of 
is a meaningful, and measurable,
observable. Using this definition, the
multipole mixing ratio is simply related
to the
=1
transition probabilities as:
Similarly, the branching ratio of competing
=1 and
=2
transitions depopulating a level is related to the transition
probabilities through the relation:
From these two measurable quantities, ratios of reduced transition
probabilities can be readily extracted as:
and
in units of 
when is in MeV.
=1 transitions (including its sign) is also calculated.
An example of the full expression for one of the ratios is:
, 
, and 
denote the K value,
g-factor and
alignment of the quasiparticles involved in the configuration,
while 
and 
denote the rotational g-factor and
total K value, respectively. 
, 
, and 
refer to
the particle causing the signature splitting.
A signature dependent term (
)
is present, and so both the mixing ratios and ratios
of reduced transition probabilities are predicted to show signature effects.
Alignments and signature splitting can be estimated from experimental
data using align. The K-values can be
estimated from the Nilsson
single-particle assignments.
The quadrupole moment,
,
can be estimated from calculated deformation parameters.
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