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11- Neutron capture and the production of heavy elements (mostly r-process
11- Neutron capture and the production of heavy elements (mostly r-process
less straightforward than s-process
heavier elements than bismuth existing support existence of r-process
in terms of calculations and observation matching
also the existence of neutron rich isotopes not easily produced by the s-process supports model
to obtain expected abundances, subtract the s-process contribution
Peaks at lower A value
Stable nuclei are not directly produced by the r-process, but indirectly through beta decay from neutron-rich nuclei
beta decay conserves A, therefore for a value of N, A will be lower
strong abundance peaks ~10 units below atomic numbers equivalent to magic number of neutrons
Neutron capture cross-section is low at these n values
Actual process
Rapid neutron absorption process is repeated over and over until the next neutron is not bound, and does not contribute to binding energy
Then process stops until beta decay occurs
where it stops are the waiting points
For each value of Z there will be a waiting point beyond which the process of neutron absorption cannot continue until a beta decay occurs
Terminated by spontaneous fission, becoming more and more likely between 230<A<270
Fission yeilds seed nuclei which can be re built up by neutron absorption
r-process can be thought of as cyclic
At high temperatures, another mechanism can halt the r-process
Photo-nuclear emission due to thermal photons
A set of coupled differential equations, where Nz is inversly proportional to the beta decay
Odd N nucleus less tightly bound than a neighbouring isotope with even N, thus the waiting points more likely to be at even N nuclei
would produce a weakly bound neutron after absorption
For of binding energy as a function of A and Z is not known for nuclei far from the region of beta stability which is a problem
Can use liquid drop/shell model with refinements to take into accound
abupt change in binding energy at neutron shell closures
changes to nuclear stability associated with deformation of large nuclei
Estimated values exist now
Total r-process time
waiting points
longer than average half lives ~0.4s
other 50 or so beta decays ~0.5s
neutron capture rate
fission cycling
about 5s for neutron densities n~e30 and T~e9 K
Relation to abundances
at neutron magic numbers (N=50,82,126) there will be a sequence of waiting points because of the subsequent low binding energy
These waiting times are considerable and gives rise to peaks in abundance curve
Lines of constant A in progenitors indicate beta decay will produce peaks in stable nuclei abundances at A-130 and 195, agrees with observations
these peaks remain visible in the overall abundance curve
S-process have somewhat sharper peaks at the magic neutron number themselves