J. Astrophys. Astr. (2009) 30, 165–175
Rapid Neutron Capture Process in Supernovae and Chemical
Rulee Baruah1,∗, Kalpana Duorah2& H. L. Duorah2
1Department of Physics, HRH The Prince of Wales Institute of Engineering and Technology,
Jorhat 785 001, India.
2Department of Physics, Gauhati University, Guwahati 781 014, India.
Received 2007 May 28; accepted 2009 September 29
major nucleosynthesis processes responsible for the synthesis of heavy
nuclei beyond iron. Isotopes beyond Fe are most exclusively formed in
neutron capture processes and more heavier ones are produced by the
r-process. Approximately half of the heavy elements with mass number
A ? 70andalloftheactinidesinthesolarsystemarebelievedtohavebeen
produced in the r-process. We have studied the r-process in supernovae for
the production of heavy elements beyond A = 40 with the newest mass
values available. The supernova envelopes at a temperature ?109K and
sites for the r-process. The primary goal of the r-process calculations is to
fit the global abundance curve for solar system r-process isotopes by vary-
ing time dependent parameters such as temperature and neutron density.
This method aims at comparing the calculated abundances of the stable
isotopes with observation. We have studied the r-process path correspond-
ing to temperatures ranging from 1.0 × 109K to 3.0 × 109K and neutron
density ranging from 1020cm−3to 1030cm−3. With temperature and den-
sity conditions of 3.0 × 109K and 1020cm−3a nucleus of mass 273 was
theoretically found corresponding to atomic number 115. The elements
obtained along the r-process path are compared with the observed data at
all the above temperature and density range.
The rapid neutron capture process (r-process) is one of the
Burbidge et al. (1957), in their seminal paper, outlined the rapid neutron capture
process in the supernova envelope at a high neutron density and a temperature of 109
degrees. According to them, this mode of synthesis is responsible for the produc-
tion of a large number of isotopes in the range 70 ≤ A ≤ 209, and also for synthe-
sis of uranium and thorium. This would explain the abundances of the neutron rich
nuclei in the periodic table. Major advances have been made in calculating r-process
nucleosynthesis in supernovae (Woosley et al. 1992) and in using a wide range of
Rulee Baruah et al.
model parameters to obtain yields that approximate the solar r-process abundances
(Kratz et al. 1993). Studies of galactic chemical evolution (Mathews & Cowan 1992)
show that the enrichment of the r-process elements in the galaxy is consistent with low
mass type II supernovae being the r-process sites. In the usual picture the r-process
stops when the neutron supply ceases (freeze-out). The produced very neutron rich
progenitor nuclei then undergo a series of β-decays until they reach a stable nucleus
whose calculated abundance can then be compared with observation. It was recog-
attainable only in dynamical events, i.e., supernovae.
The essential feature of the r-process is that a large flux of neutrons becomes avail-
able in a short time interval for addition to elements of the iron group, or perhaps, in
nuclei such as Ne22. So we started our analysis with A = 40 and obtained the abun-
dances beyond that. We have summarised our calculations within a site-independent,
classical approach based on neutron number density nnand temperature T9, defin-
ing the neutron binding (separation) energy Qnof the path, where the waiting point
approximation, i.e., (n, γ) ↔ (γ, n) equilibrium could be applied. The dependence
on nuclear masses enters via Qn.
We choose supernova as the site for r-process because the supernova light curves
show the presence of98Cf254. We have considered the r-process in supernovae for
the production of heavy elements, under extreme conditions of temperature and den-
sity. For our purpose, the most interesting evolution occurs as the temperature falls
favours the assemblage of nucleons into α-particles and heavy nuclei. As the tem-
perature drops below about 5.0 × 109K, the reactions responsible for converting
α-particles back into heavy nuclei begin to fall out of equilibrium. By 3.0 × 109K,
the charged particle reactions freeze out. Below this temperature, the r-process occurs
until the temperature reaches (1–2) × 109K, where the neutron reactions also cease
as the neutrons are depleted (Woosley et al. 1994). Using new mass tables of Audi
et al. (2003) we have calculated the average excess neutron binding energy to nuclei
with neutron number which is then used in the calculation of neutron capture chain.
We start with a temperature of 1.0 × 109K and neutron number density of 1020cm−3
as these are the conditions prevailing in supernova envelopes during the eventually
expanding stages. In our present paper, we emphasize only on the r-process path to
obtain the elements in our astrophysical conditions considered and consequent build-
up to heavier nuclei. In our next paper, we propose to present the abundances of these
elements along the path.
2. Source of neutron flux
For the r-process nucleosynthesis in supernovae, the existence of enormous neutron
as13C(α,n)16O can produce free neutrons in red giants, but the number of these free
neutrons is also small. It is possible to circumvent this problem by having the only
charged particles accompanying the neutrons be alphas. Single alpha particles do not
capture neutrons. It is proposed that (Schramm 1973) at high temperatures associated
with the collapse of massive iron core in type II supernovae, iron will photo-dissociate
Neutron Capture and Chemical Elements
into alphas and neutrons as:
56Fe → 13α + 4n.
As the material expands and cools from these photo-dissociation conditions, the
tion is hampered by the fact that alphas only systhesize heavy elements via three-body
interactions. Thus there will be a time during which a few iron peak seed nuclei have
been produced in a sea of alphas and neutrons. The ratio of neutrons to seed will be
large, so that an r-process can take place.
Another set of conditions where large number of free neutrons exist is when
the temperature and density get sufficiently high that the reaction p + e−→ n + νe
dominates over n + e+→ p + ¯ νe(Arnett 1979). Thus neutronisation refers to elec-
tron capture driven by high electron Fermi energy (i.e., high density). Subsequently,
p + e−→ n + νeat high density. Moreover, nuclei resist electron capture because of
the large threshold energies required as they become more neutron rich. Also electron
capture on free protons is limited by the small abundance of free protons. These prob-
lems are eased by higher density and higher temperature, so neutronization speeds up
as collapse continues. Once collapse begins, neutronization becomes the dominant
mode of neutrino productions, overwhelming thermal processes.
According to Mukhopadhyay (2007), the neutrino–antinutrino oscillation under
gravity explains the source of abnormally large neutron abundance to support the
r-process nucleosynthesis in astrophysical site, e.g., supernova. He also proposed two
n + νe→ p + e−;
p + ¯ νe→ n + e+
as given by Arnett (1979). If ¯ νeis over-abundant than νe, then, from this expression,
neutron production is expected to be more than proton production into the system.
Therefore,thepossibleconversionofν to ¯ νeduetogravityinducedoscillationexplains
the over-abundance of neutron.
flow and the track followed in the (A,Z) plane are the (n, γ) and (γ, n) reactions, beta
decay and at the end of the track the neutron induced fission. The timescale τnfor a
heavy nucleus to capture an additional neutron is rapid on the competing timescale τβ
for it to undergo beta decay. Whereas τβdepends only on nuclear species, τndepends
critically on the ambient neutron flux.
λn> λβ(τn< τβ).
In rapid process, a sufficient flux of neutrons makes τnmuch shorter than τβ. Then
neutron capture will proceed into the very neutron rich and unstable regions far from
the valley of beta stability. Once the neutron flux is exhausted, the unstable nuclei
produced by the r-process will beta decay to the valley of stability to form the stable
3. Nuclear physics considerations and the r-process path
To illustrate the significant differences of the astrophysical conditions during
the r-processing, we refer to the classical quantity, namely, the neutron binding
Rulee Baruah et al.
(separation Sn) energy Qn, that represents the r-process path in the chart of nuclides
once the specific values of neutron density nnand the temperature T are assigned.
The Qnvalues vary in time as well as in space along with the dynamical evolution of
our astrophysical environment.
3.1 Dynamical evolution of the neutrino heating phase in type-II supernovae
We first summarize the type-II supernova explosion scenario according to the current
understanding. We emphasize some characteristic features on the hydrodynamical
evolution of the neutrino wind phase. During the final stages of the evolution of a
massive (8 ∼25M?) star, an ‘iron’ core forms in its central region and subsequently
undergoes gravitational collapse. When the central density reaches nuclear matter
density, the collapse stops abruptly to cause a ‘core bounce’. A hydrodynamical shock
wave is created and starts to propagate outward. According to calculations (Bruenn
1989a), this shock wave loses its entire kinetic energy within a few milliseconds to
to about half a second, the neutrinos streaming out from the new born neutron star can
deposit energy behind the standing accretion shock at high enough a rate to revive its
outward motion and initiate the final explosion of the star. This is the neutrino-driven
‘delayed’ explosion mechanism originally suggested by Wilson et al. (1986).
The neutron star releases its gravitational binding energy of several 1053erg in the
form of neutrino radiation. A region of net energy deposition by neutrinos (‘neutrino
of temperature with increasing radius. The energy is transferred to the stellar gas
predominently by absorption of electron neutrinos (νe) on neutrons and electron anti-
neutrinos (¯ νe) on protons. About one percent of the neutron star’s binding energy is
sufficient to drive a powerful shock into the overlaying stellar mantle. Behind the
shock, an extended and rapidly expanding region of low density and relatively high
temperature develops and is further energized by neutrino heating.
Janka (1993) performed hydrodynamical simulations of the formation and evolu-
tion of the neutrino-wind phase of a type II supernova with a proper description
of the neutrino physics and an adequate representation of the equation of state.
The hydrodynamical investigations were carried on from an initial configuration
made available by Wilson. From Wilson’s post-collapse model the radial profiles of
density, temperature, electron concentration, composition and velocity were taken
to specify the initial conditions for the set of partial differential equations, which
was integrated in time to follow the gas composition and the evolution of the fluid
flow in spherical symmetry. The equation of state for the stellar gas contained the
contributions from nucleus, α-particles, and a representative typical heavy nucleus in
nuclear statistical equilibrium. The model evolved under the influence of the neutrino
fluxes from the protoneutron star at the center. Since all hydrodynamical and thermo-
dynamical quantities were determined from the numerically solved set of equations,
the effects of the particular choice of the initial model configuration were not cru-
cial and became even less relevant as time went on. The most important parameter
of the input model to influence the simulated evolution was the mass of the central
neutron star (Witti et al. 1994). However, the hydrodynamical evolution in the range
of temperatures below T9= 2 is not very fast (Takahashi et al. 1994).
Neutron Capture and Chemical Elements
3.2 The r-process network and the waiting-point approximation
Supernova is a dynamical event. When a constant Sn(nnand T) is assumed over a
duration time τ, then the nuclei will still be existent in the form of highly unstable
isotopes, which have to decay back to β-stability. In reality nnand T will be time
T) is important. The abundance flow from each isotopic chain to the next is governed
by beta decays. The waiting point approximation is only valid for high temperatures
and neutron number densities of the gas. If not, the flow of nuclei towards higher
neutron number N for a given proton number Z is steadily depleted by beta decay.
As a result only a small fraction of the flow can easily reach a waiting point. Cameron
et al. (1983b) found that for temperatures of 2.0 × 109K and higher, the waiting point
approximation was valid for neutron number densities as low as 1020cm−3. For lower
temperature (T < 109K) even with high values of nn≈ 1025cm−3, the waiting point
approximation is not valid. The r-process path requires a synthesis time of the order
of seconds to form the heaviest elements such as thorium, plutonium and uranium.
The r-process network includes radiative neutron capture, i.e., (n, γ) reactions, the
inverse photo-disintegration, i.e., (γ, n) reactions, β-decay, i.e., (β, γ) processes and
β-delayed neutron emission, i.e., (β, n) processes. If the neutron density is very high,
successive (n, γ) reactions may produce very neutron rich isotopes out of the limited
α-process network in a ‘mini r-process’. The (n, γ) and (γ, n) reactions are then
much faster than β-decays. Therefore, as soon as the ‘proper’ r-process is started, the
isotopic abundances, stuck at the most neutron-rich isotopes included in the α-process
network, will quickly be redistributed according to the (n, γ) ↔ (γ, n) equilibrium
(Takahashi et al. 1994). In our model, the neutron number densities are so high that
an equilibrium between the (n, γ) and (γ, n) reactions is quickly established.
Inan(n, γ) ↔ (γ, n)equilibrium(thewaiting-pointapproximation),themaximum
abundances in isotopic chains occur at the same neutron separation energy, which is
up of heavy nuclei is governed by the abundance distribution in each isotopic chain
from (n, γ) ↔ (γ, n) equilibrium and by effective decay rates λZ
After charged particle freeze-out, when only (n, γ) ↔ (γ, n) equilibrium remain
in place, matter can progress to heavier nuclei via β-decays between isotopic chains,
which is modelled by the r-process network to follow further evolution (Freiburghaus
et al. 1999).
βof isotopic chains.
4. Calculation of the r-process path
A nucleus of fixed Z cannot add neutrons infinitely even in the presence of an intense
neutron flux. The binding energy of each successive neutron becomes progressively
weaker as more and more neutrons are added until ultimately the binding falls to zero,
which sets an upper limit to neutron addition at fixed Z. The nucleus then waits until
β-decay allows it to move onto the next nucleus. Thus in a rapid process two inverse
reactions n+(Z,A) ↔ (Z,A+1)+γ come to an equilibrium. This balance governs
the equilibrium distribution of isotope abundances for a given Z. The maximum abun-
dance along an isotope chain is determined by the temperature and neutron density.