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J. Astrophys. Astr. (2009) 30, 165–175

Rapid Neutron Capture Process in Supernovae and Chemical

Element Formation

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.

∗e-mail: ruleebaruah@yahoo.co.in

Received 2007 May 28; accepted 2009 September 29

Abstract. The rapid neutron capture process (r-process) is one of the

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

A70 and all of the actinides in the solar system are believed to have been

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

neutron density of 1024 cm−3are considered to be one of the most potential

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 1.0×109Kto3.0×109K and neutron

density ranging from 1020 cm−3to 1030 cm−3. With temperature and den-

sity conditions of 3.0×109K and 1020 cm−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.

Key words. Supernova—nucleosynthesis—abundance—r-process.

1. Introduction

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

165

166 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-

nised that the extremely high neutron densities and temperatures needed were probably

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

cases where the abundances in the iron group are abnormally small, for addition to light

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 of 98Cf254. 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

from 1010 Kto10

9K. Beginning at about 1010 K, nuclear statistical equilibrium (NSE)

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 1020 cm−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

ﬂux is necessitated. Normal stellar matter has a neutron/proton ratio near unity making

it virtually impossible to free sufﬁcient neutrons relative to seed nuclei. Reactions such

as 13C(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 167

into alphas and neutrons as:

56Fe →13α+4n.

As the material expands and cools from these photo-dissociation conditions, the

alphas recombine again to produce heavy iron peak nuclei. However, these recombina-

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

related reactions

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, the possible conversion of νto ¯νedue to gravity induced oscillation explains

the over-abundance of neutron.

In the build-up of nuclei by the r-process, the reactions which govern both the rate of

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>λ

β(τn<τ

β). (1)

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

r-process elements.

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

168 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 Tare 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 ∼25 M) 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

stall well inside the outer edge of the initial iron core, and no immediate disruption (the

‘prompt’ expolsion) of the star occurs. On a timescale from several tens of milliseconds

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 1053 erg in the

form of neutrino radiation. A region of net energy deposition by neutrinos (‘neutrino

heating’) naturally emerges at the periphery of the neutron star because of the decrease

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 169

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 Twill be time

dependent. As long as these are high enough to ensure the waiting point approximation,

the system will immediately adjust to the new equilibrium and only the new Sn(nnand

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 Zis 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 1020 cm−3. For lower

temperature (T<109K) even with high values of nn≈1025 cm−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.

In an (n,γ)↔(γ, n)equilibrium (the waiting-point approximation), the maximum

abundances in isotopic chains occur at the same neutron separation energy, which is

determined by a combination of nnand T9in an astrophysical environment. Connecting

the abundance maxima in isotopic chains deﬁnes the so called r-process path. The build-

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

βof isotopic chains.

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).

4. Calculation of the r-process path

A nucleus of ﬁxed Zcannot 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)+γcome 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.

170 Rulee Baruah et al.

Given that A/(A +1)≈1, the abundance maxima in each isotopic chain are deter-

mined by the neutron number density nnand temperature T. The maximum value of

the abundance occurs at neutron separation energy Snwhich is same for all isotopic

chains irrespective of Z. Approximating abundances Y(Z,A +1)/Y (Z , A) ≈1at

the maximum and keeping all other quantities constant, the neutron separation energy

Snhas to be the same for the abundance maxima in all isotopic chains.

The condition for the dynamical equilibrium between (n, γ) and (γ, n) reactions for

nucleus X(A,Z) is expressed as (Burbidge et al. 1957):

X(A, Z) +n⇐⇒ X(A +1,Z) +γ+Qn(A, Z), (2)

where Qn(A, Z) is the neutron binding (separation energy Sn) to the nucleus X(A,Z).

Writing n(A, Z) and nnfor the number densities of the nuclei (A, Z) and neutrons

respectively, the statistical balance in this reaction is expressed by (Burbidge et al.

1957):

log(n(A +1, Z)/n(A, Z)) =log nn−34.07 −(3/2)log T9+(5.04/T9)Qn(3)

T9being temperature in units of 109degrees.

Using the condition that in equilibrium, n(A +1,Z) ≈n(A, Z) we obtain Qnas:

Qn=(T9/5.04)(34.07 +(3/2)log T9−log nn). (4)

A rough estimate of Qnvalues that are preferred for explaining the r-process abun-

dance curve can be gained by taking into account the correlation between the r-process

abundance peaks and the neutron magic numbers. The prominent peaks at A≈130

and A≈195 are correlated with the nuclear shell effects of their precursor nuclei near

the neutron magic numbers 82 and 126 respectively. With the aid of nuclear mass for-

mula, one ﬁnds from the abundance peaks that the Qnvalue is most likely somewhere

in between 2 and 4 MeV. To attain this, we take the temperature and density conditions

considered here to range from

T=1.0×109Kto3.0×109K and nn=1020 cm−3to 1030 cm−3.

The variation of Qnvalues with temperature and neutron number densities is shown

in Table 1.

We then tried to outline a method of calculation of r-process abundances which may

eventually be capable of yielding a theoretical abundance curve on the basis of nuclear

data alone. First, we consider the determination of Qn(A, Z) on the basis of smooth

Weizsacker atomic mass formula given by equation (5) neglecting shell, pairing and

quadrupole deformation effects:

Mw(A, Z) =(A −Z)Mn+ZMp−(1/c2)[αA −β(A −2Z)2/A

−γA

2/3−Z(Z −1)/A1/3],(5)

where Mnand Mpare masses of the neutron and proton and α,β,γand are constants

in energy units, which represent volume, isotopic, surface and coulomb energy para-

meters respectively, the values being taken from Burbidge et al. (1957). With these we

modify the expression for M(A,Z) as:

M(A,Z) =Mw(A, Z) −(1/c2)[f(N)+g(Z)],(6)

Neutron Capture and Chemical Elements 171

Table 1. Variation of Qnvalues with temperature and density.

T9(K) nn(cm−3)Qn(Mev) T9(K) nn(cm−3)Qn(Mev)

1.0 1020 2.79 1.0 1022 2.39

1.2 1020 3.37 1.2 1022 2.90

1.4 1020 3.96 1.4 1022 3.41

1.6 1022 4.56 1.6 1022 3.93

1.0 1024 1.99 1.8 1022 4.45

1.2 1024 2.41 1.2 1026 1.95

1.4 1024 2.85 1.4 1026 2.30

1.6 1024 3.29 1.6 1026 2.65

1.8 1024 3.73 1.8 1026 3.01

2.0 1024 4.17 2.0 1026 3.38

1.6 1028 2.02 2.2 1026 3.74

1.8 1028 2.30 2.4 1026 4.11

2.0 1028 2.58 2.2 1030 1.98

2.2 1028 2.87 2.4 1030 2.19

2.4 1028 3.16 2.6 1030 2.42

2.6 1028 3.45 2.8 1030 2.63

2.8 1028 3.74 3.0 1030 2.84

3.0 1028 4.03

where Mw(A, Z) represents the Weizsacker expression given by equation (5). With

this we calculate the neutron binding energy as:

Qn(A, Z) =Bn(A +1,Z) =c2[M(A, Z) +Mn−M(A +1,Z)].(7)

We note that Qnfor nucleus (A, Z) is equal for the neutron binding energy Bn(taken

positive) in nucleus (A +1,Z). These functions of Nand Zseparately takes into

account the important effects on nuclear masses of:

•neutron and proton shell structure

•spheroidal quadrupole deformation of partially ﬁlled shells and

•pairing of neutrons and pairing of protons.

The quantities f(N)and g(Z) will be discontinuous functions at magic closed shell

numbers for Nand Zrespectively. The sign is taken negative so that f(N)and g(Z)

as positive quantities, decrease the mass and add to the stability of the nucleus.

We now obtain:

Qn(A, Z) =f(A,Z)+f(A −Z) (8)

putting M(A,Z) from equation (6) and using:

f(A −Z) =f(N) =df (N)/d (N) =f(A +1−Z) −f(A−Z). (9)

On simpliﬁcation and on putting Z=A−N, we rewrite equation (8) as:

Qn(A, N ) =f(A,N)+f(N ).

172 Rulee Baruah et al.

Figure 1. The average excess neutron binding energy vs. neutron number N, over that given

by the smooth Weizsacker atomic mass formula.

Figure 2. The average r-process path in the (A, Z) plane at all the temperature and density

conditions considered, showing the schematic view of the isotopes produced.

Here f(N) is the excess neutron binding energy to nuclei with a speciﬁed Nover

that given by the smooth Weizsacker mass formula normalised to zero at the beginning

of the shell in which Nlies. We have used the mass tables of Audi et al. (2003) and

for various N, the resulting average values have been plotted against N. Another form

of averaging is then affected by drawing a smooth curve through the points obtained

in this way and plotted in Fig. 1. These equations are then solved for ﬁxed values of

Z, to obtain the corresponding values of Aby trial and error, at different temperature

and density conditions which specify Qnin equation (8). The neutron capture paths

so obtained are then plotted in Fig. 2.

Neutron Capture and Chemical Elements 173

5. Existence of chemical elements along the r-process path

In our classical condition we notice an element of mass 273 corresponding to atomic

number 115. Experimentally some new elements were synthesized at the Lawrence

Berkley Laboratory, e.g., elements with Z=116, 118, etc. (Swiatecki et al. 2005).

Also theories have long predicted the island of stability for nuclei with approximately

114 protons and 184 neutrons. Thus we conclude that a nuclei with mass 273 is a

possibility. The seed nuclei in the neutrino driven wind are produced early in the

expansion by alpha-capture or by proton-capture processes. When the temperature and

density become low in a short dynamic time scale and the charged particle reactions

almost cease, the r-process starts from these seed nuclei. So we start our calculation

at 20Ca40 and obtain the neutron capture path beyond that.

We notice that at densities >1030 cm−3, the r-process chain does not show the ele-

ments as seen in data of Audi et al. (2003). As we try to obtain the elements at

lower densities in our analysis, we ﬁnd them more prominently as we go from high to

low density site. Most of our observed elements are seen in the range of neutron num-

ber density 1020 cm−3to 1024 cm−3and temperature from 2.0×109Kto3.0×109K.

For example, at densities 1028 cm−3,10

26 cm−3, etc., the r-process chain does not give

us all the observable elements. But at condition of density 1020 cm−3and temperature

T9=2.0, that path contains all the elements as was given in the experimental data of

Audi et al. (2003).

We tabulate some of the elements (experimental) obtained along the r-process path

as follows:

We note that the element 98Cf254 shown by the supernova light curves is found

in our classical astrophysical condition of temperature T9=1.9 and neutron num-

ber density nn=1020 cm−3. We also note that the double magic nucleus 28Ni78

50 is

obtained at T9=1.0 and nn=1020 cm−3;T9=1.1 and nn=1022 cm−3;T9=1.2

and nn=1024 cm−3;T9=1.4 and nn=1026 cm−3;T9=2.0 and nn=1028 cm−3;

all of these conditions correspond to Qnvalue ≈2.5 Mev. Another double magic

Table 2. Chemical elements at the r-process site.

Element T9(109K)n

n(cm−3)

56Ba137 2.5 1020

82Pb207 2.5 1022

92U236 3.0 1022

98Cf254 1.9 1020

For double magic nuclei

28Ni78

50 1.0 1020

1.1 1022

1.2 1024

1.4 1026

2.0 1028

50Sn132

82 1.7 1020

1.9 1022

174 Rulee Baruah et al.

nucleus 50Sn132

82 is found in our analysis at T9=1.7 and nn=1020 cm−3;T9=1.9

and nn=1022 cm−3; these correspond to Qnvalue ≈4.5Mev.

6. Discussion and conclusion

Whenever and however the r-process operates, it appears to be very uniform and well

conﬁned in astrophysical parameter space. The temperature, density and neutron ﬂux

at r-process sites vary over a small range. This means that only a small minority of

type II supernovae produces r-process elements. The beta decay lifetimes, separation

energy, neutron ﬂux, the temperature range, the equilibrium chain and collapse time, all

are built in to the equations, which are, then numerically solved to determine the chain

for various separation energies. The neutrino winds drive out the r-process elements

which then decay to the lines nearer to the beta-stable valley, and, they are ready for

comparison with observation.

We have studied the r-process path at various temperatures ranging from 1.0×109K

to 3.0×109K and neutron number densities ranging from 1020 cm−3to 1030 cm−3.

We mostly concentrate our analysis at energies greater than 2 Mev as this is the condi-

tion prevailing in the supernova envelopes and neutron capture occurs during the later

expanding stage. We have used the mass table of Audi et al. (2003) for the calculation

of the average excess neutron binding energy which is obtained by the normalization

at the magic neutron numbers 20, 50, 82, 126. It has been found that a nucleus is stable

if the number of neutrons or protons in it is equal to the magic number, and it can-

not capture further neutrons because the shells are closed and they cannot contain an

extra neutron. With the subsequent addition of neutrons at ﬁxed Z, correspondingly

the binding falls and ultimately falls to zero. At this point, the nucleus undergoes a

β-decay and gets converted to the next element. This r-process path is shown in Fig. 2

by corresponding relations between Zand A.

As the high density conditions do not show much of the experimentally observed

elements, we propose that the heavy elements which must have been produced during

the extreme condition of supernova explosion instantly undergo photo-disintegration at

the high density and temperature situation. Only in the later expansion stages after the

explosion, where the neutron density supposedly falls, the r-process nucleosynthesis

produces the heavy elements which subsequently β-decays and the r-process path

forms. We conclude that the heavy elements were created after supernova explosion and

in the later expansion stages they were distributed all over the universe. In supernova

during the expansion stage if the ejected matter ﬂow reaches the waiting point nuclei

associated with the magic neutron numbers at rather small radii above the neutron

star, neutrino induced charged current reactions can compete with the β-decays of the

longest lived waiting point nuclei and thus speed up the matter ﬂow to heavier nuclei.

We tried to get our abundances with respect to all the nuclei whose β-decay lifetimes

are considerably higher. We conclude that our theoretical model will be successful in

providing new light to solve some problems in the r-process and the corresponding

build-up to heavier nuclei.

Acknowledgements

The authors are sincerely thankful to the Government of Assam for giving the per-

mission to carry out the research work. Grateful thanks are due to B. K. Rajkhowa of

Neutron Capture and Chemical Elements 175

POWIET and Dr S. M. Hazarika of Tezpur University for their valuable help during

the preparation of the manuscript.

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