P-nuclei
Encyclopedia
p-Nuclei are certain proton-rich, naturally occurring isotope
s of some elements
between selenium
and mercury
which cannot be produced in either s-
or r-process
.
s beyond the element Iron
can be made in two kinds of neutron capture
processes, the s- and the r-process. Some proton-rich nuclides found in Nature are not reached in these processes and therefore at least one additional process is required to synthesize them. These nuclei
are called p-Nuclei.
Since the definition of the p-nuclei depends on the current knowledge of the s- and r-process (see also nucleosynthesis
), the original list of 35 p-nuclei may be modified over the years, as indicated in the Table below.
For example, it is recognized today that the abundances
of 152Gd and 164Er contain at least strong contributions from the s-process
. This also seems to apply to those of 113In and 115Sn, which additionally could be made in the r-process
in small amounts.
The long-lived
radionuclide
s 92Nb, 97Tc, 98Tc and 146Sm are not among the classically defined p-nuclei as they do not naturally occur on Earth. By the above definition, however, they are also p-nuclei because they cannot be made in either s- or r-process. From the discovery of their decay product
s in presolar grains
it can be inferred that at least 92Nb and 146Sm were present in the solar nebula
. This offers the possibility to estimate the time since the last production of these p-nuclei before the formation of the solar system
.
p-Nuclei are very rare. Those isotopes of an element, which are p-nuclei, are less abundant typically by factors of
than the other isotopes of the same element. The abundances of p-nuclei can only be determined in geochemical
investigations and by analysis of meteoritic
material and presolar grains
. They cannot be identified in stellar spectra. Therefore the knowledge of p-abundances is restricted to those of the solar system and it is unknown whether the solar abundances of p-nuclei are typical for the Milky Way
.
production of p-nuclei is not completely understood yet. The favored
-process (see below) in core-collapse supernovae
cannot produce
all p-nuclei in sufficient amounts, according to current computer simulation
s. This is why additional production mechanisms and astrophysical sites are under investigation, as outlined below. It is also conceivable that there is not just a single process responsible for all p-nuclei but that different processes in a number of astrophysical sites produce certain ranges of p-nuclei.
In the search for the relevant processes creating p-nuclei, the usual way is to identify the possible production mechanisms (processes) and then to investigate their possible realization in various astrophysical sites. The same logic is applied in the discussion below.
s: by successively adding proton
s to a nuclide (these are nuclear reaction
s of type
) or by removing neutrons from a nucleus through sequences of photodisintegration
s of type
.
Under conditions encountered in astrophysical environments it is difficult to obtain p-nuclei through proton captures because the Coulomb barrier
of a nucleus increases with increasing Proton number. A proton requires more energy to be incorporated (captured) into an atomic nucleus when the Coulomb barrier is higher. The available average energy of the protons is determined by the temperature
of the stellar plasma
. Increasing the temperature, however, also speeds up the
photodisintegrations which counteract the 
captures. The only alternative avoiding this would be to have a very large number of protons available so that the effective number of captures per second is large even at low temperature. In extreme cases (as discussed below) this leads to the synthesis of extremely short-lived radionuclide
s which decay
to stable nuclides only after the captures cease.
Appropriate combinations of temperature and proton density of a stellar plasma have to be explored in the search of possible production mechanisms for p-nuclei. Further parameter
s are the time available for the nuclear processes, and number and type of initially present nuclides (seed nuclei).
s or stellar explosions.
Based on its historical meaning, the term p-process is sometimes sloppily used for any process synthesizing p-nuclei, even when no proton captures are involved.
The
p-Nuclei can also be obtained by photodisintegration
of s- and r-process nuclei. At temperatures around 2-3 Giga
-Kelvin
(GK) and short process time of a few seconds (this requires an explosive process) photodisintegration of the pre-existing nuclei will remain small, just enough to produce the required tiny abundances of p-nuclei. This is called γ-process because the photodisintegration proceeds by nuclear reaction
s of the types
, 
and 
, which are caused by highly energetic photon
s (Gamma ray
s).
The
Nuclear reaction
s triggered by neutrino
s can directly produce certain nuclides, for example 7Li, 11B, 19F, 138La in core-collapse supernovae
.
This is called ν-process and requires a sufficiently intensive source of neutrinos.
atomic nuclei.
If there is a high proton density in the stellar plasma, even short-lived radionuclides can capture one or more protons before they beta decay
. This quickly moves the nucleosynthesis
path from the region of stable nuclei to the very proton-rich side of the Chart of Nuclides. This is called rapid proton-capture.
Here, a series of
reactions proceeds until either the beta decay
of a nucleus is faster than a further proton capture, or the proton drip line is reached. Both cases lead to one or several sequential beta decays until a nucleus is produced which again can capture protons before it beta decays. Then the proton capture sequences continue.
It is possible to cover the region of the lightest nuclei up to 56Ni within a second because both proton captures and beta decays are fast. Starting with 56Ni, however, a number of waiting points are encountered in the reaction path. These are nuclides which both have relatively long half-lives
(compared to the process timescale) and can only slowly add another proton (that is, their cross section
for
reactions is small). Examples for such waiting points are: 56Ni, 60Zn, 64Ge, 68Se. Further waiting points may be important, depending on the detailed conditions and location of the reaction path. It is typical for such waiting points to show half-lives of minutes to days. Thus, they considerably increase the time required to continue the reaction sequences. If the conditions required for this rapid proton capture are only present for a short time (the timescale of explosive astrophysical events is of the order of seconds), the waiting points limit or hamper the continuation of the reactions to heavier nuclei.
In order to produce p-nuclei, the process path has to encompass nuclides bearing the same mass number
(but usually containing more protons) as the desired p-nuclei. These nuclides are then converted into p-nuclei through sequences of beta decays after the rapid proton captures ceased.
Variations of the main category rapid proton captures are the rp-, pn-, and νp-processes, which will be briefly outlined below.
The so-called rp-process (rp is for rapid proton capture) is the purest form of the rapid proton capture process described above. At proton densities of more than
protons/cm3 and temperatures around 2 GK the reaction path is close to the proton drip line. The waiting points can be bridged provided that the process time is 10-600 s. Waiting-point nuclides are produced with larger abundances while the production of nuclei "behind" each waiting-point is more and more suppressed.
A definitive endpoint is reached close to 107Te because the reaction path runs into a region of nuclides which decay preferably by alpha decay
and thus loop the path back onto itself. Therefore an rp-process would only be able to produce p-nuclei with mass number
s less than or equal to 107.
The waiting points in rapid proton capture processes can be avoided by
reactions which are much faster than proton captures on or beta decays of waiting points nuclei. This results in a considerable reduction of the time required to build heavy elements and allows an efficient production within seconds. This requires, however, a (small) supply of free neutron
s which are usually not present in such proton-rich plasmas. One way to obtain them is to release them through other reactions occurring simultaneously as the rapid proton captures. This is called neutron-rich rapid proton capture or pn-process.
Another possibility to obtain the neutrons required for the accelerating
reactions in proton-rich environments is to use the anti-neutrino capture on protons 
, turning a proton and an anti-neutrino into a positron
and a neutron. Since (anti-)neutrinos interact only very weakly with protons, a high flux
of anti-neutrinos has to act on a plasma with high proton density. This is called νp-process.
s end their life in a core-collapse supernova
. In such a supernova, a shockfront from an explosion runs from the center of the star through its outer layers and ejects these. When the shockfront reaches the O/Ne-shell of the star (see also stellar evolution
), the conditions for a γ-process are reached for 1-2 s.
Although the majority of p-nuclei can be made in this way, some mass
regions of p-nuclei turn out to be problematic in model calculations. It has been known already for decades that p-nuclei with mass numbers
cannot be produced in a γ-process. Modern simulations also show problems in the range 
.
The p-nucleus 138La is not produced in the γ-process but it can be made in a ν-process. A hot neutron star
is made in the center of such a core-collapse supernova and it radiates neutrinos with high intensity. The neutrinos interact also with the outer layers of the exploding star and cause nuclear reactions which create 138La, among other nuclei. Also 180Ta may receive a contribution from this ν-process.
It was suggested to supplement the γ-process in the outer layers of the star by another process, occurring in the deepest layers of the star, close to the neutron star but still being ejected instead of falling onto the neutron star surface. Due to the initially high flow of neutrinos from the forming neutron star, these layers become extremely proton-rich through the reaction
. Although the anti-neutrino flux is initially weaker a few neutrons will be created, nevertheless, because of the large number of protons. This allows a νp-process in these deep layers. Because of the short timescale of the explosion and the high Coulomb barrier
of the heavier nuclei, such a νp-process could possibly only produce the lightest p-nuclei. Which nuclei are made and how much of them depends sensitively on many details in the simulations and also on the actual explosion mechanism of a core-collapse supernova, which still is not completely understood.
in a binary star
system, triggered by thermonuclear reactions in matter from a companion star accreted
on the surface of the White Dwarf. The accreted matter is rich in Hydrogen
(protons) and Helium
(α particles
) and becomes hot enough to allow nuclear reaction
s.
A number of models for such explosions are discussed in literature, of which two were explored regarding the prospect of producing p-nuclei. None of these explosions release neutrinos, therefore rendering ν- and νp-process impossible. Conditions required for the rp-process are also not attained.
Details of the possible production of p-nuclei in such supernovae depend sensitively on the composition of the matter accreted from the companion star (the seed nuclei for all subsequent processes). Since this can change considerably from star to star, all statements and models of p-production in thermonuclear supernovae are prone to large uncertainties.
The consensus model of thermonuclear supernovae postulates that the White Dwarf explodes after exceeding the Chandrasekhar limit
by the accretion of matter because the contraction and heating ignites explosive carbon burning under degenerate
conditions. A nuclear burning front runs through the White Dwarf from the inside out and tears it apart. Then the outermost layers closely beneath the surface of the White Dwarf (containing 0.05 solar mass
es of matter) exhibit the right conditions for a γ-process.
The p-nuclei are made in the same way as in the γ-process in core-collaps supernovae and also the same difficulties are encountered. In addition, 138La and 180Ta are not produced. A variation of the seed abundances by assuming increased s-process
abundances only scales the abundances of the resulting p-nuclei without curing the problems of relative underproduction in the nuclear mass ranges given above.
In a subclass of type Ia supernova
e, the so-called subChandrasekhar supernova, the White Dwarf may explode long before it reaches the Chandrasekhar limit because nuclear reactions in the accreted matter can already heat the White Dwarf during its accretion phase and trigger explosive carbon burning prematurely. Helium-rich accretion favors this type of explosion. Helium burning ignites degeneratively on the bottom of the accreted helium layer and causes two shockfronts. The one running inwards ignites the carbon explosion. The outwards moving front heats the outer layers of the White Dwarf and ejects them. Again, these outer layers are site to a γ-process at temperatures of 2-3 GK. Due to the presence of α particles (Helium nuclei), however, additional nuclear reactions become possible. Among those are such which release a large number of neutrons, such as 18O
21Ne, 22Ne
25Mg, and 26Mg
29Si. This allows a pn-process in that part of the outer layers which experiences temperatures above 3 GK.
Those light p-nuclei which are underproduced in the γ-process can be so efficiently made in the pn-process that they even show much larger abundances than the other p-nuclei. To obtain the observed solar relative abundances, a strongly enhanced s-process
seed (by factors of 100-1000 or more) has to be assumed which increases the yield of heavy p-nuclei from the γ-process.
in a binary star
system can also accrete matter from the companion star on its surface. Combined hydrogen and helium burning ignites when the accreted layer of degenerate matter
reaches a density of
g/cm3 and a temperature exceeding 0.2 GK. This leads to thermonuclear burning comparable to what happens in the outwards moving shockfront of subChandrasekhar supernovae. The neutron star itself is not affected by the explosion and therefore the nuclear reactions in the accreted layer can proceed longer than in an explosion. This allows to establish an rp-process. It will continue until either all free protons are used up or the burning layer has expanded due to the increase in temperature and its density falls below the one required for the nuclear reactions.
It was shown that the properties of X-ray bursts
in the Milky Way
can be explained by an rp-process on the surface of accreting neutron stars. It remains unclear, yet, whether matter (and if, how much matter) can be ejected and escape the gravitational field
of the neutron star. Only if this is the case can such objects be considered as possible sources of p-nuclei. Even if this is corroborated, the demonstrated endpoint of the rp-process limits the production to the light p-nuclei (which are underproduced in core-collapse supernovae).
Isotope
Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...
s of some elements
Chemical element
A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. Familiar examples of elements include carbon, oxygen, aluminum, iron, copper, gold, mercury, and lead.As of November 2011, 118 elements...
between selenium
Selenium
Selenium is a chemical element with atomic number 34, chemical symbol Se, and an atomic mass of 78.96. It is a nonmetal, whose properties are intermediate between those of adjacent chalcogen elements sulfur and tellurium...
and mercury
Mercury (element)
Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...
which cannot be produced in either s-
S-process
The S-process or slow-neutron-capture-process is a nucleosynthesis process that occurs at relatively low neutron density and intermediate temperature conditions in stars. Under these conditions the rate of neutron capture by atomic nuclei is slow relative to the rate of radioactive beta-minus decay...
or r-process
R-process
The r-process is a nucleosynthesis process, likely occurring in core-collapse supernovae responsible for the creation of approximately half of the neutron-rich atomic nuclei that are heavier than iron. The process entails a succession of rapid neutron captures on seed nuclei, typically Ni-56,...
.
Definition
The classical, ground-breaking works of Burbidge, Burbidge, Fowler und Hoyle (1957) and of A. G. W. Cameron (1957) showed how the majority of naturally occurring nuclideNuclide
A nuclide is an atomic species characterized by the specific constitution of its nucleus, i.e., by its number of protons Z, its number of neutrons N, and its nuclear energy state....
s beyond the element Iron
Iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...
can be made in two kinds of neutron capture
Neutron capture
Neutron capture is a kind of nuclear reaction in which an atomic nucleus collides with one or more neutrons and they merge to form a heavier nucleus. Since neutrons have no electric charge they can enter a nucleus more easily than positively charged protons, which are repelled...
processes, the s- and the r-process. Some proton-rich nuclides found in Nature are not reached in these processes and therefore at least one additional process is required to synthesize them. These nuclei
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...
are called p-Nuclei.
Since the definition of the p-nuclei depends on the current knowledge of the s- and r-process (see also nucleosynthesis
Nucleosynthesis
Nucleosynthesis is the process of creating new atomic nuclei from pre-existing nucleons . It is thought that the primordial nucleons themselves were formed from the quark–gluon plasma from the Big Bang as it cooled below two trillion degrees...
), the original list of 35 p-nuclei may be modified over the years, as indicated in the Table below.
For example, it is recognized today that the abundances
Abundance of the chemical elements
The abundance of a chemical element measures how relatively common the element is, or how much of the element is present in a given environment by comparison to all other elements...
of 152Gd and 164Er contain at least strong contributions from the s-process
S-process
The S-process or slow-neutron-capture-process is a nucleosynthesis process that occurs at relatively low neutron density and intermediate temperature conditions in stars. Under these conditions the rate of neutron capture by atomic nuclei is slow relative to the rate of radioactive beta-minus decay...
. This also seems to apply to those of 113In and 115Sn, which additionally could be made in the r-process
R-process
The r-process is a nucleosynthesis process, likely occurring in core-collapse supernovae responsible for the creation of approximately half of the neutron-rich atomic nuclei that are heavier than iron. The process entails a succession of rapid neutron captures on seed nuclei, typically Ni-56,...
in small amounts.
The long-lived
Half-life
Half-life, abbreviated t½, is the period of time it takes for the amount of a substance undergoing decay to decrease by half. The name was originally used to describe a characteristic of unstable atoms , but it may apply to any quantity which follows a set-rate decay.The original term, dating to...
radionuclide
Radionuclide
A radionuclide is an atom with an unstable nucleus, which is a nucleus characterized by excess energy available to be imparted either to a newly created radiation particle within the nucleus or to an atomic electron. The radionuclide, in this process, undergoes radioactive decay, and emits gamma...
s 92Nb, 97Tc, 98Tc and 146Sm are not among the classically defined p-nuclei as they do not naturally occur on Earth. By the above definition, however, they are also p-nuclei because they cannot be made in either s- or r-process. From the discovery of their decay product
Decay product
In nuclear physics, a decay product is the remaining nuclide left over from radioactive decay. Radioactive decay often involves a sequence of steps...
s in presolar grains
Presolar grains
Presolar grains are isotopically-distinct clusters of material found in the fine-grained matrix of primitive meteorites, such as chondrites, whose differences from the surrounding meteorite suggest that they are older than the solar system...
it can be inferred that at least 92Nb and 146Sm were present in the solar nebula
Solar nebula
In cosmogony, the nebular hypothesis is the most widely accepted model explaining the formation and evolution of the Solar System. There is evidence that it was first proposed in 1734 by Emanuel Swedenborg. Originally applied only to our own Solar System, this method of planetary system formation...
. This offers the possibility to estimate the time since the last production of these p-nuclei before the formation of the solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...
.
p-Nuclei are very rare. Those isotopes of an element, which are p-nuclei, are less abundant typically by factors of
than the other isotopes of the same element. The abundances of p-nuclei can only be determined in geochemicalGeochemistry
The field of geochemistry involves study of the chemical composition of the Earth and other planets, chemical processes and reactions that govern the composition of rocks, water, and soils, and the cycles of matter and energy that transport the Earth's chemical components in time and space, and...
investigations and by analysis of meteoritic
Meteorite
A meteorite is a natural object originating in outer space that survives impact with the Earth's surface. Meteorites can be big or small. Most meteorites derive from small astronomical objects called meteoroids, but they are also sometimes produced by impacts of asteroids...
material and presolar grains
Presolar grains
Presolar grains are isotopically-distinct clusters of material found in the fine-grained matrix of primitive meteorites, such as chondrites, whose differences from the surrounding meteorite suggest that they are older than the solar system...
. They cannot be identified in stellar spectra. Therefore the knowledge of p-abundances is restricted to those of the solar system and it is unknown whether the solar abundances of p-nuclei are typical for the Milky Way
Milky Way
The Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...
.
| Nuclide | | Comment |
|---|---|
| 74Se | |
| 78Kr | |
| 84Sr | |
| 92Nb | long-lived radionuclide; not a classical p-nucleus but cannot be made in s- and r-process |
| 92Mo | |
| 94Mo | |
| 97Tc | long-lived radionuclide; not a classical p-nucleus but cannot be made in s- and r-process |
| 98Tc | long-lived radionuclide; not a classical p-nucleus but cannot be made in s- and r-process |
| 96Ru | |
| 98Ru | |
| 102Pd | |
| 106Cd | |
| 108Cd | |
| 113In | (Partially) made in the s-process? Contributions from the r-process? |
| 112Sn | |
| 114Sn | |
| 115Sn | (Partially) made in the s-process? Contributions from the r-process? |
| 120Te | |
| 124Xe | |
| 126Xe | |
| 130Ba | |
| 132Ba | |
| 138La | made in the ν-process |
| 136Ce | |
| 138Ce | |
| 144Sm | |
| 146Sm | long-lived radionuclide; not a classical p-nucleus but cannot be made in s- and r-process |
| 152Gd | (Partially) made in the s-process? |
| 156Dy | |
| 158Dy | |
| 162Er | |
| 164Er | (Partially) made in the s-process? |
| 168Yb | |
| 174Hf | |
| 180Ta | (Partially) made in the ν-process; contributions from the s-process? |
| 180W | |
| 184Os | |
| 190Pt | |
| 196Hg |
Origin of the p-nuclei
The astrophysicalAstrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
production of p-nuclei is not completely understood yet. The favored
-process (see below) in core-collapse supernovaeType II supernova
A Type II supernova results from the rapid collapse and violent explosion of a massive star. A star must have at least 9 times, and no more than 40–50 times the mass of the Sun for this type of explosion. It is distinguished from other types of supernova by the presence of hydrogen in its spectrum...
cannot produce
all p-nuclei in sufficient amounts, according to current computer simulation
Computer simulation
A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system...
s. This is why additional production mechanisms and astrophysical sites are under investigation, as outlined below. It is also conceivable that there is not just a single process responsible for all p-nuclei but that different processes in a number of astrophysical sites produce certain ranges of p-nuclei.
In the search for the relevant processes creating p-nuclei, the usual way is to identify the possible production mechanisms (processes) and then to investigate their possible realization in various astrophysical sites. The same logic is applied in the discussion below.
Basics of p-nuclide production
In principle, there are two ways to produce proton-rich nuclideNuclide
A nuclide is an atomic species characterized by the specific constitution of its nucleus, i.e., by its number of protons Z, its number of neutrons N, and its nuclear energy state....
s: by successively adding proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
s to a nuclide (these are nuclear reaction
Nuclear reaction
In nuclear physics and nuclear chemistry, a nuclear reaction is semantically considered to be the process in which two nuclei, or else a nucleus of an atom and a subatomic particle from outside the atom, collide to produce products different from the initial particles...
s of type
) or by removing neutrons from a nucleus through sequences of photodisintegrationPhotodisintegration
Photodisintegration is a physical process in which an extremely high energy gamma ray interacts with an atomic nucleus and causes it to enter an excited state, which immediately decays by emitting a subatomic particle. A single proton or neutron is effectively knocked out of the nucleus by the...
s of type
.Under conditions encountered in astrophysical environments it is difficult to obtain p-nuclei through proton captures because the Coulomb barrier
Coulomb barrier
The Coulomb barrier, named after Coulomb's law, which is named after physicist Charles-Augustin de Coulomb , is the energy barrier due to electrostatic interaction that two nuclei need to overcome so they can get close enough to undergo a nuclear reaction...
of a nucleus increases with increasing Proton number. A proton requires more energy to be incorporated (captured) into an atomic nucleus when the Coulomb barrier is higher. The available average energy of the protons is determined by the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
of the stellar plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...
. Increasing the temperature, however, also speeds up the
photodisintegrations which counteract the captures. The only alternative avoiding this would be to have a very large number of protons available so that the effective number of captures per second is large even at low temperature. In extreme cases (as discussed below) this leads to the synthesis of extremely short-lived radionuclideRadionuclide
A radionuclide is an atom with an unstable nucleus, which is a nucleus characterized by excess energy available to be imparted either to a newly created radiation particle within the nucleus or to an atomic electron. The radionuclide, in this process, undergoes radioactive decay, and emits gamma...
s which decay
Radioactive decay
Radioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles . The emission is spontaneous, in that the atom decays without any physical interaction with another particle from outside the atom...
to stable nuclides only after the captures cease.
Appropriate combinations of temperature and proton density of a stellar plasma have to be explored in the search of possible production mechanisms for p-nuclei. Further parameter
Parameter
Parameter from Ancient Greek παρά also “para” meaning “beside, subsidiary” and μέτρον also “metron” meaning “measure”, can be interpreted in mathematics, logic, linguistics, environmental science and other disciplines....
s are the time available for the nuclear processes, and number and type of initially present nuclides (seed nuclei).
The p-process
In a p-process it is suggested that p-nuclei were made through a few proton captures on stable nuclides. The seed nuclei originate from the s- and r-process and are already present in the stellar plasma. As outlined above, there are serious difficulties explaining all p-nuclei through such a process although it was originally suggested to achieve exactly this. It was shown later that the required conditions are not reached in starStar
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
s or stellar explosions.
Based on its historical meaning, the term p-process is sometimes sloppily used for any process synthesizing p-nuclei, even when no proton captures are involved.
The 
-process
p-Nuclei can also be obtained by photodisintegrationPhotodisintegration
Photodisintegration is a physical process in which an extremely high energy gamma ray interacts with an atomic nucleus and causes it to enter an excited state, which immediately decays by emitting a subatomic particle. A single proton or neutron is effectively knocked out of the nucleus by the...
of s- and r-process nuclei. At temperatures around 2-3 Giga
Giga
Giga is a unit prefix in the metric system denoting a factor of billion . It has the symbol G.Giga is derived from the Greek γίγας, meaning 'giant'...
-Kelvin
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
(GK) and short process time of a few seconds (this requires an explosive process) photodisintegration of the pre-existing nuclei will remain small, just enough to produce the required tiny abundances of p-nuclei. This is called γ-process because the photodisintegration proceeds by nuclear reaction
Nuclear reaction
In nuclear physics and nuclear chemistry, a nuclear reaction is semantically considered to be the process in which two nuclei, or else a nucleus of an atom and a subatomic particle from outside the atom, collide to produce products different from the initial particles...
s of the types
, and , which are caused by highly energetic photonPhoton
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s (Gamma ray
Gamma ray
Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...
s).
The 
-Process
Nuclear reactionNuclear reaction
In nuclear physics and nuclear chemistry, a nuclear reaction is semantically considered to be the process in which two nuclei, or else a nucleus of an atom and a subatomic particle from outside the atom, collide to produce products different from the initial particles...
s triggered by neutrino
Neutrino
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...
s can directly produce certain nuclides, for example 7Li, 11B, 19F, 138La in core-collapse supernovae
Type II supernova
A Type II supernova results from the rapid collapse and violent explosion of a massive star. A star must have at least 9 times, and no more than 40–50 times the mass of the Sun for this type of explosion. It is distinguished from other types of supernova by the presence of hydrogen in its spectrum...
.
This is called ν-process and requires a sufficiently intensive source of neutrinos.
Rapid proton capture processes
In a p-process protons are added to stable or weakly radioactiveRadioactive decay
Radioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles . The emission is spontaneous, in that the atom decays without any physical interaction with another particle from outside the atom...
atomic nuclei.
If there is a high proton density in the stellar plasma, even short-lived radionuclides can capture one or more protons before they beta decay
Beta decay
In nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...
. This quickly moves the nucleosynthesis
Nucleosynthesis
Nucleosynthesis is the process of creating new atomic nuclei from pre-existing nucleons . It is thought that the primordial nucleons themselves were formed from the quark–gluon plasma from the Big Bang as it cooled below two trillion degrees...
path from the region of stable nuclei to the very proton-rich side of the Chart of Nuclides. This is called rapid proton-capture.
Here, a series of
reactions proceeds until either the beta decayBeta decay
In nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...
of a nucleus is faster than a further proton capture, or the proton drip line is reached. Both cases lead to one or several sequential beta decays until a nucleus is produced which again can capture protons before it beta decays. Then the proton capture sequences continue.
It is possible to cover the region of the lightest nuclei up to 56Ni within a second because both proton captures and beta decays are fast. Starting with 56Ni, however, a number of waiting points are encountered in the reaction path. These are nuclides which both have relatively long half-lives
Half-life
Half-life, abbreviated t½, is the period of time it takes for the amount of a substance undergoing decay to decrease by half. The name was originally used to describe a characteristic of unstable atoms , but it may apply to any quantity which follows a set-rate decay.The original term, dating to...
(compared to the process timescale) and can only slowly add another proton (that is, their cross section
Cross section (physics)
A cross section is the effective area which governs the probability of some scattering or absorption event. Together with particle density and path length, it can be used to predict the total scattering probability via the Beer-Lambert law....
for
reactions is small). Examples for such waiting points are: 56Ni, 60Zn, 64Ge, 68Se. Further waiting points may be important, depending on the detailed conditions and location of the reaction path. It is typical for such waiting points to show half-lives of minutes to days. Thus, they considerably increase the time required to continue the reaction sequences. If the conditions required for this rapid proton capture are only present for a short time (the timescale of explosive astrophysical events is of the order of seconds), the waiting points limit or hamper the continuation of the reactions to heavier nuclei.In order to produce p-nuclei, the process path has to encompass nuclides bearing the same mass number
Mass number
The mass number , also called atomic mass number or nucleon number, is the total number of protons and neutrons in an atomic nucleus. Because protons and neutrons both are baryons, the mass number A is identical with the baryon number B as of the nucleus as of the whole atom or ion...
(but usually containing more protons) as the desired p-nuclei. These nuclides are then converted into p-nuclei through sequences of beta decays after the rapid proton captures ceased.
Variations of the main category rapid proton captures are the rp-, pn-, and νp-processes, which will be briefly outlined below.
The rp-process
The so-called rp-process (rp is for rapid proton capture) is the purest form of the rapid proton capture process described above. At proton densities of more than
protons/cm3 and temperatures around 2 GK the reaction path is close to the proton drip line. The waiting points can be bridged provided that the process time is 10-600 s. Waiting-point nuclides are produced with larger abundances while the production of nuclei "behind" each waiting-point is more and more suppressed.A definitive endpoint is reached close to 107Te because the reaction path runs into a region of nuclides which decay preferably by alpha decay
Alpha decay
Alpha decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle and thereby transforms into an atom with a mass number 4 less and atomic number 2 less...
and thus loop the path back onto itself. Therefore an rp-process would only be able to produce p-nuclei with mass number
Mass number
The mass number , also called atomic mass number or nucleon number, is the total number of protons and neutrons in an atomic nucleus. Because protons and neutrons both are baryons, the mass number A is identical with the baryon number B as of the nucleus as of the whole atom or ion...
s less than or equal to 107.
The pn-process
The waiting points in rapid proton capture processes can be avoided by
reactions which are much faster than proton captures on or beta decays of waiting points nuclei. This results in a considerable reduction of the time required to build heavy elements and allows an efficient production within seconds. This requires, however, a (small) supply of free neutronNeutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
s which are usually not present in such proton-rich plasmas. One way to obtain them is to release them through other reactions occurring simultaneously as the rapid proton captures. This is called neutron-rich rapid proton capture or pn-process.
The νp-process
Another possibility to obtain the neutrons required for the accelerating
reactions in proton-rich environments is to use the anti-neutrino capture on protons , turning a proton and an anti-neutrino into a positronPositron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...
and a neutron. Since (anti-)neutrinos interact only very weakly with protons, a high flux
Flux
In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.* In the study of transport phenomena , flux is defined as flow per unit area, where flow is the movement of some quantity per time...
of anti-neutrinos has to act on a plasma with high proton density. This is called νp-process.
Core-collapse supernovae
Massive starStar
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
s end their life in a core-collapse supernova
Type II supernova
A Type II supernova results from the rapid collapse and violent explosion of a massive star. A star must have at least 9 times, and no more than 40–50 times the mass of the Sun for this type of explosion. It is distinguished from other types of supernova by the presence of hydrogen in its spectrum...
. In such a supernova, a shockfront from an explosion runs from the center of the star through its outer layers and ejects these. When the shockfront reaches the O/Ne-shell of the star (see also stellar evolution
Stellar evolution
Stellar evolution is the process by which a star undergoes a sequence of radical changes during its lifetime. Depending on the mass of the star, this lifetime ranges from only a few million years to trillions of years .Stellar evolution is not studied by observing the life of a single...
), the conditions for a γ-process are reached for 1-2 s.
Although the majority of p-nuclei can be made in this way, some mass
Mass number
The mass number , also called atomic mass number or nucleon number, is the total number of protons and neutrons in an atomic nucleus. Because protons and neutrons both are baryons, the mass number A is identical with the baryon number B as of the nucleus as of the whole atom or ion...
regions of p-nuclei turn out to be problematic in model calculations. It has been known already for decades that p-nuclei with mass numbers
cannot be produced in a γ-process. Modern simulations also show problems in the range .The p-nucleus 138La is not produced in the γ-process but it can be made in a ν-process. A hot neutron star
Neutron star
A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...
is made in the center of such a core-collapse supernova and it radiates neutrinos with high intensity. The neutrinos interact also with the outer layers of the exploding star and cause nuclear reactions which create 138La, among other nuclei. Also 180Ta may receive a contribution from this ν-process.
It was suggested to supplement the γ-process in the outer layers of the star by another process, occurring in the deepest layers of the star, close to the neutron star but still being ejected instead of falling onto the neutron star surface. Due to the initially high flow of neutrinos from the forming neutron star, these layers become extremely proton-rich through the reaction
. Although the anti-neutrino flux is initially weaker a few neutrons will be created, nevertheless, because of the large number of protons. This allows a νp-process in these deep layers. Because of the short timescale of the explosion and the high Coulomb barrierCoulomb barrier
The Coulomb barrier, named after Coulomb's law, which is named after physicist Charles-Augustin de Coulomb , is the energy barrier due to electrostatic interaction that two nuclei need to overcome so they can get close enough to undergo a nuclear reaction...
of the heavier nuclei, such a νp-process could possibly only produce the lightest p-nuclei. Which nuclei are made and how much of them depends sensitively on many details in the simulations and also on the actual explosion mechanism of a core-collapse supernova, which still is not completely understood.
Thermonuclear supernovae
A thermonuclear supernova is the explosion of a White DwarfWhite dwarf
A white dwarf, also called a degenerate dwarf, is a small star composed mostly of electron-degenerate matter. They are very dense; a white dwarf's mass is comparable to that of the Sun and its volume is comparable to that of the Earth. Its faint luminosity comes from the emission of stored...
in a binary star
Binary star
A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star, comes, or secondary...
system, triggered by thermonuclear reactions in matter from a companion star accreted
Accretion (astrophysics)
In astrophysics, the term accretion is used for at least two distinct processes.The first and most common is the growth of a massive object by gravitationally attracting more matter, typically gaseous matter in an accretion disc. Accretion discs are common around smaller stars or stellar remnants...
on the surface of the White Dwarf. The accreted matter is rich in Hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
(protons) and Helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...
(α particles
Alpha particle
Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus, which is classically produced in the process of alpha decay, but may be produced also in other ways and given the same name...
) and becomes hot enough to allow nuclear reaction
Nuclear reaction
In nuclear physics and nuclear chemistry, a nuclear reaction is semantically considered to be the process in which two nuclei, or else a nucleus of an atom and a subatomic particle from outside the atom, collide to produce products different from the initial particles...
s.
A number of models for such explosions are discussed in literature, of which two were explored regarding the prospect of producing p-nuclei. None of these explosions release neutrinos, therefore rendering ν- and νp-process impossible. Conditions required for the rp-process are also not attained.
Details of the possible production of p-nuclei in such supernovae depend sensitively on the composition of the matter accreted from the companion star (the seed nuclei for all subsequent processes). Since this can change considerably from star to star, all statements and models of p-production in thermonuclear supernovae are prone to large uncertainties.
Type Ia supernovae
The consensus model of thermonuclear supernovae postulates that the White Dwarf explodes after exceeding the Chandrasekhar limit
Chandrasekhar limit
When a star starts running out of fuel, it usually cools off and collapses into one of three compact forms, depending on its total mass:* a White Dwarf, a big lump of Carbon and Oxygen atoms, almost like one huge molecule...
by the accretion of matter because the contraction and heating ignites explosive carbon burning under degenerate
Degenerate matter
Degenerate matter is matter that has such extraordinarily high density that the dominant contribution to its pressure is attributable to the Pauli exclusion principle. The pressure maintained by a body of degenerate matter is called the degeneracy pressure, and arises because the Pauli principle...
conditions. A nuclear burning front runs through the White Dwarf from the inside out and tears it apart. Then the outermost layers closely beneath the surface of the White Dwarf (containing 0.05 solar mass
Solar mass
The solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...
es of matter) exhibit the right conditions for a γ-process.
The p-nuclei are made in the same way as in the γ-process in core-collaps supernovae and also the same difficulties are encountered. In addition, 138La and 180Ta are not produced. A variation of the seed abundances by assuming increased s-process
S-process
The S-process or slow-neutron-capture-process is a nucleosynthesis process that occurs at relatively low neutron density and intermediate temperature conditions in stars. Under these conditions the rate of neutron capture by atomic nuclei is slow relative to the rate of radioactive beta-minus decay...
abundances only scales the abundances of the resulting p-nuclei without curing the problems of relative underproduction in the nuclear mass ranges given above.
subChandrasekhar supernovae
In a subclass of type Ia supernova
Type Ia supernova
A Type Ia supernova is a sub-category of supernovae, which in turn are a sub-category of cataclysmic variable stars, that results from the violent explosion of a white dwarf star. A white dwarf is the remnant of a star that has completed its normal life cycle and has ceased nuclear fusion...
e, the so-called subChandrasekhar supernova, the White Dwarf may explode long before it reaches the Chandrasekhar limit because nuclear reactions in the accreted matter can already heat the White Dwarf during its accretion phase and trigger explosive carbon burning prematurely. Helium-rich accretion favors this type of explosion. Helium burning ignites degeneratively on the bottom of the accreted helium layer and causes two shockfronts. The one running inwards ignites the carbon explosion. The outwards moving front heats the outer layers of the White Dwarf and ejects them. Again, these outer layers are site to a γ-process at temperatures of 2-3 GK. Due to the presence of α particles (Helium nuclei), however, additional nuclear reactions become possible. Among those are such which release a large number of neutrons, such as 18O
21Ne, 22Ne25Mg, and 26Mg29Si. This allows a pn-process in that part of the outer layers which experiences temperatures above 3 GK.Those light p-nuclei which are underproduced in the γ-process can be so efficiently made in the pn-process that they even show much larger abundances than the other p-nuclei. To obtain the observed solar relative abundances, a strongly enhanced s-process
S-process
The S-process or slow-neutron-capture-process is a nucleosynthesis process that occurs at relatively low neutron density and intermediate temperature conditions in stars. Under these conditions the rate of neutron capture by atomic nuclei is slow relative to the rate of radioactive beta-minus decay...
seed (by factors of 100-1000 or more) has to be assumed which increases the yield of heavy p-nuclei from the γ-process.
Neutron stars in binary star systems
A neutron starNeutron star
A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...
in a binary star
Binary star
A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star, comes, or secondary...
system can also accrete matter from the companion star on its surface. Combined hydrogen and helium burning ignites when the accreted layer of degenerate matter
Degenerate matter
Degenerate matter is matter that has such extraordinarily high density that the dominant contribution to its pressure is attributable to the Pauli exclusion principle. The pressure maintained by a body of degenerate matter is called the degeneracy pressure, and arises because the Pauli principle...
reaches a density of
g/cm3 and a temperature exceeding 0.2 GK. This leads to thermonuclear burning comparable to what happens in the outwards moving shockfront of subChandrasekhar supernovae. The neutron star itself is not affected by the explosion and therefore the nuclear reactions in the accreted layer can proceed longer than in an explosion. This allows to establish an rp-process. It will continue until either all free protons are used up or the burning layer has expanded due to the increase in temperature and its density falls below the one required for the nuclear reactions.It was shown that the properties of X-ray bursts
X-ray burster
X-ray bursters are one class of X-ray binary stars exhibiting periodic and rapid increases in luminosity peaked in the X-ray regime of the electromagnetic spectrum...
in the Milky Way
Milky Way
The Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...
can be explained by an rp-process on the surface of accreting neutron stars. It remains unclear, yet, whether matter (and if, how much matter) can be ejected and escape the gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...
of the neutron star. Only if this is the case can such objects be considered as possible sources of p-nuclei. Even if this is corroborated, the demonstrated endpoint of the rp-process limits the production to the light p-nuclei (which are underproduced in core-collapse supernovae).