p-nuclei

p-nuclei (p stands for proton-rich) are certain proton-rich, naturally occurring isotopes of some elements between selenium and mercury inclusive which cannot be produced in either the s- or the r-process.

Definition[]

Part of the Chart of Nuclides showing some stable or nearly-stable s-, r-, and p-nuclei

The classical, ground-breaking works of Burbidge, Burbidge, Fowler and Hoyle (1957)^[1] and of A. G. W. Cameron (1957)^[2] showed how the majority of naturally occurring nuclides 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.^[3] This also seems to apply to those of ¹¹³In and ¹¹⁵Sn, which additionally could be made in the r-process in small amounts.^[4]

The long-lived radionuclides ⁹²Nb, ⁹⁷Tc, ⁹⁸Tc and ¹⁴⁶Sm are not among the classically defined p-nuclei as they no longer occur naturally on Earth. By the above definition, however, they are also p-nuclei because they cannot be made in either the s- or the r-process. From the discovery of their decay products 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.^[5]

p-nuclei are very rare. Those isotopes of an element which are p-nuclei are less abundant typically by factors of ten to one thousand 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.^[6]

Origin of the p-nuclei[]

The astrophysical production of p-nuclei is not completely understood yet. The favored γ-process (see below) in core-collapse supernovae cannot produce all p-nuclei in sufficient amounts, according to current computer simulations. 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.^[7]

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 nuclides: by successively adding protons to a nuclide (these are nuclear reactions of type (p,γ) or by removing neutrons from a nucleus through sequences of photodisintegrations of type (γ,n).^[6][7]

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 (γ,p) photodisintegrations which counteract the (p,γ) 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 radionuclides which decay to stable nuclides only after the captures cease.^[6][7]

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 parameters are the time available for the nuclear processes, and number and type of initially present nuclides (seed nuclei).

Possible processes[]

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.^[1][2][6] It was shown later that the required conditions are not reached in stars or stellar explosions.^[8]

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 γ-process[]

p-Nuclei can also be obtained by photodisintegration of s-process and r-process nuclei. At temperatures around 2–3 gigakelvins (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.^[6][9] This is called γ-process (gamma process) because the photodisintegration proceeds by nuclear reactions of the types (γ,n), (γ,α) and (γ,p), which are caused by highly energetic photons (Gamma rays).^[9]

The ν-process (nu process)[]

If a sufficiently intensive source of neutrinos is available, nuclear reactions can directly produce certain nuclides, for example ⁷Li, ¹¹B, ¹⁹F, ¹³⁸La in core-collapse supernovae.^[10]

Rapid proton capture processes[]

In a p-process protons are added to stable or weakly radioactive 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.^[7]

Here, a series of (p,γ) 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 (p,γ) 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.^[11]

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 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 10²⁸ protons/cm³ and temperatures around 2 GK the reaction path is close to the proton drip line.^[11] 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 ¹⁰⁴Te because the reaction path runs into a region of nuclides which decay preferably by alpha decay and thus loop the path back onto itself.^[12] Therefore, an rp-process would only be able to produce p-nuclei with mass numbers less than or equal to 104.

The pn-process[]

The waiting points in rapid proton capture processes can be avoided by (n,p) 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.^[6] This requires, however, a (small) supply of free neutrons 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.^[13]

The νp-process[]

Another possibility to obtain the neutrons required for the accelerating (n,p) reactions in proton-rich environments is to use the anti-neutrino capture on protons (
ν
_e +
p
→
e⁺
+
n
), 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 (nu p process).^[14]

Possible synthesis sites[]

Core-collapse supernovae[]

Massive stars 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