p-nuclei (p stands forproton-rich) are certainneutron-deficient, naturally occurringisotopes of someelements betweenselenium andmercury inclusive which cannot be produced in either thes- or ther-process.

The classical, ground-breaking works ofBurbidge, Burbidge, Fowler and Hoyle (1957)^[1] and of A. G. W. Cameron (1957)^[2] showed how the majority of naturally occurringnuclides beyond the elementiron can be made in two kinds ofneutron capture processes, the s- and the r-process. Someneutron-deficient nuclides found in nature are not reached in these processes and therefore at least one additional process is required to synthesize them. Thesenuclei are calledp-nuclei.

Since the definition of the p-nuclei depends on the current knowledge of the s- and r-process (see alsonucleosynthesis), 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 theabundances of¹⁵²Gd and¹⁶⁴Er contain at least strong contributions from thes-process.^[3] This applies more weakly to those of¹¹³In and^114,115Sn,^[4] and the first and last also by ther-process (as they can as fission products): the paths pass throughmetastable isomers, and may have been overlooked.

Thelong-livedradionuclides⁹²Nb,⁹⁷Tc,⁹⁸Tc,¹⁴⁶Sm,¹⁵⁰Gd, and¹⁵⁴Dy^[5] 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 theirdecay products inpresolar grains it can be inferred that at least⁹²Nb and¹⁴⁶Sm were present in thesolar nebula. This offers the possibility to estimate the time since the last production of these p-nuclei before the formation of theSolar System.^[6]

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 ingeochemical investigations and by analysis ofmeteoritic material andpresolar grains. They cannot be identified instellar 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 theMilky Way.^[7]

Half-lives quoted below are copied from the linked isotope page.Possible s- and r-process paths are from references above.

Theastrophysical production of p-nuclei is not completely understood yet. The favored γ-process (see below) incore-collapse supernovae cannot produce all p-nuclei in sufficient amounts, according to currentcomputer 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.^[8]

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.

In principle, there are two ways to produce proton-richnuclides: by successively addingprotons to a nuclide (these arenuclear reactions of type (p,γ)) or by removing neutrons from a nucleus through sequences ofphotodisintegrations of type (γ,n).^[7][8]

Under conditions encountered in astrophysical environments it is difficult to obtain p-nuclei through proton captures because theCoulomb barrier of a nucleus increases with increasingproton number. A proton requires more energy to be captured by an atomic nucleus when the Coulomb barrier is higher. The available average energy of the protons is determined by thetemperature of the stellarplasma. 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-livedradionuclides whichdecay to stable nuclides only after the captures cease.^[7][8]

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

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][7] It was shown later that the required conditions are not reached instars or stellar explosions.^[9]

Based on its historical meaning, the termp-process is sometimes used for any process synthesizing p-nuclei, even when no proton captures are involved, but this usage is discouraged.

p-nuclei can also be obtained byphotodisintegration ofs-process andr-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.^[7][10] This is called theγ-process (gamma process) because the photodisintegration proceeds bynuclear reactions of the types (γ,n), (γ,α) and (γ,p), which are caused by highly energeticphotons (gamma rays).^[10]

If a sufficiently energetic source of neutrinos is available, as incore-collapse supernovae,nuclear reactions can occur with the neutrinos serving the same purpose as the photons in the γ-process, to cause disintegration of the nuclei by energy transfer. This is thought to contribute significantly to, for example,⁷Li,¹¹B,¹⁹F,¹³⁸La.^[11]

In a p-process protons are added to stable or weaklyradioactiveatomic nuclei. If there is a high proton density in the stellar plasma, even short-livedradionuclides can capture one or more protons before theybeta decay. This quickly moves thenucleosynthesis path from the region of stable nuclei to the very proton-rich side of thechart of nuclides. This is calledrapid proton capture.^[8]

Here, a series of (p,γ) reactions proceeds until either thebeta decay of a nucleus is faster than a further proton capture, or theproton 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 to⁵⁶Ni within a second because both proton captures and beta decays are fast. Starting with⁵⁶Ni, however, a number ofwaiting points are encountered in the reaction path. These are nuclides which both have relatively longhalf-lives (compared to the process timescale) and can only slowly add another proton (that is, theircross section for (p,γ) reactions is small). The most important such waiting points are⁶⁴Ge,⁶⁸Se,⁷²Kr, and further points depending on the detailed conditions and location of the reaction path. It is typical for such waiting points to show half-lives of tens of seconds. 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.^[12]

In order to produce p-nuclei, the process path has to encompass nuclides bearing the samemass 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 categoryrapid proton captures are the rp-, pn-, and νp-processes, which will be briefly outlined below.

The so-calledrp-process (rp is forrapid proton capture) is the purest form of the rapid proton capture process described above. At proton densities of more than10²⁸ protons/cm³ and temperatures around2×10⁹ K, the reaction path is close to theproton drip line.^[12] 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 increasingly suppressed.

The last waiting point reached is¹⁰⁴Sn and the definitive endpoint is reached at¹⁰⁷Te because of instability towardalpha decay, and primarily photon-induced decay or (γ,α) reactions loop the path back onto itself.^[13] Therefore, an rp-process would only be able to produce p-nuclei withmass numbers up to 106 or 107, or up to¹⁰⁶Cd.

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.^[7] This requires, however, a (small) supply of freeneutrons 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 calledneutron-rich rapid proton capture orpn-process.^[14]

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 apositron and a neutron. Since (anti-)neutrinos interact only very weakly with protons, a highflux of anti-neutrinos has to act on a plasma with high proton density. This is calledνp-process (nu p process).^[15]

Massivestars end their life in acore-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 alsostellar 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, somemass regions of p-nuclei turn out to be problematic in model calculations. It has been known already for decades that p-nuclei with mass numbersA < 100 cannot be produced in a 𝛾-process.^[7][10] Modern simulations also show problems in the range150 ≤ A ≤ 165.^[8][16]

The p-nucleus¹³⁸La is not produced in the 𝛾-process but it can be made in aν-process. A hotneutron 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 create¹³⁸La, among other nuclei.^[11][16] Also^180mTa may receive a contribution from thisν-process.

It was suggested^[15] 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 reactionν
_e +n →e⁻
+p. 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${\displaystyle \nu \mathrm{p}}$⁠-process in these deep layers. Because of the short timescale of the explosion and the highCoulomb 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.^[15][17]

Athermonuclear supernova is the explosion of awhite dwarf in abinary star system, triggered by thermonuclear reactions in matter from a companion staraccreted on the surface of the white dwarf. The accreted matter is rich inhydrogen (protons) andhelium (α particles) and becomes hot enough to allownuclear reactions.

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 (theseed 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.^[7]

The consensus model of thermonuclear supernovae postulates that the white dwarf explodes after exceeding theChandrasekhar limit by the accretion of matter because the contraction and heating ignites explosivecarbon burning underdegenerate 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 0.05solar masses of matter) exhibit the right conditions for a γ-process.^[18]

The p-nuclei are made in the same way as in the γ-process in core-collapse supernovae and also the same difficulties are encountered. In addition,¹³⁸La and^180mTa are not produced. A variation of the seed abundances by assuming increaseds-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.^[7]

In a subclass oftype Ia supernovae, the so-calledsubChandrasekhar 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 as¹⁸O(α,n)²¹Ne,²²Ne(α,n)²⁵Mg, and²⁶Mg(α,n)²⁹Si. This allows apn-process in that part of the outer layers which experiences temperatures above 3 GK.^[7][14]

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 enhanceds-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.^[7][14]

Aneutron star in abinary star system can also accrete matter from the companion star on its surface. Combinedhydrogen andhelium burning ignites when the accreted layer ofdegenerate matter reaches a density of10⁵–10⁶ g/cm³ and a temperature exceeding0.2 GK. This leads tothermonuclear 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.^[12]

It was shown that the properties ofX-ray bursts in theMilky Way can be explained by an rp-process on the surface of accreting neutron stars.^[19] It remains unclear, yet, whether matter (and if, how much matter) can be ejected and escape thegravitational 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).^[13]

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