Automated Formulation of Reactions and Pathways in Nuclear Astrophysics

AUTOMATED FORMULATION OF REACTIONS AND PATHWAYS IN NUCLEAR ASTROPHYSICS: NEW RESULTS

Sakir Kocabas

Department of Space Engineering


Abstract

This paper describes some of the new results from ASTRA, a knowledge based research aid for the formulation and analysis of process explanations in nuclear astrophysics. The program formulates valid fusion and decay reactions for the elements by using its knowledge of quantum theory, and from these reactions constructs all theoretically possible reaction chains as process explanations for the nucleosynthesis of elements. Earlier applications of ASTRA generated reactions of the elements and isotopes from hydrogen to oxygen, and found novel reactions that involve proton, electron and neutron capture for these elements, and a series of new reaction chains for hydrogen burning processes. We have recently extended the system’s knowledge base for elements from oxygen to sulphur. The new applications of ASTRA generated a series of reactions and pathways involving the heavier elements fluorine, neon, sodium, magnesium, aluminium, silicon and sulphur, some of which we did not see in the texts. The program also generated a complete series of carbon, nitrogen and oxygen burning reactions some of which may be of interest to astrophysicists.

Key words: Automated reasoning, scientific discovery.

1 Introduction

Computational design and construction of chemical and nuclear reaction processes have recently become an active area of research in computer aided scientific discovery. Three examples of such efforts are Hendrickson's (1995) SYNGEN which designs the synthesis of some organic compounds from initial and intermediate compounds, Valdes-Perez's (1995) MECHEM which has found new reaction pathways in physical chemistry (see, also Zeigarnik, et al., 1997), and Kocabas and Langley’s (1998) ASTRA system has found new reactions and pathways in nuclear astrophysics. This system was designed to support scientists in explaining various fusion processes, the nucleosynthesis of elements and their relative abundance in stars.

ASTRA differs from the earlier systems mainly in its focus on astrophysics, and in its ability to generate the basic reactions of the elements by using the principles of quantum physics. In this respect, the program is a successor of BR-4 (Kocabas & Langley, 1995), which carries out theory revision in particle physics much like its predecessor BR-3 (Kocabas, 1991). The BR-3 system in turn uses techniques and ideas from STAHL (Zytkow & Simon, 1986) and STAHLp (Rose & Langley, 1986), which modeled qualitative discovery in chemistry.

The behavior ASTRA was described elsewhere (see, Kocabas & Langley, 1998; 1999), so the focus here will be on some of the new results of this program with an emphasis on the system's abilities as a research tool in astrophysics.

2 Application Area: Nuclear Astrophysics

Nuclear astrophysics is a branch of astrophysics that mainly concerns with the formation of heavier elements such as carbon (12C), nitrogen (14N) and oxygen (16O) from hydrogen (H) and helium (4He), through a series of fusion and decay processes in stars. Exploration of the processes in which the heavier elements from oxygen (16O) to iron (56Fe) participate is another main topic in this field.

Current astrophysical theories suggest that, stars go through several stages in their lifetimes after their initial formation by the condensation of cosmic clouds and hydrogen gas. The first is called the “hydrogen burning stage” during which stars radiate energy emitted by a series of exothermic fusion reactions in which hydrogen is transformed into helium. Astrophysicists propose several different pathways (Audouze & Vauclair, 1980, p. 52; Williams, 1991, p. 351) to account for hydrogen burning in stars. Later stages, depending on the size of the star, involve processes such as helium burning, carbon, nitrogen and oxygen burning.

Astrophysicists explain nucleosyntheses by first adopting a stellar model in thermal equilibrium which makes certain assumptions about the mass, temperature, density, and the element distribution in the star. They then formulate the nuclear reactions using the constraints of quantum physics. They also calculate the rates of these reactions, by using experimental and theoretical knowledge about nuclear cross-sections and reactant abundances. Theoretically, there are many possible reactions, and a great number of reaction pathways even for a small number of elements. Astrophysicists deal with this problem by deleting the less likely reactions and focusing their attention on the reactions with high rates.

In our previous work with ASTRA (Kocabas & Langley, 1998; 1999; Kocabas & Langley, in press), we examined the resuts of the program on several research topics in nuclear astrophysics. These were: 1) hydrogen-burning processes, 2) helium burning processes, 3) formation of heavier elements carbon, nitrogen and oxygen through hydrogen and helium burning, and other fusion chains, 4) the role of neutrons in such processes, and 5) the anomaly in the relative abundance of the light elements.

In evaluating the results of ASTRA, we have examined a number of books and journal papers on nuclear astrophysics, notably the following work: Audouze & Vauclair (1980); Clayton (1983); Fowler (1986); Fowler, et al., 1967; Fowler et al., 1975; Harris & Fowler, et al., 1983; Cujec & Fowler, 1980; Kippenhahn & Weigert (1994); Lang (1974); Williams (1991); and Adelberger, E.G., et al. (1998). We have also discussed the results of the system with experts in astrophysics.

In the next section, we describe ASTRA in terms of its inputs, outputs and operations. Section 4 describes the experimental results of ASTRA, Section 5 discusses these results, and Section 6 discusses related reseach. The paper ends with a summary of the conclusions.

3 The ASTRA System

We first describe briefly, ASTRA’s inputs, outputs and operations, before we describe our application of the system to nuclear astrophysics with some of the earlier and the new results. A more detailed description can be found in Kocabas and Langley (1998). The program operates in two stages: the first generates all theoretically valid reactions, and the second produces reaction chains as process explanations for the nucleosynthesis of elements.

3.1 Formulating Reactions

The knowledge base of ASTRA includes descriptions for a set of elements and isotopes. The current version has information about 68 such entities. Each entity is characterized in terms of five quantum properties: rest mass (in MeV/c2), electric charge, spin, lepton, and baryon counts. ASTRA also has theoretical knowledge about conservation rules concerning the quantum values, which hold in reactions among the elements and isotopes. Typically, the exothermic reactions play the major role in stellar nucleosynthesis, but the program allows the selection of the energy band to assist more detailed study.

Based on this information, ASTRA systematically generates all collision and decay reactions among these elements that obey the conservation laws, together with their energy emissions, or Q-values, in terms of mega electron volts (MeV). The reactions generated by the program are in the form: Rm -> Pn , m = 1,2,3; n = 1,2,3 where Rm and Pn are the sets of the reacting and resulting elements respectively, and m and n are the number of elements in the sets. (For m = 1, m=2 and m=3 the formula represents decays, and double and triple collision reactions respectively). Examples of the runs of this module based on information about elements from hydrogen to oxygen can be found in Kocabas & Langley (1998).

Here we describe the new results of ASTRA with information about the elements from hydrogen to sulphur, their isotopes and a few elementary particles like the electron, proton, neutron and the neutrino with their antiparticles, giving a total of 68 distinct entities. From these, the system generated more than 600 different reactions, but some were minor variations on one another. We eliminated such variants manually, leaving 472 reactions that included 344 fusion reactions and 28 decays.

3.2 Constructing Reaction Chains

In order to construct reaction chains, ASTRA’s second stage takes as input the reactions generated by its first stage, an element E whose syntheses we want explained, and a starting element (typically hydrogen). The system generates all reaction chains that lead from the starting element to the final element through the various reactions identified in the first stage. ASTRA’s mechanisms for constructing reaction chains has been described elsewhere (see, Kocabas & Langley, 1998).

The program constructs a large number of reaction chains, most of which would be ruled out by physicists on grounds of low reaction rates. However, as a research aid, ASTRA provides a full range of possible reaction mechnisms to astrophysicists for more complete analysis of the the nuclear processes in their field of research.

4 The New Results of ASTRA

In this section we report the new results of our tests with ASTRA concerning hydrogen burning with heavier elements such as oxygen, fluor, neon, sodium, magnesium, aluminium, silicon and phosphorus. We begin with three classes of reactions that are believed to play an important role in stellar nucleosyntheses: proton, electron and neutron captures. We then turn to processes of helium, carbon and oxygen burning which explain the synthesis of heavier elements.

4.1 Proton, Electron and Neutron Captures

Three main processes for the nucleosynthesis of elements in stellar systems are proton, electron and neutron captures in which a nucleus reacts with a proton, electron or a neutron, giving a heavier element or isotope.

Proton captures are an important class of exothermic reactions that take part in hydrogen burning processes. In astrophysics literature we have found 33 examples of proton captures (e.g., Fowler, et al., 1967, 1975, 1983) for elements from hydrogen to oxygen (16O), and 20 more for elements from oxygen to sulphur (32S).

ASTRA’s first stage predicts that all elements from hydrogen to sulphur(32S), with the exception of 4He, participate in exothermic proton capture. The program produces 46 such reactions for elements from hydrogen to oxygen, including all 33 examples we have found in texts, but also 13 others which we have not seen in astrophysics texts that we examined. The program also finds 72 proton captures for elements from oxygen (16O) to sulphur (32S), including the 20 such reactions cited in the same literature.

In electron capture reactions, an electron is absorbed by the atomic nucleus to be transformed into one with a smaller atomic number. ASTRA’s first stage produces 6 electron capture reactions for elements from hydrogen to oxygen of which only one appears in astrophysics texts. The program also found 8 electron capture reactions for elements from oxygen to sulphur, none of which we have seen in the texts.

In neutron capture, an element combines with a neutron to form a heavier isotope of the same element. We found 17 neutron captures for elements from hydrogen to oxygen in the literature, while ASTRA predicts 59 such reactions that are theoretically possible for the same elements. Some examples of these reactions can be found in Kocabas and Langley (1998). Recent runs of the system generated 76 reactions for elements from oxygen to sulphur, none of which we have seen in the texts we have examined.

4.2 Hyrogen Burning Processes

In the main sequence stars hydogen is transformed into helium in a series of nuclear reaction chains called hydrogen burning processes. These processes are the main source of energy for such stars. The standard processes given in astrophysics texts (e.g. Audouze & Vauclair, 1980, p. 52; Williams, 1991, p. 351) for helium synthesis in such stars are called “proton-proton” or pp chains. Other hydrogen burning reactions that appear in texts involve heavier elements carbon, nitrogen and oxygen, and the pathway is called the CNO-chain.

When asked to generate reaction chains from hydrogen to helium, the ASTRA system finds all of these reaction chains including the CNO cycle. Yet, ASTRA also produces a viable variant of the CNO cycle using the electron capture of 13N (see, Kocabas & Langley, 1998).

Recently, we have run ASTRA on hydrogen burning reactions involving the elements heavier than oxygen. Such reactions are hypothesized to occur in stars larger than the sun. Some of the hydrogen burning chains that the program found, involving the elements fluorine, neon, sodium, magnesium, silicon, phosphorus and sulphur are:

H + 16O -> 17O + nu

H + 17O -> 18F

H + 18F -> 19Ne

19Ne + e -> 19F + e + nu (e-capture)

H + 19F -> 16O + 4He

------------------------------

Cumulative account: 4 H -> 4He + 2 nu



H + 23Na -> 24Mg

H + 24Mg -> 25Mg + nu

H + 25Mg -> 26Al

H + 26Al -> 27Si

27Si + e -> 27Al + e + nu

H + 27Al -> 24Mg + 4He

---------------------------------

H + 28Si -> 29Si + nu

H + 29Si -> 30P

H + 30P -> 31S

31S -> 31P + nu

H + 31P -> 28Si + 4He

----------------------------

ASTRA produces many more alternatives to these reactions, providing a complete framework to be examined by researchers in this field.

4.3 Helium Burning Processes

One of the main concerns of astrophysics has been the origin and the relative abundance of carbon and. The standard account (e.g., Fowler, 1986, pp. 5-6) assumes the reaction of helium nuclei to form carbon and oxygen. Earlier runs of ASTRA produced 24 additional chains that differ in their final steps to 12C. These include:

n + 8Be --> 9Be

4He + 9Be --> 12C + n ,

which relies on a neutron capture reaction. Astrophysicists qualified this process as one that can compete with the standard account in explosive stars that produce many neutrons. We have discussed ASTRA’s results on the nucleosynthesis of carbon and oxygen including the related helium burning processes elsewhere (Kocabas & Langley, 1998; Kocabas & Langley, in press) in more detail. So we now turn to the new results of the program on this issue.

ASTRA finds 24 helium burning reactions involving the range of elements from oxygen to silicon, including the 16 such reactions cited in the texts. Some of these are:

4He + 16O -> 20Ne + 5.16

4He + 20Ne -> 24Mg + 9.3

4He + 23Na -> 27Al + 10.2

4He + 24Mg -> 28Si + 10.1

4He + 28Si -> 32S + 6.9

where the figures on the right represent the energy emissions in MeV.

A comparison of the helium burning reactions produced by ASTRA with the natural abundances of the elements from oxygen to sulphur in the CRC Handbook (Weast, R.C. & Astle, M.J., 1981) reveals an interesting result: The elements fluorine, neon, sodium, magnesium, silicon, phosphorus and sulphur in the solar system must have been formed by helium burning processs, rather than neutron captures. This is because, the stable isotope abundances of these elements indicate a parallelism with the stepwise alpha-capture (helium burning) of the stable lighter isotopes of the elements in the series. This matter seemed to deserve further analysis.

4.4 Carbon, Nitrogen and Oxygen Burning

Carbon burning takes place after the helium burning stage in a star. ASTRA finds four carbon burning reactions which produce the elements neon, sodium, and magnesium:


12C + 12C -> 24Mg + 14.4

12C + 12C -> H + 23Na + 2.72

12C + 12C -> 4He + 20Ne + 5.1

In nitrogen burning, two nitrogen atoms fuse together to form elements ranging from oxygen to silicon. ASTRA finds 10 such reactions, two of which are:


14N + 14N -> 28Si + 27.82

14N + 14N -> 12C + 16O + 10.46


Finally, ASTRA formulates six oxygen burning reactions in which the elements magnesium, silicon, phosphorus and sulphur are generated. Three of these reactions are

16O + 16O -> 32S + 17.12

16O + 16O -> n + 31S + 2.05

16O + 16O -> 8Be + 24Mg + 0.02

Carbon, nitrogen and oxygen burning reactions happen only in massive stars as they require higher energies to initiate. The astrophysics texts that we examined mention only a few of these reactions, such as 12C + 12C -> 24Mg, 14N + 14N -> 28Si, and 16O + 16O -> 32S, while ASTRA provides a full account of such reactions.

5. Discussion of Results



We have dicussed some of the results of ASTRA with astrophysicists and carefully compared its outputs to those available in astrophysics texts (Clayton, 1983; Audouze & Vauclair, 1980; Kippenhahn & Weigert, 1994; Fowler et al., 1967, 1975, 1983; Cujec & Fowler, 1980; Adelberger, E.G., et al. (1998). We received some encouraging comments from domain experts about the results of the program but we need more detailed analysis before claims of originality.

Earlier we examined the results of ASTRA only on exothermic reactions. Following discussions with domain experts, we have improved the system to formulate reactions in any selected energy band. In certain stellar conditions, some endothermic reactions can contribute to speed up certain nuclear processes.

The current version of ASTRA does not calculate the reaction rates which are used by astrophysicists in determining the more likely reactions and reaction chains. Astrophysicists suggested that this feature would be very useful in a research tool like ASTRA. However, the current version can receive as input the rate values for each reaction it has formulated, and by deleting those with low rates, can effectively eliminate a large number of reaction chains for their slow rates. We are considering to fully implement this capability in the program's future versions with the help of domain experts.

On the other hand, without a computational aid like ASTRA, it would be impossible for astrophysicists even to formulate all the theoretically possible reactions for an exhaustive research. The program can handle a very large volume of data for constructing reaction chains, and although the hydrogen and helium burning processes have been dealt with extensively for lighter elements in the current literature, there is still much scope for research on the processes of the heavier elements. A complete analysis on the reactions and pathways can only be carried out with the aid of a computational tool such as our program.

Although we tested ASTRA on the reactions of the elements from hydrogen (H) to sulphur (32S), the system can be used in exploring the reactions of heavier elements from sulphur to iron (56Fe) and further, which take place in stellar and interstellar processes.

While we are in the process of evaluating the new results of the system, we are also planning to add the ability to use the rates of the reactions to distinguish more likely mechanisms, and finally, we are improving its interface to make the system a more useful research aid for astrophysicists.

6. Conclusions

In this paper we described the new results of ASTRA, a computational tool which formulates reactions and pathways for researchers in nuclear astrophysics. We received encouraging comments from astrophysicsts about the earlier results of the program, and suggestions on how to further imporve its features. We continue to collaborate with domain experts to evaluate the behavior of the current system in terms of the novelty and plausibility of its latest results, and to improve ASTRA in its functionalities to make it a more useful research tool for astrophysicists.

References

Adelberger, E.G., et al. (1998). Solar fusion cross sections. Reviews of Modern Physics, vol. 70, No. 4. Pp 1266-1291.

Audouze, J., & Vauclair, S. (1980). An introduction to nuclear astrophysics. Holland: D. Riedel.

Clayton, D.D. (1983). Principles of Stellar Evolution and Nucleosynthesis. Chicago: The University of Chicago Press.

Cujec, B. & Fowler, W.A. (1980). Neglect of D, T, and 3He in advanced stellar evolution. The Astropysical Journal, 236: 658-660.

Fowler, W.A. (1986). The synthesis of the chemical elements carbon and oxygen. In S.L. Shapiro & S.A. Teukolsky (Eds.), Highlights of modern astrophysics. New York: John Wiley & Sons.

Fowler, W.A., Caughlan, G.R., and Zimmermann, B.A. (1967). Thermonuclear Reaction Rates. Ann. Rev. Astron. Astrphysics, 5, 525-570.

Fowler, W.A., Caughlan, G.R., and Zimmermann, B.A. (1975). Thermonuclear Reaction Rates. Ann. Rev. Astron. Astrphysics, 13, 69-112.

Harris, M.J., Fowler, W.A. Caughlan, G.R., and Zimmermann, B. (1983). Thermonuclear reaction rates. Ann. Rev. Astron. Astrophysics, 21: 165-176.

Hendrickson, J.B. (1995). Systematic synthesis design: The SYNGEN program. Working Notes of the AAAI Spring Symposium on Systematic Methods of Scientific Discovery (pp. 13-17). Stanford, CA: AAAI Press.

Kippenhahn, R. and Weigert, A. (1994). Stellar Structure and Evolution. London: Springer-Verlag.

Kocabas, S. (1991). Conflict resolution as discovery in particle physics. Machine Learning, 6, 277-309.

Kocabas, S., & Langley, P. (1995). Integration of research tasks for modeling discoveries in particle physics. Working notes of the AAAI Spring Symposium on Systematic Methods of Scientific Discovery (pp. 87-92). Stanford, CA: AAAI Press.

Kocabas, S. & Langley, P. (1998). Generating process explanations in nuclear astrophysics. Proceedings of the ECAI-98 Workshop on Machine Discovery (pp.4-9), Brighton, UK.

Kocabas, S. & Langley, P. (1999). Automated formulation of Reactions and reaction chains in nuclear astrophysics. Proceedings of the 8th Turkish Symposium of Artificial Intelligence and Neural Networks. Boğaziçi University. pp. 247-256.

Kocabas, S. & Langley, P. (in press). Computer generation of process explanations in nuclear astrophysics. International Journal of Human-Computer Studies.

Lang, K.R. (1974). Astrophysical formulae: A compendium for physicists and astrophysicists. New York: Springer-Verlag.

Rose, D., & Langley, P. (1986). Chemical discovery as belief revision. Machine Learning, 1, 423-451.

Valdes-Perez, R.E. (1995). Machine discovery in chemistry: New results. Artificial Intelligence, 74, 191-201.

Zeigarnik, A.V., Valdes-Perez, R.E., Temkin, O.N., Bruk, L.G. & Shalgunov, S.I. (1997). Computer-aided mechanism elucidation of acetylene hydrocarboxylation to acrylic acid based on a novel union of empirical and formal methods. Organometallics, 16(14): 3114-3127.

Weast, R.C. & Astle, M.J. (Eds.). (1981). CRC handbook of chemistry and physics (62dn ed.). Florida: CRC Press.

Williams, W.S.C. (1991). Nuclear and Particle Physics. Oxford: Clarendon Press.

Zytkow, J.M., & Simon, H.A. (1986). A theory of historical discovery: The construction of componential models. Machine Learning, 1, 107-137.