primordial state, this approach is intimately related to the known fact that nuclear ... cosmological model of synthesizes has been stimulated by the discovery of Penzias and ... the cosmic microwave background radiation, and this result strongly ...
Cluster Structure of Atomic Nuclei and Nucleosynthesis Roman Ya. Kezerashvili New York City College of Technology, City University of New York 300 Jay Street, Brooklyn, NY11201. Email: rkezerashvili@citytech. cuny. edu Abstract. It is shown that the static and dynamic cc-cluster models of nuclei, which describe an elastic electron scattering, photodisintegration reactions and pion double charge exchange reactions on a-cluster nuclei are in favor of the a-capture and a process of the formation of these nuclei.
One of the fundamental problems of astrophysics is the problem of the origin of chemical elements. There are different theories of the origin of the elements. Here we concentrated our attention on the formation of a-cluster or a-particle nuclei. The helium nucleus is the fundamental building block, which build up all these nuclei. There are basically two approaches to explain the origin of helium in its measured abundance through hydrogen burning. In the 1950s Gamow, Alpher and Herman (cf. Ref.l) proposed that 4He produced by hydrogen burning in the early stage of a big bang some 1010 years ago. In Ref. 2 proposed that the stars are the seats on origin of the elements, and only hydrogen is primeval. In contrast with the theories, which demand matter in a particular primordial state, this approach is intimately related to the known fact that nuclear transformations are currently taking place inside stars, and many of detail of the observed abundances of the elements were explained in terms of stellar processes. Yet one major problem remained, the origin of helium. In the late 60th interest to a hot big bang cosmological model of synthesizes has been stimulated by the discovery of Penzias and Wilson [3] of the cosmic microwave background. In Refs. 4 and 5 were demonstrated that the existence of 4He and the other light elements, together with the cosmic microwave background radiation, as a primary evidence in favor of the a big bang cosmological model. New measurements of the wavelength of the cosmic microwave background radiation have shown that it corresponds to the temperature of 2.728 K. Just a few years later, based on this fact Burbidge and Hoyle [6] found that the energy released in the synthesis of cosmic 4He from hydrogen is almost exactly equal to the energy contained in the cosmic microwave background radiation, and this result strongly suggests that the 4He was produced by hydrogen burning in stars and not in the early stage of a big bang. Let's now begin by reviewing the nuclear reaction leading to a-particle element production at various stages of stellar evolution. When hydrogen burning in a star's main sequence stage leads eventually to hydrogen exhaustion, a helium core remains at the star's center. As helium builds up in the core of a star, the burning ceases, and the core contracts, and part of gravitational energy converted into thermal energy. When the CP698, Intersections of Particle and Nuclear Physics: 8th Conference, edited by Z. Parsa © 2003 American Institute of Physics 0-7354-0169-1/03/$20.00 353
temperature exceeds 108 K, and densities of about 105 g/cm3 helium nuclei can overcome their mutual electrical repulsion, leading to the fusion processes: 4He+4He-:>*Be and then %Be+*He-*nC + y. The net result of these reactions is that three 4He nuclei are combined into one carbon-12C nucleus. At temperature above 2 • 108 K the 12C produced in the helium fusion can capture an a particle to form 16O and thus, continue the element synthesis: 4//e+12C-»160 + y. Further a-capture reactions depend critically on the existing excited states and parity. For example the rate of the 16O(a,^20Ne process depends on the excited states in 2(^sfe at 4.95 and 5.62 MeV have a proper spin and parity to formed by 16O and the a particles in their ground states. A resonance can also be expected to occur through helium capture by 20Ne. But in the reaction 20Ne(a^24Mg the 24 Mg production will be small because of the large Coulomb barrier factor for a-particle. It is understandable that as the star evolves, heavier elements tend to form through helium capture rather than fusion of like nuclei, like the fusion of two 12C nuclei to form 24Mg or fusion of two 16O to form 32S. Because the repulsive force between two carbon nuclei is three times greater than the repulsion between carbon and helium, carbon-helium fusion occurs at a lower temperature than that at which carbon-carbon fusion occurs. Similarly the 16O, which produced through helium capture by 12C, may fuse with other 16O to form 32 S, but it is much more probable that the capture process 16O(#,7)20Ne to form 20Ne. As a result, elements 4He, 12C, 160,20Ne, and 24Mg stand out as prominent peaks in the chart of cosmic abundances, a-capture processes occur at temperatures between 108 and 2 • 108 K and as results in the exhaustion of the helium produced in hydrogen burning. An inner core of 12C, 16O, 20Ne and perhaps a little 24Mg develops in the star and eventually undergoes gravitation contraction and as a result conversion of the gravitation energy into heat just as occurred previously in the case of helium core. Gravitation is "a built-in" mechanism in stars, which leads to the development of high temperature in the ashes of exhausted nuclear fuel. Gravitation takes over whenever nuclear reaction stops; it raises the temperature to the point where the ashes of the previous process begin to burn. Implicit in this argument is the assumption that mixing of core and surrounding zones does not occur. Around the time 28Si appears in the core of a star, a competitive struggle begins between the continued capture of helium to produce even heavier nuclei and the tendency of more complex nuclei to break down into simpler ones. The cause of this breakdown is heat. By now the star's core temperature has reached the unimaginably large value of 3-10 9 K, and the gamma rays associated with that temperature have enough energy to promote photodisintegration reactions, a-particle binding energy in 12C, 16O, and 20Ne nuclei are 7.15 MeV, 7.37 MeV and 4.75 MeV, respectively. This means that the sequence of photodisintegration reactions will be the following: 20Ne(y,a)16O, 16O (y,a)12C and y+nC -> 3a. The photodisintegration reaction (y,a) precedes (y,p) and (y,n) processes on 12C, 16O, and 20Ne nuclei, because the proton and neutron binding energies in these nuclei are larger, therefore photo-dissociation threshold falls higher, aparticle released in the process 20Ne(y,a)16O, can now penetrate the Coulomb barrier of the other nearby 20Ne nuclei that have not yet photodisintegrated may capture some or all of these 4He nuclei, leading to the formation of still heavier elements: 20Ne(a,y)24Mg. Thus, once some 24Mg is produced we also expect 24Mg(cr,^28Si to take place, since it is possible to penetrate the Coulomb barrier of 24Mg at that temperature. Once an
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appreciable concentration of 28Si is built up, the reaction 28Si(a^)32S take place, and so on for the production of 36A and 40Ca. This two-step process—photodisintegration followed by the direct capture of some or all of the resulting 4He nuclei—is called the a process [2]. The a process is responsible for building, in decreasing proportion, the a-particle nuclei from 24Mg to 40Ca. All these elements stand out as prominent peak in the relative abundances of cosmic matter. Of course, a proportion of the releasing a-particles is consumed in scouring out the previous a-particle nuclei. Thus, a-particle nuclei are synthesis through two sources: helium burning (a-capture) process and a process. The a process is very similar to helium burning. However, these processes are different from a point of view that a particle sources are quite different in the two cases and they occur in the different range of temperatures. In atomic nuclei, as is well known, there are two type of correlations: short range correlation due to the strong repulsive part of nucleon-nucleon interaction and long range correlation, which lead to the formation of the nucleon associations or clusters within atomic nuclei. Let's consider the static cluster model of atomic nuclei. Following Ref. 6, we represent the spatial configurations of alpha-cluster nuclei of 12C, 160,20Ne 24Mg, 28Si, and 32S respectively in the form of an equilateral triangle, tetrahedron, and regular triangular, quadrangular, pentagonal, and hexagonal bipyramids. The nuclei 12C, 16O are characterized by one parameter RI, namely the distance from the center of nucleus to the center of the a-particle formation, which is located in one the vertices of the triangle or tetrahedron. The nuclei of 2s-ld shells are characterized by two parameters: the distance RI from the center of nucleus to the center of the a-particle formation located at one of the vertices of the bipyramid, and the distance R2 from the center of nucleus to the center of the a-particle formation located at the base of the bipyramid. Maximum-symmetry consideration [7] indicate that the centers of the a-particles formation, the distances between which are fixed, are singled out in the a-cluster model. Since the four nucleons are in the Is states relative these centers, the density of a nucleus with 4N nucleons can be expressed in the form
where N is the number of a-clusters, p(r-Rk) is the density distribution in the aparticle formation, and will be calculated using shell model wave function with Jastrow factor. Under these assumptions, the charge form factor for the elastic scattering of electron by an a-cluster nucleus takes a form i where fa(q) is the elastic form factor of 4He, q is a transferred momentum and the coefficients A and B are related to the number of a-clusters. In our calculations the Jastrow short-range correlation are included into the 4He charge form factors and charge form factors for the elastic scattering of electrons on the 12C, 16O, 20 Ne 24Mg, 28Si, and 32S nuclei are calculated. Figure presents the results of our calculation. 355
Consideration of the short-range correlation in description of the charge form factor fa(q) of 4He, results an essential improvements of the agreements between the theoretical and experimental form factors. The best-fit values for R\ and ^2 also predict the reasonable values for the size of the a-cluster nuclei. The considered model enables one to conclude on the extent of the cluster separation on the mass number. We also observe that the size of a-cluster increases with the increment of atomic number of a nucleus. The static cluster model of atomic nuclei also describes the quasielastic electron scattering on a-cluster nuclei under the assumption that the corresponding elementary process proceeds by the a-particle formation within the nucleus. In Ref. 8 a dynamic model of a-cluster nuclei have been suggested and developed using the method of hyperspherical functions. A theory of complete a-particle photodisintegration of light nuclei was developed, assuming that the elementary process occurs through quasi-a-particle formation inside the nucleus. One of the examples of reactions with several a-particles in the final state is /+12C -> Na. The general reversibility of nuclear reactions makes it possible to obtain the information about reverse reaction 3a—»12C + y and understand its role in the evolution of the stars and production of the 12C. We consider the internal structure of the a particle and studied the process of 3 a photodisintegration by the method of hyperspherical functions in the coordinate representation. Expanding the wave function in the basis of four-particle hyperspherical functions and using NN potential from Ref. 9, calculate the internal structure of the a-particle. In the region of photon energies from the threshold up to 30 MeV the photodisintegration of 12C into three a particles can proceed by two mechanisms: /. direct disintegration of 12C into three interacted a particles as a result of the interaction of photon with a quasi-a-particle cluster inside the nucleus; //. Two step disintegration of 12 C, with formation of 8Be subsystem in an excited state as a first step, and its subsequent decay into two a particles as a second step. As our calculations show, the maximum in the cross section can be explained by the first mechanism, and there is no need that the process goes through the intermediate 2+ state of 8Be. The success of the a-cluster model of atomic nuclei was also demonstrated in Ref. 10, where the quasi-a-particles mechanism of pion double charge exchange reaction on light nuclei has been suggested and developed. Thus, assumption of a-cluster structure of atomic nuclei is in very good agreement with varieties of observing experimental phenomena, and is just a reflection of the history of matter, on which we can make observations today.
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