By taking the "0 + "O system as an example, the property of nucleus-nucleus interaction is investigated by the use of resonating group method. Special attention is paid to the nuclear saturation property which is satisfied in all the interaction region from compact 32-nucleon configuration to two separated "0 nuclei. A new kind of effective nuclear force with a repulsive three-body interaction is introduced in order to take account of density dependent effects in relation to the saturation property. A kind of core in the inner region and a weak attraction in the intermediate region are discussed quantitatively for the "0+ "0 interaction. § 1. Introduction Experimental systematics on heavy-ion collisions have stimulated the study on nucleus-nucleus interaction.ll~al Theoretical interest has been mainly concentrated upon a potential description by the use of a local density approximation as an intuitive approach!l,ol On the other hand, the orthogonality condition model has made a modern current for the study of light two-nucleus systems particularly in Japanese group. 6 l In this model the nucleus-nucleus potential is assumed as some kind of modification of a direct potential. These models, however, are not still placed on a foundation of a fully microscopic consideration on nucleus-nucl~us interaction.Microscopic treatments of the interactions between composite particles have their essential significance in clarifying the interplay of the nuclear force and the Pauli principle during the collision process of two nuclei. 7 l,sl Recent progress of the microscopic treatments has rapidly extended their applicability to heavy two· nucleus systems with (Op) or (lsOd) shell nuclei. 9 l An introduction of the generator coordinate 10 l with respect to the relative motion is a key point to succeed in avoiding a serious cumbersomeness in the computational procedures by the use of the resonating group method (RGM). This is because the generator coordinate method (GCM) allows us to utilize the well-known systematics of harmonic oscillator (h.o.) wave function.(And note that when the center-of-mass motion is separated,w the GCM becomes equivalent to the RGM under a Gaussian transfer-
The exchange kernels due to the antisymmetrization are derived in an analytical way with the symbolical use of computer memory by taking the a+ 16 0 system as a typical example. Starting with the harmonic oscillator shell model wave functions around the centres as internal states of 'nuclei, we present new algorisms of deriving analytically the generator coordinate kernel (GCM kernel). We have developed two different algorisms for this purpose; one is named the UFPN and the other the "R~ndez-Vous". Contents of such algorisms areex-plain~d in detaiL Transformation from the GCM kernel to the resonating group one (RGM one) is also llnalytically carried out by the aid of computer memory . through differ~ntial formulas of the GCM kernel. Here, we make use of explicit form of Bell's polynomials for performing complex differentiations. A pew GCM kernel free from the spurious c.m. component is presented for cases with different oscillator parameters. An algorism of procec;lure to eliminate the c.m. component is the same as that of deriving the RGM kernel from the GCM one.Considerations are given to a simple methop. of calculating . the direct potential, decomposition method of the kernel and a method of expanding the GCM kernel. The methods mentioned in this report will' extend applicability of . microscopi~ study of· nucleus-nucleus interactions. Contents 4.2. Decomposition method of the kernel 4.3. Series expansion of the GCM kernel § 5. Concluding remarks Appendix-Coulomb interaction part of the GCM energy kernel-at Univ of Iowa-Law Library on May 27, 2015 http://ptps.oxfordjournals.org/ Downloaded from 192 A. Tohsaki-Suzuki § I. IntroductionMicroscopic treatment of interactions between· complex nuclei had been carried out. by laborious and tedious manual works. Most part of these works was to. derive the exchange kernel due to antisyrnrnetrization procedute corning from the Pauli principle. Several years ago, it was impossible t~ calculate _correctly kernels
An eliminating method of the spurious e.m. motion m generator coordinate method (GCM) is presented for nucleus-nucleus interactions in a general case with different oscillator parameters. The GCM kernel free from the spurious c.m. motion is constructed by the use of a simple procedure which starts with the usual GCM. Consideration is given on a characteristic behavior of the spurious c.m. component in the usual GCM kernel. § I. IntroductionRecently, rapid progress has been made in understanding the interaction between complex nuclei.ll.zl Applicability of the microscopic theory, which takes into account the Pauli principle correctly, has been successfully extended to two-nucleus systems inxolving Por sd-shell nuclei, such as a+ 16 0, 3 l~ol 16 0+ 16 0 71~91 and a + 4°C a 101~121 collisions. Many of these studies were carried out based on the generator coordinate method (GCM) by the use of harmonic oscillator (H.O.) wave functions for nuclei with a common oscillator parameter. For cases with different oscillator parameters, howe\·er, there are not only very much laborious and tedious task of deriving the exchange kernel but also basic difficulties of removing the spurious c.m. motion. On the other hand, the resonating group method (RGM) is free from the c.m. motion. Adopting the RGM, several authors 61 ' 121 ' 131 have studied nucleus-nucleus interaction for cases with different oscillator parameters. For example, Horiuchi's method, vvhich employs a valence-orbit technique, simplifies the construction procedure of the kernel and gives directly the RGM kernel by a single Fourier transformation from a momentum space one. It is, however, very difficult to derive the RGM kernels for more complex systems than a+ 16 0.Recent physical interest in the microscopic study has lain in rearrangement reactions, such as 12 C C 2 C, a) 20 Ne and 16 0 ( 12 C, a) 2 'Mg, and in dynamical treatment of distortions of nuclei during scattering processes, which may take into account coupling with breathing modes of nuclei. To investigate such problems, it is necessary to confirm a new theoretical framework of a microscopic model exactly free from the spunous c.m. motion.It is the main purpose of this paper to propose a new GCM free from the spunous c.m. motion and to demonstrate that a new GCM kernel can be obtained by a simple procedure. We denote the new GCM space by the S-space and the usual at National Institute of Education Library, Serials Unit on June 4, 2015 http://ptp.oxfordjournals.org/ Downloaded fromwhere Jl 12 is the antisymmetrization operator between two nuclei, v/ the oscillator parameter of the i-th nucleus and N/ the mass number. The wave function IJI/ *> The RGM space (dynamical variable space) is also denoted by the r-space.
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