Chapter II. Comprehensive Study of Alpha-Nuclei

Abstract

Downloaded from the self-conjugate 4n nuclei which we call a-nuclei are especially stable energetically, therefore the fragmentation (or fission) thresholds of respective nuclei into constituent a-nuclei plus a residual nucleus lie in series starting in the region of quite low excitation energy.Since a-nuclei are strongly bound systems, they are hardly excited even when two a-nuclei are in a close distance. The fact that inter-nucleus forces between spin-isospin saturated nuclei are generally weak promotes further the tendency that a-nuclei preserve their identity in their interaction process. Furthermore the repulsive force of a short range part of the inter-nucleus inter-at Purdue University Libraries ADMN on June 1, 2015 http://ptps.oxfordjournals.org/ Downloaded from factorily the low-lying positive-parity excited states, 02 + at 7.66 MeV and 22 + (or 08 + ?) at ,...__,10.3 MeV shown in Fig. 1-1.From these studies, the ground rotational band (consisting of ground 01 +, 2 1 + at 4.44 MeV and 41 + at 14.08 MeV) was regarded as having a strong shellmodel-like character, although a-clustering effect is important. The latter nature (namely the persistency of a-clustering) was investigated in detail by Abe, Hiura and Tanaka 17 l by the use of the molecular orbital method preserving the spatial symmetry of [ 4 8 ]. Takigawa and Arima 18 l investigated the *> Many works were made with various frameworks and a-a potentials. Here, however, we do not mention them in detail. See a review article given by Tamagaki and Fujiwara for the works on the 3a problem.••> at Purdue University Libraries ADMN on June 1, 2015 http://ptps.oxfordjournals.org/ Downloaded from 15 0, 15 N, 17 0 and 11 F, the spacing between the centroids of the p and the sd shells is estimated as about 17 MeV. ii) We can deduce a value of fiw = 13.4 MeV corresponding to the harmonic oscillator parameter b = 1.76 fm at Purdue University Libraries ADMN on June 1, 2015 http://ptps.oxfordjournals.org/ Downloaded from Another standpoint for incorporating a 4p-4h configuration was the weak coupling model by Arima, Horiuchi and Sebe 58 >• 59 >• 60 > which assumed that the at Purdue University Libraries ADMN on June 1, 2015 http://ptps.oxfordjournals.org/ Downloaded from at Purdue University Libraries ADMN on June 1, 2015 http://ptps.oxfordjournals.org/ Downloaded from *' The RGM study for the "O+a system was also carried out by Siinkel and Wildermuth."'l **l Similar RGM analysis of the "0-a interaction was made by Ando, Ikeda and Suzuki 106 J by comparing with the a-a and "0-16 0 cases. at Purdue University Libraries ADMN on June 1, 2015 http://ptps.oxfordjournals.org/ Downloaded from at Purdue University Libraries ADMN on June 1, 2015 http://ptps.oxfordjournals.org/ Downloaded from *> As for wi'lr(t), harmonic oscillator functions and locally peaked Gaussian functions are also available by the use of fPNLM(J., v, S). Actually, the latter functions were examined and were found to give the same results obtained by the set (2·5) (Ref. 41)). at Purdue University Lib...

6He + 6He Clustering of 12Be in a Microscopic Algebraic Approach

“…Meanwhile, the asymptotic behavior is known not for these coefficients, but for the coefficients C (l1,l2,l) k (E) appearing in the expansion of the wave function over the states of the "physical", angular momentum-coupled basis {Φ (l1,l2,l) k }. The states of this basis (referred to as "l-basis" in what follows) are labelled by the number of quanta 2k, angular momenta of each of the 6 He clusters l 1 and l 2 , and the angular momentum of their relative motion l. In AVRGM, the asymptotic behavior of C (l1,l2,l) k (E) is expressed in terms of the Hankel functions of the first and second kind H (1,2) l+1/2 ( √ 2E √ 4k + 2l + 3) and the scattering S-matrix elements [23]. The angular momentum-coupled basis for the system 6 He+ 6 He, at a given k and L = 0, consists of five orthonormalized functions, with the following structure,…”

“…In a number of known papers [1,2,3] the resonating-group method (RGM) has been applied to studies of collisions between light magic nuclei. The fact that it takes a considerable amount of energy to excite these nuclei simplifies the calculations but leaves beyond the scope of the studies multi-channel features of the continuum spectra of compound systems.…”

“…[13] and references therein) and Fujiwara et al [1]. Both groups utilize the Bargmann space technique [14] and the SU (3)-scalar property of the norm kernels.…”

Symmetry-unrestricted Skyrme–Hartree–Fock–Bogoliubov calculations for exotic shapes in nuclei from 64Ge to 84Mo

“…It should be noted here that, although extensive theoretical calculations and rich experimental evidences have been accumulated for axially symmetric octupole (Y 30 ) deformations, as reviewed in [36,37], only a few calculations using WoodsSaxon Strutinsky methods are available [38][39][40][41] except for light nuclei, and no firm experimental evidence exists up to now concerning the non-axial octupole (Y 31 , Y 32 , Y 33 ) deformations in the mean fields. For light nuclei, non-axial octupole deformations have been discussed [42][43][44][45][46] in connection with alpha-cluster structures [47]; for instance, a triangular structure of 12 C [42,44] and a tetrahedral shape for 16 O [45, 46].…”

Equilateral-Triangular Shape inC14

“…In 12 C, a 3 ÿ state has been observed at E x 9:6 MeV [6]. This state may correspond to the band head of the above-mentioned K 3 ÿ rotational band [7]. However, this 3 ÿ state is already above the 3 threshold by about 2 MeV, suggesting that no bound system can be expected with a triangular configuration.…”