Structure of the Excited States in 12C. II

Abstract

Nuclear wave functions of microscopic a-particle model, which were obtained in the generator coordinate calculation by the present authors, are found to reproduce properties of low energy levels of 12 C nucleus, i.e., a-decay widths, electric transitions and charge form factors for electron scattering. Especially calculated widths of the Oz +and 10.3 MeV levels are found to be in excellent agreement with experiment, assuming that the spin of the latter is 2. The monopole transition from the o, + state to the ground state is also well reproduced as well as the E2 transition to the 2, + state. Furthermore analysis of the reduced width amplitudes is made which clarifies characters of the levels. It is found that in the o, + and 10.3 MeV states an a-particle is coupled mainly to the 'Be ground state with orbital angular momenta l equal to 0 and 2 respectively. In the predicted higher positive-parity states O, +, 2, + and 4, +, an a-particle is coupled mainly to the first excited state of 'Be with l equal to 2. § 1. IntroductionIn 12 C nucleus the 0/ level at 7.7 MeV and the next positive-parity level at 10.3 MeV are well known as anomalous states due to their low excitation energies and extremely large a-reduced widths. v From the viewpoint of nuclear shell model, low-lying o+ states in 12 C and 16 0 are considered to come from four-particle excitations. But the experimental excitation energies are too low to be reproduced by simple four-particle four-hole shell-model configurations. Morinaga suggested that the 0, + and 10.3 MeV levels form a rotational band with a linear chain structure of 3 a-particles.') According to Ikeda's diagram,') we can expect the appearance of nuclear states with some cluster structure near the threshold energies for decay into a-particles. The above-noted excited states in 12 C are expected to be such states, that is, to have distinct cluster structure which is associated with the 8 Be+a channel open at 7.4 MeV. Ikeda et al. 4 l analyzed a-decay widths of 3 a-cluster configurations by using the Bloch-Brink wave function 5 J and suggested a structure of loosely coupled 3 a-particles for the excited states. Horiuchi succeeded in obtaining a shell-like ground state and an excited state with a well-developed cluster structure by extending the orthogonality condition model to three-cluster system.At the same time, full microscopic calculations were made on this nucleus by several authors. 6 l, 7 l They, however, restricted freedom of 3 a-particle motion to by guest on April 10, 2015 http://ptp.oxfordjournals.org/ Downloaded from 1622 E. Uegaki, Y. Abe, S. Okabe and I-I. Tanalw the linear chain configuration 61 or to the hinge-angle vibration.n As a result they obtained only moderate success for the excited states.We recently investigated the structure of 12 C nucleus by using the microscopic ct-particle model of Bloch-Brink and by taking full account of motion of :1 a-clusters (Ref. 8), hereafter referred to as I). vVe succeeded in reproducing all the low energy levels of 12 C nucleus (except f...

Three-body decay of linear-chain states in C14

“…Since the linear-chain configuration of 3α clusters (linearly aligned 3α clusters) was suggested in 1950s [1], many studies have been devoted to search it in the excited states of 12 C [2][3][4][5][6][7][8][9][10]. Nevertheless, no positive evidence has been obtained, and it is considered that the linear chain is unstable against the bending motion [5,8].…”

Isoscalar dipole transition as a probe for asymmetric clustering

“…It was known that many of those resonances are associated with the α cluster states such as the Hoyle state of 12 C [15][16][17][18][19][20][21][22][23][24], the α + 12 C cluster states in 16 O [25,26], the α + 16 O cluster states in 20 Ne [27], and the α + α + t cluster state in 11 B [28][29][30]. Therefore, the IS monopole transition has been utilized as a probe to search for the cluster states in light nuclei.…”

“…For example, the 1 − state of 16 O at 9.6 MeV and that of 20 Ne at 5.8 MeV are the evidence of the asymmetric clustering with α + 12 C and α + 16 O configurations [41].…”

“…For this purpose, by using α + 16 O and α + 40 Ca cluster states in 20 Ne and 44 Ti as examples, we investigate the excitation mechanism of the IS dipole transition from the ground state to the asymmetric cluster states. We first discuss an analytic expression of the IS transition matrix from the shell-model ground state to the cluster states.…”

Removal of forbidden states in a three-α system

“…In this case, cluster-cluster interactions are usually represented by appropriate local potentials which are, more or less, phenomenologically determined so as to reproduce the relevant data on the cluster-cluster systems. One of the simplest and well-investigated examples is a 3α model for 12 C. Many calculations based on the microscopic 3α model show that it reproduces the general features of the low-lying spectrum and the spectroscopic properties of 12 C [5,6]. Thus we would expect that the macroscopic version of the 3α system could give results of similar quality if it would be a realistic substitute of the microscopic model.…”