4He3H2H three-body model of the 9Be nucleus

Abstract

Within the framework of the single-channel approximation, an { } td α model of the 9 Be nucleus is presented. A comparative analysis of the 6 Li t wave functions describing relative motion of bound states constructed in { } n αα and { } td α cluster representations is carried out on the example of calculations of the 9 6 0 Be( , ) Li t γ process characteristics. Wave functions in binary channels with the lithium isotope and light Li fragment have been constructed in [1, 2], for the initial wave function of the 9 Be nucleus chosen for the { } n αα multicluster dynamic model with Pauli design (MDMP) [3]. One of the reliability requirements for the construction of various model representations of nucleus wave functions of the p-shell is considered to be their conformity to the classification of translation-invariant shell models (TISM) [4]. The so-called oscillator limit, according to which it is possible to compare the wave functions obtained by the Pauli design and the TISM functions, has been formulated in [1]. The radial functions obtained in the 9 6 Be{ } Li{ } n n p t αα → α + channel correspond to 3P-functions of the TISM model, that is, have nodal behavior [1, 2]. The possibility of constructing the 9 Be nucleus model in the { } td α representation was discussed in [2]. It is clear that for small bond energy in the 2 n α channel ( 1.573 Q = − MeV), the { } n αα configuration is obviously more diffusive than the { } td α configuration bonded by an order of magnitude stronger ( 19.166 Q = − MeV). Thus, it is obvious that channels with neutron or α-particle radiation can well be described within the framework of the { } td α model of the 9 Be nucleus. At the same time, it seems very attractive to investigate by the 9 6 Be Li t → + and 9 7 Be Li d → + strongly bound channels in the unified successive approach on the basis of the { } td α model. In the present work, we discuss the 6 Li t + two-particle channel of 9 Ве and present the result of calculations of the wave functions in the { } td α single-channel approximation suggested in [5]. The functions obtained are projected onto the 6 Li t + cluster channel and subsequently approbated in calculations of the 9 6 Be( , ) Li t γ photonuclear reaction characteristics [6]. The results obtained are compared with results of calculations for the { } n αα model. We now discuss briefly the main points of formal calculations of the { } td α functions in the single-channelapproximation. In contrast with the MDMP statement of the problem, only one potential is involved in a partial wave of each arm of pairwise intercluster interaction in calculations of three-cluster wave functions in the single-channel approximation. To find the bond energy of this system, the nonorthogonal variational method [5] is used. In this case, the initial radial functions, as well as in MDMP, are represented in the form of expansion in the Gauss basis.For the examined problem, we write down the wave function of the 9 Be nucleus in the { } td α representation in the following form [1]: