Spectroscopic amplitudes for complex cluster systems

Abstract

By expanding the Bargmann-Segal integral transform of norm and overlap kernels in appropriately SU(3) coupled Bargmann space functions, the calculation of norm and overlap matrix elements in a cluster model basis is reduced to purely algebraic techniques involving the algebra of SU(3) recoupling transformations. This technique has been further developed to make calculations possible for systems of two heavy fragments other than closed-shell nuclei. In one application of the method, analytic expressions are given for the norms of binary fragment systems in which a light fragment of mass number f, f < 4, is combined with a heavy fragment of mass number A-J with A-f< 24. The A-j' fragment nuclei with different p and sd-shell structure illustrate somewhat different problems in the recoupling technique. In a second application, spectroscopic amplitudes are calculated for the most important open channels of the "C+ "C resonances. Eigenvalues and eigenvectors ofthe antisymmetrizer are evaluated in a "molecular basis" of the "C+ "C system, in which each "C nucleus is assumed to have SU(3) symmetry (04) with internal rotational excitations ofO+, 2+ and 4+. Reduced width amplitudes are calculated connecting such normalized, fully antisymmetrized molecular basis states to exit channels which include: a+20Ne with *ONe internal functions of (80) SU(3) symmetry, (K = O+ band), and (82) SU(3) symmetry, (K = 2-band); 160+sBe; and 23Na+p or 23Mg+n fragments with 23Na or 23Mg excitations in K = jj and f rotational bands of SU(3) symmetry (83).

Symmetry-guided large-scale shell-model theory

“…Another important feature is that once the overlaps are calculated in labframe coordinates, the translationally-invariant overlaps can be straightforwardly calculated using an U(A)× U(3) approach, which is especially suitable for the SU(3)-coupled wave functions [207]. Applications of the model to the intermediate-mass region typically employ leading SU(3) configurations in the cluster wave functions and Gaussian-like interactions, and have successfully calculated α and 8 Be cluster amplitudes, spectroscopic amplitudes for heavy-fragment clusters, and sub-Coulomb 12 C+ 12 C resonances [209][210][211]. Sp(3, R)-scheme RGM.…”

Wigner and the groups in classifying elementary particles and nuclear states

“…The contracted symplectic model (of U b (6)⊗U s (3)), is a collective model, obtained as the large N limit of the multi major-shell symplectic model [37,38]. The fully microscopic [39,40] as well as the semimicroscopic algebraic cluster model [25] are equiped with a U C (3)⊗U R (3) basis. All these models are based on the L-S-coupled scheme, and the spin-isospin sector is described by Wigner's SU S T (4) symmetry.…”

AlgebraicC12+12Cseh1, Lévai2, Scheid3 1993Phys. Rev. C350270View full textAdd to dashboardCite

“…But, since the clusters are identical in our case, these quantum numbers characterizing the internal cluster configuration of the C+ C system can not be combined with any excitation of the relative motion. It can be shown [15] that combinations with only n + A~+ pc =even are allowed here, i.e. , (Ac, pc) = (0,8), (2,4), and (4,0) can be combined with even values of n (and positive parity), while (Ac, pc) = (1,6) and (3,2) can occur only if n"( ad nconsequently the parity) is odd.…”

“…The model space obtained this way turned out to be larger than that derived from the solution of the eigenvalue problem of the norm kernel [12,15]. In particular, we had some extra multiplicities for each value of n we studied (i.e.…”

“…One of the major differences between the previous calculations and the present one is that earlier the clusters were considered structureless, therefore the treatment was a single-channel one [8 -10], while here we take into account the non-closed-shell nature of the C nuclei. Semimicroscopic [12,13], as well as single [14] and multichannel [15] microscopic cluster model calculations also addressed this region.…”