Particle alignments and shape change inGe66andGe68

Abstract

The structure of the N ≈ Z nuclei 66 Ge and 68 Ge is studied by the shell model on a spherical basis. The calculations with an extended P + QQ Hamiltonian in the configuration space (2p 3/2 , 1f 5/2 , 2p 1/2 , 1g 9/2 ) succeed in reproducing experimental energy levels, moments of inertia and Q moments in Ge isotopes. Using the reliable wave functions, this paper investigates particle alignments and nuclear shapes in 66 Ge and 68 Ge. It is shown that structural changes in the four sequences of the positive-and negative-parity yrast states with even J and odd J are caused by various types of particle alignments in the g 9/2 orbit. The nuclear shape is investigated by calculating spectroscopic Q moments of the first and second 2 + states, and moreover the triaxiality is examined by the constrained Hatree-Fock method. The changes of the first band crossing and the nuclear deformation depending on the neutron number are discussed.

Nonsequential Two-Photon Double Ionization of Atoms: Identifying the Mechanism

“…However, it is only during the last 15 years or so, that advances in theory, modeling and experiment have enabled scientists to gain a deeper insight into the role of electron correlations in this ionization process [1][2][3][4][5]. The corresponding problem of two-photon double ionization of helium, in the photon energy interval between 39.4 and 54.4 eV, is an outstanding quantum mechanical problem that has been, and still is, subject to intense research worldwide, both theoretically [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and experimentally, employing state-of-the-art high-order harmonic [20][21][22] and free-electron (FEL) light sources [23,24]. Despite all the interest and efforts that have been put into this research, major fundamental issues remain unresolved.…”

“…As mentioned in the introduction, the problem of nonsequential two-photon double ionization of helium has been subject of intense research in recent years, and accurate predictions for the generalized cross section remain elusive [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] as the values obtained for the cross section for the reaction may differ by as much as an order of magnitude. On the theoretical side, the great discrepancies that remain between different approaches are usually ascribed to the different ways electron correlations are handled in the final state.…”

Medium-spin states inGe70and the role of theg9/2orbital

“…For details on the calculation methods and parameter values, please refer to Refs. [13][14][15], respectively, except that A-dependent parameters are used for the EPQQM interaction. However, first we focus on the similarities between neighboring even Ge isotopes, namely 70 Ge and 66,68 Ge.…”

“…Recently large-scale shell-model calculations have become available with the model space (2p 3/2 , 1f 5/2 , 2p 1/2 , 1g 9/2 ) for both protons and neutrons. For example, Hasegawa et al successfully applied the shell model with an extended P + QQ interaction with monopole interactions to both the description of high-spin states in 66,68 Ge [13] and the systematic behavior of the low-lying states in Ge isotopes [14]. Another effective interaction was constructed starting from a renormalized G-matrix interaction and successfully applied to describing irregular behavior of the 0 + 2 states in Ge isotopes by Honma et al [15].…”

Overview of neutron–proton pairing

“…Hasegawa and Kaneko et al [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49] systematically studied N ≈ Z nuclei in the regions 44 ≤ A ≤ 74 and 88 ≤ A ≤ 96. They diagonalized the Extended Paring plus Quadrupole -Quadrupole (EPQQ) Hamiltonian in various model spaces with manageable dimensions constructed from the spfg orbitals.…”