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Hexadecapole strength in the rare isotopes 74,76 Kr

In the Ge-Sr mass region, isotopes with neutron number N ≤ 40 are known to feature rapid shape changes with both nucleon number and angular momentum. To gain new insights into their structure, inelastic proton scattering experiments in inverse kinematics were performed on the rare isotopes 74,76 Kr. This work focuses on observables related to the J π = $4$$^{+}_{1}$ states of the Kr isotopes and, in particular, on the hexadecapole degree of freedom. By performing coupled-channels calculations, hexadecapole deformation parameters β 4 were determined for the J π = $4$$^{+}_{1}$ states of 74,76 Kr from inelastic proton scattering cross sections. Two possible coupled-channels solutions were found. A comparison to predictions from nuclear energy density functional theory, employing both non-relativistic and relativistic functionals, clearly favors the large, positive β 4 solutions. These β 4 values are unambiguously linked to the well deformed prolate configuration. Given the β 2 - β 4 trend, established in this work, it appears that β 4 values could provide a sensitive measure of the nuclear shell structure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Materials Data on SrGe2 by Materials Project

SrGe2 is Magnesium tetraboride-like structured and crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. there are two inequivalent Sr sites. In the first Sr site, Sr is bonded in a 9-coordinate geometry to nine Ge atoms. There are a spread of Sr–Ge bond distances ranging from 3.23–3.52 Å. In the second Sr site, Sr is bonded in a 11-coordinate geometry to eleven Ge atoms. There are a spread of Sr–Ge bond distances ranging from 3.36–3.63 Å. There are three inequivalent Ge sites. In the first Ge site, Ge is bonded in a 8-coordinate geometry to five Sr and three Ge atoms. There are two shorter (2.58 Å) and one longer (2.64 Å) Ge–Ge bond lengths. In the second Ge site, Ge is bonded in a 8-coordinate geometry to five Sr and three Ge atoms. Both Ge–Ge bond lengths are 2.59 Å. In the third Ge site, Ge is bonded in a 8-coordinate geometry to five Sr and three Ge atoms. The Ge–Ge bond length is 2.57 Å.

36 MATERIALS SCIENCE↗

Materials Data on SrGe by Materials Project

SrGe crystallizes in the orthorhombic Cmcm space group. The structure is three-dimensional. Sr is bonded in a 7-coordinate geometry to seven equivalent Ge atoms. There are a spread of Sr–Ge bond distances ranging from 3.30–3.40 Å. Ge is bonded in a 9-coordinate geometry to seven equivalent Sr and two equivalent Ge atoms. Both Ge–Ge bond lengths are 2.66 Å.

36 MATERIALS SCIENCE↗

Materials Data on Sr2Ge by Materials Project

Sr2Ge is Cotunnite structured and crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. there are two inequivalent Sr sites. In the first Sr site, Sr is bonded to four equivalent Ge atoms to form a mixture of edge and corner-sharing SrGe4 tetrahedra. There are a spread of Sr–Ge bond distances ranging from 3.21–3.27 Å. In the second Sr site, Sr is bonded in a 3-coordinate geometry to three equivalent Ge atoms. There are one shorter (3.28 Å) and two longer (3.48 Å) Sr–Ge bond lengths. Ge is bonded in a 7-coordinate geometry to seven Sr atoms.

36 MATERIALS SCIENCE↗

Materials Data on SrGe2 by Materials Project

SrGe2 is hexagonal omega structure structured and crystallizes in the trigonal P-3m1 space group. The structure is three-dimensional. Sr is bonded to six equivalent Ge atoms to form SrGe6 octahedra that share corners with six equivalent GeSr3Ge3 octahedra, edges with six equivalent SrGe6 octahedra, and edges with six equivalent GeSr3Ge3 octahedra. The corner-sharing octahedral tilt angles are 18°. All Sr–Ge bond lengths are 3.19 Å. Ge is bonded to three equivalent Sr and three equivalent Ge atoms to form distorted GeSr3Ge3 octahedra that share corners with three equivalent SrGe6 octahedra, corners with three equivalent GeSr3Ge3 octahedra, edges with three equivalent SrGe6 octahedra, and edges with nine equivalent GeSr3Ge3 octahedra. The corner-sharing octahedra tilt angles range from 0–18°. All Ge–Ge bond lengths are 2.61 Å.

36 MATERIALS SCIENCE↗

Materials Data on SrGe3 by Materials Project

SrGe3 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. there are two inequivalent Sr sites. In the first Sr site, Sr is bonded in a 12-coordinate geometry to twelve Ge atoms. There are a spread of Sr–Ge bond distances ranging from 3.35–3.61 Å. In the second Sr site, Sr is bonded in a 12-coordinate geometry to twelve Ge atoms. There are four shorter (3.30 Å) and eight longer (3.36 Å) Sr–Ge bond lengths. There are two inequivalent Ge sites. In the first Ge site, Ge is bonded in a 9-coordinate geometry to four Sr and five Ge atoms. There are one shorter (2.55 Å) and four longer (2.81 Å) Ge–Ge bond lengths. In the second Ge site, Ge is bonded in a 9-coordinate geometry to four Sr and five Ge atoms. There are one shorter (2.60 Å) and two longer (2.83 Å) Ge–Ge bond lengths.

36 MATERIALS SCIENCE↗

Materials Data on Sr7Ge6 by Materials Project

Sr7Ge6 is delta Molybdenum Boride-like structured and crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. there are four inequivalent Sr sites. In the first Sr site, Sr is bonded in a 6-coordinate geometry to six Ge atoms. There are a spread of Sr–Ge bond distances ranging from 3.20–3.34 Å. In the second Sr site, Sr is bonded in a 7-coordinate geometry to seven Ge atoms. There are a spread of Sr–Ge bond distances ranging from 3.34–3.77 Å. In the third Sr site, Sr is bonded in a 7-coordinate geometry to seven Ge atoms. There are a spread of Sr–Ge bond distances ranging from 3.24–3.62 Å. In the fourth Sr site, Sr is bonded in a 3-coordinate geometry to five Ge atoms. There are a spread of Sr–Ge bond distances ranging from 3.12–3.67 Å. There are four inequivalent Ge sites. In the first Ge site, Ge is bonded in a 9-coordinate geometry to eight Sr and one Ge atom. The Ge–Ge bond length is 2.62 Å. In the second Ge site, Ge is bonded in a 5-coordinate geometry to seven Sr and one Ge atom. The Ge–Ge bond length is 2.55 Å. In the third Ge site, Ge is bonded in a 9-coordinate geometry to eight Sr and one Ge atom. In the fourth Ge site, Ge is bonded in a 9-coordinate geometry to seven Sr and two Ge atoms. The Ge–Ge bond length is 2.57 Å.

36 MATERIALS SCIENCE↗