Unrestricted Configuration Research Articles

A benchmark quantum Monte Carlo study of the ground state chromium dimer

AbstractWe report calculations of the ground state energy and binding curve of the chromium dimer using the variational and diffusion quantum Monte Carlo (VMC and DMC) methods. We examined various single‐determinant and multideterminant wavefunctions multiplied by a Jastrow factor as a trial/guiding wavefunction for VMC/DMC. The molecular orbitals in the single determinants were calculated using restricted or unrestricted Hartree–Fock or density functional theory (DFT) calculations where five commonly used local (SVWN5), semilocal (PW91 and BLYP), and hybrid (B1LYP and B3LYP) functionals were examined. The multideterminant expansions were obtained from the generalized valence bond and (truncated) unrestricted configuration interaction with single and double excitations (UCISD) methods. We also examined a UCISD wavefunction in which UCISD expansions were added to the UB3LYP single‐determinant reference, and their coefficients were optimized at the VMC level. In addition to the wavefunction dependence, the effects of pseudopotentials and backflow transformation were also investigated. The UB3LYP single‐determinant and multideterminant wavefunctions were found to give the variationally best DMC energies within the framework of single‐determinant and multideterminants, respectively, though both the DMC energies were higher than twice the DMC atomic energy. Some of the VMC binding curves show a flat or quite shallow well bottom, which gets recovered deeper by DMC. All the DMC binding curves have a minimum indicating a bound state, but the unrestricted ones overestimate the equilibrium bond length. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Structure of the mirror nuclei21Ne and21Na

Theγ-decay of levels in21Ne up to 10 MeV excitation energy has been investigated byn — γ coincidence measurements initiated with the18O(α, nγ) reaction at 12, 13, 14.5 and 15.4 MeV bombarding energies. Spin(-parity) assignments of excited states are obtained by combining then — γ angular correlation measurements performed atE α=11, 11.82 and 13.6 MeV with a consideration of lifetimes, neutron penetrabilities of the unbound states, and information from the mirror nucleus21Na. The resulting values of Ex[keV]−J π are as follows: 4525-5+, 4686-3+, 5431-7+, 5549-3+, 5819-7−, 6175-7+, 6268-9+, 6550-9, 6639-9, 7006-7+, 7041-9, 7356-7 or 9, 7422-11(−), 7648-7+, 7981-11 or (7+), 8154-9, 8240-11, 8664-9− or 11 or 13−, 9401-13−, 9867-13− or 15+, 9941-13− or 15 or 17+. The assignment of mirror levels in21Ne —21Na has been extended to the 6175 keV level of21Ne. Excitation energies, electromagnetic properties, Gamow−Teller matrix elements and spectroscopic factors of positive parity states are compared with the results of shell-model calculations which employ a unifieds—d shell Hamiltonian and the unrestricted configuration space of the 0d 5/2 —1s 1/2—0d3/2 shell. Collective properties contained in shell model wave functions are explored up to the termination of bands atJ=17/2 or 19/2. The spectrum of intruder states in21Ne is observed to begin with a 5628 keV,J π=7/2+ state. The 7422, 8664 and 9401 keV levels are assigned as members of previously established negative-parity rotational bands.

High-spin states in26Mg

Theγ-decays of levels in26Mg have been investigated up to 12.5 MeV excitation energy by proton-γ-ray coincidence measurements in the23Na(α, pγ) reaction at 14.2 and 16 MeV bombarding energy. Lifetime-measurements, made with the Doppler-shift attenuation method, and proton-γ-ray angular-correlation measurements were performed at Eα=14.2 MeV. Many high-spin states were observed, among them levels at 6,978 (5+), 7,283(4−), 7,395(5+), 7,953(5−), 8,202(6+), 8,472(6+), 9,065(5), 9,112(6+), 9,169(6−), 9,383 (6+), 9,542(5), 9,829(7+), 9,989(6+) and 12,479(8+, 7−) keV excitation energy. The spectrum of positive-parity states and their electromagnetic properties are reproduced with good accuracy by shell-model calculations which employ a unifieds-d shell Hamiltonian and the unrestricted configuration space of the 0d5/2 1s1/2 0d3/2 shell. Members of five inferred rotational bands, withKπ=0+, 2+, 3+, 0+ and 3− have been observed up to at leastI=6. TheKπ=2+ band shows strong anomalies of excitation energies andE2 transition rates near theI=6 state. The static intrinsic quadrupole moments calculated from the shell model wave functions indicate transitions from prolate to oblate deformation within theKπ=2+ band and also the ground state band. The lowest lyingIπ=4+ state appears to be “spherical” and cannot be associated with a rotational band.

Problems of classical and quantum-gravitational collapse

Various aspects of the statics and dynamics of spherical gravitational distributions of an ideal fluid with distributed sources of zero-mass and massive vector fields are investigated. Both unrestricted configurations and isolated configurations with the appropriate matching to the external geometry are considered.