Configuration Mixing Calculations Research Articles

Alpha-particle type four-body correlation in 212Po

It is shown that a configuration in which two protons are excited from the pure shell-model ground state configuration to the same orbit as the uppermost occupied neutron orbit contributes appreciably to the α-decay reduced width of 212Po. This configuration has been neglected in most shell-model calculations. It is noted that the four-body correlation is enhanced by this new configuration if the effective interaction is attractive in the singlet-even state; this condition coincides with that on the effective interaction in order that an α-cluster be formed. If the conventional low-lying configurations are included, the α-decay reduced width of 212Po becomes twice as large as that for the configuration mixing calculations by Harada. It is also suggested that there may be states with strong α-type correlation among excited states.

Improved inverse gap equation procedure for quasi-particle calculations

An improvement in the inverse gap equation (IGE) method is proposed in which the fed single-quasi-particle-energies are corrected either by the second-order perturbation theory or by the modified Tamm-Dancoff approximation (MTDA) theory at each iteration. The procedure is fast converging. The behaviour of the extracted quantities for odd Ni isotopes is reasonably close to their expected theoretical behaviour. The extracted Hartree-Fock (HF) energies are highly sensitive to the choice of the effective two-body interaction. These quantities are used in calculating the various quasi-particle quantities for the corresponding even Ni isotopes through the BCS or pairing-model equations. Quasi-particle configuration-mixing calculations are performed for both odd and even Ni isotopes using their respective sets of quasi-particle quantities obtained by (i) the conventional BCS, (ii) IGE and (iii) the improved IGE procedures. These sets of quasi-particle results are compared and their relative merits discussed.

Nuclear Magnetic Moments ofCu60andCu62: hfs Experiment and Configuration-Mixing Calculation

The hyperfine structures of 24-min ${\mathrm{Cu}}^{60}$ and 10-min ${\mathrm{Cu}}^{62}$ have been measured by the atomic-beam magnetic-resonance method. Our results are: ${\mathrm{Cu}}^{60} (I=2)$, $\ensuremath{\Delta}\ensuremath{\nu}=6033(4)$ Mc/sec, ${\ensuremath{\mu}}_{I}=+1.219(3)$ nm (diamagnetically corrected); ${\mathrm{Cu}}^{62} (I=1)$, $\ensuremath{\Delta}\ensuremath{\nu}=\ensuremath{-}2257.2(5)$ Mc/sec, ${\ensuremath{\mu}}_{I}=\ensuremath{-}0.380(4)$ nm. The spins were previously known. Configuration-mixing calculations in the $1{f}_{\frac{5}{2}}\ensuremath{-}2p$ shell reproduce fairly well the spectra and binding energies of ${\mathrm{Cu}}^{58}$, ${\mathrm{Cu}}^{60}$, and ${\mathrm{Cu}}^{62}$, as well as these moments.

Level spectra of Ni-isotopes with realistic interaction

Quasiparticle configuration-mixing calculations are made for the Ni-isotopes with an approximate reaction matrix of Hamada-Johnston potential reported by Kuo. The results are very close to those obtained by the exact shell-model calculations. But the agreement with the experimental spectra is poor in both these cases. A remarkable improvement is achieved in the quasiparticle results when the renormalized force strength and the quasiparticle quantities extracted by the inverse gap equation procedure are used. A possible further improvement in the inverse gap equation procedure is discussed.

Exact Shell-Model Calculation ofNi58andNi60

Exact configuration-mixing calculations have been done for ${\mathrm{Ni}}^{58}$ and ${\mathrm{Ni}}^{60}$, which have two and four neutrons, respectively, in unfilled shell-model orbitals. Several different types of effective potentials have been used; they are: (1) the surface-delta interaction, (2) Serber exchange, (3) a potential similar to the Rosenfeld mixture, (4) an approximate reaction matrix calculated with the Hamada-Johnston two-nucleon potential, and (5) Tabakin's nonlocal separable two-nucleon potential. These results are compared with those obtained by using the two-body matrix elements given by Cohen et al. (EIC) and by Auerbach (EIA). The overlap of the BCS projected wave function with the exact shell-model ground-state wave function is calculated. The odd-even mass difference obtained from pairing theory using these potentials is compared with the experimental values. It is found that the first three potentials give nearly the same quantitative results as that calculated with EIC and EIA, while the Hamada-Johnston and Tabakin potentials are rather weak.

Inelastic electron scattering cross sections for odd-parity excitations of Ca 40

Cross sections for excitation of the odd-parity states of Ca 40 are calculated in the shell model, using the results of a detailed configuration mixing calculation. Both longitudinal and transverse electric contributions are included. The resulting form factors are compared with the predictions of the surface interaction model and with experimental form factors.

Configuration mixing in mass 14 nuclei

The ground state configuration of C 14 and N 14 have been determined using a zero-range force. Two models have been used, one with O 16 as the core and the other with C 12 as the core. For the sake of simplicity, C 12 is treated as a closed shell of 1 p 3 2 nucleons, and 1 d 2 5 2 and 2 s 2 1 2 configurations are mixed into the ground states of C 14 and N 14 with a spin-dependent zero-range potential. It is suggested that a realistic model would be one wherein an intermediate coupling configuration mixing calculation is made. This is necessary in order to explain the stripping and pick-up data on mass 14 nuclei.

On the collective quadrupole state of C 12

A configuration-mixing calculation has been carried out for the 4.43 MeV, 2 + state of C 12. The hole-particle pairing interaction has been treated on a model where the matrix elements consist of two factorable terms, one of them representing no spin flip, and the other spin flip. The quadrupole transition probability has been calculated with and without ground state correlations. It is concluded that ground state correlations are important in C 12 and responsible for the observed enhancement of the transition rate of the quadrupole level.

Long range correlations and photo effect in nuclei

A detailed quantum mechanical treatment of the collective model for the giant dipole resonance in the low energy nuclear photo effect is presented. A relation ω D = c k D for the resonance energy ω D is derived from sum rule considerations, where k D is related to the nuclear radius by k D ≈ π 2R and c to the structure factor s( k) of nuclear matter at small momenta k by s( k) = k 2mc . The velocity c is calculated and the semiclassical expresssion for c in terms of the symmetry energy K (c = ( 2K m ) 1 2 ) is found to be valid only for extremely strong interactions. For weaker forces one obtains a larger value of c than indicated by this relation and a value of ω D in better agreement with the results of shell model configuration mixing calculations.