T. Sebe

The structure of the sd-shell nuclei (I). C18, F18, O19, F19 and Ne20

Abstract A shell-model calculation for nuclei at the beginning of the 1s-0d shell has taken account of the configuration mixing of the 1s and 0d shells. The position of the 1s level relative to the 0d level and the strength of the spin-orbit interaction are taken from the observed 017 and F17 spectra. A residual interaction is introduced and is assumed to be central. The strength of this interaction is treated as a free parameter. The positions of the even-parity levels and their properties agree well with experiment. In particular, a rotational level structure in Ne20 is well explained. It is pointed out that the harmonic-oscillator w wave functions should be modified in the 1s wave function to reproduce the spectrum of O18. The configuration mixing is very large especially in nuclei of low isobaric spin. the central residual interaction favours the higher symmetric states in the ordinary space. Thus the concept of the symmetry has important physical meaning in these nuclei. The wave functions are found to be very similar to those given by the SU3 model, as was discovered by Elliot, but the mixing of different states is caused by the deviation of the residual interaction from the simple Q-Q force. The spin-orbit interaction also destroys the elegance of this SU3 model. Although this mixing is not so large, the M1 transition probabilities are strongly influenced.

Electromagnetic properties of sd shell nuclei

Abstract The electromagnetic properties of the nuclei 19, 20 O, 19, 20, 21 F, 19, 20, 21, 22 Ne, 21, 22 Na and 22 Mg are studied in a shell-model basis in which the valence nucleons are restricted to the (0d, 1s) shell and the 16 O core is assumed to be inert. Central two-body interactions are taken as the residual interactions. Beyond mass number A = 20, the SU(3) and SU(4) groups are used to truncate the shell-model space to a dimension less than sixty. Good agreement with experiment is obtained, except for 22 Na.

Anomalous Parity States of C13, N13 and N14

The low-lying anomalous parity states of CIS and NIB are shown to be well described in terms of the shell model states in which a positive-parity nucleon couples to a core which corresponds to Cl2 and its lowest two states are taken into account in the actual calculation. The Hamiltonian with a single-body spin-orbit interaction and a two-body central interaction is diagonalized among the above states and supplementary basic states. The latter basic states are necessary, in our method of treatment, to remove spurious states, which must not be contained in our wave functions. The center-of-mass correction is seen to have a very important effect on our results. The results for the energy spectra in C1s are found to be in fair agreement with the experiments: Especially we have succeeded in elucidating the reason why the lowest positive-parity level 1/2+ of C1S is observed at a very small excitation energy (3.08 Mev). The agreements with the experiments are also good on the Coulomb shifts between the isotopic doublets, on the reduced widths for the proton emission and on various kinds of radiative transitions. A similar method of calculation is performed to investigate the properties of the negative-parity states of N14, getting fair agreements with the experiments.

The structure of the sd-shell nuclei: (II). Spectroscopic factor of one-nucleon transfer reaction

Coefficients of fractional parentage of (sd)3 and (sd)4 are given. Wave functions of 20Ne are presented and spectroscopic factors of the single-nucleon transfer are calculated.

A shell-model study onM1 andE2 properties of Zn, Ga, and Ge

Electromagnetic properties of Zn, Ga, and Ge are studied by using the nuclear shell model. Empirically determinedM1 operators are found to be very successful to explainM1 transitions, moments, and mixing ratios. ManyE2 properties are also understood by the present shell-model calculations with effective charges.

Electrodisintegration of He 4 Nucleus

The inelastic continuum of scattered electrons by He 4 nuclei, observed experimentally by the Stanford group, is worked theoretically by using the conventional forms of wave functions for He 4, He 3, and the triton. It is pointed out that two kinds of scattering are involved in the cross section; one is connected with the direct process in which a nucleon can be ejected through the direct interaction with the electromagnetic field induced by the ess in which a nucleon is capable of being ejected through the intermediary of nuclear interaction with another nucleon which does interact with the electromagnetic field. Comparison with experiments appears to be rather good, though qualitatively, allowing far the approximate nature of the method of computation. The main nuclear reaction connected with the observed inelastic continuum is shown to be the ejection of nucleon from He 4 except for the low-energy tail where the pion production is observed to take place according to the Stanford group. (auth)

Calculations of the energy spectra of Zn, Ga, and Ge isotopes by the shell model

The effective Hamiltonian which was determined empirically by Koops and Glaudemans is tested in shell model calculations for the65–68Zn,67–69Ga, and68–70Ge nuclei in the full (1p3/2,0f5/2,1p1/2)n space. The resulting energy spectra are compared with the experimental spectra and results of previous calculations. The overall agreement with experiment is as satisfactory for these nuclei as for the Ni and Cu isotopes, by which the Hamiltonian was determined. It is noticed that the spectra of67Zn and67,69Ga calculated in this work are similar to those provided by the Alaga model.

Electrodisintegration of He4 Nucleus

The inelastic continuum of scattered electrons by He 4 nuclei, observed experimentally by the Stanford group, is worked theoretically by using the conventional forms of wave functions for He 4, He 3, and the triton. It is pointed out that two kinds of scattering are involved in the cross section; one is connected with the direct process in which a nucleon can be ejected through the direct interaction with the electromagnetic field induced by the ess in which a nucleon is capable of being ejected through the intermediary of nuclear interaction with another nucleon which does interact with the electromagnetic field. Comparison with experiments appears to be rather good, though qualitatively, allowing far the approximate nature of the method of computation. The main nuclear reaction connected with the observed inelastic continuum is shown to be the ejection of nucleon from He 4 except for the low-energy tail where the pion production is observed to take place according to the Stanford group. (auth)

The structure of the sd-shell nuclei: (III). Effect of non-central interactions

Abstract The effects of non-central interactions on 18 O, 18 F, 19 O and 19 F are studied by the shell model. These effects are not important in 18 O and 19 F; but the level structures of 18 F and 19 O are found to be affected by these non-central interactions. The possibility of the core excitation is also pointed out. The levels at 1.08 MeV and 2.10 MeV and the 1 + level at 1.7 MeV in 18 F belong possibly to the core-excited states. Phenomenological matrix elements found in this paper are compared with the reaction matrices derived from the Hamada-Johnston potential.

Realistic shell-model calculations of the 2νββ nuclear matrix elements and the role of the shell structure in intermediate states

Abstract We discuss two conditions needed for the correct computation of the 2νββ nuclear matrix elements within the realistic shell-model framework. An algorithm in which intermediate states are treated based on Whiteheads moment method is inspected by taking examples of the double GT+ transitions 36Ar → 36S, 54Fe → 54Cr and 58Ni → 58Fe. This algorithm yields rapid convergence on the 2νββ matrix elements, even when neither the relevant GT+ nor GT− strength distribution is convergent. A significant role of the shell structure is pointed out, which makes the 2νββ matrix elements highly dominated by the low-lying intermediate states. Experimental information of the low-lying GT± strengths is strongly desired. Half-lives of T 1 2 2ν ( EC/EC; 36 Ar → 36 S ) = 1.7 × 10 29 yr , T 1 2 2ν ( EC/EC; 54 Fe → 54 Cr ) = 1.5 × 10 27 yr T 1 2 2ν ( EC/EC; 58 Ni → 58 Fe ) = 6.1 × 10 24 yr and T 1 2 2ν (β + / EC; 58 Ni → 58 Fe ) = 8.6 × 10 25 yr are obtained from the present realistic shell-model calculation of the nuclear matrix elements.