Proton single - particle energies in 23 F

Nucleon transfer reaction experiments on nuclei far from stability give information on the single-particle properties of these nuclei. The single-particle properties are essential for the basic test of nuclear models used for making predictions and extrapolations for the properties of nuclei even further from stability. In this paper we consider results obtained in a recent experiment by Michimasa et al. [1] for proton transfer onto 22O to make low-lying excited states in 23F, together with information from other reactions leading to 23F. In the experimental paper, some results were compared to the universal sd-shell (USD) Hamiltonian [2,3] that has provided realistic sd-shell (0d5/2, 0d3/2, 1s1/2) wave functions for use in nuclear structure models, nuclear spectroscopy and nuclear astrophysics for over two decades. However, the derivation of the USD Hamiltonian has been revised using an updated and complete set of available energy data. The resultant Hamiltonians USDA and USDB [4] lead to a new level of precision for realistic shell-model wave functions. Therefore, in addition to USD, we use the USDA and USDB to compare with the experimental results. We find that the lowest fragments of proton single-particle strength found in these experiments are in agreement with the new Hamiltonians, but that there is a large fragmentation of single-particle strength to higher levels, unobserved in the experiment, that push the single-particle centroid energy to much higher energy. The primary sources of experimental data are Figs. 3 and 5 of Ref. [1]. Figure 3 shows the level scheme derived from the analysis of γ spectra, along with the relative cross section at each level for each reaction. Figure 5 compares this scheme to results obtained with the USD Hamiltonian. The theoretical calculations for energy levels, gamma decay, and spectroscopic factors in this paper were obtained in the sd-shell model space with the USD, USDA, and USDB Hamiltonians using the shell-model code OXBASH [5]. The electromagnetic matrix elements were obtained with free-nucleon g-factors for M1, effective charges of ep = 1.5 and en = 0.5 for E2 and harmonic oscillator radial wave functions. This information was used to infer which of the experimental levels could be matched with the sd-shell predictions. Nine of the 16 levels listed in the Michimasa paper have been identified by their energy and spin based on this analysis below. The complete level scheme up to 7.0 MeV for each Hamiltonian is included in Figs. 1, 2, and 3, with a comparison to the experimental level scheme. The lowest five levels could be matched with the sd-shell calculations. Near 4 MeV the experimental level density is higher than theory, indicating that some of these states may have negative parity. Above 4.5 MeV the theoretical level density is much higher than experiment, indicating an incomplete experimental level scheme, and unique associations between experiment and theory could not be made. As discussed in [4], USDA and USDB are determined from a least squares fit to 608 energy data by varying linear combinations of two-body matrix elements (TBME) that are relatively well determined by the data and by using the renormalized G matrix for the sd-shell model space (RGSD) for the other linear combinations. For USDA (USDB), 30 (56) linear combinations were varied to achieve an rms deviation of 170 (126) keV for the 608 energy data with resulting TBME that differ from the RGSD by an rms of 290 (375) keV. USDA is a “conservative” Hamiltonian with a good but not best fit to energy data, and with TBME closest to the RGSD. USDB provides the best fit with TBME that differ more from RGSD. Comparison of USDA and USDB results can provide a measure of the theoretical error for various calculated quantities. This paper provides one of the first examples for such a comparison. The proton transfer reaction, 22O (0+) → 23F reaction, should be strong only to low-lying sd-shell states that can be made with the addition of a proton in the state with (n j ) equal to 1s1/2, 0d3/2, or 0d5/2 to spin zero, leading to states with spin-parity 1/2+, 3/2+ or 5/2+, respectively. The neutron knockout reaction, 24F (3+) →23F, can lead to sd-shell states with spin-parity 1/2+ to 11/2+, or to p-shell states with 3/2− to 9/2−. The two-nucleon knockout, 25Ne (1/2+) → 23F is most complicated with possible final states of 1/2+ to 11/2+ and 1/2− to 9/2−. The USDB Hamiltonian results will be used for a discussion of the gamma decay and nucleon transfer spectroscopic factors, with a comparison to USD and USDA results when the differences are large. The first level is the ground state, already assigned as the 5/2+ state [6]. The binding energy of 23F relative to 16O is 47.65 MeV to be compared with the theoretical values of 47.67, 47.76, and 47.75 MeV, for USD, USDA, and USDB, respectively (the theoretical values