Comparison of Core and No-Core Shell Models in Excitation of Negative Parity States of _9^19F
Abstract
The present study investigates the nuclear structure of low-lying negative parity states in 919Fe using a combination of the shell model and Hartree-Fock (HF) approaches. A comprehensive analysis of nuclear properties—including energy spectra, electron scattering form factors, transition strengths, binding energies, and charge radii—was performed within four model spaces: the zbm-model space, the psd-model space, the spsdpf-model space, and the extended no-core shell model space. Various effective interactions were applied within each model space to assess their impact on nuclear behavior. The HF method, utilizing multiple Skyrme parameterizations, along with harmonic oscillator and Woods-Saxon potentials, was employed to compute single-particle radial wave functions essential for matrix element calculations. The results demonstrate that Skyrme-based HF calculations, when integrated with shell model techniques, effectively capture fundamental nuclear properties. A systematic comparison with experimental data reveals that transitioning from core-restricted model spaces to a fully no-core framework significantly improves the reproduction of electron scattering form factors, particularly in both longitudinal (C1, C3) and transverse (E1, M2) components. Notably, specific states exhibit optimal agreement at different core levels: the 3/21- and 5/21- states are best reproduced in the no-core shell model, while the 7/21- state achieves high accuracy within the sbm and psd model spaces. Overall, this research underscores the critical influence of model space selection and interaction choice in theoretical nuclear studies. The progressive refinement from core-based to no-core calculations highlights the role of many-body correlations in nuclear excitations and provides deeper insight into the intrinsic structure of 919Fe, contributing to advancements in nuclear structure theory and reaction dynamics.
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References
R. Hofstadter, “Electron scattering and nuclear structure,” Reviews of Modern Physics, 28(3), 214 (1956). https://doi.org/10.1103/RevModPhys.28.21
D. Vautherin, and D.M.T. Brink, “Hartree-Fock calculations with Skyrme's interaction. I. Spherical nuclei,” Physical Review C, 5(3), 626 (1972). https://doi.org/10.1103/PhysRevC.5.626
B.A. Brown, et al., “Shell-model analysis of high-resolution data for elastic and inelastic electron scattering on F19,” Physical Review C, 32(4), 1127 (1985). https://doi.org/10.1103/PhysRevC.32.1127
T. Sakuda, “Cluster Model Study of Electron Scattering on 19F,” Progress of Theoretical Physics, 87(5), 1159-1169 (1992). https://doi.org/10.1143/ptp/87.5.1159
R.A. Radhi, A.A. Abdullah, and A.H. Raheem, “Calculations of elastic and inelastic electron scattering on 19F using large-basis no core-shell model wave functions,” Nuclear Physics A, 798(1-2), 16-28 (2008). https://doi.org/10.1016/j.nuclphysa.2007.10.010
R.A. Khaleq, et al., “Impact of shell model interactions on nuclear responses to WIMP elastic scattering,” Physical Review D, 109(7), 075036 (2024). https://doi.org/10.1103/PhysRevD.109.075036
R.A. Radhi, A.A. Alzubadi, and E.M. Rashed, “Shell model calculations of inelastic electron scattering for positive and negative parity states in 19F,” Nuclear Physics A, 947, 12-25 (2016). https://doi.org/10.1016/j.nuclphysa.2015.12.002
A.P. Zuker, B. Buck, and J.B. McGrory, “Structure of O16,” Physical Review Letters, 21(1), 39 (1968). https://doi.org/10.1103/PhysRevLett.21.39
J.B. McGrory, and B.H. Wildenthal, “Shell-model calculations for A=18, 19, and 20 nuclei with core excitation included explicity,” Physical Review C, 7(3), 974 (1973). https://doi.org/10.1103/PhysRevC.7.974
Y. Utsuno, and S. Chiba, “Multiparticle-multihole states around O 16 and correlation-energy effect on the shell gap,” Physical Review C – Nuclear Physics, 83(2), 021301(R) (2011). https://doi.org/10.1103/PhysRevC.83.021301
B.M. Preedom, and B.H. Wildenthal, “Shell-Model Calculations for Na22 and Ne22,” Physical Review C, 6(5), 1633 (1972). https://doi.org/10.1103/PhysRevC.6.1633
S. Cohen, and D. Kurath, “Effective interactions for the 1p shell,” Nuclear Physics, 73(1), 1-24 (1965). https://doi.org/10.1016/0029-5582(65)90148-3
E.K. Warburton, and B.A. Brown, “Effective interactions for the 0p1s0d nuclear shell-model space,” Physical Review C, 46(3), 923 (1992). https://doi.org/10.1103/PhysRevC.46.923
E.K. Warburton, J.A. Becker, and B.A. Brown, “Mass systematics for A= 29–44 nuclei: The deformed A∼ 32 region,” Physical Review C, 41(3), 1147 (1990). https://doi.org/10.1103/PhysRevC.41.1147
B.A. Brown, “Synthesis of mean-field and shell-model configuration-mixing methods,” Riken Review, (26), 53-57 (2000).
J.P. Elliott, and T.H.R. Skyrme, “Centre-of-mass effects in the nuclear shell-model,” Proceedings of the Royal Society of London Series A. Mathematical and Physical Sciences, 232(1191), 561-566 (1955). https://doi.org/10.1098/rspa.1955.0239
H. Euteneuer, et al., “Elastic electron scattering from the multipole moment distributions of Mg25,” Physical Review C, 16(5), 1703 (1977). https://doi.org/10.1103/PhysRevC.16.1703
T.W. Donnelly, and J.D. Walecka, “Electron scattering and nuclear structure,” Annu. Rev. Nucl. Sci. 25, 329-405 (1975). https://doi.org/10.1146/annurev.ns.25.120175.001553
D. Vautherin, “Hartree-Fock calculations with Skyrme's interaction. II. Axially deformed nuclei,” Physical Review C, 7(1), 296 (1973). https://doi.org/10.1103/PhysRevC.7.296
B.A. Brown, and W.D.M. Rae, “The shell-model code NuShellX@ MSU,” Nuclear Data Sheets, 120, 115-118 (2014). https://doi.org/10.1016/j.nds.2014.07.022
I. Angeli, and K.P. Marinova, “Table of experimental nuclear ground state charge radii: An update,” Atomic Data and Nuclear Data Tables, 99(1), 69-95 (2013). https://doi.org/10.1016/j.adt.2011.12.006
National Nuclear Data Center (NNDC), Brookhaven National Laboratory, Upton, NY 11973-5000, http://www.nndc.bnl.gov/
N.J. Stone, “Table of nuclear magnetic dipole and electric quadrupole moments,” Atomic Data and Nuclear Data Tables, 90(1), 75-176 (2005). https://doi.org/10.1016/j.adt.2005.04.001
N.J. Stone, Table of recommended nuclear magnetic dipole moments. No. INDC (NDS)--0794. International Atomic Energy Agency, 2019.
N.J. Stone, Table of Recommended Nuclear Magnetic Dipole Moments: Part II, Short-Lived States. No. INDC (NDS)--0816. International Atomic Energy Agency, 2020.
K. Kazunari, et al., “Shell-model study for neutron-rich sd-shell nuclei,” Physical Review C – Nuclear Physics, 83(1), 014320 (2011). https://doi.org/10.1103/PhysRevC.83.014320
A.J.H. Donné, et al., “Elastic magnetic electron scattering from 19F,” Nuclear Physics A, 455(3), 453-476 (1986). https://doi.org/10.1016/0375-9474(86)90317-9
A.J.H. Donné, et al., “Transverse electroexcitation of positive-and negative-parity states in 19F,” Nuclear Physics A, 469(3), 518-530 (1987). https://doi.org/10.1016/0375-9474(87)90037-6
D.R. Tilley, et al., “Energy levels of light nuclei A= 18–19,” Nuclear Physics A, 595(1), 1-170 (1995). https://doi.org/10.1016/0375-9474(95)00338-1
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