Spectroscopic factors in the N=20 island of inversion: The Nilsson strong-coupling limit

Abstract

Spectroscopic factors, extracted from one-neutron knockout and Coulomb dissociation reactions, for transitions from the ground state of 33 Mg to the ground-state rotational band in 32 Mg, and from 32 Mg to low-lying negative parity states in 31 Mg, are interpreted within the rotational model. Associating the ground state of 33 Mg and the negative parity states in 31 Mg with the 3 2 [321] Nilsson level, the strong coupling limit gives simple expressions that relate the amplitudes (C j ) of this wavefunction with the measured cross-sections and derived spectroscopic factors (S j ). To obtain a consistent agreement with the data within this framework, we find that one requires a modified 3 2 [321] wavefunction with an increased contribution from the spherical 2p 3/2 orbit as compared to a standard Nilsson calculation. This is consistent with the findings of large scale Shell Model calculations and can be traced to weak binding effects that lower the energy of low-orbitals.

Consistency of nucleon-transfer sum rules in well-deformed nuclei

“…In the era of radioactive ion beams, there has been a resurgence of interest in interpreting transfer reaction data for lighter nuclei using the Nilsson model [36][37][38]. As data become more plentiful, exploiting the sum rules across wider ranges of isotopes will become increasingly important.…”

In-beam $γ$-ray spectroscopy of $^{32}$Mg via direct reactions

“…According to the Nilsson-model based analysis presented in Ref. [74], the spectroscopic factors for the 0 + 1 , 2 + 1 , and 4 + 1 states are predicted to be C 2 S(2p 3/2 ) = 0.24, [C 2 S(2p 3/2 ), C 2 S(1f 7/2 )] = [0.24, 0.18], and C 2 S(1f 7/2 ) = 0.33, respectively, calculated with empirically adjusted Nilsson wave functions. The values for 2 + 1 and 4 + 1 are about half of the experimental spectroscopic factors, and the reason for this difference remains to be understood.…”

Analysis of the 18Fg,m(d,p)FMacchiavelli1, Crawford2, Fallon3 et al. 2020Phys. Rev. CSelf Cite3010View full textAdd to dashboardCite

“…In the following, we briefly review the formalism in Ref. [11], which we have recently applied to the N = 8 and N = 20 islands of inversion [22,23]. We begin with the strong-coupling limit, applicable to transfer from the 18 F ground state.…”