Valence <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn><mi>s</mi><mtext>−</mtext><mn>0</mn><mi>d</mi></mrow></math> proton vacancy of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi>Si</mi><mprescripts></mprescripts><none></none><mn>32</mn></mmultiscripts></math> ground state

N. Watwood; C. R. Hoffman; B. P. Kay; I. A. Tolstukhin; J. Chen; T. L. Tang; D. Bazin; Y. Ayyad; S. Beceiro-Novo; S. J. Freeman; L. P. Gaffney; R. Garg; H. Jayatissa; A. N. Kuchera; P. T. MacGregor; A. J. Mitchell; A. Muñoz-Ramos; C. Müller-Gatermann; F. Recchia; C. Santamaria; M. Z. Serikow; D. K. Sharp; G. L. Wilson; A. H. Wuosmaa; J. C. Zamora

doi:10.1103/4lzs-mv3l

Valence $1 s − 0 d$ proton vacancy of the ${}^{32}{Si}$ ground state

N. Watwood ^1,*, C. R. Hoffman ^1,†, B. P. Kay ¹, I. A. Tolstukhin ¹, J. Chen ², T. L. Tang ¹, D. Bazin ³, Y. Ayyad ⁴, S. Beceiro-Novo ⁵ et al.

S. J. Freeman ^6,7, L. P. Gaffney ⁸, R. Garg ³, H. Jayatissa¹, A. N. Kuchera ⁹, P. T. MacGregor ⁶, A. J. Mitchell ¹⁰, A. Muñoz-Ramos ⁴, C. Müller-Gatermann ¹, F. Recchia^11,12, C. Santamaria¹³, M. Z. Serikow ³, D. K. Sharp ⁶, G. L. Wilson¹⁴, A. H. Wuosmaa ¹⁵, and J. C. Zamora ³

¹Physics Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
²Department of Physics, Southern University of Science and Technology, 1088 Xueyuan Blvd, Nanshan, Shenzhen, Guangdong Province 518055, China
³FRIB/NSCL Laboratory, Michigan State University, East Lansing, Michigan 48824, USA
⁴IGFAE, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain
⁵Universidade da Coruña, Campus Industrial, Departamento de Fisica y Ciencias de la Tierra, CITENI, 15471 Ferrol, Spain
⁶Department of Physics, University of Manchester, Manchester M13 9PL, United Kingdom
⁷EP Department, CERN, CH-1211 Geneva, Switzerland
⁸Department of Physics, University of Liverpool, Liverpool L69 3BX, United Kingdom
⁹Department of Physics, Davidson College, Davidson, North Carolina 28035, USA
¹⁰Department of Nuclear Physics and Accelerator Applications, Research School of Physics, Australian National University, Canberra ACT 2601, Australia
¹¹Dipartimento di Fisica e Astronomia, Universitá degli Studi di Padova, I-35131 Padova, Italy
¹²Istituto Nazionale di Fisica Nucleare, Sezione di Padova, I-35131 Padova, Italy
¹³Department of Physics and Engineering Physics, Morgan State University, Baltimore, Maryland 21251, USA
¹⁴Department of Physics and Astronomy, Louisiana State University, Louisiana 70803, USA
¹⁵Department of Physics, University of Connecticut, Storrs, Connecticut 06269, USA

^*Contact author: nwatwood@anl.gov; nwatwood@tamu.edu
^†Contact author: crhoffman@anl.gov

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Phys. Rev. C 112, 054304 – Published 5 November, 2025

DOI: https://doi.org/10.1103/4lzs-mv3l

Abstract

The ${}^{32}{Si} (^{3} He, d) {}^{33}P$ reaction was studied in inverse kinematics at $6.3 MeV / u$ . States in ${}^{33}P$ corresponding to the proton $1 s − 0 d$ single-particle orbitals were identified up to $\approx 4.5$ MeV in excitation energy. The ( ${}^{3}{He}, d$ ) spectroscopic factors were determined from distorted-wave Born approximation calculations. When combined with complementary neutron-adding data, the $1 s − 0 d$ proton vacancies in the ${}^{32}{Si}$ ground state were extracted. In conjunction with a reanalysis of data from previous single-particle measurements, the trends in proton and neutron vacancy were explored across the ${}^{28, 30, 32, 34}{Si}$ isotopes. Both proton and neutron vacancy data show gradual changes in their occupancies. The proton $1 s_{1 / 2}$ orbitals in ${}^{32}{Si}$ and ${}^{34}{Si}$ are both consistent with being empty. The ground-state nucleon distributions are described by shell-model calculations constrained to the $1 s − 0 d$ model space.

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Valence $1 s − 0 d$ proton vacancy of the ${}^{32}{Si}$ ground state

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Valence 1s−0d proton vacancy of the Si32 ground state

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Valence $1 s − 0 d$ proton vacancy of the ${}^{32}{Si}$ ground state