Empirical formulas for fragmentation production cross section
DOI:
https://doi.org/10.63907/ansa.v1i4.63Keywords:
neutron-rich nuclei, fragment production, cross sections, neutron drip lineAbstract
Production cross sections of neutron-rich nuclei in projectile fragmentation reactions measured at zero degrees are systematically analyzed using published experimental data. By comparing the yields of O, F, Ne, Na, Mg, Al, Si, and P isotopes produced in $^{40}$Ar-induced fragmentation at beam energies of 35~MeV/nucleon, 57--120~MeV/nucleon, and 1~GeV/nucleon, we demonstrate that the production cross sections of neutron-rich fragments are, within experimental uncertainties, essentially independent of the projectile energy over this broad range. Motivated by this limiting-fragmentation behavior, we propose an empirical systematics for neutron-rich fragment production based on the binding energy per nucleon ($\mathrm{BE}/A$) of the final nuclei. The cross sections are found to follow a steep exponential dependence on $\mathrm{BE}/A$, spanning 8--9 orders of magnitude for small variations of $\mathrm{BE}/A$. The systematics is tested for reactions induced by $^{40}$Ar, $^{48}$Ca, $^{58,64,68}$Ni, $^{72}$Zn, $^{76}$Ge, $^{82}$Se, and $^{86}$Kr projectiles on Be and Ta targets, and the corresponding fit parameters are shown to correlate with the fragment charge $Z$ and the projectile neutron-to-proton ratio $(N/Z)_{\mathrm{projectile}}$. Additionally, a complementary analysis based on $Q_{gg}$ systematics (mass difference between projectile and detected fragments) is also presented, and the advantages and limitations of the $\mathrm{BE}/A$-based description for extrapolating yields toward the neutron drip line are discussed.
References
V. V. Volkov, Treatise on Heavy-Ion Science, Ed. D. A. Bromley, Plenum Press, Vol. 8, 101 (1989).
G. D. Westfall et al., Phys. Rev. C 17, 1368 (1978).
D. Guillemaud-Mueller, Yu. E. Penionzhkevich et al., Z. Phys. A 332, 189 (1989).
D. Guillemaud-Mueller et al., Phys. Rev. C 41, 937 (1990).
O. Tarasov et al., Phys. Rev. C 80, 034609 (2009).
O. Tarasov et al., Phys. Rev. C 87, 054612 (2013).
M. Notani, Phys. Rev. C 76, 044605 (2007).
K. Summerer et al., Phys. Rev. C 61, 034607 (2000).
T. Baumann et al., Nature 449, 1022 (2007).
G. G. Adamian et al., Phys. Rev. C 78, 024613 (2008).
Yu. Sereda, S. Lukyanov, Yad. Fiz. 77, 864 (2014).
E. Kwan et al., Phys. Rev. C 86, 014612 (2012).
A. Ozawa et al., Nucl. Phys. A 673, 411 (2000).
X. H. Zhang et al., Phys. Rev. C 85, 024621 (2012).
S. Momota et al., Nucl. Phys. A 701, 150 (2002).
M. Mocko et al., Europhys. Lett. 79, 12001 (2007).
B. M. Tsang et al., Phys. Rev. C 76, 041302(R) (2007).
G. Chaudhuri et al., Phys. Rev. C 76, 067601 (2007).
M. Mocko et al., Phys. Rev. C 76, 014609 (2007).
S. Lukyanov et al., Phys. Rev. C 80, 014609 (2009).
C.-W. Ma et al., Prog. Part. Nucl. Phys. 121, 103911 (2021).
J. M. Boillos et al., Phys. Rev. C 105, 014611 (2022).
B. Mei et al., Phys. Rev. C 108, 034602 (2023).
N. Tang et al., Phys. Rev. C 107, 014603 (2023).
P. Feng et al., Phys. Rev. C 111, 024603 (2025).
Downloads
Published
Issue
Section
License
Copyright (c) 2025 The Author(s)
This work is licensed under a Creative Commons Attribution 4.0 International License.
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided that the original author(s) and source are properly credited.
Authors retain copyright and grant the journal a non-exclusive right of first publication.
