# Universal Nuclear Equation of State Introducing the Hypothetical X17 Boson

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Tolman–Oppenheimer–Volkoff Equations and the Equation of State

## 3. Analysis Results

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Krasznahorkay, A.J.; Csatlós, M.; Csige, L.; Gácsi, Z.; Gulyás, J.; Hunyadi, M.; Kuti, I.; Nyakó, B.M.; Stuhl, L.; Timár, J.; et al. Observation of Anomalous Internal Pair Creation in
^{8}Be: A Possible Indication of a Light, Neutral Boson. Phys. Rev. Lett.**2016**, 116, 042501. [Google Scholar] [CrossRef] [PubMed][Green Version] - Krasznahorkay, A.J.; Csatlós, M.; Csige, L.; Gulyás, J.; Hunyadi, M.; Ketel, T.J.; Krasznahorkay, A.; Kuti, I.; Nagy, A.; Nyakó, B.M.; et al. New experimental results for the 17 MeV particle created in
^{8}Be. EPJ Web Conf.**2017**, 137, 08010. [Google Scholar] [CrossRef][Green Version] - Krasznahorkay, A.J.; Csatlós, M.; Csige, L.; Gulyás, J.; Koszta, M.; Szihalmi, B.; Timár, J.; Firak, D.S.; Nagy, Á.; Sas, N.J.; et al. A new anomaly observed in
^{4}He supporting the existence of the hypothetical X17 particle. J. Phys. Conf. Ser.**2020**, 1643, 012001. [Google Scholar] [CrossRef] - Krasznahorkay, A.J.; Krasznahorkay, A.; Begala, M.; Csatló, M.; Csige, L.; Gulyás, J.; Krakó, A.; Timár, J.; Rajta, I.; Vajda, I.; et al. New anomaly observed in
^{12}C supports the existence and the vector character of the hypothetical X17 boson. arXiv**2022**, arXiv:2209.10795. [Google Scholar] - Feng, J.F.; Fornal, B.; Galon, I.; Gardner, S.; Smolinsky, J.; Tait, T.M.P.; Tanedo, P. Protophobic Fifth-Force Interpretation of the Observed Anomaly in
^{8}Be Nuclear Transitions. Phys. Rev. Lett.**2016**, 117, 071803. [Google Scholar] [CrossRef][Green Version] - Feng, J.F.; Fornal, B.; Galon, I.; Gardner, S.; Smolinsky, J.; Tait, T.M.P.; Tanedo, P. Particle physics models for the 17 MeV anomaly in beryllium nuclear decays. Phys. Rev. D
**2017**, 95, 035017. [Google Scholar] [CrossRef][Green Version] - Veselský, M.; Petousis, V.; Leja, J. Anomaly in the decay of
^{8}Be and^{4}H—Can an observed light boson mediate low-energy nucleon-nucleon interactions? J. Phys. G Nucl. Part. Phys.**2021**, 48, 105103. [Google Scholar] [CrossRef] - Petousis, V.; Veselský, M.; Leja, J. Neutron star structure with nuclear force mediated by hypothetical X17 boson. EPJ Web Conf.
**2021**, 252, 04008. [Google Scholar] [CrossRef] - Serot, B.D.; Walecka, J.D. Recent Progress in Quantum Hadrodynamics. Int. J. Mod. Phys. E
**1997**, 6, 515. [Google Scholar] [CrossRef] - Adhikari, D.; Albataineh, H.; Androic, D.; Aniol, K.; Armstrong, D.S.; Averett, T.; Barcus, S.; Bellini, V.; Beminiwattha, R.S.; Benesch, J.F.; et al. Accurate Determination of the Neutron Skin Thickness of
^{208}Pb through Parity-Violation in Electron Scattering. Phys. Rev. Lett.**2021**, 126, 172502. [Google Scholar] [CrossRef] - Ring, P.; Gambhir, Y.K.; Lalazissis, G.A. Computer program for the relativistic mean field description of the ground state properties of even-even axially deformed nuclei. Comput. Phys. Commun.
**1997**, 105, 77–97. [Google Scholar] [CrossRef] - Lalazissis, G.A.; König, J.; Ring, P. New parametrization for the Lagrangian density of relativistic mean field theory. Phys. Rev. C
**1997**, 55, 540. [Google Scholar] [CrossRef][Green Version] - Danielewicz, P.; Lacey, R.; Lynch, W.G. Determination of the Equation of State of Dense Matter. Science
**2002**, 298, 1592. [Google Scholar] [CrossRef] [PubMed][Green Version] - Riley, T.E.; Watts, A.L.; Bogdanov, S.; Ray, P.S.; Ludlam, R.M.; Guillot, S.; Arzoumanian, Z.; Baker, C.L.; Bilous, A.V.; Chakrabarty, D.; et al. A NICER View of PSR J0030+0451: Millisecond Pulsar Parameter Estimation. Astrophys. J. Lett.
**2019**, 887, L21. [Google Scholar] [CrossRef][Green Version] - Miller, M.C.; Lamb, F.K.; Dittmann, A.J.; Bogdanov, S.; Arzoumanian, Z.; Gendreau, K.C.; Guillot, S.; Harding, A.K.; Ho, W.C.G.; Lattimer, J.M.; et al. PSR J0030+0451 Mass and Radius from NICER Data and Implications for the Properties of Neutron Star Matter. Astrophys. J. Lett.
**2019**, 887, L24. [Google Scholar] [CrossRef][Green Version] - Romani, R.W.; Kel, D.; Filippenko, A.V.; Brink, T.G.; Zheng, W. PSR J0952-0607: The Fastest and Heaviest Known Galactic Neutron Star. Astrophys. J. Lett.
**2022**, 934, L18. [Google Scholar] [CrossRef] - Abbott, R.; Abbott, T.D.; Abraham, S.; Acernese, F.; Ackley, K.; Adams, C.; Adhikari, R.X.; Adya, V.B.; Affeldt, C.; Agathos, M.; et al. GW190814: Gravitational Waves from the Coalescence of a 23 Solar Mass Black Hole with a 2.6 Solar Mass Compact Object. Astrophys. J.
**2020**, 896, L44. [Google Scholar] [CrossRef]

**Figure 1.**(Color online). Binding energy (BE) of the ${}^{208}Pb$ versus its neutron skin using 30% admixture of the $17\phantom{\rule{3.33333pt}{0ex}}$ MeV boson in an EoS.

**Figure 2.**(Color online). The pressure as function of nuclear density for three EoSs with admixtures of 30% and 40% of the $17\phantom{\rule{3.33333pt}{0ex}}$ MeV boson plus the NL3 EoS. The parameters are defined in Table 2.

**Figure 3.**(Color online). The mass–radius relation for three EoSs plus the NL3 with admixtures of 30% and 40% of the $17\phantom{\rule{3.33333pt}{0ex}}$ MeV boson plus the NL3 EoS.

**Table 1.**Constrained parameter sets for three EoSs with three admixtures q and incompressibility K${}_{0}$ = 250 ± 20 MeV.

K${}_{0}$ | q | $\mathit{\kappa}$ | $\mathit{\lambda}$ | g${}_{\mathit{v}}$ | g${}_{\mathit{s}}$ | m${{}^{*}}_{\mathit{v}}$ [MeV] | m${}_{\mathit{\sigma}}$ [MeV] |
---|---|---|---|---|---|---|---|

235.95 | 0.3 | 21.50 | −163.33 | 8.38 | 9.20 | 547.77 | 482.16 |

269.14 | 0.4(A) | 11.00 | −50.00 | 6.85 | 7.23 | 469.55 | 391.44 |

257.50 | 0.4(B) | 11.50 | −60.00 | 6.85 | 7.23 | 469.55 | 391.44 |

**Table 2.**Polytropes for three EoSs plus the NL3 EoS used for the Tolman–Oppenheimer–Volkoff calculations. The 0.3 EoS represents a 30% admixture of the $X17$ boson and the 0.4A and 0.4B EoSs represent a 40% admixture with different values of parameters $\kappa $ and $\lambda $.

EoS q-Admixture (%) | ${\mathit{a}}_{0}$ | ${\mathsf{\Gamma}}_{1}$ | ${\mathsf{\Gamma}}_{2}$ | ${\mathsf{\Gamma}}_{3}$ | K${}_{0}$ (MeV) |
---|---|---|---|---|---|

0.3 (30%) | 34.703 | 3.741 | 3.118 | 2.497 | 235.95 |

0.4(A) (40%) | 34.673 | 3.744 | 3.036 | 2.517 | 269.14 |

0.4(B) (40%) | 34.653 | 3.643 | 3.095 | 2.540 | 257.50 |

NL3 (0%) | 34.846 | 3.872 | 2.925 | 2.394 | 332 |

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**MDPI and ACS Style**

Veselský, M.; Petousis, V.; Leja, J.; Navarro, L.
Universal Nuclear Equation of State Introducing the Hypothetical X17 Boson. *Symmetry* **2023**, *15*, 49.
https://doi.org/10.3390/sym15010049

**AMA Style**

Veselský M, Petousis V, Leja J, Navarro L.
Universal Nuclear Equation of State Introducing the Hypothetical X17 Boson. *Symmetry*. 2023; 15(1):49.
https://doi.org/10.3390/sym15010049

**Chicago/Turabian Style**

Veselský, Martin, Vlasios Petousis, Jozef Leja, and Laura Navarro.
2023. "Universal Nuclear Equation of State Introducing the Hypothetical X17 Boson" *Symmetry* 15, no. 1: 49.
https://doi.org/10.3390/sym15010049