# On the Shape of Nucleons at High Energies

## Abstract

**:**

## 1. Introduction

## 2. Fast Nucleons in the Transverse Projection

#### 2.1. The Mode of Uncorrelated Motion of the Partons

#### 2.2. The mode of Correlated Motion of the Partons

## 3. The Longitudinal Size

## 4. Discussion

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The energy dependence of the slope B of the diffraction cone [14].

**Table 1.**Estimated parameters in the mode of uncorrelated motion of the partons: the effective transverse radius of the nucleon $\mathcal{R}$; transverse RMS momenta of the peripheral partons, average $\mathcal{K}$ and maximum ${\mathcal{K}}_{m}$ in cascades; the number of the partons in cascades, average $\overline{N}$ and maximum ${N}_{m}$; cascade saturation parameter $\phantom{\rule{-0.166667em}{0ex}}\varkappa $.

$\sqrt{\mathit{s}}$ [GeV] | $\mathcal{R}$ [fm] | $\mathcal{K}$ [GeV] | ${\mathcal{K}}_{\mathit{m}}$ [GeV] | $\overline{\mathit{N}}\phantom{\rule{2.em}{0ex}}\phantom{\rule{0.222222em}{0ex}}$ | ${\mathit{N}}_{\mathit{m}}\phantom{\rule{2.em}{0ex}}$ | $\mathit{\varkappa}$ |
---|---|---|---|---|---|---|

10 | 0.66 | 0.35 | 0.60 | 1.18 | 3.36 | 0.35 |

50 | 0.70 | 0.38 | 0.78 | 1.35 | 5.68 | 0.24 |

500 | 0.76 | 0.41 | 0.98 | 1.59 | 9.00 | 0.18 |

2000 | 0.80 | 0.43 | 1.08 | 1.74 | 11.00 | 0.16 |

7000 | 0.83 | 0.45 | 1.17 | 1.87 | 12.81 | 0.15 |

13,000 | 0.84 | 0.45 | 1.21 | 1.94 | 13.70 | 0.14 |

100,000 | 0.89 | 0.48 | 1.33 | 2.15 | 16.64 | 0.13 |

**Table 2.**Estimated parameters in the mode of correlated motion at $\sqrt{{s}_{1}}=2$ TeV / 7 TeV. The notation is similar to that of Table 1.

$\sqrt{\mathit{s}}$ [GeV] | $\widehat{\mathcal{R}}$ [fm] | r [fm] | $\widehat{\overline{\mathit{N}}}$ | ${\mathit{N}}_{\mathit{m}}$ | $\widehat{\mathit{\varkappa}}$ |
---|---|---|---|---|---|

2000 | 0.80 | 0. | 1.74 | 11.00 | 0.16 |

7000 | 0.90/0.83 | 0.31/0. | 1.97/1.87 | 12.81 | 0.15/0.15 |

13,000 | 1.02/0.85 | 0.48/0.15 | 2.23/1.93 | 13.70 | 0.16/0.14 |

100,000 | 1.55/1.23 | 1.08/0.70 | 3.39/2.78 | 16.64 | 0.20/0.17 |

$\sqrt{\mathit{s}}$ [GeV] | 10 | 50 | 500 | 2000 | 7000 |
---|---|---|---|---|---|

${R}_{L}$ [fm] ($\sqrt{{s}_{1}}=2$ TeV) | 0.76 | 0.85 | 1.92 | 5.47 | 5.47 |

${R}_{L}$ [fm] ($\sqrt{{s}_{1}}=7$ TeV) | 0.75 | 0.77 | 1.08 | 2.77 | 5.47 |

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**MDPI and ACS Style**

Nekrasov, M.L.
On the Shape of Nucleons at High Energies. *Particles* **2021**, *4*, 381-390.
https://doi.org/10.3390/particles4030032

**AMA Style**

Nekrasov ML.
On the Shape of Nucleons at High Energies. *Particles*. 2021; 4(3):381-390.
https://doi.org/10.3390/particles4030032

**Chicago/Turabian Style**

Nekrasov, Maksim L.
2021. "On the Shape of Nucleons at High Energies" *Particles* 4, no. 3: 381-390.
https://doi.org/10.3390/particles4030032