Spallation residues in the reaction<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">Fe</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>56</mml:mn></mml:mrow></mml:mmultiscripts><mml:mo>+</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:math>at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>0.3</mml:mn><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mn>0.5</mml:mn><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mn>0.75</mml:mn><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mn>1.0</mml:mn><mml:mi>A</mml:mi></mml:mrow></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1.5</mml:mn><mml:mi>A</mml:mi></mml:mrow></mml:math>GeV

The spallation residues produced in the bombardment of $^{56}\mathrm{Fe}$ at $1.5A,1.0A,0.75A,0.5A$, and $0.3A$ GeV on a liquid-hydrogen target have been measured using the reverse kinematics technique and the fragment separator at GSI (Darmstadt). This technique has permitted the full identification in charge and mass of all isotopes produced with cross sections larger than ${10}^{\ensuremath{-}2}$ mb down to $Z=8$. Their individual production cross sections and recoil velocities at the five energies are presented. Production cross sections are compared with previously existing data and with empirical parametric formulas, often used in cosmic-ray astrophysics. The experimental data are also extensively compared with the results of different combinations of intranuclear cascade and deexcitation models. It is shown that the yields of the lightest isotopes cannot be accounted for by standard evaporation models. The GEMINI model, which includes an asymmetric fission decay mode, gives an overall good agreement with the data. These experimental data can be directly used for the estimation of composition modifications and damages in materials containing iron in spallation sources. They are also useful for improving high-precision cosmic-ray measurements.