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Employing numerical and theoretical methods, we investigate the structuralcharacteristics of random sequential addition (RSA) of congruent spheres in$d$-dimensional Euclidean space $\mathbb{R}^d$ in the infinite-time orsaturation limit for the first six space dimensions ($1 \le d \le 6$).Specifically, we determine the saturation density, pair correlation function,cumulative coordination number and the structure factor in each =of thesedimensions. We find that for $2 \le d \le 6$, the saturation density $\phi_s$scales with dimension as $\phi_s= c_1/2^d+c_2 d/2^d$, where $c_1=0.202048$ and$c_2=0.973872$. We also show analytically that the same density scalingpersists in the high-dimensional limit, albeit with different coefficients. Abyproduct of this high-dimensional analysis is a relatively sharp lower boundon the saturation density for any $d$ given by $\phi_s \ge(d+2)(1-S_0)/2^{d+1}$, where $S_0\in [0,1]$ is the structure factor at $k=0$(i.e., infinite-wavelength number variance) in the high-dimensional limit.Consistent with the recent "decorrelation principle," we find that paircorrelations markedly diminish as the space dimension increases up to six. Ourwork has implications for the possible existence of disordered classical groundstates for some continuous potentials in sufficiently high dimensions.Comment: 38 pages, 9 figures, 4 table

Random sequential addition of hard spheres in high Euclidean dimensions