3 (details can be found in [20]). The central part of the potential ( R$_{i}$ ≤ R ≤ R$_{a}$ ) is described by with the nonlinear mapping function The inner repulsive wall ( R < R$_{i}$ ) is given by while the long range part ( R > R$_{a}$ ) is represented by The coefficients a$_{j}$ are the main fitting parameters, while the parameter T$_{m}$ is adjusted to obtain at the point R$_{a}$ a continuous connection between the central and the long range part of the potential. R$_{m}$ in eqn. (2) is chosen close to the minimum of the potential. The parameters b and R$_{i}$ are manually chosen to optimize the fitting re- sult with a small number of parameters a$_{j}$ . The real parameter n [21] is an additional fitting parameter, while the parameters A and B are adjusted for a continuously differentiable connection at the point R$_{i}$ . The radius R$_{a}$ should be close to the LeRoy radius R$_{b}$ ( AB ) = 2 [ √ 〈 r 2 $_{A}$〉 + √ 〈 r 2 $_{B}$〉 ] [22], where r$_{A}$ and r$_{B}$ are the radial coordinates of the outermost electrons of atom A and atom B , here r$_{A}$ = r$_{B}$ = r$_{Sr}$ . The resulting LeRoy radius R$_{b}$ is 9.7 ˚ A or 10.5 ˚ A for the X state of Sr$_{2}$, if 〈 r 2 Sr 〉 is taken from [23] or from [24], respectively. The larger value R$_{a}$ = 10 . 5 ˚ A was chosen for the final potential evaluation. This choice should justify the neglect of a formal term for an exchange energy in the long range part according to eq. (4). The residuals of the potential fit can be found as his- tograms in figure 2 compared to Gaussian profile fits. The plot for the main isotopologue $^{88}$Sr$_{2}$ shows a sym- metric profile with a FWHM of 0.8, while the shapes for the other two isotopologues are significantly wider and are not as symmetric as for the main isotopologue. This can be attributed to the much lower number of data for the isotopologues $^{86}$Sr$^{88}$Sr and $^{87}$Sr$^{88}$Sr and on average significantly weaker line intensities, which lead to a less precise determination of the frequencies. The derived potential coefficients are given in table I. The normalized standard deviation of this potential fit is σ = 0 . 80 which indicates that the applied measure- ment uncertainties are as a whole not underestimated. It correlates to the width of the histogram in fig. 2 which also gives a normalized FWHM of 0.8 for the main iso- topologue. The values of the dissociation energy D$_{e}$ and the equilibrium internuclear distance R$_{e}$ depend on the chosen potential description, namely on the number of potential coefficients a$_{i}$ , on the parameter b and on the connection radii R$_{i}$ and R$_{a}$ . The given uncertainties are 1 σ standard deviations derived by comparing 35 differ- ent potential versions with different parameter settings which all had almost the same σ values. Compared to D$_{e}$ the value for D$_{0}$ (dissociation energy with respect to (v=0,J=0) for the main isotopologue $^{88}$Sr$_{2}$ ) is less model dependent. For the first potential fits the long range coefficients C$_{6}$ , C$_{8}$ , and C$_{10}$ were treated as free parameters. De- FIG. 2: (Color online) The residuals of the X $^{1}$Σ+ g potential fit divided by the specific uncertainties represented by his- tograms compared to Gaussian fits. V$_{c}$ ( R ) = T$_{m}$ + ∑ j ≥ 1 a$_{j}$x j (1) x = R − R$_{m}$ R + bR$_{m}$ . (2) V$_{i}$ ( R ) = A + B R n , (3) V$_{a}$ ( R ) = U$_{∞}$ − C$_{6}$ R 6 − C$_{8}$ R 8 − C$_{10}$ R 10 . (4) -4 -2 0 2 4 0 200 400 600 800 1000 1200 Number of Lines $^{88}$Sr$_{2}$ GaussianGLYPH<.notdef>fit -4 -3 -2 -1 0 1 2 3 4 0 20 40 60 80 100 Number of Lines 86 88 Sr Sr GaussianGLYPH<.notdef>fit -4 -3 -2 -1 0 1 2 3 4 0 10 20 30 40 50 Number of Lines ResidualsGLYPH<.notdef>/GLYPH<.notdef>Uncertainty 87 88 Sr Sr GaussianGLYPH<.notdef>fit