Figure 1

Some (out of a total of 25) of the Mayer diagrams considered in the calculation of the diagonal (a),(b) and nondiagonal (c),(d) OBDM, Eq. (1), and TBDM, Eq. (2). Here, open dots denote the “active” particles, full dots labeled by an index “$i$” represent an integration over the coordinates of particle $i$, an oriented line originating and ending in the same dot denotes the mean field diagonal OBDM ${\rho }_o(i)$, whereas an oriented line joining two different dots denotes the nondiagonal OBDM, ${\rho }_o(i,j)$; the correlation operator (${\widehat{\eta }}_{i{i}^{\prime }j}={\widehat{f}}_{ij}{\widehat{f}}_{i^{\prime }j}-1$) is represented by dashed lines. Note that diagrams (a) and (b) are obtained from diagrams (c) and (d) by setting $1=1^{\prime }$, $2=2^{\prime }$, whereas diagrams (a) are obtained from diagrams (b) by integrating over particle “2”. Upper (lower) diagrams belong to the class of hole (particle) diagrams.Reuse & Permissions

Figure 2

Top: the ONMD [Eq. (3)] for ${}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}$, and ${}^{40}\mathrm{Ca}$ ($AV{8}^{\prime }$ interaction [18]). Bottom: the MF and central correlation contributions to the momentum distribution of ${}^{16}\mathrm{O}$; the difference between the solid and dashed curves yields a measure of noncentral (mainly tensor) correlations. The results obtained within the cluster expansion (solid line) are compared with the VMC, Ref. 19 (full dots), and the FHNC, Ref. 20 (open stars). The normalization of the momentum distributions is $\int d\mathit{k}n(k)=A$ [note that in Figs. 11 and 12 of Ref. 16 $n(k)$ is normalized to 1].Reuse & Permissions

Figure 3

Top: the relative TNMD [Eq. (4)] of ${}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}$, and ${}^{40}\mathrm{Ca}$ integrated over ${\mathit{K}}_{\mathrm{c}.\mathrm{m}.}$ ($AV{8}^{\prime }$ interaction [18]). Bottom: the MF and central correlation contributions to the TNMD of ${}^{16}\mathrm{O}$. The normalization is $\int d{\mathit{k}}_{\mathrm{rel}}n(k_{\mathrm{rel}})=(2\pi {)}^{6}A(A-1)/2$.Reuse & Permissions

Figure 4

Top: the relative TNMD [Eq. (4)] of ${}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}$, and ${}^{40}\mathrm{Ca}$ calculated in correspondence of $K_{\mathrm{c}.\mathrm{m}.}=0$ (back-to-back nucleons). Bottom: the $pn$ and $pp$ relative TNMD in ${}^{16}\mathrm{O}$ for back-to-back nucleons [the total TNMD is given by $n(k_{\mathrm{rel}},K_{\mathrm{c}.\mathrm{m}.}=0)=n_{pn}(k_{\mathrm{rel}},K_{\mathrm{c}.\mathrm{m}.}=0)+2n_{pp}(k_{\mathrm{rel}},K_{\mathrm{c}.\mathrm{m}.}=0)$]. The inset shows the ratio $R_{pN}=n_{pN}(k_{\mathrm{rel}},K_{\mathrm{c}.\mathrm{m}.}=0)/n_{pN}^{\mathrm{central}}(k_{\mathrm{rel}},K_{\mathrm{c}.\mathrm{m}.}=0)$.Reuse & Permissions

Figure 5

Comparison of the many-body TNMD of this Letter [Eq. (4)] with the factorized form of Ref. 8 $n({\mathit{k}}_{\mathrm{rel}},{\mathit{K}}_{\mathrm{c}.\mathrm{m}.})=C_A{n}_D(k_{\mathrm{rel}})n_{CS}(K_{\mathrm{c}.\mathrm{m}.})$ (see text); the values of $K_{\mathrm{c}.\mathrm{m}.}$ corresponding to the various curves are $K_{\mathrm{c}.\mathrm{m}.}=0{\mathrm{fm}}^{-1}$ (squares), $0.5{\mathrm{fm}}^{-1}$ (full triangles), $1{\mathrm{fm}}^{-1}$ (open dots).Reuse & Permissions