IGNOU MPH 17 2026 - For the nuclear charge density , compute the charge form fa

Question

For the nuclear charge density $\rho_{ch} = \rho_0 e^{-q_0r}$ , compute the charge form factor and the mean square charge radius $\langle r^2 \rangle$ .

19 Jan 2026

Answer :

Word Count : 212

The nuclear charge density is given by [ \rho_{ch}(r)=\rho_0 e^{-q_0 r}, ] where (\rho_0) is a normalization constant and (q_0) is a positive parameter. The charge form factor is defined as the Fourier transform of the normalized charge density, [ F(\mathbf{q})=\frac{1}{Z}\int \rho_{ch}(\mathbf{r}) e^{i\mathbf{q}\cdot \mathbf{r}}, d^3r, ] with (Z=\int \rho_{ch}(\mathbf{r}), d^3r). For a spherically symmetric density, this reduces to [ F(q)=\frac{4\pi}{Z}\int_0^\infty \rho_{ch}(r)\frac{\sin(qr)}{qr} r^2, dr . ] First,

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