Integral of a product of Bessel functions of the first kind

I want to do this integral $H(rho)=int_{0}^{infty} J_1(2 pi Lr)J_0(2pi rho r)dr$, where $J_1$ and $J_0$ are Bessel functions of the first kind and $Lin mathbb{R}$ is a constant, so I tried to do this in the Mathematica, but he failed. When I tried to put some value to $L$ and $rho$, the software calculate numerically, so I ploted $H(rho)$ for a fixed $L$ and the result of the plot is a function like $rect(x/L)$, such that

begin{equation}
{displaystyle operatorname {rect} (t)=left{{begin{array}{rl}0,&{text{if }}|t|>{frac {1}{2}}\{frac {1}{2}},&{text{if }}|t|={frac {1}{2}}\1,&{text{if }}|t|<{frac {1}{2}}.end{array}}right.}
end{equation}

I’m not sure about this result for $H(rho)$, so I searched in the internet and didn’t find none property for solve this integral, I don’t know if, in fact $H(rho)=rect(x/L)$ or something of this type. Someone knows if this result is correct? This integral have an analytic solution?