  Recent experiments have discovered two exponents in the $pp$ elastic
differential cross sections with two different slope parameters, of the order
$(16-20)$~GeV$^{-2}$ and $(4-4.8)$~GeV$^{-2}$ in the regions $ -t \la 0.5
$~GeV$^2$ and $ -t \ga 1$~GeV$^2$, respectively. We suggest a simple model of
the $pp$ elastic scattering with two types of particle exchanges: 1) when the
exchanged particle transfers the momentum $\veQ$ from a quark of the proton
$p_1$ to one quark in another proton $p_2$, producing the slope $B_1$; 2) when
the transfer occurs from two quarks in the $p_1$ to two quarks in the $p_2$,
giving the exponent with the slope $B_2$. The resulting amplitude is
proportional to the product of the form factors of two protons, depending on
$\veQ$, but with different coefficients in the cases 1) and 2). Using the only
parameter - the proton charge radius $r^2_{ch}= 0.93$~fm$^2$, one obtains $B_1
= 16$~GeV$^{-2}$,~$ B_2 = 4$~GeV$^{-2}$ with the strict value of the ratio,
$\frac{B_1}{B_2} = 4.0$, independent of $r_{ch}$. These predictions are
surprisingly close to the data both in the $pp$ and in the $\bar p p$
differential cross sections. Comparison to experimental data and theoretical
approaches is discussed, together with possible implications for the future
development of the theory.
