  In this work we investigate the effect of the H$\alpha$ bandpass width in the
correlation between the CaII H&K and H$\alpha$ indices with the aim of
improving the H$\alpha$ index to better identify and model the signals coming
from activity variability. We used a sample of 152 FGK dwarfs observed with
HARPS for more than 13 years with enough cadence to be able to detect
rotational modulations and cycles in activity proxies. We calculated the CaII
H&K and H$\alpha$ activity indices using a range of bandwidths for H$\alpha$
between 0.1 and 2.0 Ang. We studied the correlation between the indices time
series at long and short timescales and analysed the impact of stellar
parameters, activity level and variability on the correlations. The correlation
between CaII H&K and H$\alpha$ both at short and long timespans is maximised
when using narrow H$\alpha$ bandwidths, with a maximum at 0.6 Ang. For some
inactive stars, as the activity level increases, the flux in the H$\alpha$ line
core increases while the flux in the line wings decreases as the line becomes
shallower and broader. The balance between these fluxes can cause stars to show
the negative correlations observed in the literature when using a wide
bandwidth on H$\alpha$. These anti-correlations may become positive
correlations if using the 0.6 Ang bandwidth. Calculating the H$\alpha$ index
using a bandpass of 0.6 Ang maximises the correlation between CaII H&K and
H$\alpha$ both at short and long timescales. On the other hand, the use of the
broader 1.6 Ang, generally used in exoplanet detection to identify stellar
activity signals, degrades the signal by including the flux in the line wings.
In face to these results we strongly recommend the use of a 0.6 Ang bandwidth
when computing the H$\alpha$ index for the identification of activity
rotational modulation and magnetic cycle signals in solar-type stars.
(Abridged)
