The process of Primordial black holess (PBHs) formation would be inevitably accompanied by
scalar induced gravitational waves (SIGWs). This strong correlation between PBHs and SIGWs
signals could be a promising approach to detecting PBHs in the upcoming gravitational wave (GW)
experiments, such as Laser Interferometer Space Antenna (LISA). We investigate the third order
SIGWs during a radiation-dominated (RD) era in the case of a monochromatic primordial power
spectrum Pζ = Aζ k∗δ (k − k∗). For LISA observations, the relations between signal-to-noise ratio
(SNR) and monochromatic primordial power spectrum are studied systematically. It shows that the
effects of third order SIGWs extend the cutoff frequency from 2f∗ to 3f∗ and lead to about 200%
increase of the SNR for frequency band from 10−5Hz to 1.6 × 10−3Hz corresponding to PBHs with
mass range 4 × 10−12M ∼ 10−7M. We find that there exists a critical value A∗ = 1.76 × 10−2
for the amplitude of the monochromatic primordial power spectra, such that when Aζ > A∗, the
energy density of third order SIGWs will be larger than the energy density of second order SIGWs.
Recently, from 12 $\gamma$-ray Galactic sources, the LHAASO has detected ultrahigh-energy photons up to 1.4PeV. 
The $\gamma$-ray spectra of the sources J2226+6057, J1908+0621, J1825-1326 and the suggested origin pulsars near the sources 
have been published. In our previous work, we studied the hadronic $\gamma$-ray spectra of the sources J2226+6057, J1908+0621, J1825-1326 
in terms of the Hertzian dipole model of pulsar. In this paper, we investigate the possibility of the leptonic origin of the 
$\gamma$-ray. We use the Hertzian dipole model to describe the pulsars around the sources. The electrons around the pulsars can be accelerated to PeV
by the electromagnetic fields of pulsars. Under the assumption that the initial electrons are uniform distributed in a
spherical shell between $10^{7}$ to $10^{9}$m around the pulsar,
we obtain the energy distribution of electrons. The leptonic $\gamma$-ray spectra can be calculated through inverse Compton scattering processes. The leptonic $\gamma$-ray can roughly conform to the observation of LHAASO.
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