Amplification of energy of low-energy neutrinos

Abstract We investigate the elastic scattering of sufficiently low-energy neutrinos by the ultra-relativistic electrons passing through the single crystal possessing a sufficiently strong internal electrostatic field. When the energy of the accelerated electron in the initial state is $$500 GeV$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>500</mml:mn> <mml:mi>G</mml:mi> <mml:mi>e</mml:mi> <mml:mi>V</mml:mi> </mml:mrow> </mml:math> , the influence of the effective magnetic field generated by the relative motions of the crystalline electrostatic field and accelerated electrons passing through the single crystal on the elastic scattering of relic neutrinos by the accelerated electrons becomes significant if the generated magnetic field strength changes in the range $$4.50\times {10}^{8}G\lesssim B_{ef} \lesssim 1.42\times {10}^{9}G$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>4.50</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mn>8</mml:mn> </mml:msup> <mml:mi>G</mml:mi> <mml:mo>≲</mml:mo> <mml:msub> <mml:mi>B</mml:mi> <mml:mrow> <mml:mi>ef</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≲</mml:mo> <mml:mn>1.42</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mn>9</mml:mn> </mml:msup> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> . After the elastic scattering of relic neutrinos by the ultra-relativistic electrons possessing energy $$500 GeV$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>500</mml:mn> <mml:mi>G</mml:mi> <mml:mi>e</mml:mi> <mml:mi>V</mml:mi> </mml:mrow> </mml:math> , the average energy of the scattered relic neutrinos is amplified up to $$\sim {10}^{2} GeV$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>G</mml:mi> <mml:mi>e</mml:mi> <mml:mi>V</mml:mi> </mml:mrow> </mml:math> . The numerical estimations show that the flux of the boosted relic neutrinos originated from the accelerated electrons passing through the tungsten single crystal is on the detectable level at the IceCube detector. If the boosted relic neutrinos originated from the elastic scattering of relic neutrinos by the ultra-relativistic electrons passing through the tungsten located in the way of the accelerated electrons are detected at the IceCube or any other related neutrino detector, it would constitute direct evidence for the existence of the cosmic neutrino background. The comparison of the boosted solar thermal neutrino flux and the boosted relic neutrino flux arriving at the detector shows that the former is much smaller than the latter and does not prevent a detection of the boosted relic neutrinos.