Suppose you were to use nuclear fission to generate your energy? Fission converts about 0.1% of the mass of the fuel to energy. The energy in mass is equal to mc^2 or, for one kilogram it is equal to 9x10^16 Joules.
You need 1x10^18 joules for your rocket to reach 44x10^6 meters per second, or 11 kilograms of pure energy, or 11,000 kilograms of uranium. You need to do this four times. Accelerate to leave Earth, deccelerate when you get there, accelerate to come home and deccelerate once you reach Earth. You must also convert the heat to electriciy to power your ion thrusters, this is only about 30% efficient at best (Stirling engine). This means you need 11 * 4 * 3 times the mass of your vehicle, or 132 times its mass so this won't work.
How about fusion? Fusion of hydrogen to helium is within reason, anything above that requires the pressures of the center of a star thus is not reasonable. Hydrogen fusion gives 1% conversion to energy. Your fuel need would be 13 times the mass of your vehicle. This is not reasonable.
How about anti matter? Anti matter converts 100% of the mass of the reaction with matter into energy. Only 1/4 is available as gamma rays, which could be used to generate heat. The rest goes out as uncontrollable neutrinos. You would then only need about 25% of the mass of your vehicle as fuel. This is within reason. There are practical problems with anti matter though. One is that we don't know how to contain it, even held in a magnetic field in the vacuum of interstellar space, enough random atoms would degrade it over time, Another is the energy cost of production which is about a billion to one. Rough calculation shows we would need about 30,000 years of sunlight falling on Earth to generate enough antimatter for one trip. Again, not reasonable.