I had 2 parakeets that I believe were male and female. One recently died, the female. The next day we got a?

new bird. We put her in a cage next to his for a day. The next day we put them in the same cage together. They seemed ok at first, but then the male started pecking at the new bird. He'd leave her alone for a while. But then it seemed like anytime he wanted to get past her, he would peck at her. She would then fly down to the bottom of the cage, and then immediately fly back up to the top perch. She didnt seem afraid at all. I watched them for hours and there would be periods that they would sit next to each other and fall asleep. Then they would wake up and the whole thing would start over again with him pecking at her, her flying to the bottom and then eventually flying back up to the top perch next to him again. Also, whenever the new bird would try to do anything, drink, eat, play with the toy, he would try and stop her. Also it seemed like throughout the day they were doing an awful lot of preening, way more than I've ever seen. And they were sleeping a lot as well. I let them sleep in the same cage together, but the next day it was the same thing all over. I didnt want to subject the new bird to this behavior so I separated them again. I left the new bird in the cage they were in together so she could become comfortable with her new surroundings. I put our old bird in a different cage and in a different room. The new bird is now eating and drinking freely, playing with the toys and becoming comfortable. I've had birds for the last 23 years and I've never seen this behavior before. I mean I've definitely seem them peck at each in more of a playfull way, but never like this. So at this point, I'm not sure if I should keep them separate, or put them back in together and hope they start to get along?