Cook artichoke hearts according to package instructions, then drain well and finely chop. Cook bell pepper in 1 tablespoon butter in a 2- to 3-quart heavy saucepan over moderately low heat, stirring occasionally, until softened, about 5 minutes. Stir in artichokes and transfer mixture to a bowl.
Melt remaining 2 tablespoons butter in saucepan over moderately low heat, then add flour and cook roux, stirring, 3 minutes. Add half-and-half in a stream, whisking, and bring to a boil, whisking. Reduce heat and simmer, whisking, 3 minutes.
Remove from heat and stir in artichoke mixture, scallions, 1/3 cup parmesan, lemon juice, jalapeños, salt, and celery salt. Gently stir in crab. Transfer to a buttered 1 1/2-quart shallow baking dish and sprinkle with remaining parmesan.
Bake dip in middle of oven until bubbling, 20 to 25 minutes. Serve warm.
