Melt butter in heavy medium saucepan over medium heat. Add onion and saute until tender, about 4 minutes. Add clam juice and rice and bring to boil. Reduce heat to low, cover and simmer until rice is tender, about 15 minutes. Mix in shrimp. Cover and simmer until shrimp arc heated through, about 1 minute. Set aside 6 shrimp for garnish.
Working in batches, puree soup with remaining shrimp in blender until smooth. Return soup to same saucepan. Whisk in tomato paste and l/8 teaspoon cayenne pepper Gradually whisk in half and half. Bring soup to simmer. Season soup to taste with salt and pepper.
Ladle soup into bowls. Garnish with reserved shrimp. Sprinkle with additional cayenne pepper, if desired, and serve.